Answer:
<h2>80=5x+4y</h2>
Step-by-step explanation:
Step one:
given
let binders be x
and notebooks be y
let the total sale be T
the cost of binder is $5 each
the cost of notebook is $4 each.
the total sales expected is $80
step two:
the linear model for the total sales is given as
T=x+y
using the given data, the situation can be represented linearly as
80=5x+4y
Therefore the linear expression for the total sale is 80=5x+4y
Given:
circular merry-go-round that has a diameter of 15 feet.
Find: How much trim does he need to buy to put around the edge of the merry-go-round?
We need to find the circumference of the merry-go-round to get the measurement of the trim needed.
Circumference = π d
π = 3.14
d = diameter = 15 feet
Circumference = 3.14 * 15 feet
Circumference = 47.10 feet.
Mr. Osterhout needs to buy 47.10 feet of trim to put around the circular merry-go-round.
Answer:
1/3
Step-by-step explanation:
When working with balanced expressions (stuff on both sides of the equal sign), "what you do to one side, you do to the other", which keeps it balanced.
The first thing we notice is the exponent 1/4, which is one both sides, so we can get rid of it on both sides by using the <u>reverse operation</u>.
The reverse of exponents is <u>square root</u>.
![(4x + 10)^{\frac{1}{4}} = (9 + 7x)^{\frac{1}{4}}\\\sqrt[\frac{1}{4}]{(4x + 10)^{\frac{1}{4}}} = \sqrt[\frac{1}{4}]{(9 + 7x)^{\frac{1}{4}}}\\\\4x + 10 = 9 + 7x](https://tex.z-dn.net/?f=%284x%20%2B%2010%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%20%3D%20%289%20%2B%207x%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5C%5C%5Csqrt%5B%5Cfrac%7B1%7D%7B4%7D%5D%7B%284x%20%2B%2010%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%7D%20%3D%20%5Csqrt%5B%5Cfrac%7B1%7D%7B4%7D%5D%7B%289%20%2B%207x%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%7D%5C%5C%5C%5C4x%20%2B%2010%20%3D%209%20%2B%207x)
Isolate x to solve. Separate the variables and non-variables.
4x + 10 = 9 + 7x
4x - 4x + 10 = 9 + 7x - 4x Subtract 4x from both sides
10 = 9 + 3x
10 - 9 = 9 - 9 + 3x Subtract 9 from both sides
1 = 3x Divide both sides by 3 to isolate x
x = 1/3 Answer
The two angles (6x+4) and 32 degrees are complementary angles. They add to 90 degrees. The two angles are adjacent and form a right angle. The right angle marker is the square marker. Two adjacent right angles form a straight angle (180 degrees)
Add up the angles and set the sum equal to 90. Then solve for x
(6x+4) + (32) = 90
6x+4 + 32 = 90
6x+36 = 90
6x+36-36 = 90-36 .... subtract 36 from both sides
6x = 54
6x/6 = 54/6 ... divide both sides by 6
x = 9
Since x = 9, this means that
6x+4 = 6*9+4 = 54+4 = 58
So the missing angle is 58 degrees (note how 58+32 = 90)
