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3 years ago

Which graph represents the linear function below? y-4= (4/3)(x-2)

Mathematics

1 answer:

svp [43]3 years ago

8 0

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

$y-4=(4/3)(x-2)$

This is the equation of a line into point slope form

The point is (2.4)

The slope is m=4/3

To plot the line find the intercepts

The y-intercept is the value of y when the value of x is equal to zero

For x=0

y-4=(4/3)(0-2)

y=(-8/3)+4

y=4/3

The x-intercept is the value of x when the value of y is equal to zero

0-4=(4/3)(x-2)

-4=(4/3)x-(8/3)

Multiply by 3 both sides

-12=4x-8

4x=8-12

x=-1

we have the points

(2,4), (0,4/3),(-1,0)

Plot the line

Note With only two points it was necessary to draw the line. The third point was calculated for didactic purposes.

see the attached figure

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valkas [14]

Answer: $\boxed{y=\frac{4}{5}x-2}$

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals, so as the slope of the given line is -5/4, the slope of the perpendicular line is 4/5.

Substituting into point-slope form,

$y-6=\frac{4}{5}(x-10)\\\\y-6=\frac{4}{5}x-8\\\\\boxed{y=\frac{4}{5}x-2}$

4 0

2 years ago

F(x) = -7x2 + 9x - 15 and g(x) = -12x2 – 15x + 7

djyliett [7]

Answer:

${5x}^{2} + 6x = - 8$

Step-by-step explanation:

This question is asking you to insert two equations, f(x) and g(x), into the equation g(x) - f(x). This will lead to the equation below.

${ - 12x}^{2} - 15x + 7 - ({ - 7)x}^{2} + 9x - 15$

Now we can solve for the equation.

${ - 5x}^{2} - 6x - 8 = 0 \\ {5x}^{2} + 6x = - 8$

3 0

2 years ago

Perimeter of a mirror is 260. The length is x cm. Find the height of the mirror in terms of x

Elenna [48]

$\bf \textit{perimeter of a rectangle}\\\\ P=2(L+h)~~ \begin{cases} L=length\\ h=height\\[-0.5em] \hrulefill\\ P=260\\ L=x \end{cases}\implies 260=2(x+h) \\\\\\ \cfrac{260}{2}=x+h\implies 130=x+h\implies 130-x=h$

4 0

3 years ago

Ali and Heather drew floor models of their living room Ellie model represented 20 feet by 15feet Heather model represented 18fee

alina1380 [7]

Ellie: 20*15=300
Heather: 18*18= 324
Heather's floor model is greater by 24 feet

4 0

3 years ago

Can you see an easy way to work out the value of <img src="https://tex.z-dn.net/?f=%5Csqrt%7B%201%5E3%20%2B%202%5E3%20%2B%203%5E

Lina20 [59]

We have the sum of cubes identity

$a^3 + b^3 = (a + b) (a^2 - ab + b^2)$

and observing that 1 + 4 = 2 + 3, we have

$1^3 + 4^3 = (1 + 4) (1^2 - 4 + 4^2) = 5 \times 13$

and

$2^3 + 3^3 = (2 + 3) (2^2 - 6 + 3^2) = 5 \times 7$

Then

$\sqrt{1^3+2^3+3^3+4^3+5^3} = \sqrt{5\times13 + 5\times7 + 5\times5^2} = \sqrt{5 \times (20 + 25)} \\\\ ~~~~~~~~ = \sqrt{5^2 \times (4 + 5)} = \sqrt{5^2\times9} = \sqrt{5^2\times3^2} = 5\times3 = \boxed{15}$

Alternatively, we have the well-known sum of cubes formula

$\displaystyle \sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}4$

The sum under the square root is this sum with $n=5$ . Then

$1^3+2^3+3^3+4^3+5^3 = \dfrac{5^2\times6^2}4 = 225 = 15^2$

and so the square root again reduces to 15.

5 0

2 years ago