About how far does the flag have to travel to complete full rotation?1. 37.68 ft2. 75.36 ft3. 150.72 ft4. 452.16 ftPlease explain if possible!

About How Far Does The Flag Have To Travel To Complete Full Rotation?1. 37.68 Ft2. 75.36 Ft3. 150.72

Answers

Answer 1

Due to the circular shape, one complete rotation of the flag is equal to the circumference of a circle with radius 12 ft.

Then, use the following formula for the cirumference:

C = 2π·r

where r is the radius. In this case, r = 12 ft and π = 3.14. Replace the previous values into the formula for C:

C = 2(3.14)(12 ft)

C = 75.36 ft

Hence, the flag has to travel 75.36 ft to complete a full rotation


Related Questions

solve the given system of equations2y=x+93x-6y=-15

Answers

Answer:

No solutions

Explanation:

The given system of equations is

2y = x + 9

3x - 6y = -15

To solve the system, we first need to solve the first equation for x, so

2y = x + 9

2y - 9 = x + 9 - 9

2y - 9 = x

Then, replace x = 2y - 9 on the second equation

3x - 6y = -15

3(2y - 9) - 6y = -15

3(2y) + 3(-9) - 6y = -15

6y - 27 - 6y = -15

-27 = -15

Since -27 is not equal to -15, we get that this system of equation doesn't have solutions.

If h(x)=-3x and g(x)=2x-1 what input value would make h(x)=12?

Answers

The question gives the function h(x) as

[tex]h(x)=-3x[/tex]

To find the value that will make the function 12, we equate the function to 12, such that

[tex]-3x=12[/tex]

Solving to get x, we have

[tex]\begin{gathered} x=\frac{12}{-3} \\ x=4 \end{gathered}[/tex]

Therefore, h(x) = 12 when x = 4.

In the figure, LMN is congruent to QRS.What is the value of x and y?

Answers

If they are congruent, then;

3x + 5 = 2x + 10

collect like term

3x - 2x = 10 - 5

x = 5

Similarly,

y + 6 = 2y - 12

collect like term

2y - y = 6 + 12

y = 18

What is the parallel slope to this equation? f(x)=-5x + 6

Answers

Remember the equation of a line with slope m and y-intercept b:

[tex]y=mx+b[/tex]

Which can be expressed in terms of functions by replacing y=f(x)

[tex]f(x)=mx+b[/tex]

Any line with the same slope will be parallel to that equation.

By comparing with:

[tex]f(x)=-5x+6[/tex]

We can know that its slope is equal to -5.

Since the "parallel slope" is just the slope, then

The system of equations y= -x - 1 is graphed. what is the solution to the system of equations ?

Answers

We solve as follows:

*First: Given one function, we corroborate and find the second one.

*We have that the first function passes by the points (0, -1) & (1, 0); we find its function:

[tex]m=[/tex]

A property owner paid $960 for the tiles to cover a 800 sq. ft yard. Then he decided to tile an additional 260 sq. ft. How much will be paid for the additional tiles?

Answers

Answer:

$312 will be paid for the addditional tile

Explanation:

Given that the property owner paid $960 for tiles to cover a 800 sq. ft yard

Since he decided to tile an additional 260 sq. ft, to know how much will be paid for the additional tiles, we need to know how much he paid for each of the last set of tiles.

The amount is

960/800 = 1.2

He paid $1.2 per tile.

For 260 sq. ft, he will pay:

$1.2 * 260

= $312

The circumference of the hub cap of a tire is 79.63 centimeters. Find the area of this hub cap. Us3.14 for a. Use pencil and paper. If the circumference of the hub cap were smaller, explain how twould change the area of the hub cap.The area of this hub cap is about square centimeters.(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearestthousandth as needed.)

Answers

Recall that the circumference of a circle is given by the following formula:

[tex]C=2\pi r,[/tex]

where r is the radius of the circle.

We are given that:

[tex]79.63cm=2\pi r,[/tex]

therefore:

[tex]r=\frac{79.63}{2*\pi}cm.[/tex]

Now, the area of a circle is given by the following formula:

[tex]A=\pi r^2,[/tex]

Therefore, the area of the hub cap is:

[tex]A=\pi *(\frac{79.63cm}{2})^2*\frac{1}{\pi^2}\approx505cm^2.[/tex]

Answer:

[tex]\begin{equation*} 505cm^2. \end{equation*}[/tex]

Given that the radius of the circle and the circumference are proportionally related, if the circumference is smaller then the radius is smaller. The area is proportionally related to the radius squared, therefore, a smaller circumference implies a smaller radius which implies a smaller area.

Elisa's school is selling tickets to a choral performance. On the first day of ticket sales the school sold 8 senior citizen tickets and 5 child tickets for a total of $94. The school took in $152 on the second day by selling 4 senior citizen tickets and 10 child tickets. What is the price each of one senior citizen ticket and one child ticket?

Answers

Let's define the next variables:

x: price of one senior ticket

y: the price of one child ticket

On the first day of ticket sales, the school sold 8 senior citizen tickets and 5 child tickets for a total of $94. That is:

8x + 5y = 94 (eq. 1)

The school took in $152 on the second day by selling 4 senior citizen tickets and 10 child tickets. That is:

4x + 10y = 152 (eq. 2)

Multiplying equation 2 by 2, we get:

2(4x + 10y) = 2*152

8x + 20y = 304 (eq. 3)

Subtracting equation 1 to equation 3, we get:

8x + 20y = 304

-

8x + 5y = 94

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

15y = 210

y = 210/15

y = 14

Substituting this result into equation 1:

8x + 5(14) = 94

8x + 70 = 94

8x = 94 - 70

8x = 24

x = 24/8

x = 3

Each senior citizen ticket cost $3 and each child ticket cost $14

Consider the following graph. Explain why it is possible to find an Euler circuit for this graph. Then, using Fleury's algorithm, identify and draw an Euler circuit starting with point A and choosing the first edge as A to F. Show all work using the required method. Draw the graph properly. (If you choose not to draw on my graph, then draw a LARGE graph on your paper.)

Answers

The Euler circuit for the graph using Fleury's algorithm is attached below.

The following steps are to be used to form the circuit.

Of the three edges coming from vertex "2" should I choose? We avoid choosing the edge "2-3" because it is a bridge and we cannot return to "3".

Any of the two remaining edges is ours to choose. Let's say we choose "2-0." By eliminating this edge, we can travel to vertex "0."

We pick the one edge from vertex "0" that is present, remove it, and then move to vertex "1." The Euler tour changes to "2-0 0-1."

We take the lone edge from vertex "1," delete it, and then move to vertex "2." The Euler tour is now "2-0 0-1 1-2."

Once more, vertex 2 has just one edge, so we pick it, remove it, and continue on to vertex 3.

Hence we get the required circuit.

The term "Eulerian graph" has two different meanings in graph theory. One interpretation applies to a graph with an Eulerian circuit, whereas the other applies to a graph where each vertex has an even degree. These definitions apply to linked graphs.

To learn more about Euler circuit visit:

https://brainly.com/question/22089241

#SPJ9

Use the graph to respond to the questions. 6a. What is the height of the ball before its thrown? b. Approximately how high in the air did the ball go? C. NWAOOOOO INW Approximately long did it take the ball to reach the max height? d. How long was the ball in the air? 34(0.3) 2 e. (-0.2.0) -2 -1 (3.0) t 3 4 What does the point (3, 0) tell us about this situation? 1 INV

Answers

Given data:

The given graph is shown.

a)

The initial height of the ball is 3 units.

b)

The maximum height of the ball is approx 12.5 units.

c)

The time taken by the ball to reach maximum height is 1.5 units.

d)

The time ball was in air is 3 units.

e)

The point (3,0) denoted the coordinate of time is 3 when height is zero.

Convert 59°F to degrees Celsius.If necessary, round your answer to the nearest tenth of a degree.Here are the formulas.C= (5/9) (F -32).

Answers

15 ° C

Explanation

to convert form Farenheit to Celcius degree we need to use the formula

[tex]C=\frac{5}{9}(F-32)[/tex]

then

Let

F=59

now, replace and evaluate

[tex]\begin{gathered} C=\frac{5}{9}(F-32) \\ C=\frac{5}{9}(59-32) \\ C=\frac{5}{9}(27) \\ C=15 \end{gathered}[/tex]

therefore, the answer is

15 ° C

I hope this helps you

a. Make a scatter plot of the data in the table below.b. Does it appear that a linear model or an exponential model is the better fit for the data?

Answers

a) Option C

b) A linear model

Explanation:

To determine the correct plot from the options, we trace the x and y values given

Option A:

When x = 5, y = 1

when x = 6.6, y = 2

We see this is exact opposite of the values in the given table

Option B:

when x = 5, y = 5

when x = 6.6, y = 6.6

This is also different from the given values in the table

Option C:

when x = 1, y = 5

when x = 2, y = 6.6

when x = 3, y = 8.4

This is the same as the given values in the table.

Hence, the correct scatter plot is option C

We need to check if the points are linear:

[tex]\begin{gathered} u\sin g\text{ any two points on the table,} \\ \text{rate = }\frac{6.6\text{ - 5}}{2-1}\text{ = 1.6/1 = 1.6} \\ \text{rate = }\frac{8.4\text{ - 6.6}}{3-2}\text{ = 1.8/1 = 1.8} \\ \text{rate = }\frac{10.2\text{ - 8.4}}{3\text{ - 2}}\text{ = 1.8/1 = 1.8} \\ \text{rate = }\frac{12-10.2}{4-3}\text{ = 1.2/1 = 1.2} \end{gathered}[/tex]

A linear model fit the data

When simplified, |9+ (4-3) – 17| has a value of ______.

Answers

We have the following expression:

[tex]|9+(4-3)-17|[/tex]

First, let's solve the operation inside the parenthesis.

[tex]|9+1-17|[/tex]

Second, we add and subtract accordingly.

[tex]\lvert-7\rvert[/tex]

Third, we apply the absolute value property.

[tex]\lvert-7\rvert=7[/tex]

In conclusion, the values is 7

ans (alpha particles) at Figure 127 Exercises 12.6. complete the following: Find the intercepts and domain and perform the symmetry test (a) 9x^2 - 16y^2 = 144

Answers

We have that the general equation of the hyperbola is the following:

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]

where 'a' and '-a' are the x-intercepts.

In this case, we have the following equation:

[tex]9x^2-16y^2=144[/tex]

then, we have to divide both sides by 144 to get on the right side 1, thus, we have the following:

[tex]\begin{gathered} (9x^2-16y^2=144)(\frac{1}{144}) \\ \Rightarrow\frac{9}{144}x^2-\frac{16}{144}y^2=1 \\ \Rightarrow\frac{x^2}{16}-\frac{y^2}{9}=1 \end{gathered}[/tex]

now, notice that we have that:

[tex]a^2=16[/tex]

then, the x-intercepts are:

[tex]\begin{gathered} a^2=16 \\ \Rightarrow a=\pm\sqrt[]{16}=\pm4 \\ a_1=4 \\ \text{and} \\ a_2=-4 \end{gathered}[/tex]

therefore, the x-intercepts are 4 and -4.

Now that we know that the intercepts are on those points, we can see that the hyperbola has the following graph:

we can see that the hyperbola is not defined between -4 and 4, therefore, the domain of the hyperbola is:

[tex](-\infty,-4\rbrack\cup\lbrack4,\infty)[/tex]

finally, to perform the symmetry test, we have to check first both axis simmetries by changing x to -x and y to -y:

[tex]\begin{gathered} \frac{x^2}{16}-\frac{(-y)^2}{9}=1 \\ \Rightarrow\frac{x^2}{16}-\frac{y^2}{9}=1 \\ then \\ \frac{(-x)^2}{16}-\frac{y^2}{9}=1 \\ \Rightarrow\frac{x^2}{16}-\frac{y^2}{9}=1 \end{gathered}[/tex]

since the hyperbola got symmetry about the x-axis and the y-axis, we have that the hyperbola got symmetry about the origin

Find the midpoint and distance on points (5,5) and (-1,3)

Answers

Given:

Two points (5, 5) and (-1, 3).

To find the midpoint and distance:

Using the midpoint formula,

[tex]\begin{gathered} m=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ =(\frac{5-1}{2},\frac{5+3}{2}) \\ =(\frac{4}{2},\frac{8}{2}) \\ =(2,4) \end{gathered}[/tex]

Thus, the mid-point formula is (2, 4).

Using the distance formula,

[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2_{}} \\ =\sqrt[]{(-1-5)^2+(3-5)^2} \\ =\sqrt[]{(-6)^2+(-2)^2} \\ =\sqrt[]{36+4} \\ =\sqrt[]{40} \\ =2\sqrt[]{10}\text{ units} \end{gathered}[/tex]

Thus, the distance between the two points is,

[tex]2\sqrt[]{10}units[/tex]

What is the equation of the line shiwn graphed below

Answers

we are given the horizontal line. To determine the equation of this line let's remember that the equation of any horizontal line is of the form:

[tex]y=k[/tex]

Where "k" is the point where the line touches the y-axis, in this case, the equation of the line is:

[tex]y=4[/tex]

Can you please help me with this question D and E

Answers

Solution

Part d

T= -2ºC, V=15 km/hr

We can convert to F and mi/h like this:

T= 1.8*(-2)+ 32= 28.4ºF

Ms= As/0.62= 15 km/hr /0.62= 24.19 mi/hr

Replacing we have:

[tex]WC=35.74+0.6215\cdot(28.4)-35.75(24.19^{0.16})+0.4275(28.4)(24.19^{0.16})[/tex]

Solving we got:

[tex]WC=35.74+17.651-59.519+20.213=14.08[/tex]

Rounded to one decimal we got:

14.1

Part e

T= 10ºC = 1.8(10)+ 32=50ºF

Ms = 34 km/hr

Ms= As/0.62= 34 km/hr/ 0.62= 54.84 mi/hr

Replacing we got:

[tex]WC=35.74+0.6215\cdot(50)-35.75\cdot(54.84^{0.16})+0.4275(50)(54.84^{0.16})[/tex][tex]WC=35.74+31.075-67.847+40.566=39.53[/tex]

Rounded to the nearest tenth we got:

39,5

Althought the reported temperature is 50 ºFahrenheit, because of wind it feels like 39.5 Fahrenheit

Section 1- Question 10Use the quadratic formula to solve the following equation:4m2-7m +2=57+√97A87+√17B87 + √1C87+√-63D8

Answers

The Solution:

Given:

[tex]4m^2-7m+2=5[/tex]

We are required to use the Quadratic Formula to solve the equation above.

[tex]\begin{gathered} 4m^2-7m+2-5=0 \\ 4m^2-7m-3=0 \end{gathered}[/tex]

The Quadratic Formula is:

[tex]m=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case:

[tex]\begin{gathered} a=4 \\ b=-7 \\ c=-3 \end{gathered}[/tex]

Substitute:

[tex]m=\frac{-(-7)\pm\sqrt{(-7)^2-4(4)(-3)}}{2(4)}[/tex][tex]m=\frac{7\pm\sqrt{49+48}}{8}=\frac{7\pm\sqrt{97}}{8}[/tex]

Therefore, the correct answer is [option A]

A building has two sizes of apartments, small and regular. The ratio of small apartments to regular apartments is 6 to 18. What percent of apartments in the building are small?

Answers

25 percent. You have 24 total apartments so 6/24 is .25, or 25 percent.

I would like someone to help me so I can understand what to do. Pls anyone

Answers

we have that

2 cups in a pint

2 pints in a quart

4 quarts in a gallon

so

4 cups in 2 pints

4 cups in a quart

16 cups in 4 quarts

16 cups in a gallon

and

we have

3 parts red and 5 parts yellow

3 parts +5 parts=8 parts

8 parts=1 gallon

red paint fraction is 3/8 gallon

yellow paint fraction is 5/8 gallon

Remember that

I need 16 cups for a gallon

Apply proportion

16/1=x/(3/8)

x=(3/8)16

x=6 cups

Which function is nonlinear?Which equation represents a nonlinear function? (Let me know if you can’t read the possible answers for the equation and I will send them)

Answers

Given:

There are 4 equation representations are given.

To find:

The nonlinear equation.

Explanation:

A)

[tex]\begin{gathered} 3x-2y=7 \\ i.e)3x-2y-7=0 \end{gathered}[/tex]

Which is of the linear form,

[tex]ax+by+c=0[/tex]

B)

[tex]y=\frac{2}{3}x+8[/tex]

Which is of the linear form,

[tex]y=mx+c[/tex]

C)

Let us consider the two points.

[tex](5,0),(6,2)[/tex]

Using the two-point formula,

[tex]\begin{gathered} \frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1} \\ \frac{y-0}{2-0}=\frac{x-5}{6-5} \\ \frac{y}{2}=\frac{x-5}{1} \\ y=2x-10 \end{gathered}[/tex]

Substituting the first point to verify the linear equation,

[tex]\begin{gathered} -4=2(3)-10 \\ -4=-4 \end{gathered}[/tex]

Therefore, the linear equation is satisfied for all 4 points.

Thus, options A, B, and C are linear equation.

So, the nonlinear equation must be given options D.

Final answer:

The correct option is D.

18. Light Bulbs: The mean lifespan of a standard 60 watt incandescent light bulb is 875 hours with a standard deviation of 80 hours. The mean lifespan of a standard 14 watt compact fluorescent light bulb (CFL) is 10,000 hours with a standard deviation of 1,500 hours. These two bulbs put out about the same amount of light. Assume the lifespan’s of both types of bulbs are normally distributed to answer the following questions. (a) I select one incandescent light bulb and put it in my barn. It seems to last forever and I estimate that it has lasted more than 2000 hours. What is the probability of selecting a random incandescent light bulb and having it last 2000 hours or more. Did something unusual happen here? (b) I select one CFL bulb and put it in the bathroom. It doesn’t seem to last very long and I estimate that it has lasted less than 5,000 hours. What is the probability of selecting a random CFL and having it last less than 5,000 hours. Did something unusual happen here? (c) Compare the the lifespan of the middle 99% of all incandescent and CFL light bulbs. (d) Is there much of a chance that I happen to buy an incandescent light bulb that lasts longer than a randomly selected CFL?

Answers

Set

[tex]\begin{gathered} \mu_1=875,\sigma_1=80 \\ \text{and} \\ \mu_2=10000,\sigma=1500 \end{gathered}[/tex]

a) The Z-score formula is

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

Therefore, in our case, if x=2000

[tex]\Rightarrow Z=\frac{2000-875}{80}=\frac{1125}{80}=14.0625[/tex]

Using a Z-score table,

[tex]\begin{gathered} P(z\ge2000)=1-P(z<2000)\approx1-1=0 \\ \Rightarrow P(z\ge2000)=0 \end{gathered}[/tex]

A value of 2000 hrs is 14 standard deviations away from the mean. The probability is practically zero.

b) Similarly, set x=5000; then,

[tex]Z=\frac{5000-10000}{1500}=-\frac{5000}{1500}=-3.333\ldots[/tex]

Thus, using a z-score table

[tex]P(z\le5000)=0.0004[/tex]

The probability is 0.0004=0.04%. It is quite improbable but not an impossible event.

c) According to the empirical rule 99.8% of the data lies within 3 standard deviations; thus,

[tex]\begin{gathered} Incandescent \\ \mu_1\pm3\sigma_1=\lbrack875-240,875+240\rbrack=\lbrack635,1115\rbrack \\ \text{CFL} \\ \mu_2\pm3\sigma_2=\lbrack10000-4500,10000+4500\rbrack=\lbrack5500,14500\rbrack \end{gathered}[/tex]

The lifespan of 99% of all incandescent bulbs is between 635 and 1115 hrs, whereas that of all CFL bulbs is between 5500 and 14500 hrs.

d) If we randomly select a CFL, the most probably lifespan is the mean of the distribution, in other words, 10000 hrs.

The probability of an incandescent bulb lasting 10000 hrs is

[tex]\begin{gathered} Z=\frac{10000-875}{80}=114.0625 \\ \Rightarrow P(z\ge10000)=1-P(z<10000)=0 \end{gathered}[/tex]

The event is practically impossible.

Which of the following is not a step in solving the equation 3/x = 8/7 (1) Divide both sides of the equation by 8(2) Use cross products to write the equation 3.7 =8x(3) Divide both sides of the equation by 3(4) Rewrite 3.7 as 21

Answers

Let's solve the equation:

3/x = 8/7

8x = 3 * 7 Cross product

8x = 21 Rewrite 3 * 7 as 21

Dividing both sides by 8:

8x/8 = 21/8

x = 2.625

As you can see, we do not follow step 3. Divide both sides of the equation by 3.

How would you solve this question or similar questions? It is solving for x.

Answers

Given the initial expression

[tex]\sqrt[]{2x+3}=\sqrt[]{2x}+3[/tex]

Then,

[tex]\begin{gathered} \sqrt[]{2x+3}=\sqrt[]{2x}+3 \\ \Rightarrow(\sqrt[]{2x+3})^2=(\sqrt[]{2x}+3)^2 \\ \Rightarrow2x+3=2x+6\sqrt[]{2x}+9 \end{gathered}[/tex]

Therefore,

[tex]\begin{gathered} \Rightarrow3=6\sqrt[]{2x}+9 \\ \Rightarrow-6=6\sqrt[]{2x} \\ \Rightarrow\sqrt[]{2x}=-\frac{6}{6}=-1 \\ \Rightarrow\sqrt[]{2x}=-1 \\ \Rightarrow\sqrt[]{2}\sqrt[]{x}=-1 \\ \Rightarrow\sqrt[]{x}=-\frac{1}{\sqrt[]{2}} \end{gathered}[/tex]

And sqrt(x)>=0 for any real number.

Therefore, there is no real solution to the equation.

In right triangle XYZ, the hypotenuse measures 14 inches and one leg measures 10 inches. Find the length of the other leg. Show your work and write your answer in simplest radical form.

Answers

As per given by the question,

There are given that a triangle XYZ, and the hypotenuse of the triangle is 14 in., and one leg is 10 in.

Now,

First draw the triangle XYZ.

Now,

From the triangle XYZ, XZ is hypotenuse of the triangle, XY is the first leg of the triangle, and YZ is second leg of the triangle.

So,

First leg z is 10, then find the value of second leg x.

Then,

To find the value of second leg, here use pythagoras theorem.

So,

From the pythagoras theorem;

[tex]XY^2+YZ^{2^{}^{}}=XZ^2[/tex]

Now,

[tex]\begin{gathered} XY^2+YZ^2=XZ^2 \\ 10^2+x^2=14^2 \\ 100+x^2=196 \\ x^2=196-100 \\ x^2=96 \end{gathered}[/tex]

Then,

[tex]\begin{gathered} x^2=96 \\ x=\sqrt{96}^{} \\ x=9.79 \end{gathered}[/tex]

Hence, the length of the other leg is 9.79.

Last week you worked 28 hours, and earned $266. What is your hourly pay rate? $ per hour Give your answer in dollars and cents (like 5.50)

Answers

1) Gathering the data

Last week

28 worked hours = $266

What is your hourly pay rate?

2) To find out that, let's set a proportion

Worked hours $

28------------------------ 266

1--------------------------- x

Let's use the fundamental property of a proportion that allows us to cross multiply the ratios of that proportion

So the hourly pay rate is approximately $11.08 per hour.

whats the constant proportionality of the table. x 30 24 9 y 10 8 3

Answers

Let:

y = kx

Where:

k = constant proportionality of the table

If x = 30, y = 10:

10 = k30

Solving for k:

k = 10/30 = 1/3

Verify the answer:

If x = 24, y = 8:

y = kx = 1/3*24 =24/3 = 8

Therefore, the constant proportionality of the table is 1/3

The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 34minutes of calls is $25.92, and the remaining credit after 53 minutes of calls is $23.64. What is the remaining credit after 71 minutes of calls?

Answers

The remaining credit after 71 minutes is $21.48

To solve this, we can calculate the equation of the linear function that represents the remaining credit

x is the time in minutes, y is the remaining credit. the we have two points of the line and we can calculate the equation

34 min and $25.92 => (34,25.92)

53 min and 23.64 => (53,23.64)

the formula to calculate the slope of a line is

[tex]m=\frac{y_2-y_1}{x_2-x_1_{}}=\frac{23.64-25.92}{53-34}=-0.12[/tex]

now we know the slope, we can get the line euqation

[tex]y=m(x-x_1)+y_1\Rightarrow\text{ y=-0.12(x-34)+25.92=-0.12x+30}[/tex]

Now for wathever x we ask, just plug it in to the equation and will give you the reamining credit.

for x=71 min:

[tex]y=-0.12(71)+30=-8.52+30=21.48[/tex]

theremaining credit is $21.48.

I need help answering this question and the solution set

Answers

Let's first try to rewrite the expression to see if we can write it in a fomr more familiar:

[tex]\begin{gathered} x-\sqrt{10-3x}=0, \\ x=\sqrt{10-3x}, \\ x^2=10-3x, \\ x^2+3x-10=0. \end{gathered}[/tex]

This is the same equation, but now we recognize a quadratic expression equal to 0. We can use the quadratic formula to find the solutions of this equation:

[tex]x_{1,2}=\frac{-3\pm\sqrt{3^2-4\cdot1\cdot(-10)}}{2\cdot1}[/tex]

And solve:

[tex]\begin{gathered} x_{1,2}=\frac{-3\pm\sqrt{9+40}}{2}=\frac{-3\pm7}{2} \\ x_1=\frac{-3+7}{2}=\frac{4}{2}=2 \\ x_2=\frac{-3-7}{2}=\frac{-10}{2}=-5 \end{gathered}[/tex]

Thus, the solution set of the equation is x = -5, x = 2

I A bar of gold is 10 cm long,5 cm wide, and 7 cm high. What is it's volume?

Answers

Assuming the bar of gold has a rectangular form, its volume would be the product between all three dimensions.

[tex]A=10\operatorname{cm}\cdot5\operatorname{cm}\cdot7\operatorname{cm}=350\operatorname{cm}^3[/tex]

Therefore, the volume is 350 cubic centimeters.

19.3 g/cm³
Explained- Density of a substance refers to the mass of the substance per unit volume.
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6 a. Sketch a reflection triangleAABC about the line y - X.Label the image AA'B'C'. I know youdon't have graph paper, just sketch.b. What are the coordinates of C'? Write down the first five terms of the sequence an=(n+4)!2n2+6n+7a1 = a2 = a3 = a4 = a5 = You can only use a Boolean Operator one time in a search string. True False What does the constant 0.98 reveal about the rate of change of the quantity? Select the correct answer.Which is the best definition of anabolic steroids?O A.a synthetic version of the hormone testosterone B.a vitamin supplement that increasesmuscle massC.a prescribed medicine that helps athletes recover from injuries help me with this 1. They must write the end of this story in English using the key words in the box (strange, dark, noise, silence and door)2. You must invent a creative ending, consistent with the story presented and without grammatical errors.3. The end of this story must have a minimum of 5 lines and a maximum of 10 linesscary storyIt's a rainy night. Kate is home alone watching TV on the sofa. A thunder roars, and she realizes that she's always hated storms. The wind, outside, shakes the trees, and hits the windows with deep fury.I hate storms she says to herself in a whisper. She is thirsty, so she goes to the kitchen to drink some water.Suddenly the lights go out. Luckily, there are some candles in the drawer. She lights 2 of them, drink her water, and comes back to the living-roomThere's complete silence in the house. The only sound she hears comes from the outside: it's the rain hitting the roof. kate shivers Use sigma notation to represent the sum of the first eight terms of the following sequence: 4,7. 10, Hi! I just wanted to know may you please help me on knowing how to solve an inequality? I did 4/cos(62) but it didn't give me any of the answer options Write a paragraph that tells readers what impact new technologies had on the development of industry in the Gilded Age. Will give brainliest for the first correct answer! Write an explanation of how you solved the problem. Write the explanation so that another student could follow your thought process. A zero-coupon bond is a bond that is sold now at a discount and will pay its face value at the time when it matures; no interest payments are made.A zero-coupon bond can be redeemed in 20 years for $10,000.How much should you be willing to pay for it now if you want the following returns?(a) 8% compounded daily(b) 8% compounded continuously The number of cups of strawberries in a shortcake recipe is proportional to the number of cups of sugar in the recipe. The recipe uses 5 cups of strawberries per 1/4 cup of sugar.PART A - What is the constant of proportionality for the relationship between cups of strawberries and cups of sugar Use substitution to determine the solution of the system of equations. Write the solution as an ordered pair.x + 2y = 14y = 3x 14solution = In KLM, l = 710 cm, k = 130 cm and K=161. Find all possible values of L, to the nearest 10th of a degree. PLEASE HELP a person must score in the upper 7% of the population on an admissions test to qualify for membership in society catering to highly intelligent individuals. if test scores are normally distributed with a mean of 110 and a standard deviation of 15, what is the minimum score a person must have to qualify for the society? (round your answer to the nearest integer.) 4. Can you curl your tongue up on the sides? tongue-curling in humans is a dominant genetic trait. Suppose a man who is tt for tongue-curling marries a woman who is also tt for this trait. What are the possible genotypes and phenotypes of their children and the percent chance for each?. which story element is most likely to appear in a short story's first few paragraphs? He starts by finding the sum of the exterior angles of a Pentagon, which isand then he solves to find that x is 1. A 26.6g sample of mercury is heated to 110.0 and then placed in 125g of water in a coffee-cupcalorimeter. The initial temperature of the water is 23.00. (c Hg = 0.139 J/g). What is the finaltemperature of the water and the mercury? 2. Draw the Lewis bonding structure for PCl3. what would be the hybrid orbitals