What is the complete factorization of the polynomial below?

ANSWER:

500.5 m²

STEP-BY-STEP EXPLANATION:

To know how much artificial grass should be purchased to cover the athletic field, we must calculate the area corresponding to the figure.

The area of a trapezoid has the following formula:

Where b is the small base, B is the large base and h is the height, we substitute and calculate the area, like this:

It is necessary to purchase the amount of 500.5 m² to be able to cover the athletic field

A quadrant is simply a part of the coordinate plane

The possible position of point P is (b) quadrant II or quadrant III

The coordinates of point P is given as:

\(\mathbf{P =(-5,\_)}\)

Represent the missing y-coordinate with y.

So, the coordinate becomes

\(\mathbf{P =(-5,y)}\)

The above coordinate shows that the x-coordinate of point P is negative.

The x-coordinate is negative in the second and the third quadrants

i.e. quadrant II and quadrant III

Hence, the position of point P is (b) quadrant II or quadrant III

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Quadrant 2 or 3

Remember, the first coordinate is -5.

And the first coordinate in an ordered pair is always on the x axis, or the horizontal line

On a coordinate plane, you would have to start from the origin, or the center of the plane where the y and x axis intersect, and move left 5 times.

That section of the x axis your dot is on is between quadrant 2 and 3.

If your other coordinate was a positive (say, 6), you would move up six times and land in the second quadrant

If your other coordinate was -6, you would move down six times and land in the third quadrant

Answer:

12e - 32j

Step-by-step explanation:

Simply distribute the 4.

4 (3e) = 12e

4 (-8j) = - 32j

Put it together: 12e - 32j

Answer:

a

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I did the test

0.2829

I think it would be thousandths I'm pretty sure :)

Answer:

C

Step-by-step explanation:

If you look at the constant terms for each of them, ABD is 18, and only C is 14

ఊhe directional derivative of f at the point (1, 2, 2) in the direction of the vector v = (1/5√2)i + (1/5√2)j is 2√2.

To find the directional derivative of the function f(x, y, z) = 2z^2x + y^3 at the point (1, 2, 2) in the direction of the vector v = (1/5√2)i + (1/5√2)j, we can use the formula for the directional derivative:

D_v(f) = ∇f · v

where ∇f is the gradient of f.

Taking the partial derivatives of f with respect to each variable, we have:

∂f/∂x = 2z^2

∂f/∂y = 3y^2

∂f/∂z = 4xz

Evaluating these partial derivatives at the point (1, 2, 2), we get:

∂f/∂x = 2(2)^2 = 8

∂f/∂y = 3(2)^2 = 12

∂f/∂z = 4(1)(2) = 8

Therefore, the gradient ∇f at (1, 2, 2) is given by ∇f = 8i + 12j + 8k.

Substituting the values into the directional derivative formula, we have:

D_v(f) = ∇f · v = (8i + 12j + 8k) · (1/5√2)i + (1/5√2)j

= 8(1/5√2) + 12(1/5√2) + 8(0)

= (8/5√2) + (12/5√2)

= (8 + 12)/(5√2)

= 20/(5√2)

= 4/√2

= 4√2/2

= 2√2

Hence, the directional derivative of f at the point (1, 2, 2) in the direction of the vector v = (1/5√2)i + (1/5√2)j is 2√2.

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Answer:

27x-24

Step-by-step explanation:

Using distributive property, we can simplify 8(2x-3) to 16x-24. That becomes 16x-24+11x.

Then, we can add 16x and 11x to get 27x.

The answer will be 27x-24.

I hope you found this helpful, and if it was, please mark this answer as brainliest! Thank you! :)

Answer:

222222222222222222222

Answer:

a = 8, b = \(\frac{3}{2}\)

Step-by-step explanation:

Given the exponential function

f(x) = a\(b^{x}\)

To find a and b use the given coordinate points on the graph

Using (0, 8 ), then

8 = a\(b^{0}\) [ \(b^{0}\) = 1 ] , then

a = 8

f(x) = 8\(b^{x}\)

Using (2, 18 ) , then

18 = 8b² ( divide both sides by 8 )

\(\frac{18}{8}\) = b² , that is

b² = \(\frac{9}{4}\) ( take the square root of both sides )

b = \(\sqrt{\frac{9}{4} }\) = \(\frac{3}{2}\)

Thus

f(x) = 8\((\frac{3}{2}) ^{x}\)

Correct question is;

A rectangular storage container with an open top has a volume of 20 m³. The length of its base is twice its width. Material for the base costs $20 per square meter; material for the sides costs $8 per square meter. Express the cost of materials as a function of the width of the base.

Answer:

C = 40W² + 480/W

Step-by-step explanation:

We are given;

Volume; V = 20 m³

Length of base is L

Width of base is W

We are told L = 2W

Formula for volume of a cuboid = LWH

Thus;

20 = 2W × W × H

20 = 2W²H

H = 10/W²

Now, we are given cost of materials for base and sides.

Formula for base area = LW = 2W²

Formula for side areas = 2(LH) + 2(WH) = 2(2WH) + 2WH = 6WH = 6W(10/W²) = 60/W

Cost per Sq.m of base = $20.

Thus, base cost = 20(2W²) = 40W²

Cost per Sq.m of sides = 8(60/W)

Thus,sides cost = 480/W

Total cost of sides and base is;

C = 40W² + 480/W

The value of m<1 = 105 degrees.

Vertical angles are a pair of non-adjacent angles formed when two lines intersect. They are congruent, meaning they have the same measure. Therefore, if m<2 = (-5x + 75)°, then m<1 must be equal to it as they are vertical angles.

Substituting m<2 into the equation:

Since m<1 and m<2 are vertical angles, they must be equal to each other, so we can set the equation equal to m<2:

Solving for x:

Now we can substitute x = 8 into the original equation for m<1:

m<1 = (7x - 21)° = (7*8 - 21)° = 105°

Therefore, m<1 = 105 degrees.

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Answer:

28

Step-by-step explanation:

90 - 62 = 28

Answer:

28

Step-by-step explanation:

hence it forms 90degree 90-62=28

1) The common-difference is -1.2.

2) The 15th term is 40.4.

3)The sum of the first 292 terms is 35,553.6.

1. The first term of an arithmetic sequence is 9, and the sixth term is 3. We need to find the common difference.

Using the formula for the nth term of an arithmetic sequence:

Tn = a + (n - 1)d

We can plug in the values:

T1 = 9

T6 = 3

n = 6

3 = 9 + (6 - 1)d

3 = 9 + 5d

-6 = 5d

d = -6/5

d = -1.2

The common difference is -1.2.

2.The 32nd term of an arithmetic sequence is 14.9, and the common difference is -1.5. We need to find the 15th term.

Using the formula for the nth term of an arithmetic sequence:

Tn = a + (n - 1)d

We can plug in the values:

T32 = 14.9

n = 32

d = -1.5

T32 = a + (32 - 1)(-1.5)

14.9 = a + 31(-1.5)

14.9 = a - 46.5

a = 14.9 + 46.5

a = 61.4

Now we can find the 15th term:

T15 = 61.4 + (15 - 1)(-1.5)

T15 = 61.4 + 14(-1.5)

T15 = 61.4 - 21

T15 = 40.4

The 15th term is 40.4.

3.The first term of an arithmetic sequence is 5, and the common difference is 0.8. We need to find the sum of the first 292 terms.

Using the formula for the sum of an arithmetic sequence:

Sn = (n/2)(2a + (n - 1)d)

We can plug in the values:

a = 5

n = 292

d = 0.8

Sn = (292/2)(2(5) + (292 - 1)(0.8))

Sn = 146(10 + 233.6)

Sn = 146(243.6)

Sn = 35,553.6

The sum of the first 292 terms is 35,553.6.

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1) The common difference in the arithmetic sequence is -1.2.

2) The 15th term of the arithmetic sequence is 40.4.

3) The sum of the first 292 terms of the arithmetic sequence is 28626.4.

4) The balance in the account after 5 years will be $13,760.

5) The balance in the account after 30 months will be $8,474.4.

6) The monthly payment amount will be $137.90

7) The simple annual interest rate charged by The Saver is 415%

Exp:

Question 1:

To find the common difference in an arithmetic sequence, we can use the formula:

common difference = (sixth term - first term) / (6 - 1)

In this case, the first term is 9 and the sixth term is 3. Plugging these values into the formula:

common difference = (3 - 9) / (6 - 1)

common difference = -6 / 5

common difference = -1.2

Therefore, the common difference in the arithmetic sequence is -1.2.

Question 2:

To find the 15th term of an arithmetic sequence, we can use the formula:

nth term = first term + (n - 1) * common difference

In this case, the 32nd term is given as 14.9, and the common difference is -1.5. Plugging these values into the formula:

14.9 = first term + (32 - 1) * (-1.5)

14.9 = first term + 31 * (-1.5)

14.9 = first term - 46.5

first term = 14.9 + 46.5

first term = 61.4

Now we can find the 15th term using the first term and the common difference:

15th term = first term + (15 - 1) * common difference

15th term = 61.4 + 14 * (-1.5)

15th term = 61.4 - 21

15th term = 40.4

Therefore, the 15th term of the arithmetic sequence is 40.4.

Question 3:

To find the sum of the first n terms of an arithmetic sequence, we can use the formula:

sum = (n/2) * (2 * first term + (n - 1) * common difference)

In this case, the first term is 5 and the common difference is 0.8. Plugging these values into the formula:

sum = (292/2) * (2 * 5 + (292 - 1) * 0.8)

sum = 146 * (10 + 233 * 0.8)

sum = 146 * (10 + 186.4)

sum = 146 * 196.4

sum = 28626.4

Therefore, the sum of the first 292 terms of the arithmetic sequence is 28626.4.

Question 4:

To calculate the balance in the account after a certain number of years with monthly interest payments, we can use the formula:

balance = principal * (1 + (interest rate / 100) * (number of months / 12))

In this case, the principal is $8,600, the interest rate is 12% (0.12 as a decimal), and the time is 5 years. Plugging these values into the formula:

balance = 8600 * (1 + (0.12 / 100) * (5 * 12 / 12))

balance = 8600 * (1 + 0.12 * 5)

balance = 8600 * (1 + 0.6)

balance = 8600 * 1.6

balance = 13760

Therefore, the balance in the account after 5 years will be $13,760.

Question 5:

To calculate the balance in the account after a certain number of months with monthly interest payments, we can use the formula:

balance = principal * (1 + (interest rate / 100) * (number of months / 12))

In this case, the principal is $6,284, the interest rate is

14% (0.14 as a decimal), and the time is 30 months. Plugging these values into the formula:

balance = 6284 * (1 + (0.14 / 100) * (30 / 12))

balance = 6284 * (1 + 0.14 * 2.5)

balance = 6284 * (1 + 0.35)

balance = 6284 * 1.35

balance = 8474.4

Therefore, the balance in the account after 30 months will be $8,474.4.

Question 6:

To calculate the monthly payment amount for a loan with a given principal, interest rate, and number of equal monthly payments, we can use the formula:

monthly payment = (principal + (principal * (interest rate / 100) * (number of months))) / number of months

In this case, the principal is $1,709, the interest rate is 182% (1.82 as a decimal), and the number of equal monthly payments is 16. Plugging these values into the formula:

monthly payment = (1709 + (1709 * (1.82 / 100) * 16)) / 16

monthly payment = (1709 + (1709 * 0.0182 * 16)) / 16

monthly payment = (1709 + (1709 * 0.2912)) / 16

monthly payment = (1709 + 497.3848) / 16

monthly payment = 2206.3848 / 16

monthly payment = 137.8993

Therefore, the monthly payment amount will be $137.90 (rounded to two decimal places).

Question 7:

To calculate the simple annual interest rate for a loan with a given principal, monthly payment amount, and number of months, we can use the formula:

interest rate = ((monthly payment * number of months) / principal - 1) * 100

In this case, the principal is $1,000, the monthly payment amount is $859, and the number of months is 6. Plugging these values into the formula:

interest rate = ((859 * 6) / 1000 - 1) * 100

interest rate = (5154 / 1000 - 1) * 100

interest rate = (5.154 - 1) * 100

interest rate = 4.154 * 100

interest rate = 415.4

Therefore, the simple annual interest rate charged by The Saver is 415% (rounded to the nearest whole number).

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Answer: 33.375 feet

Step-by-step explanation:

To find the maximum height, we need to find the vertex of the parabolic function h = 16t² + 12t + 30.

The vertex of a parabola with equation y = ax^2 + bx + c is located at x = -b/2a and y = c - b^2/4a.

In this case, a = 16, b = 12, and c = 30.

So,

t = -b/2a = -12/(2*16) = -3/8

h = 16(-3/8)² + 12(-3/8) + 30 = 33.375

Therefore, the maximum height reached is 33.375 feet.

a) The solution of the system is: (λ, a, b) = (- 5, - 11, - 26).

b) The coordinates of the point P are (x, y, z) = (- 16 / 3, - 43, 152 / 3).

c) Vectors AP and PB are collinear for their ends lie on the line. The ratio AP : PB is 83.248 : 73.491 (1.133 : 1).

a) In this problem we have a equation of the line in vector form, whose form is:

r = (5, 19, - 1) + λ · (1, 6, - 5)

Now we find the value of λ for the case r = (0, a, b):

(0, a, b) = (5, 19, - 1) + λ · (1, 6, - 5)

5 + λ = 0

19 + 6 · λ = a

- 1 + 5 · λ = b

The solution of the system is: (λ, a, b) = (- 5, - 11, - 26).

b) Then, the following condition must be fulfilled:

OP • PB = 0

(5 + λ, 19 + 6 · λ, - 1 + 5 · λ) • [(4, 13, 4) - (5 + λ, 19 + 6 · λ, - 1 - 5 · λ)] = 0

(5 + λ, 19 + 6 · λ, - 1 + 5 · λ) • (- 1 - λ, - 6 - 6 · λ, 5 + 5 · λ) = 0

(5 + λ) · (- 1 - λ) + (19 + 6 · λ) · (- 6 - 6 · λ) + (- 1 + 5 · λ) · (5 + 5 · λ) = 0

- (5 + λ) · (1 + λ) - 6 · (19 + 6 · λ) · (1 + λ) + 5 · (- 1 + 5 · λ) · (1 + λ) = 0

- (5 + 6 · λ + λ²) - 6 · (19 + 25 · λ + 6 · λ²) + 5 · (- 1 + 4 · λ + 5 · λ²) = 0

- 5 - 6 · λ - λ² - 114 - 150 · λ - 36 · λ² - 5 + 20 · λ + 25 · λ² = 0

- 12 · λ² - 136 · λ - 124 = 0

There are two solutions: λ₁ = - 1, λ₂ = - 31 / 3, whose points P are:

r₁ = (5, 19, - 1) + (- 1) · (1, 6, - 5)

r₁ = (4, 13, 4)

r₂ = (5, 19, - 1) + (- 31 / 3) · (1, 6, - 5)

r₂ = (- 16 / 3, - 43, 152 / 3)

Then, the coordinates of the point P are (x, y, z) = (- 16 / 3, - 43, 152 / 3).

c) Vectors AP and PB are collinear for their ends lie on the line. The ratio can be found by using the magnitudes of each vector:

Vector AP

AP = (- 16 / 3, - 43, 152 / 3) - (0, - 11, - 26)

AP = (- 16 / 3, - 32, 230 / 3)

AP = √(AP • AP)

AP ≈ 83.248

Vector PB

PB = (4, 13, 4) - (- 16 / 3, - 43, 152 / 3)

PB = (28 / 3, 56, - 140 / 3)

PB = √(PB • PB)

PB ≈ 73.491

The ratio AP : PB is 83.248 : 73.491 (1.133 : 1).

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Answer:

20

Step-by-step explanation:

any thing multiplied by a fraction gets divided so you need to reverse it and divide to get the answer

Answer:

20

Step-by-step explanation:

1/2 times 20 = 10

its like the same thing as 10 times 2 = 20

Answer:

Table 1: Not proportional

Table 2: Proportional, y is 4 times x.

Step-by-step explanation:

The numbers are the same if the ratio between the values of x and y is the same.

Table 1:

10/5 = 2

32/8 = 4

66/11 = 6

Not proportional, because the values of the divisions are not the same

Table 2:

16/4 = 4

24/6 = 4

32/8 = 4

Values the same, so proportional.

y is 4 times x.

According to the conversation we can infer that the information focused on the conversation of two people; one of them is studing for an exam.

To identify what is the conversation about we have to consider who is talking and what are the ideas that they share. In this case, we can infer that the main idea of this conversation is that one of them is studying for an exam this week.

Also, the second person is apologizing because he considered that he is distracting the other person. So, the correc information about de conversation is a short conversation about study.

Note: This question is incomplete. Here is the complete information:

Conversation:
Hello

Hello, How are you?

I am fine, and you?

i am fine too, What are you doing?

I am studing for an exam this week.

Oh, sorry I won´t distract you.

Don´t worry.

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Answer:

B, 4,797,896

Step-by-step explanation:

599,737 multiplied by 2 is 1,199,474 then multiplied by 2 is 2,398,948 then multiplied by 2 is 4,797,896.

I multiplied by 2, 3 times because the population of a certain kind of bacteria doubles in size every 5 minutes and 15/5=3.

Answer:

The other number is 14.

Step-by-step explanation:

To find the other number, all you have to do is divide 1/7 by 2.

\(\frac{2}{1/7}\)

\(= 2 \cdot 7\)

\(= 14\)

Hope this helped!

Answer:

science makes you understand the world understand the living organisms understand electricity and understand chemical reactions which is one of the most important things to know in life

\(3x-30=2x-9\\\\\implies 3x -2x = -9 +30\\\\\implies x = 21\)

Vertical angles are equal

Done!

Answer: $52.50

Step-by-step explanation: Divide 28.00 by 8. It would equal $3.50, and that's how much per gallon. Multiply 3.50 by 15. So, the final answer is $52.50.

Expression that has the same addend twice, such as 3 + 3 = 6 or 8 + 8 = 16

What do you mean by One-to-One Correspondence?

the capability of relating one object to another. For each number spoken aloud, the learner should be able to count or move one object while saying "1,2,3,4". She has not learned one-to-one correspondence if she accidentally counts an object twice or skips one of the things while counting. Before starting Giggle Facts, students must be able to match one object to each number counted.

Remind your kids that a double fact is a mathematical expression that has the same addend twice, such as 3 + 3 = 6 or 8 + 8 = 16. Give children the chance to practise combining groups of the same number using manipulatives or other classroom supplies.

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Answer:

A double expression

Step-by-step explanation:

Tyler will need to score an 85 on Test 6 to finish the year with an average score of 75.

To calculate the score that Tyler needs to get on Test 6 to achieve an average score of 75, we need to use the following formula

(average score) = (total points earned / total number of tests)

Let's assume that Tyler has taken five tests so far, and his total points earned are X. Also, let's assume that Test 6 is worth Y points.

Therefore, the equation becomes:

75 = (X + Y) / 6

Multiplying both sides by 6, we get:

X + Y = 450

Now, let's say Tyler's scores on his first five tests are as follows

Test 1: 65, Test 2: 72, Test 3: 70, Test 4: 78 and Test 5: 80

To find out how many points Tyler has earned so far (X), we simply add up his scores on the first five tests

X = 65 + 72 + 70 + 78 + 80

X = 365

Substituting this value of X in the equation we derived earlier, we get

365 + Y = 450

Solving for Y, we get:

Y = 85

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The given expression can be written as ln[(x-1)^6(x+1)]. This is a single term expression that represents the given expression.

To write the given expression in a single term, we can use the logarithmic identity log(a/b) = log(a) - log(b). Using this identity, we can simplify the expression as follows:
3[2ln(x-1) - ln(x)] + ln(x+1)
= 3ln[(x-1)^2/x] + ln(x+1)
= ln[(x-1)^6(x+1)]
Therefore, the given expression can be written as ln[(x-1)^6(x+1)]. This is a single term expression that represents the given expression.
To simplify the given expression, first apply the properties of logarithms. Here is the expression:
3[2ln(x-1) - ln(x)] + ln(x+1)
Step 1: Use the logarithmic property a*log_b(x) = log_b(x^a) for the 2ln(x-1) term:
3[ln((x-1)^2) - ln(x)] + ln(x+1)
Step 2: Apply the logarithmic property log_b(x) - log_b(y) = log_b(x/y) for the terms inside the brackets:
3[ln(((x-1)^2)/x)] + ln(x+1)
Step 3: Apply the logarithmic property a*log_b(x) = log_b(x^a) again for the 3 in front of the brackets:
ln((((x-1)^2)/x)^3) + ln(x+1)
Step 4: Apply the logarithmic property log_b(x) + log_b(y) = log_b(xy) for the final expression:
ln(((((x-1)^2)/x)^3)(x+1))
Now, the expression has been simplified into a single term.

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