Graph the triangle with vertices X(−3, 2), Y(2, 3), and Z(1,−1) and its image after a dilation with scale factor k=3

A regular polygon with an interior angle of 172 degrees has 20 sides.

The formula to find the measure of an interior angle of a regular polygon is:

Interior angle = (n-2) x 180 / n

where n is the number of sides of the polygon.

Setting the equation equal to 172 and solving for n, we get:

172 = (n-2) x 180 / n

172n = 180n - 360

8n = 360

n = 45

Therefore, the regular polygon has 45 sides, but since the question asks for a regular polygon, all sides must be equal and all interior angles must be congruent. The only regular polygon that satisfies these conditions with an interior angle of 172 degrees is a regular 20-sided polygon.

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Answer:

= (3 + 11)/4

= 14/4

= 7/2 or 3\(\frac{1}{2}\)

Answer:

x= 6 y=40

Step-by-step explanation:

The linear cost function is C(x) is (2100 + 20x).

What is Cost function?

The cost function calculates the absolute lowest cost of generating a specified level of output at some fixed factor prices. A firm's economic potential is described by the cost function.

As given,

Marginal cost $20; 170 items cost $5500 to produce.

Evaluate the Fixed cost:

Fixed cost = 5500 - 20 × 170

                  = 5500 - 3400

                  = 2100

Now,

cost function = fixed cost + x × (marginal cost)

Substitute values respectively,

cost function = 2100 + 20x.

Hence, the linear cost function is C(x) is (2100 + 20x).

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Answer:a scale facter is a scale of how much is one each side or corner and the shape

Step-by-step explanation:

Answer:

after 10 months farm a and b have the same amount of animals

Step-by-step explanation:

hope this helps :)

Answer:

20%

Step-by-step explanation:

Discount= $30 - $24 = $6

Discount%= \(\frac{6}{30}\) × \(\frac{100}{1}\) = 20%

Elimination method is the best method to solve the system of equations below

Two or more expressions with an Equal sign is called as Equation.

The given system of equations

6x + 3y = 21...(1)

2x – 3y = -13...(2)

Add equations (1) and (2)

6x+3y+2x-3y=21-13

8x=8

Divide both sides by 8

x=1

Now plug in x value in equation 1

6+3y=21

Subtract 6 from both sides

3y=15

Divide both sides by 3

y=5

By Elimination method we find the values of x and y.

Hence, Elimination method is the best method to solve the system of equations below

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On solving the provided question we can say that The missing metric expression prefixes are: Deci, Hecto-, Kilo ,Base Unit, Milli, Centi-

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

The missing metric prefixes are:

Deci-

Kilo-

Milli-

Complete the list below. Fill in the blanks with the missing metric prefixes.

Deci, Hecto-, Kilo ,Base Unit, Milli, Centi-

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Answer:

18 units to the right.

Step-by-step explanation:

Hope this helps!

Answer:

95%

Step-by-step explanation:

The 68-95-99.7 rule to find the percentage of people is also know as the empirical rule.

The empirical rule formula states that:

68% of data falls within 1standard deviations from the mean - between μ – σ and μ + σ .

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .

From question:

Mean (μ) = 505

Standard deviation (σ) = 146

Hence, we are to find the number of standard deviation which is represented as x

The score is between 213 and 797

μ - xσ

= 505 - 146x = 0

= 505 - 146x = 213

146x = 505 - 213

146x = 292

x = 292/146

x = 2

μ + xσ

505 +146x = 797

146x = 797 - 505

146x = 292

x = 292/146

x = 2

Hence, the percentage falls within 2 standard deviation from the mean.

Thus, from the formula above:

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

Therefore, the percentage of people taking the test who score between 213 and 797 is 95%

Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).

Answer:

\(f(x)=-(x+8)(x-2)\)

Step-by-step explanation:

Start by factoring out a -1...

\(f(x)=-(x^2+6x-16)\)

Now, we have to find two integers that multiply to get -16 and have a sum of 6:

(-2)*8=-16

-2+8=8-2=6

Using this, we can split 6x into -2x and 8x...

\(f(x)=-(x^2-2x+8x+16)\)

Factor  the first and second half separately...

\(f(x)=-[(x^2-2x)+(8x-16)]\\f(x)=-[x(x-2)+8(x-2)]\\\)

Since both x and 8 are being multiplied by x-2, we can combine them to get...

\(f(x)=-(x+8)(x-2)\)

Answer: 2.5, 5.3

Step-by-step explanation:

\(-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3\)

Answer:

f(-1) means value of f when x = -1

From the above table we can say when x =-1

value of f i.e f(-1) = 2

f(x) =2

when x =0, -2

Answer:

224

Step-by-step explanation:

Base:

A = Bh

A = 8(8) = 64

Sides:

A = 1/2 Bh

A = 1/2 8(10)

A = 40

Then you do 40(4) because there are 4 sides:

40 (4) = 160

Then you add up the base and the sides:

160 + 64 = 224

(I think this is the right answer)

The rule says that the sum of any two sides has to be smaller than the third side so, no it can't

The general solution of the differential equation is `y = Ce^(-2x) - 2x + 5/2`, where `C` is a constant and the differential equation is `dy/dx = -2y + 3x + 4`.

The given differential equation is: `dy/dx = -2y + 3x + 4`. To solve this differential equation, we first need to solve the homogeneous part and then the particular part. The homogeneous part of the differential equation is: `dy/dx = -2y`.This can be rewritten as:`dy/y = -2dx`Now integrating both sides, we get:`ln|y| = -2x + C_1`where `C_1` is the constant of integration.Solving for `y`, we get:`y = Ce^(-2x)`where `C = ±e^(C_1)`.

Thus, the general solution of the homogeneous part is given by:`y_h = Ce^(-2x)`where `C` is the constant of integration.The particular part of the differential equation is given by:`dy/dx = 3x - 2y + 4`To solve this, we need to use the method of undetermined coefficients. For this, we assume the particular solution to be of the form:`y_p = Ax + B`where `A` and `B` are constants.Using this particular solution, we have:`dy_p/dx = A`Plugging this into the differential equation, we get:`A = 3x - 2(Ax + B) + 4`Simplifying and solving for `A` and `B`, we get:`A = -2` and `B = 5/2`.

Therefore, the particular solution is:`y_p = -2x + 5/2`Hence, the general solution of the given differential equation is:`y = y_h + y_p` `= Ce^(-2x) - 2x + 5/2`Where `C` is the constant of integration.Answer: The general solution of the differential equation is `y = Ce^(-2x) - 2x + 5/2`, where `C` is a constant and the differential equation is `dy/dx = -2y + 3x + 4`.

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The machine is not operating satisfactorily, and an adjustment is needed because the sample mean is outside the acceptable range.

Based on the given information, we need to determine if the soft-drink machine is operating satisfactorily and does not require any adjustment.

To do this, we will compare the sample mean (x) with the acceptable interval of the population mean (µ) as per the provided condition.

We are given that:
Population mean (µ) = 12 ounces
Standard deviation (σ) = 0.15 ounces
Sample size (n) = 81 drinks
Sample mean (x) = 11.8 ounces
z-score = ±1.960

Step 1: Calculate the standard error (SE) using the formula SE = σ/√n:
SE = 0.15/√81 = 0.15/9 = 0.0167

Step 2: Calculate the acceptable range using the provided z-score:
Lower limit = µ - z × SE

= 12 - 1.960 × 0.0167

≈ 11.967

Upper limit = µ + z × SE

= 12 + 1.960 × 0.0167

≈ 12.033

The acceptable range for the average content of the drinks is between 11.967 ounces and 12.033 ounces.

Since the sample mean (11.8 ounces) is outside this acceptable range, the machine is not operating satisfactorily, and an adjustment is needed.

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With a credit card balance of $17,426, a minimum monthly payment of $461, and an interest rate of 15.5%, we need to calculate the number of years it will take to pay off the card without adding any additional debt.

To determine the time required to pay off the credit card, we consider the monthly payment and the interest rate. Each month, a portion of the payment goes towards reducing the balance, while the remaining balance accrues interest.

To calculate the time needed for repayment, we track the decreasing balance each month. First, we determine the interest accrued on the remaining balance by multiplying it by the monthly interest rate (15.5% divided by 12).

We continue making monthly payments until the remaining balance reaches zero. By dividing the initial balance by the monthly payment minus the portion allocated to interest, we obtain the number of months needed for repayment. Finally, we divide the result by 12 to convert it into years.

In this scenario, it will take approximately 3.81 years to pay off the credit card (17,426 / (461 - (17,426 * (15.5% / 12))) / 12).

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Answer: b

Step-by-step explanation:

The inequality that represents the number of hours you will need to work in order to afford the video game is x ≥ 5.58.

Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤ 

Let the number of hours be represented as x.

The person is paid $10.75 an hour at your job and the newest video game costs $60.00. This will be illustrated as:

10.75x ≥ 60

Divide

x ≥ 60 / 10.75

x ≥ 5.58

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Option d. dependent variable. In an experiment, the dependent variable is the factor that is being measured or observed.

It is the variable that is expected to change or be affected as a result of the manipulation of the independent variable. The independent variable is the factor that is being manipulated or controlled in the experiment, while the controlled variable is a factor that is kept constant or consistent throughout the experiment to prevent it from affecting the dependent variable. The dependent variable is often used to draw conclusions about the relationship between the independent variable and the outcome of the experiment.

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An equation that could be used to represent the context if a represents the number of miles in the taxi ride is ​1.70 + 1.75a = 17.45

We are given;

Base pick up fee = $1.70

Additional taxi fee per mile covered = $1.75

Total taxi fare = $17.45

Now, if we assume that a represents the number of miles in the taxi ride, then we can form the equation to represent the given scenario above as;

1.70 + 1.75a = 17.45

We conclude that an equation that could be used to represent the context if a represents the number of miles in the taxi ride is ​1.70 + 1.75a = 17.45

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Answer: answer is C

Step-by-step explanation:

The question asks us to find the a graph which represents the width of the rectangle increasing by 1 unit while the area remains constant. The best graph to model this, would be answer choice C

Step-by-step explanation:

The common factor in the expression is 3x, so we can factor it out:

3x(x² - 4x + 4)

Now, we can factor the quadratic expression inside the parentheses as a perfect square:

3x(x - 2)²

Therefore, the factored form of the expression is 3x(x - 2)².

a. The chances of the offspring having type A blood when both parents have blood type O and unknown Rh factor is 0%.

b. The chances of the offspring having type B blood when both parents have blood type O and unknown Rh factor is 0%.

c. The chances of the offspring having type AB blood when both parents have blood type O and unknown Rh factor is 0%.

d. The chances of the offspring having type O blood when both parents have blood type O and unknown Rh factor is 100%.

7a. The chances of the offspring being Rh+ when one parent is heterozygous for the Rh factor (+/-) and the other parent is Rh- are 50%.

7b. The chances of the offspring being Rh- when one parent is heterozygous for the Rh factor (+/-) and the other parent is Rh- are 50%.

a. Both parents having blood type O means they do not carry the A antigen, so the offspring cannot have type A blood.

b. Similarly, both parents having blood type O means they do not carry the B antigen, so the offspring cannot have type B blood.

c. Since both parents have blood type O and do not carry the A or B antigens, the offspring cannot have type AB blood.

d. The child will inherit the O blood type since both parents have blood type O.

7a. When one parent is heterozygous for the Rh factor (+/-), there is a 50% chance of passing the Rh+ allele to the offspring.

7b. If the other parent is Rh-, the offspring will have a 50% chance of inheriting the Rh- allele.

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Answer:

3× + 3 = 10 + 2× find like terms 3× -2× = 10 -3 × = 7 final answer 7