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3 years ago

Consider the graph shown.

Mathematics

1 answer:

Butoxors [25]3 years ago

4 0

Answer:

$Slope=\frac{3}{4}$

The equation of line is $y=\frac{3}{4}x+1$ .

Step-by-step explanation:

If a line passes through two points $(x_1,y_1)$ and $(x_2,y_2)$ , then the slope of the line is

$m=\frac{y_2-y_1}{x_2-x_1}$

From the given graph it is clear that the line is passes through the points (0,1) and (4,4).

$Slope=\frac{4-1}{4-0}$

$Slope=\frac{3}{4}$

The

The slope intercept form of a line is

$y=mx+b$

where, m is slope and b is y-intercept

The slope of the line is $\frac{3}{4}$ and y-intercept is 1, so the equation of line is

$y=\frac{3}{4}x+1$

Therefore, the equation of line is $y=\frac{3}{4}x+1$ .

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The perimeter of a rectangle is 42 feet. The length decreased by three times the width is 1 foot. What are the dimensions of the

madreJ [45]

First you want to make an equation to express the problem. For this one in particular, let's make the length be represented by "L" and the width "W."

The length minus three times the width is 1 foot. This can be represented as L - 3W = 1. This means that L = 3W + 1. This will be our substitute for the length.

The perimeter of a rectangle is 2 times the length plus the width P = 2(L + W). By substituting these variables from what we now know we can find out the dimensions of the rectangle.

42 = 2(3W + 1 + W)
42 = 6W + 2 + 2W Multiply everything in parenthesis by 2.
42 = 8W + 2 Add the like terms.
40 = 8W Subtract 2 on both sides to get the variable (W) by itself.
5 = W Divide 8 from 40 to get what W equals.

The width is equal to 5. We can now plug in this answer to the original equation (P = 2(L + W)) or the length equation we made earlier (L = 3W + 1) to find the length.

42 = 2(L + 5)
42 = 2L + 10 Multiply everything in parenthesis by 2.
32 = 2L Subtract 10 from both sides to get the variable (L) by itself.
16 = L Divide 2 from 32 to get what L equals.
Or
L = 3(5) + 1 Replace the variable (W) with 5.
L = 15 + 1 Multiply 3 by 5 to get 15.
L = 16 Add the remaining terms!

So the dimensions of the rectangle are 5 and 16, where 5 is the width and 16 is the length. I hope this answer made sense and that you can solve these on your own in the future!

4 0

4 years ago

Using the expansion for the binomial: ( x^3 − y^4 )^9 :The coefficient for the 6th term is

Lelechka [254]

Answer:

-126

Step-by-step explanation:

For the binomial expression $(a-b)^{n}$ the coefficient of $(r+1)^{th}$ term is given by ${n \choose r} \times -1^{(r)}$ .

We have to find the coefficient of 6th term in the binomial expansion of

$(x^{3}-y^{4})^{9}$ .

Hence n=9 and r=5

The coefficient of 6th term = ${9 \choose 5} \times (-1)^{5}$

= $-{9 \choose 5}$

= -126

8 0

3 years ago

35. Cindy walks at a constant rate of 2 miles per hour. She leaves home to walk to her friend Jenny's house at 9 am. When she is

GarryVolchara [31]

Answer:

you're screwed

Step-by-step explanation:

don't forget your phone so anyon doesn't ever have to do this

8 0

3 years ago

Ashley is a member of the Movie-a-Month Club, where she rents movies each monthShe uses the table below to keep track of the num

vovikov84 [41]

Answer:

The slope is m=2.5 $/movie

Step-by-step explanation:

The slope of the graph could be found using any two points $(x_{1} ,y_{1} )$ y $(x_{2} ,y_{2} )$ and the equation for slope of a line, which is

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

So, we select the points $(12,35)$ y $(22,60)$ , and we replace the values in the equation for slope,

$m=\frac{60-35}{22-12}=2.5$

And in this case, represents the cost to rent one movie.

8 0

3 years ago

Read 2 more answers

What is 143/15 simplified

V125BC [204]

$\sf \frac{143}{15}=?$

$\sf{ 15 \times 9 = 135}$

$\sf{143- 135 = 8}$

$\sf{ \frac{143}{15} = \frac{135+8}{15} = \frac{135}{135} + \frac{8}{15}$

$\sf{ \frac{143}{15} =\boxed{\huge{ 9 \frac{8}{15} }}}$

8 0

3 years ago

Read 2 more answers