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3 years ago

I need help with this?

Mathematics

1 answer:

antiseptic1488 [7]3 years ago

4 0

1.) 58

2.) 205

3.) 134

4.) 150

5.) 21

6.) 670

7.) 33

8.) 50/7 or 7 1/7

9.) 42

These are all your answers

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Y=-1/3x^2-4x-5 in vertex form

grigory [225]

Answer:

$Y=-\frac{1}{3}(x+6)^2+7$ [Vertex form]

Step-by-step explanation:

Given function:

$Y=-\frac{1}{3}x^2-4x-5$

We need to find the vertex form which is.,

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

where $(h,k)$ represents the co-ordinates of vertex.

We apply completing square method to do so.

We have

$Y=-\frac{1}{3}x^2-4x-5$

First of all we make sure that the leading co-efficient is =1.

In order to make the leading co-efficient is =1, we multiply each term with -3.

$-3\times Y=-3\times\frac{1}{3}x^2-(-3)\times4x-(-3)\times 5$

$-3Y=x^2+12x+15$

Isolating $x^2$ and $x$ terms on one side.

Subtracting both sides by 15.

$-3Y-15=x^2+12x-15-15$

$-3Y-15=x^2+12x$

In order to make the right side a perfect square trinomial, we will take half of the co-efficient of $x$ term, square it and add it both sides side.

square of half of the co-efficient of $x$ term = $(\frac{1}{2}\times 12)^2=(6)^2=36$

Adding 36 to both sides.

$-3Y-15+36=x^2+12x+36$

$-3Y+21=x^2+12x+36$

Since $x^2+12x+36$ is a perfect square of $(x+6)$ , so, we can write as:

$-3Y+21=(x+6)^2$

Subtracting 21 to both sides:

$-3Y+21-21=(x+6)^2-21$

$-3Y=(x+6)^2-21$

Dividing both sides by -3.

$\frac{-3Y}{-3}=\frac{(x+6)^2}{-3}-\frac{21}{-3}$

$Y=-\frac{1}{3}(x+6)^2+7$ [Vertex form]

8 0

3 years ago

Find the length of a side of the square shown below. х 6V2 X = x = [?]

Leona [35]

Answer:

x=6

Step-by-step explanation:

In a square, its angles are all 90 degrees. So, cutting a square in half into two triangles from corner to corner produces 45 degree angles on both sides. Since the triangles are now 45-45-90 triangles, we can use the rule where the hypotenuse of the triangle is equal to the square root of 2 times the length of either side. So, the side length is 6.

4 0

2 years ago

The weights (in ounces) of 14 different apples are shown below. Find Q 3. 5.7 5.5 4.7 4.4 6.8 5.7 5.5 6.9 6.0 4.4 5.7 6.9 4.4 4.

elena55 [62]

I Think 5.7 I’m Not Sure

6 0

3 years ago

Alicia has five times as many dimes as she has quarters. Combined the dimes and quarters total to $9.75. How many dimes does Ali

olasank [31]

Five dimes and one quarter = .75.
9.75/.75=3.25*4/1=13
there are 13 "5 dimes and 1 quarter"s
so 65 dimes

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3 years ago

5(x-8)=30 WILL GIVE BRAINLIST AND THANKS IF CORRECT

zvonat [6]

Answer:

x = 14

Step-by-step explanation:

5x - 40 = 30

+40 +40

5x = 70

divide by 5 on both sides

x= 14

7 0

3 years ago