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2 years ago

The vertex form of the equation of a parabola is y = 2(x+ 4)2 - 21.

Mathematics

1 answer:

Ivanshal [37]2 years ago

8 0

Answer:

y = 2x² + 16x + 11

Step-by-step explanation:

first foil (x + 4)² to get x² + 8x + 16

distribute 2 to get 2x² + 16x + 32

subtract 21 from 32

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Will mark brainliest! Questions are in the picture!

alexdok [17]

Answer:

52.9 inches .

Step-by-step explanation:

Given that the triangular indentation has an area of 100 in.² and the base and height of this traingle are represented by expressions 3x and x+3 respectively . We need to find out the perimeter to the nearest tenth.

As we know that the area of triangle is ,

$\rm\longrightarrow Area_{\triangle}=\dfrac{1}{2}(base)(height)$

Substituting the respective values,

$\rm\longrightarrow 100\ =\dfrac{1}{2}(x+3)(3x)\\\\\rm\longrightarrow 2(100) = 3x(x+3)\\\\\rm\longrightarrow200 = 3x^2+9x\\\\\rm\longrightarrow 3x^2+9x-200=0$

On using the Quadratic formula , we have;

$\rm\longrightarrow x =\dfrac{-9\pm\sqrt{9^2-4(3)(-200)}}{2(3)} \\\\\rm\longrightarrow x =\dfrac{-9\pm \sqrt{81+1200}}{6}\\\\\rm\longrightarrow x =\dfrac{-9\pm \sqrt{1281}}{6}$

On simplifying above , we will get ,

$\rm\longrightarrow x = 6.802,-9.802$

Since sides can't be negative, therefore,

$\rm\longrightarrow\underline{\underline{ x =6.802}}$

Therefore ,

$\rm\longrightarrow Base = 3x =3(6.802)in = 20.406\ in\\$
$\rm\longrightarrow Height = x +3=6.802+3=9.802\ in$

Next let's find out the hypotenuse using Pythagoras theorem, as ;

$\rm\longrightarrow h=\sqrt{ b^2+p^2}\\$

$\rm\longrightarrow h =\sqrt{ (20.406)^2+(9.802)^2}\\$

$\rm\longrightarrow h =\sqrt{416.40+96.07}\\$

$\rm\longrightarrow h = 22.63\ in$

Now we may find perimeter as ,

$\rm\longrightarrow P = p + b + h \\$

$\rm\longrightarrow P = (22.63 + 9.802 + 20.406)in.$

$\\\rm\longrightarrow P = 52.89 \ in.\\$

$\rm\longrightarrow \underline{\underline{ Perimeter = 52.9\ in .}}$

8 0

2 years ago

HOW MUCH MORE WILL YHE INVESTMENT BE?

dalvyx [7]

Answer:

more then america is in dept

5 0

2 years ago

cuboid of length 24cm and volume 768cm^3 the width and hight are not equal.give a pair of possible values for their length.

Brilliant_brown [7]

Answer:

Possible values of dimensions are (24,16,2) or (24,8,4)

Step-by-step explanation:

We are given the volume of the Cuboid and length . We are required to find the possible values of width and height from this information.

Let us say that the width is x and height is y

Length = 24

Volume of a cuboid = length * width * height

Volume = 768

768=24*x*y

$xy=\frac{768}{24}\\xy=32\\$

xy=32

Now the possible factors of 32

32=1*32 ( Which shall not be taken into consideration as length is already given as 24 and width or height can not be more length)

32=2*16

32=4*8

Hence the possible values width are 8, 16 and that of height 4 and 2

Hence the possible values of dimensions are (24,16,2) or (24,8,4)

3 0

2 years ago

I NEEDDDDDDD HELPPPPPPPP PLEASEEEEEEEE

zysi [14]

Cross section of a sphere is a circle

8 0

2 years ago

Read 2 more answers

A PHN is studying the rate of H1N1 in the community. If there are five cases of H1N1 in the community of 1,000 people, what is t

BigorU [14]

Answer:

0.5%

Step-by-step explanation:

The prevalence rate shows the proportion of people that have a disease in a population and to be able to calculate it, you have to divide the number of people that have a disease by the population:

Prevalence rate=(5/1,000)*100

Prevalence rate=0.005*100

Prevalence rate=0.5%

According to this, the answer is that if there are five cases of H1N1 in the community of 1,000 people, the prevalence rate is 0.5%.

8 0

2 years ago