All categories

3 years ago

What is the value of x in the diagram?

Mathematics

1 answer:

makvit [3.9K]3 years ago

6 0

Answer:

x=5

Step-by-step explanation:

Since this is a right triangle, we can use the pythagorean theorem

a^2 + b^2 = c^2

x^2+ ( 2x+2)^2 = (2x+3)^2

FOIL the squared terms

x^2 +(4x^2 + 4x+4x+4) = 4x^2 + 6x+6x +9

Combine like terms

5x^2+8x +4 = 4x^2 +12x +9

Subtract 4x^2 +12x +9 from each side

5x^2+8x +4 -4x^2 -12x -9= 4x^2 +12x +9-4x^2 -12x -9

x^2 -4x -5 =0

Factor

(x-5) (x+1) = 0

Using the zero product property

x=5 x=-1

But x cannot be negative or we would have negative length

x=5

You might be interested in

How do i do this pls help me

Delvig [45]

Answer:

$y = \frac{1}{7} x + 7$

Step-by-step explanation:

x-7y = -49

i) move x to the right-hand side and change its sign

-7y = -49-x

ii) change the signs on both sides of the equation

7y = 49+x

iii) divide both sides of the equation by 7

$\frac{7y}{7} = \frac{49}{7} + \frac{x}{7}$

$y = 7 + \frac{1}{7} x$

iv) use the commutative property to reorder the terms

* commutative property: a+b = b+a

$y = \frac{1}{7} x + 7$

3 0

3 years ago

biologists have found that the number of chirps some crickets make per minute is related to temperaturehow warm is it when the c

Sliva [168]

Answer:

Step-by-step explanation:

4 0

3 years ago

A water storage tank is in the shape of a cone with the pointed end down. If the radius is 21 feet and the depth of the tank is

andre [41]

The volume of the water storage tank is the amount of space in it

The volume of the water storage tank is 6468 cubic feet

<h3>How to determine the volume?</h3>

The given parameters are:

Radius (r) = 21 feet

Height (h) = 14 feet

The shape of the water storage tank is a cone.

And the volume of a cone is:

V = 1/3πr^2h

So, we have:

V = 1/3 * 22/7 * 21^2 * 14

This gives

V = 6468

Hence, the volume of the water storage tank is 6468 cubic feet

Read more about volumes at:

brainly.com/question/1972490

4 0

3 years ago

Emma has money into savings accounts. One rate is 8% and the other is 12%. If she has $450 more in the 12% account and the total

AveGali [126]

Let's say that the value invested in the account with a rate of 8% is "x", then the amount invested in the account with a rate of 12% is:

$x+450$

To calculate the total interest we need to calculate the interest of each individual account and sum them:

$\begin{gathered} \frac{8}{100}\cdot x=0.08\cdot x \\ \frac{12}{100}\cdot(x+450)=0.12\cdot x+54 \end{gathered}$

The total interest is the sum of the two expressions above:

$\begin{gathered} 220=(0.08\cdot x)+(0.12\cdot x+54) \\ 220=0.08\cdot x+0.12\cdot x+54 \\ 220-54=0.2\cdot x \\ 166=0.2\cdot x \\ 0.2\cdot x=166 \\ x=\frac{166}{0.2} \\ x=830 \end{gathered}$

The value invested in the account with 8% interest is 830, the one invested in the account with 12% interest is 1280.

7 0

1 year ago

Translate the verbal phrase into an algebraic expression. Simplify the expression.

adoni [48]

X(x+6)
hope that helps :)

7 0

3 years ago