Unit 10: Circles Homework 4: Inscribed Angles

Find each angle measure

The value of x in the direct and indirect varoation is calculated as: x = 2.

If k is the constant of proportionality among two or more variables (x, y, z), a combined equation of direct and indirect variation is, z = kx/y, if z varies directly with x and indirectly with y.

With the information stated, we would have the following:

z = kx/y³

Find k, by plugging in the values of x, y, and z:

12 = k(8/2³)

12 = k(8/8)

12 = k

k = 12

Find x when y = 1 and z = 24:

24 = 12(x)/1³

24 = 12x

24/12 = x

x = 2.

Therefore, the value of x in the direct and indirect varoation is calculated as: x = 2.

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Answer:

it is the last graph

Step-by-step explanation:

Answer:

The correct answer is D:-15,120

[tex]^{n}P_{r}=\dfrac{n!}{(n-r)!}\\\\\implies ^{9}P_5 = \dfrac{9!}{(9-5)!} =\dfrac{9!}{4!} = 15120[/tex]

The answer is D.

Step-by-step explanation:

Let w = width and h = height. Then we have

w = 3*h - 17

and

4*w + h = 30 (4 shelves and 1 sides).

Plug in the first equation into the second and solve for h:

4*(3*h - 12) + h = 30

12*h - 48 + h = 30

13*h = 78

h = 78/13

h = 6

Plug that in the first equation to find w = 3*6 - 17 = 1

So width = 1 feet.

height = 6 feet

Answer:

x > 2

Step-by-step explanation:

The graph starts at x = 2

The graph goes up and to the right so x can't be less than 2.

Answer:

  90°

Step-by-step explanation:

The angle between the vectors can be found any of several ways. Here, we observe that the segments from the origin to the two points are at right angles to each other. (Their slopes are opposite reciprocals.) Hence the angle between the vectors is 90°.

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The slope to point 'a' is y/x = 2/1 = 2.

The slope to point 'b' is y/x = (-1/2)/1 = -1/2.

The product of these slopes is (2)(-1/2) = -1, indicating the vectors are perpendicular. The angle between them is 90°.

__

We can also use the trig formula for the tangent of the difference of angles.

  tan(α-β) = (tan(α) -tan(β))/(1 +tan(α)tan(β))

The tangents are the slopes, calculated above, so we have ...

  tan(α -β) = (2 -(-1/2))/(1 +(2)(-1/2)) = (5/2)/0 = undefined

The tangent is undefined for angles that are odd multiples of 90°. The angle between the vectors is 90°.

Answer:

1

Step-by-step explanation:

Choose two points on the line:  (-5, 0) and (0, 5)

Let the first point [tex](x_1,y_1)[/tex] = (-5, 0)

Let the second point [tex](x_2,y_2)[/tex] = (0, 5)

Use the gradient formula:

[tex]\textsf{gradient}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{5-0}{0-(-5)}=1[/tex]

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If you want to find the equation of the line, use the point-gradient form of a linear equation:  [tex]y-y_1=m(x-x_1)[/tex]

(where [tex]m[/tex] is the gradient and [tex](x_1,y_1)[/tex] is a point on the line)

Substituting the values into the formula:

[tex]\implies y-0=1(x-(-5))[/tex]

[tex]\implies y-0=x+5[/tex]

[tex]\implies y=x+5[/tex]

Therefore, the equation of the line is y = x + 5

Answer: −5

Step-by-step explanation:

simplify: (−5)

Re-order terms so constants are on the left:

(−5)f(−5)−5

360 degrees / 24 hours = 15 degrees per hour

150 degrees / 15 degrees per hour = 10 hours

Answer: 10 hours

[tex]area \: = 78[/tex]

[tex]area = length \: \times \: width[/tex]

[tex]78 = (x)(2x + 1)[/tex]

[tex]x = 6[/tex]

Thus the dimensions are 6 & 13

Answer:

6&13.All you need to do is find the factors of 78 and plug the smaller number into the equation provided in the equation. 2x+1 is our equation. so6*13 is 78 and 2x+1=13... 6for x to get 2*6+1=13

Step-by-step explanation:

Step-by-step explanation:

Step 1: Take the First Derivative This means only differentiate once.

Disclaimer: Since absolute value only take positve outputs and quadratics only take positve outputs, we can get rid of the absolute value signs so we now have

[tex]e {}^{ {x}^{2} - 1 } [/tex]

We have the function x^2-1 composed into the function e^x.

So we use chain rule

Which states the derivative of a function composed is the

derivative of the main function times the derivative of the inside function.

So the derivative of the main function is

[tex] \frac{d}{dx} (e {}^{x} ) = e {}^{x} [/tex]

Then we replace x with x^2-1

[tex]e {}^{ {x}^{2} - 1} [/tex]

Then we take the derivative of the second function which is 2x so qe multiply them

[tex]e { }^{ {x}^{2} - 1 } 2x[/tex]

Step 2: Set the equation equal to zero.

[tex]e {}^{x {}^{2} - 1} 2x = 0[/tex]

Since e doesn't reach zero. We can just set 2x=0.

[tex]2x = 0 = x = 0[/tex]

So the critical point is 0.

Since e^x will never reach zero

Since 0 is the only critical point, this where the max or min will occur at.

Next we pick any numbergreater than zero, and plug them in the derivative function which gives us a positve number.

Any pick less than zero will give us a negative number.

Since the function is decreasing then increasing, we have a minimum.

Since 0 is the only critical point, we have a absolute minimum at 0.

To find the y coordinate, plug 0 in the orginal function.

Which gives us

[tex]e {}^{ {0}^{2} - 1 } = e {}^{ - 1} = \frac{1}{e} [/tex]

So the minimum occurs at

(0,1/e).

This is the war between the communist governmrnt of Vietnam North and the South Vietnam.  The United States of America were the main ally of the Vietnam south during the war.

The communist Vietnam North later united with the south with a common name Socialist Reepublic of Vietnam, After a fierce onslaught that took the life of about 58000 americans and over 2 million Vietnamese.

The influence of the Vietnam war in United States today

1. End of the drafts

The drafts is the method of conscription to the military that requires vitually every male between the age of 18 - 25 in United States to register with the selective service. since the end of the Vietnam war in 1975 the draft stopped hence no penalty for not registering to the draft.

2. Granting 18 years old the right to vote

26th Amendment of the United States Constitution gave right to vote to the 18 years old citizens. Today 18 tear old American has right to vote. This was evolvement of the war and still holds till date.

3. It is easier getting into a war than getting out of a war

Americans was pulling out of the Vietnam war when they suffered the huge massacre. This lesson was helpful for president George H W Bush during the 1991 Persian Gulf War were he systematically exited after liberating Kuwait

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Answer:

(7, -1)

Step-by-step explanation:

Let's remember our key words:

Down/up means to translate the y axis.

Right/left means to translate the x axis.

Now that we know what to do, let's look at our equation.

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A point located at (5, 3) is translated down 4 units and right 2 units.

Let's work on the x axis first.

It says that you are translating to the right. That means your value is going higher, so you go to the right 2. 5+2=7

So now that we have our x, (7), let's rewrite our equation. (7, 3)

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Next, let's do y.

The points are translating down. That means our value will lessen.

Since we are going down on our y axis by 4, we will subtract our current y coordinate with 4. 3-4=-1.

Now we know our y, so let's rewrite our equation with our new y. (7, -1).

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Our final coordinates are (7, -1).

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I hope this helps!

-No one

[tex]v(y) = 0[/tex]

[tex] - 32t + 105 = 0[/tex]

[tex]t = \frac{ - 105}{ - 32} = 3.28[/tex]

[tex]h = - 16(3.28) {}^{2} + 105(3.28) + 17[/tex]

[tex]h = 189.26[/tex]

Answer:

angles of triangle adds up to 180 degrees

Answer: 134. 89 $

Step-by-step explanation: Dina wishes to 1000$ deposit  into an investment account and then withdraw the total in the account in five years. She has the choice of two different accounts. Blue Star account: interest is earned at an annual interest rate of 6.13%  compounded weekly (52 weeks in a year). Red Star account: interest is earned at an annual interest rate of 5.95%  compounded continuously. Which investment account - Blue Star or Red Star - will result in the greatest total at the end of five years? What is the total after five years for this account? How much more is it than the total for the other account?

Answer: The domain of this function is any real number. More mathematically it is put as

-∞ < x <+∞

Answer:

The domain of this function is any real number. More mathematically it is put as

-∞ < x <+∞

Step-by-step explanation:

Answer:

g = -3, h = 4.

Step-by-step explanation:

5h - 2g = 26

2h + 2g = 2      Adding the 2 equations:

7h = 28

h = 4.

Substituting for h in the first equation:

5(4) - 2g = 26

-2g = 26 -20 = 6

g = -3.

The margin of error would tell how many percentage differs from  Harris County's sample

The range of reasonable means for Harris County's sample is 77.7 to 82.3

The given parameters are:

The range (R) is calculated as:

[tex]R = \bar x \pm E[/tex]

Substitute known values

[tex]R = 80 \pm 2.3[/tex]

Expand

[tex]R = (80 - 2.3,80 + 2.3)[/tex]

Evaluate the difference and sum

[tex]R = (77.7,82.3)[/tex]

Hence, the range of reasonable means for Harris County's sample is 77.7 to 82.3

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Using the Central Limit Theorem, it is found that the condition that applies to this test is:

C. The sample includes at least 30 employees from each department.

It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.

From this, since we have a skewed variable, it is found that a sample size of at least 30 is needed, hence option C is correct.

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Answer:

=57

Step-by-step explanation:

Multiply and divide left to right

then add and subtract left to right

Step-by-step explanation:

a)[tex] \sf \: Factor 6x2−3x \\ \sf {6x}^{2} −3x \\ \sf \: =3x(2x−1) \\ \sf \: Answer:3x(2x−1) \\ [/tex]

b)Let's factor x²+3x−28

⇒x²+3x−28

⇒x² - 4x + 7x - 28

⇒(x² - 4x) + (7x - 28)

⇒x( x - 4) + 7(x - 4)

⇒(x -4) (x + 7)

Answer:

(x−4)(x+7)

Answer:

28

Step-by-step explanation:

a is equal to 7,

so where there is 'a' you replace

with 7

4(7)=7×4=

28

Answer: first one is y=9x+5

second on is 4x-3y=-2

Step-by-step explanation:

Answer:

120

Step-by-step explanation: 4x10x2 +2x5x4 =80+40=120 cubic inches

Answer:

Step-by-step explanation:

Answer:

18 pupils

Step-by-step explanation:

11 like cola

32 like other stuff

11+32=43 - 50-43=7

therefore 11+7=18

18 students like cola the best

Answer:

7(3/bc)c

Step-by-step explanation:

3/bc+c+7

(3/bc)c+7

7(3/bc)c

Answer:

Step-by-step explanation:

Equation

Part A

# Calculators = Total amount / Cost of 1 calculator

Givens

# Calculators = ?

Total amount of money = 195 dollars

Cost of one calculator = 6.50

Solution

# Calculators = 195/6.50

# Calculators = 30

Answer: He can buy 30 calculators.

Answer:

⠀

Step-by-step explanation:

⠀

We know,

[tex] {\longrightarrow \qquad \boldsymbol{\pmb{Total \: \: surface \: \: area_{(cube)} = 6a {}^{2} }}}[/tex]

⠀

Where,

⠀

Now, Substituting the values in the formula :

⠀

[tex]{\longrightarrow \qquad \rm{{Total \: \: surface \: \: area_{(cube)} = \sf 6 \times( 2.5) {}^{2} }}}[/tex]

⠀

[tex]{\longrightarrow \qquad \rm{{Total \: \: surface \: \: area_{(cube)} = \sf 6 \times6.25 }}}[/tex]

⠀

[tex]{\longrightarrow \qquad \boldsymbol{ \pmb{Total \: \: surface \: \: area_{(cube)} = \it 37.5 }}}[/tex]

⠀

Therefore,

Answer:

37.5 cm²

Step-by-step explanation:

Given:-

To find:-

Solution:-

Total surface area of cube :- 6a²

6(2.5)² sq. cm

37.5 cm²