Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42

Answer:

We are given the function S = m^2 + 6m + 8 which models the growth of book sales in m months, where S is an amount in thousands of dollars. We want to find in how many months book sales reach $80,000.

We can set up an equation as follows:

S = m^2 + 6m + 8 = 80

Subtracting 80 from both sides, we get:

m^2 + 6m - 72 = 0

We can factor this quadratic equation as:

(m + 12)(m - 6) = 0

This gives us two possible solutions:

m + 12 = 0 or m - 6 = 0

Solving for m in each case, we get:

m = -12 or m = 6

Since we are looking for a number of months, we can discard the negative solution.

Therefore, book sales reach $80,000 in 6 months.

So, the answer is: 6 months.

A = [-4/3 -1/3; 10 10/3] is the matrix that fulfills the equation A × [1 0; -1 3] = [-1 -3; 1 6].

Rows and sections of integers are arranged in a matrix. Learn about matrices' lengths and components as you begin your study of them. A rectangle matrix is a grouping of integers into rows as well as columns. The matrix A, for instance, has two rows along with three columns.

To find the matrix A, we need to solve the matrix equation:

A × [1 0; -1 3] = [-1 -3; 1 6]

We can do this by multiplying both sides by the inverse of [1 0; -1 3] on the left:

A × [1 0; -1 3] × [3 0; 1 1/3] = [-1 -3; 1 6] × [3 0; 1 1/3]

Simplifying the left-hand side using the associative and commutative properties of matrix multiplication, we get:

A × [3 0; -1 1] = [-3 -1; 10 3]

Now, we can solve for A by multiplying both sides by the inverse of [3 0; -1 1]:

A × [3 0; -1 1] × [1/3 0; 1/3 1] = [-3 -1; 10 3] × [1/3 0; 1/3 1]

Simplifying the left-hand side using the associative and commutative properties of matrix multiplication, we get:

A × [1 1/3; 0 1] = [-2/3 -1/3; 10/3 3]

Multiplying both sides by the inverse of [1 1/3; 0 1]:

A = [-2/3 -1/3; 10/3 3] × [1 1/3; 0 1]⁻¹

We can easily find the inverse of [1 1/3; 0 1]:

[1 1/3; 0 1]⁻¹ = [1 -1/3; 0 1]

So, substituting this into the equation for A, we get:

A = [-2/3 -1/3; 10/3 3] × [1 -1/3; 0 1]

Multiplying the matrices on the right-hand side, we get:

A = [-2/3 -1/3; 10/3 3] × [1 -1/3; 0 1] = [-4/3 -1/3; 10 10/3]

Therefore, the matrix A that satisfies the equation A × [1 0; -1 3] = [-1 -3; 1 6] is:

A = [-4/3 -1/3; 10 10/3]

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The resultant values are as follows:

Radius = 11.94 ft; Diameter: 23.87 ft; Circumference = 75 ft

The circumference of a circle or ellipse in geometry is its perimeter.

That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc.

The curve length around any closed figure is more often referred to as the perimeter.

The length of a circle's outline is referred to as its circumference, and the length of a form with straight sides is referred to as its perimeter.

So, since the fence around the circular pool is given, then it will also be the value of the circumference of the pool.

Circumference = 75 ft

Radius:

2πr = 75

r = 75/2π = 75/(2×3.14) ≈ 11.937

radius = 11.94 ft

Diameter:

2r = 2×11 ≈ 23.87 ft

Therefore, the resultant values are as follows:

Radius = 11.94 ft; Diameter: 23.87 ft; Circumference = 75 ft

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Complete question:

The fence around a circular pool is 75 ft long. Find: Radius, Diameter, and Circumference.

the container needs to have a volume of  0.01514 cubic meters to hold 205 kg of mercury.

Volume is the measure of the amount of three-dimensional space enclosed by an object or space. It is typically expressed in cubic units, such as cubic meters (m³) or cubic centimeters (cm³).

The density of mercury is approximately 13,534 kg/m³.

We can use the formula:

Volume = mass/density

To find the volume of mercury that has a mass of 205 kg:

Volume = 205 kg / 13,534 kg/m³

Volume ≈ 0.01514 m³

Therefore, the container needs to have a volume of approximately 0.01514 cubic meters to hold 205 kg of mercury.

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The complete question is:

What volume should a container have to hold 205 kg of mercury?

Answer:

Step-by-step explanation:

After the first year, the number of rabbits will double from 50 to 100.

After the second year, the number of rabbits will double again from 100 to 200.

This doubling process will continue for a total of 5 years, so after 5 years, the number of rabbits will be:

Number of rabbits after 5 years = 50 x 2^5 = 50 x 32 = 1600

Therefore, there will be 1600 rabbits on Groff Farm after 5 years.

Similarly, after 10 years, the number of rabbits will double 10 times:

Number of rabbits after 10 years = 50 x 2^10 = 50 x 1024 = 51200

Therefore, there will be 51,200 rabbits on Groff Farm after 10 years.

Answer:

53 in2 is the answer for this question

Answer:

53

Step-by-step explanation:

If you divide the figure into two parts by extending the 4 in side, you get a right triangle and a rectangle.

Area of rectangle:

6*8 = 48 in²

Area of triangle:

1/2*(13 - 8)*(6 - 4) = 1/2 times 5 times 2 = 5 in²

Total area is:

48 + 5 = 53 in²

hope this helps x

Answer:

8x²-30x+18

Step-by-step explanation:

8x²-24x-6x+18

8x²-30x+18

Answer:

[tex]8x^{2} -30x+18[/tex]

Step-by-step explanation:

[tex]8x^{2} -24x-6x+18[/tex]

[tex]8x^{2} -30x+18[/tex]

Answer:

it is not likey bc inless the class have over 2 mil ppl in it itis doouptfull

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

f(-1) = 2

g(2)= 4

10³•10⁵•10³

Step-by-step explanation:

10³means 10×3,10⁵means 10×5and 10³means 10×3 30+50+30=110

(x-2)(x-20) is the factored form of the trinomial equation

Given the quadratic equation below

x² - 22x + 40

To factorise this expression, we need to find two factors of 40 that add up to -22.

The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40.

To get a sum of -22, we can choose the factors -2 and -20.

Therefore, we can write:

x² - 22x + 40 = (x - 2)(x - 20)

Thus, the factored form of the expression 40-22x+x² is (x-2)(x-20).

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Step-by-step explanation:

The measure of angle p is 60°

Answer:

Step-by-step explanation:

Let's assume that the width of the flag is "w" ft.

According to the problem, the length of the flag is 400 ft greater than the width, which means it can be expressed as:

length = w + 400

Now, we know that the perimeter of the flag is 2,120ft. The perimeter of a rectangle is given by:

perimeter = 2(length + width)

Substituting the values, we get:

2120 = 2[(w+400) + w]

2120 = 2[2w + 400]

2120 = 4w + 800

4w = 1320

w = 330

Hence, the width of the flag is 330ft.

From our equation for the length, we have:

length = w + 400

length = 330 + 400

length = 730

Therefore, the length of the flag is 730ft.

Answer:

Step-by-step explanation:

The figure is a rectangular trapezoid, and this answers one question, the second question is the area, which we find by making the major base plus the minor base multiplied by the height and we divide everything by two, the two bases are the parallel ones (12 and 8) and the height is 7.

Then it is resolved with this expression

Area = [(12 + 8) ×  7] : 2

Area = (20 × 7) : 2

Area = 140 : 2

Area = 70 cm²

Answer: The building is approximately 16.6 feet tall.

Step-by-step explanation:

Use Pythagorean theorem (a²+b²=c²) to solve this.

We know that the ladder is 26 feet long so that would be our hypotenuse (c²). and the distance between the ladder and the building is 20 feet. So, this is the base. The remaining side is x.

Your equation would be: 20²+x²=26²

subtract 20² from 26² --> 276=x²

then take the square root --> 16.6=x

Answer:

18

Step-by-step explanation:

siz times three is eighteen

We may conclude after answering the presented question that where equation V(z) is the value of the car z years after 1964.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilized in many different areas of mathematics, such as algebra, calculus, and geometry.

To model the value of the car, we can use the exponential growth formula:

[tex]V(t) = V0 * (1 + r)^t\\V(t) = ab^t\\a = V0 = $2000\\b = 1 + r = 1 + 0.113 = 1.113\\V(z) = 2000 * 1.113^z\\[/tex]

where V(z) is the value of the car z years after 1964.

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Answer:

Let x be the number of miles completed by the participant before the mark. Then, the total distance of the triathlon is:

2.6 + 110 + 26.2 = 138.8 miles

At the mark, the participant has completed x miles and has the remaining distance to complete, which is:

138.8 - x

According to the problem, x is equal to the remaining distance:

x = 138.8 - x

Solving for x, we get:

2x = 138.8

x = 69.4

Therefore, the participant had completed 69.4 miles at the mark.

The probability of the complementary event of E occurring is 0.57.

What is probability?

Probability is a branch of mathematics that deals with the study of random events or phenomena. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to happen.

In probability theory, P(E) represents the probability of an event E occurring, while P(Ec) represents the probability of the complementary event of E occurring. The complementary event of E is the event that E does not occur. In other words, it consists of all outcomes that are not in E.

To find P(Ec), we can use the formula:

P(Ec) = 1 - P(E)

where 1 represents the total probability of all possible outcomes.

In this case, we are given that P(E) = 0.43. Substituting this value into the formula, we get:

P(Ec) = 1 - P(E)

P(Ec) = 1 - 0.43

P(Ec) = 0.57

Therefore, the probability of the complementary event of E occurring is 0.57.

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Answer:

The average rate of change of the function from x=-1 to x=1 is 6.

Step-by-step explanation:

The average rate of change of a function from x=-1 to x=1 is the change in the output of the function (y-value) divided by the change in the input of the function (x-value). In other words, it is the slope of the line connecting the two points (x=-1 and x=1).

Answer:

D) 115.2π cm².

Step-by-step explanation:

The surface area of a cylinder can be calculated using the formula:

Surface Area = 2πr² + 2πrh

where r is the radius and h is the height of the cylinder.

In this case, r = 4 cm and h = 10.4 cm. Substituting these values in the formula, we get:

Surface Area = 2π(4)² + 2π(4)(10.4)

Surface Area = 2π(16) + 2π(41.6)

Surface Area = 32π + 83.2π

Surface Area = 115.2π

Therefore, the exact surface area of the candle is 115.2π cm².

The answer is (D) 115.2π cm².

Answer: The answer is D, 115.2π cm²

Step-by-step explanation: When we use the formula of 2πrh+2πr2=2·π·4·10.4+2·π·42 to get the surface area, which equals 361.91

We can divide this by pi to get 115.2π cm²

Hope this helped!

Answer: The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

Step-by-step explanation:

I hope it helped! :)

The graph of the functions are given as attached.

Graphs are visual representations of functions that provide valuable insights into their behavior. They allow us to see the relationship between the input and output of a function, and how it changes over time or across different values.

The relationship between the two functions is that they are reciprocals of each other. Specifically, f(x) = 2sin(2x) + 1 is the reciprocal of f(x) = 2csc(2x) + 1, since csc(2x) is the reciprocal of sin(2x). Therefore, they have the same shape, but their values are inverted. See the attached graph.

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Based on this estimate, the insurance company's projected value of this probability insurance policy is negative, implying that the insurance company will lose money on this policy.

Probabilistic theory is a branch of mathematics that calculates the chance of an event or a claim being true. A risk is a number between 0 and 1, where 1 represents certainty and a probability of about 0 shows how likely an event appears to be to occur. Probability is a mathematical term for the likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1, or as percentages ranging from 0% to 100%. The proportion of occurrences among equally likely choices that result in a certain event in compared to all possible outcomes.

The total of the potential payouts multiplied by the odds of each payout occurring equals the anticipated value of the insurance policy. In this scenario, the possible compensation is the $1500 insurance payout, and the likelihood of the client being involved in an accident is 3.3%, or 0.033.

Expected value = (Payout if event happens) x (Probability of event happening) - (Annual premium)

($1500) x (0.033) - ($120) = expected value

Value expected = $49.50 - $120

-$70.50 is the expected value.

Based on this estimate, the insurance company's projected value of this insurance policy is negative, implying that the insurance company will lose money on this policy.

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Answer: 6

Step-by-step explanation:

21 - 1 = 20

20 - 2 = 18

18 - 3 = 15

15 - 4 = 11

11 - 5 = 6

Problem 7)  The model labelling p, q and p + q is given in the attached. The addition equation using integers that could represent p, q, and p +  q are:
(-1) + 2 = 1

Problem 8) The model would change if p > q

7) Addition equation is given as:

(-1) + 2) = 1

Where ;

p = -1

q = 2

Hence,

-1 + 2 = 1

8) The model in the equation above would change if p > q

That is

|p| > |q|

⇒ p > q

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Full Question:

Although part of your question is missing, you might be referring to this full question: See attached image.

In the standard algorithm

Reminder = 2

quotient  = 13

What does quotient in mathematics mean?

The number being divided is known as the dividend, in this case, 15. The number being divided is known as the divisor (in this case, 3). The remainder following division is the quotient.

                                When we divide two integers, the result is a quantity known as the quotient. As an example, since the division resulted in the number 2, the quotient in the equation 8 4 = 2 is 2.

= 93÷7​

Reminder = 2

quotient  = 13

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Answer:

26° 180 -81 - 73 = 26

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

triangle= 180

81 + 73 = 154

180 - 154= 26

Jordan spend 25 minutes writing each dayNoHow much time does Jordan spend writing each dayFrom the question, we have the following parameters that can be used in our computation:D + W = 75W + 25 = DSo, we haveW + W + 25 = 75EvaluateW = 25This means that Jordan spends 25 minutes on writing is it possible?Based on the answer in (a), the truth statement is No