suppose that z varies jointly with x and y. When x=2, y=2, z=7 write the equation that models the relationship

Answers

Answer 1
[tex]\begin{gathered} z=\text{ x + y + b} \\ 7\text{ = 2+2+b} \\ 7\text{ = 4+b} \\ 7-4=b \\ b=\text{ 3} \\ z=\text{ x + y +3} \end{gathered}[/tex]


Related Questions

3. The number line below represents the solution to which inequality of he 0 1 2 3 4 5 6 7 8 9 10

Answers

let x be the money daniel has. So we get that

[tex]x\ge72+15\rightarrow x\ge87[/tex]

Daniel has at least $87

what is 5/6 converted to decimal form

Answers

5/6 in decimal form is

[tex]\frac{5}{6}=0.8\bar{3}[/tex]

9. The exchange rate of a certain foreign currency with the Indian rupee is Rs 62.50.How much of the foreign currency can be had for Rs3125 ?

Answers

Answer

Rs. 3125 is equivalent to 50 units of the foreign currency.

Step-by-step Explanation

The exchange rate of the foreign currency in Indian Rupee is Rs. 62.50

This means that

1 unit of that foreign currency = Rs. 62.50

Or better written as

Rs. 62.50 = 1 unit of the foreign currency

So, we are then told to find how much Rs. 3125 is in the foreign currency

Let Rs. 3125 be equal to x units of the foreign currency

Rs. 62.50 = 1 unit of the foreign currency

Rs. 3125 = x units of the foreign currency

A simple mathematics relation obtained by cross multiplying will give us the value of x

After cross multiplying

62.50 × x = 3125 × 1

62.50x = 3125

Divide both sides by 62.50

(62.50x/62.50) = (3125/62.50)

x = 50

Therefore, Rs. 3125 is equivalent to 50 units of the foreign currency.

Hope this Helps!!!

-10 x is greater than or equal to 2x

Answers

We need to solve the following inequality:

[tex]-10\text{ }\ge2x[/tex]

We need to isolate the "x" variable, when we do that the number that is multiplying it should go to the other side with its inverse operation, which is division.

[tex]\begin{gathered} \frac{-10}{2}\ge x \\ -5\ge x \end{gathered}[/tex]

Now we need to flip the expression, so the variable is isolated on the left side. Since this is an inequality we also need to flip the inequality signal. This is done below.

[tex]x\leq-5[/tex]

For the expression to be true x must be less or equal to -5.

The top of the hill rises 243 feet above checkpoint 2, which is -162. What is the altitude of the top of the hill?

Answers

The altitude of the top of the hill or the difference in elevation point is 406 feet.

Difference in Elevation Point

The vertical distance between two points is called the difference in elevation. The process of measuring differences in elevation is called levelling , and is a basic operation in topographical surveys.

To determine the difference in elevation between two points, determine the elevation at each point and then calculate the difference.

Point A = 243 feetPoint B = -162 feet

The difference in elevation between the two points is

Point A - Point B = 243 - (-162) = 243 + 162 = 406

The difference in the elevation point is 406 feet.

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If L = 4 inches and KL = 7 inches, what is the length of the diameter JK? Round your answer to at least the nearest hundredth of an inch (2 decimal places).

Answers

We have a right triangle and two sides we will use the Pythagorean theorem in order to find the missing side

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

a=7 in

b= 4 in

c=JK

we substitute the values

[tex]JK=\sqrt[]{7^2+4^2}[/tex][tex]JK=8.06[/tex]

I need help This is from my trig prep guide

Answers

From the question given, we have the following data;

Height of the tree = 80 feet

Angle of elevation to the top of the tree = 68 degrees

Distance from Corey to the tree = unknown

We shall now call the unknown variable x.

With that we shall have the following diagram;

We now have a diagram detailing the triangle and the dimensions showing Corey, the tree and the eagle at the tree top.

To get a better look, Corey moves several steps away from the tree and now determines his new angle of elevation to be 41 degrees.

This can now be illustrated as follows;

From triangle EDC, we shall calculate the distance from point C to point D using trigonometric ratios. The reference angle is at point C, which means the opposite side is side ED. The adjacent side is side CD (labeled x). Using trig ratios we have;

[tex]\begin{gathered} \tan \theta=\frac{\text{opp}}{\text{adj}} \\ \tan 68=\frac{80}{x} \end{gathered}[/tex]

We cross multiply and we now have;

[tex]\begin{gathered} x=\frac{80}{\tan 68} \\ U\sin g\text{ a calculator, we have tan 68 as 2.475086}\ldots \\ x=\frac{80}{2.475086} \\ x=32.322109\ldots \\ \text{Rounded to the nearest hundredth of a foot;} \\ x=32.32ft \end{gathered}[/tex]

Looking at triangle EDB;

The reference angle is 41 which makes the opposite side ED and the adjacent side BD. To calculate the distance BD, we'll have;

[tex]\begin{gathered} \tan \theta=\frac{\text{opp}}{\text{adj}} \\ \tan 41=\frac{80}{BD} \\ We\text{ cross multiply and we now have;} \\ BD=\frac{80}{\tan 41} \\ BD=\frac{80}{0.869286} \\ BD=92.02955\ldots \\ \text{Rounded to the nearest hundredth;} \\ BD=92.03 \end{gathered}[/tex]

Take note that the distance Corey moved before he had a new angle of elevation is line segment CD which is indicated as y. Note also that

[tex]\begin{gathered} BC+CD=BD \\ CD=x=32.32ft \\ BC+32.32=92.03 \\ \text{Subtract 32.32 from both sides;} \\ BC=59.71 \end{gathered}[/tex]

The distance Corey stepped back is indicated as y (line segment BC).

ANSWER:

Corey stepped back 59.71 feet

What is the vertex of the graph of the function below?y = x^2 + 10x + 24O A. (-4,-1)O B. (-5, -1)O C. (-5,0)O D. (4,0)

Answers

For any given parabola in the form

[tex]f(x)=ax^2+bx+c[/tex]

The vertex is the point:

[tex]V=(-\frac{b}{2a},f(-\frac{b}{2a}))[/tex]

This way,

[tex]\begin{gathered} y=f(x)=x^2+10x+24 \\ \rightarrow a=1 \\ \rightarrow b=10 \\ \rightarrow c=24 \\ \\ \rightarrow-\frac{b}{2a}=-\frac{10}{2\cdot1}=-5 \\ \\ \rightarrow f(-5)=(-5)^2+10(-5)+24=-1 \end{gathered}[/tex]

Therefore, the vertex is:

[tex]V(-5,-1)[/tex]

Answer: Option B

At what rate (%) of simple intrest will $5,000 amount to $6,050 in 3 years?

Answers

Rate of interest for

A = $5000

THEN apply formula

A-P= P•R•T/100

T = 3 years

Then

6050 - 5000= 1050 =

1050= P•R•T/100

Now find R

R= (1050•100)/(P•T) = (105000)/(5000•3) = 7

Then ANSWER IS

ANUAL RATE(%) = 7%

Fido ran away from home at a speed of 5 mi/hour. He ran in a straight line. After a while he decided to go back home for dinner so turned around and walked home along the same path he had run on. He walked at 2 mi/hour. The walk home took one hour longer than the run did. How long did Fido run?

Answers

Distance = Speed x time

For the run; speed = 5 mi/hr, time = t

For the walk: speed= 2 mi/hr, time = t + 1

Since he walked on a straight line and he returned following the same path

Distance travelled for the run = distance travelled for the walk

Distance for run: 5 x t = 5t

Distance for walk : 2 (t + 1) =2t + 2

Thus , 5t = 2t + 2

5t - 2t = 2

3t = 2

t = 2/3 hour = 2/3 x 60 minutes = 2x 20 = 40 minutes

He took him 40 minutes to run

If the radius of a sphere increases from 3 feet to 9 feet, by how many cubic feet does the volume of the sphere increase? 967 ft3 A 1087 ft3 936 ft 0

Answers

The volume of a sphere is given by:

[tex]V=\frac{4}{3}\pi r^3[/tex]

The original sphere, with radius r=3, has volume:

[tex]\begin{gathered} V=\frac{4}{3}\pi(3)^3 \\ =36\pi \end{gathered}[/tex]

The second sphere, with radius r=9, has volume:

[tex]\begin{gathered} V=\frac{4}{3}\pi(9)^3 \\ =972\pi \end{gathered}[/tex]

To find how much the volume increased we substract the first volume to the second one:

[tex]972\pi-36\pi=936\pi[/tex]

Therefore the v

Draw a sketch of f(x) = (x-4)^2+5. Plot the point for the vertex, label the coordinates as a maximum or minimum, draw and write the equation for the axis of symmetry

Answers

Given the function:

[tex]f(x)=(x-4)^2+5[/tex]

the given function is a quadratic function

The graph of the function is as shown in the following picture

As shown the function has a minimum point at ( 4, 5 )

So, vertex = ( 4, 5 )

And Axis of symmetry: x = 4

A store manager or tshirts so that 15 out of every 35 are a medium. How many medium Tshirts would you expect to find when there are 126 T-shirt's on a rack?

Answers

Given:

Out of every 30 t-shirts, 15 are medium.

Let's find the number of medium t-shirts you expect to find when there are 126 t-shirts on a rack.

We have:

35 t-shirts = 15 medium

126 t-shirts = x medium

Now, let's solve for x.

Apply the proportioanlity equation:

[tex]\frac{35}{15}=\frac{126}{x}[/tex]

Cross multiply:

[tex]\begin{gathered} 35x=126\times15 \\ \\ 35x=1890 \end{gathered}[/tex]

DIvide both sides by 35:

[tex]\begin{gathered} \frac{35c}{35}=\frac{1890}{35} \\ \\ x=54 \end{gathered}[/tex]

Therefore, there will be 54 medium t-shirts when there are 126 t-shirts.

ANSWER:

54

Find the equation in standard form of lines P that are A) parallel to and B) perpendicular to line L P(1,2); L: 3x-2y=1P(8,7);L: y= -4

Answers

To find if two lines are parallel, the slope must be the same.

so m=m

for P(1,2); L: 3x-2y=1

First, solve the equation for y:

3x-2y=1

Subtract both sides by 3x

3x-2y=1

3x-3x-2y =1-3x

-2y=1-3x

Now, divide both sides by -2y

-2y/-2 = 1-3x

y =1/-2 +3x/2

The parallel line using the point P(1,2)

y-y1 =m(x-x1)

Replace the values and solve for y.

y-2=3x/2 -1

y=3x/2+2

So the parallel lines is y=3x/2+2

To find a perpendicular line, when you multiply the slopes the result must be equal to -1.

So:

m1*m2 = -1

Replace m1=3/2

m1*m2 = -1

3x/2* m2 = -1

m2 = -1/(3x/2)

m2 = -2/3

To find the line use:

y-y1 =m(x-x1)

y-2=-2/3(x-1)

y-2=-2x/3 +2/3

y= -2x/3 +8/3

So y= -2x/3 +8/3 is the perpendicular line.

Patrick is responsible for choosing the company his local community group will use for having T-shirts printed. He must choose between Initial Me and Monogram Mania. Both companies charge an initial set-up fee and then charge per T-shirt printed.

The graph shows the cost of purchasing T-shirts from Initial Me and the cost of purchasing T-shirts from Monogram Mania.

Which statements are true about Initial Me and Monogram Mania?

Select each correct answer.

Answers

Step 1:

The initial cost of Initial Me = 50

The initial cost of Monogram Mania = 80

Step 2:

Both Initial Me and Monogram Mania cost the same for 10 T-shirts printed of 130

Step 3:

Monogram Mania charges less per T-shirt printed than Initial Me charges.

The average cost of Monogram Mania is less than that of Initial Me.

Final answer

Monogram Mania charges less per T-shirt printed than Initial Me charges.

whats x+7, y equals and how do i find it?

Answers

The figure HGD was translated 7 units right; and then it was translated 9 units up. This can be shown as:

(x, y) → (x + 7, y + 9)

Answer = 9

Question 3 of 10A digital scale reports a 10 kg weight as weighing 8.975 kg. Which of thefollowing is true?A. The scale is precise but not accurate.B. The scale is accurate but not precise.OC. The scale is neither precise nor accurate.O D. The scale is both accurate and precise.SUBMIT

Answers

Solution:

The real weight is 10kg;

But the digital scale reports 8.975kg.

Thus;

Accuracy refers to the closeness of the measure to the real value, while precision, in this case, refers to the level of significant figures that the scale report.

The fact that the scale reports the number with 4 significant figures means that it is very precise, but we still observe that the report is not so close to the real value, thus, it means that the scale is not accurate.

FINAL ANSWER: A. The scale is precise but not accurate

For every 4 songs on Mary's playlist, 3 of the songs are longer than 5 minutes.
Complete the table of values to compare the total money spent to tickets purchased.
Total Number of Songs on Playlist
Number of Songs Longer Than 5 Minutes
8
32
40
136

Answers

we were told that in every 4 songs on the playlist, 3 of the songs are longer than 5

so if in for 4 songs, 3 is longer than 5

for 8 songs,

we divide the the number of songs in the playlist by 4 in other to get the numbers of 4 in it then muliply by the number of songs longer than 5

for 8 songs on the playlist:

= 8/4 X 3

= 2 X 3

= 6

For 32 songs on the playlist

= 32/4 X 3

= 8 X 3

= 24

For 40 songs on the playlist

= 40/4 X 3

= 10 X 3

= 30

For 136 number of songs on the playlist

= 136/4 X 3

= 34 X 3

= 102

so in completing the table:

Total Number of Songs on the Playlis Number of songs longer than 5min.

8 6

32 24

40 30

136 102

Rowan is taking his siblings to get ice cream. They can't decide whether to get a cone or a cup because they want to get the most ice cream for their money. If w = 4 in, x =6 in, y = 6 in, z = 2 in, and the cone and cup are filled evenly to the top with no overlap, which container will hold the most ice cream? Use 3.14 for π, and round your answer to the nearest tenth.

Answers

EXPLANATION:

Given;

We are given two ice cream cups in the shapes of a cone and a cylinder.

The dimensions are;

[tex]\begin{gathered} Cone: \\ Radius=4in \\ \\ Height=6in \\ \\ Cylinder: \\ Radius=3in \\ \\ Height=2in \end{gathered}[/tex]

Required;

We are required to determine which of the two cups will hold the most ice cream.

Step-by-step solution;

Take note that the radius of the cylinder was derived as follows;

[tex]\begin{gathered} radius=\frac{diameter}{2} \\ \\ radius=\frac{6}{2}=3 \end{gathered}[/tex]

The volume of the cone is given by the formula;

[tex]\begin{gathered} Volume=\frac{1}{3}\pi r^2h \\ \\ Therefore: \\ Volume=\frac{1}{3}\times3.14\times4^2\times6 \\ \\ Volume=\frac{3.14\times16\times6}{3} \\ \\ Volume=100.48 \end{gathered}[/tex]

Rounded to the nearest tenth, the volume that the cone can hold will be;

[tex]Vol_{cone}=100.5in^3[/tex]

Also, the volume of the cylinder is given by the formula;

[tex]\begin{gathered} Volume=\pi r^2h \\ \\ Volume=3.14\times3^2\times2 \\ \\ Volume=3.14\times9\times2 \\ \\ Volume=56.52 \end{gathered}[/tex]

Rounded to the nearest tenth, the volume will be;

[tex]Vol_{cylinder}=56.5in^3[/tex]

ANSWER:

Therefore, the results show that the CONE will hold the most ice cream.

An animal shelter spends $1.50 per day to care for each cat and $6.50 per day to carefor each dog. Gavin noticed that the shelter spent $97.00 caring for cats and dogs onMonday. Gavin found a record showing that there were a total of 18 cats and dogs onMonday. How many cats were at the shelter on Monday?

Answers

4 cats and 14 dogs.

Explanation:

Data :

Amount of cats : c = ?

Cost per cats : $1.50

Amount of dogs : d = ?

Cost per dogs : $6.50

Total spent for dogs and cats : $97.00

Total number of dogs and cats : 18

Formulas:

1.50c + 6.50d = 97.00

c + d = 18

Solution:

c + d = 18 => c = 18 - d

1.50(18 -d) + 6.50d = 97.00

27 - 1.50d + 6.50d = 97.00

27 - 1.50d + 6.50d - 27 = 97 -

Find the distance between the two points. 15.) (-3, -1), (-1, -5)-use Pythagorean Throrem

Answers

Answer:

4.5 units

Explanation:

First, we need to draw the points (-3, -1) and (-1, -5) as follows

Therefore, the distance between the points is the length of the yellow line. This distance is the hypotenuse of a triangle with legs a and b.

The length of a is 2 and the length of b is 4

Then, using the Pythagorean theorem, we can calculate the length of c as follow

[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=2^2+4^2 \\ c^2=4+16 \\ c^2=20 \end{gathered}[/tex]

So, using the calculator, we get that the value of c is equal to

[tex]\begin{gathered} \sqrt{c^2}=\sqrt{20} \\ c=\sqrt{20} \end{gathered}[/tex]

To find an approximate value for c, we will use the following:

We know that √16 = 4 and √25 = 5

Since 20 is between 16 and 25, the square root of 20 is a number between 4 and 5, so we can approximate it to 4.5.

Therefore,

c = 4.5

7 singles, 13 fives, 4 twenties, and 3 hundred dollar bills are all placed in a hat. If a player is to reach into the hat and randomly choose one bill, what is the fair price to play this game?

Answers

So,

The probability to obtain one bill of the four, is 1/4.

So, the expected value is:

[tex]\begin{gathered} \frac{1}{4}(7)+\frac{1}{4}(13)+\frac{1}{4}(4)+\frac{1}{4}(3) \\ \\ =6.75 \end{gathered}[/tex]

Therefore, the fair price to play this game is 6.75.

If the inflation has been 2.7%, how much more do you have to pay this year foran item that cost $11.50 last year?

Answers

Given data:

The cost of the item is $11.50.

The inflation percentage is 2.7%.

Increase in the price is,

[tex]\begin{gathered} =11.50\times(\frac{2.7}{100}_{}) \\ =11.50\times0.027 \\ =0.3105 \end{gathered}[/tex]

Total amount to be paid last year,

[tex]\begin{gathered} =11.50+0.3105 \\ =11.8105 \end{gathered}[/tex]

Therefore you will have to pay $ 0.3105 more.

5. How would you solve the system of equations y = 5x + 1 and -2x + 3y =-10 ? What is the solution? *

Answers

SOLUTION:

Step 1:

In this question, we are given the following:

Solve the system of equations y = 5x + 1 and -2x + 3y =-10 ?

What is the solution?

Step 2:

The solution to the systems of equations:

[tex]\begin{gathered} y\text{ = 5x + 1 -- equation 1} \\ -2x\text{ + 3y = -10 -- equation 2} \end{gathered}[/tex]

check:

Given y = -4 , x = -1

Let us put the values into the equation:

y = 5x + 1 and -2x + 3y = -10

[tex]\begin{gathered} y\text{ = 5x + 1} \\ -4=5(-1)\text{ + 1} \\ -4=-5+1 \\ -4\text{ = - 4 (COR}\R ECT) \end{gathered}[/tex][tex]\begin{gathered} -2x+3y\text{ = -10} \\ -2(-1)+3(-4)_{}_{} \\ 2-12=-10\text{ (COR}\R ECT) \end{gathered}[/tex]

CONCLUSION:

The solution to the system of equations are:

[tex]\begin{gathered} \text{x = -1} \\ y=-4 \end{gathered}[/tex]

Simplify the expression.

the expression negative one seventh j plus two fifths minus the expression three halves j plus seven fifteenths
negative 19 over 14 times j plus 13 over 15
negative 19 over 14 times j minus 13 over 15
negative 23 over 14 times j plus negative 1 over 15
23 over 14 times j plus 1 over 15

Answers

The expression is simplified to negative 23 over 14 times j plus negative 1 over 15. Option C

What is an algebraic expression?

An algebraic expression can be defined as an expression mostly consisting of variables, coefficients, terms, constants and factors.

Such expressions are also known to be composed or made up of some mathematical or arithmetic operations, which includes;

AdditionSubtractionDivisionBracketMultiplicationParentheses. etc

From the information given, we have that;

negative one seventh j = - 1/7jtwo fifths = 2/5three halves j = 3/2 jseven fifteenths = 7/15

Substitute the values

- 1/7j + 2/5 - 3/2j - 7/15

collect like terms

- 1/7j - 3/2j + 2/5 - 7/15

-2j - 21j /14 + 6  7 /15

-23j/14 + -1/15

Hence, the correct option is negative 23 over 14 times j plus negative 1 over 15

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Find the one-sided limit (if it exists). (If the limit does not exist, enter DNE.)

Answers

Answer:

0

Explanation:

Let us call

[tex]f(x)=\frac{\sqrt[]{x}}{\csc x}[/tex]

The function is continuous on the interval [0, 2pi]; therefore,

[tex]\lim _{x\to\pi^+}f(x)=\lim _{x\to\pi^-}f(x)[/tex]

To evaluate the limit itself, we use L'Hopital's rule which says

[tex]\lim _{x\to c}\frac{a(x)}{b(x)}=\lim _{x\to c}\frac{a^{\prime}(x)}{b^{\prime}(x)}[/tex]

Now in our case, we have

[tex]\lim _{n\to\pi}\frac{\sqrt[]{x}}{\csc x}=\lim _{n\to\pi}\frac{\frac{d\sqrt[]{x}}{dx}}{\frac{d \csc x}{dx}}[/tex]

[tex]=\lim _{n\to\pi}\frac{d\sqrt[]{x}}{dx}\div\frac{d\csc x}{dx}[/tex]

[tex]=\frac{1}{2\sqrt[]{x}}\div(-\frac{\cos x}{\sin^2x})[/tex]

since

[tex]\frac{d\csc x}{dx}=-\frac{\cos x}{\sin^2x}[/tex]

Therefore, we have

[tex]\lim _{n\to\pi}\frac{\sqrt[]{x}}{\csc x}=\lim _{n\to\pi}\frac{1}{2\sqrt[]{x}}\div(-\frac{\cos x}{\sin^2x})[/tex][tex]=\lim _{n\to\pi}-\frac{1}{2\sqrt[]{x}}\times\frac{\sin^2x}{\cos x}[/tex]

Putting in x = π into the above expression gives

[tex]-\frac{1}{2\sqrt[]{x}}\times\frac{\sin^2x}{\cos x}\Rightarrow-\frac{1}{2\sqrt[]{\pi}}\times\frac{\sin^2\pi}{\cos\pi}[/tex][tex]=0[/tex]

Hence,

[tex]=\lim _{n\to\pi}-\frac{1}{2\sqrt[]{x}}\times\frac{\sin^2x}{\cos x}=0[/tex]

Therefore, we conclude that

[tex]\boxed{\lim _{n\to\pi}\frac{\sqrt[]{x}}{\csc x}=0.}[/tex]

which is our answer!

Find the equation of a line passing through (-7,9) with a slope of -5.

Answers

y=-5x-26

Explanation

the equation of a line can be written as:

[tex]\begin{gathered} y=mx+b \\ where\text{ m is the slope} \\ and\text{ b is the y-intercept} \end{gathered}[/tex]

now, when we have the slope and a passing point, we need to use the slope-point formula , it says

[tex]\begin{gathered} y-y_1=m(x-x_1) \\ where\text{ m is the slope and \lparen x}_1,y_1)\text{ is a point from the line} \end{gathered}[/tex]

so

Step 1

a)let

[tex]\begin{gathered} slope=-5 \\ (x_1,y_1)=(-7,9) \end{gathered}[/tex]

b) now replace in the slope-point formula and solve for y

[tex]\begin{gathered} y-y_{1}=m(x-x_{1}) \\ replace \\ y-9=-5(x-(-7)) \\ y-9=-5(x+7) \\ y-9=-5x-35 \\ add\text{ 9 in both sides} \\ y-9+9=-5x-35+9 \\ y=-5x-26 \end{gathered}[/tex]

therefore, the equaton of the line is

y=-5x-26

I hope this helps you

Which expression is equivalent to cot2B(1 – cos-B) for all values of ß for which cot2B(1 - cos2B) is defined?

Answers

From the Pythagorean identity,

[tex]\sin ^2\beta+\cos ^2\beta=1[/tex]

we have

[tex]\sin ^2\beta=1-\cos ^2\beta[/tex]

Then, the given expression can be rewritten as

[tex]\cot ^2\beta\sin ^2\beta\ldots(a)[/tex]

On the other hand, we know that

[tex]\begin{gathered} \cot \beta=\frac{\cos\beta}{\sin\beta} \\ \text{then} \\ \cot ^2\beta=\frac{\cos^2\beta}{\sin^2\beta} \end{gathered}[/tex]

Then, by substituting this result into equation (a), we get

[tex]\begin{gathered} \frac{\cos^2\beta}{\sin^2\beta}\sin ^2\beta \\ \frac{\cos ^2\beta\times\sin ^2\beta}{\sin ^2\beta} \end{gathered}[/tex]

so by canceling out the squared sine, we get

[tex]\cos ^2\beta[/tex]

Therefore, the answer is the last option

A car can travel 43/1/2 miles on 1/1/4 gallons of gas. What is the unit rate for miler per gallon

Answers

The unit rate for the car is 34.8 miles per gallon.

How to get the unit rate for mile per gallon?

The unit rate will be given by the quotient between the distance traveled and the gallons of gas consumed to travel that distance.

Here we know that the car travels 43 and 1/2 miles on 1 and 1/4 gallons of gas, then the quotient is:

U = (43 + 1/2)/(1 + 1/4) mi/gal = (43.5)/(1.25) mi/gal = 34.8mi/gal

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- What is the closed linear form of the sequence 3, 4,5, 6, 7, ...?

Answers

[tex]\begin{gathered} Sequence\text{ general equation} \\ a_n=a_1+(n-1)d \\ \text{From given information} \\ a_1=3 \\ \text{From the general equation} \\ a_n=a_1+(n-1)d \\ a_n-a_1=(n-1)d \\ d=\frac{a_n-a_1}{n-1} \\ \text{Choosing second term, n=2, a}_2=4 \\ d=\frac{4-3}{2-1} \\ d=1 \\ \text{Hence The closed linear form of the sequence is} \\ a_n=3_{}+(n-1)\cdot1 \\ a_n=3_{}+(n-1) \\ a_n=3_{}+n-1 \\ a_n=3_{}-1+n \\ a_n=2+n \end{gathered}[/tex]

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