Answer:
He invested 3,000 at 7% and 4,000 at 9%.
Step-by-step explanation:
From the information given, you can write the following equations:
x+y=7,000 (1)
0.07x+0.09y=570 (2)
You can solve for x in (1)
x=7,000-y (3)
Now, you can replace (3) in (1) and solve for "y":
0.07(7,000-y)+0.09y=570
490-0.07y+0.09y=570
0.02y=80
y=80/0.02
y=4,000
Finally, you can replace the value of "y" in (3):
x=7,000-4,000
x=3,000
According to this, the answer is that he invested 3,000 at 7% and 4,000 at 9%.
Answer:
The measure of angle HBC is m∠HBC=61°
Step-by-step explanation:
In this problem we have that
The line BH bisects angle EBC,
see the attached figure to better understand the problem
then
m∠EBC=m∠EBH+m∠HBC
m∠EBH=m∠HBC
so
m∠EBC=2(m∠EBH)
substitute the given values and solve for a
<em>Find the measure of angle EBH</em>
m∠EBH=(4(4)+45)=61°
Remember that
m∠EBH=m∠HBC
therefore
The measure of angle HBC is m∠HBC=61°
Answer:
11 inches by 11 inches
Step-by-step explanation:
The dimensions of the original photo were 11 inches by 11 inches.
We are informed that the area of the reduced photo is 64 square inches and that In the equation (x – 3)^2 = 64, x represents the side measure of the original photo.
In order to solve for x, we shall first take square roots on both sides of the equation;
The square root of (x – 3)^2 is simply (x - 3).
The square root of 64 is ±8 but we ignore -8 since the dimensions of any figure must be positive.
Therefore, we have the following equation;
x - 3 = 8
x = 8 + 3
x = 11
