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garik1379 [7]
3 years ago
12

What is the solution to sqrt 17-x=x+3? Show your work.

Mathematics
1 answer:
snow_lady [41]3 years ago
3 0

Answer:

x=1

Step-by-step explanation:

Remember:

(\sqrt[n]{a})^n=a\\\\(a+b)=a^2+2ab+b^2

Given the equation \sqrt{17-x}=x+3, you need to solve for the variable "x" to find its value.

You need to square both sides of the equation:

(\sqrt{17-x})^2=(x+3)^2

17-x=(x+3)^2

Simplifying, you get:

17-x=x^2+2(x)(3)+3^2\\\\17-x=x^2+6x+9\\\\x^2+6x+9+x-17=0\\\\x^2+7x-8=0

Factor the quadratic equation. Find two numbers whose sum be 7 and whose product be -8. These are: -1 and 8:

(x-1)(x+8)=0

Then:

x_1=1\\x_2=-8

Let's check if the first solution is correct:

\sqrt{17-(1)}=(1)+3

4=4 (It checks)

Let's check if the second solution is correct:

\sqrt{17-(-8)}=(-8)+3

5\neq-5 (It does not checks)

Therefore, the solution is:

x=1

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The pyramid shown has a height of 14 inches and a base area of 60 in2. Find the volume of the pyramid.
Kamila [148]

Volume of pyramid is 280 in^{3}.

The pyramid has a height 14 inches and a base area of 60 in2.

What is volume?

Volume is a three - dimensional quantity that is used to measure the capacity of a solid shape.

Volume of the pyramid = Area base X \frac{height}{3}

                                    = 60.\frac{14}{3}

                                    = 280 in^{3}

So the volume of pyramid = 280 in^{3}

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8 0
2 years ago
A circle's circumference is approximately 44 cm.
Sav [38]
<h3>Answers</h3><h3>diameter = 14</h3><h3>radius = 7</h3><h3>area = 154</h3>

these are all approximate

======================================

Explanation:

C = pi*d is the formula for the circumference. We know that C = 44 approximately, so,

C = pi*d

d = C/pi

d = 44/3.14

d = 14.01 approximately

d = 14 also approximate

take half of this to get the radius

r = d/2 = 14/2 = 7

Then use this radius to find the circle's area

A = pi*r^2

A = 3.14*7^2

A = 153.86

A = 154  rounding to the nearest whole number

7 0
3 years ago
Sarahs craft project uses peices of yarn that are 1/8 yard long.She has a peice of yarn that is 3 yards ling.How many 1/8 yard p
motikmotik
Pieces of yarn .... 1/8 yard long (each)
a piece of yarn ... n = 3 yards long
remaining ... 1 1/4 yards = 5/4 yards

If you would like to calculate how many 1/8 yard pieces can Sarah cut and still have 1 1/4 yards left, you can do this using the following steps:

n - 1 1/4 = <span>3 - 1 1/4 </span>= 3 - 5/4 = 12/4 - 5/4 = 7/4 = 1 3/4 yards

7/4 / 1/8 = 7/4 * 8/1 = 14 pieces

Result: Sarah can cut 14 1/8 yard pieces and still have 1 1/4 yards left.

3 0
3 years ago
Read 2 more answers
1Joe gets a job picking fruit. Joe is paid $5 for every bushel of apples he
steposvetlana [31]

Answer:

B

Step-by-step explanation:

The number of bushels of apples he picks (B) would be times by 5 as he would earn that much per bushel to get his pay (P)

7 0
3 years ago
beaus recipefor granola bars calls for 3 1/2 cups of oatmeal. he only have 1/6 cup scoop.how many scoops of oatmeal will he need
Stells [14]
<h2>Answer:</h2>

The number of scoops of oatmeal  he will need for the recipe is:

                             21 scoops.

<h2>Step-by-step explanation:</h2>

It is given that:

Beaus recipe for granola bars calls for 3 1/2 cups of oatmeal.  

i.e. the cups of oatmeal required is:

3\dfrac{1}{2}\ cups=\dfrac{3\times 2+1}{2}\ cups

i.e.

\dfrac{7}{2}\  \text{cups\ of\ oatmeal\ is\ required}

Also, he has:

\dfrac{1}{6}\ \text{cup scoop}

This means that:

\text{Number of scoops of oatmeal he need}=\dfrac{\text{Number of cups of oatmeal}}{\text{Number of cup scoop he has}}\\\\i.e.\\\\\text{Number of scoops of oatmeal he need}=\dfrac{\dfrac{7}{2}}{\dfrac{1}{6}}\\\\i.e.\\\\\text{Number of scoops of oatmeal he need}=\dfrac{7\times 6}{1\times 2}\\\\i.e.\\\\\text{Number of scoops of oatmeal he need}=21\ \text{scoops}

7 0
3 years ago
Read 2 more answers
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