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3 years ago

The height of a triangle is 7 cm longer than its base.

1 answer:

6 0

A) Height -7 = base
B) .5 * height * base = 60
Substituting A into B
B) .5 * height * (height -7) = 60
B) .5*height^2 -3.5*height = 60
B) .5*height^2 -3.5*height -60 = 0
Using the quadratic formula:
Height = 15
Subtracting 7 gives us the base length
Base = 8
**************************************************************
Double-Check
.5 * 15 * 8 = 60

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What is f(x) = 7x2 + 42x written in vertex form?

amid [387]

Answer:

$\boxed{\boxed{y = 7(x+3)^2-63}}$

Step-by-step explanation:

The general vertex form of parabola is,

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

where,

(h, k) is the vertex of the parabola.

The given function is,

$\Rightarrow f(x) = 7x^2 + 42x$

$\Rightarrow y = 7x^2 + 42x$

$\Rightarrow y = 7(x^2 + 6x)$

$\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3)$

$\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3+3^3-3^2)$

$\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3+3^3)-7\cdot 3^2$

$\Rightarrow y = 7(x+3)^2-7\cdot 9$

$\Rightarrow y = 7(x+3)^2-63$

This is vertex form the given function.

7 0

3 years ago

Read 2 more answers

A cylinder and a cone have the same radius and height. The volume of the cylinder is 639 ft ^3. what is the volume of the cone?

AURORKA [14]

The volume of the cone is: A. 213 ft³.

<h3>Volume of a Cylinder and a Cone</h3>

Volume of cylinder = πr²h.
Volume of cone = ⅓πr²h.

Given:

radius and height of both the cylinder and the cone are equal.

Volume of Cylinder = 639 ft³

Therefore:

πr²h = ⅓πr²h

This means that volume of cone would be ⅓ of the volume of the cylinder.

Volume of cone = ⅓(639) = 213 ft³

Therefore, the volume of the cone is: A. 213 ft³.

Learn more about volume of cone on:

brainly.com/question/13677400

7 0

3 years ago

PLEASE HELP!!!<br><br>Can sometime help me solve this?

damaskus [11]

Hope you understand. tell me if u need help

3 0

3 years ago

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There are 24 boys in a class, and 2/3 of the students in the class are boys. How many students are girls ?

tresset_1 [31]

Answer:

12 girls.

Step-by-step explanation:

24 ÷ 2 = 12

(This is divided to find out 1 part of the whole class as ⅓)

⅓ = 12

1 (whole) take away ⅔ = ⅓

Since ⅔ + ⅓ = 1

⅓ = fraction of girls in class

1 part = 12

So ⅓ = 12 girls out of 36 total students

Hope this helps. :)

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3 years ago

Jayson baked a pan of cornbread for a family dinner. He cut the cornbread into equal size pieces. At the end of the dinner, ther

VARVARA [1.3K]

If 1/6 of the pan was left and there were 2 pieces left you just need to set 1/6 equal to 2/some number, this allows you to say that 1/6=2/x --> x/6=2-->x=12. My explanation might be a little poor since this becomes fairly fundamental later on but hopefully it helps.

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4 years ago