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2 years ago

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Mathematics

1 answer:

dedylja [7]2 years ago

4 0

Answer:

cool

Step-by-step explanation:

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What is the range of the function graphed below?

Nadya [2.5K]

Answer:

Step-by-step explanation:

Range is the 'y' values a graph can have

you can see that the 'y' values can be anythig from - inf to + 2

3 0

1 year ago

The area of the triangle formed by x− and y− intercepts of the parabola y=0.5(x−3)(x+k) is equal to 1.5 square units. Find all p

Juliette [100K]

Check the picture below.

based on the equation, if we set y = 0, we'd end up with 0 = 0.5(x-3)(x-k).

and that will give us two x-intercepts, at x = 3 and x = k.

since the triangle is made by the x-intercepts and y-intercepts, then the parabola most likely has another x-intercept on the negative side of the x-axis, as you see in the picture, so chances are "k" is a negative value.

now, notice the picture, those intercepts make a triangle with a base = 3 + k, and height = y, where "y" is on the negative side.

let's find the y-intercept by setting x = 0 now,

$\bf y=0.5(x-3)(x+k)\implies y=\cfrac{1}{2}(x-3)(x+k)\implies \stackrel{\textit{setting x = 0}}{y=\cfrac{1}{2}(0-3)(0+k)} \\\\\\ y=\cfrac{1}{2}(-3)(k)\implies \boxed{y=-\cfrac{3k}{2}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of a triangle}}{A=\cfrac{1}{2}bh}~~ \begin{cases} b=3+k\\ h=y\\ \quad -\frac{3k}{2}\\ A=1.5\\ \qquad \frac{3}{2} \end{cases}\implies \cfrac{3}{2}=\cfrac{1}{2}(3+k)\left(-\cfrac{3k}{2} \right)$

$\bf \cfrac{3}{2}=\cfrac{3+k}{2}\left( -\cfrac{3k}{2} \right)\implies \stackrel{\textit{multiplying by }\stackrel{LCD}{2}}{3=\cfrac{(3+k)(-3k)}{2}}\implies 6=-9k-3k^2 \\\\\\ 6=-3(3k+k^2)\implies \cfrac{6}{-3}=3k+k^2\implies -2=3k+k^2 \\\\\\ 0=k^2+3k+2\implies 0=(k+2)(k+1)\implies k= \begin{cases} -2\\ -1 \end{cases}$

now, we can plug those values on A = (1/2)bh,

$\bf \stackrel{\textit{using k = -2}}{A=\cfrac{1}{2}(3+k)\left(-\cfrac{3k}{2} \right)}\implies A=\cfrac{1}{2}(3-2)\left(-\cfrac{3(-2)}{2} \right)\implies A=\cfrac{1}{2}(1)(3) \\\\\\ A=\cfrac{3}{2}\implies A=1.5 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{using k = -1}}{A=\cfrac{1}{2}(3+k)\left(-\cfrac{3k}{2} \right)}\implies A=\cfrac{1}{2}(3-1)\left(-\cfrac{3(-1)}{2} \right) \\\\\\ A=\cfrac{1}{2}(2)\left( \cfrac{3}{2} \right)\implies A=\cfrac{3}{2}\implies A=1.5$

7 0

2 years ago

Cody's rent is increasing by $51 per month starting next year. That is an increase of 15% from his current monthly rent. Let r r

Inessa05 [86]

Answer:

$r = 43.35$

Step-by-step explanation:

Given

$Current\ Rent = r$

$Increment = 15\%$

$New\ Rent = \$51$

Required

Determine the value of r

The value of r can be set up percentage increase formula as follows:

$\%Increment = \frac{New\ Rent - Current\ Rent}{Current\ Rent}$

Substitute values in the above equation

$15\% = \frac{51 - r}{51}$

Cross Multiply

$51 - r = 15\% * 51$

Convert percentage to decimal

$51 - r = 0.15 * 51$

$51 - r = 7.65$

And the value of $r\ is\ calculated\ using:$

$r = 51 -7.65$

$r = 43.35$

Hence, Cody's current rent is $43.35 monthly

8 0

2 years ago

Deedra has the equations for lines A and B. When she solved for the point where these two lines intersect, she ended up with the

KonstantinChe [14]

we can take a peek at two of those lines hmmm say y = 5x + 3 and y = 5x + 7.

let's notice, those two equations for those lines are in slope-intercept form, so let's solve the system.

since y = y then

5x + 3 = 5x + 7

3 = 7 what the?

well, notice, both lines have the same slope of 5, but different y-intercept, one has it at y = 3 and the other at y = 7, what does that mean?

it means that both lines are parallel to each other, one may well be above the other, but both are parallel, and since a solution to the system is where their graphs intersect, well, parallel lines never touch, so a system with two parallel lines has no solutions.

3 0

3 years ago

Read 2 more answers

sherry read 1/3 of the book in 90 minutes then slept for 3 hours. she continued reading after she woke up and finished the rest

Vadim26 [7]

Answer:

You don’t have question

4 0

2 years ago