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3 years ago

Which expression is equivalent to 3(x + 4y)?

Mathematics

1 answer:

RUDIKE [14]3 years ago

4 0

Just distribute the 3. 3(x + 4y) = 3x + 12y

3x + 12y is the answer.

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Can anyone help me solve 23, 24?

zimovet [89]

Answer:

Problem 23) $y=3x+6$

Problem 24) $y=-\frac{1}{3}x-5$

Step-by-step explanation:

step 1

Find the slope of the given line

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$A(0,2)\ B(3,1)$

Substitute the values

$m=\frac{1-2}{3-0}$

$m=-\frac{1}{3}$

step 2

Problem 23

we know that

If two lines are perpendicular then the product of its slopes is equal to minus 1

$m1*m2=-1$

Find the slope of the line

we have

$m1=-\frac{1}{3}$

substitute in the equation and solve for m2

$(-\frac{1}{3})*m2=-1$

$m2=3$

with the slope m2 and the point $(0,6)$ find the equation of the line

Remember that

The equation of the line in slope intercept form is equal to

$y=mx+b$

we have

$m=3$

$b=6$ -----> the given point is the y-intercept

substitute

$y=3x+6$

step 3

Problem 24

we know that

If two lines are parallel, then its slopes are the same

with the slope m1 and the point $(0,-5)$ find the equation of the line

The equation of the line in slope intercept form is equal to

$y=mx+b$

we have

$m=-\frac{1}{3}$

$b=-5$ -----> the given point is the y-intercept

substitute

$y=-\frac{1}{3}x-5$

8 0

3 years ago

What’s the answers for this?

marshall27 [118]

I cant see it is too blurrry

6 0

3 years ago

Evaluate the difference quotient for the given function. Simplify your answer.

nasty-shy [4]

I suppose you mean

$f(x) = \dfrac{x+5}{x+1}$

Then

$f(3) = \dfrac{3+5}{3+1} = \dfrac84 = 2$

and the difference quotient is

$\dfrac{f(x)-f(3)}{x-3} = \dfrac{\frac{x+5}{x+1}-2}{x-3} \\\\ \dfrac{f(x)-f(3)}{x-3} = \dfrac{\frac{x+5-2(x+1)}{x+1}}{x-3} \\\\ \dfrac{f(x)-f(3)}{x-3} = \dfrac{-x+3}{(x+1)(x-3)} \\\\ \dfrac{f(x)-f(3)}{x-3} = \boxed{-\dfrac{x-3}{(x+1)(x-3)}}$

If it's the case that <em>x</em> ≠ 3, then (<em>x</em> - 3)/(<em>x</em> - 3) reduces to 1, and you would be left with

$\dfrac{f(x)-f(3)}{x-3}\bigg|_{x\neq3} = -\dfrac1{x+1}$

4 0

3 years ago

Mrs.Johnsons new car has an 18 gallon gas tank. If she can travel 400 miles on one tank of gasoline, what is her miles per gallo

serious [3.7K]

Answer:

Step-by-step explanation:

400/18=22.222222222

Round to 22

5 0

3 years ago

Describe the pair of angles shown in the figure.

Gelneren [198K]

Answer:

<h3>Adjacent angles or Supplementary angles I am not sure tho:)</h3>

Step-by-step explanation:

4 0

3 years ago