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2 years ago

In the figure, mAB = 45° and mCD = 23°. The diagram is not drawn to scale.

Mathematics

1 answer:

Yakvenalex [24]2 years ago

4 0

Answer:

Option A. $x=34\°$

Step-by-step explanation:

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

$x=\frac{1}{2}(arc\ CD+arc\ AB)$

substitute the values

$x=\frac{1}{2}(23\°+45\°)$

$x=34\°$

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A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, thi

marysya [2.9K]

For this problem, I think there is no need for the details of 12 inches width and 4 inches length. This is because an equation is already given. It was clearly specified that A as a function of θ represents the area of the opening. Then, we are asked to find exactly that: the area of opening. Moreover, the value of θ was also given. Therefore, I am quite sure that the initial details given are for the purpose of red herring only.

So, all we have to do is substitute θ=45° to the function given.
A = 16 sin 45° ⋅ (cos 45° + 1)

The angle 45° is a special angle in trigonometry. So, it would be easy to remember trigonometric functions of this angle. Sine of 45° is equal to √2/2 while cosine of 45° is also √2/2.

A = 16(√2/2) ⋅ (√2/2 + 1)
A = 8+8√2
A = 19.31 square inches

8 0

2 years ago

Read 2 more answers

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:

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

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

f(x) and g(x) and not inverse functions

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

Hence, f(x) and g(x) and not inverse functions

4 0

2 years ago

A share of stock in the Lofty Cheese Company is quoted at 251/4. Suppose you hold 30 shares of that stock, which you bought at 2

inn [45]

You'll make a profit of $150.

3 0

2 years ago

In developing an interval estimate for a population mean, a sample of 50 observations was used. the interval estimate was 19.76

alexandr402 [8]

The formula for interval estimate would be: μ = M ± Z(sM)

Where: μ is estimate

M is the mean

Z is the z value

(sM) is the standard error

μ = M ± Z(sM)

n = 200 rather than 50 (√200 = 2√50)

⇒ ME = (1/2) * 1.32 = .66

Using the formula above, plugging this in will give us: μ = 19.76 ± .66

= 19.76 ± .66 is the confidence interval or interval estimate

4 0

2 years ago

There are 360 people in my school. 15 take calculus, physics, and chemistry, and 15 don't take any of them. 180 take calculus. T

lesantik [10]

Answer:

150 students take physics.

Step-by-step explanation:

To solve this problem, we must build the Venn's Diagram of this set.

I am going to say that:

-The set A represents the students that take calculus.

-The set B represents the students that take physics

-The set C represents the students that take chemistry.

-The set D represents the students that do not take any of them.

We have that:

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

In which a is the number of students that take only calculus, $A \cap B$ is the number of students that take both calculus and physics, $A \cap C$ is the number of students that take both calculus and chemistry and $A \cap B \cap C$ is the number of students that take calculus, physics and chemistry.

By the same logic, we have:

$B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)$

$C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

This diagram has the following subsets:

$a,b,c,(A \cap B), (A \cap C), (B \cap C), (A \cap B \cap C), D$

There are 360 people in my school. This means that:

$a + b + c + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) + D = 360$

The problem states that:

15 take calculus, physics, and chemistry, so:

$A \cap B \cap C = 15$

15 don't take any of them, so:

$D = 15$

75 take both calculus and chemistry, so:

$A \cap C = 75$

75 take both physics and chemistry, so:

$B \cap C = 75$

30 take both physics and calculus, so:

$A \cap B = 30$

Solution:

The problem states that 180 take calculus. So

$a + (A \cap B) + (A \cap C) + (A \cap B \cap C) = 180$

$a + 30 + 75 + 15 = 180$

$a = 180 - 120$

$a = 60$

Twice as many students take chemistry as take physics:

It means that: $C = 2B$

$B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)$

$B = b + 75 + 30 + 15$

$B = b + 120$

-------------------------------

$C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

$C = c + 75 + 75 + 15$

$C = c + 165$

----------------------------------

Our interest is the number of student that take physics. We have to find B. For this we need to find b. We can write c as a function o b, and then replacing it in the equations that sums all the subsets.

$C = 2B$

$c + 165 = 2(b+120)$