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Ugo [173]
3 years ago
8

What is the vertex of the graph of the function below?

Mathematics
1 answer:
inna [77]3 years ago
8 0

Answer:

D. (4, -4)

Step-by-step explanation:

Convert to vertex form by completing the square.

For a polynomial y = x² + bx + c, first add and subtract (b/2)² to the polynomial.  Then factor.

Here, b = -8.  So (b/2)² = (-8/2)² = 16.

y = x² − 8x + 12

y = x²− 8x + 16 − 16 + 12

y = (x − 4)² − 16 + 12

y = (x − 4)² − 4

The vertex is (4, -4).

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183.3 ÷ 0.78=????????????<br> Who ever answers 1st gets brainleist!!!
faust18 [17]

Answer:

235

Step-by-step explanation:

183.3 ÷ 0.78 = 235

This is due to the rules of division.

6 0
3 years ago
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Simplify: cos2x-cos4 all over sin2x + sin 4x
GrogVix [38]

Answer:

\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}=\tan\left(x\right)

Step-by-step explanation:

\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}

Apply formula:

\cos\left(A\right)-\cos\left(B\right)=-2\cdot\sin\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right) and

\sin\left(A\right)+\sin\left(B\right)=2\cdot\sin\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right)

We get:

=\frac{-2\cdot\sin\left(\frac{2x+4x}{2}\right)\cdot\sin\left(\frac{2x-4x}{2}\right)}{2\cdot\sin\left(\frac{2x+4x}{2}\right)\cdot\cos\left(\frac{2x-4x}{2}\right)}

=\frac{-\sin\left(\frac{2x-4x}{2}\right)}{\cos\left(\frac{2x-4x}{2}\right)}

=\frac{-\sin\left(\frac{-2x}{2}\right)}{\cos\left(\frac{-2x}{2}\right)}

=\frac{-\sin\left(-x\right)}{\cos\left(-x\right)}

=\frac{-\cdot-\sin\left(x\right)}{\cos\left(x\right)}

=\frac{\sin\left(x\right)}{\cos\left(x\right)}

=\tan\left(x\right)

Hence final answer is

\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}=\tan\left(x\right)

6 0
2 years ago
What is the length of segment AE?
nexus9112 [7]

Answer:

AE=\frac{50}{3}\ units

Step-by-step explanation:

step 1

In the right triangle ABC

Applying the Pythagoras Theorem fin the hypotenuse AC

AC^{2} =AB^{2}+BC^{2}

substitute

AC^{2} =6^{2}+8^{2}

AC^{2} =100

AC =10\ units

step 2

we know that

If two figures are similar, then the ratio of its corresponding sides is equal

so

\frac{AB}{CD}=\frac{AC}{CE}

substitute and solve for CE

\frac{6}{4}=\frac{10}{CE}\\ \\CE=4*10/6\\ \\CE=\frac{20}{3}\ units

step 3

Find the length of segment AE

AE=AC+CE

substitute the values

AE=10\ units+\frac{20}{3}\ units=\frac{50}{3}\ units

6 0
3 years ago
How do you know when to use the less than symbol and when to use the less than or equal to symbol when writing an inequality for
xenn [34]

Answer:

This depends on the situation. For context, you use less than when your inequality CANNOT exceed more than.

You would use less than or equal to if your inequality can be equal to a number. Here's an example.

John needs to buy X oranges and Y apples. He can AT MOST buy 10 total fruits.

x + y (equal to or less than) 45

John needs to buy X oranges and Y apples. He CANNOT buy more than 10 total fruits.

x + y < 45

5 0
3 years ago
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