Find the volume of the solid generated when R (shaded region) is revolved about the given line. T x=2- 73 sec y, x=2, y = ő and y= 0; about x = 2 The volume of the solid obtained by revolving the reg

Answer:

\(-6\leq x < 5\)

Step-by-step explanation:

Given compound inequality:

\(31 \geq-4x+7\;\;\;\textsf{and}\;\;\;-4x+7 > -13\)

Solve the first inequality:

\(\begin{aligned}31 & \geq -4x+7\\\\31 +4x& \geq -4x+7+4x\\\\4x+31& \geq 7\\\\4x+31-31 & \geq 7-31\\\\4x & \geq -24\\\\\dfrac{4x}{4} & \geq \dfrac{-24}{4}\\\\x & \geq -6\end{aligned}\)

Solve the second inequality:

\(\begin{aligned}-4x+7& > -13\\\\-4x+7-7& > -13-7\\\\-4x& > -20\\\\\dfrac{-4x}{-4}& > \dfrac{-20}{-4}\\\\x& < 5\end{aligned}\)

Therefore, combining the solutions, the solution to the compound inequality is:

\(\large\boxed{-6\leq x < 5}\)

When graphing inequalities:

To graph the solution:

For dilation, a figure's size and shape only change during transformation, but during translation, the size of the figure's image and preimage are congruent.

Congruent in geometry refers to being the same size and shape. Congruence can be used with figures, angles, and line segments. If any two line segments are equal in length, they are said to be congruent. If two angles have the same measure, they are said to be congruent.

Techniques for transformation: In a xy-plane, transformation involves changing the size and shape of an item.

Translation and dilation are a couple of the transformation methods used.

For dilation, a figure's size and shape only change during transformation, but during translation, the size of the figure's image and preimage are consistent.

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Answer:

Step-by-step explanation:

first i would combine like terms so 1/4a + 1/3a is equal to 7/12 then the equation would be 7/12a+8=22 simplify the isolate the variable so i think it A=24

Answer:

Hey there!

Step-by-step explanation:

Equation: 1/4a + 1/a + 8 = 22

(The answer is 24)

(You have to do 3 steps in order to solve this question! The steps are below!)

~1. First you have to simplify both sides of the equation.

=> (1/4a + 1/3a) + (8) = 22

=> 7/12a + 8 = 22

~2. Next, subtract 8 from both of the sides.

After you do that you will get, 14

7/12a=14

~3. Lastly, you just multiply both sides by 12/7.

(12/7) x (7/12a)

(12/7) x (14)

~Therefore, A would equal to 24.

A=24

~Hope this helps!

~Good luck! :)

~If you still don’t understand, ask for help! (I would be glad to answer any questions you have! :D )

The main difference is interest charged for a payday loan is typically over a short period, whereas  credit card represents the annualized interest rate over a year.

The payday loan interest is a one-time charge, while the credit card APR accumulates over time if the balance is not paid in full.

For a payday loan, the 30% interest is typically charged over a short period, often within a few weeks.

This means that if you borrow $100, you would need to repay $130, including the $30 interest, within that short timeframe.

On the other hand, a 30% APR on a credit card represents the annualized interest rate charged on the outstanding balance. This interest is spread out over a year.

If you have an outstanding balance of $100 on a credit card with a 30% APR, the interest charged over a year would be $30.

In summary, the main difference is that the 30% interest charged for a payday loan is typically applied over a short period, whereas the 30% APR on a credit card represents the annualized interest rate over a year.

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Answer:

5 tractors can plow a square field of side length 1,000 meters in 3.33 hours (3 hours 20 minutes)

Step-by-step explanation:

Let's find out how much each tractor can plow each hour.

\(\frac{600^{2} }{3*2}=60,000m^{2}\) per tractor per hour

\(1,000^{2}=1,000,000m^{2}\) is the area of the field of side length 1,000 meters

5 tractors can plow \(300,000m^{2}\) per hour.

\(\frac{1,000,000}{300,000}=3.33\) hours

The equation that can be used to express the relationship between total cost and tickets is t = $2.91n.

The first step is to determine the cost of one ticket. The cost of one ticket can be determined by dividing the total cost of the ticket by the total number of tickets. Division is the operation that is used to determine the quotient of two or more numbers.

Cost of one ticket = $34.92 / 12 = $2.91

The equation that can be used to determine the total cost would have this form:

Total cost = cost per ticket x number of tickets

t = $2.91 x n

t = $2.91n

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Answer:

Step-by-step explanation:

A number, a variable, or the product of a number and variable(s)

A letter used to represent an unknown number

The number in front of a variable in a term

A single term, multiple terms connected by an addition or subtraction sign

A number, a term containing no variables

Answer:

\( - x ^{2} - 2x + 5\)

pls mark as brainliest lol

The bearing of Manchester from Cambridge is 270⁰.

Bearing refers to the direction or angle between two points, usually measured in degrees, that indicates the horizontal angle between a reference point or line and a target point or object.

Bearing is typically expressed as an angle measured clockwise from north, which is known as "true north" or "geographic north".

The bearing of Manchester from Cambridge is the angle made by the plane from Cambridge back to Manchester.

From the diagram the bearing of Manchester from Cambridge is 270⁰.

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Answer:

\((x -12)(x + 12)\)

Step-by-step explanation:

Given

See attachment for chart

Required

The factors of \(x^2 - 144\)

First, express \(x^2 - 144\) as \(ax^2 + bx + c\)

So, we have:

\(x^2 - 144 = x^2 + 0x - 144\)

Compare the above expression to: \(ax^2 + bx + c\)

We have:

\(ax^2 + bx + c = x^2 + 0x - 144\)

So:

\(a =1\)

\(b =0\)

\(c = -144\)

and

\(a * c = d * e\)

Calculate ac

\(a* c = 1 * -144\)

\(a* c = -144\)

Rewrite as:

\(a* c = -12 * 12\)

Recall that:

\(a * c = d * e\)

Hence:

\(d = -12; e = 12\)

So, on the x chart, we have:

        ac

d                  e

        b

This gives:

        -144

-12                  12

        0

The factors are

\((x + d)(x + e)\)

\((x -12)(x + 12)\)

Answer:

✔ (x – 12)

 and  

✔ (x + 12)

Step-by-step explanation:

Answer:

24 x 1.24 = 29.76

$29.76

works?

Answer: (7, 1)

Step-by-step explanation:

To find the coordinates of Q' which is the image of point Q(0, 6) under the translation (x, y) → (x + 7, y − 5), we can apply the translation to the coordinates of Q as follows:

x-coordinate of Q' = x-coordinate of Q + 7

= 0 + 7

= 7

y-coordinate of Q' = y-coordinate of Q - 5

= 6 - 5

= 1

Therefore, the coordinates of Q' are (7, 1).

Hallie can use the equation p = 4l + 4w + 4h to determine the sum of the lengths of the edges of a rectangular prism. She begins to solve the equation for h but runs out of time. Her partial work is shown below:

p = 4l + 4w + 4h

2. StartFraction p Over 4 EndFraction equals StartFraction 4 l plus 4 w plus 4 h Over 4.

3. StartFraction p Over 4 EndFraction equals l plus w plus h. = l + w + h

h = 4. h equals StartFraction p Over 4 EndFraction minus blank. –

Which expression should follow the subtraction in Hallie’s equation?

(l + w)

(l – w)

left-parenthesis StartFraction l plus w Over 4 right-parenthesis.

left-parenthesis StartFraction l plus w Over 4 EndFraction right-parenthesis.

The expression (w + h) + p/4 should follow the subtraction if Hallie's equation is

p = 4l + 4w + 4h

p/4 = l + w + h

h = -

Hallie can use the following equation to solve the problem

p = 4l + 4w + 4h

She can proceed to make h the subject of the formula.

p = 4l + 4w + 4h

When we factor out 4 on the right hand side, we get:

p = 4(l + w + h)

We then divide both side by 4, we have

p/4 = l + w + h

Then, subtracting (l + w) from both sides, we get:

p/4 - (l + w) = h.

We can write it as:

h = - (l + w) + p/4

And that is what Hallie wanted to obtain.

Answer:

The correct answer is 5 11/12

Step-by-step explanation:

HAVE A GOOD DAY!

Answer:

I do believe that the lighthouse is 160 feet tall.

Step-by-step explanation:

I do believe this is the right answer. Hope this helps you!

The required height of the lighthouse is given as 160 ft tall.

Given that,
A scale model of a lighthouse has a scale of 1 in. : 8 ft. The scale model is 20 inches tall.

The scale factor is defined as the ratio of the modified change in length to the original length.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

here,
scale factor = 1 / 8 in per ft
Now,
The actual length of the lighthouse =  20 / [1 / 8]
                                                             = 20 × 8 = 160 ft

Thus, the required height of the lighthouse is given as 160 ft tall.

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The monthly pay for Jerry is $6500.

Jerry hit the maximum taxable social security income in the 3.36 months.

The social security tax Jerry paid in January is $403

The social security tax Jerry paid in December is zero

What is monthly gross pay?

Monthly gross pay is the amount received by an employee monthly prior to the time at which tax and other deductions are being taken from his/her account.

From the parameters given:

A.

Jerry earned $78000 yearly; her monthly gross pay can be computed as:

\(\mathbf{=\dfrac{78000}{12}}\)

= $6500

B.

The federal tax rate for a single person in 1990 is 28.0%

From $78000, Jerry tax rate = $21840

Therefore, the month that Jerry reaches maximum taxable social security income is computed as:

\(\mathbf{=\dfrac{\$21840}{\$6500/month}}\)

= 3.36 months

C.

Let's assume that the social security tax rate in 1990 was 6.20%.

Then, the amount of social security tax paid in January (since it is a single month) is:

\(\mathbf{= \dfrac{6.20}{100} \times \$6500}\)

= $403

D.

Provided that the number of months required to complete the maximum social security tax is 3.36 months and the social security tax we are to determine is more than 3.36 months(December);

We can conclude that the social security tax Jerry paid for the month of December is zero.

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Based on the fact that the iron ball of 80 pounds has 8 inches in diameter., the iron ball with 12 inches would weigh 120 pounds

The weight of the iron ball can be found by the formula:

= (Diameter of target iron ball x Weight of referrent iron ball) / Diameter of referent iron ball

Solving gives:

= (12 x 80) / 8

= 960 / 8

= 120 pounds

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The image doesn't load for me.

Answer:

Step-by-step explanation:

(a) and (b) see diagram

(c) you can see from the graph, the purple line hits the parabola twice which is y=6   or k=6

(d)  Solving simultaneously can mean to set equal

6x - x² = k                        >subtract k from both sides

6x - x² - k = 0                  >put in standard form

- x² + 6x - k = 0               >divide both sides by a -1

x² - 6x + k = 0

(e) The new equation is the same as the original equation just flipped (see image)

(f)  The discriminant is the part of the quadratic equation that is under the root. (not sure if they wanted the discriminant of new equation or orginal.  I chose new)

discriminant formula = b² - 4ac

equation:   x² - 6x + 6 = 0            a = 1      b=-6    c = 6

discriminant = b² - 4ac

discriminant= (-6)² - 4(1)(6)

discriminant = 36-24

discriminant = 12

Because the discriminant is positive, if you put it back in to the quadratic equation, you will get 2 real solutions.

Answer:

149

Step-by-step explanation:

JUST TOOK TEST

Answer:

149

Step-by-step explanation:

Answer:

y = -2x + 1

Step-by-step explanation:

Y2 - Y1 / X2 - X1

-3 - 1 / 2 - 0

-4 / 2

= -2

y = -2x + b

-3 = -2(2) + b

-3 = -4 + b

1 = b

y = -2x + 1

(a) To show that var(ß) = 0²/21 (xi – F),  derive the expression for var(ß) using the formula provided. (b) To show that var(Bo) = oʻ[1/n+3/11 (xi – )), we need to derive the expression for var(Bo) using the given formula.

(a) The formula for var(ß) is given as 0²/21 (xi – F) in equation (6.9). To show that this is true, we need to derive the expression for var(ß) using the provided formula. This involves calculating the variance of the estimated coefficients ß.

(b) The formula for var(Bo) is given as oʻ[1/n+3/11 (xi – )) in equation (6.10). Similar to part (a), we need to derive the expression for var(Bo) using the given formula. This involves calculating the variance of the intercept coefficient Bo.

Both parts require applying the appropriate mathematical operations to obtain the final expressions for var(ß) and var(Bo). The detailed derivation of these expressions may involve statistical concepts such as covariance and summation calculations. By following the derivation steps and performing the necessary calculations, we can verify that the provided formulas for var(ß) and var(Bo) are indeed correct.

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We can find the orthogonal vector when we use the dot product.

Then, the result must be equal to zero.

The vector u is given by coordinates <-7,-4>

Then, we need to find a vector in which their dor product will be equal to zero:

<-7,-4>*<1/7,-1/4> =-7*1/7 +(-4)*-1/4 = -1+1 =0

Therefore, the orthogonal vector is <1/7,-1/4>

The correct answer is option B

Answer:

Step-by-step explanation:

1.c

2.c

3.a

4.d

5.d

6.c

7. they are equal

8 A.a

8 B.d

9 A. c

9 B. b

10 A.c

10 B. b

11.b

12.d

13.b

14.b

15. a

16.d

17.c

18. 26.56 degrees

The argument states that since all paintings by Matisse are beautiful and the museum has a painting by Matisse, the museum must have a beautiful painting.

The argument presented is an example of a logical fallacy known as affirming the consequent. It follows the form of a logical fallacy known as the fallacy of the converse. The fallacy of the converse occurs when one assumes that if the consequent (in this case, having a painting by Matisse) is true, then the antecedent (in this case, the painting being beautiful) must also be true. However, this is not a valid logical inference.

While it is true that the argument assumes that all paintings by Matisse are beautiful, it does not necessarily follow that the museum's painting by Matisse is also beautiful. There may be exceptions to the generalization that all Matisse paintings are beautiful. Additionally, beauty is subjective, and what one person finds beautiful, another may not.

Therefore, based on the argument presented, we cannot conclude with certainty that the museum has a beautiful painting solely because it possesses a painting by Matisse. The argument relies on a logical fallacy and does not provide sufficient evidence to support the claim that the museum's painting is beautiful.

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Answer:

A)

Adventureland.

B)

Coaster City

C)

5 People

Step-by-step explanation:

The cost of Adventureland for p people is:

\(A=20+9p\)

And the cost of Coaster City for p people is:

\(C=40+5p\)

Part A)

If four people is going on the trip, p = 4. So, the cost for Adventureland is:

\(20 + 9(4) = \$ 56\)

And the cost for Coaster City is:

\(40+5(4)=\$60\)

Since $56 < $60, Adventureland will be a better option.

Part B)

If three extra people were invited, the total amount of people p is now 7. So, the cost to Adventureland is:

\(20 + 9(7) = \$ 83\)

And the cost to Coaster City is:

\(40+5(7)=\$ 75\)

Since $75 < $83, Coaster City is the better option in this case.

Part C)

So, we can set the two cost equations equal to each other:

\(20+9p=40+5p\)

Solve for p. Subtracting 20 from both sides yields:

\(9p=20+5p\)

And subtracting 5p from both sides yields:

\(4p=20\)

And dividing both sides by 4:  

\(p=5\)

So, if 5 people went on a trip, the cost of going to either Adventureland or Coaster City will be the same.

Answer:

120%

Step-by-step explanation: