A line contains the points R (-5, -6) S (1, 5) and T (x, 10). Solve for x. Be sure to show and explain all work. ( How did this person get this answer?

Answer:

1. f(x) = 3x + 7

2. [tex]f(x) = -\dfrac12x + 2[/tex]

3. f(x) = x + 5

4. f(x) = -2x - 5

5. [tex]f(x) = -\dfrac32 x + 2[/tex]

Step-by-step explanation:

Rearrange all the equations to make y the subject,
then substitute f(x) for y:

1.   y - 3x = 7

Add 3x to both sides:

⇒ y = 3x + 7

⇒ f(x) = 3x + 7

2.   2x + 4y = 8

Subtract 2x from both sides:

⇒ 4y = -2x + 8

Divide both sides by 4:

⇒ [tex]y = -\dfrac12x + 2[/tex]

⇒ [tex]f(x) = -\dfrac12x + 2[/tex]

3.   -x + y = 5

Add x to both sides:

⇒ y = x + 5

⇒ f(x) = x + 5

4. y + 5 = -2x

Subtract 5 from both sides:

⇒ y = -2x - 5

⇒ f(x) = -2x - 5

5.   3x + 2y - 4 = 0

Subtract 3x from both sides:

⇒ 2y - 4 = -3x

Add 4 to both sides:

⇒ 2y = -3x + 4

Divide both sides by 2;

⇒ [tex]y = -\dfrac32 x + 2[/tex]

⇒ [tex]f(x) = -\dfrac32 x + 2[/tex]

Answer:

im pretty sure its distributive property

Step-by-step explanation:

Answer:

I believe it is 5 < √32 < 6.

Step-by-step explanation:

√25 = 5 and √36 = 6 so therefore, the answer is 5 < √32 <  6. I hope I helped! ^-^

Answer:

2(5x-12) = -3(2x-8)

10x-24 = -6x+24

10x+6x = 48

16x= 48

x= 3

Answer:

6

Step-by-step explanation:

STATISTICS" is the 10 letters word in which "S" appears 3 times, "T" appears 3 times, "A" appears 1 time, "I" appears 2 times and "C" appears 1 times. To arrange this word letter "T" must be first letter so there is only one way to choose first place. Since vowel can not be the last letter there are 6 choices...

Answer:

  1/4 cup

Step-by-step explanation:

To make half a recipe, each of the quantities in the recipe must be multiplied by 1/2. Alvin will need ...

  (1/2) × (1/2 cup) = 1/4 cup

of bread crumbs.

Answer:

(a) dp/dx = 90/(x+2)

(b) $2.25

(c) approx = $2.25

    exact = $2.22

Step-by-step explanation:

[tex]p = 20 + 90 \ln(2x + 4)[/tex]

(a) To find the rate of change, differentiate [tex]p[/tex] with respect to [tex]x[/tex] :

[tex]\implies \frac{d}{dx}(p) = \frac{d}{dx}(20) + \frac{d}{dx}(90 \ln(2x + 4))[/tex]

[tex]\implies \frac{dp}{dx}=0+90\times\dfrac{1}{2x+4}\times2[/tex]

[tex]\implies \frac{dp}{dx}=\dfrac{180}{2x+4}[/tex]

[tex]\implies \frac{dp}{dx}=\dfrac{90}{x+2}[/tex]

(b)  Find  [tex]\frac{dp}{dx}[/tex]  when [tex]x=38[/tex] :

[tex]\implies \frac{dp}{dx}=\dfrac{90}{38+2}[/tex]

[tex]\implies \frac{dp}{dx}=\dfrac{90}{40}[/tex]

[tex]\implies \frac{dp}{dx}=2.25[/tex]

(c)  Approximate price increase associated with the number of units supplied changing from 38 to 39 is  [tex]\frac{dp}{dx}[/tex]  when [tex]x=38[/tex]

[tex]\implies \$2.25[/tex]

Exact price increase:

[tex]\implies \left. p \right_{x=39}-\left. p \right_{x=38}\\\\\implies [20 + 90 \ln(2 \times 39 + 4)]-[20 + 90 \ln(2\times38 + 4)]\\\\\implies 416.6047323...-414.3823972...\\\\\implies 2.222335133...\\\\\implies \$2.22[/tex]

Answer:

b = -3/4

Step-by-step explanation:

b/4 = -3

b = -3/4

[tex]\frac{b}{4}+2 = -1[/tex]

[tex]\frac{b}{4}=-1 -2\\ \frac{b}{4}=-3\\ b=-12[/tex]

b= -12 so that hope that helps!

Based on the sequence of numbers, the next two numbers in the sequence will be:

The numbers on the right side of the equation are meant to show to number of circles on all the numbers on the left side.

For instance:

The number six is drawn such that it has a single circle in it = 6

The number of sixes in the first number are 3 so there will be 3 circles.

The number of circles in 8688 will be 7 because each "8" has 2 circles.

The number of circles in 5971 will be 1 because 9 is the only number drawn with a circle.

Find out more on predicting number sequences at https://brainly.com/question/89459.

#SPJ9

Answer: What is this troll question

Its -21

Step-by-step explanation:

-21+-21=42

Answer:

highest umber is correct answer

Answer:

The answer is 10.25

Step-by-step explanation:

They want the approximate average ring size between the men, the lowest being 9 and the highest 12.

The average between those two numbers would be 10.5

But the said 'the best approximation'

So it's 10.25

Answer:

a.the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe people's habits as they sneeze.

b.the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe people's habits as they sneeze.

c.the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe people's habits as they sneeze.

Step-by-step explanation: Because of science their is a chance but the matter of individual dose not matter nor count unless there are a same matter

Answer:

The answer is in Step-by-step explanation

Step-by-step explanation:

x,y,z (-3, 3/2, 2

Hope this helps!!

Answer:

Step-by-step explanation:

One side is 9 more than the other regardless of the value of of x

This is because:

4(x+3)=3(x+1)+x

4x+12=3x+3+x

4x+12=4x+3 So the right hand side is 9 less than the left.

Since they are not equal the answer to part be is 0.

There are 0 solutions to this equation. If there were 1 or 2 solutions then the question would ask for those solutions.  

Answer:

Yes. It is accurate for the data shown

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

Since the residuals for each point are large when compared to the line, the line of best fit isn't accurate. A higher-degree function will most likely work here.

Answer:37 1/3

Step-by-step explanation:

if you multiply 56 (2/3)=37 1/3

Answer:

40

Step-by-step explanation:

[tex]\frac{2}{3}[/tex]×[tex]60 = 2[/tex]×[tex]20[/tex]

40 = 40

Answer:

c)

6.1 x 5 = 30.5

6.1 + 12.9 = 19

19/2 = 9.5

9.5 x 10= 95

95 + 30.5 = 125.5 cm squared

d) 4.1 x 4.7 = 19.27

2.05 squared x pi = 13.5

13.5 /2 = 6.6

19.27 + 6.6 = 25.87 cm squared

e) 16 x 22 = 352

352/2= 176

pi x 11 squared = 95.03

95.03+176 = 271.03 cm squared

f) 8 x 8 =64

pi x 4 squared= 50.27

50.27 x 3 = 150.81

150.81 + 64 = 214.81cm squared

Answer: B

Step-by-step explanation: Rearrange the equation to get it in intercept form, or solve y = 0 for x-intercept ... 2. a = 5, b = 2, c = 1, d = 2, e = 2, f = −3, g = 1, h = −1, i = 3.

Answer:

Step-by-step explanation:

[tex]\frac{14}{7} =\frac{n}{21}[/tex]

Let us divide by 14 by 7 which is 2, so the equation is:

[tex]2 = \frac{n}{21}[/tex]

Let us multiple 21 over the other side since 21 is in the denominator of the equation, so we get

[tex]n = 21*2 = 42[/tex]

So the answer is 42.

Answer:

H = 19 cm

B = 17 cm

Step-by-step explanation:

A = (H x B) / 2 (formula for the area of a triangle)

161.5 = ((X + 2)(X)) / 2 (with X acting as the base)

323 = X^2 + 2X

0 = x^2 + 2x - 323

(X - 17) (X + 19) = 0

X = 17 or X = -19

You can't have a negative number as a side length so -19 doesn't work.

Because the height is larger than the base, you add the 2 to the one you will use as the height. Then just add the units (cm) because the area is in cm squared.

Answer:

10 cups of flour

Step-by-step explanation:

Ratios tell you how much of one thing there are compared to another.

It is stated that the ratio of water to flour is 1:4.

This means for every 1 cup of water, there are 4 cups of flour.

If there are 2.5 cups of water, we do 2.5 x 4 = 10 cups of flour.

Answer:

[tex]x=10[/tex]

Step-by-step explanation:

[tex]1\div4=2.5\divx[/tex] ÷ [tex]x[/tex]

a. Find the domain

[tex]\frac{1}{4}=\frac{2.5}{x}[/tex]

If the fraction is defined, the denominator cannot equal 0.

[tex]x\neq 0[/tex]

Append the inequality as the domain

[tex]x\neq 0[/tex]

b. Solve the equation

[tex]\frac{1}{4}=\frac{2.5}{x}[/tex]

Cross multiply

[tex]x=2.5\times4[/tex]

Calculate the product or quotient

[tex]x=10[/tex]

c. Find the intersection

[tex]x=10[/tex]

I hope this helps you

:)

Answer:

1 / 3 (one third)

Step-by-step explanation:

Divide the number of chickens by the number of people:

1 / 3