Answer:
$2000 was invested at 5% and $5000 was invested at 8%.
Step-by-step explanation:
Assuming the interest is simple interest.
<u>Simple Interest Formula</u>
I = Prt
where:
- I = interest earned.
- P = principal invested.
- r = interest rate (in decimal form).
- t = time (in years).
Given:
- Total P = $7000
- P₁ = principal invested at 5%
- P₂ = principal invested at 8%
- Total interest = $500
- r₁ = 5% = 0.05
- r₂ = 8% = 0.08
- t = 1 year
Create two equations from the given information:


Rewrite Equation 1 to make P₁ the subject:

Substitute this into Equation 2 and solve for P₂:





Substitute the found value of P₂ into Equation 1 and solve for P₁:



$2000 was invested at 5% and $5000 was invested at 8%.
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Answer:
18,771 $
Step-by-step explanation:
there are 52.1429 weeks in one year with 40 hours of work each week and then 9 dollars made an hour this equals to 18,771 $
Answer:
24) x = 9.2
25) x = 30.8
Step-by-step explanation:
Given
See attachment for triangles
Solving (24)
To solve for x, we make use of cosine formula
i.e.
cos(40) = adjacent ÷ hypotenuse
So, we have:
cos(40) = x ÷ 12
Multiply both sides by 12
12 cos(40) = x
12 * 0.7660 = x
x = 9.2
Solving (25)
To solve for x, we make use of sine formula
i.e.
sin(25) = opposite ÷ hypotenuse
So, we have:
sin(25) = 13 ÷ x
Multiply both sides by
x sin(25) = 13
Divide by sin(25)
x = 13 ÷ sin(25)
Using a calculator
x = 30.8
Answer:
√3
Step-by-step explanation:
We cannot solve this operation directly. Because cot7pi/6 is undefined.
We know that 1/tan= cot.
so we will first take the reciprocal of cot that is 1/tan.
So,
cot7pi/6= 1/tan 7π/6
∵7π/6 = 210 where pi=180
so cot7π/6 =1/tan210
cot7π/6 =1/1÷√3
cot7π/6 = √3
Answer:
A.
and 
Step-by-step explanation:
Given:
Vertices of triangle RST are
and
.
Rotation is 90° about the center O(0,0). The rotation is counter-clockwise as the angle of rotation is positive.
Now, the co-ordinate rule for 90° rotation counter-clockwise is given as:
→ 
and
values interchange their places with
becoming negative when interchanged.
So,
→ 
→ 
→
⇒
→ 
Therefore, the image of the vertices are
and
.