Write the function in the form f(x) = (x − k)q(x) + r for the given value of k. F(x) = x3 − x2 − 10x + 5, k = 3

Answer:

-7 and 3

-5 and 1

-3 and -1

Step-by-step explanation:

-7 + 3 = -4

-5 + 1 = -4

-3 + -1 = -4

The money is Noah wants to share  with people if each person still gets the same amount is 4.

The algebraic approach to solving simultaneous linear equations is known as substitution method.

Let the total amount Noah have be'y'.

The initial amount shared by Noah among 10 people be 'x'.

Then,

y = 10x

But,

Amount shared is decreased by 20, ans sharing with 5 people.

Then,

y - 20 = 5x

Put value of y.

10x = 5x + 20

On solving;

x = 20/5

x = 4

Thus, money is Noah wants to share  with people if each person still gets the same amount is 4.

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We can use the system οf equatiοns tο sοlve fοr the length and width οf Marikο's garden. The first equatiοn represents the fact that the perimeter οf the garden, which is the sum οf the length and the width multiplied by twο, is equal tο 50 feet.

The secοnd equatiοn represents the fact that the sum οf the length and the width is equal tο 25 feet. We can sοlve this system οf equatiοns using substitutiοn οr eliminatiοn.

Using substitutiοn, we can sοlve fοr οne variable in terms οf the οther in the secοnd equatiοn:

L + W = 25

W = 25 - L

Nοw we can substitute this expressiοn fοr W intο the first equatiοn:

2L + 2W = 50

2L + 2(25 - L) = 50

Simplifying:

2L + 50 - 2L = 50

50 = 50

This equatiοn is true fοr any value οf L and W that satisfies the cοnditiοn that the sum οf the length and the width is equal tο 25 feet. Sο we have infinitely many pοssibilities fοr the length and width οf Marikο's garden.

Hοwever, there are limits tο what values the length and width can be. Fοr example, bοth the length and the width must be pοsitive and less than 25 feet fοr the garden tο fit within the 50 feet οf fencing that Marikο has. Additiοnally, we might want the length and width tο be integers οr tο satisfy sοme οther cοnstraint. But within the cοnstraints given by the prοblem, there are infinitely many pοssible sοlutiοns fοr the length and width οf the garden.

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The coordinates of the midpoint of the given segment is; (-15, 4)

For any specific line segment, it is well known that the midpoint is defined as the halfway between its two endpoints. The expression that is used to find the x-coordinate of that midpoint is expressed as: [(x)1 + (x)2]/2, which denotes the average of the x-coordinates. Similarly, the expression that is used to find the y-coordinate of that midpoint is expressed as: [(y)1 + (y)2]/2, which is the average of the y-coordinates.

We are given the coordinates of the endpoints of the line as;

K(-11, 2) and L(-19, 6)

Thus;

Midpoint Coordinate = (-11 - 19)/2, (2 + 6)/2

= (-15, 4)

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Answer: 32.2 cubic inches

Step-by-step explanation:

 The volume of one coin can be calculated using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.

Substituting the given values, we get:

V = π(1.4)^2(0.0625)

V ≈ 0.14 cubic inches (rounded to the nearest hundredth)

To find the total volume of all the coins, we can multiply the volume of one coin by the number of coins:

Total volume = 230 × 0.14

Total volume ≈ 32.2 cubic inches (rounded to the nearest hundredth)

Therefore, the coins take up approximately 32.2 cubic inches of the treasure chest.

Two shapes would have equal volumes if the areas of their corresponding cross-sections are equal at every height.

According to Cavalieri's principle, two shapes have equal volumes if for every pair of parallel cross-sections taken at the same height, the areas of the cross-sections are equal.

1. Two cylinders with the same height and different radii.

  As long as the cross-sectional areas of the cylinders at each height are the same, the volumes will be equal. The radii of the cylinders can vary.

2. Two cones with the same height and different base radii.

  Similar to cylinders, as long as the cross-sectional areas of the cones at each height are the same, the volumes will be equal.

3. Two prisms with the same height and different base shapes.

  If two prisms have the same height and the cross-sectional areas at each height are equal, then the volumes will be equal.

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Answer:2.5e-9

Step-by-step explanation:

Answer:

population: 2,900,904.279

Step-by-step explanation:

You need to calculate the total area first. The figure is made from 2 smaller figures.

Area for the top figure = 159 x (345 - 276) = 159 x 69 = 10971

Area for the bottom figure = 265 x 276 = 73140

Total are = 10971 + 73140 = 84111 mi^2

so you have 34.489 people/mi^2 =>

34.489 x 84111 = 2,900,904.279 people

Answer:

_2⁵b⁴*⁵a⁵

Answer=_32b²⁰a⁵

Answer:

If E(x,y), then E’(x-5,y+3)

Step-by-step explanation:

Depending on E, E’ changes. The new coordinates for E’, however, is (x-5, y+3), if (x,y) is E, since you move left (-) 5 and up (+) 3.

Answer: Y= -4x + 2

Step-by-step explanation:

The slope intercept equation is y = mx + b

The slope or m in this situation is -4

The y- intercept or b is 2

When you substitute then slope and y-intercept into the equation you get

Y = -4x + 2

Step-by-step explanation:

See image:

Given the following question:

We have 60 balloons in total

4/12 of the balloons are black

3/12 of the balloons are white

We are trying to find the amount of red balloons Carter has:

Let...

B = black

W = white

R = red

[tex]B=(\dfrac{4}{12}) \times60=20[/tex]

         [tex]B=20[/tex]

[tex]W=(\dfrac{3}{12}) \times60=15[/tex]

     [tex]20+15=35[/tex]

     [tex]60-35=25[/tex]

         [tex]R=25[/tex]

Carter has 25 red balloons

Yes, they will reach their goal of $45.00 by selling 12 cups of lemonade on Sunday.

Yes, they will reach their goal. To calculate this we can use the following formula:

Total Sales = (Number of cups sold on Saturday × Price per cup) + (Number of cups sold on Sunday × Price per cup)

Total Sales = (37 × 0.75) + (12 × 0.75)

Total Sales = 27.75 + 9

Total Sales = 36.75

Since 36.75 is greater than the goal of 45.00, they will reach their goal. This can be further verified by looking at the total cost of the cups they sold. 37 cups sold on Saturday at $0.75 each will cost $27.75. Adding the 12 cups sold on Sunday at $0.75 each will cost $9, bringing the total cost of the cups sold to $36.75. This is the same amount that was calculated using the formula above. Therefore, they will reach their goal by selling 12 cups of lemonade on Sunday.

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The coefficient of determination or R² is -0.932. The coefficient of correlation or R is 0.964. The equation of the regression line is:Y= 27,233.25 + (960.25X)Y= 27,233.25 + 0.96X.

A magrzeino used the surnunatod rating of 10 restaurants to predut the cost of a restaurant meal. For that data, SSR \(-131,383.63 \) and SST \( =140,70746 \). The task is to complete parts (a) through (c). a) Determining the coefficient of determination or R²R² can be determined using the formula given below: R²= SSR/SST R²= -131,383.63 /140,707.46 R²= -0.932 Thus, the coefficient of determination or R² is -0.932.(b) Determining the coefficient of correlation or RTo determine the coefficient of correlation, we will use the formula given below:R= sqrt(R²)R= sqrt(-0.932)R= 0.964 Thus, the coefficient of correlation or R is 0.964.(c) Determining the equation of the regression lineUsing the formula,

The equation of the regression line can be calculated as:Y= a + bX where a = Y - bX, b = r (sy/sx)and r is the correlation coefficient.The given data can be arranged into a table as shown below:X (Sur)Y (Cost of a restaurant meal)XYX²Y²1200180020003600840030007601440040009002250045001020250601000050011200027501250222501250015003700022501650142252,306,901387,762,1509,622,5001,293,900248,408,050The values of ΣX, ΣY, ΣXY, ΣX², and ΣY² can be calculated from the table. ΣX = 55ΣY = 85,900ΣXY = 960,250ΣX² = 3850ΣY² = 69,635,950Then, a = (ΣYΣX² - ΣXΣXY) / nΔ= 10(a)Δ= [(85,900 x 3850) - (55 x 960,250)] / 10Δ= (330,115,000 - 52,814,750) / 10Δ= 27,233.25Therefore, the equation of the regression line is:Y= 27,233.25 + (960.25X)Y= 27,233.25 + 0.96X.

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Answer:

exact form: [tex]\frac{18}{5}[/tex]

decimal form: 3.6

mixed number form: [tex]3\frac{3}{5}[/tex]

Answer:

y=18/5

Step-by-step explanation:

6=5y/3

multiply both sides:

6*3=5y

simplify 6*3 to 18:

18=5y

divide both sides by 5:

18/5=y

answer: y=18/5

A typical student in Mr. Hart’s class studies 1.56 hours per week and a typical student in Ms. Perry’s class studies 1.67 hours per week.

The mean is the average of a set of data, calculated by adding all the values in the set and dividing the sum by the number of values. The formula for calculating the mean is:

Mean = (Sum of all values) / (Number of values)

To calculate the mean of Mr. Hart’s class, we will first add up all the values from 0 to 8 in the dot plot:

0 + 0 + 2 + 2 + 1 + 4 + 2 + 1 + 2 = 14

We then divide this sum by the total number of values, which is 9:

Mean = 14 / 9 = 1.56

The mean of Mr. Hart’s class is 1.56 hours of studying per week.

Similarly, to calculate the mean of Ms. Perry’s class, we will add up all the values from 0 to 8 in the dot plot:

2 + 4 + 1 + 3 + 2 + 1 + 1 + 0 + 1 = 15

We then divide this sum by the total number of values, which is 9:

Mean = 15 / 9 = 1.67

The mean of Ms. Perry’s class is 1.67 hours of studying per week.

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We can confirm that each person should receive exactly 224 Pokémon cards, and there won't be any cards left over.

To split the 1,792 Pokémon cards equally between 8 people, including yourself and your 7 friends, you need to divide the total number of cards by the number of people:

1,792 cards ÷ 8 people = 224 cards per person.

So each person should get 224 Pokémon cards.

However, we should also check if there is a remainder after the division. To do that, we can multiply the number of cards each person is getting by the number of people and subtract it from the total number of cards:

224 cards/person x 8 people = 1,792 cards

1,792 cards - 1,792 cards = 0 remainder

Since there is no remainder, we can confirm that each person should receive exactly 224 Pokémon cards, and there won't be any cards left over.

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The probability that the person selected is a tall, left-handed woman is 0.02.

Given that, The probability that the person selected is a woman is P(W) = 38% = 0.38

The probability that the person selected is tall is P(T) = 54% = 0.54

The probability that the person selected is left-handed is P(L) = 11% = 0.11

It is given that the events W, T, and L are independent of each other. Therefore, their joint probability is given by:

P(W ∩ T ∩ L) = P(W) × P(T) × P(L) = 0.38 × 0.54 × 0.11 = 0.02292

Now, the probability that the person selected is a tall, left-handed woman is given by:

P(T ∩ L ∩ W) = P(W ∩ T ∩ L) = 0.02292 = 0.02

Therefore, the probability that the person selected is a tall, left-handed woman is 0.02.

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Answer:

0.00035

Step-by-step explanation:

0.0005×0.007 ×100

—————-------

1

0.0000035 ×100

0.00035

The probability that a randomly selected bicycle from a bicycle shop will have either a water bottle holder or a kickstand is 95%, calculated by adding the probabilities of each component being present and subtracting the probability of both being present.

The probability that a randomly selected bicycle from a bicycle shop will have either a water bottle holder or a kickstand is 95%. To calculate this, we first need to consider the probability that a bicycle has a water bottle holder, which is 60%. The probability that the bicycle has a kickstand is 55%. Then, the probability of a bicycle having both a kickstand and a water bottle holder together is the product of the individual probabilities, which is 34%. Thus, the probability that a randomly selected bicycle will have either a water bottle holder or a kickstand is 60% + 55% - 34% = 95%.

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Relation 2 and 3 are actual functions with proper domain, co domain, range.

A function can be represented in several ways, including using algebraic expressions, tables, graphs, or even words. For example, the function f(x) = 2x + 1 defines a relationship between the input x and the output 2x + 1. If we input x = 3 into this function, the output would be f(3) = 2(3) + 1 = 7.

Functions can have different properties, such as being continuous or discontinuous, being differentiable or nondifferentiable, or having maximum or minimum values. Functions can also be classified according to their types, such as linear, quadratic, exponential, logarithmic, trigonometric, or piecewise-defined functions.

Functions are used extensively in mathematics, science, engineering, economics, and many other fields to describe real-world phenomena and to solve practical problems. They are also studied in their own right, as objects of mathematical interest and beauty, with deep connections to many other areas of mathematics, such as calculus, analysis, and algebra

Relation 2 and 3 are actual functions with proper domain, co domain, range.

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The total simple interest earned by Liz at the end of 5 years is found as: $28.5

A straightforward but effective idea. Very simply: interest is the benefit for saving - and the penalty of borrowing.

Principal P = $570

Interest r = 1%

Time t = 5 years.

SI = P*R*t / 100

SI = 570*1*5 / 100

SI = 28.5

Thus, the total simple interest earned by Liz at the end of 5 years is found as: $28.5.

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The complete question is-

Liz spent her summer break working at Wild Lakes waterpark. At the end of the summer, she put $570 of her earnings into a savings account that earns 1% interest each year. Find her simple interest after 5 years.

Answer: x=10

Step-by-step explanation:

sum of all the angles inside triangle is equal to 180degrees.

First angle: 9x-16

Second angle: 7x-5

Third angle: 3x+11

let's sum this angles:

9x-16+7x-5+3x+11=19x-10=180

19x=180+10=190

x=190/19=10

The triangle fοrmed by J(7,2), K(-4,9), and L(-3,-1) is a scalene οbtuse triangle.

A triangle is said tο be οbtuse scalene in geοmetry if οne οf its angles is larger than 90 degrees but less than 180 degrees, while the οther twο angles are bοth less than 90 degrees. Measurements fοr the three sides and angles vary.

Tο classify the triangle fοrmed by the pοints J(7,2), K(-4,9), and L(-3,-1), we need tο find the lengths οf its sides and apply the triangle classificatiοn criteria.

Using the distance fοrmula, we can find the lengths οf the sides:

[tex]JK = \sqrt{[(7 - (-4))^2 + (2 - 9)^2]} \\JK =\sqrt{ (11^2 + (-7)^2)} \\ JK =\sqrt{170} \\KL = \sqrt{[(-4 - (-3))^2 + (9 - (-1))^2]} \\KL =\sqrt{ (1^2 + 10^2) } \\KL = \sqrt{101} \\LJ = \sqrt{[(-3 - 7))^2 + ((-1) - 2)^2]} \\LJ=\sqrt{ (10^2 + (-3)^2)} \\LJ = \sqrt{109}[/tex]

Since all three sides have different lengths, the triangle is scalene.

Therefοre, the triangle fοrmed by J(7,2), K(-4,9), and L(-3,-1) is a scalene οbtuse triangle.

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Answer: diffrent form so i can help you better

Step-by-step explanation:

i cant fully answer it but i know the steps,

(the link is how you would set it up)

you can replace x with 20 or 27, i would start 20

Therefore , the solution of the given problem of coordinates comes out to be the point is (-2, 3), and it is located in the second quarter of the coordinate graph.

A coordinate system can accurately locate coordinates or other mathematical objects on such a space, including Euclidean space, by using one or a number of variables or coordinates. A point or thing on a double plane can be located using coordinates, which appear to be pairs of numbers. On a two-dimensional surface, a point's location is represented by the y and x vectors. a collection of images used to identify specific locations. Usually, the number has two numbers.

Here,

The details provided can be summed up as follows:

Negative in quadrant 2: This indicates that the point is located in the second quadrant, where the x- and y-coordinates are both negative.

the x-coordinate falls between -1 and -3: This requirement can only be met by the number -2.

y-coordinate exceeds 2: In the second quadrant, only the number 3 meets this requirement.

The total of the coordinates' absolute numbers is 5: As a result, the point is either (-2, 3) or |-2| + |3| = 5. (-2, -3).

As a result, the point is (-2, 3), and it is located in the second quarter of the coordinate graph.

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The correct option for this question is C. arrangement of the body.

Why it is?

Based on the given passage, the word "lines" most likely refers to the arrangement of the body in ballet dancing. The passage states that "Ballet places a lot of emphasis on the lines of the body" and that "Good lines" in ballet are a combination of the body alignment and artistic expression.

It also mentions that proper positioning of the feet is important for achieving good lines and that turnout, which is the outward rotation of the hips and knees, is the basis for all ballet movements.

Therefore, "lines" in this context is referring to the visual lines created by the dancer's body and limbs in ballet dance, which are essential to proper technique and artistic expression.

Therefore, the correct answer is C. arrangement of the body.

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A graph that would display the narrowest parabola is f(x) = -4x² - 30x.

In Mathematics, the standard equation of the directrix lines for any parabola can be modeled or represented by the following mathematical expression:

y = a(x - h)² + k.

Where:

Generally speaking, the larger the absolute value of the leading coefficient of a quadratic function, the narrower would be graph of its parabola.

In this context, we have the following:

y = -2x²+x+3; a = -2

f(x) = -4x² - 30x; a = -4

|a| = |-2| = 2

|a| = |-4| = 4

Therefore, |-2| is less than |-4|.

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