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3 years ago

Solve y=3x-7 and 4x+3y=18 by substitution

Mathematics

2 answers:

Schach [20]3 years ago

5 0

Answer:

x = 3

y = 2

Step-by-step explanation:

4x + 3(3x - 7) = 18 Substitute y

4x + 9x - 21 = 18 Simply

13x - 21 = 18 Add like terms

13x = 39 Add 21

x = 3 Divide by 13

y = 3(3) - 7 Substitute x

y = 9 - 7 Simply

y = 2 Subtract

Let's check:

4(3) + 3(2) = 18

12 + 6 = 18

18 = 18

It works!

Monica [59]3 years ago

5 0

Answer:

$\huge\boxed{x=3,\ y=2\to(3,\ 2)}$

Step-by-step explanation:

$\left\{\begin{array}{ccc}y=3x-7&(1)\\4x+3y=18&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\4x+3(3x-7)=18\qquad\text{use the distributive property}\\\\4x+(3)(3x)+(3)(-7)=18\\\\4x+9x-21=18\qquad\text{add 21 to both sides}\\\\4x+9x-21+21=18+21\qquad\text{cobine like terms}\\\\13x=39\qquad\text{divide both sides by 13}\\\\\dfrac{13x}{13}=\dfrac{39}{13}\\\\\boxed{x=3}\\\\\text{Substitute it to (1):}\\\\y=3(3)-7\\\\y=9-7\\\\\boxed{y=2}$

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Jennifer has carpet in her square bedroom. She decides to also purchase carpet for her living room which is rectangular in shape

shtirl [24]

Answer/Step-by-step explanation:

Let's highlight the dimensions of the bedroom and living room using the information given in the question:

==>Squared Bedroom dimensions:

Side length = w = x ft

Area = x*x = x²

==>Rectangular living room dimensions:

width = side length of the squared bedroom = x

length = (x + 9) ft

Area = L*W = x*(x+9) = x² + 9x

Now let's match each given expression with what they represent:

==>"the monomial, x, a factor of the expression x² + 9x" represents "the width of the carpet in the living room"

As we have shown in the dimensions of the squared bedroom above.

==>"the binomial, (x + 9), a factor of the expression x² + 9x" represents "the length of the carpet in the living room" as shown above in the dimensions for living room

==>"the second-degree term of the expression x² + 9x" represents "the area of the carpet in the bedroom"

i.e. the 2nd-degree term in the expression is x², which represents the area of the carpet of the given bedroom.

==>"the first-degree term of the expression x2 + 9x" represents "the increase in the area of carpet needed for the living room".

i.e. 1st-degree term in the expression is 9x. And it represents the increase in the area of the carpet for the living room. Area of bedroom is x². Area of carpet needed for living room increased by 9x. Thus, area of carpet needed for living room = x² + 9x

7 0

3 years ago

If g(x) = 2x2 + 6x + 5, use synthetic division to find g(-5).

diamong [38]

<h3>Answer: 25</h3>

=================================================

Explanation:

Check out the image below. I've posted the synthetic division table. The value at the very end of the bottom row is the remainder. By the remainder theorem, this is exactly the value of g(-5).

Recall the remainder theorem says: If you divide p(x) by (x-k), then the remainder is p(k). In this case, k = -5 is our test root which is the value placed in the box on the left.

As a way to check the answer, we can say

g(x) = 2x^2 + 6x + 5

g(-5) = 2(-5)^2 + 6(-5) + 5

g(-5) = 25

So the answer is confirmed.

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3 years ago

Heart 1 is translated 3 units down to heart 2. Which shows this transformation?

Marina CMI [18]

Answer:

It is the 4th image

Step-by-step explanation:

I took the test

7 0

3 years ago

Read 2 more answers

What is the rational number equivalent to 3.24

aev [14]

Answer:

The rational number equivalent to 3.24 repeating is 321/99

Step-by-step explanation:

To convert the decimal number to a rational number we can state this number and its multiples of 10, trying to find two number with identical decimal parts:

n=3.24242424...

10n=32.4242424....

100n=324.2424242...

Now, 100n and n have the same decimal part, then by subtracting these numbers we obtain:

100n-n=324.24242424...-3.24242424... = 321

99n = 321

n = 321/99

8 0

3 years ago

2. Suppose over several years of offering AP Statistics, a high school finds that final exam scores are normally distributed wit

nirvana33 [79]

Answer:

By the Central Limit Theorem, the mean is 78, the standard deviation is $s = \frac{6}{\sqrt{n}}$ and the shape is approximately normal.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .