The drawing shows a bridge design. the measurement of angle 1 is 125°. the measurement of angle 1 and angle 2 equal 180°. classify the relationship between angle 1 and 2, then find the measurement of angle 2.
Answers
The measurement of angle 2 is 55°, if the measurement of angle 1 and angle 2 equal 180° and measurement of angle 1 is 125° in the drawing of the bridge design.
The measurement of angle 1 is 125°, and the sum of angle 1 and angle 2 is 180°. The relationship between angle 1 and angle 2 is supplementary since their sum is equal to 180°. To find the measurement of angle 2,
Recall the given information: angle 1 = 125°, and angle 1 + angle 2 = 180°.Set up an equation using the supplementary relationship: 125° + angle 2 = 180°.Subtract 125° from both sides of the equation: angle 2 = 180° - 125°.Calculate the result: angle 2 = 55°.Therefore, angle 2 has a measurement of 55°.
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Related Questions
Help!!! 100 POINTS
Examine the number line and select all the statements that are true.
The sum of a and 0 is positive.
The product of a and c is negative.
The quotient of b and a is positive.
The sum of a and b is positive.
The quotient of c and 0 is undefined.
b < a
Answers
Answer:
the product of a and c is negitive
Step-by-step explanation:
Answer:
The second one is true
The third one is true
The fourth one is false
The fifth one is true
The sixth one is false
Your teacher wants to use a point system to select the winning pet. She wants each pet to get a certain number of points for each 1st choice vote and a certain number of points for each 2nd choice vote.
Your teacher decides to use these rules for her point system:
Points need to be positive whole numbers
Points for a 1st choice vote have to be greater than or equal to the points for a 2nd choice vote.
Determine point values for the 1st and 2nd choice that would result in the turtle winning. Use words and numbers to explain how this point system results in the turtle winning
Answers
In the above case, the possible point system will be:
1st choice vote: 4 points
2nd choice vote: 2 points
What is the point system?In arranging for the turtle to win in this point framework, the point values relegated for 1st choice and 2nd choice votes have to be meet the taking after criteria:
The point got to be positive entire numbersThe point for a 1st choice vote need to be more noteworthy than or rise to to the focuses for a 2nd choice voteLets say:
1st choice vote: 4 points
2nd choice vote: 2 points
Thus by the use of these point values, the turtle would have the next chance of winning since 1st choice votes would be worth more point (4 point ) compared to 2nd choice votes (3 point ). This would push individuals to select the turtle as their 1st choice, because it would allow the turtle a better add up to point gains and increase its chances of winning.
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What might be 3 reasons that a grocery store would have higher prices on items than another store
Answers
Answer:
Different Distributor Pricing. Supermarkets pay different prices for the same product through distributors.The difference in Quality.Different Supplier Deals.A computer system costs $275.
The sales person receives a 2%
commission on the sale. How
much in commission does the
salesperson make from the sale
of the computer system?
Answers
Answer: $5.50
Step-by-step explanation:
$275 x 2% = 550
550/100 = 5.5
The salesperson makes $5.50 in commission.
whats y⁵ ×y im confused lol pls respond to this
Answers
Answer:
5y^5
Step-by-step explanation:
there is no real solution. really i just simplified. if you wanted a real answer y would have to be giving. if not then this is all the question is asking. for you to simplify
Use dimensional analysis to determine which rate is greater.
Tortoise A walks 71.0 feet per hour and tortoise B walks 12 inches per minute. Which tortoise travels faster? Complete the explanation.
Answers
Answer:
Tortoise A: see below
Step-by-step explanation:
Let's convert Tortoise B's rate of speed to feet per hour. To do so, we can use dimensional analysis and our knowledge of conversion rates.
\(\displaystyle \frac{12 \ in}{1 \ min}\)Multiply this rate by 60 minutes per 1 hour.
\(\displaystyle \frac{12 \ in}{1 \ min} \times \frac{60\ min}{1\ hr}\)Multiply this rate by 1 foot per 12 inches.
\(\displaystyle \frac{12 \ in}{1 \ min} \times \frac{60\ min}{1\ hr} \times \frac{1 \ ft}{12 \ in}\)By canceling out the units, we can see that ft/hr is left. This is our final answer's unit.
\(\displaystyle \frac{12 \ in}{1 \ min} \times \frac{60\ min}{1\ hr} \times \frac{1 \ ft}{12 \ in} = \frac{720 \ ft} {12\ hr} = 60 \ \frac{ft}{hr}\)Tortoise B travels at a rate of 60 ft per hour, which is less than Tortoise A's speed, 71 ft per hour. Therefore, Tortoise A travels faster.
What is the soloution to the difference of squares problem a squared minus 64
Answers
The solution to the difference of squares problem a squared minus 64 is (a + 8)(a - 8).
The difference of squares problem, a squared minus 64, can be factored using the formula for the difference of squares, which states that a squared minus b squared is equal to (a + b)(a - b). In this case, a squared is equivalent to a squared minus 64.
So, applying the difference of squares formula, we have:
a^2 - 64 = (a + 8)(a - 8)
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Using the figure below, find the measure of z ( just enter in the number for your answer don’t worry about the degree symbol or saying “ degrees” after the number
Answers
Answer:
z = 29°
Step-by-step explanation:
We know that the 3 angles in a triangle always add up to 180°. So for triangle ABC, angle A = 59° (given), and angle B = 43° + 49° = 92° (given).
angle A + angle B + angle C = 180°
59° + 92° + z = 180°
151° + z = 180°
Subtract 151° from both sides of the equation
z = 180° -151°
z = 29°
Consider the linear program: Maximize z=−3x1+6x2, subject to: 5x1+7x2≤35
−x1+2x2≤2
x1≥0, x2≥0.
a) Solve this problem by the simplex method. Are there alternative optimal solutions? How can this be determined at the final simplex iteration? b) Solve the problem graphically to verify your answer to part (a).
Answers
Using the simplex method, the optimal solution for the given linear program is z = 14, with x1 = 0 and x2 = 5. There are no alternative optimal solutions.
To solve the linear program using the simplex method, we start by converting the problem into standard form with all constraints in the form of inequalities and non-negative variables. The initial tableau for the problem is as follows:
| x1 | x2 | s1 | s2 | b |
--------------------------------------------
z | -3 | 6 | 0 | 0 | 0 |
--------------------------------------------
s1| 5 | 7 | 1 | 0 | 35 |
--------------------------------------------
s2| -1 | 2 | 0 | 1 | 2 |
--------------------------------------------
Next, we perform the simplex iterations to improve the objective function value. After performing the necessary row operations, we arrive at the final tableau:
| x1 | x2 | s1 | s2 | b |
--------------------------------------------
z | 0 | 1 | 3/2 | -1/2 | 14 |
--------------------------------------------
s1| 0 | 0 | 4 | 3 | 5 |
--------------------------------------------
s2| 1 | 0 | -1/2 | 5/2 | 3 |
--------------------------------------------
From the final tableau, we can see that the optimal solution is z = 14, with x1 = 0 and x2 = 5. The decision variable x1 is at its lower bound, indicating that it is non-basic. Therefore, there are no alternative optimal solutions in this case.
In summary, the optimal solution for the given linear program is z = 14, with x1 = 0 and x2 = 5. There are no alternative optimal solutions.
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Need help ;)
Fast?!!
On number 2 to 9
Not sure how to do it.
Answers
Answer:
answer of 4 nbr is 5 x=5 cointerior
I have ADHD and cannot focus on this question, please help me
Pavan is on his high school bowling team and scores an average number of 135 pins per game. During the course of a match, he bowls 146 in the first game and 135 in the second game. In his third game, he bowled 8 less pins than in his forth game.
a.) Let p be the score Pavan scored in his forth game. Set up an equation that models this equation.
b.) What were Pavan's score in the third and forth game?
Answers
9514 1404 393, H76, 5668 8637 469
Answer:
a) (146 +135 +(p-8) +p)/4 = 135
b) 3rd game: 125.5; 4th game: 133.5
Step-by-step explanation:
The average score is the sum of scores divided by the number of games.
We are told the 4th game score is p, and the third game score is p-8. So, the scores in the four games are ...
146, 135, p-8, p
__
a) Their average is 135, so we have ...
(146 +135 +(p-8) +p)/4 = 135 . . game average
__
b) Solving the equation, we get ...
273 +2p = 540 . . . . . . . . . . . . . multiply by 4, collect terms
2p = 267 . . . . . . . . . . . . . . . . . . subtract 273
p = 133.5 . . . . . . divide by 2
Then the third game score is p-8 = 133.5-8 = 125.5, and the fourth game score is 133.5
Pavan's scores in the 3rd and 4th games were 125.5 and 133.5, respectively.
_____
Comment on the question
Of course, these scores make no sense as bowling scores.
which of the following fractions are equivalent to 15/21 ? select all that apply. a. 5/7 b. 30/42 c. 21/15 d. 25/31 e. 45/84
Answers
The fractions a. 5/7 b. 30/42 e. 45/84 are equivalent to 15/21.
When it comes to fractions, equivalent means that both fractions show the same part of a whole. The numerator and denominator of equivalent fractions may be multiplied or divided by the same number or the number multiplied by the numerator and denominator should be the same.
The following are steps to simplify fractions:
First, find the greatest common factor (GCF) of both numbers.
And then divide both numbers by the GCF. The result is the simplified fraction.
The greatest common factor of 15 and 21 is 3. By dividing both 15 and 21 by 3, the simplified fraction will be found.
15/21 = 5/7
By dividing both 30 and 42 by 6, the simplified fraction will be found.
30/42 = 5/7
By dividing both 45 and 84 by 3, the simplified fraction will be found.
45/84 = (5/12)21/15 and 25/31 are not equivalent to 15/21.
Therefore, the correct options are a. 5/7 b. 30/42 e. 45/84
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Six different names were put into a hat. A name is chosen 116 times and the name Grace is chosen 15 times. What is the experimental probability of the name Grace being chosen? What is the theoretical probability of the name Grace being chosen? Use pencil and paper. Explain how each probability would change if the number of names in the hat were different.
Answers
Answer:
Try this!!!
Step-by-step explanation:
Experimental Probability:
The experimental probability of an event is found by dividing the number of times the event occurs by the total number of trials. In this case, the name Grace was chosen 15 times out of 116 trials, so the experimental probability of choosing Grace is:
Experimental Probability = Number of times Grace was chosen / Total number of trials
Experimental Probability = 15 / 116
Experimental Probability = 0.1293 or approximately 12.93%
Theoretical Probability:
The theoretical probability of an event is found by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, there are six names in the hat, so the probability of choosing Grace is:
Theoretical Probability = Number of favorable outcomes / Total number of possible outcomes
Theoretical Probability = 1 / 6
Theoretical Probability = 0.1667 or approximately 16.67%
If the number of names in the hat were different, both the experimental and theoretical probabilities would change. For example, if there were only three names in the hat, the theoretical probability of choosing Grace would be 1/3 or approximately 33.33%. The experimental probability would also change based on the number of times Grace was chosen out of the total number of trials. As the number of names in the hat increases, the theoretical probability of choosing Grace decreases, and the experimental probability becomes more accurate as the number of trials increases.
Let z=f(x,y)=6x 2
−9xy+4y 2
. Find the following using the formal definition of the partial derivative. a. ∂x
∂z
b. ∂y
∂z
c. ∂x
∂f
(2,3) d. f y
(4,−1)
Answers
The required partial derivatives of the given function have been calculated.
a. [6(x+Δx)² − 9(x+Δx)y + 4y²] − [6x² − 9xy + 4y²] / Δx
b. [6x² − 9x(y+Δy) + 4(y+Δy)²] − [6x² − 9xy + 4y²] / Δy
c. [6(2+Δx)² − 9(2+Δx)(3) + 4(3)²] − [6(2)² − 9(2)(3) + 4(3)²] / Δx
d. 16/Δy
Let
z = f(x,y)
= 6x² − 9xy + 4y²
be the given function.Formal definition of the partial derivative
For the function,
z = f(x, y),
the partial derivative of z with respect to x is defined as,
f x = lim Δx → 0
f(x+Δx, y) − f(x, y) / Δx
provided the limit exists.
The partial derivative of z with respect to y is defined as,
f y = lim Δy → 0
f(x, y+Δy) − f(x, y) / Δy
provided the limit exists.
Using the formal definition of the partial derivative, we can find the following:
a. ∂x∂z = f(x + Δx, y) − f(x, y) / Δx
= [6(x+Δx)² − 9(x+Δx)y + 4y²] − [6x² − 9xy + 4y²] / Δx
b. ∂y∂z = f(x, y + Δy) − f(x, y) / Δy
= [6x² − 9x(y+Δy) + 4(y+Δy)²] − [6x² − 9xy + 4y²] / Δy
c. ∂x∂f(2,3) = f(2 + Δx, 3) − f(2, 3) / Δx
= [6(2+Δx)² − 9(2+Δx)(3) + 4(3)²] − [6(2)² − 9(2)(3) + 4(3)²] / Δx
d. f y(4,−1) = f(4, −1 + Δy) − f(4, −1) / Δy
= [6(4)² − 9(4)(−1+Δy) + 4(−1+Δy)²] − [6(4)² − 9(4)(−1) + 4(−1)²] / Δy
= [24Δy - 8]/Δy
= 24 - 8/Δy
= 16/Δy
Thus, the required partial derivatives of the given function have been calculated.
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The following table shows the number of hours some middle school students in two cities spend texting each week: City A 9 27 17 24 21 12 25 25 18 City B 6 20 26 15 23 25 14 14 11 Part A: Create a five-number summary and calculate the interquartile range for the two sets of data. (5 points) Part B: Are there any outliers present for either data set ?Justify your answer. (5 points)
Answers
A. Five-number summary for City A and B are given below. IQR for City A is 10.5; IQR for City B is 11.5
B. There are no outliers present in either data set.
What is the Five-number Summary?The values in the five-number summary include, lower and upper quartiles, max and min values, and the median.
What is the Interquartile Range (IQR)?Interquartile range (IQR) = upper quartile (Q3) - lower quartile (Q1)
What is an Outlier?Outlier of a data set is any value that is lower than Q1 - 1.5 × IQR or greater than Q3 + 1.5 × IQR.
The five-number summary for City A, 9, 27, 17, 24, 21, 12, 25, 25, 18, is:
Minimum: 9Quartile Q1: 14.5Median: 21Quartile Q3: 25Maximum: 27IQR = 25 - 14.5 = 10.5
Outlier for City A:
Q1 - 1.5 × IQR = 14.5 - 1.5 × 10.5 = -1.25
Q3 + 1.5 × IQR = 25 + 1.5 × 10.5 = 40.75
No value is less than -1.25 or greater than 40.75, therefore, there is no outlier in City A.
The five-number summary for City B, 6, 20, 26, 15, 23, 25, 14, 14, 11, is:
Minimum: 6Quartile Q1: 12.5Median: 15Quartile Q3: 24Maximum: 26IQR = 24 - 12.5 = 11.5
Outlier for City B:
Q1 - 1.5 × IQR = 12.5 - 1.5 × 11.5 = -4.75
Q3 + 1.5 × IQR = 24 + 1.5 × 11.5 = 41.25
No value is less than -4.25 or greater than 41.25, therefore, there is no outlier in City B.
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Sarah practiced the piano twice as long as Ashley. If their combined practice time was 60 minutes, how long did Sarah practice?
Answers
Answer:
40 Minutes
Step-by-step explanation:
Ashley practiced for 20 minutes, 20x2=40 and 40+20=60
Write vector a in terms of other vectors using the following image:
Answers
Answer:
Step-by-step explanation:
2a = -b - d + c
= c - b - d
x = c/2 - b/2 - d/2
The vector a in terms of other vectors for the given vectors in the image is c/2 - b/2 - d/2.
A vector is a quantity that determines both an object, its magnitude, and its direction.
The resultant vector is obtained when the tail of one vector is attached to the head of another vector such the resultant vector is formed from the sum of the two vectors.
Let a be the total vector of the given figure.
The vectors are written as:
2a = -b - d + c
a = c - b - d
a = c/2 - b/2 - d/2
Hence, the vector a in terms of other vectors is c/2 - b/2 - d/2.
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As you move to the right of this place value chart you are multiplying by what value
Answers
Answer: 1/10 or 0.1
For example, going from 700 to 70 is
700*(1/10) = 700*0.1 = 70
which is us going from the hundreds place value to the tens place value.
If we move to the left instead of right, we would multiply each item by 10.
If a cone is 5 meters tall and has a radius of 3 meters, What is its volume?
15π m3
60π m3
45π m3
30π m3
Answers
Answer: 15π m³
Step-by-step explanation:
Volume of a cone = 1/3πr²h
where,
r = radius = 3 meters
h = height = 5 meters
Volume = 1/3πr²h
Volume = 1/3 × π × 3² × 5
Volume = 1/3 × π × 9 × 5
Volume = 1/3 × π × 45
Volume = 45π/3
Volume = 15π m³
Find the y-intercept of the line by substituting 0 in for x and solving for y. y = 4x -12
Answers
Answer:
y-intercept = -12
Step-by-step explanation:
The y-intercept is the "y" value when x = 0. You can find the y-intercept by plugging 0 into the equation and simplifying.
y = 4x - 12 <----- Original equation
y = 4(0) - 12 <----- Plug 0 in "x"
y = 0 - 12 <----- Multiply 4 and 0
y = -12 <----- Subtract 12 from 0
How far can she travel in 4 hours 53 minutes?
Answers
Step-by-step explanation:
1 hour she travels = 19 km
60 min = 1 hr
53 min = 1/60 * 53 hr = 53/60 hr
Now,
1 hr = 19 km
4 + 53/60 hrs = 19 * ( 4 + 53/60) km
She travels 92.78 km in 4 hrs and 53 minutes.
What is the value of (4 minus 2) cubed minus 3 times 4? Negative 20 Negative 4 4 20
Answers
Answer:
-4
Step-by-step explanation:
(4-2)^3 - 3*4
PEMDAS
P arentheses
(2)^3 - 3*4
E xponents
8 -3*4
MD multiply and divide from left to right
8 - 12
AS add and subtract from left to right
-4
Answer:
-4
Step-by-step explanation:
When solving an expression, use PEMDAS!
4-2 = 2
2^3 (Cubed means to the 3rd) = 8
3 x 4
8-12 = -4
consider the quadratic function y equals short dash x squared plus 6 x minus 5. what do we know about the graph of this quadratic equation, based on its formula?
Answers
Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.
Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.
First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.
Next, we can find the vertex using the formula:
Vertex = (-b/2a, f(-b/2a))
where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:
Vertex = (-b/2a, f(-b/2a))
= (-6/(2*-1), f(6/(2*-1)))
= (3, -14)
So the vertex of the parabola is at the point (3,-14).
Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.
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HiI'm bad at math I decided topractice but get confusedNot is not assignment
Answers
Two angles that have the same initial side and share the same terminal side are called coterminal angles.
The answer for the first blank space is:
Coterminal
---------------------
Increasing or decreasing the degree measure of an angle in standard position by an integer multiple of 360 results in a coterminal angle.
Therefore, the answer for the second blank space is:
360 degrees
26. A car's fuel efficiency is listed as 20 miles per gallon
(mpg). Which function represents this situation when x
represents the actual mpg the car gets and f(x)
represents the difference between the actual mpg and
listed mpg-
f(x)= x - 201
f(x) = x + 201
f(x)= x - 20
f(x)= x - 20
Answers
Which function represents this situation when x represents the actual mpg the car gets and f(x) represents the difference between the actual mpg and listed mpg is f(x)= |x| - 20. Option C
How to determine the functionWe have the function as;
f(x)= |x| - 20
In this function, x represents the actual mpg the car gets, and by subtracting 20 from x, we obtain the difference between the actual mpg and the listed mpg of 20 miles per gallon.
This function allows us to calculate the deviation from the listed fuel efficiency and provides a measure of how many miles per gallon the car is either above or below the listed value.
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Use coordinate notation to enter the rule that maps each preimage to its image. Then identify the transformation and confirm that it preserves length and angle measure.
S (−3, 4) arrowright S′ (−2, 2)
T (3, 4) arrowright T′ (4, 2)
U (−1, 0) arrowright U′ (0, −2)
The transformation is a
(select)
given by the rule: (x, y)= ____
Since ST =
(select)
, SU =
(select)
, and TU =
(select)
, the transformation preserves length.
Since mangleS =
(select)
, mangleT =
(select)
, and mangleU =
(select)
, the transformation preserves angle measure.
Answers
In geometry, transformations are used to move points from one position to another.
The transformation is a rigid transformation given by \((x,y) \to (x + 1, y-2)\). It preserves lengths and anglesThe preimage is given as:
\(S =(-3,4)\)
\(T = (3,4)\)
\(U = (-1,0)\)
The image is given as:
\(S' = (-2,2)\)
\(T' =(4,2)\)
\(U' = (0,-2)\)
Using points S and S' as our reference point, we have:
\(S =(-3,4)\) and \(S' = (-2,2)\)
Calculate transformation
\((x,y) \to S -S'\)
\((x,y) \to (-2,2)-(-3,4)\)
Rewrite as:
\((x,y) \to (-2--3,2-4)\)
\((x,y) \to (-2+3,2-4)\)
\((x,y) \to (1,-2)\)
So, the transformation from the preimage to image is:
\((x,y) \to (x + 1, y-2)\)
Calculate the lengths of the sides of the preimage and the image
Using the following distance formula, we have:
\(d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)
So, we have:
\(ST = \sqrt{(-3 - 3)^2 + (4 - 4)^2} = 6\)
\(SU = \sqrt{(-3 - -1)^2 + (4 - 0)^2} = \sqrt{20\)
\(TU = \sqrt{(3 - -1)^2 + (4 - 0)^2} = \sqrt{32\)
and
\(S'T' = \sqrt{(-2 - 4)^2 + (2 - 2)^2} = 6\)
\(S'U' = \sqrt{(-2 - 0)^2 + (2 -- 2)^2} = \sqrt{20\)
\(T'U' = \sqrt{(4 -0)^2 + (2 -- 2)^2} = \sqrt{32\)
Since
\(ST = S'T'= 6\)
\(SU = S'U'= \sqrt{20\)
and
\(TU = T'U'= \sqrt{32\)
Then, the transformation preserves length
From the graph of \(\triangle STU\) and \(\triangle S'T'U'\)
Since
\(\angle S = \angle S' = 76^o\)
\(\angle T = \angle T' = 45^o\)
\(\angle U = \angle U' = 59^o\)
Then, the transformation preserves angle measure.
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In which of the following cases can we use the Law of Cosines to solve a triangle? Choose all that apply. A. SAA (side, angle, angle) B. ASA (angle, side, angle) C.SSS (side, side, side) D.SSA (side, side, angle) E. SAS (side, angle, side)
Answers
The Law of Cosines can be used to solve a triangle in the following cases: A. SAA (side, angle, angle), B. ASA (angle, side, angle), and E. SAS (side, angle, side).
The Law of Cosines is a mathematical equation that relates the lengths of the sides of a triangle to the cosine of one of its angles. It can be used to solve a triangle when certain information about the triangle is known.
A. In the SAA case, if the lengths of two sides and the measure of the included angle are known, the Law of Cosines can be used to find the remaining side or angles.
B. In the ASA case, if the measures of two angles and the length of the included side are known, the Law of Cosines can be used to find the remaining sides or angles.
C. In the SSS case, where the lengths of all three sides are known, the Law of Cosines is not needed since the Law of Sines or other methods can be used to solve the triangle.
D. In the SSA case, where the lengths of two sides and the measure of an angle not between them are known, the Law of Cosines alone is insufficient to solve the triangle.
E. In the SAS case, if the lengths of two sides and the measure of the included angle are known, the Law of Cosines can be used to find the remaining side or angles.
Therefore, the Law of Cosines can be used in cases A (SAA), B (ASA), and E (SAS) to solve a triangle.
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Coach Smith purchases sports equipment.
Golf balls cost $25 per pack and lacrosse balls
cost $10. He has $250 dollars in the budget for
golf balls and lacrosse balls.
Part A. Write an inequality where g is the number
of golf balls purchased and I is the number of
lacrosse balls.
Part B. Given the coaches budget, which of the
following is a viable option for the equipment he
can purchase?
Answers
Therefore , the solution of the given problem of inequality comes out to be the inequality is: 25g + 10l ≤ 250.
Inequality: What is it?In mathematics, an inequality is a connection that does not have an equal sign between equations or values. Inequality precedes imbalance, therefore. When two numerical values are not equal, an inequality establishes a connection between them. Difference between equality and inequality Have used the not equal symbol, which is most often used, when values are not similar (). No issue how little or huge the values, variable inequalities are employed to contrast them.
Here,
Given:
Lacrosse balls cost $10 per pack
while golf balls price $25 per pack.
Total funds equal $250.
In order to create an inequality,
we must multiply g by the quantity of golf balls you bought and I by the quantity of lacrosse balls.
So, the inequality is:
25g + 10l ≤ 250
Therefore , the solution of the given problem of inequality comes out to be the inequality is: 25g + 10l ≤ 250.
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The population of Winnipixie, Georgia is growing by 7.2%. In an exponential equation for this situation, what would be the growth factor?
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The growth factor in an exponential equation for the given scenario is 1.072. The growth factor represents the rate at which the quantity increases over time. In this case, the growth factor of 1.072 means that the population of Winnipixie, Georgia, is growing at a rate of 7.2% per year.
The population of Winnipixie, Georgia, is growing by 7.2%; we have to find out the growth factor in an exponential equation. In the given scenario, the growth factor of the population of Winnipixie, Georgia, can be calculated by using the following formula:
Growth factor = 1 + growth rate expressed as a decimal. Putting the values, we get,-
Growth factor = 1 + 0.072
Growth factor = 1.072
Hence, the growth factor in an exponential equation for the given scenario is 1.072.
In the given question, we are asked to find the growth factor in an exponential equation for the population of Winnipixie, Georgia, which is growing by 7.2%. Exponential growth is a growth pattern where a quantity increases rapidly over time. It is a mathematical model of continuous growth and is used to model many natural phenomena, including population growth.
In an exponential equation, the growth factor is the base of the exponential function. It represents the rate at which the quantity increases over time. In this case, the growth factor is calculated using the formula 1 + growth rate expressed as a decimal. By substituting the given values, we get a growth factor of 1.072.
This means that the population of Winnipixie, Georgia, is increasing at a rate of 7.2% per year. Hence, the growth factor in an exponential equation for the given scenario is 1.072. In this case, the growth factor of 1.072 means that the population of Winnipixie, Georgia, is increasing at a rate of 7.2% per year.
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Evaluate the integral by hand, and check your answer with a CAS if you have one. NOTE: Enter the exact answer. | 72 cos(4x) dx 2 + 6 sin(4x) - +C
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The integral to be evaluated is ∫(72cos(4x))dx. The answer is 2sin(4x) + 6cos(4x) + C, where C is the constant of integration. To solve this integral and verify the answer using a CAS (Computer Algebra System).
To evaluate the given integral, we can use the integral of the cosine function. The integral of cos(x) is sin(x), so we can apply this rule to our integral. The coefficient 72 is a constant and can be factored out of the integral.
Integrating cos(4x) with respect to x gives us (1/4)sin(4x). Multiplying this result by the coefficient 72 gives us (72/4)sin(4x), which simplifies to 18sin(4x).Therefore, the exact answer to the given integral is 18sin(4x) + C, where C is the constant of integration.
To check the answer, you can use a CAS (Computer Algebra System) like Wolfram Alpha or Mathematica, which can perform symbolic integration. Inputting the original integral ∫(72cos(4x))dx into a CAS will confirm that the result is indeed 18sin(4x) + C, validating our solution.
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