All categories

3 years ago

Analyze the solution set of the following system by

Mathematics

1 answer:

blsea [12.9K]3 years ago

7 0

Answer:

The equations in the slope-intercept form

y = - 2 x + 5

y = - 2 x + 3

Step-by-step explanation:

The slope-intercept form of the linear equation is y = m x + b, where

m is the slope of the line.

b is the y-intercept.

To put any equation in the slope-intercept form state y on the left side, x and the numerical term on the right side, the coefficient of y must be 1.

Let us do that with the given equations

∵ 2x + y = 5

→ Subtract 2x from both sides to move x to the right sides

∴ 2x - 2x + y = 5 - 2x

∴ y = 5 - 2x

→ Switch 5 and - 2x

∴ y = - 2x + 5

∵ 3y = 9 - 6x

→ Divide each term by 3 to make the coefficient of y = 1

∴ $\frac{3y}{3}=\frac{9}{3}-\frac{6x}{3}$

∴ y = 3 - 2x

→ Switch 3 and - 2x

∴ y = - 2x + 3

The equations in the slope-intercept form

y = - 2x + 5

y = - 2x + 3

You might be interested in

1/4 + 23/28 - 1 <br><br> please help

AnnZ [28]

Answer:

$\frac{1}{14}$

Step-by-step explanation:

$\frac{1}{4} + \frac{23}{28} - 1 = ?$

First off, let's change everything to a common denominator. This will allow us to add the fractions!

To find a common denominator, we find a number that both 4, 28, and 1 can go into. 28 is the best choice, as 4 goes into it 7 times, 28 goes into it once, and 1 goes into it 28 times.

Let's change the first fraction into a number with a denominator of 28!

$\frac{1}{4} * \frac{7}{7} = \frac{7}{28}$

$\frac{7}{7}$ = 1. Multiplying a number by one doesn't change its value.

The second fraction, $\frac{23}{28}$ , already has a denominator of 28, so we don't have to do anything with it.

Now to the third number, -1:

$-1 = -\frac{1}{1} * \frac{28}{28} = -\frac{28}{28}$

Now, let's add them all up!

$\frac{7}{28} + \frac{23}{28} - \frac{28}{28} = \frac{7 + 23 - 28}{28} = \frac{2}{28}$

One last step, to simplify:

$\frac{2}{28} = \frac{1}{14}$

<h2>Your answer is 1/14!</h2>

8 0

3 years ago

HELP ASAP!!! Giving brainliest to whoever answers first!!!

Lady_Fox [76]

Answer:

basically do 23+35+27+48+18+35= 186 then divide it by how many there are (6) = 31 so the answer is 31

7 0

3 years ago

Read 2 more answers

Hey! i’ll give brainliest pls help.

babunello [35]

I believe the answer is A. because the theory of continental drift and sea-floor spreading causes new rock to form and creates the old rock .. older

6 0

3 years ago

Read 2 more answers

If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Consider the cost func

olga2289 [7]

Answer:

a. C(1,000) = 420,491.11

b. c(1,000) = 420.49

c. dC/dx(1,000) = 429.72

d. x = 900

e. c(900) = 420

Step-by-step explanation:

We have a cost function for x units written as:

$C(x) = 54,000 + 240x + 4x^{3/2}$

a. The total cost for x=1000 units is:

$C(1,000) = 54,000 + 240(1,000) + 4(1,000)^{3/2}\\\\C(1,000)=54,000+240,000+4\cdot 31,622.78\\\\C(1,000)=54,000+240,000+ 126,491.11 \\\\C(1,000)= 420,491.11$

b. The average cost c(x) can be calculated dividing the total cost by the amount of units:

$c(1,000)=\dfrac{C(1,000)}{1,000}=\dfrac{ 420,491.11 }{1,000}= 420.49$

c. The marginal cost can be calculated as the first derivative of the cost function:

$\dfrac{dC}{dx}=240(1)+4(3/2)x^{3/2-1}=240+6x^{1/2}\\\\\\\dfrac{dC}{dx}(1,000)=240+6(1,000)^{1/2}=240+6\cdot 31.62=429.72$

d. This value for x, that minimizes the average cost, happens when the first derivative of the average cost is equal to 0.

$c(x)=\dfrac{C(x)}{x}=\dfrac{54,000+240x+4x^{3/2}}{x}=54,000x^{-1}+240+4x^{1/2}\\\\\\ \dfrac{dc}{dx}=54,000(-1)x^{-2}+0+4(1/2)x^{-1/2}=0\\\\\\\dfrac{dc}{dx}=-54,000x^{-2}+2x^{-1/2}=0\\\\\\2x^{-1/2}=54,000x^{-2}\\\\\\x^{-1/2+2}=54,000/2=27,000\\\\\\x^{3/2}=27,000\\\\\\x=27,000^{2/3}=900$

e. The minimum average cost is:

$c(900)=54,000(900)^{-1}+240+4(900)^{1/2}\\\\c(900)=60+240+120\\\\c(900)=420$

7 0

3 years ago

3. Given ABCD ≅ FGHJ and mC = 9x - 7, mH = 5x + 13, find the value of x and the measures of angle C and angle H. Show all work

kondor19780726 [428]

Answers:

x = 5

m∠C = m∠H = 38 degrees

WORKINGS

Given that ABCD ≅ FGHJ

We know that corresponding angles of two congruent quadrilaterals are equal

Therefore,

m∠A = m∠F

m∠B = m∠G

m∠C = m∠H

m∠D = m∠I

Given,

m∠C = 9x – 7

m∠H = 5x + 13

Since m∠C = m∠H

9x – 7 = 5x + 13

Add 7 to both sides of the equation

9x – 7 + 7 = 5x + 13 + 7

9x = 5x + 20

Subtract 5x from both sides of the equation

9x – 5x = 5x – 5x + 20

4x = 20

Divide both sides of the equation by 4

4x/4 = 20/4

x = 5

To determine the measures of angle C and angle H

m∠C = m∠H

We know that m∠C = 9x – 7

Since x = 5

m∠C = 9(5) – 7

m∠C = 45 – 7

m∠C = 38

Therefore, m∠C = m∠H = 38 degrees

4 0

3 years ago