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2 years ago

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A diagonal of a parallelogram is 50 inches long and makes angles of 37.1° and 49.2° with the sides. Solve for the longest side o

f the parallelogram.
A)30 in.
B)38 in.
C)40 in.
D)66 in.

2 answers:

kodGreya [7K]2 years ago

3 0

The solution is attached as a word file

Musya8 [376]2 years ago

3 0

The correct answer would be 38 inches

Let me know if you need me to show my work, i'm too lazy to type it, haha

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F(x)=3x 2 +9f, left parenthesis, x, right parenthesis, equals, 3, x, squared, plus, 9 and g(x)=\dfrac{1}{3}x^2-9g(x)= 3 1 x 2

34kurt

Answer:

$f(g(x)) = \frac{1}{3}x^4 - 18x^2 + 252$

$g(f(x)) = 3x^4 + 18x^2 + 18$

<em>f(x) and g(x) and not inverse functions</em>

Step-by-step explanation:

Given

$f(x) = 3x^2 + 9$

$g(x) = \dfrac{1}{3}x^2 - 9$

Required

Determine f(g(x))

Determine g(f(x))

Determine if both functions are inverse:

Calculating f(g(x))

$f(x) = 3x^2 + 9$

$f(g(x)) = 3(\frac{1}{3}x^2 - 9)^2 + 9$

$f(g(x)) = 3(\frac{1}{3}x^2 - 9)(\frac{1}{3}x^2 - 9) + 9$

Expand Brackets

$f(g(x)) = (x^2 - 27)(\frac{1}{3}x^2 - 9) + 9$

$f(g(x)) = x^2(\frac{1}{3}x^2 - 9) - 27(\frac{1}{3}x^2 - 9) + 9$

$f(g(x)) = \frac{1}{3}x^4 - 9x^2 - 9x^2 + 243 + 9$

$f(g(x)) = \frac{1}{3}x^4 - 18x^2 + 252$

Calculating g(f(x))

$g(x) = \dfrac{1}{3}x^2 - 9$

$g(f(x)) = \frac{1}{3}(3x^2 + 9)^2 - 9$

$g(f(x)) = \frac{1}{3}(3x^2 + 9)(3x^2 + 9) - 9$

$g(f(x)) = (x^2 + 3)(3x^2 + 9) - 9$

Expand Brackets

$g(f(x)) = x^2(3x^2 + 9) + 3(3x^2 + 9) - 9$

$g(f(x)) = 3x^4 + 9x^2 + 9x^2 + 27 - 9$

$g(f(x)) = 3x^4 + 18x^2 + 18$

Checking for inverse functions

$f(x) = 3x^2 + 9$

Represent f(x) with y

$y = 3x^2 + 9$

Swap positions of x and y

$x = 3y^2 + 9$

Subtract 9 from both sides

$x - 9 = 3y^2 + 9 - 9$

$x - 9 = 3y^2$

$3y^2 = x - 9$

Divide through by 3

$\frac{3y^2}{3} = \frac{x}{3} - \frac{9}{3}$

$y^2 = \frac{x}{3} - 3$

Take square root of both sides

$\sqrt{y^2} = \sqrt{\frac{x}{3} - 3}$

$y = \sqrt{\frac{x}{3} - 3}$

Represent y with g(x)

$g(x) = \sqrt{\frac{x}{3} - 3}$

Note that the resulting value of g(x) is not the same as $g(x) = \dfrac{1}{3}x^2 - 9$

<em>Hence, f(x) and g(x) and not inverse functions</em>

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2 years ago

If 30% is lost by selling a sofa set for RS 980, at what price must it be sold to gain 10%.

PSYCHO15rus [73]

Answer:

1078

Step-by-step explanation:

first: multiply 980 by 0.10 to get 10% of 980

second: take that value (98) and add it to 980

then: you get 1078 after adding

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2 years ago

How many ounces of pure nickel must be added to 150 ounces of alloy 70% pure to make an alloy which is 85% pure?

galben [10]

Answer:

150 oz.

Step-by-step explanation:

There are already 150 ounces of alloy of nickel.

Of this 150 oz, 70% is pure i.e. nickel content = 150(0.7) = 105 oz

Now available is

Nickel Other metals

105 45

Let x oz of pure nickel is added.

Then new alloy will have 105+x oz nickel in total of 150+x oz.

Percentage pure = $\frac{105+x}{150+x} =85%$

Simplify to get

$\frac{105+x}{150+x} =\frac{85}{100} \\\\Cross multiply:\\85(150+x) =100(105+x)\\12750+85x =10500+100x\\100x-85x = 12750-10500\\15x = 2250\\x = 150$

Hence answer is 150 oz should be added.

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2 years ago

Javier deposited $250 into a savings account with an interest rate of 1.6%. He made no deposits or withdrawals for 9 months. If

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Answer:

A = 250(1 + 0.016)^0.75.

Step-by-step explanation:

9 months = 0.75 years

So A = 250(1 + 0.016)^0.75.

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2 years ago

The average of Johnny’s two tests is a 92. What must he get on a 3rd test to raise his average to a 94?

zheka24 [161]

Reread, take time, and concentrate

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2 years ago

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