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3 years ago

What is the area of the figure? A. 52 cm2 B. 52 cm O C. 130 cm O D. 130 cm2

Mathematics

2 answers:

IgorLugansk [536]3 years ago

5 0

Answer:

B is the answer

Art [367]3 years ago

5 0

Answer:

130 cm^2

Step-by-step explanation:

split the figure into two rectangles, one can be 4x5 rectangle and the other can be the 11x10 rectangle. now multiply.

4x5 = 20

11x10=110

20+110 = 130 cm^2

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Right triangles abc and dbc with right angle c are given below. If cos(a)=15,ab=12 and cd=2, find the length of bd.

dmitriy555 [2]

see the attached figure to better understand the problem

we have that

$cos(A)=\frac{1}{5} \\ AB=12\ units\\ CD=2\ units$

Step 1

Find the value of AC

we know that

in the right triangle ABC

$cos (A)=(AC/AB)\\AC=AB*cos(A)$

substitute the values in the formula

$AC=12*(1/5)\\ AC=2.4\ units$

Step 2

Find the value of BC

we know that

in the right triangle ABC

Applying the Pythagorean Theorem

$AB^{2} =AC^{2}+BC^{2}\\ BC^{2}=AB^{2} -AC^{2}$

substitute the values

$BC^{2}=12^{2} -2.4^{2}\\BC^{2}= 138.24\\ BC=11.76\ units$

Step 3

Find the value of BD

we know that

in the right triangle BCD

Applying the Pythagorean Theorem

$BD^{2} =DC^{2}+BC^{2}$

substitute the values

$BD^{2} =2^{2}+11.76^{2}$

$BD=11.93\ units$

therefore

the answer is

the length of BD is 11.93 units

8 0

3 years ago

Read 2 more answers

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lys-0071 [83]

Answer:

a b

Step-by-step explanation:

7 0

3 years ago

Suppose that two openings on an appellate court bench are to be filled from current municipal court judges. The municipal court

Ksju [112]

Answer:

$(a)\dfrac{92}{117}$

$(b)\dfrac{8}{39}$

$(c)\dfrac{25}{117}$

Step-by-step explanation:

Number of Men, n(M)=24

Number of Women, n(W)=3

Total Sample, n(S)=24+3=27

Since you cannot appoint the same person twice, the probabilities are without replacement.

(a)Probability that both appointees are men.

$P(MM)=\dfrac{24}{27}X \dfrac{23}{26}=\dfrac{552}{702}\\=\dfrac{92}{117}$

(b)Probability that one man and one woman are appointed.

To find the probability that one man and one woman are appointed, this could happen in two ways.

A man is appointed first and a woman is appointed next.
A woman is appointed first and a man is appointed next.

P(One man and one woman are appointed) $=P(MW)+P(WM)$

$=(\dfrac{24}{27}X \dfrac{3}{26})+(\dfrac{3}{27}X \dfrac{24}{26})\\=\dfrac{72}{702}+\dfrac{72}{702}\\=\dfrac{144}{702}\\=\dfrac{8}{39}$

(c)Probability that at least one woman is appointed.

The probability that at least one woman is appointed can occur in three ways.

A man is appointed first and a woman is appointed next.
A woman is appointed first and a man is appointed next.
Two women are appointed

P(at least one woman is appointed) $=P(MW)+P(WM)+P(WW)$

$P(WW)=\dfrac{3}{27}X \dfrac{2}{26}=\dfrac{6}{702}$

In Part B, $P(MW)+P(WM)=\frac{8}{39}$

Therefore:

$P(MW)+P(WM)+P(WW)=\dfrac{8}{39}+\dfrac{6}{702}\\$P(at least one woman is appointed)=\dfrac{25}{117}$

5 0

3 years ago

The radius of a circle is 8 feet. What is the area of sector bounded by a 90° arc?

Lera25 [3.4K]

Since 90 degree is 1/4 of a circle, the area will be 1/4 th area of the full circle.

The radius is given by, r = 8 ft, therefore, the area of the full circle is,

$\begin{gathered} A=\pi\times r^2 \\ A=3.14\times8^2=200.96ft^2 \end{gathered}$

Therefore, the area of the sector is,

$A^{\prime}=\frac{1}{4}\times200.96ft^2=50.24ft^2$ $\begin{gathered} A^{\prime}=\frac{\theta}{360}\times\pi\times r^2 \\ \text{ =}\frac{\text{90}}{360}\times\pi\times8^2 \\ \text{ =}\frac{1}{4}\pi\times64=16\pi \end{gathered}$

4 0

2 years ago

Two thirds of a number is 46, what is the number

Thepotemich [5.8K]

Answer:

Step-by-step explanation:

If 46 is 2/3 then 1/3 should be 23 and 23 times 3 is 69.I hope this helps

5 0

3 years ago