Rectangle ABCD has vertices A(15, 18), B(−5, 3), C(1, −5), and D(21, 10).

Enter your answers in the boxes.

What is the length of AB¯¯¯¯¯?




What is the length of AD¯¯¯¯¯?




What is the area of rectangle ABCD?

Answer:

Therefore, the volume of the diversion tunnel is approximately 9,839,916,800 cubic feet and the surface area is approximately 1,000,530.9 square feet.

Step-by-step explanation:

To find the volume and surface area of a diversion tunnel, we can use the formulas for the volume and lateral surface area of a cylinder.

The volume of a cylinder is given by the formula:

V = πr^2h

Where:

V is the volume,

π is a mathematical constant approximately equal to 3.14159,

r is the radius of the cylinder, and

h is the height (or length) of the cylinder.

Substituting the given values:

r = 56 feet

h = 4,000 feet

V = π(56^2)(4,000)

V ≈ 3.14159 * 56^2 * 4,000

Calculating the volume:

V ≈ 9,839,916,800 cubic feet

The surface area of the lateral (curved) part of a cylinder is given by the formula:

A = 2πrh

Where:

A is the surface area,

π is a mathematical constant approximately equal to 3.14159,

r is the radius of the cylinder, and

h is the height (or length) of the cylinder.

Substituting the given values:

r = 56 feet

h = 4,000 feet

A = 2π(56)(4,000)

A ≈ 2 * 3.14159 * 56 * 4,000

Calculating the surface area:

A ≈ 1,000,530.9 square feet

Therefore, the volume of the diversion tunnel is approximately 9,839,916,800 cubic feet and the surface area is approximately 1,000,530.9 square feet.

Answer:

60'' × 52'' or a 79.4'' TV

Step-by-step explanation:

Leaving a room of 2 inches on all sides means we subtract 4 inches from the height and length to find the maximum dimensions of the TV.

With this, we get 60'' × 52''. To find the diagonal length of the TV, use the Pythagorean Theorem which simply states the length of the diagonal is equal to the square root of the sum of the squared dimensions.

\(\sqrt{a^2+b^2} =c\)

\(\sqrt{60^2+52^2}=79.4\)

Therefore your TV can have a maximum size of 79.4 inches.

Explanation:

The constant of proportionality is the same as the slope for equations of the form y = kx.

To find the value of k, we divide the y over x values.

k = y/x = 12/8 = 1.5

or

k = y/x = 6/4 = 1.5

Either way the answer is 1.5

This means Ziah ran at a rate of 1.5 city blocks per minute.

Answer:

7 seconds

Step-by-step explanation:

Given the height equation of the motion;

s = -16t^2 + 256t

At s = 1008 ft

The equation becomes;

1008 = -16t^2 + 256t

16t^2 - 256t + 1008 = 0

Solving the quadratic equation for t;

Factorising, we have;

16(t-7)(t-9) = 0

t = 7 or t = 9

When the ball is going up it would reach the given height at time t = 7 seconds.

When it is coming down it would reach the given height at time t = 9 seconds.

The equation of the line having slope 0 and passing through (-3,-2) is f(x) = -2.

Any horizontal line has the same y-value for every point on the line. We are given that the line passes through the point (-3,-2). This means that f(-3) = -2, since the y-value of the point (-3,-2) corresponds to the value of the function at x = -3.

This is because no matter what x-value we plug into the function, the output (y-value) will always be -2. Therefore, the equation of the line in function notation is f(x) = -2.

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Answer:

volume = 33965.39

Step-by-step explanation:

Attached below is a detailed solution of the problem and the required sketch

volume of this solid is calculated integrating about the axis of : 5,3

Y = In x = x = e^y

the shaded region in the sketch represent the region where the rotating takes place.

which class is this because I am in 7th class so that's why I can't give

Answer:

the gram

Step-by-step explanation:

casegunnell is my gram, follow if your a real g

Following are the calculation to the given points:

When the ABCD is parallelogram:

The properties of parallelogram:

\(\to \angle CBD = \angle ADB \\\\\)

\(\to \angle BCA = \angle DAC \\\\\)

When the Two-lines are parallel and alternate interior angles are equal:

\(\to \Delta BEC \cong \Delta AED \ \ \ \ \ \ \ \{ASA\} \\\\\to \overline {AE} \cong \overline{CE}\\\\ \to \overline{BE} \cong \overline{ED} \\\\\)

When the properties of congruent triangle.

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The equation that models the relationship between the number of guests, x, and the total charge, y is A. y = 450 + 125x. The base charge for a single guest is $450, and for each additional guest, the charge increases by $125. So, we add 125 times the number of additional guests to the base charge of $450.

In this case, we are to determine the probability of selecting two even numbers. This can be solved as follows:There are six even numbers: {2, 4, 6, 8, 10, 12}.We can use the concept of conditional probability since the first event affects the probability of the second event. This can be expressed as follows:

In this case, P(A) represents the probability of selecting an even number, and P(B|A) represents the probability of selecting an even number given that the first card selected was even. P(A) = 6/12 = 1/2 (there are six even numbers and twelve cards in total)P(B|A) = 5/11 (there are five even numbers left in the box after the first even number is selected, and eleven cards are left in total).

The probability of selecting two even numbers can be found by multiplying these probabilities: P(A) x P(B|A) = (1/2) x (5/11) = 5/22Therefore, the probability of selecting two even numbers is 5/22.Answer: 5/22

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The probability of having at least 2 red balls in the 3 that I picked will be 1/3.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

I have 3 red balls, 3 blue balls, and 3 yellow balls in a crate. All out of 9 balls.

If the three balls are picked randomly, then the probability of having at least 2 red balls in the 3 that I picked will be given as,

P = 3/9

P = 1/3

The probability of having at least 2 red balls in the 3 that I picked will be 1/3.

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Answer:

-4

Step-by-step explanation:

m = y2-y1 / x2-x1

m = -11-(-7) / 3-2

m = -11+7 / 3-2

m = -4 / 1

m = -4

m = -39-(-27) / 10-7

m = -39+27 / 10-7

m = -12 / 3

if you simplify if further,

m = -4 / 1

m = -4

Answer:

-4.

Step-by-step explanation:

The slope formula is y2-y1/x2-x1. if we plug in the numbers we can get the formula -11 - (-7)/ 3-2. This gets us -4/1 which equals -4. Therefore the slope of the equation is -4.

The correct answer is B. Debra

Explanation:

The word "beneficiary" is used to describe the individual that receives a benefit. In the case of a life insurance policy, the receiver is always the person that receives money and other benefits when the person covered by the policy dies. This implies that in the case presented, Denise is the individual covered by the policy and the beneficiary is Debra because she will receive the money once Denise dies, and therefore she is the recipient of the benefits related to the insurance policy.

By using the substitution method, we will see that the value of y is 23.

Here we have a system of linear equations, the system is:

y - x = 11

x = 12

The second equation is trivial, it just gives the value of x. Then we can use the substitution method and replace it in the first equation, then we will get:

y - 12 = 11

Now we can solve this for y, we will get:

y = 11 + 12

y = 23

That is the value of y.

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The end behavior of the graph of f(x) = x⁵ – 8x⁴ + 16x³ does not cross the x-axis at x = 4 and crosses the x-axis at x = 0. This is about the end behavior of a graph of a function at the end of the x-axis. Also, f(x) => -∞ as x => -∞; f(x) => +∞ as x => +∞.

We are given the function;

f(x) = x⁵ - 8x⁴ + 16x³

A) As x approaches negative infinity -∞, x⁵ will also approach negative infinity -∞. This is because when we raise a negative number to the power of an odd number, the result remains negative.

B) As x approaches positive infinity +∞, x⁵ will also approach positive infinity -∞. This is because when we raise a positive number to the power of an odd number, the result remains positive.

Let's now find the roots of this function;

f(x) = x⁵ - 8x⁴ + 16x³

Let's factorize it first to get;

f(x) = x³(x² – 8x + 16)

(x² – 8x + 16) is a perfect square trinomial and can be expressed as (x – 4)(x - 4).

Thus;

f(x) = x³ (x – 4)(x - 4)

C) Since we have found the factorized form to be;

f(x) = x³ (x – 4)(x - 4)

The roots are at f(x) = 0;

The roots are; x³ = 0; (x – 4) = 0 ; (x - 4) = 0

This means the roots of f(x) are; x=0 and x=4.  x = 4

This means the graph has a repeated root and so it will touch the x-axis but not at the repeated root of x=4.

D) Since, 0 is a root and it does not cross at x = 4, the graph will cross at x = 0.

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The standard error represents the average deviation of the sample means from the true population mean. Rounding this value to four decimal places, the standard error of X¯¯¯ is approximtely 0.6500 mpg.

A smaller standard error indicates that the sample means are more likely to be close to the population mean.To calculate the standard error of X¯¯¯, the mean from a random sample of 25 fill-ups by one driver, we can use the formula:

Standard Error (SE) = σ / sqrt(n),

where σ is the standard deviation and n is the sample size.

In this case, the standard deviation (σ) is given as 3.25 mpg, and the sample size (n) is 25.

Plugging in these values into the formula, we have:

SE = 3.25 / sqrt(25).

Calculating the square root of 25, we get:

SE = 3.25 / 5.

Performing the division, we find:

SE ≈ 0.65.

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Answer

The missing digit is 2.

Explanation

Let the missing digit be x

We are asked to determine the missing digit if

3549 × x7 = 95823

The way to solve this is to divide both sides by 3549

x7 = 95823 ÷ 3549

= 27

Hence, the missing digit is 2.

Hope this Helps!!!

Answer:

t = 3.74165738677 or 3.74

Step-by-step explanation:

Step 1:

( t - 3 )² = 6      Equation

Step 2:

t² - 3² = 6       Open Parentheses

Step 3:

t² - 9 = 6          Exponents

Step 4:

t² = 14         Add 9 on both sides

Step 5:

t = \(\sqrt{14}\)       Find the square root of 14

Answer:

t = 3.74165738677 or 3.74        Round

Hope This Helps :)

Answer:

The arrow is at a height of 48 ft after approximately 0.55s and after 5.45s.

Step-by-step explanation:

took the assignment

Answer: The answer is x²+3x

Step-by-step explanation:

hope that helps.

Answer:

If you earn $15 every week then you will have earned $75 by the end of 5 weeks.

Step-by-step explanation:

If $15 is 1 week,

and you need to find how much money after 5 weeks,

you multiply by the same number on both sides

1 = 15

1*5 = 15*5

5 = 75

So after 5 weeks you get $75

Answer:

\(\frac{8}{15}\)

Step-by-step explanation:

Therefore, the answer is \(\frac{8}{15}\).

Answer:

The answer is (-1 3/7)

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

1)

So we have:

\(\exists x\in\mathbb{N},y\in\mathbb{Z}|x^2=y^2\)

This can be interpreted as:

"There exists a natural number x and an integer y such that x² is equal to y²."

2)

So we want even numbers are in the set of integers.

\(\{2n:n\in\mathbb{Z}\}\in\mathbb{Z}\)

This is interpreted as:

"The set of even numbers (2n such that n is an integer) is in the set of integers"

Answer:

\(n_1=(3 + 1\sqrt{5} )/2\\\\n_2=(3 - 1\sqrt{5} )/2\)

Step-by-step explanation:

\(2n^2= 6n - 2\\\\2n^2-6n+2=0\\\\a=2\\\\b=-6\\\\c=2\)

\(n=(-b \pm \sqrt{b^2-4ac} )/2a\\\\n=(-(-6) \pm \sqrt{(-6)^2-4(2)(2)} )/2(2)\\\\n=(6 \pm \sqrt{36-16} )/4\\\\n=(6 \pm \sqrt{20} )/4\\\\n=(6 \pm 2\sqrt{5} )/4\\\\n=(3 \pm 1\sqrt{5} )/2\\\\n_1=(3 + 1\sqrt{5} )/2\\\\n_2=(3 - 1\sqrt{5} )/2\)

Answer:

D. -3x² + 2x

Step-by-step explanation:

Start by distributing the negative throughout the second quantity.

-5x + 4 - 3x² + 7x - 4

Combine like-terms and reorder so the variable with the highest power comes first.

-3x² + 2x

The +4 and -4 cancel out and are not in our final solution.

Answer:

21 % increase

Step-by-step explanation:

Lets imagine the sides of the rectangle are 100 & 200 cms.

The area would be 100 x 200 = 20000cm^2

If we added 10% onto each side, the sides would now be 110 & 220 cms.

The area would be 110 x 220 = 24200cm^2

We can now find percentage change:

\(\frac{24200-20000}{20000}\) = 21/100 = 21% increase.

The reason we can just pick random values of sides to do this question with is because we worked out percentage change, which will be the same no matter the proportion of the sides.

Hope this helped! Let me know if you have any questions :)

Answer:

d

Step-by-step explanation:

\(-2\frac{1}{6}- (-7\frac{1}{3})=-2\frac{1}{6} + 7\frac{1}{3}\\\\\)

                    \(=\frac{-13}{6} + \frac{22}{3}\\\\=\frac{-13}{6} + \frac{22*2}{3*2}\\\\=\frac{-13}{6} + \frac{44}{6}\\\\=\frac{-13+44}{6} \\\\= \frac{31}{6}\\\\=5\frac{1}{6}\)

Answer:

pathetic how you comment bs under questions on here and expect the same people to help you answer questions, grow up.