how to use the gcf and distributive property to find each some: 32+48, 15+57, 98+14, 55+88

Answer:

Equation of this line is y = 1

Step-by-step explanation:

We have to write an equation of a line passing through (0,1) and slope 0.

Standard equation of a line in slope form is y = mx + c

Where m = slope and c = y intercept.

Since m = 0

so y = c is the equation.

This line passes through (0,1)

so equation will be Y = 1

Equation of this line is y = 1

Step-by-step explanation:

Hope this helps:)

Answer:

y = 1

Step-by-step explanation:

Answer:

k=3

Step-by-step explanation:

p²-q²

p²-q²= (p+q)(p-q)

[by formula: (A+B)(A-B) = A²-B²]

Proof of the formula

Proof of the formula (A+B) • (A-B)

Proof of the formula (A+B) • (A-B) = A2 - AB + BA - B2

Proof of the formula (A+B) • (A-B) = A2 - AB + BA - B2 = A2 - AB + AB - B2

Proof of the formula (A+B) • (A-B) = A2 - AB + BA - B2 = A2 - AB + AB - B2 = A2 - B2

Answer:

The model should look like this: ⚫⚫⚫⚫⚫

⚫⚫⚫⚫⚫

Step 1

Given;

Required; To find the independent and dependent quantities in the relationship.

Step 2

An independent variable is a variable that represents a quantity that is being manipulated in an experiment. x is often the variable used to represent the independent variable in an equation. Notice that as L the length of the shoe changes it affects s(L), the size of the shoe. The independent variable is not affected by the dependent variable. From this the question the independent quantity is;

A dependent variable represents a quantity whose value depends on how the independent variable is manipulated. y is often the variable used to represent the dependent variable in an equation. For this question, the dependent quantity is;

Answer;

Answer:

2.45

Step-by-step explanati

Is "perimeter". The perimeter is the sum of all the sides of a two-dimensional figure. For example, if you have a rectangle with sides of length 3 and 5, then the perimeter would be 3+3+5+5 = 16.

In explanation, the perimeter is an important measure of a two-dimensional figure because it gives us an idea of how much boundary or fence we would need if we were to enclose the figure. Additionally, the perimeter can be used to calculate other properties of a figure such as its area or volume.

the perimeter is an essential concept in geometry that helps us measure the boundaries of two-dimensional figures.


Perimeter refers to the total length of the sides or edges of a two-dimensional shape. To calculate the perimeter, you simply add the lengths of all the sides of the figure.

Conclusion: In summary, the term you are looking for is "perimeter," which represents the total length of the sides of a two-dimensional figure.

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The statement "In a buying center, individuals who have the formal and informal power to select or approve the supplier that receives the contract. for routinely purchased products, the decider is likely to be the buyer but for more complex product, the decider could come from R&D, engineering, or quality control." is correct.

What is a buying center?

The buying center is a group of people or organizations who participate in the purchasing process, each with their own interests, responsibilities, and power. The buying center could consist of a few individuals or numerous individuals who represent different departments or functional areas.

The members of the buying center are divided into several groups based on their roles and responsibilities, including initiators, users, influencers, deciders, and buyers.

What is a decider?

The decider is the person or group of people within a buying center who has the power to make the final decision on a purchase. The decider is typically the person who is responsible for the function or process that the purchase will affect.For routine purchases, such as office supplies, the decider is typically the buyer or the person responsible for making the purchase.

However, for more complex purchases, such as new equipment or software, the decider may come from research and development, engineering, or quality control.

These individuals have a greater understanding of the technical specifications and requirements for the product or service and are better equipped to evaluate the alternatives and make the best decision for the organization.

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Answer:

They are all equal sides so divide 180 by 3

Step-by-step explanation:

The lower confidence interval of the population mean is 34.16.

To construct a 95% confidence interval for the population mean, we can use the formula:

CI = sample mean ± (z-score)(standard error)

Where the z-score is determined by the level of confidence and can be found using a z-table or calculator. For a 95% confidence interval, the z-score is 1.96.

The standard error can be calculated using the formula:

standard error = population standard deviation / √(sample size)

Substituting the given values, we get:

standard error = 2.9 / √46 = 0.427

Now we can plug in the values into the formula to get the confidence interval:

CI = 35 ± (1.96)(0.427) = 35 ± 0.837

The lower confidence interval of the population mean is obtained by subtracting the margin of error from the sample mean:

lower confidence interval = 35 - 0.837 = 34.16 (rounded to 2 decimal places)

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The absolute value function which will be narrower than  the parent function is:

f(x) = 2.9|x|

Given parent function is f(x)=|x|

Now we have to find which function from given choices will be narrower than the parent function.

Notice that adding or subtracting some number from the parenth function only shifts the graph up, down, left of right side.

But that will not make function narrorwer or broader.

So f(x) = |x – 2| and  f(x) = |x| + 3, can't be the answer.

Multiplying by some positive real number which is more than 1, makes function narrower.

Only f(x) = 2.9|x| from remaining choices fits that case.

Hence f(x) = 2.9|x| is the final answer.

f(x) = 1.2|x + 8|  will also make the function narrower but will shift the parent function too.

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The maximum number of possible effects that could be tested in a 2x2x2 factorial design with 3 main effects, 3 two-way interactions, and 1 three-way interaction is 7.

In a 2 x 2 x 2 factorial design, we can test the following maximum number of possible effects:
Main effects:

There are 3 main effects in this design, one for each factor (A, B, and C). You would analyze the effect of each factor independently on the outcome variable.

Two-way interactions:

There are 3 possible two-way interactions that can be tested in this design: AxB, AxC, and BxC.

These interactions examine the combined effects of two factors on the outcome variable.
Three-way interactions:

There is 1 possible three-way interaction that can be tested in this design: AxBxC.

This interaction examines the combined effect of all three factors (A, B, and C) on the outcome variable.

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The solution to the equation \(\sqrt{(x+8)^{3}} + \sqrt{(x+8)^{5}} =\) 0 is x = -8.

To solve the equation \(\sqrt{(x+8)^{3}} + \sqrt{(x+8)^{5}} =\) 0, we can follow these steps:

1. Set each square root term equal to zero:

  \(\sqrt{(x+8)^{3}} = 0 and \sqrt{(x+8)^{5}} = 0\)

2. Solve each equation separately:

  For\(\sqrt{(x+8)^{3}} = 0:\)

  Square both sides to eliminate the square root:

  (x+8)^{3} = 0

  For \(\sqrt{(x+8)^{5}} = 0:\)

  Square both sides to eliminate the square root:

 \((x+8)^{5} = 0\)

3. Solve for x in each equation:

  For \((x+8)^{3}\) = 0:

  Taking the cube root of both sides:

  x+8 = 0

  x = -8

  For\((x+8)^{5}\) = 0:

  Taking the fifth root of both sides:

  x+8 = 0

  x = -8

4. Check for extraneous solutions:

  Substitute the found solutions back into the original equation:

  For x = -8:

  \(\sqrt{(-8+8)^{3}} + \sqrt{(-8+8)^{5}} = \sqrt{0} + \sqrt{0}\) = 0 + 0 = 0

  Therefore, x = -8 is a valid solution to the original equation.

The solution to the equation \(\sqrt{(x+8)^{3}} + \sqrt{(x+8)^{5}} =\) 0 is x = -8.

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solve the equation\(\sqrt{(x+8)^{3}} + \sqrt{(x+8)^{5}} = 0,\)

Answer:

(3, 3 )

Step-by-step explanation:

y = x → (1)

3x - 2y = 3 → (2)

substitute y = x into (2)

3x - 2x = 3

x = 3

substitute x = 3 into (1)

y = 3

solution is (3, 3 )

The vertex of the function is (7, 30)

The axis of symmetry of the function is 7.

The maximum value of the function is 166.

The domain of the function is  {-∞, ∞)

The range of the function is  (-∞, 30] U [30, ∞)

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -(x - 7)² - 30

f(x) = -(x² - 14x + 49) - 30

f(x) = -x² + 14x - 49 - 30

f(x) = -x² + 14x - 79

The function is in the form of ax² + bx + c

The axis of symmetry is -b/2a.

= -b/2a

= -(14)/(2 x -1)

= 14/2

= 7

The vertex of the function.

= (x, y)

x = -b/21

x = 7

Now,

f(x) = -x² + 14x - 79

y = -49 + 98 - 19

y = -68 + 98

y = 30

Now,    

f'(x) = 0

-2x + 14 = 0

-2x = 14

x = -7

f''(x) = -2 (negative)

f(x) has maximum value at x = -7.

The maximum value.

f(-7) = (-7 - 7)² - 30 = 166

Now,

f(0) = 49 - 30 = -1

f(1) = 36 - 30 = 6

f(2) = 25 - 30 = -5

f(3) = 16 - 30 = -14

f(4) = 9 - 30 = -21

f(5) = 4 - 30 = -26

f(6) = 1 - 30 = -29

f(7) = -30 = -30

f(8) = 1 - 30 = -29

Domain = {-∞, ∞)

Range = (-∞, 30] U [30, ∞)

Thus,

The vertex is (7, 30)

The axis of symmetry is 7.

The maximum value of the function is 166.

The domain and range of the function are  {-∞, ∞) and (-∞, 30] U [30, ∞).

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The answer is option A. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity.

Probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is 0.0229.Round to four decimal places as needed.Based on the calculations the elevator does not appear to be safe.The solution for the given problem is as follows:

Given that, the maximum capacity of the elevator is 1884 lb - 12 passengers.

We can write as below:

Maximum capacity per person=1884/12=157lb.

And, weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.Thus, Z = (157-165) / (32 / √12) = -1.7321Then, P(Z > -1.7321) = 0.9586

Hence, the probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is:P(Z > -1.7321) = 1 - P(Z < -1.7321) = 1 - 0.0229 = 0.9771 (rounded off to 4 decimal places).This probability is greater than 5% and therefore, the elevator does not appear to be safe.

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The hexadecimal system numbering system is base 16; in other words, 16 numerals are used to express any given number.

In this system, 16 numerals are used to represent any given number. The numerals used in this system are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F, where A represents 10, B represents 11, and so on, up to F, which represents 15.

This system is commonly used in computer science, as it is more compact than the decimal system, and allows for easier conversion between binary and decimal systems. In the hexadecimal system, each digit represents a power of 16, just as each digit in the decimal system represents a power of 10.

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Answer:

575.71

Step-by-step explanation:

Year 1: 960 x .88 (100%-12%)=844.80

Year 2: 844.80 x .88 =743.424

Year 3: 743.424x.88=654.21

Year 4: 654.21 x .88=575.71

Answer:

B= 18x

Step-by-step explanation:

use identity :  (a+b)² = a²+2ab+b²   you have a =3x  and b =3 so: B =2ab

the second term of this trinomial is : 2ab  means : 2(3x)(3) = 18x

(3x +3)2=9x2+2(3x)(3)+3²

The equation of parabola is y = -8(x -3)² - 9.

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.

Given Data

Focus = (3, -9)

Directrix: y = -5

The focus-passing line has an equation of x = -5 that is perpendicular to the directrix. The symmetry line of a parabola is seen here.

The parameter of the parabola is the separation between the focus and the directrix, so

p = -9 - 3

p = -12

p = 12

The distance between the focus and the directrix is divided into two equal portions by the parabola's vertex, which is located on the line of symmetry. Its coordinates are as follows: (3,-9).

Since a parabola moves in the opposite direction of y, its equation is

y -(-9) = -2(4(x -3)²)

y + 9 = -8(x-3)²

y = -8(x -3)² - 9

The equation of parabola is y = -8(x -3)² - 9.

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Answer:

4

Step-by-step explanation:

x = 7 - 3

x = 4

Answer:

x = 4

Step-by-step explanation:

3+x = 7

Subtract 3 from each side

3+x-3 = 7-3

x = 4

Her mental age would be 8 yrs old.

IQ [ Intelligent Quotient ]  is a type of standard score that indicates how far above, or how far below, his/her peer group an individual stands in mental ability.

IQ of a person is given by the formula -

IQ = MA/CA * 100

IQ = Mental Age / Chronological Age * 100

According to the question, IQ = 100, CA = 8

⇒ 100 = MA / 8 *100

⇒1 = MA / 8

⇒ MA = 8 Yrs

Hence, the estimated mental age of susan is 8 yrs old.

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Answer:

Each person should share 1 and 1/2

Answer:The answer is -4

Step-by-step explanation:-4+-5=-9

Answer:

-4

Step-by-step explanation:

your basically adding

Answer:

28.26 square feet

Step-by-step explanation:

Area of a circle is: \(A=\pi r^2\)

'r' is the radius.

We are given the diameter of 6ft. Since the diameter is twice the radius, the radius is 3 ft.

6/2 = 3

Using 3.14 for pi:

\(A=3.14*3^2\\\rightarrow 3^2=9\\A=3.14*9\\\boxed{A=28.26}\)

The area of the circle should be 28.26 square feet.

Answer:

28.26 ft²

Step-by-step explanation:

If the diameter is 6 feet, then the radius is 3 feet since 2r=d

The area formula in this case is 3.14×r² since it says "Use 3.14 for π".

3.14×3²=

3.14×9=

28.26 ft²

Answer:

20,701 feet

Step-by-step explanation:    

29,028-8,327= 20,701

Positive value of a vertically stretches the graph of f when a > 1 or shrinks the graph of f when a < 1. h translates the graph of f to the left when h < 0 or right when h > 0.

Several real-world scenarios use exponential functions, including population increase, compound interest, radioactive decay, and the spread of diseases. For instance, an exponential function may be used to simulate the expansion of a bacterial population, with the rate of increase being proportional to the population size. Similarly, compound interest, which applies the rate of interest to the principal sum across a number of periods, can be represented by an exponential function.

Positive value of a vertically stretches the graph of f when a > 1 or shrinks the graph of f when a < 1. h translates the graph of f to the left when h < 0 or right when h > 0 and k translates the graph of f up when k > 0 and down when k < 0.

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