Construct parallelogram ABCD with the following guidelines.

Point A is located at (- 3, - 3) Point C is located at (3,2). The base is 4 units long. The area is 20 square units.

Step-by-step explanation:

to graph a line always find 2 points out has to go through. that means the points' coordinates make the equation true.

I usually start with x = 0.

point 1 of equation 1 is then

y = -2×0 + 6 = 6

(0, 6)

point 1 of equation 2 is then

y = (3/2)×0 - 1 = -1

(0, -1)

then I pick a value for x that makes the handling of any fractions easier. like in our case x = 2.

point 2 of equation 1 is then

y = -2×2 + 6 = -4 + 6 = 2

(2, 2)

point 2 of equation 2 is then

y = (3/2)×2 - 1 = 3 - 1 = 2

(2, 2)

oh, so I have found the intersection point right away (point 2 of both equations).

so, let's pick a different point 2 for equation 1, like x = 4

y = -2×4 + 6 = -8 + 6 = -2

(4, -2)

with these 4 points you define the 2 lines, and you have the intersection point at (2, 2).

(2x + 3) (x^2 - 6x + 9)

0.0764 is the probability that the scores differ by 5 or more points in either direction

The word "probability" derives from the Latin word "probitatem," which means "credibility, likelihood," from the noun probabilis in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

According to the information, the mean and standard deviation of "X" are:

μ(X) = 24

σ (X) = 2

We have to find the probability the scores differ by 5 or more points on either direction.

Consider X₁ and X₂ as the random variable, which showing the scores of Leon and Fred.

D = X₁ - X₂

According to the information the two scores are independent

The mean of μ(D) = 0

The standard deviation σ(D) = 2.828

Let's standardize D = -5

z = [x - μ(D)] /  σ(D)

z = - 1.77

Let's standardize D = 5

z = [x - μ(D)] /  σ(D)

z = 1.77

Using a table of typical normal probabilities as a guide:

= P (D ≤ -5) or P (D ≥ 5)

= P (z ≤ -1.77) + P (z ≥ 1.77)

= P (z ≥ 1.77) + P (z ≥ 1.77)

= 2P (z ≥ 1.77)
= 2(1 - P (z ≤ 1.77))

= 2 (1 - 0.9618)

= 0.0764

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Answer:

k+2 or k=2

Step-by-step explanation:

combine -5 and 7 to get your answer

Answer:

K+2

Step-by-step explanation:

K - 5 + 7 ....add -5 and 7

K+2

Answer: Firstly the area of parallelogram is. = b×h. so value of base is 9cm and height is 45cm . So area is equal to. base×height. = 9×45= 405² cm.

405cm²

Answer:

12, 16, 20

Step-by-step explanation:

Consider the Pythagorean triplet

3, 4, 5

Multiplying each by 4 gives

12, 16, 20 ( with 20 as a member )

Answer:

x < 1 2/15

Step-by-step explanation:

You can solve using PEMDAS, or the order of operations ( parentheses, exponents, multiplication, division, addition, subtraction )

2x < -2 ÷ 3 (4x + 4 )

Use the distributive property:

3 ( 4x + 4 )

( 3 * 4x ) + ( 3 * 4 )

12x + 12

2x < -2 ÷ 3 + 12x + 12

now divide:

-2 ÷ 3

-2/3

2x < -2/3 + 12x + 12

Now combine like terms:

2x < 12x + ( -2/3 + 12 )

2x < 12x + 11 1/3

Subtract 12x from each side:

-10x < 11 1/3

Divide each side by -10:

x < 1 2/15

There is your answer

Answer:

1250

Step-by-step explanation:

that's what I got please let me know if I'm correct

Answer:

881.5 meters.

Step-by-step explanation:

The horizontal plane at the level of wai-kin's eyes divide the height of the cliff into two parts. Let the upper part be represented by x and the lower part be represented by y.

The height of the cliff = x + y

Applying the appropriate trigonometry functions.

To determine the value of x;

Tan θ = \(\frac{opposite}{adjacent}\)

Tan \(36^{o}\) = \(\frac{x}{490}\)

⇒ x = 490 x Tan \(36^{o}\)

      = 490 x 0.7265

     = 355.985

x = 356 meters

To determine the value of y;

Tan θ = \(\frac{opposite}{adjacent}\)

Tan \(47^{o}\) = \(\frac{y}{490}\)

⇒ y = 490 x Tan \(47^{o}\)

      = 490 x 1.0724

      = 525.476

y = 525.5 meters

Therefore,

The height of the cliff = x + y

                                   = 355.985 + 525.476

                                   = 881.461

The height of the cliff is 881.5 meters.

it can be concluded that the rate of cancer of the brain or nervous system is different among those who use cell phones as compared to those who do not use cell phones.

According to the given data, Avtedy of 420.000 cell phone users found that 00317% of the developed cancer of the brain or nervous system. Prior to this study of cell phone, the rate of such cancer was found to be 00:27% for those using cell phones.

We use this sample data to estimate the percentage of total phone users who develop cancer of the brain or nervous system at a 95% confidence interval.

Hence, the option that is included in the 95% confidence interval is 0.0927%, which is approximately 0.003522 * 100, but the option that is not included in the 95% confidence interval is 0.027%.

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Answer:

(x-15)(x-1) x²

Step-by-step explanation:

x² (x²-16x+15)

a+b=-16

ab=15

a=-15

b=-1

x(x²-15)- (x-15)

(x-15)(x-1)

(x-15)(x-1) x²

The amount raised by a booster club compared with the number of  raffle tickets sold shows a constant rate of change;

A constant rate of change is realized when a change in one situation always results in a change in another. In the scenario of a booster club that regularly sells raffle tickets, the more tickets it sells, the higher the club gets.

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Answer:

x is 4/7 :)

Step-by-step explanation:

All three points (25, 3), (1, -1), and (100, 8) lie on the graph of the equation y = √x - 2.

To determine which of the given points lie on the graph of the equation y = √x - 2, we can substitute the x and y coordinates of each point into the equation and check if the equation holds true.

Let's check each point:

(25, 3):

Substituting x = 25 and y = 3 into the equation:

3 = √25 - 2

3 = 5 - 2

3 = 3

The equation holds true for this point.

(1, -1):

Substituting x = 1 and y = -1 into the equation:

-1 = √1 - 2

-1 = 1 - 2

-1 = -1

The equation holds true for this point as well.

(100, 8):

Substituting x = 100 and y = 8 into the equation:

8 = √100 - 2

8 = 10 - 2

8 = 8

The equation also holds true for this point.

Therefore, all three points (25, 3), (1, -1), and (100, 8) lie on the graph of the equation y = √x - 2.

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Answer:

$14.00

Step-by-step explanation:

So, the 20 peaches all weigh 4 oz, and there are 16 oz in 1 pound. 16 oz divided by 4 is also equal to 4 oz, so we need to divide $2.80 by 4, which would be $0.70. That means that a 4 oz peach would be $0.70, so we multiply that by 20, which gives us $14.00, so Stacey will need $14.00 to buy 20 peaches that each weigh 4 oz.

Answer: x = 13

Step-by-step explanation: When solving an equation like this, we are trying to get our variable which is our letter by itself.

So we first want to ask ourselves what is the 14 doing to x. Well, we can see that it's being added to x so to get x by itself, we will do the opposite of addition which is subtraction. So we subtract 14 from both sides of the equation.

The +14 -14 cancels out so we're left with x on the left.

On the right, we must subtract 14 from 27 to get 13.

So we have x = 13 which is the solution to this equation.

Answer:

\(x = 13\)

Step-by-step explanation:

\(x + 14 = 27 \\ x = 27 - 14 \\ x = 13\)

Answer: 5.3

Step-by-step explanation:

\(12.6-(5.1+2.2)\\\\=12.6-7.3\\\\=5.3\)

Answer:

16.8

Step-by-step explanation:

just took it on USA test-prep

In William Shakespeare's play "The Tempest," the main character is Prospero. He is the protagonist and central figure of the story.

In Act 1, the main challenge or obstacle that Prospero faces is his desire for revenge against those who wronged him. He was the Duke of Milan but was betrayed and exiled to a remote island along with his young daughter, Miranda. Throughout Act 1, Prospero uses his knowledge of magic and manipulation of the island's spirits to create a tempest, shipwrecking those who wronged him on the island.

His ultimate goal is to regain his position and power and seek justice for the past. Aside from seeking revenge, Prospero also faces challenges in protecting his daughter, managing the spirits on the island, and navigating his complex relationships with characters like Caliban and Ariel. However, his primary focus and obstacle in Act 1 revolve around his quest for retribution and asserting his authority.

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Answer:

40

Step-by-step explanation:

A. 50 - 10 = b

B. Finding the equivalence is the first step

C. b = 40

D. Subtracting 10 from 50

E. Already did b = 40

F. Yes, they both work the same way.

G. you have choices to make to get the right answer.

Answer:

20

Step-by-step explanation:

Rise over run

Answer:

m = 20

Step-by-step explanation:

Answer:

2430kg

Step-by-step explanation:

3 tonnes is 3000kg so 3 tonnes 335kg is 3335kg. Take 3335 - 905 you get 2430

P(female) × P(fail) = 0.100 and P(female and fail) = 0.127, the two events are not equal so the events are dependent.

We can calculate the probabilities as follows:

Total number of students = 25 + 10 + 20 + 8 = 63

P(female) = Number of females / Total number of students

= 20 / 63

= 0.317

P(fail) = Number of students who failed / Total number of students

= (10 + 8) / 63

= 0.317

P(female and fail) = Number of female students who failed / Total number of students

= 8 / 63

= 0.127

Since P(female) × P(fail) = (0.317) × (0.317) = 0.100 and P(female and fail) = 0.127, the two events are not equal so the events are dependent.

Therefore, based on the calculations, we can conclude that gender and passing the test are dependent events, not independent.

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Answer:

B. x=6

Step-by-step explanation:

the (3x+2)° angle and the 20° angle are vertical angles, which means that they're congruent

to solve for x:

3x+2=20

3x=18

x=6

Answer:

it b

Step-by-step explanation:

The surface area obtained by rotating the curve y = x² from x = 0 to x = 8 about the y-axis is 2048π square units.

We are given that the curve y = x² is rotated from x = 0 to x = 8. So our range of integration is from x = 0 to x = 8.

To use the disk method, we need to express the curve in terms of y instead of x. For the equation y = x², we can rewrite it as x = √y.

The radius of each disk is the distance between the y-axis and the curve. Since we are rotating the curve around the y-axis, the radius will be the value of x for a given y. Therefore, the radius is x = √y.

The area of each disk can be found using the formula for the area of a circle, which is A = πr². In this case, the area is A = π(x²) = π(√y)² = πy.

To find the total surface area, we need to sum up the areas of all the disks. We integrate the area function πy with respect to y from y = 0 to y = 64 (since x = 8 corresponds to y = 64).

Surface Area = ∫(πy)dy from 0 to 64

= π∫y dy from 0 to 64

= π[y²/2] from 0 to 64

= π[(64²/2) - (0²/2)]

= π[2048]

= 2048π square units.

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Below, you will learn how to solve the problem.

(a) To find the linear relationship y = mx + b between x = year and y = profit, we first need to find the slope (m) and the y-intercept (b).

The slope (m) is the change in y (profit) divided by the change in x (year):
m = (17 - 5)/(6 - 2)

m = 12/4

m = 3

Next, we can use one of the data points (2, 5) and the slope (3) to find the y-intercept (b):
5 = 3(2) + b
b = 5 - 6

b = -1

So the linear relationship between x = year and y = profit is:

y = 3x - 1

(b) To find the company's profit at the end of 3 years, we can plug in x = 3 into the equation:
y = 3(3) - 1

y = 8

So the company's profit at the end of 3 years is $8 million.

(c) To predict the company's profit at the end of 8 years, we can plug in x = 8 into the equation:

y = 3(8) - 1 = 23

So the company's profit at the end of 8 years is predicted to be $23 million.

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It is a graph of a function

The third degree - polynomial can be factored into a linear factor of x+2 and a quadratic factor of 2x²+x+5.

A third degree polynomial is a collection of algebraic expressions such that the highest degree of the variable is 3 and there are no fractional degrees and exponential variable.

To factor a polynomial we will use the factor theorem to find the linear factor. Then by dividing the polynomial by the linear factor we will calculate the quadratic factor.

Given polynomial P(x) = 2x³ + 5x² + 7x + 10

Now by using the trial and error method factor theorem we see that

g(x) = (x+2) is a factor of P(x) .

Now let us find the quadratic factor as:

P(x) ÷ g(x) = ( 2x³ + 5x² + 7x + 10) ÷ (x+2) = 2x²+x+5

Hence the third degree - polynomial can be factored into a linear factor of x+2 and a quadratic factor of 2x²+x+5.

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Disclaimer: The correct polynomial is  P(x) = 2x³ + 5x² + 7x + 10 .

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Answer:

r = 106

Step-by-step explanation:

113 + 38 = 151

151 - 45 = 106

r = 106