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3 years ago

Find the equation in standard form of the parabola passing through the giving points.

Mathematics

1 answer:

zaharov [31]3 years ago

4 0

Let y = ax²+bx+c then substitute all of orders. we'll be doing equations system.

$a-b+c=0\\c=3\\a+b+c=2$

Ok we are at this.

Substitute c = 3 into equation 1 and equation 3.

$a-b+3=0\\a-b=-3$

$a+b+3=2\\a+b=2-3\\a+b=-1$

then addition and subtract for a-b = 3 and a+b = -1

$a-b=-3\\a+b=-1\\2a=-4\\a=-2$

Therefore a = -2, substitute a = -2 in a-b+c=0 or a+b+c=2 but i'm doing a-b+c=0 one.

$a-b+c=0\\\\-2-b+3=0\\-b+1=0\\-b=-1\\b=1$

Therefore b = 1, substitute both a, b and c into y=ax²+bx+c as we get,

$y=-2x^2+x+3$ #

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The height of a pyramid is doubled, but its length and width are cut in half. What is true about the volume of the new pyramid?

chubhunter [2.5K]

Answer:

B.)The new pyramid has a volume that is One-half the volume of the original pyramid.

Step-by-step explanation:

got it right on test.

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3 years ago

Read 2 more answers

Which does NOT show a reasonable estimate for 673 × 18?

Yakvenalex [24]

Answer:

A. 14,000

Step-by-step explanation:

because 673 rounded would equal 700

and 18 rounded would be 20

so 700x20 would be 14,000

hopefully you understand

and i hope you have a good day :)

6 0

3 years ago

10]The graph of a function is a line that passes through the coordinates (2, 11) and (8. 14).Which is an equation in terms of x

aksik [14]

We know that the graph of a function is a line that passes through the coordinates (2, 11) and (8, 14) and we must find the equation for the line.

1. We must use the next formula to find the slope

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

Where (x1, y1) and (x2, y2) are the points.

Now, replacing the points in the formula for the slope

$m=\frac{14-11}{8-2}=\frac{3}{6}=\frac{1}{2}$

2. We must replace the slope and one of the points in the next formula

$y-y_1=m(x-x_1)$

Now, replacing the slope and the point (2, 11)

$\begin{gathered} y-11=\frac{1}{2}(x-2) \\ \end{gathered}$

3. We must delete the parenthesis and solve the equation for y

$\begin{gathered} y-11=\frac{1}{2}x-\frac{1}{2}\cdot2 \\ y-11=\frac{1}{2}x-1 \\ y=\frac{1}{2}x-1+11 \\ y=\frac{1}{2}x+10 \end{gathered}$

ANSWER:

$y=\frac{1}{2}x+10$

8 0

1 year ago

What does the equal

sergejj [24]

Plug it in your y= screen of your graphing calculator and hit 2nd and then graph. it will give u a table of values

7 0

3 years ago

Given that cot θ = 1/√5, what is the value of (sec²θ - cosec²θ)/(sec²θ + cosec²θ) ?

Bogdan [553]

Step-by-step explanation:

$\mathsf{Given :\;\dfrac{{sec}^2\theta - co{sec}^2\theta}{{sec}^2\theta + co{sec}^2\theta}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{{sec}\theta = \dfrac{1}{cos\theta}}}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{co{sec}\theta = \dfrac{1}{sin\theta}}}}$

$\mathsf{\implies \dfrac{\dfrac{1}{cos^2\theta} - \dfrac{1}{sin^2\theta}}{\dfrac{1}{cos^2\theta} + \dfrac{1}{sin^2\theta}}}$

$\mathsf{\implies \dfrac{\dfrac{sin^2\theta - cos^2\theta}{sin^2\theta.cos^2\theta}}{\dfrac{sin^2\theta + cos^2\theta}{sin^2\theta.cos^2\theta}}}$

$\mathsf{\implies \dfrac{sin^2\theta - cos^2\theta}{sin^2\theta + cos^2\theta}}$

Taking sin²θ common in both numerator & denominator, We get :

$\mathsf{\implies \dfrac{sin^2\theta\left(1 - \dfrac{cos^2\theta}{sin^2\theta}\right)}{sin^2\theta\left(1 + \dfrac{cos^2\theta}{sin^2\theta}\right)}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{cot\theta = \dfrac{cos\theta}{sin\theta}}}}$

$\mathsf{\implies \dfrac{1 -cot^2\theta}{1 + cot^2\theta}}$

$\mathsf{Given :\;cot\theta = \dfrac{1}{\sqrt{5}}}$

$\mathsf{\implies \dfrac{1 - \left(\dfrac{1}{\sqrt{5}}\right)^2}{1 + \left(\dfrac{1}{\sqrt{5}}\right)^2}}$

$\mathsf{\implies \dfrac{1 - \dfrac{1}{5}}{1 + \dfrac{1}{5}}}$

$\mathsf{\implies \dfrac{\dfrac{5 - 1}{5}}{\dfrac{5 + 1}{5}}}$

$\mathsf{\implies \dfrac{5 - 1}{5 + 1}}$

$\mathsf{\implies \dfrac{4}{6}}$

$\mathsf{\implies \dfrac{2}{3}}$

Hence, option (a) 2/3 is your correct answer.

3 0

3 years ago