20 points ) What is the length of the line segment graphed on the coordinate grid?

Answer: y = 17x + 114

Step-by-step explanation:

The equation for the slope-intercept form is y = mx + b.

Arrange the equation so that it resembles y = mx + b.

You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.

y + 5 = 17(x + 7)

y + 5 = 17x + 119

y + 5 - 5 = 17x + 119 - 5

y = 17x + 114

Answer:

Y = 17x + 114

Step-by-step explanation:

1. Y + 5 = 17 (x+7)

2. Y + 5 = 17x + 119   [Multiply the numbers in parenthesis by 17.]

3. Y = 17x + 114.     [To keep the balance and move the 5 over, subtract it from 119.]

Answer:

they are 10km 32 degrees far from each other

Step-by-step explanation:

scott - 100km - 30 degrees

spork - 110km - 62 degrees

how far = difference between them

as spork's distance and degrees are greater than scott we substract Scott's from spork's

110 - 100 = 10 km

62 - 30 = 32 degrees

they are 10km 32 degrees far from each other

The monthly annuity yield would be $1,962.85. To calculate this, first determine the number of months between age 59 and 70 (which is 132 months).

Then use the present value formula to solve for the monthly payment: $300,000 = PMT x ((1 - (1 + (0.085/12))^(-132))/(0.085/12)). Solving for PMT, you get a monthly payment of $1,962.85, which is the monthly annuity yield.

It's important to note that this calculation assumes that the annuity payments stop at age 70 and that there are no additional fees or taxes associated with the annuity. It's always a good idea to consult with a financial advisor to determine the best retirement strategy for your individual circumstances.

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The statement "If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent" is a conditional statement.

The statement presents a logical relationship between two conditions: having three sides of one triangle equal to three sides of another triangle, and the congruence of the triangles. A conditional statement, also known as an "if-then" statement, consists of an "if" clause (antecedent) and a "then" clause (consequent). In this case, the "if" clause states the condition that the sides of the triangles are equal, and the "then" clause states the consequence that the triangles are congruent.

A conditional statement takes the form "if p, then q," where p represents the antecedent and q represents the consequent. The antecedent is the condition that must be satisfied for the consequent to occur. In this case, p is "three sides of one triangle are equal to three sides of another triangle," and q is "the triangles are congruent." The statement asserts that if the condition p is true, then the consequent q is also true. If the condition is not met, the truth value of the statement is not determined.

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The Z-score for the minimum age is -2.1449 and the Z-score for the maximum age is 1.8306 and the more extreme Z-score is the one with the larger absolute value

To standardize the minimum and maximum ages, we need to calculate the Z-score for each. The formula for Z-score is (value - mean) / standard deviation.

Mean = 32.04,

Standard Deviation = 9.800
Minimum age = 11,

Maximum age = 50

For the minimum age: Z-score = (11 - 32.04) / 9.800 = -2.1449
For the maximum age: Z-score = (50 - 32.04) / 9.800 = 1.8306

So, someone with a Z-score of 3 would be approximately 61.44 years old.

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Answer:

Step-by-step explanation:

4x-2 +3x+7 = 180

7x + 5 = 180

7x = 175

x = 25

3(25) + 7 = 82

Answer:

82 (degrees)

Step-by-step explanation:

4x-2+3x+7=180=7x+5...175=7x...x=175/7... x=25

This is both angles combined which we know adds up to half of the entire quadrilateral (180 degrees). Then solve.

3(25) +7=82 which is equal to f

f=82

Answer:

The number of hours and weeks start at (0,0). This is a strong positive association. The numbers of hours is increased by 3 each week. The graph is moving upward, which means it is positive, and it is not scattered and strong.

The equation and interpret the slope is given below.

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

The number y of hours of cello lesson time you take after x weeks is represented by the equation y=3x graph

now,

The number of hours and weeks start at (0,0). This is a strong positive association. The numbers of hours is increased by 3 each week. The graph is moving upward, which means it is positive, and it is not scattered and strong.

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Answer:

She drove 12 hours

5+4+3=12

Step-by-step explanation:

The question is an example of theoretical probability, since it does not involve actually selecting marbles from the bag, while empirical probability is based on actual observations or experimental data.

Theoretical probability is the probability of an event based on mathematical analysis or reasoning, without actually performing an experiment or collecting data.

Here given question is an example of theoretical probability.

Theoretical probability is the probability of an event based on a theoretical or mathematical calculation, without actually performing an experiment or collecting data. In this case, we can calculate the probability of choosing a blue marble by dividing the number of blue marbles (8) by the total number of marbles;

the total number of marbles in the bag = 7 + 8 + 9 = 24

P(Blue) = 8/24 = 1/3

This calculation is based on theoretical probability, since it does not involve actually selecting marbles from the bag to determine the proportion of blue marbles. In contrast, empirical probability is based on actual observations or experimental data.

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Answer:

7

Step-by-step explanation:

(4+6+7+8+10)/5=7

the median is the middle number=7

After making a $150 deposit in the bank in one year, two years, and three years, Homer will have a total of $689 in the bank in four years, considering the interest rate of 5.6%.

Let's break down the problem step by step. In one year, Homer makes a $150 deposit. After one year, his initial deposit will earn interest at a rate of 5.6%. Therefore, after one year, his account balance will be $150 + ($150 * 0.056) = $158.40.

After two years, Homer makes another $150 deposit. Now, his initial deposit and the first-year balance will both earn interest for the second year. So, after two years, his account balance will be $158.40 + ($158.40 * 0.056) + $150 = $322.46.

Similarly, after three years, Homer makes another $150 deposit. His account balance at the beginning of the third year will be $322.46 + ($322.46 * 0.056) + $150 = $494.62.

Finally, after four years, Homer's account balance will be $494.62 + ($494.62 * 0.056) = $689.35, which rounds down to $689. Therefore, Homer will have $689 in the b in four years, considering the interest rate of 5.6%.

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Answer:

I guess that you want to find the profit:

We have two equations:

the cost equation:

C(x) = -0.1*x^2 + 100.

And the selling equation, that is a vertical stretch of the cost equation by a factor of 1.4:

S(x) = 1.4*C(x) = 1.4*( -0.1*x^2 + 100.) = -0.14*x^2 + 140

Now, whit those two equations we can find the profit equation, that is defined as the difference between the selling price, and the cost:

P(x) = S(x) - C(x) = 1.4*C(x) - C(x) = (1.4 - 1)*C(x) = 0.4*C(x).

Then the profit is 0.4 times the initial cost.

P(x) = 0.4*( -0.1*x^2 + 100.) = -0.04*x^2 + 40

Answer:

D. S(C(x))= –0.14x^2+140; $108.50

Step-by-step explanation:

Cause the others are wrong

Answer:

142 506

Step-by-step explanation:

here the order does not matter

Then

we the number of sets is equal to the number of combinations.

Using the formula :

the number of sets is 30C5

\(C{}^{5}_{30}=\frac{30!}{5!\left( 30-5\right) !}\)

      \(=142506\)

There are 142506 ways in which 5 students can be selected out of 30 students.

The selection of 5 students out of 30 students can be achieved with the use of combination since the order of selection is not required to be put into consideration.

By using the formula:

\(\mathbf{^nC_r = \dfrac{n!}{r!(n-r)!}}\)

where;

\(\mathbf{^nC_r = \dfrac{30!}{5!(30-5)!}}\)

\(\mathbf{^nC_r = \dfrac{30!}{5!(25)!}}\)

\(\mathbf{^nC_r = 142506}\)

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Answer:

  \(\sqrt[5]{2^4}\)

Step-by-step explanation:

Maybe you want 2^(4/5) in radical form.

The denominator of the fractional power is the index of the root. Either the inside or the outside can be raised to the power of the numerator.

  \(2^{\frac{4}{5}}=\boxed{\sqrt[5]{2^4}=(\sqrt[5]{2})^4}\)

__

In many cases, it is preferred to keep the power inside the radical symbol.

Answer:

-3

Step-by-step explanation:

Answer:

y= -1/2 x -8  

Step-by-step explanation:

as following the two points,

formula must be y=mx+b

slope= - (1/2) x

b= -8

The density of the lobster population in the area labeled NBHK is C) 9.02 lobsters/mi^2.

Population density refers to the number of people living in a given area, usually expressed as the number of individuals per square mile or kilometer.

To calculate population density, you can divide the total population of a given area by its land area. For example, if a city has a population of 1 million people and an area of 100 square miles, its population density would be 10,000 people per square mile.

The figure has two trapezoid and the areas are 306 and 756. Total area will be 1062 miles².

Lobster population will be:

= 6817 / 756

= 9

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Answer:

rational

Step-by-step explanation:

   Value of \(10^x\) will be between 1 and 10.

 Given in the question,

If we have to find the range of the value of the number, substitute x = 0 and 1

\(10^0=1\)

\(10^1=10\)

  Therefore, value of \(10^x\) will vary between 1 and 10.

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Let us consider the breadth(B) of the rectangle to be x.

So now,

Length of Rectangle(L) = 2x-3

Perimeter of Rectangle = 2 (Length + Breadth) = 2(L+B)

So according to the question,

Perimeter = 2(L+B) = 24 feet

                     L + B   = 12 feet

                     2x - 3 + x = 12 feet

                     3x - 3 = 12 feet

                        3x = 12+3

                         x = 15/3

                          x = 5 feet = Breadth

So ,                   Length = 2x - 3 = 2x5 - 3 = 10 - 3 = 7 feet

Hence the length of the Rectangle is 7 feet.

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The domain of f is the range of f −1, and the domain of f −1 is the range of f.

The domain of a function f is the set of all possible input values for which the function is defined and produces a unique output. The inverse function of f, denoted by f^(-1), is a function that reverses the input and output of f. That is, if f(x) = y, then f^(-1)(y) = x.

The domain of f^(-1) is the range of f because the output values of f become the input values of f^(-1), and the input values of f become the output values of f^(-1). Therefore, the range of f becomes the set of possible input values for f^(-1), which is the domain of f^(-1). Similarly, the range of f^(-1) is the domain of f because the output values of f^(-1) become the input values of f, and the input values of f^(-1) become the output values of f.

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Unfortunately, I am unable to directly interpret or visualize figures or images. However, I can provide you with a general explanation. In a discretized reservoir using block-centered grids, the standard ordering refers to the arrangement of grid cells or blocks in a particular pattern.

This pattern is often used to establish the connectivity and adjacency relationships between the cells in the reservoir model. Typically, the standard ordering arranges the grid cells in a sequential manner, starting from the top-left corner and moving row by row. Each grid cell represents a discrete volume or unit in the reservoir. The non-zero elements, indicated by the "x" positions in the coefficient matrix, would correspond to the active or connected cells within the reservoir model. These active cells are the ones that contribute to fluid flow and other reservoir properties. To visualize the discretized reservoir using the standard ordering, you would need to refer to the coefficient matrix and determine the dimensions of the reservoir model, such as the number of rows and columns. Then, starting from the top-left corner, you can represent each active cell or block using a graphical representation, such as a square or rectangle, in a sequential manner based on the standard ordering. This way, you can construct a visual representation of the discretized reservoir model.

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Answer:

The answer is No

I literally tried Yes

The cost of endless chicken wings at Restaurant X is $5. So cost equation for n chicken wings at Restaurant X is,

The cost of chicken wings at Restaurant Z is 20 cents and $1.40 for sauce. So cost equation for Restaurant Z is,

So answer is,

Restaurant X: c = 5

Restaurant Z: 0.20n + 1.40

(b)

Plot the system of equation on the graph.

(c)

The lines of two restaurant X and restaurant Z intersect each other at point (18,5). This means that restaurant X and restaurant Z has same cost 5 at n = 18. So both restanurant has same cost for 18 chicken wings.

Answer: 18

Answer:

The shortest altitude is 6.72 cm

Step-by-step explanation:

Given that the side lengths are

24 cm, 25 cm, 7 cm

The area of a triangle =

\(A = \sqrt{s \cdot (s-a)\cdot (s-b)\cdot (s-c)}\)

Where;

s = Half the perimeter = (24 + 25 +  7)/2 = 28

A = √((28×(28 - 24)×(28 - 25)×(28 - 7)) = 84 cm²

We note that 84/7 = 12

Therefore, the triangle is a right triangle with hypotenuse = 25, and legs, 24 and 7, the height of the triangle = 7

To find the shortest altitude, we utilize the formula for the area of the triangle A = 1/2 base × Altitude

Altitude  = A/(1/2 ×base)

Therefore, the altitude is inversely proportional to the base, and to reduce the altitude, we increase the base as follows;

We set the base to 25 cm to get;

Area of the triangle A =  1/2 × base × Altitude

84 = 1/2 × 25 × Altitude

Altitude = 84/(1/2 × 25) = 6.72 cm

The shortest altitude = 6.72 cm.

Answer:

Step-by-step explanation:

let r be the radius of the circle.

→ We know that in circle , the length of an arc

and the corresponding central angle are proportional.

180 corresponds to πr

120 corresponds to 10π

Then

\(\frac{\uppi r}{180} =\frac{10\uppi }{120}\)

\(\Longrightarrow r=\frac{180\times 10\pi }{120\pi } =\frac{180}{12} =15\)

The sled is moving at approximately 9.38 m/s when you reach the other side of the pond.

To solve this problem, we can use the concept of work and energy. The work done on an object is equal to the force applied multiplied by the distance over which the force is applied. In this case, the work done is equal to the change in kinetic energy of the sled.

Let's break down the problem into two parts: when you're pulling with a constant force of 200 N and when you're pulling with a force increasing linearly from 200 N to 500 N.

First, let's calculate the work done during the first part of the motion, where the force is constant. The work done is given by:

Work = Force × Distance

Work = 200 N × (24 m/2)

Work = 200 N × 12 m

Work = 2400 N·m

The work done during this part is 2400 N·m. This work contributes to the sled's change in kinetic energy.

Next, let's calculate the work done during the second part of the motion, where the force is increasing linearly. The average force during this part is (200 N + 500 N) / 2 = 350 N. The distance covered during this part is 24 m/2 = 12 m. The work done is given by:

Work = Average Force × Distance

Work = 350 N × 12 m

Work = 4200 N·m

The total work done on the sled is the sum of the work done in both parts:

Total Work = Work (constant force) + Work (linearly increasing force)

Total Work = 2400 N·m + 4200 N·m

Total Work = 6600 N·m

Now, we can equate the work done to the change in kinetic energy:

Total Work = Change in Kinetic Energy

6600 N·m = (1/2) × mass × (final velocity)^2

Here, the mass of the sled is 150 kg. We need to solve for the final velocity.

Rearranging the equation:

(final velocity)^2 = (2 × Total Work) / mass

(final velocity)^2 = (2 × 6600 N·m) / 150 kg

(final velocity)^2 = 88 N·m/kg

final velocity = √(88 N·m/kg)

final velocity ≈ 9.3808 m/s

Therefore, the sled is moving at approximately 9.38 m/s when you reach the other side of the pond.

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Answer:

Period: 2π

Phase Shift: -π (π to the left)

Vertical Shift: 0

so hmmm we look at hmm x³ + x² - 8x - 6 so how do squeak out a factor out of it, well, using the rational root test and using our p/q checking for factors, we find that likely factors can be ± 6/1 and ±(3, 2, 1) / 1, anyhow so we check some of those and hopefully without boring you to death we find that -3 works, we can always use the remainder theorem to check if that's true, by simply plugin in f(-3) and if it's indeed a factor, that'd give us 0, well, f(-3) = -27 + 9 +24 +6 = 0, holly smokes!! is a factor.

well, all that jazz means that -3 is a factor, namely the factor is really x = -3 or x + 3 = 0 so the factor is (x+3) and for our synthetic division we'll use the -3 version, Check the picture below.

so we end up with the factors of (x+3)(x²-2x-2), now for the 2nd factor what we can do to break it up is use the quadratic formula

\(~~~~~~~~~~~~\textit{quadratic formula} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-2}x\stackrel{\stackrel{c}{\downarrow }}{-2} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}\)

\(x= \cfrac{ - (-2) \pm \sqrt { (-2)^2 -4(1)(-2)}}{2(1)} \implies x = \cfrac{ 2 \pm \sqrt { 4 +8}}{ 2 } \\\\\\ x= \cfrac{ 2 \pm \sqrt { 12 }}{ 2 }\implies x=\cfrac{2\pm\sqrt{2^2\cdot 3}}{2}\implies x=\cfrac{2\pm 2\sqrt{3}}{2}\implies x=1\pm\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} (x+3)(x-1+\sqrt{3})(x-1-\sqrt{3}) \end{array}}~\hfill\)

now, just to clarify, all those are real roots, and the last two come from simply setting x = 1 ± √3 to 0 to get the factors.