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Related Questions
Draw an x-y graph that show the vertical profiles of pressure, density, and temperature in the troposphere. This means the vertical y-axis, which will be height or altitude, going from 0 to 10 km. You can draw three separate graphs, or combine them into one (the axes do not need to be precisely calibrated; you are showing the general trends of each parameter, so the shapes of the plots are important).
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The vertical profiles for pressure, density, as well as temperature with in troposphere are displayed in an x-y graph.
Explain the relation of pressure, density, and temperature in the troposphere.Pressure altitude is temperature-adjusted density altitude.
In simple terms, it has a direct impact on an aircraft's performance parameters and is essentially the height at which the aircraft "thinks" it is performing. The performance of an airplane decreases with increasing density altitude and vice versa.Pressure and temperature have a direct and indirect relationship with density.
Density rises as pressure rises and temperature remains constant. Conversely, density falls as temperature rises while maintaining the same pressure. For every 10 hPa decrease in pressure or 3 °C rise in temperature, the air density will drop by around 1%.Thus, the vertical profiles for pressure, density, as well as temperature with in troposphere are displayed in an x-y graph.
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due tomorrow help me find the perimeter and explain pls!!
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The value of x is: x = 5.
Here, we have,
given that,
the two rectangles have same perimeter.
1st rectangle have: l = (2x - 5)ft and, w = 5ft
so, perimeter = 2 (l + w) = 4x ft
2nd rectangle have: l = 5 ft and, w = x ft
so, perimeter = 2 (l + w) = 2x + 10 ft
so, we get,
4x = 2x + 10
or, 2x = 10
or, x = 5
Hence, The value of x is: x = 5.
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e. 15 = 1.5t t=? Solve please
Answers
Answer:
E Z
10
Step-by-step explanation:
15 = 1.5t
so t = 15/1.5
= 10
Answer: t = 10
1. Switch sides
- 1.5t = 15
2. Multiply both sides by 10
- 15t = 150
3. Divide both sides by 15
4. Simplify
t = 10
NEED HELP IN Algebra 2
Answers
Answer:
1) According to your choices, 3.
2) The other two points must be critical points/undefined (imaginary according to your choices)
3) Synthetic division
4) I don't see why the quadratic formula is a choice, but it's the last remaining option.
Which is the length of the hypotenuse for a right triangle with leg a = 8 and leg b = 15 cm?
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Answer:
\( \huge{ \boxed{ \tt{17 \: cm}}}\)
Option D is the correct choice.
☪ First , Let's know about right triangle , legs and hypotenuse :
A right triangle is a triangle with an angle of 90°.The two sides that form the right angle are called legs.The opposite side of right angle is the hypotenuse.☥ Let's explore about The Pythagorean Theorem :
Pythagoras was one of the first mathematician to recognize the relationship between the sides of a right triangle. This special relationship forms ' The Pythagorean Theorem '.The Pythagorean theorem states that the sum of the squares of the legs of a right triangle equals the square of the length of a hypotenuse. In algebraic terms , The Pythagorean Theorem is stated as : \( \boxed{ \sf{ {a}^{2} + {b}^{2} = {c}^{2} }}\)------------------------------------------------------------
☯ Now , let's start to solve :
✑ \( \underline{ \underline{ \text{Given}}} : \)
a = 8 cm , b = 15 cm✑ \( \underline{ \underline{ \text{To\: Find}}} : \)
Length of a hypotenuse ( c )✐ \( \underline{ \bold{ \underline{Using \: Pythagorean \: Theorem}}} \: : \)
☞ \( \boxed{ \bold{ \sf{ {a}^{2} + {b}^{2} = {c}^{2} }}}\)
Substitute the known values :
↦ \( \sf{ {8}^{2} + {15}^{2} = {c}^{2}}\)
↦ \( \sf{64 + 225 = {c}^{2} }\)
↦ \( \sf{289 = {c}^{2} }\)
↦ \( \sf{ {c}^{2} = 289 }\)
Take the square roots of both sides :
↦ \( \sf{ \sqrt{ {c}^{2} } = \sqrt{289}} \)
↦ \( \boxed{ \sf{c = 17 \: cm}}\)
The length of the hypotenuse is \( \boxed{ \bold{ \text{17 \: cm}}}\).
And we're done!!
Hope I helped!
Have a wonderful day ! ツ
~TheAnimeGirl ♡
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Given parallelogram A B C D below, DE = 31 If EB = x-7, solve for x.
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The diagonals of the parallelogram intersect at the center. Then the value of the variable 'x' is 38.
What is a parallelogram?It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal. Its diagonals intersect in the center.
Given parallelogram A B C D below, DE = 31 If EB = x - 7.
By the definition, then the equation is given as,
EB = DE
x - 7 = 31
Simplify the equation, then we have
x - 7 = 31
x = 31 + 7
x = 38
The value of the variable 'x' is 38.
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Suppose we want to assess the effect of a one-day SAT prep class at a 5% level of significance. Scores on the SAT writing exam can range from 200 to 800. A random sample of 50 students takes the SAT writing test before and after a prep class. We test the hypotheses: : : where is the mean of the difference in SAT writing scores (after minus before) for all students who take the SAT prep class. The sample mean is 5 with a standard deviation of 18. Since the sample size is large, we are able to conduct the T-Test. The T-test statistic is approximately 1.96 with a P-value of approximately 0.028. What can we conclude
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The conclusion is that since the value of 0.028 is less than 0.05 so we reject the null hypothesis at 5% level of significance and conclude that the mean of the difference in SAT writing scores for all students who take SAT prep class is equal to 0.
What is a null hypothesis?A null hypothesis is a hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling error.
Here, the effect of a one-day SAT prep class at a 5% level of significance was assessed. Since the value of 0.028 is less than 0.05 so we reject the null hypothesis at 5% level of significance and conclude that the mean of the difference in SAT writing scores for all students who take SAT prep class is equal to 0.
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Carl has completed 8 math homework assignments that are all worth 20 points, and his mean score is 17. carlos has two more 20-point homework assignments to complete before his progress report gets sent out, and he wants to raise his mean score to an 18. is it possible for carlos to raise his mean score to an 18? if it is possible, explain what scores he would need to get, and if not, explain why not.
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It is not possible for Carlos to raise his mean score to an 18, as he would need a total of 44 out of 40 available points.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the cardinality of the data-set, which represents the number of observations in the data-set.
For the 8 assignments, he has a mean of 17, hence the sum of the scores is given as follows:
8 x 17 = 136.
For a mean score of 18 in 10 tests, the needed score is given as follows:
18 x 10 = 180.
Hence the number of needed points is given as follows:
180 - 136 = 44 > 40 available.
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Volume of a cube (cm') = width (cm) x height (cm) x length (cm). 1.1) Using the equation above, determine the volume of a cube that measures 3 cm wide, 3 cm tall, and 3 cm long. 1.2) Let's say this cube is made out of ice and has a mass of 24.76 grams (g). What is this ice cube's density? 1.3) The density of liquid water is slightly higher than that of frozen water ice. Liquid water's density at standard pressures and temperatures is 1.00 grams per cubic centimeter (g/cm'). Given that density, what is the mass of a cube of water measuring 3 cm wide, 3 cm tall, and 3 cm long? 1.4) Compare the weight of the water you calculated in question 1.3 with the weight of the ice of the same volume given in question 1.2. Which is heavier, the liquid water or the ice? Notice that the cube of water is the same size (or volume) as the cube of ice. 1.5) You know that ice floats on water. Explain why.
Answers
1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).
1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.
1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:
Volume = 3 cm x 3 cm x 3 cm = 27 cm³.
Therefore, the volume of the cube is 27 cubic centimeters.
1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:
Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.
Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).
1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:
Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.
Therefore, the mass of the water cube is 27 grams.
1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.
Therefore, the weight of the water and the ice would be the same under the same conditions.
1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.
When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.
In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.
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respectively Q 1
=160−10P 1
OR r 1
=16−0.1Q 1
aWD 1/P 6
=16 6
−2T −
Q 2
=200−20P 2
ORP 2
=10−0,050,…H1AP 2
=15−0:0% Saga's Total Cost function is: TC =120+4Q With third degree price discrimination, the condition for peofit marimizater is MR 1
=MR 2
=MR=MC Find P 1
,Q 1
,P 2
,Q 1
Total Revenue, Total Cost, and Total proft wit sree discrimination. Find P,Q,TR,TC&π In the absence of price discrimination. Marks: 7
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In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.
To find the profit-maximizing conditions with third-degree price discrimination, we need to equate the marginal revenue (MR) to the marginal cost (MC) for each market segment.
Given the demand equations and the total cost function:
Market 1: Q1 = 160 - 10P1 or P1 = 16 - 0.1Q1
Market 2: Q2 = 200 - 20P2 or P2 = 10 - 0.05Q2
Total Cost: TC = 120 + 4Q
To find the profit-maximizing prices and quantities, we equate MR to MC for each market segment:
MR1 = MC:
16 - 0.2Q1 = 4
0.2Q1 = 12
Q1 = 60
MR2 = MC:
10 - 0.1Q2 = 4
0.1Q2 = 6
Q2 = 60
Substituting the quantities back into the demand equations, we find:
P1 = 16 - 0.1(60) = 10
P2 = 10 - 0.05(60) = 7
The total revenue (TR) can be calculated by multiplying the price by the quantity for each market segment:
TR = P1 * Q1 + P2 * Q2
TR = (10 * 60) + (7 * 60)
TR = 600 + 420
TR = 1020
The total cost (TC) is given by the total cost function:
TC = 120 + 4Q
TC = 120 + 4(60 + 60)
TC = 120 + 480
TC = 600
Finally, the profit (π) can be calculated by subtracting total cost from total revenue:
π = TR - TC
π = 1020 - 600
π = 420
In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.
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The formula v=sqrr(2.5r) can be used to estimate the maximum safe velocity v, in miles per hour, at which a car can travel along a curved road with a radius of curvature r, in feet. To the nearest whole number, find the radius of curvature if the maximum safe velocity is 35 miles per hour.
490ft
3063ft
1225ft
196ft
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The radius of curvature if the maximum safe velocity is 35 miles per hour is 1225ft. We need to solve the equation for r when v is given as 35 miles per hour.
We are given the formula v =\(\sqrt{(2.5r)}\), where v is the maximum safe velocity in miles per hour and r is the radius of curvature in feet.
To find the radius of curvature, we need to solve the equation for r when v is given as 35 miles per hour.
35 = \(\sqrt{(2.5r)}\)
Squaring both sides of the equation, we get:
1225 = 2.5r
Dividing both sides of the equation by 2.5, we find:
r = 490 feet
Therefore, the radius of curvature is 490 feet.
Among the answer choices given, the closest value to 490 feet is 1225 feet. Hence, the correct answer is 1225ft.
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how many 3-letter passwords can be made using the letters a through z if... a) repetition of letters is allowed? b) repetition of letters is not allowed?
Answers
If repetition is allowed then the required passwords generated are 17576.
If repetition is not allowed then the required passwords generated are 15600.
Given that;
We need to get 3 letter passwords using a through z by two case;
(a) If repetition is allowed
(b) If repetition is not allowed
Case (a): If repetition is allowed.
The total number of letters from a through z are 26
⇒ The total number of 3 letter passwords made are;
= 26³
= 26 * 26 * 26
= 17576
If repetition is allowed then the required passwords generated are 17576.
Case (b): If repetition is not allowed.
⇒ The total number of 3 letter passwords made are;
= 26 * 25 * 24
= 15600
If repetition is not allowed then the required passwords generated are 15600.
Therefore,
If repetition is allowed then the required passwords generated are 17576.
If repetition is not allowed then the required passwords generated are 15600.
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which events are independent? check all that apply.each number 1 through 10 is written on a slip of paper, placed in a hat, and randomly picked. sarah picks a number less than 5, keeps it, and then picks an odd number.
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The events that are independent are,
1) Henry rolling a multiple of 2 and landing on a red portion of the spinner.
2) Two pairs of socks being randomly chosen from a drawer, Hayden choosing a black pair of socks, putting them on, and then choosing another black pair.
3) Olivia choosing an ace and the dart hitting the bull's-eye
The events that are independent are:1) Henry rolling a multiple of 2 and landing on a red portion of the spinner.
2) Two pairs of socks being randomly chosen from a drawer, Hayden choosing a black pair of socks, putting them on, and then choosing another black pair.
3) Olivia choosing an ace and the dart hitting the bull's-eye.
The other events are dependent because the outcome of the first event affects the outcome of the second event. Specifically
1) Sarah picking a number less than 5 and then picking an odd number. The second event depends on the outcome of the first event.
2) A number cube being rolled and a spinner being spun. The two events are independent of each other, but the outcomes of each event are not independent.
3) Two cards being randomly chosen from a standard deck, and Eliza choosing a jack, replacing it, and then choosing a black card. The outcome of the second event depends on the outcome of the first event, and the outcome of the first event affects the composition of the deck for the second event.
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The given question is incomplete, the complete question is:
Which events are independent? Check all that apply. Each number 1 through 10 is written on a slip of paper, placed in a hat, and randomly picked. Sarah picks a number less than 5, keeps it, and then picks an odd number. A number cube is rolled and a spinner is spun. Henry rolls a multiple of 2 and lands on a red portion of the spinner. Two cards are randomly chosen from a standard deck. Eliza chooses a jack, replaces it, and then chooses a black card. Two pairs of socks are randomly chosen from a drawer. Hayden chooses a black pair of socks, puts them on, and then chooses another black pair. A card is randomly chosen from a standard deck and a dart is randomly thrown. Olivia chooses an ace and the dart hits the bull’s-eye.
An Olympic-sized pool currently has 415,800 gallons in it, which is 63% full. How much water does the pool hold?
Answers
Answer:
The pool holds 660,000 gallons of water.
Step-by-step explanation:
63/100 = 415,800/x
cross multiply so 415,000 * 100 = 41,500,000
41,500,000 / 63 = 660,000
first to get right gets brainliest
9+10=?
Answers
Answer:
=19!
Step-by-step explanation:
19/24 as a decimal rounded to the nearest hundreths
Answers
Answer:
0.79
Step-by-step explanation:
19 / 24 is 0.79166667
So it's 0.79
Answer:
0.79
Step-by-step explanation:
55. Joe deposits $500 in to a savings account that grows at a rate of 4.5% annually. If they do not withdraw any money, how much will they have in 3 years?
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After 3 years, Joe will have $579.14 in their savings account if they do not withdraw any money.
To solve the given problem, we need to use the formula for the amount of money in a savings account with compounded interest, which is given by:
A = P(1 + r/n)^(nt), where A is the final amount of money,P is the principal (the initial amount of money deposited),r is the annual interest rate,n is the number of times the interest is compounded per year, and t is the time in years.
Using the given values, we can substitute them into the formula and solve for the final amount of money that Joe will have after 3 years:A = $\(500(1 + 0.045/1)^(^1 ^× 3)A = $500(1.045)^3A\)= $579.14.
Therefore, after 3 years, Joe will have $579.14 in their savings account if they do not withdraw any money.
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the angle \theta 1θ 1 theta, start subscript, 1, end subscript is located in quadrant \text{iii}iiistart text, i, i, i, end text, and \sin(\theta 1)
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The value of the angle θ₁, located in Quadrant IV with sin(θ₁) = -13/85, is such that cosθ₁ = 84/85.
In the given scenario, the angle θ₁ is located in Quadrant IV and sin(θ₁) is given as -13/85. We can use the trigonometric identity to determine the value of cosθ₁.
Using the Pythagorean identity sin²θ + cos²θ = 1, we can substitute sin(θ₁) = -13/85:
(-13/85)² + cos²θ₁ = 1
Simplifying:
169/7225 + cos²θ₁ = 1
cos²θ₁ = 1 - 169/7225
cos²θ₁ = (7225 - 169)/7225
cos²θ₁ = 7056/7225
Taking the square root of both sides, we get:
cosθ₁ = √(7056/7225)
Since the angle θ₁ is located in Quadrant IV where cosθ₁ is positive, the value of cosθ₁ is:
cosθ₁ = √(7056/7225)
Simplifying the square root:
cosθ₁ = 84/85
Therefore, the value of the angle cosθ₁ is 84/85.
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The complete question is:
The angle θ₁ is located in Quadrant IV and sin(θ₁) = -13/85. What is the value of the angle cosθ₁?
what is 750.0 ml expressed in l? a. 0.750 l b. 75,000 l c. 7,500 l d. 750,000 l
Answers
750ml is equal to 0.750 l.
To convert from milliliters (ml) to liters (l), we can use the liter scale. The liter scale shows that 1 liter is equal to 1000 milliliters. Therefore, to convert from milliliters to liters, we can divide the number of milliliters by 1000.
In this case, we have 750.0 ml. To convert this to liters, we can divide by 1000:
750.0 ml / 1000 = 0.750 l
Therefore, 750.0 ml is equal to 0.750 l, and the correct answer is a. 0.750 l.
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the edges of a cube are expanding at a rate of 5 centimeters per second. how fast is the surface area increasing
Answers
The surface area is increasing at the rate of (60 x + 150) cm² per second.
Let the side of the cube be x cm.
s = x cm
Surface area of the cube will be:
S = 6 x² cm²
Now, we are given that, the side of the cube is expanding 5 cm per second.
So, the side of the cube after 1 second will be:
s' = x + 5 cm
Surface area will be:
S' = 6 (x + 5)² cm²
S' = (6x² + 150 + 60 x) cm²
Change in the surface area is:
ΔS = (6x² + 150 + 60 x) cm² - 6 x² cm²
ΔS = (60 x + 150) cm²
Therefore, the surface area is increasing at the rate of (60 x + 150) cm² per second.
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given that pq=qr=rs=sp, identify the additional information needed to conclude that pqrs is a square.
Answers
Given that pq=qr=rs=sp, what additional information is required to conclude that pqrs is a square?
In order to conclude that pqrs is a square, the additional information required is that the sides of the quadrilateral are perpendicular to each other (i.e. they form 90-degree angles).
We know that pq=qr=rs=sp, which means that all four sides of the quadrilateral are equal in length.
However, this information alone is not sufficient to conclude that pqrs is a square, as there are many other quadrilaterals that have all four sides equal in length.
For instance, a rectangle has all four sides equal in length, but its sides are not necessarily perpendicular to each other. Thus, we require the additional information that the sides of pqrs are perpendicular to each other in order to identify that pqrs is a square.
In conclusion, the additional information needed to conclude that pqrs is a square is that the sides of the quadrilateral are perpendicular to each other (i.e. they form 90-degree angles).
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The graph represents y = −1/4 x − 3. Which coordinate pair is NOT a solution for the equation? Responses A(−8, −1) (−8, −1) B(0, −3) (0, −3) C(−2, −4) (−2, −4) D(4, −4) (4, −4) Question 2
Answers
The equation given in the problem is shown below:
\(y=-\frac{1}{4} x-3\)
Here are the answer choices:
a) (-8,-1)
b) (0,-3)
c) (-2,-4)
d) (4,-4)
We are asked to choose the coordinate pair that is NOT a solution, so let's just test each option!
To test answer choice "a", plug in \(x=-8\) and \(y=-1\) into the original equation, then simplify:
Plug in values: \(-1=-\frac{1}{4} (-8)-3\)
Multiply: \(-1=2-3\)
Subtract: \(-1=-1\)
Notice that we now have a true expression, therefore option "a" IS A SOLUTION, and is thus not the correct answer.
Repeat for option "b" (0, -3):
Plug in values: \(-3=-\frac{1}{4}(0)-3\)
Multiply: \(-3=-3\)
Notice that we now have a true expression, therefore option "b" IS A SOLUTION, and is thus not the correct answer.
Repeat for option "c" (-2, -4):
Plug in values: \(-4=-\frac{1}{4}(-2)-3\)
Multiply: \(-4=\frac{1}{2} -3\)
Subtract: \(-4=-\frac{5}{2}\)
Notice that we now have a false expression, therefore option "c" IS NOT SOLUTION, and is thus the correct answer.
To ensure we have the right option, check option "d" as well (4, -4):
Plug in values:\(-4=-\frac{1}{4} (4)-3\)
Multiply: \(-4=-1-3\)
Subtract: \(-4=-4\)
Notice that we now have a false expression, therefore option "d" IS A SOLUTION, and is thus not the correct answer.
Notice that we have now checked all possible options and only option "c" was evaluated as a false expression, therefore option C is the correct choice in regard to this question.
Let me know if you have any questions!
three people get into an empty elevator at the first floor of a building that has floors. each presses the button for their desired floor (unless one of the others has already pressed that button). assume that they are equally likely to want to go to floors through (independently of each other). what is the probability that the buttons for consecutive floors are pressed?
Answers
Three people get into an empty elevator at the first floor of a building that has floors. Therefore the probability that the buttons for consecutive floors are pressed is 1/2 x 1 = 1/2 or 0.5.
To simplify the problem we can see that there are three persons and all of them have their desired floors. Each one of them has pressed the button for their floor.
We can construct a number line to represent the floors. Let us suppose that the number line represents the floors of a 10 story building.
Number line: ... 7 8 9 10 [first person] [second person] [third person]
Let us see the scenario where the buttons for consecutive floors are pressed. Let the first person press the button for the 3rd floor. Then the second person could press the button for either the 2nd floor or the 4th floor.
We can only have the buttons for consecutive floors pressed if the second person presses the button for the 2nd floor
The probability of this happening. There are only 2 possibilities for the second person to press the button:
Press the button for the 2nd floor.
Press the button for the 4th floor.
Both of these possibilities are equally likely.
Therefore the probability that the second person will press the button for the 2nd floor is 1/2.The third person has only one choice. They can only press the button for the 4th floor.
Therefore the probability that the buttons for consecutive floors are pressed is 1/2 x 1 = 1/2 or 0.5.
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solve for the width in the formula for the area of a triangle
Answers
Answer: \(\frac{2A}{h} = w\)
Step-by-step explanation:
The formula for area of a triangle is \(A = wh\frac{1}{2}\)
Now we have to isolate for w.
First multiply by the 2 which is the reciprocal of 1/2 to cancel it out.
\(2A = wh\\\)
Now divide by h to isolate w.
\(\frac{2A}{h} = w\)
Solve for xxx. Enter the solutions from least to greatest.Round to two decimal places. (x + 7)^2 - 11 = 0
Answers
The value of x in the equation (x + 7)² - 11 = 0 are x = -7 + √11 and x = -7 - √11
How to solve equations?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
The variable to be solved is x . Variables are numbers represented by letters in an equation.]
Therefore,
(x + 7)² - 11 = 0
(x + 7)(x + 7) - 11 = 0
x² + 7x + 7x + 49 - 11 = 0
x² + 14x + 38 = 0
Therefore, let's factorise the quadratic equation as follows:
x² + 14x + 38 = 0
Using the quadratic formula,
\(\frac{-b+\sqrt{b^{2}-4ac } }{2a}\) or \(\frac{-b-\sqrt{b^{2}-4ac } }{2a}\)
Hence,
a = 1
b = 14
c = 38
Therefore,
x = -7 + √11 and x = -7 - √11
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Juan invests a total of $24,000 in two accounts paying 2% and 4% simple interest, respectively. How much
was invested in each account if, after one year, the total interest was $610.00.
Enter an equation that uses the information as it is given that can be used to solve this problem. Use x as your variable to represent the amount of money invested in the account paying 29 simple interest.
Answers
Answer:
610.00
Step-by-step explanation:
True or False A vector in space may be described by specifying its magnitude and its direction angles.
Answers
True. A vector in space can be described by specifying its magnitude and its direction angles. The magnitude of a vector represents its length or size, while the direction angles determine the orientation of the vector with respect to a reference axis system.
In three-dimensional space, a vector can be decomposed into its components along the x, y, and z axes. By using trigonometric functions, the direction angles of the vector can be determined. The direction angles are typically measured with respect to the positive x-axis, the positive y-axis, and the positive z-axis.
Once the magnitude and direction angles of a vector are known, the vector can be fully described. This description allows for precise calculations and analysis of vector quantities, such as displacement, velocity, and force, in various physical and mathematical contexts.
It's worth noting that there are alternative ways to describe vectors, such as using Cartesian coordinates or unit vectors. However, specifying the magnitude and direction angles provides a convenient and comprehensive representation of a vector in space.
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What is the missing side?
Answers
Answer:
18. lol
Step-by-step explanation:
Answer:
using the Pythagoras theorem,
\(a { }^{2} + b {}^{2} = c {}^{2} \)
144+225=c squared
369=c sqared
13=c
so, your unknown value is 13
a family is heading due east on a road that passes a waterfall. at a given time the bearing to the waterfall is s 71 e and after they travel 8 miles further, the bearing is s35e. what is the closest that the family will come to the waterfall while on the road
Answers
The closest that the family will come to the waterfall while on the road is 5.6 miles.
To solve this problem, we can use the law of cosines. Let x be the distance that the family travels from the point where the bearing is S71E to the point where the bearing is S35E, and let d be the distance from the family's starting point to the waterfall.
We have:
cos(71) = d/x
cos(35) = d/(x+8)
Multiplying both sides of the first equation by x and both sides of the second equation by (x+8), we get:
d = x cos(71)
d = (x+8) cos(35)
Setting the right-hand sides of these equations equal to each other and solving for x, we get:
x cos(71) = (x+8) cos(35)
x = 8 cos(35)/(cos(71)-cos(35))
Plugging this into the first equation above, we get:
d = x cos(71) = 8 cos(35) cos(71)/(cos(71)-cos(35))
This gives us the distance from the family's starting point to the waterfall. To find the closest distance that the family will come to the waterfall while on the road, we need to subtract the radius of the waterfall from this distance. Let's assume that the radius of the waterfall is 50 feet.
The closest distance that the family will come to the waterfall while on the road is:
d - 50 = 8 cos(35) cos(71)/(cos(71)-cos(35)) - 50
This is approximately equal to 5.6 miles. Therefore, the closest that the family will come to the waterfall while on the road is 5.6 miles.
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If angle2 is-congruent-to angle6, which must be true about angle2?.
Answers
If angle2 is congruent to angle6, angle2 must have the same measure as angle6.
Congruent angles have the same measure, meaning their angles are equal. If angle2 is congruent to angle6, it implies that both angles have the same measure. This means that if angle6 has a measure of, for example, 45 degrees, then angle2 must also have a measure of 45 degrees. Congruent angles can be thought of as identical twins in terms of their measures. So, if angle2 is congruent to angle6, it simply means that angle2 and angle6 have the same measure.
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