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Naily [24]
3 years ago
14

What are the values of a and b?

Mathematics
1 answer:
ivann1987 [24]3 years ago
3 0

Answer:

<h2>a = 400/21, b = 580/21</h2>

Step-by-step explanation:

Small triangles are similar. Therefore, the sides are proportional

\dfrac{a}{20}=\dfrac{20}{21}               <em>cross multiply</em>

21a=(20)(20)       <em>divide both sides by 21</em>

a=\dfrac{400}{21}

For b, we can use the Pythagorean theorem:

b^2=\left(\dfrac{400}{21}\right)^2+20^2\\\\b^2=\dfrac{160000}{441}+400\\\\b^2=\dfrac{160000}{441}+\dfrac{176400}{441}\\\\b^2=\dfrac{336400}{441}\to b=\sqrt{\dfrac{336400}{441}}\\\\b=\dfrac{\sqrt{336400}}{\sqrt{441}}\\\\b=\dfrac{580}{21}

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Frederick designed an experiment in which he spun a spinner 20 times and recorded the results of each spin.
Maru [420]

Answer:

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Step-by-step explanation:

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3 0
3 years ago
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A woman invested 4 times as much as 5% as she did at 6%. The total amount of interest she earns is 1 year from both accounts is
Mnenie [13.5K]

Answer:

at 5% interest, she invested $8,000

at 6% interest, she invested $2,000

Step-by-step explanation:

Let the invested amount at 5% interest = x

Let the invested amount at 6% interest = y

x = 4y - - - - (1) (A woman invested 4 times as much as 5% as she did at 6%)

5% of x = 0.05x

6% of y = 0.06y

0.05x + 0.06y = 520 - - - - (2) (The total amount of interest she earns is $520)

putting the value of x gotten in equation (1) into eqn (2):

0.05x + 0.06y = 520

where x = 4y

∴ 0.05(4y) + 0.06y = 520

0.2y + 0.06y = 520

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y = 520 ÷ 0.26

y = $2000

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x = 4y

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7 0
3 years ago
For which values of a does ???? a a − 4<br> a + 4 a<br> ???? have an inverse matrix?
Aleks [24]

Answer:

A =  \dfrac{1}{16}\begin{bmatrix}a &-(a-4) \\ -(a+4) & a\end{bmatrix}

Step-by-step explanation:

given,

Matrix =

A = \begin{bmatrix}a &a-4 \\ a+4 & a\end{bmatrix}

determinant of matrix

|A| = a×a - (a-4)(a+4)

|A| = a² - a² +16

|A| = 16

inverse of the matrix

to calculate inverse of two matrix interchange the term a₁₁ with a₂₂ and multiply the -ve with a₁₂ and a₂₁

the inverse is

A =  \dfrac{1}{16}\begin{bmatrix}a &-(a-4) \\ -(a+4) & a\end{bmatrix}

6 0
4 years ago
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Yanka [14]

Answer: 32

Step-by-step explanation:

The output is 1/3 of the input +2

8 0
3 years ago
5a (b - c) = d Solve for b
Allisa [31]
Solve for b:
5 a (b - c) = d
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4 years ago
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