40 (pts)
show work and answer(not multiple choice)
Quadrilateral OPQR is inscribed inside a circle as shown below. What is the measure of angle Q? You must show all work and calculations to receive credit.

Circle N is shown with an inscribed quadrilateral labeled OPQR. O is labeled 2x degrees. P is labeled y degrees. Q is labeled 2x plus 4 degrees. R is labeled 3y plus 8 degrees.

Answer:

[tex] \displaystyle y _{ \text{parallel}} = \frac{5}{6} x- 2[/tex]

Step-by-step explanation:

we are given a equation of line

[tex] \displaystyle y = \frac{5}{6} x - 10[/tex]

we want to figure out the line Parallel to the given line and passes through (12,8)

to figure out the parallel line we need to figure out two things one is the Slope of the parallel line another is the y-intercept of the parallel line

figuring out the slope of the parallel line is easy because we know that parallel lines have the same slope therefore,

[tex] \displaystyle m _{ \text{parallel}} = \frac{5}{6} [/tex]

now we need to figure out the y-intercept and the equation to do so we can consider the following formula:

[tex] \displaystyle y - y_{1} = m(x - x_{1})[/tex]

we the point where the parallel line passes i.e [tex](x_1,y_1)=(12,8)[/tex] and we already got that the slope is ⅚ thus substitute:

[tex] \displaystyle y - 8= \frac{5}{6} (x- 12)[/tex]

we can figure out the equation by simplifying the above equation to slope-intercept form in order to do so

distribute:

[tex] \displaystyle y - 8= \frac{5}{6} x- \frac{5}{6} \times 12[/tex]

reduce fraction:

[tex] \displaystyle y - 8= \frac{5}{6} x- 5 \times 2[/tex]

simplify multiplication:

[tex] \displaystyle y - 8= \frac{5}{6} x- 10[/tex]

add 8 to both sides:

[tex] \displaystyle y = \frac{5}{6} x- 2[/tex]

and we are done!

Answer:

[tex]\sqrt{85}  or 9.22[/tex]

Step-by-step explanation:

You need to remember the following equation:

[tex]a^{2} + b^{2} = c^{2}[/tex]

Where a and b is the lengths of the two sides and c is the hypotenuse.

So simply plug these values into this:

[tex]6^{2} + 7^{2} = h^{2}[/tex]

36 + 49 = h^2

36 + 49 = 85

So the hypotenuse is the square root of 85:

[tex]\sqrt{85}  = 9.22[/tex]

Answer:

$0.25 per pound.

Step-by-step explanation:

Let us find unit rate for both quantities.

[tex]\text{Price per pound}=\frac{8.75\text{ dollars}}{2.5\text{ pound}}[/tex]

[tex]\text{Price per pound}=3.5\frac{\text{ dollars}}{\text{ pound}}[/tex]  

Therefore, cost of per pound for first given rate is $3.5.

Now let us find unit rate for second quantity.

[tex]\text{Price per pound}=\frac{9.75\text{ dollars}}{3\text{ pound}}[/tex]

[tex]\text{Price per pound}=3.25\frac{\text{ dollars}}{\text{ pound}}[/tex]

We can see that price for second quantity is less than 1st. To find the savings per pound we will subtract 3.25 from 3.5.

[tex]\text{Savings per pound}=3.50-3.25[/tex]

[tex]\text{Savings per pound}=0.25[/tex]

Therefore, we will save $0.25 per pound by buying the least expensive.

Answer:

0.25

Step-by-step explanation:

Answer:  True, False, True

Step-by-step explanation:

To determine steepness, compare the coefficients of each function:

f(x) = 4x²      coefficient is: 4

g(x) = [tex]\dfrac{15}{4}x^2[/tex]   coefficient is: 4.75

h(x) = [tex]\dfrac{4}{15}x^2[/tex]   coefficient is: 0.27

f(x)  ??? h(x)

 4    >  0.27

f(x) is steeper than h(x)

               h(x) ??? g(x)

               0.27 <   4.75

               h(x) is LESS steep than g(x)

                                              g(x) ??? f(x)

                                              4.75 >   4

                                              g(x) is steeper than f(x)

Answer:

16 rotations.  

Step-by-step explanation:

We have been given that Shawn is coasting down a 500 cm long ramp on his inline skates. The wheels on his inline skates are 32 cm in circumference.

To find the number of rotations we will divide length of ramp by 32 as distance covered by wheels in one rotation will be equal to 32 cm.

[tex]\text{Number of rotations}=\frac{\text{Total distance}}{\text{Circumference of wheel}}[/tex]

[tex]\text{Number of rotations}=\frac{500}{32}[/tex]

[tex]\text{Number of rotations}=15.625\approx 16[/tex]

Therefore, each wheel must make 16 rotations while Shawn is coasting down the ramp.

C. It is not always possible to calculate theoretical probability in complex situations, but experimental probability can be calculated any time experiments can be run.

The advantage of experimental probability over theoretical probability is that option C. It is not always possible to calculate theoretical probability in complex situations, but experimental probability can be calculated any time experiments can be run.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Experimental probability is the probability where the probability of something is found by real experiments.

This is not computed by assuming or calculation.

Theoretical probability is the probability where the probability of something is found theoretically.

The probability is found using formulas and calculation.

So, it is not always possible to calculate theoretical probability in complex situations.

But experimental probability can be found in any case using experiments.

Hence the correct option is C.

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Answer:

767

Step-by-step explanation:

Plug the coordinates of the point in the equation and solve for b:

[tex] y=bx-2 \iff -3=4b-2 \iff 4b=-1 \iff b=-\dfrac{1}{4} [/tex]

Answer:

A F(x)=30x

Step-by-step explanation:

just plug number in to the equations to see which one matches

Answer: [tex]f(x)=30\cdot2^{2x}[/tex]

Step-by-step explanation:

Given: A wildlife preservation group records the number of squirrels in a city park.

The first count recorded = 30 squirrels.

A second count of 60 squirrels is recorded six months later, and 120 squirrels are counted at the end of one year.

The growth rate of squirrel=[tex]\frac{120}{30}=4=2^2[/tex]

The exponential growth equation is given by :-

[tex]y=Ab^n[/tex], where A is the initial amount , b is the growth rate and n is the time period.

If the growth rate remains constant, then the function represents the number of squirrels after x years is given by :-

[tex]f(x)=30\cdot(2^2)^x=30\cdot2^{2x}[/tex]

Answer: Zoe is closer to the actual product because 6.80 is closer to 6.8493 than 6.90 mathematically. Another way to estimate 6.8493 is to round to the nearest hundredth place: 6.85

Zoe will have an estimate closer to the actual product.

To determine who will have an estimate closer to the actual product, we can compare the rounding methods used by Zoe and Andrew. Zoe rounded 6 * 8493 to 6 * 8000, while Andrew rounded 6 * 8493 + 6 * 9000. In this case, Andrew's estimate will be closer to the actual product because he considered additional terms in his calculation.

Another way to estimate 6 * 8493 that would give a better estimate is to round each term separately before multiplying. For example, rounding 6 to 10 and 8493 to 8500, the estimate would be 10 * 8500 = 85,000.

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Answer:

It is 80

Step-by-step explanation:

This because of when we divided the number 400 by 15 we got 26.6' an infinite number this is how many times the survey 12/15 was taken then if we then times this by 3 we get 80 which is the amount of people who prefer their own dinner

Answer:

Given the function:

f(x) = the quantity of x squared plus 3x minus 4 , all over x plus 4

i,e

[tex]f(x) = \frac{x^2+3x-4}{x+4}[/tex]

or

[tex]f(x) = \frac{x^2+4x-x-4}{x+4}[/tex]

or

[tex]f(x) = \frac{x(x+4)-1(x+4)}{x+4}[/tex]

or

[tex]f(x) = \frac{(x+4)(x-1)}{x+4}[/tex]

⇒y= f(x) = x -1                 ......[1]

Find the x-intercepts and y-intercepts for the equation [1] ;

y-intercepts defined as the graph crosses the y-axis;

substitute x =0 to solve for y;

y = 0-1 = -1

y = -1

x-intercepts defined as the graph crosses the x-axis;

substitute y =0 to solve for x;

0 = x-1

or

x = 1

Plot these points (0 , -1) and (1, 0) on the graph for the given function as shown below.

Answer:

l = 20.5 cm

h = 17.5 cm

w =  9.5 cm

Step-by-step explanation:

Conditions

l+w =30     Solving for w     30 - l = w

h = l-3

V = l*w*h

Substituting in

V = l * (30-l) * (l-3)

   = (30l-l^2) (l-3)

   = 30 l^2 - l^3 - 90l + 3l^2

Combining like terms

Step-by-step solution

-l^3 + 33 l^2 - 90 l

To find the maximum we need to take the first derivative and then set it equal to zero

-3l^2 + 66l -90 = 0

Factor out a -3

-3 (l^2 -22l +30) =0

Using my calculator and the quadratic formula

l = 11 - sqrt(91)

l = 11 + sqrt(91)

l = 1.5 or 20.5  approximately

If l = 1. then

h= l-3   would be negative  so

l = 20.5

h = l-3

h = 17.5 approximately

w = 30-l = 9.5 approximately

Answer:

Step-by-step explanation:

Applying BODMAS here;

We first solve what is in the brackets:

9x - 81 -3 = -8x - 16

We then put the like terms together:

9x + 8x = -16 + 81 + 3

We then do the addition:

17x = -16 + 84

We then do the subtraction:

17x = 68

Simplifying this gives:

x = [tex]\frac{68}{17}[/tex] = 4

Answer:

Thus; Jupiter travels at 480 miles/m and in 6 minutes, it will travel 2880 miles.

Step-by-step explanation:

First to convert it you need to multiply 8 miles per second by 60 seconds because there are 60 seconds in a minute:

 8 miles    x    60 s 

1 second        1 min

The unit of seconds will cancel out so you will get 480 miles/ min

To get how far it travels in 6 min you need to multiply the speed by 6 minutes

480 miles   x  6 min = 2880

  1 min

The unit of minutes will cancel out to get 2880 miles

I hope this helps, sorry for my messy handwriting. If you have any questions feel free to ask me!

Choose a graph from the list of graph, like in the picture.

Answer: The triangle mentioned here is an acute angled triangle.

Step-by-step explanation: x+x+10+2x-6=180°(angle sum prop. of triangles)

               =                             4x+4=180°

               =                             4x=174°

               =                             x=44°

therefore, x=44°

                 ,x+10=44+10=54°

                 ,2x-6=2(44)-6=82°

Answer:

13 miles

Step-by-step explanation:

Write and solve an equation involving this information, using x as the distance traveled, in miles:

Cost(x) = $6.75 = $3.50 + ($0.25/mile)x

First, subtract $3.50 from both sides, obtaining:  $3.25 = ($.25/mile)x.

Next, divide both sides by $0.25/mile:

        $3.25

x = ------------------ = 13 miles

      $0.25/mile

The length of the taxi ride was 13 miles.

Answer:

left 3 units

down 1 unit

Step-by-step explanation:

The required transformation is obtained by shifting of 3 units left and 1 unit down. The correct options are (c) and (d).

The graph of a function can be transformed by either shifting it in the right, left, up or down.

When the transformation is rightwards, the function becomes as f(x - a).

The given functions are as below,

f(x) = [tex]2^{x - 6} + 3[/tex]

And, g(x) = [tex]2^{x - 3} + 2[/tex]

It can be rewritten as,

g(x) = [tex]2^{x - 3} + 2[/tex] = [tex]2^{x - 6 + 3} + 3 - 1[/tex]

It clearly shows as per the rule of transformation, f(x) is shifted 3 units left and 1 unit down to get g(x).

Hence, the parent function f(x) is shifted 3 units left and 1 unit down.

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Answer: length = 7 c, and width = 6 cm

Step-by-step explanation:

Answer:

The balance after 15 year is  $831.25 .

Step-by-step explanation:

Formula

[tex]Amount = P (1 + r)^{t}[/tex]

Where P is the principle and r is the rate of interest in the decimal form and t is the time.

As given

Caiden earned $475 from mowing lawns last summer.

He deposited this money in an account that pays an interest rate of 3.8% compounded annually.

Here

P = $475

3.8% is written in the decimal form.

[tex]= \frac{3.8}{100}[/tex]

= 0.038

r = 0.038

t = 15 years

Put in the formula

[tex]Amount = 475 (1 + 0.038)^{15}[/tex]

[tex]Amount = 475 (1.038)^{15}[/tex]

[tex]Amount = 475\times 1.75(Approx)[/tex]

Amount = $831.25

Therefore the balance after 15 year is  $831.25 .

Caiden will have approximately $850.91 in his account after 15 years of interest compounded annually at a rate of 3.8%.

In this problem, we're dealing with compound interest, not simple interest. The formula to calculate compound interest is: A = P (1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest; P is the principal amount (the initial money); r is the annual interest rate (in decimal); n is the number of times that interest is compounded per year; and t is the time the money is invested for in years. In this case, P equals $475, r equals 3.8/100 or 0.038 (transforming percentage to decimal), n is 1 (because the interest is compounded annually), and t is 15 years. Substituting these values into the formula gives: A = $475 (1 + 0.038/1)^(1*15). Calculate the bracketed part first, resulting in a figure around 1.038 and raise it to the power of 15, so we get a value around 1.7914. Multiply this by the initial amount of $475 to get the final balance after 15 years which will be approximately $850.91. Hence, Caiden will have $850.91 in his account after 15 years.

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Answer:

35.7

Step-by-step explanation:

First, you would calculate how many gallons of gasoline the car gets. To do this, divide your total mileage of 500 miles by the mpg (30). Now you know how many gallons of gasoline will be used by the car. After calculating, you get 16.67. Multiply this by how much it costs per gallon of gasoline, and you get an answer of $35.7.

Answer: 11.6 units.

Step-by-step explanation:

1. Plot the points as you can see in the graph attached.

2. As you can see, the lenght TA is 3 units.

3. Apply the formula for calculate the distance between two points, to calculate the length TP and TA. The formula is:

[tex]d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]

4. Therefore, you have:

[tex]TP=\sqrt{(1-3)^{2}+(4-0)^{2}}=4.47units[/tex]

[tex]AP=\sqrt{(4-3)^{2}+(4-0)^{2}}=4.12units[/tex]

5. The perimeter is the sum of the the lenght of each side, therefore:

[tex]Perimeter=3units+4.47units+4.12units\\Perimeter=11.59units[/tex]

6. To the nearest tenth unit:

[tex]Perimeter=11.6units[/tex]

Answer: 7 + 2/3(12) = 15

90/15 = $6 for adult tickets

Answer: [tex]10(512 – c) + 5c = 3,570[/tex]

Step-by-step explanation:

Given : The number of student tickets sold is represented by c.

For a school drama performance, student tickets cost $5 each and adult tickets cost $10 each.

The sellers collected $3,570 from 512 tickets sold.

Since , the total tickets sold = 512

Therefore , the number of adults ticket = [tex]512-c[/tex]

Now, cost of total child tickets : [tex]5c[/tex]

Cost of total adult tickets = [tex]10(512 – c)[/tex]

Now, according to the cost of the tickets , we have the following equation :-

[tex]10(512 – c) + 5c = 3,570[/tex]

Answer:

280 minutes

Step-by-step explanation:

First, you must find the miles per minute:

112/14 = 8

Then you must multiply the miles per minute by the amount of miles:

35 * 8 = 280

Answer:

The regular price was $93.03

Step-by-step explanation:

In order to find the regular price, divide the amount spent by the percentage of which she paid for it. Since it was 25% off, she paid 75% of the overall price.

$69.77/75% = $93.03