which formulas can be used to find the surface area of a regular pyramid where p is the perimeter of the base, s is the slant height, BA is the base area, and LA is the lateral area click all that apply options: A. SA= 1/2BA + 1/2ps B. SA= BA-LA C. SA= BA+LA D. SA= BA • LA E. SA= BA + 1/2ps

Answers

Answer 1

Answer:

C and E

Step-by-step explanation:

He got it on ap.ex

Answer 2

The area of the pyramid can be found using the formula SA = BA + LA and SA= BA + 1/2ps option (C) and (E) are correct.

What is a square pyramid?

In geometry, it is defined as the shape having a square base with equal sides length and all the vertex of the square's joints at the top, which is perpendicular to the center of the square.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a pyramid with a square base:

The perimeter of the base is p

The slant height is s.

The base area is BA

The lateral area is LA.

We can find the area of the pyramid as follows:

SA = BA + LA

SA= BA + 1/2ps

Thus, the area of the pyramid can be found using the formula SA = BA + LA and SA= BA + 1/2ps option (C) and (E) are correct.

Learn more about the pyramid here:

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Which Formulas Can Be Used To Find The Surface Area Of A Regular Pyramid Where P Is The Perimeter Of

Related Questions

You have $9000 with which to build a rectangular enclosure with fencing. The fencing material costs $30 per meter. You also want to have two partitions across the width of the enclosure, so that there will be three separated spaces in the enclosure. The material for the partitions costs $25 per meter. What is the maximum area you can achieve for the enclosure

Answers

Answer:i explained it

Step-by-step explanation:

The total cost of the fence will be 30(2L + 2W) + 2*25 W <= 9000

60L + 110W <= 9000

60 L <= 9000 - 110W

L <= 150 - 11/6 W

For a given width, the maximum area will correspond to the maximum length, so we can just go ahead and say L = 150 - 11/6 W

A = LW = (150 - 11/6 W) W

A = 150 W - 11/6 W2

A' = 150 - 11/3 W = 0

150 = 11/3 W

W = 450/11

Identify the conclusion in a hypothesis test of the following claim and sample data:
Claim: "The average battery life (between charges) of this model of tablet is at least 12 hours."
A random sample of 80 of these tablets is selected, and it is found that their average battery life is 11.58 hours with a standard deviation of 1.93 hours. Test the claim at the 0.05 significance level.
a. There is not sufficient evidence to warrant rejection of the claim.
b. There is sufficient evidence to warrant rejection of the claim.
c. There is sufficient evidence to support the claim.
d. There is not sufficient evidence to support the claim.

Answers

Answer:

C

Step-by-step explanation:

Firstly, we set up the null and alternative hypothesis as follows;

The null hypothesis is;

H0: μ ≥ 12

The alternative hypothesis is;

Ha : μ < 12

Next step is to calculate the test statistic z

Mathematically;

z = (x - μ )/ σ /√n

= (11.58 - 12) /1.93/√(80

Test statistic z = -1.92

Now we proceed to find the probability value that is equal to the value of the test statistic. We can find this by using the standard normal table or NORMSTD function on excel

P(z < -1.92) = 0.0274

P-value = 0.0274

alpha = 0.05

From the above, we can see that

P-value < alpha

And because of this, we are going to reject the null hypothesis and therefore accept the alternative.

We then conclude that there is sufficient evidence to conclude that "The average battery life (between charges) of this model of tablet is at least 12 hours."

I need some help, see the picture for the question. Solve for V

Answers

Answer:

the answer is A) h=3V/(Pi*r^2)

Step-by-step explanation:

This question is asking to solve for h, the equation is allready solved for V.

to solve for h means to get h by itself on one side of the equation.

1) V=(1/3)*pi*r^2*h. Divide 1/3*pi*r^2 to the other side of the equation

2) V/(1/3)*pi*r^2=h. 1/3 on the bottom denominator means we can multiply the reciprocal to the bottom and the top and get an equivalent answer. In short, move the 3 from the 1/3 onto the top.

3) (3*V)/(pi*r^2)=h. Simplify.

4) 3V/(Pi*r^2)=h.

Shawna spent half of her weekly allowance playing arcade games. To earn more money her parents let her clean the windows in the house for $4.37. What is her weekly allowance if she ended with $11.18?

Answers

Answer:

$13.62

Step-by-step explanation:

By working backward we can see that before she cleaned the windows she had $6.81.

We know that she spent half her allowance on the arcade and the $6.81 she had before cleaning the windows is the other half.

So, if you multiply by 2 you get that here weekly allowance is $13.62.

Answer:

$13.62

Step-by-step explanation:there

Em uma prova de conhecimentos gerais, Fernando errou 3/8 do total de 72 questões. Quantas são as questões que Fernando ACERTOU?

Answers

Vamos lá.....

Duas maneiras praticas:

1 - Multiplicar a fraçao pelo total, vai informar quanto a fracao representa (o que é questionado na questao)

2 - Regra de 3.

1:

72 × (3/8)

216/8

27

Ele acertou 27 questoes

(pergunta mais que interessante: qntas questoes havia na prova??? 72)

Consider the following estimated regression equation based on 10 observations y 29.1270 5906x, 4980x2 011
a. Develop a point estimate of the mean value of y when x 1 = 180 and x 2-310 (to 3 decimals).
b. Develop a point estimate for an individual value of y when x 1 180 and x 2-310 (to 3 decimals)

Answers

Answer:

no tiene mas informaion?

Step-by-step explanation:

Researchers recorded that a certain bacteria population declined from 800,000 to 500,000 in 6 hours after the administration of medication. At this rate of decay, how many bacteria would there have been at 24 hours? Round to the nearest whole number

Answers

Answer:

We can assume that the decline in the population is an exponential decay.

An exponential decay can be written as:

P(t) = A*b^t

Where A is the initial population, b is the base and t is the variable, in this case, number of hours.

We know that: A = 800,000.

P(t) = 800,000*b^t

And we know that after 6 hours, the popuation was 500,000:

p(6h) = 500,000 = 800,000*b^6

then we have that:

b^6 = 500,000/800,000 = 5/8

b = (5/8)^(1/6) = 0.925

Then our equation is:

P(t) = 800,000*0.925^t

Now, the population after 24 hours will be:

P(24) = 800,000*0.925^24 = 123,166

Answer:

122,070 bacteria.

Step-by-step explanation:AA0ktA=500,000=800,000=?=6hours=A0ekt

Substitute the values in the formula.

500,000=800,000ek⋅6

Solve for k. Divide each side by 800,000.

58=e6k

Take the natural log of each side.

ln58=lne6k

Use the power property.

ln58=6klne

Simplify.

ln58=6k

Divide each side by 6.

ln586=k

Approximate the answer.

k≈−0.078

We use this rate of growth to predict the number of bacteria there will be in 24 hours.

AA0ktA=?=800,000=ln586=24hours=A0ekt

Substitute in the values.

A=800,000eln586⋅24

Evaluate.

A≈122,070.31

At this rate of decay, researchers can expect 122,070 bacteria.

What is the value of 3X to the 2nd power

Answers

It would depend what x is, but it is written in as 3x^2 and you would just plug x in

Answer:

9 x^2

Step-by-step explanation:

( 3x) ^2

We are multiplying 3x * 3x

9 x^2

A car dealership earns a portion of its profit on the accessories sold with a car. The dealer sold a Toyota Camry loaded with accessories for $24,000. The total cost of the car was 8 times as much as the accessories. How much did the accessories cost? Cost of Accessories

Answers

Answer:

y = 2666.67

Step-by-step explanation:

Well to solve this we can make a system of equations.

x = cost of car alone

y = cost of accesories,

[tex]\left \{ {{x+y=24000} \atop {x=8y}} \right.[/tex]

So now we plug in 8y for x in x + y = 24000.

(8y) + y = 24000

9y = 24000

Divide both sides by 9

y = 2666.666666

or 2666.67 rounded to the nearest hundredth.

Now that we have y we can plug that in for y in x=8y.

x = 8(2.666.67)

x = 21,333.33 rounded to the nearest hundredth.

Thus,

accessories "y" cost around 2666.67.

Hope this helps :)

For a certain type of tree the diameter D (in feet) depends on the tree's age t (in years) according to the logistic growth model. Find the diameter of a 21-year-old tree. Please give the answer to three decimal places.

Answers

Answer:

[tex]D(21) = 1.612\ ft[/tex]

Step-by-step explanation:

The question has missing details;

[tex]D(t) = \frac{5.4}{1+2.9e^{-0.01t}}[/tex]

Given that t = 21

Solve for Diameter, D

To do this, we simply substitute 21 for t in the above function

[tex]D(t) = \frac{5.4}{1+2.9e^{-0.01t}}[/tex] becomes

[tex]D(21) = \frac{5.4}{1+2.9e^{-0.01 * 21}}[/tex]

[tex]D(21) = \frac{5.4}{1+2.9e^{-0.21 }}[/tex]

Solve for [tex]e^{-0.21}[/tex]

[tex]D(21) = \frac{5.4}{1+2.9* 0.81058424597}[/tex]

Simplify the denominator

[tex]D(21) = \frac{5.4}{1+2.35069431331}[/tex]

[tex]D(21) = \frac{5.4}{3.35069431331}[/tex]

[tex]D(21) = 1.61160628069[/tex]

[tex]D(21) = 1.612\ ft[/tex] (Approximated)

Hence, the diameter of the 21 year old tree is 1.612 feet

Please help. I’ll mark you as brainliest if correct

Answers

Answer:

1,-1,3,4

1,6,-2,-4

-4,6,-6,6

Step-by-step explanation:

I believe you just put in the values into the box. Watch the video to see how they did it to make sure it looks like how I did it.

6th grade math help me, please :))

Answers

Answer:

D

Step-by-step explanation:

100/5=20

20*7=140

Please help. I’ll mark you as brainliest if correct!

Answers

Answer:

x +0y+0z = 400

-x +y+0z = 150

-8x +0y +z = 250

Step-by-step explanation:

The last column is the solution

The rest of the columns are the coefficients of the variables

x +0y+0z = 400

-x +y+0z = 150

-8x +0y +z = 250

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Second-degree, with zeros of −7 and 6, and goes to −∞ as x→−∞.

Answers

Answer:

Step-by-step explanation:

Hello, because of the end behaviour it means that the leading coefficient is negative so we can construct such polynomial function as below.

[tex]\large \boxed{\sf \bf \ \ -(x+7)(x-6) \ \ }[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

The polynomial function will be f ( x ) = - x² - x + 42

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+ bx + c = 0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

Given data ,

The polynomial function is of second degree with zeros of -7 and 6

So , x = -7 and x = 6

Let the function be f ( x ) where f ( x ) = ( x + 7 ) ( x - 6 )

Now , as x tends to infinity , the negative makes no such difference on the zeros of the function f ( x ) ,

And , f ( x ) = - ( x + 7 ) ( x - 6 )

Therefore , to find the polynomial function , f ( x ) = - ( x + 7 ) ( x - 6 )

f ( x ) = - [ x² - 6 x + 7 x - 42 ]

        = - [ x² + x - 42 ]

        = - x ² - x + 42

Hence , the polynomial function f ( x ) = - x ² - x + 42

To learn more about polynomial function click :

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Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.)

f ''(x)= 6x +sinx

Answers

Answer:

[tex]f(x) = x^3 -sinx +Cx+D[/tex]

Step-by-step explanation:

Given that:

[tex]f ''(x)= 6x +sinx[/tex]

We are given the 2nd derivative of a function f(x) and we need to find f(x) from that.

We will have to integrate it twice to find the value of f(x).

Let us have a look at the basic formula of integration that we will use in the solution:

[tex]1.\ \int {(a\pm b)} \, dx =\int {a} \, dx + \int {b} \, dx \\2.\ \int {x^n} \, dx = \dfrac{x^{n+1}}{n+1}+C\\3.\ \int {sinx} \, dx = -cosx+C\\4.\ \int {cosx} \, dx = sinx+C[/tex]

[tex]\int\ {f''(x)} \, dx =\int\ {(6x +sinx)} \, dx \\\Rightarrow \int\ {6x} \, dx + \int\ {sinx} \, dx \\\\\Rightarrow 6\dfrac{x^2}{2} -cosx +C\\\Rightarrow 3{x^2} -cosx +C\\\Rightarrow f'(x)=3{x^2} -cosx +C\\[/tex]

Now, integrating it again to find f(x):

[tex]f(x) =\int {f'(x)} \, dx =\int{(3{x^2} -cosx +C)} \, dx \\\Rightarrow \int{3{x^2}} \, dx -\int{cosx} \, dx +\int{C} \, dx\\\Rightarrow 3\times \dfrac{x^3}{3} -sinx +Cx+D\\\Rightarrow x^3 -sinx +Cx+D\\\\\therefore f(x) = x^3 -sinx +Cx+D[/tex]

An article reported on the results of an experiment in which half of the individuals in a group of 66 postmenopausal overweight women were randomly assigned to a particular vegan diet, and the other half received a diet based on National Cholesterol Education Program guidelines. The sample mean decrease in body weight for those on the vegan diet was 6 kg, and the sample SD was 3.2, whereas for those on the control diet, the sample mean weight loss and standard deviation were 3.8 and 2.4, respectively. Does it appear the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg? Carry out an appropriate test of hypotheses at significance level .05 based on calculating a P-value.

Answers

Answer:

We conclude that the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg.

Step-by-step explanation:

We are given that an article reported on the results of an experiment in which half of the individuals in a group of 66 postmenopausal overweight women were randomly assigned to a particular vegan diet, and the other half received a diet based on National Cholesterol Education Program guidelines.

The sample mean decrease in body weight for those on the vegan diet was 6 kg, and the sample SD was 3.2, whereas, for those on the control diet, the sample mean weight loss and standard deviation were 3.8 and 2.4, respectively.

Let = true average weight loss for the vegan diet.

[tex]\mu_2[/tex] = true average weight loss for the control diet.

So, Null Hypothesis, : 1 kg      {means that the true average weight loss for the vegan diet exceeds that for the control diet by less than or equal to 1 kg}

Alternate Hypothesis, : > 1 kg      {means that the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg}

The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;

                            T.S.  =  [tex]\frac{(\bar X_1-\barX_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex]   ~    [tex]t__n_1_+_n_2_-_2[/tex]

where, = sample mean weight loss for the vegan diet = 6 kg

 = sample mean weight loss for the control diet = 3.8 kg

 = sample standard deviation weight loss for the vegan diet = 3.2 kg

 = sample standard deviation weight loss for the control diet = 2.4 kg

[tex]n_1[/tex]  = sample of vegan diet women = 33

[tex]n_2[/tex] = sample of control diet women = 33

Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex]  = [tex]\sqrt{\frac{(33-1)\times 3.2^{2}+(33-1)\times 2.4^{2} }{33+33-2} }[/tex] = 2.83

So, the test statistics =  [tex]\frac{(6-3.8)-(1)}{2.83 \times \sqrt{\frac{1}{33}+\frac{1}{33} } }[/tex]  ~  [tex]t_6_4[/tex]

                                    =  1.722  

The value of t-test statistics is 1.722.

Also, the P-value of the test statistics is given by;

               P-value = P([tex]t_6_4[/tex] > 1.722) = 0.0461 or 4.61%

Since the P-value of our test statistics is less than the level of significance as 0.0461 < 0.05, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg.

A coin is thrown at random into the rectangle below.

A rectangle is about 90 percent white and 10 percent green.

What is the likelihood that the coin will land in the green region?
It is certain.
It is impossible.
It is likely.
It is unlikely.

Answers

Answer:

It is unlikely.

Step-by-step explanation:

Certain = 100%

Impossible = 0%

Likely = more than 50%

Unlikely = less than 50%

It is less than 50%, so it is unlikely.

Answer:

(A) it is likely

Step-by-step explanation:

i took the test on edge

Linda earned $13,500 in 3 months. What is her annual salary?

Answers

Answer:

$54,000

Step-by-step explanation:

Assuming that her salary does not change. Note that annual means "a year", which would mean 12 months.

First, find how much Linda makes per month. Divide the total earned in 3 months with 3 months:

13,500/3 = 4,500

Next, multiply 4,500 (the amount made per month) with 12 to get your annual salary:

4,500 x 12 = 54,000

Linda makes $54,000 annually.

Find the Slope of the line
-4
1
1/4
4

Answers

Answer:

Hey there!

The slope is rise over run, or 1/-4.

This gives us the slope, which is -1/4.

Hope this helps :)

Answer:

1/4

Step-by-step explanation:

( i mean i think it is - 1/4 but that isn't an answer choice- )

Slope (m) =

ΔY overΔX= -1 over 4  = -0.25

subtract x^1 and x^2 also y^1 and y^2

and put the answer of y' s over the answer of x 's

divide and you got your answer!

A disc has a diameter of centimeters while a mini disc has a diameter of centimeters. Write the ratio of the mini disc diameter to the disc diameter.

Answers

Answer:

2 : 3

Step-by-step explanation:

A disc has a diameter of 21 cm while a mini disc has a diameter of 14cm. Write the ratio of the mini disc diameter to the disc diameter.

Answer: Let the diameter of the mini disc be [tex]d_1[/tex] while the diameter of the disc be [tex]d_2[/tex]. To get the ratio of the mini disc diameter to the disc diameter, we just simply have to divide the diameter of the mini disc by the diameter of the disc and then represent the fraction in ratio form. The ratio of the disc diameters is given by:

Ratio of the mini disc diameter to the disc diameter = Diameter of mini disc / diameter of disc

Ratio of the mini disc diameter to the disc diameter = [tex]\frac{14}{21}=\frac{2}{3}[/tex]

Ratio of the mini disc diameter to the disc diameter = 2 : 3

Does Kerri's dot plot match the data in the tally
table?
Use Kerri's dot plot to complete the statements.
_classmates spent 3 hours at the park.
_classmates spent 4 hours at the park.
_classmates spent 5 hours at the park.
_classmates spent 6 hours at the park.

Answers

Answer:

no 5,3,6,4

Step-by-step explanation:

i got it right

Answer:

first one is no second is 5 third is 3 forth one is 6 and last one is 4

Step-by-step explanation:

PLZ give me brainless.

The Buzz Tool Company issued 1,000 shares of common stock. If the total value of this was $50,000,what's the par value of each share.

Answers

Answer:

$50.

Step-by-step explanation:

The formula for the stocks is...

Par value of preferred stock = (Number of issued shares) * (par value per share)

So, we can say that...

Par value per share = par value of preferred stock / number of issued shares.

The par value of the Buzz Tool Company is $50,000. There are 1,000 issued shares. So, each stock would be $50,000 / 1,000 = $50 / 1 = $50.

Hope this helps!

Answer: par value is $50.00

Step-by-step explanation:

$50,000.00 ÷ 1,000

= $50.00

PLEASE HELP ?

A: 111.6 square centimeters

B: 323 square centimeters

C: 7.75 square centimeters

Answers

Answer:

B. 323 square centimeters

Step-by-step explanation:

multiply the inches by the conversion number

50 x 6.45 = 322.5

Answer:

[tex]\boxed{Option \ B}[/tex]

Step-by-step explanation:

[tex]1 \ inch^2 = 6.45 \ cm^2[/tex]

Multiplying both sides by 50

[tex]1 * 50 \ inch^2 = 6.45 * 50 \ cm^2\\[/tex]

[tex]50 \ inch^2 = 323 \ cm^2[/tex]

What is the simplified value of $\frac{10! + 11! + 12!}{10! + 11!}$?

Answers

Answer:

12

Step-by-step explanation:

We can factor out 10! on the numerator and the denominator,.

This gives: 10! (1 + 11 + (11 * 12)) / 10! (1 + 11)

This is because 10! * 11 is equal to 11! meaning we can factor out 10!.

10! * 11 * 12 also equals 12! which is why we can factor 10! out of that too.

Seeing as 10! is at the top and bottom we can cancel those out.

This leaves us with: 144 / 12 which is equal to 12.

Good evening can I get help please?​

Answers

Answer:

Yes.

Step-by-step explanation:

1+1=2

3+5=8

7+1=8

9+23=32

5+13=18

An odd number is an even number plus 1, and 1 plus 1 is an even number. even numbers added together are also always even numbers, so two even numbers (in the second example it'd be 2+1 & 4+1, so 2 and 4) plus an even number(1+1=2) must be an even number.

Find the total area of the prism.

Answers

Answer:

A=1,728

Step-by-step explanation:

To find the area of a prism, you must find the area of one side, then multiply it by so it would be Width*Hight*Depth, W*H*D.

The width is 12, the hight is 12, and the depth is 12 so you can write

A=12*12*12

Multiply 12 by 12

A=144*12

Multiply 12 by 144 to get your final total area

A=1,728

Hope this helps, feel free to ask follow-up questions if confused.

Have a good day! :)

A=1728 if u multiply and u will get it answer

Write the equation in slope intercept form for the line that passes through the point (0,-3) with slope -1/2.

Answers

Answer:

y = -1/2x - 3

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Step 1: Determine known variables

Slope = -1/2 (m = -1/2)

y-intercept - (0, -3), so b = -3

Step 2: Write in known variables

y = -1/2x - 3

Answer:

y = -1/2 - 3

Step-by-step explanation:

Well slope intercept is y = ax + b

ax is the slope which is given,

b is the y intercept which is -3 because the point (0,-3)

doesn’t have a x coordinate meaning if the line goes through that point it touches the y intercept at -3.

Thus,

the equation in slope-intercept is y = -1/2 - 3.

Hope this helps :)

What is the factored form of this expression?
x2 + 15x + 56

Answers

Answer:

To factor this, we need to find two numbers that have a sum of 15 and product of 56; these numbers are 7 and 8. Therefore, the factored form is (x + 7)(x + 8).

Answer:

( x + 8 ) ( x + 7)

Step-by-step explanation:

[tex] {x}^{2} + 15x + 56[/tex]

Write 15x as a sum

[tex] {x}^{2} + 8x + 7x + 56[/tex]

Factor out X from the expression

[tex]x(x + 8) + 7x + 56[/tex]

Factor out 7 from the expression

[tex]x(x + 8) + 7(x + 8)[/tex]

Factor out X+8 from the expression

[tex](x + 8)(x + 7)[/tex]

Hope this helps...

Good luck on your assignment..

Assume a significance level of alpha equals 0.05 and use the given information to complete parts​ (a) and​ (b) below. Original​ claim: More than 47​% of adults would erase all of their personal information online if they could. The hypothesis test results in a​ P-value of 0.0433.

Required:
a. State a conclusion about the null hypothesis.​
b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.

Answers

Answer:

Step-by-step explanation:

a. A conclusion with regards to the null hypothesis is this:

Since the p value observed which is 0.0433 is less than the alpha level of significant 0.05, we can reject the null hypothesis.

b. A final conclusion that addresses the original claim is this:

Since we rejected the null hypothesis, it means it means there was enough statistical evidence to support the claim that more than 47​% of adults would erase all of their personal information online if they could.

Four times a number added to 3 times a larger number is 31. Seven subtracted from the larger number is equal to twice the smaller number. Let x represent the smaller number and y represent the larger number. Which equations represent this situation? y = negative four-thirds x + 31. y = 2 x + 7. y = negative four-thirds x + StartFraction 31 Over 3 EndFraction. Y = 2 x + 7. y = negative four-thirds x + 31. y = negative 2 x + 7. y = negative four-thirds x + StartFraction 31 Over 3 EndFraction. Y = negative 2 x + 7.

Answers

Answer:

y = negative four-thirds x + StartFraction 31 Over 3 EndFraction

y = 2 x + 7

Step-by-step explanation:

Let x represent the smaller number and y represent the larger number.

Part 1

Four times a number added to 3 times a larger number is 31.

It is translated as:

4x + 3y = 31

Then, solving for y:

4x + 3y=31 ⇒ 3y= -4x+31 ⇒ y= (-4x+31)/3 = - 4/3x + 31/3

    ⇒  y= - 4/3x + 31/3

Correct answer choice for this equation:

y = negative four-thirds x + StartFraction 31 Over 3 EndFraction

Part 2

Seven subtracted from the larger number is equal to twice the smaller number.

It is translated as:

y-7= 2x

Then, solving for y:

y-7= 2x ⇒ y= 2x+ 7

Correct answer choice for this equation:

y = 2 x + 7

Answer:

It's A.

Step-by-step explanation:

I just got it correct on my unit test review.

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