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3 years ago

Identify the vertex of the parabola given by f(x) = (x + 2)^2 – 4

Mathematics

1 answer:

kicyunya [14]3 years ago

8 0

Answer:

The vertex is ( -2, -4)

Step-by-step explanation:

The vertex form is

y = a( x-h) ^2 +k

where ( h,k) is the vertex

f(x) = (x + 2)^2 – 4

Rewriting

f(x) = (x - -2)^2 – 4

The vertex is ( -2, -4)

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Write an equation in standard form for the line, where the points (-2, -1) and (0, 4) are on the line

DedPeter [7]

Answer:

An equation in standard form for the line is:

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

Step-by-step explanation:

Given the points

(-2, -1) and (0, 4)

The slope between two points

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-2,\:-1\right),\:\left(x_2,\:y_2\right)=\left(0,\:4\right)$

$m=\frac{4-\left(-1\right)}{0-\left(-2\right)}$

$m=\frac{5}{2}$

Writing the equation in point-slope form

As the point-slope form of the line equation is defined by

$y-y_1=m\left(x-x_1\right)$

Putting the point (-2, -1) and the slope m=1 in the line equation

$y-\left(-1\right)=\frac{5}{2}\left(x-\left(-2\right)\right)$

$y+1=\frac{5}{2}\left(x+2\right)$

$y=\frac{5}{2}x+4$

Writing the equation in the standard form form

As we know that the equation in the standard form is

$Ax+By=C$

where x and y are variables and A, B and C are constants

$y=\frac{5}{2}x+4$

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

Therefore, an equation in standard form for the line is:

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

7 0

2 years ago

O is the center of both circles containing arcs AB and CD

victus00 [196]

Answer:

Step-by-step explanation:

You need to solve the area sector of the bigger circle. Since we now the length of sector is 270, we can set up an equation.

Length of sector DC = 2 $\pi$ r

270 = 2 $\pi$ (8+OA) *(8+OA is the raidus of the bigger circle/sector)*

270/2 $\pi$ = 8 + OA (division)

135/ $\pi$ -8 = OA

135/ $\pi$ -8 = OB (because OA and OB are the raidus of the same circle, so they are congruent)

I hope this helps you! Please correct me if you see a miscalculation <3<3

5 0

2 years ago

PLZZZZZ NEED HELP!!!!!!

mylen [45]

Remember the rules of Sohcahtoa (Sine, cosine, tangent). For this problem we take the cosine of 38 because the labeled sides are the adjacent leg and the hypotenuse.

Cos(38)=79/x

Cosine of 38 is about 0.7880

0.7880=79/x

Next we multiply both sides by the denominator

(x) 0.7880=79 (x)

Then divide.

0.7880x= 79

0.7880 0.7880

X=100.25

Hope this helped :)

5 0

2 years ago

1) x² 2(x+y) - y^2 2) x^4+ x^2y^2+ y^4

spin [16.1K]

Answer: 1) Let's simplify step-by-step.

x22(x+y)−y2

Distribute:

=(x22)(x)+(x22)(y)+−y2

=x23+x22y+−y2

Answer:

=x23+x22y−y2

2)Let's simplify step-by-step.

x4+x2y2+y4

There are no like terms.

Answer:

=x4+x2y2+y4

5 0

3 years ago

a model car has a scale of 3 cm : 2 m. The length of the actual hood of the car is 1 m. What is the length of the model?

nadezda [96]

Yes
that it jusf de aima noi neo curh

3 0

3 years ago