please write neatly and show work
5) solve the following equations using an algebraic method Show all work. There may . 11 or a real solutions for each answer. be a. 1.2x² = 45 b. 3x + 122.5= 465.5 c. 8x² - 2x=1
Answers
a. The solutions to the equation 1.2x² = 45 are x = √37.5 and x = -√37.5.
b. The solution to the equation 3x + 122.5 = 465.5 is x ≈ 114.333.
c. The solutions to the equation 8x² - 2x = 1 are x = 0.5 and x = -0.25.
a. 1.2x² = 45
To solve this equation, we can start by dividing both sides by 1.2:
1.2x² / 1.2 = 45 / 1.2
x² = 37.5
Next, we take the square root of both sides to isolate x:
√(x²) = √37.5
x = ±√37.5
Therefore, the solutions to the equation 1.2x² = 45 are x = √37.5 and x = -√37.5.
b. 3x + 122.5 = 465.5
To solve this equation, we can start by subtracting 122.5 from both sides:
3x + 122.5 - 122.5 = 465.5 - 122.5
3x = 343
Next, we divide both sides by 3 to isolate x:
3x / 3 = 343 / 3
x = 114.333...
Therefore, the solution to the equation 3x + 122.5 = 465.5 is x ≈ 114.333.
c. 8x² - 2x = 1
To solve this equation, we can rearrange it to a quadratic form:
8x² - 2x - 1 = 0
To solve the quadratic equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this case, a = 8, b = -2, and c = -1.
x = (-(-2) ± √((-2)² - 4(8)(-1))) / (2(8))
x = (2 ± √(4 + 32)) / 16
x = (2 ± √36) / 16
x = (2 ± 6) / 16
x = (2 + 6) / 16 or x = (2 - 6) / 16
x = 8 / 16 or x = -4 / 16
x = 0.5 or x = -0.25
Therefore, the solutions to the equation 8x² - 2x = 1 are x = 0.5 and x = -0.25.
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Related Questions
Mike can sell 20 glasses of lemonade for 10¢ each. If heraises the price to 20¢, he estimates that he'll only be able tosell 15 glasses. How much more money can he earn if hecharges 20¢ per glass instead of 10¢?
Answers
Okay, here we have this:
First let's calculate how much is he earning selling 20 glasses each glass for 10¢:
Actual Earnings=20*10¢=200¢
Now, let's calculate how much will he earn if raises the price to 20¢ and sell the 15 glasses that he is estimating:
Future Earning=15*20¢=300¢
Let's calculate the diference now:
Diference=300¢-200¢=100¢
According with this he will earn 100¢ more if he charges 20¢ per glass instead of 10¢.
What is the distance between each pair of points?
Answers
Answer:
The square root of 145.
Step-by-step explanation:
For this problem, make a right triangle between these two points. To solve for distance, use the Pythagorean formula. We know that one side is 8, and the other side is 9, so square 8 and 9 to get 64 plus 81. When you add these together, you get the square root of 145. You cannot further simplify the square root of 145, so that is the distance between the pair of points.
Answer:
For any two points there is exactly one line segment connecting them. The distance between two points is the length of the line segment connecting them. Note that the distance between two points is always positive. Segments that have equal length are called congruent segments.
Step-by-step explanation:
PLEASE SOMEBODY HELP! I’ve been stuck on this question for nearly 5 hours because I literally have no idea what to do somebody please help
Answers
Answer:
Well We need to get rid of 1200 mb so your estimated guess would be to delete~2523~ photos If i get this wrong Im very sorry.
Step-by-step explanation:
You are the director of the customer service center in Company Alpha. You find that the mean time between calls to the center is 6 minutes with standard deviation of 4 minutes. The effective response time is 11 minutes with a standard deviation of 20 minutes. (a) Identify the following parameters: ta
tθ
∂a
∂θ
ra:
rθ:
Answers
The identified parameters are:
ta = 6 minutes
tθ = 11 minutes
∂a = 4 minutes
∂θ = 20 minutes
ra = 1/6 minutes^(-1)
rθ = 1/11 minutes^(-1)
ta: Mean time between calls to the center
tθ: Effective response time
∂a: Standard deviation of the time between calls to the center
∂θ: Standard deviation of the effective response time
ra: Rate of calls to the center (inverse of ta, i.e., ra = 1/ta)
rθ: Rate of effective response (inverse of tθ, i.e., rθ = 1/tθ)
Given information:
Mean time between calls to the center (ta) = 6 minutes
Standard deviation of time between calls (∂a) = 4 minutes
Effective response time (tθ) = 11 minutes
Standard deviation of effective response time (∂θ) = 20 minutes
Using this information, we can determine the values of the parameters:
ta = 6 minutes
tθ = 11 minutes
∂a = 4 minutes
∂θ = 20 minutes
ra = 1/ta = 1/6 minutes^(-1)
rθ = 1/tθ = 1/11 minutes^(-1)
So, the identified parameters are:
ta = 6 minutes
tθ = 11 minutes
∂a = 4 minutes
∂θ = 20 minutes
ra = 1/6 minutes^(-1)
rθ = 1/11 minutes^(-1)
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Marco budget $1,600 a month for expenses.
According to the graph, how much does he pay
for his credit card, groceries, and rent?
$908
$1,008
$1,029
$1,142
Answers
He has used the highest recommended percentages to calculate the amounts for the three categories: credit cards, groceries, and rent.
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he pay = $2487
He has used the highest recommended percentages to calculate the amounts for the three categories: credit cards, groceries, and rent.
The amount added to his account each month is
$908 + $1,008 + $1,029 + $1,142 = $4087
Marco budget $1,600 a month for expenses
$4087 - $1600 = $2487
According to the graph, he pay = $2487
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my feet are asleep,,,.T.T, I'm also stressed and cold and tired
Answers
Answer:
Ok its friday be happy
Step-by-step explanation:
4. Following the steps below, what is the next step in constructing a congruent angle?
1. Start by drawing angle BAC.
2. Make a point P that will be the vertex of the new angle.
3. From P, draw a ray PQ. This will become one side of the new angle. This ray can go off in any direction. It does not have to be parallel to anything else.
4. Place the compass tip on point A, set to any convenient width.
5. Draw an arc across both sides of the angle, creating the points J and K as shown.
6. Without changing the compass's width, place the compass point on P and draw a similar arc there, creating point M as shown.
7. Set the compass on K and adjust its width to point J.
8. Without changing the compass's width, move the compass to M and draw an arc across the first one, creating point L where they cross.
9.?
Draw a line segment of any length, PQ. P will be the angle's vertex.
From B, mark off a short arc above P.
Using the straight edge, draw a line from A to where the arcs cross.
Draw a ray PR from P through L and onwards a little further. The exact length is not important.
Answers
Based on the given steps, the next step would be: Draw a ray PR from point P through point L and extend it further. The correct option is D.
How to explain the informationAfter drawing the ray PR, you can proceed with the remaining steps to complete the construction.
The reason why we draw a ray PR from P through L is that this will create two angles with the same measure. The measure of an angle is the amount of rotation between its two rays. When we draw a ray from P through L, we are essentially rotating the ray PQ by the same amount that we rotated the ray BA. This means that the two angles will have the same measure.
Once we have drawn the ray PR, we can check to see if the two angles are congruent.
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PLEASE HELP, WILL GIVE BRAINLIEST FOR RIGHT ANSWER!
Indicate the equation of the given line in standard form, writing the answer in the equation box below.
The line that contains the point Q (1, -2) and is parallel to the line whose equation is
y − 4 = 2/3 ( x − 3)
Answers
Answer:
Y = 2/3x-8/3
Step-by-step explanation:
y − 4 = 2/3 ( x − 3)
y − 4 = 2/3x -2
y = 2/3x +2
~~~~~~~~~~~~~~~~~
-2 = 2/3(1) + b
b = -2 2/3 = -8/3
A rectangular prism-shaped display case is 30 1/2 inches wide, 10 1/2 inches long, and 32 1/4 inches tall.
What is the volume of the display case in cubic inches?
Responses
73 1/4 in³
73 and 1 fourth, in³
320 1/4 in³
320 and 1 fourth, in³
10,328 1/16 in³
10328 and 1 sixteenth, in³
28,372 5/8 in
Answers
The volume of the display case is 2161 1/8 cubic inches.To find the volume of a rectangular prism-shaped display case, we multiply its length, width, and height.
Given that the display case is 30 1/2 inches wide, 10 1/2 inches long, and 32 1/4 inches tall, we can calculate the volume as follows:
Volume = Length * Width * Height
Using the given measurements:
Volume = 10 1/2 inches * 30 1/2 inches * 32 1/4 inches
To simplify the calculation, we can convert the mixed numbers to improper fractions:
Volume = (21/2) inches * (61/2) inches * (129/4) inches
Next, we multiply the fractions:
Volume = (21/2) * (61/2) * (129/4) = 17289/8
The resulting fraction, 17289/8, is an improper fraction. To convert it back to mixed number form:
Volume = 2161 1/8 in³.
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dy/dt =y+2u, y(0)=5, u= step change of unity
Answers
The solution to the provided differential equation with the initial condition y(0) = 5 and u as a step change of unity is y = -2
The provided differential equation is: \(\[\frac{{dy}}{{dt}} = y + 2u\]\) with the initial condition: y(0) = 5 where u is a step change of unity.
To solve this differential equation, we can use the method of integrating factors.
First, let's rearrange the equation in the standard form:
\(\[\frac{{dy}}{{dt}} - y = 2u\]\)
Now, we can multiply both sides of the equation by the integrating factor, which is defined as the exponential of the integral of the coefficient of y with respect to t.
In this case, the coefficient of y is -1:
Integrating factor \(} = e^{\int -1 \, dt} = e^{-t}\)
Multiplying both sides of the equation by the integrating factor gives:
\(\[e^{-t}\frac{{dy}}{{dt}} - e^{-t}y = 2e^{-t}u\]\)
The left side of the equation can be rewritten using the product rule of differentiation:
\(\[\frac{{d}}{{dt}}(e^{-t}y) = 2e^{-t}u\]\)
Integrating both sides with respect to t gives:
\(\[e^{-t}y = 2\int e^{-t}u \, dt\]\)
Since u is a step change of unity, we can split the integral into two parts based on the step change:
\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 2\int_{t}^{{\infty}} 0 \, dt\]\)
Simplifying the integrals gives:
\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 0\]\)
\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt\]\)
Evaluating the integral on the right side gives:
\(\[e^{-t}y = 2[-e^{-t}]_{{-\infty}}^{t}\]\)
\(\[e^{-t}y = 2(-e^{-t} - (-e^{-\infty}))\]\)
Since \(\(e^{-\infty}\)\) approaches zero, the second term on the right side becomes zero:
\(\[e^{-t}y = 2(-e^{-t})\]\)
Dividing both sides by \(\(e^{-t}\)\) gives the solution: y = -2
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The diagram shows the net of a square pyramid.
The height of the pyramid is 15 cm. Calculate the value of x..
Help me plsss
Answers
Answer:
Given,
Base (b) = 16 cm
slant Height (h) = 15 cm
a= 8 cm {a is the half of base}
x = ?
Using Pythagoras Theorem
p^2 = h^2 - b^2
x^2= 15 - 8
x^2 = 7
x = 2.64 cm
After solving the equation, the value obtained for x will be equal to 17.
What is Pyramid?Three dimensions can be seen in a pyramid. A pyramid's flat triangular faces and polygonal base all come together in a summit known as the apex. By joining the bases to the peak, a pyramid is created. The base's edges are joined at the apex to produce the triangular face known as the lateral face.
As per the given information in the question,
The side edge will be half of the side of the base, so,
a = 16/2 = 8
Height, h = 15 cm
Then, use the equation of Pythagoras' theorem:
x² = h² + a²
x² = 15² + 8²
x² = 225 + 64
x = √289
x = 17 cm
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PLS HELP ME I WILL GIVE BRAIN THINGY
Answers
Which function has the greatest growth rate?
5) 1x) = 2(7)5
B {x) = 7(2)
© 1x) =3(5)+ 6
O f(x) = 5(3)+
Answers
option C is correct, \(f(t)=1.36^{t}\) has greatest growth rate.
What is a function?A relation is a function if it has only One y-value for each x-value.
Growth rates are the percent change of a variable over time
Formula for the exponential growth is,
f(x)=a(1+r/100)ⁿ
where r = rate of exponential growth
a = initial amount
n = duration or time
The greatest growth rate is in the form of percentage.
We have to check for the value which is higher in the given options.
Hence, option C is correct, \(f(t)=1.36^{t}\) has highest growth rate.
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The given question is not complete, similar kind of question is attached below.
Let k(x) = 3(x-4) and m(x) = x^2 + 3x + 1. find k(x) + m(x)
Answers
Step by step explanation:
Alonzo split 3/4 pounds of candy among 4 people. What is the unit rate in pounds per person? Write your answer in simplest form.
(10 points, brainliest, thanks and 5 if correct! IF! also it is due today)
Answers
When Alonzo splits 3/4 pounds of candy among 4 people the unit rate in pounds per person is 3/16 pounds per person
What is unit rate?The ratio of two measures, with one as the second of the item, is known as unit rate.
For the problem where Alonzo have to split 3/4 pounds of candy, the unit rate is solved by division.
In this case, Alonzo will divide each the 3/4 pounds by 4 to get a value of which is the unit rate
The unit rate of candy in pounds per person
= 3/4 pounds / 4 persons
= 3/16 pounds per person
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A machine fills bags with sweets there are 4275 sweets there are 28 sweets in each full bag the machine fills as many bags as possible how many sweets are left must show your working
Answers
19 sweets are lefted.
Lets simplify the problem,
Maximum no. of bag filled by 4275 sweets
Through Simple Division we get,
4275/28 ~=152
Therefore , there is 4256 sweets in 152 bags
Therefore, 4275-4256=19 sweets are left
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can u solve two questions. .. Mark brilliant student
Answers
sorry I don't know if you ask to other sure I think they will tell you ans
Solve the following equation for the variable x. Show your complete work (looking for exact steps not just the answer) 2+x+6-2+8= 24
Answers
8-2=6
6+8=14
14-24=10
X=10
what angle has a tangent and sine that are both negative?
300
210
45
150
Answers
Answer:
\(300^{\circ}\)
Step-by-step explanation:
\(\text{In quadrant IV, both ratios of tangent and sine are negative.}\\ \\300^{\circ}~ \text{lies in the fourth quadrant, so}~ \tan 300^{\circ} ~ \text{and}~ \sin 300^{\circ}~ \text{are negative.}\)
A collection of dimes and nickels is worth 3.30. if there are 42 coins in total how many of each kind of coin are there?
Answers
Answer:1 nickels =$0.05
1 dime= $0.1
Step-by-step explanation:
1 nickels =$0.05
1 dime= $0.1
let the number of nickels be x and that of dimes be y.
total number of coins is given by:
x+y=42
hence:
y=42-x.......i
total amount of cash will be:
0.05x+0.1y=3.30.........ii
substituting i in ii we get:
0.05x+0.1(42-x)=3.30
0.05x+4.2-0.1x=3.3
-0.05x=-0.9
x=-0.9/(-0.05)
x=18
hence the the number nickels is x=18, the number of dimes will be y=42-x=42-18=24
Given the circle below with secants KLM and ONM, find the length of KL.
Round to the nearest tenth if necessary.
M
21
22
N
27
K
Answers
The length of KL is approximately 24.4 units.
The theorem of intersecting chords allows us to write:
ML * NL = KL * LM
Inputting the values provided yields:
(KL + 21) * KL = KL * (KL + 22) 27
When we extend the right side, we obtain:
22KL + KL2 = 27KL + 567
By condensing and rearrangeing, we obtain:
KL^2 - 5KL - 567 = 0
The quadratic formula can be used to solve for KL:
KL is equal to [5 sqrt(52 + 4(567))] / 2
KL is equal to [5sqrt(2809)] / 2
After simplifying to one decimal place and taking the positive root, we obtain:
KL ≈ 24.4
KL thus measures around 24.4 units in length.
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The equation of a circle is (x-2)2+(y+3)2=26. What are the coordinates of the center of the circle?
Answers
A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant. The circle's centre will lie at (2,-3).
What is the equation of the circle with radius r units, centred at (x,y)?If a circle O has a radius of r units length and it has got its centre positioned at (h, k) point of the coordinate plane, then, its equation is given as:
(x-h)² + (y-k)² = r²
Given the equation of a circle is (x-2)²+(y+3)²=26. Compared with the equation of the circle. The circle's centre will lie at (2,-3).
Hence, the circle's centre will lie at (2,-3).
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Type an equation for the
following pattern.
x
1
2
3
4
5
y
55
90
125
160
195
y=35x+[?]
Answers
Answer:
y = 35x + 20
Step-by-step explanation:
See attached graph.
![Type an equation for thefollowing pattern.x12345y5590125160195y=35x+[?]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/wmIdD93URaXOufcYtLbef0i7wPqjWwM4.jpeg)
PLEASE HELP 1 MILLIOM POINTS!!! line n containing Q(-2,5), and perpendicular to the graph of y= -1/2x+5
PLEASE EXPLAIN IF YOU DO YOU ARE AEWSOME!! I WILL GIVE BRAINLIEST TO BEST ANSWER!!!
Answers
Answer:
y = 2x + 9Step-by-step explanation:
Perpendicular lines have negative - reciprocal slopes
Given line:
y = -1/2x + 5Perpendicular line:
y = 2x + bUse point Q(-2, 5) to complete the equation of the line:
y - 5 = 2(x - (-2))y - 5 = 2x + 4y = 2x + 9please help!! I'm really confused:(
Answers
\(60\% = 180\\1\%=\frac{180}{60} = 3\)
\(100\% - 60\% = 40\%\\40\% = 3*40=120\)
Answer: 120 cans.
Find the measure of the indicated angle in each triangle.
A) 90
B) 136
C) 180
D) 44
Answers
Answer: 44
Step-by-step explanation:
The sum of the angles of a triangle is 180 degrees, so angle B = 180-90-46=44 degrees.
WILL GET BRAINIEST!!!! I-ready!!! PLEASE HELP!!!
Answers
Answer:
i am not sure but i think it is 280
Could someone please help me with this?
A regular child admission ticket to the San Diego Zoo is $52. If you have a special pass, you can get a 20% discount on the original ticket price. What is the discounted amount of the ticket when you use the discount?
Answers
If I started at 7:20 and ended at 8:07 how much times is that?
Answers
Answer:
47 minutes
Step-by-step explanation:
the heart is a four-chambered muscular pump. in one day, how many gallons of blood are pumped throughout the body?
Answers
Answer:
Step-by-step explanation:
6,000-7,500 liters (1,500-2,000 gallons) of blood daily. The average adult body contains about five quarts of blood, which continually circulates throughout the body. Hope this helps!