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3 years ago

9

Simplify:(y²+z²) -2yz

1 answer:

VMariaS [17]3 years ago

5 0

Answer:

$(y-z)^{2}$

Step-by-step explanation:

$(y^{2}+z^{2} ) -2yz\\\\y^{2} +z^{2} - 2yz\\\\y^{2} +2yz + z^{2}\\\\(y-z)^2\\$

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If the vertex of a parabola is at (2, 3) and the point (0, -1) is also on the parabola, find an equation for the parabola. Write

STALIN [3.7K]

Answer:

$y=-1(x-2)^2+3$

Step-by-step explanation:

W have been given that the vertex of a parabola is at (2, 3) and the point (0, -1) is also on the parabola. We are asked to find the equation of parabola in the form $y=(x-h)^2+k$ .

We know that vertex form of parabola in form $y=a(x-h)^2+k$ , where (h,k) in vertex of parabola.

Upon substituting coordinates of vertex, we will get:

$y=a(x-2)^2+3$

To find the value of a, we will substitute coordinates of point (0, -1) as:

$-1=a(0-2)^2+3$

$-1=a(4)+3$

$-1=4a+3$

$-1-3=4a+3-3$

$-4=4a$

$\frac{-4}{4}=\frac{4a}{4}$

$-1=a$

Therefore, our required equation would be $y=-1(x-2)^2+3$ .

3 0

3 years ago

If n ll m, find the value of x and the value of z.

aliina [53]

Answer: A

Explanation: the two triangles are proportional, so find the “proportion” between the two sides
12/4=3
3*3=9
3z=6

7 0

3 years ago

Use a half-angle identity to find the exact value

Tatiana [17]

Given:

$\cos 15^{\circ}$

To find:

The exact value of cos 15°.

Solution:

$$\cos 15^{\circ}=\cos\frac{ 30^{\circ}}{2}$

Using half-angle identity:

$$\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos (x)}{2}}$

$$\cos \frac{30^{\circ}}{2}=\sqrt{\frac{1+\cos \left(30^{\circ}\right)}{2}}$

Using the trigonometric identity: $\cos \left(30^{\circ}\right)=\frac{\sqrt{3}}{2}$

$$=\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}$

Let us first solve the fraction in the numerator.

$$=\sqrt{\frac{\frac{2+\sqrt{3}}{2}}{2}}$

Using fraction rule: $\frac{\frac{a}{b} }{c}=\frac{a}{b \cdot c}$

$$=\sqrt{\frac {2+\sqrt{3}}{4}}$

Apply radical rule: $\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$

$$=\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}$

Using $\sqrt{4} =2$ :

$$=\frac{\sqrt{2+\sqrt{3}}}{2}$

$$\cos 15^\circ=\frac{\sqrt{2+\sqrt{3}}}{2}$

5 0

3 years ago

https://app31.studyisland.com/userFiles/nc6line1.gif Which of the following are alternate exterior angles? A. ∠B and ∠G B. ∠E an

tatuchka [14]

<span>B. ∠E and ∠H are alternate exterior angles</span>

7 0

3 years ago

What is the answer to this

ICE Princess25 [194]

2. -28

5. -60

8. -135

The answers are above. :)

7 0

3 years ago