K
Factor out the greatest common factor.
3x³+18x²-12x
3x³ +18x²-12x=(Type your answer in factored form.)

The formula holds true for matrices A and B.

The formula (A + B)^2 = A^2 + 2AB + B^2 holds true for all matrices A and B that are of the same size and can be added and multiplied. To prove this, we calculate the left-hand side and the right-hand side of the equation:

(A + B)^2 = (A + B)(A + B) = A^2 + AB + BA + B^2

Since AB = BA, we can simplify the equation to:

(A + B)^2 = A^2 + 2AB + B^2

So, the formula holds true for matrices A and B.

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Kelly flew a total of [tex]6\frac{17}{42}[/tex] hours..

A fraction represents a part of a whole.

Given that Kelly took  2 4/7 hours to fly from City A to City B

Again Kelly took another 3 5/6 hours to fly from City B to City C.

We have to find the total time taken by Kelly to fly from City A to city B

To find this we have to add the fractions.

[tex]2\frac{4}{7} +3\frac{5}{6}[/tex]

Convert mixed fractions to proper fraction and solve.

18/7 + 23/6

The LCM of 7 and 6 is 42

108+161/42

269/42

[tex]6\frac{17}{42}[/tex]

Hence, Kelly flew a total of [tex]6\frac{17}{42}[/tex] hours.

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The 5th term of the geometric sequence described by an = 5(1.5)-1 is 6.5

Geometric progression,  which is also called geometric sequence, is defined as a sequence with non-zero numbers where all of the terms after the first is determined by multiplying the previous one by a fixed, non-zero number that is termed the common ratio.

The general formula for a geometric sequence is given as;

an = ar^n-1

From the information given, we have that the nth term of the geometric sequence is expressed with the equation;

an = 5(1.5)-1

expand the bracket

an = 7.5 - 1

Now, subtract the value, we get;

an = 6.5

Hence, the value of the term of the geometric sequence is 6.5

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Step-by-step explanation:

Given:

Present value =₹ 40000

Interest rate =6% per annum

Time =6 months

To find the amount we have the formula,

Amount (A)=P(1+(r/100))n

where P is present value, r is rate of interest, n is time in years

Now substituting the values in above formula we get,

∴A=40000(1+(6/4)/100) ²

⇒A=40000(1+3/200)²

⇒A=40000(203/200)²

⇒A=40000(203/200) ²

⇒A=203×203

⇒A=₹ 41209

∴ Compound interest =A–P

=41209–40000=₹ 1209

The sequence 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30 has 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 of 2's

A number system is defined as a system of writing to express numbers.

The concept on skip counting by 2’s or twos is an essential skill to get the idea when we progress to learn the concept on counting to basic addition.

2=2×1

4=2×2=2 times

6=2×3=3 times

10=2×5=5 times

12=2×6= 6 times

14=2×7=7 times

16=2×8=8 times

18=2×9=9 times

20=2×10= 10 times

22=2×11=11 times

24=2×12=12 times

26=2×13=13 times

28=2×14=14 times

30=2×15=15 times

Hence, the sequence 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30 has 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 of 2's.

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The solution for the system of equations is negative one fourth comma three fourths.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Slope intercept form of a line is y = mx + c, where m is the slope and c is the y intercept.

Given two lines on a graph.

Let y = m₁x + c₁ and y = m₂x + c₂ are the equations of two lines.

One line passes through (0, 1) and (1, 2).

m₁ = (2 - 1) / (1 - 0) = 1

Substituting m₁ = 1 and a point (x, y) = (0, 1) in y = m₁x + c₁,

1 = c₁

Equation of one line is y = x + 1.

Other line passes through (0, 0) and (1, -3).

m₂ = (-3 - 0) / (1 - 0) = -3

Substituting m₂ = 1 and a point (x, y) = (0, 0) in y = m₂x + c₂,

0 = c₂

Equation of second line is y = -3x

Solving both the equations y = x + 1 and y = -3x,

-3x = x + 1

-4x = 1

x = -1/4

y = -3x = 3/4

Solution is (-1/4, 3/4).

Hence the solution of the system of equations is the point (-1/4, 3/4).

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Answer: X divided by 5

               X/5

Step-by-step explanation:

if x is the cost of the dinner each person pays x divided by 5 because there are 5 people

Answer:

[tex]x2 + 4x + 4 = 0 [/tex]

Answer: this is like multiplying. this is way to easy.the answer is 25.

Step-by-step explanation:

the answer is 25 bc its just saying

whats 5 times 5 which the answer is 25 right ?

The probability that all have type B​+ blood is 0.000286 The probability that none of the have type B​+ blood is 0.572898.

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

Given;

The probability that a person in the United States has type B​+ blood is 13​%.

Since four unrelated people in the United States are selected at random, we can say that each person is independent of the other to have B+ blood group;

Let X be the number of persons who have blood group B+ in the group of 4 persons;

X is Binomial with p = 0.13;

a) P(X = 4) = (0.13)4 = 0.000286

b) P(x =0) = (1 -0.13)¹ = 0.572898

Therefore, the probabilities will be 0.000286 and 0.572898

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Answer:

192 in²

Step-by-step explanation:

The surface area of a square pyramid can be calculated by summing up the area of its base and four lateral faces.

The base area of the square pyramid is 8 x 8 = 64 in².

The area of each lateral face is a triangle with base 8 in and height 8 in, so its area is 1/2 x 8 x 8 = 32 in².

So the total surface area of the pyramid is 64 + 4 x 32 = 192 in².

192in²

Step-by-step explanation:

Each side of the base of a square pyramid measures 8 inches.The height of each lateral face of the pyramid is also inches.

What is the surface area of the pyramid?

192in²

Based on the proportionate equation of the selling price (S), cost price (C), and profit (P), the change in S caused by decrease of C and increase of P is decrease by 4%

Based on the given information, we know that:

S ∝ √C --> S directly varies as the square root of C

S ∝ 1/P³ --> S inversely as the cube of P

We can combine both relationships to make a proportionate equation:

S = √C / P³

We know from the case that:

ΔC = - 2%

ΔP = 1%

Then:

C' = C + ΔC

C' = C + (-0.02)P

C' = 0.98C

P' = P + ΔP

P' = P + (0.01)P

P' = 1.01P

S' = √C' / P'³

S' = √(0.98C) / (1.01P)³

S' = 0.96 √C/P³

S' = 0.96S

ΔS = S' - S

ΔS = 0.96S - S

ΔS = - 4%

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Step-by-step explanation:

x = 2 3/4

y = -1 1/4

I think this is the answer

A

The graph of the function g(x) = 1/x + 13 is a transformation of the graph of f(x) = 1/x. The transformation that has been applied is a vertical shift of 13 units upward. This means that every point on the graph of f(x) has been moved upward by 13 units along the y-axis, resulting in the new graph of g(x). In other words, the graph of g(x) will be parallel to the graph of f(x) but shifted upward by 13 units.

Work Shown:

Complementary angles add to 90 degrees.

A+B = 90

(3x+18)+(2x+17) = 90

5x+35 = 90

5x = 90-35

5x = 55

x = 55/5

x = 11

Then we can determine each angle:

As a check: A+B = 51+39 = 90 to confirm the answer.

Answer:

what is the period of the sinusoidal function?

4

Step-by-step explanation:

You're welcome.

All the correct statements are,

a) 3 lb plaster / 1 qt water is a unit rate for the mis.

c) Using the same rate, the potter mixes 9 pounds of plaster with 3 quarts of water.

e) Using the same rate, the potter mixes 12 pounds of plaster with 4 quarts of water.

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

We have to given that;

A potter mixes 6 pounds of pottery plaster with 2quarts of water.

Now, We get;

The unit rate for the mis = 6/2

                                      = 3/1

Thus, 3 lb plaster / 1 qt water is a unit rate for the mis.

And, Using the same rate, the potter mixes 9 pounds of plaster with 3 quarts of water.

Using the same rate, the potter mixes 12 pounds of plaster with 4 quarts of water.

Thus, All the correct statements are,

a) 3 lb plaster / 1 qt water is a unit rate for the mis.

c) Using the same rate, the potter mixes 9 pounds of plaster with 3 quarts of water.

e) Using the same rate, the potter mixes 12 pounds of plaster with 4 quarts of water.

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The complete question is shown in figure.

The vertex of the absolute value function y = |3x - 9| is at (3, 0).

The actual name is the vertex, and to find the vertex we first need to find the value of x such that the argument of the absolute value part becomes zero, then we need to solve:

3x - 9 = 0

3x = 9

x = 9/3 = 3

x = 3

Now we can evaluate the absolute value function there:

y = |3*3 - 9|

y = 0

The vertex is at (3, 0).

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The different ways can the program select which students will answer the five questions will be 1,72,10,368.

A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

Given, Mrs. Mortlock uses a calculator program to select students at random to answer questions during class. Each of the 28 students in her class is equally likely to be chosen every time she runs the program.

Multiplication counting principle: If the first event could occur in m ways and the second event could occur in n ways, then the number of ways that the two events could occur in the sequence is m⋅n.

There are 28 students, and each of the 28 students is equally likely to be selected to answer each question among 5 questions.

First question: 28 ways

Second question: 28 ways

Third question: 28 ways

Fourth question: 28 ways

Fifth question: 28 ways

Use the multiplication counting principle.

Thus,

Combination = 28^5

Combination = 1,72,10,368

Therefore, The different ways can the program select which students will answer the five questions will be 1,72,10,368.

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The equation of the circle can be written as:

(x - 3)^2 + (y + 2)^2 = 16

We know that for a circle of radius R and the center is (a, b) can be written as:

(x - a)^2 + (y - b)^2  = R^2

Here we want to find the equation for a circle of radius of 4 units and a center at (3, -2), then the equation is:

(x - 3)^2 + (y -( - 2))^2 = 4^2

Now we can simplify that equation to get:

(x - 3)^2 + (y + 2)^2 = 16

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The sum of the angles of the triangle below are angle A = 34.91°, angle B = 86.41°, and angle C = 58.68°.

According to the triangle sum theorem, a triangle's internal angles can be added up to 180 degrees. The triangle sum theorem, often referred to as the angle sum theorem of the triangle, states that the total of the measures of a triangle's internal angles in a Euclidean space adds up to 180 degrees, whether the triangle is acute, obtuse, or right.

Let a = 8, b = 14 and c = 12 for the given triangle.

Then,

cos (A) = (b² + c² − a²) / 2bc

cos (A) = (14² + 12² - 8²)/ (2)(14)(12)

cos (A) = (196 + 144 - 64)/ 336

cos (A) = 0.82

A = cos⁻¹ (0.82)

A = 34.91°

Similarly, for angle B.

Cos (B) = (c² + a² − b²)/2ca

Cos (B) = (12² + 8² - 14²)/ (2)(12)(8)

A = cos⁻¹ (0.0625)

B = 86.41°

The sum of all the angles of a triangle is 180:

A + B + C = 180°

34.91° + 86.41° + C = 180°

C = 58.68°

Hence, the sum of the angles of the triangle below are angle A = 34.91°, angle B = 86.41°, and angle C = 58.68°.

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The inequality nature is discussed below.

Given is a inequality.

Assume the inequality to be -

ax + b > g

Now, if for the value of g = - 7, the expression - (ax + b) is greater than g       {for any specific value of x} then the inequality is said to be true.

Therefore, the inequality nature is discussed above.

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Answer:

Step-by-step explanation:

...........

Answer: I understand that you're feeling overwhelmed. Let's try to solve this problem together.

To evaluate the function f(x) = -3x + 5 at a specific value of x, we substitute that value into the expression and simplify. For example, if we want to evaluate the function at x = 2:

f(2) = -3 * 2 + 5 = -6 + 5 = -1

So f(2) = -1. This means that the value of the function when x = 2 is -1.

If you have any other questions or concerns, I'm here to help!

Step-by-step explanation:

Answer:

30,000 ÷6=

5,000 a month

Answer:

M

Step-by-step explanation:

The total amount Jill paid for the curtains and comforter is, 216.25.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

Jill was remodeling her bedroom she bought 4 curtains for 37 each and comforter for 68.25.

Now, The cost of 4 curtains = 4 × 37

                                           = 148

And, The cost of comforter = 68.25

Thus, The total amount jill paid for the curtains and comforter is,

⇒ 148 + 68.25

⇒ 216.25

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