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2 years ago

What are the slope and y-intercept of the line described by the equation y= 4x - 7?

Mathematics

1 answer:

Verdich [7]2 years ago

8 0

Answer:

A. Slope: 4; y-intercept: (0-7)

Step-by-step explanation:

The equation given is in slope-intercept form, y =mx+b, where m is the slope and b is the y-intercept.

Our equation is y=4x -7,

Where m = 4 b = -7

If m = to the slope and b = to the y-intercept, our slope would be 4/1 or 4, and our y-intercept would be (0,-7).

The answer, A would be the best for the question.

Hope it helps!

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Which of the following points are solutions to the system of inequalities shown below?

Ira Lisetskai [31]

Y > 6x + 5
y < -6x + 7
(2,17)
17 > 6(2)+5 ; 17> 17 NO
(8,8)
8>6(8)+5 NO
(-2,18)
18>6(-2)+5
18>-7 YES
18< -6(-2)+7
18< 12+7 YES (-2,18) is an answer
(0,6)
6>6(0)+5
6>5 YES
6<-6(0)+7
6<7 YES (0,6) is an answer
(-2,19)
19>6(-2)+5
19>-7 NO
(2,18)
18>6(2)+5
18>17 YES
18< -6(2)+7
18< -5 NO

3 0

3 years ago

Question regarding logarithms.

Eddi Din [679]

$5^{x-2}-7^{x-3}=7^{x-5}+11\cdot5^{x-4}\\\\5^{x-2}-7^{x-2-1}=7^{x-2-3}+11\cdot5^{x-2-2}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\5^{x-2}-\dfrac{7^{x-2}}{7^1}=\dfrac{7^{x-2}}{7^3}+11\cdot\dfrac{5^{x-2}}{5^2}\\\\5^{x-2}-\dfrac{1}{7}\cdot7^{x-2}=\dfrac{1}{343}\cdot7^{x-2}+\dfrac{11}{25}\cdot5^{x-2}\\\\-\dfrac{1}{7}\cdot7^{x-2}-\dfrac{1}{343}\cdot7^{x-2}=\dfrac{11}{25}\cdot5^{x-2}-5^{x-2}\\\\\left(-\dfrac{1}{7}-\dfrac{1}{343}\right)\cdot7^{x-2}=\left(\dfrac{11}{25}-1\right)\cdot5^{x-2}$

$\left(-\dfrac{49}{343}-\dfrac{1}{343}\right)\cdot7^{x-2}=-\dfrac{14}{25}\cdot5^{x-2}\\\\-\dfrac{50}{343}\cdot7^{x-2}=-\dfrac{14}{25}\cdot5^{x-2}\qquad\text{multiply both sides by}\ \left(-\dfrac{25}{14}\right)\\\\\dfrac{50\cdot25}{343\cdot14}\cdot7^{x-2}=5^{x-2}\qquad\text{divide both sides by}\ 7^{x-2}\\\\\dfrac{25\cdot25}{343\cdot7}=\dfrac{5^{x-2}}{7^{x-2}}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}$

$\dfrac{5^2\cdot5^2}{7^3\cdot7}=\left(\dfrac{5}{7}\right)^{x-2}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\\dfrac{5^4}{7^4}=\left(\dfrac{5}{7}\right)^{x-2}\\\\\left(\dfrac{5}{7}\right)^4=\left(\dfrac{5}{7}\right)^{x-2}\iff x-2=4\qquad\text{add 2 to both sides}\\\\\boxed{x=6}$

6 0

3 years ago

Read 2 more answers

To the nearest whole number, what is the surface area or the right triangular prism

Andrej [43]

Answer:

502 Square Meters

Step-by-step explanation:

Surface Area is the sum of the areas of all the surfaces. There are 5 surfaces in total, so we find each surface area and find total Surface Area.

Shown Below:

Bottom Surface is a rectangle, so area is length * width = 10 * 16 = 160

Back Surface is a rectangle, so area is 6 * 16 = 96

Top (front) surface is a rectangle so area is 11.6 * 16 = 185.6

Left and right sides are 2 triangles, so are would be 0.5(base * height) for each. So,

Left triangle = 0.5 * 10 * 6 = 30

Right triangle = 30

Sum of all the surfaces = 160 + 96 + 185.6 + 30 + 30 = 501.6

Rounded to nearest whole number, that is 502

The surface area = 502 m^2

6 0

3 years ago

Your cousin has a goat in his backyard, tied with a 4 foot rope. The goat can move in a circular motion the length of the rope.

rosijanka [135]

The stake the rope is tied to is the center of the circle. If the goat pulls the rope as far as it can go and walks around like this he makes a circle and he can eat the grass anywhere within this circle.

(a) Since the area of a circle is given by $A= \pi r^{2}$ this is the formula we can use to find the area of the yard where the goat can roam/eat/reach.

(b) Since the rope is 4 feet the radius r = 4 and the area is given by $4^{2} \pi =16 \pi ^{2}$ square feet. That's the exact area. For an approximation you could substitute 3.14 for pi and get 50.24 square feet.

(c)Since the rope is 5 feet the radius r = 4 and the area is given by $5^{2} \pi =25 \pi ^{2}$ square feet. That's the exact area. For an approximation you could substitute 3.14 for pi and get 78.5 square feet.

6 0

3 years ago

Multiply or divide as indicated. X^5 ____ X^-3

Sophie [7]

x^5
____ = x^8
x^-3

[x^5 - (-3) = x^8

i hope this helps

3 0

2 years ago