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2 years ago

5. What is the complement of the supplement of a 110° angle?

Mathematics

1 answer:

Slav-nsk [51]2 years ago

3 0

<h2>Answer: 20°</h2>

<h3>Step-by-step explanation:</h3>

Supplementary angles sum up to 180 °

Complementary angles sum up to 90°.

The supplement of 110° = 180° - 110° = 70°

The complement of 70° = 90° - 70° = 20°

<u>Simplier version:</u>

The complement of the supplement of 110° = (90° - (180° - 110°))

= 20°

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If the product of two positive fractions a and b is 15/56, find three pairs of possible values for a and b

Andrews [41]

Answer:

First possible pairs = (3/7)*(5/8) = 15/56

second possible pairs = (3/4)*(5/14) = 15/56

third possible pairs = (1/2)*(15/28) = 15/56

Step-by-step explanation:

According to the question,

a x b = 15/56

three possible pairs will be as follows:

Before proceeding to make possible pairs, we have to know the prime factorization of the numbers -

15 = 1, 3, 5, 15

56 = 1, 2, 4, 7, 8, 14, 28, 56

As we need three possible pairs, we have to check which pairs take us to 15/56. Again, since the fraction is positive, therefore, the fractions will be proper. Therefore, 3/2, or 5/4 will not be counted. Therefore,

First possible pairs = (3/7)*(5/8) = 15/56

second possible pairs = (3/4)*(5/14) = 15/56

third possible pairs = (1/2)*(15/28) = 15/56

fourth possible pairs = (3/8)*(5/7) = 15/56

So, we can get those four possible pairs. Among those, first 3 pairs are different. Therefore, those are possible pairs.

4 0

2 years ago

Plz answer for 20 pts

KATRIN_1 [288]

Answer to Problem 1: 5√3

Answer to Problem 2: 21√5

5 0

2 years ago

Read 2 more answers

Please Explain/Show Your Work, for each part of the question! Thank You!

mina [271]

Answer:

1. The graph represents a proportional relationship

2. 70,000 miles

Step-by-step explanation:

1. The graph represents a proportional relationship since the graph line is straight and begins at the origin.

2. Plot 5.5 hours on the graph and it'll give you 70,000 miles

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3 years ago

Paul has an eight-year loan with a principal of $26,900. The loan has an interest rate of 8.18%, compounded quarterly. If Paul p

babymother [125]

Answer:

The answer is "option b"

Step-by-step explanation:

Amount = $26,900

r= 0.0818 %

$i=\frac{r}{4}\\\\$

$=\frac{0.0818}{4}\\\\=0.02045$

t= 8 years

$n= 8 \times 4$

$=32$

$D=\frac{1-(1+i)^{-n}}{i}\\$

$=\frac{1-(1+0.02045)^{-32}}{0.02045}\\\\=\frac{1-(1.02045)^{-32}}{0.02045}\\\\=\frac{1-0.52319627}{0.02045}\\\\=\frac{0.47680373}{0.02045}\\\\=23.3155858$

$Q= \frac{Amount}{Discount \ factor }\\$

$=\frac{26900}{23.3155858} \\\\=1153.73468$

Payment $=1153.73468 \times 32\\\\$

$= \$ 36919.5098\\$

$\text{Total interest = Payment - amount}$

$= \$ 36919.5098 - \$ 26900 \\\\ = \$ 10019.5098$

$\text{Finance charge = Total interest + service charge}$

$= \$ 10019.5098 + \$ 1527\\\\ = \$ 11546.5098$

3 0

3 years ago

The volume of a hemisphere is 144 pi. Find the radius and total surface area.

sineoko [7]

Formula of the Volume of a hemisphere:
V = $\frac{2}{3}$ $\pi$ r³
144 $\pi$ = $\frac{2}{3}$ $\pi$ r³
Multiply by 3 to cancel fraction in the right side
144 $\pi$ × 3 = 2 $\pi$ r³
432 $\pi$ = 2 $\pi$ r³
Divide by 2 $\pi$ on either sides to isolate r³
$\frac{432 \pi }{2 \pi }$ = $\frac{2 \pi }{2 \pi }$ r³
2 $\pi$ and $2 \pi$ cancel out
216 = r³
Take cube root to find the radius
$\sqrt[3]{216}$ = $\sqrt[3]{r^3}$
6 = r
Radius is 6 units

The formula of the surface area of a hemisphere is:
S.A = 2 $\pi$ r² + $\pi$ r²
= $2\pi$ (6)² + $\pi$ (6)²
=2 $\pi$ × 36 + 36 $\pi$
= 72 $\pi$ + 36 $\pi$
= 108 $\pi$ units² (in terms of $\pi$ )
≈ 339.12 units²

Surface area = 108 $\pi$ units

8 0

3 years ago