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spin [16.1K]
3 years ago
14

Find the length of side AB. Give your answer to 1 decimal place.

Mathematics
1 answer:
ehidna [41]3 years ago
7 0

Answer:

Length of side AB = 5.6 cm

Step-by-step explanation:

From the figure attached.

In right triangle ABC,

m∠ABC = 62°

m(BC) = 12 cm

By applying Cosine rule in this triangle,

Cos62° = \frac{\text{Adjacent side}}{\text{Hypotenuse}}

Cos62°= \frac{AB}{BC}

0.46947 = \frac{AB}{12}

AB = 12 × 0.46947

AB = 5.63

     ≈ 5.6 cm  

Therefore, length of side AB = 5.6 cm

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5cosx -2sin(x/2) +7=0<br>Help me to find x step by step<br>pls​
miskamm [114]

Answer:

x = 180

Step-by-step explanation:

First, you need to know

1. Double-angle formula:

cos(2x) = cos^{2}x - sin^{2}x

2. Pythagorean identity:

cos^{2}x + sin^{2}x = 1

Back to your problem, replacing the variable by the above:

5cosx-sin\frac{x}{2}+7 = 0

5(cos^{2}\frac{x}{2}-sin^{2}\frac{x}{2}) - 2sin\frac{x}{2} + 7 = 0 By Double-angle formula

5(1 - 2sin^{2}\frac{x}{2}) - 2sin\frac{x}{2} + 7 = 0 By Pythagorean identity

Given y = \frac{x}{2}

5(1-2sin^{2}y) - 2siny + 7 = 0

10sin^{2}y+2siny-12=0

5sin^{2}y+siny-6=0

(5siny + 6)(siny - 1)=0, we know -1 < sinx < 1, for every x ∈ R

siny = 1, y =90

y = \frac{x}{2}

x = 180

8 0
3 years ago
If 65 percent of the population of a large community is in favor of a proposed rise in school taxes, approximate the probability
xz_007 [3.2K]

Answer:  a) 0.99917  b)  0.7054  c) 0.9820

Step-by-step explanation:

Let X denotes the number of people are in favor of a proposed rise in school taxes.

Era re given that p(probability that a person is in favor of a proposed rise )= 0.65

Sample size : n= 100

Mean= np = 100(0.65)=65

Standard deviation: \sigma=\sqrt{np(1-p)}\\\\=\sqrt{100(0.65)(0.35)}\\\\=4.76969600708\approx4.77

a) Now, the probability that a random sample of 100 people will contain  at least 50 who are in favor of the proposition :

P(x\geq50)=P(\dfrac{x-\mu}{\sigma}\geq\dfrac{50-65}{4.77})\\\\=P(z\geq-3.144)\\\\=P(z-z)=P(Z

b) between 60 and 70 inclusive who are in favor;

P(60

c) fewer than 75 in favor.

P(x

3 0
3 years ago
What is the mode interval for the set of data?
yan [13]
Well the mode is like the most set it numbers so
6 0
3 years ago
Not sure how to work this one out please help :)
stepladder [879]

Answer:

147.03 cm²

Step-by-step explanation:

Area of a parallelogram:

A = bh

A - area

b - base

h - height

From the figure,

Base = 16.9 cm

Height = 8.7 cm

A = (16.9)(8.7)

A = 147.03 cm²

4 0
3 years ago
Read 2 more answers
Which graph represents y &gt; 2x - 1?
GrogVix [38]
I believe b because it would be dotted and has a slope of 2 or 2/1
6 0
2 years ago
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