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The remainder you got when 3x³ - 5x² - 23x + 24 is divided by x - 3 is -9.

Polynomials are expressions in algebra which consist of both variables and coefficients. Sometimes, variables are also known as indeterminates. Polynomials are classified as monomials, binomials, and trinomials based on the degree of the variables in the expression.

Variables in the monomials, binomials and trinomials have the highest degree equals 1, 2 and 3 respectively.

By doing the long division method, we will bet the quotient as 3x² + 4x - 11 and the remainder equals -9.

Let's check this using division algorithm.

Dividend = 3x³ - 5x² - 23x + 24

Divisor = x - 3

Quotient = 3x² + 4x - 11

Remainder = -9

By division algorithm,

Dividend = (Divisor × Quotient) + Remainder

3x³ - 5x² - 23x + 24  = [(x - 3) (3x² + 4x - 11)] + -9

                                 = [3x³ + 4x² - 11x - 9x² - 12x + 33] + -9

                                 = 3x³ + 4x² - 9x² - 11x - 12x + 33 - 9

                                 = 3x³ - 5x² - 23x + 24

Hence -9 is the remainder of this division process.

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The description of the relationship is a linear relationship, the equation is y = 301.7 - 2.158x and the actual selling price of the home is $275

The given parameter is in the attached figure

Also from the question, we have:

House price decreases by approximately every mile

The above implies that the relationship is an approximately linear relationship

From the table, we have

Coefficient constant = 301.7

Coefficient distance = -2.158

This means that

y-intercept = 301.7

Slope = -2.158

So, the equation is

y = y-intercept + slope * x

This gives

y = 301.7 - 2.158x

The interpretation of the slope and y-intercept in context are:

Slope implies that the house price decreases by 2.158 miles, and the y-intercept implies that the initial house price is 301.7

Here, we have

Residual =  -2.962

Miles = 11

This means that

Predicted price = 301.7 - 2.158 * 11

Evaluate

Predicted price = 277.96

So, we have

residual = actual - predicted

This gives

actual = residual + predicted

So, we have

actual = -2.962 +  277.96

Evaluate

actual = 275

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Answer: 1

Step-by-step explanation: becuase 2/4 + 3/6 = 1

Answer: 6/6 = 1

Step-by-step explanation:

First, if you were to look at both fractions they both equal to 0.5 or one half.

Therefore, 2/4 = 1/2

And, 2/4 = 1/2

1/2 + 1/2 = 1

Distance formula = Distance = SQRT((x2-x1)^2 + (y2-y1)^2)

Distance = sqrt((2- -1)^2 + (-1 -7)^2)

Distance = sqrt(3^2 + -8^2)

Distance = sqrt(9+64)

Distance = sqrt(73)

Answer: √73

Answer:

8(3+4p)

Step-by-step explanation:

8 goes into 24 and 32, so it can be factored out:

\(24+32p=8(3+4p)\)

Answer:

8(3 + 4p)

Step-by-step explanation:

Factor 24 + 32p

First, factor out the GCF. In this case, the GCF is 8, and we have

8(3 + 4p)

We can't factor anymore so the answer is 8(3 + 4p)

As, the ratios of the side of both triangles NHS and NAB are found equal they are similar triangles. Thus, NHS ≈ NAB

Congruent triangles and similar triangles are two distinct but closely related concepts. Similar triangles are any two or more triangles having the identical proportions of their corresponding sides, an equal pair of corresponding angles, and their similar shape.

For the given two triangles: NHS and NAB.

The ratios of side are equal in the similar triangles.

NH/HA = NS/SB

12/48 = 15/60

1/4 = 1/4

As, the ratios of the side of both triangles NHS and NAB are found equal they are similar triangles.

Thus, NHS ≈ NAB

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Correct question-

Question 7: Prove or disprove :

NHS ≈ NAB

The maximum amount of water that can be used by each house on a daily basis is 100 liters.

From the information given, the gated community consists of 40 houses and requires 500 liters of water everyday for common utilities of the community.

The maximum amount of water that can be used by each house on a daily basis will be:

4500 = 40x + 500

40x = 4500 - 500

40x = 4000

x = 4000/40

x = 100

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With the help of the 68-95-99 rule (see picture above) we know that those values with a z-score less than -2 are located in the 2.5% zone on the left.

Z-score is computed as follows:

where x is the observed value, μ is the mean and σ is the standard deviation.

Substituting with z = -2, μ = 30, and σ = 10, we get:

It is expected that 2.5% of the students spend less than 10 minutes.

The impact on Carns Company's income from eliminating the Small Tools Division would be a decrease of $1,209,000.

To determine the impact on Carns Company's income from eliminating the Small Tools Division, we need to consider the avoidable costs associated with the division.

The avoidable costs include all of the variable costs of the division and a portion of the fixed costs that are specifically related to the Small Tools Division. In this case, the variable costs of the division are $1,295,000, and $119,000 of the fixed costs are avoidable.

To calculate the impact on income, we subtract the avoidable costs from the loss reported by the division:

Impact on income = Loss - Avoidable costs

Impact on income = $205,000 - ($1,295,000 + $119,000)

Impact on income = $205,000 - $1,414,000

Impact on income = -$1,209,000

The negative sign indicates a decrease in income.

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Answer:

\(g(x) = \frac{1}{4}3^x +3\)

Step-by-step explanation:

Given

\(f(x) =\frac{1}{4}3^x -6\)

\(g(x) \to\) translate f(x) 9 units up

Required

Find g(x)

The translation rule is:

\(g(x) \to f(x) + 9\)

So, we have:

\(g(x) = f(x) + 10\)

\(g(x) = \frac{1}{4}3^x - 6 + 9\)

\(g(x) = \frac{1}{4}3^x +3\)

Answer:

I think the answer is For a basic oil change in Seattle you can expect to pay somewhere between $40 and $70

Step-by-step explanation:

I hope this helps. Have a good Day!

The bus that is the most consistent, given the data collected on travel times to school from two groups of students is C Bus 18, with a range of 10

To determine which bus is the most consistent, we should use the interquartile range (IQR) as the measure of variability. The IQR measures the spread of the middle 50% of the data, which makes it less sensitive to outliers compared to the range.

Bus 47:

Median (Q2): 16

Q1: 10

Q3: 22

IQR = Q3 - Q1 = 22 - 10 = 12

Bus 18:

Median (Q2): 12

Q1: 8

Q3: 18

IQR = Q3 - Q1 = 18 - 8 = 10

Bus 18 has a smaller IQR than Bus 47 (10 vs. 12), which means the travel times for Bus 18 are more consistent.

Note: Figures might be different due to options being for different variant but Bus 18 is the most consistent.

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On solving the question, we can say that - herefore , the required inequality expression is 4.50x+1.75y ≤50

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations.. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers.An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

One cupcake costs $4.50,

So, “x” cupcakes cost = 4.50x.

One brownie cost $1.75,

so “y” brownies cost = 1.75y.

thus, the total 4.50x+1.75y  must be less or equal to $50.

Therefore , the required inequality expression is 4.50x+1.75y ≤50

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Answer:

x=2-y

Step-by-step explanation:

subtract y from both sides

x+y-y=z+y

x=2-y

Answer:

31120 ounce

Step-by-step explanation:

Answer:31120

Step-by-step explanation:Use google

The slope of the tangent line that passes through the point (-1, 2) is 4, and the equation of the line is: y - 2 = 4(x + 1) or y = 4x + 6

To find the slope of the tangent line to a circle, we first need to find the equation of the circle.

Given the center and radius, the equation of a circle can be written as:

(x + 5)^2 + (y - 3)^2 = 17

Next, we find the equation of the line that passes through the point (-1, 2) and is tangent to the circle.

We can use the slope-point form of the equation of a line:

y - 2 = m(x + 1)

where m is the slope of the line.

To find the value of m, we need to find the slope of the line that is tangent to the circle at the point (-1, 2).

The slope of a tangent line to a circle at a point is equal to the derivative of the equation of the circle at that point.

Taking the partial derivatives of x and y in the equation of the circle, we get:

2(x + 5)dx + 2(y - 3)dy = 0

Rearranging and solving for the slope:

dy/dx = -(x + 5)/(y - 3)

Evaluating the slope at the point (-1, 2), we get:

dy/dx = -(−1 + 5)/(2 − 3) = 4

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The annualized return for the entire period is the closest to 10.5%.

To calculate the annualized return for the entire period, we need to consider the returns for each year and the return in the first quarter of Year 4. Since the returns are given for each period, we can use the geometric mean to calculate the annualized return.

The formula for calculating the geometric mean return is:

Geometric Mean Return = [(1 + R1) * (1 + R2) * (1 + R3) * (1 + R4)]^(1/n) - 1

Where R1, R2, R3, and R4 are the returns for each respective period, and n is the number of periods.

Given the returns:

Year 1 return: 5% or 0.05

Year 2 return: 12% or 0.12

Year 3 return: -6% or -0.06

First quarter of Year 4 return: 2% or 0.02

Using the formula, we can calculate the annualized return:

Annualized Return = [(1 + 0.05) * (1 + 0.12) * (1 - 0.06) * (1 + 0.02)]^(1/3) - 1

Annualized Return = (1.05 * 1.12 * 0.94 * 1.02)^(1/3) - 1

Annualized Return = 1.121485^(1/3) - 1

Annualized Return ≈ 0.105 or 10.5%

Therefore, the annualized return for the entire period is approximately 10.5%.

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Step-by-step explanation:

75 = 3 x 5 x 5    in prime factorization

Answer:

Step-by-step explanation:

3x5x5

Answer:

6(3m + 6)

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To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

Answer:

5.75.

Step-by-step explanation:

The mean = (8+5+7+10+3+4+31+12)/ 8

= 80/8

= 10.

Now we calculate the difference of each value from the mean We take the absolute ( positive) differences

10 - 8 = 2

10 - 5 = 5

10 - 7 = 3

10 - 10 = 0

10-3 = 7

10 = 4 = 6

10 - 31 = 21

10 - 12 = 2

Sum of the differences = 46

and the mean deviation  is 46/8 = 5.75.

The amount received from loans as a number in millions is 242,700 million rand.

Deducing value A requires computation of collective income sources, for which the following summation suffices:

Total Income = Tax + Loans + ASC + QP + Other income + Non-tax income = 1370 + 242.7 + 180.3 + 31.5 + A + 0 = 1825.5 + A

In this context, it follows that A amounts to (1825.5 - 1370 - 242.7 - 180.3 - 31.5) = 0 million rand.

Conversely determining missing value B necessitates subtraction of total expenditure from accumulated revenue, giving rise to the subsequent formula:

Total Income - Total Expenditure = B

(1825.5 - 112.7 - 278.4 - 262.4 - 222.6 - 211.0 - 209.2 - 208.5 - 202.2 - 0) = B

Following calculation, B equates to -77.1 million rand, indicating an overage in expenses during fiscal year 2019/20.

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Answer:

\(AB = 8.38\)

Step-by-step explanation:

Given

\(AC = 9\)

\(BC =10\)

\(\angle B = 52\)

Required

Determine AB

This question will be answered using the cosine law.

\((AB)^2 = (AC)^2 + (BC)^2 - 2(AC)(BC)\ \cos \angle B\)

Substitute the expected values

\((AB)^2 = 9^2 + 10^2 - 2 * 9 * 10 * cos(52)\)

\((AB)^2 = 81 + 100 - 180* cos(52)\)

\((AB)^2 = 181 - 180* cos(52)\)

\((AB)^2 = 181 - 180* 0.6157\)

\((AB)^2 = 70.174\)

Take square roots of both sides

\(AB = \sqrt{70.174\)

\(AB = 8.38\) -- approximated

Answer:

RS/XY = ST/YZ

Step-by-step explanation:

They need to follow the same direction and same length in comparision to the rest. From what I can see, that seems to be the one that does that best.

Answer:

13 inches, 11 + t inches.

Step-by-step explanation:

1 hour 1 inch, so after 2 hours, the snow is 11 + 1*2 = 13 (inches).

After t hours, the snow is 11 + 1*t = 11 + t (inches).

The range of the starting salaries is 53,000

Given,

The box and whisker plot below shows the starting salaries

The number of graduates in a small college = 120

We have to find the range of the starting salaries;

Range of a data;

The difference between the highest and lowest values for a given data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation.

Here,

Lowest value = 19,000

Highest value = 72,000

Then,

Range of the set = 72,000 - 19,000 = 53,000

That is,

The range of the given data set is 53,000

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9514 1404 393

Answer:

  (c)  lies in the shaded regions of both the top and bottom inequalities.

Step-by-step explanation:

A point that is a solution to the system must be a solution to all of the inequalities in the system. It must lie in the shaded regions of both.

Answer:252

Step-by-step explanation: 302 - 123 = 179. 179 + 73 =252

Answer:

302

-123

=179

+73

=252

so the answer would be 252