Choose the answer to complete each statement.

The slope of the line is ___.

The y-intercept is at ___.

The graph represents the function ___.

The unit rate for inches per mile is 0.8 inches.

The length of road B is 9.6 inches on map.

Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc.

Road in inches = 1 1/5 = 6/5 inches

Road in miles = 1 1/2 miles =

Inches per mile = 6/5 / (3/2)

                         = 6/5 x 2/3

                         = 4/5

                         = 0.8 inches

If the road B is 12 miles long, on the map it would be;

= 0.8 x 12

= 9.6 inches

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The x-intercept is (-3,0) and the y-intercept is (0,9).

The x-intercept of a quadratic function is the point where the function intersects with the x-axis. This point represents the value of x for which the function is equal to 0. The x-intercept can be found by setting the function equal to 0 and solving for x.

The y-intercept of a quadratic function is the point where the function intersects with the y-axis. This point represents the value of y for which the function is equal to 0. The y-intercept can be found by setting x equal to 0 and solving for y.

1. The x-intercept of the function is (-3,0) and it represents the point where the function intersects with the x-axis.
2. The y-intercept of the function is (0,9) and it represents the point where the function intersects with the y-axis.

To find the x-intercept, set the function equal to 0 and solve for x:

0 = x^2 + 6x + 9

0 = (x+3)(x+3)

x = -3

To find the y-intercept, set x equal to 0 and solve for y:

y = 0^2 + 6(0) + 9

y = 9

Therefore, the x-intercept is (-3,0) and the y-intercept is (0,9).

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C= (1.17,9.93,−32.25

D= (3.33,14.9,−47).

For Exercise 5, the coordinates of the segment PQ are P = (2,3,1) and Q = (0,5,7). To calculate the distance from the midpoint to the origin, use the midpoint formula:  M = [(P + Q) / 2].

In this case, M = [(2,3,1) + (0,5,7)] / 2 = (1,4,4).

Then calculate the distance from the midpoint to the origin by using the distance formula:  d = √[(x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2], where (x1, y1, z1) is the midpoint coordinates and (x2, y2, z2) is the origin coordinates. In this case, d = √[(1-0)2 + (4-0)2 + (4-0)2] = √17.

For Exercise 6, the coordinates of the segment PQ are P = (1,0,3) and Q = (3,2,5). To calculate the distance from the midpoint to the origin, use the midpoint formula:  M = [(P + Q) / 2]. In this case, M = [(1,0,3) + (3,2,5)] / 2 = (2,1,4). Then calculate the distance from the midpoint to the origin by using the distance formula:  d = √[(x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2], where (x1, y1, z1) is the midpoint coordinates and (x2, y2, z2) is the origin coordinates. In this case, d = √[(2-0)2 + (1-0)2 + (4-0)2] = √21.

For Exercise 7, let A = (−1,0,−3) and E = (3,6,3). To find points B, C, and D on the line segment AE such that d(A,B)=d(B,C)=d(C,D)=d(D,E)= 41d(A,E), first calculate the distance between A and E using the distance formula: d(A,E) = √[(x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2], where (x1, y1, z1) is the coordinates of A and (x2, y2, z2) is the coordinates of E. In this case, d(A,E) = √[(3-(-1))2 + (6-0)2 + (3-(-3))2] = √122.

To find the coordinates of points B, C, and D, use the following formula: B = A + (d(A,B)/d(A,E))(E-A), where d(A,B) is the distance from A to B, d(A,E) is the distance from A to E, A is the coordinates of A, and E-A is the vector pointing from A to E. Using this formula, the coordinates of B can be calculated as B = (−1,0,−3) + (41/122)((3,6,3) - (−1,0,−3)) = (−1,4.97,−17.5). Similarly, the coordinates of C and D can be calculated as C = (−1,4.97,−17.5) + (41/122)((3,6,3) - (−1,4.97,−17.5)) = (1.17,9.93,−32.25) and D = (1.17,9.93,−32.25) + (41/122)((3,6,3) - (1.17,9.93,−32.25)) = (3.33,14.9,−47).

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The restriction on the variablex is that it must be greater than or equal to 1/3. If x is less than 1/3, the expression √6x-2 will not be a real number.

The restrictions on the variablex in the expression √6x-2 are determined by the fact that the square root of a negative number is not a real number. Therefore, the expression under the square root must be greater than or equal to zero. This gives us the following inequality:

6x-2 ≥ 0

Solving for x, we get:

6x ≥ 2

x ≥ 2/6

x ≥ 1/3

So the restriction on the variablex is that it must be greater than or equal to 1/3. If x is less than 1/3, the expression √6x-2 will not be a real number.

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To find f(x)-g(x), we need to subtract the two given functions.

f(x) = x^(2)-6x-40

g(x) = x+4

f(x)-g(x) = (x^(2)-6x-40) - (x+4)

Next, we need to distribute the negative sign to the terms inside the parentheses:

f(x)-g(x) = x^(2)-6x-40 - x - 4

Then, we can combine like terms: f(x)-g(x) = x^(2)-7x-44

Therefore, the result of f(x)-g(x) is a polynomial in simplest form: x^(2)-7x-44.

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AB =

BC = 2x

T.P. =>

4x² = x² + 6²

3x² = 36

x² = 12

=> x = 2sqrt3

Answer:

12

Step-by-step explanation:

g(-4)=2(-4)^2+4(-4)-8

g(-4)=8

f(8)=2(8)-4

f(8)=12

The required gradient and  y-intercept for the given lines is given by ,

1. gradient = 10 and y-intercept = 20

2.  gradient = -20 and y-intercept = 10

3.  gradient = 0.5 and y-intercept = 2.5

Equation of a line in slope-intercept form = y = mx + c.

where 'm' is the slope of the line

And 'c' is the y-intercept.

For the line Y = 10x + 20

Compare with standard form we get,

Slope of the line is 10 .

And the y-intercept is 20.

This implies,

gradient is 10 and the y-intercept is (0, 20).

For the line  Y=10-20x

Compare with standard form we get,

Slope of the line is -20

And the y-intercept is 10.

This implies,

the gradient = -20

And the y-intercept = (0, 10).

For the line  Y=-2. 5+0. 5x

Compare with standard form we get,

Slope of the line is 0.5

And the y-intercept is -2.5

This implies,

the gradient = 0.5

And the y-intercept = (0, -2.5)

Therefore, the gradient and the y-intercept for each line is equal to,

Y=10x+20 , gradient = 10 and y-intercept = 20

Y=10 -20x  , gradient = -20 and y-intercept = 10

Y=-2. 5+0. 5x , gradient = 0.5 and y-intercept = 2.5

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The result obtained from the long division of the polynomial is n² + 2n - 1 + 3/(n - 9).

The quotient of the polynomial is obtained by applying long division method as shown below.

        n²   +   2n   -   1

   ________________________

n - 9 √ (n³ - 11n² + 21n - 24)

            (n³ -  9n²)  

       ____________

               -2n² + 21n

               -2n² + 18n

               __________

                       3n - 24

                       3n - 27

                       ______

                            3

Therefore, the quotient is n² + 2n - 1 and the remainder is 3.

n³ - 11n² + 21n - 24 =  (n - 9)(n² + 2n - 1) + 3.

So when we divide the polynomial using long division method we would obtain the following result.

(n³ - 11n² + 21n - 24) ÷ (n - 9) = n² + 2n - 1 + 3/(n - 9)

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Find the quotient of this long division; (n³ - 11n² +21n-24)÷(n-9)

1.3567% is the average percent change in population in California from 2000-2009.

The term "population" is frequently used to describe the total number of people living in a particular location. To estimate the number of the residents within a certain territory, governments conduct censuses.

Population is referred to a group of people who share some established characteristics, such as region, race, culture, nationality, or religion, in sociology or population geography. The social science of demography involves the statistical analysis of populations.

average percent change in population =1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93/9

= 1.3567%

Therefore, 1.3567% is the average percent change in population in California from 2000-2009.

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The lines are parallel , based on their. So the C option  is correct.

What is slope formula?

The formula to find the slope between 2 coordinates of a line is given by;

m = (y₂ - y₁)/(x₂ - x₁)

Line f has a slope of -2 and line g has a slope of -8/4. To determine the relationship between the lines based on their slopes, we can compare their slopes.

If two lines have the same slope, they are parallel. If two lines have slopes that are negative reciprocals of each other, they are perpendicular (and intersect to form right angles). Otherwise, the lines are neither parallel nor perpendicular and will intersect at some point.

The slope of line g can be simplified to -2, which is the same as the slope of line f. Therefore, the lines f and g have the same slope and are parallel (option C).

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By applying synthetic division concept, it can be concluded that if f(v) = 8v⁴ + 34v³ - 26v² + 21v + 11, then, f(-5) = 6.

Synthetic division is a shorthand way of dividing polynomials where we can divide the coefficients of the polynomial by omitting variables and exponents. As a result, we get the coefficient of the quotient and the remainder.

Polynomial remainder theorem states that the value of p in argument b is equal to the remainder of the polynomial division p(x) / (x - b). Specifically, p(x) is divided by x - b with a remainder of zero if, and only if, b is a root of p.

We have the following polynomial:

f(v) = 8v⁴ + 34v³ - 26v² + 21v + 11

To find f(-5) using synthetic division, we will divide the polynomial f(v) by (z + 5). The steps are as follows:

1. Put the coefficients in a row and multiply the outside coefficient by the divisor: 8(-5)= -40.

2. Add the inside coefficient to the product from the previous step: -40 + 34 = -6.

3. Multiply the result from the previous step by the divisor: -6(-5) = 30.

4. Add the next coefficient to the product from the previous step: 30 - 26 = 4.

5. Multiply the result from the previous step by the divisor: 4(-5) = -20.

6. Add the next coefficient to the product from the previous step: -20 + 21 = 1.

7. Multiply the result from the previous step by the divisor: 1(-5) = -5.

8. Add the last coefficient to the product from the previous step: -5 + 11 = 6.

The final result of the synthetic division is 6, so the answer to the question is f(-5) = 6.

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The area of the parallelogram formed by the vectors u and v is 12.

The area of a parallelogram formed by two vectors u and v can be determined by finding the cross product of the two vectors and then taking the magnitude of the resulting vector.

First, we need to find the cross product of u and v:

u × v = [(2)(0) - (2)(4), (2)(4) - (1)(0), (1)(4) - (2)(4)] = [-8, 8, -4]

Next, we need to find the magnitude of the resulting vector:

|u × v| = √((-8)² + (8)² + (-4)²) = √(64 + 64 + 16) = √144 = 12

Therefore, the area of the parallelogram formed by the vectors u and v is 12.

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The given polynomial is P(x) = x^3 + 5x^2 - 6x + 6. The given c is 3. To use the Remainder Theorem, we must divide P(x) by (x - c). The result of this division will be a quotient and a remainder. The remainder is the value of the polynomial when x = c, so in this case when x = 3, the remainder is 45.

This is because when x = 3, P(x) = 45. Therefore, according to the Remainder Theorem, the remainder when we divide P(x) by (x - 3) is 45. This means that when we divide P(x) by (x - 3), the remainder is 45. Thus, the Remainder Theorem can be used to determine the remainder when we divide a polynomial P(x) by (x - c), where c is some given constant.

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The solution set for the absolute value equation |2x-4|=20 is {-14, 14}.

An absolute value equation is one that contains an absolute value expression, such as ||x| - 1| = 2.

These types of equations are solved by breaking them down into two separate equations and solving each one separately:

one with the original absolute value expression and a positive value for the other side, and the other with the negated absolute value expression and a negative value for the other side.

The steps to solving an absolute value equation are as follows:

1. Write the equation in the form |expression| = value, where expression is the absolute value expression and value is the constant on the right-hand side.

2. Separate the equation into two equations: expression = value and expression = -value.

3. Solve each equation for the variable.

4. Check the solution(s) to ensure that they satisfy the original equation.

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Answer:

8.50667 or approximately 8.51 feet per second

Step-by-step explanation:

The most approximate way to get the feet per second is to multiply the miles per hour by 1.467.

Answer:

Step-by-step explanation:

For any cube the total edge length is equal to 12n, with n being the length of an edge side. Knowing this:

Cube A - Total edge length = 12(3) or 36

Cube B - 12(5) or 60

Cube C - 12(9.5) or 114

If any cube has edge length s, the total edge length is 12s

Hope this helps!

Answer:

x=63

Step-by-step explanation:

------------------

The answer: no real solutions to this equation

To solve the equation, we need to find a common denominator for all of the fractions on the left side of the equation. The common denominator will be (y-2)(y-3), so we will multiply each fraction by the appropriate factor to get the common denominator.

[tex]y/y -2y+ 4/y-3 = 4/ y2-5y+6[/tex]

[tex]y(y-3)/(y-2)(y-3) - 2y(y-2)/(y-2)(y-3) + 4(y-2)/(y-2)(y-3) = 4/(y-2)(y-3)[/tex]

Now we can combine the fractions on the left side of the equation:

[tex](y2-3y-2y2+4y+4y-8)/(y-2)(y-3) = 4/(y-2)(y-3)[/tex]

Simplifying the numerator on the left side gives us:

[tex](-y2+5y-8)/(y-2)(y-3) = 4/(y-2)(y-3)[/tex]

Now we can cross-multiply and simplify:

[tex](-y2+5y-8) = 4[/tex]

[tex]-y2+5y-12 = 0[/tex]

To solve this equation, we can use the quadratic formula:

[tex]y=\left(-5\pm \sqrt{52-4\left(-1\right)\left(-12\right)}\right)[/tex]

[tex]y=\left(-5\pm \sqrt{25-48}\right)[/tex]

[tex]y=\left(-5\pm \sqrt{-23}\right)[/tex]

Since the square root of a negative number is not a real number, there are no real solutions to this equation. Therefore, the answer is no solution.

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Answer: Im pretty sure its B

Step-by-step explanation:

It will take Mrs. Reed 3 hours to catch up to Mr. Reed.

First we can start by figuring out how far Mr. Reed will have traveled when Mrs. Reed starts her journey.

Distance traveled by Mr. Reed in 3 hours at a speed of 40 mph:

When Mrs. Reed starts her journey, Mr. Reed is 120 miles ahead of her.

Now, let's determine how long it will take Mrs. Reed to catch up to Mr. Reed.

We can use the formula:

time = distance / relative speed

Where "distance" is the distance Mrs. Reed needs to travel to catch up to Mr. Reed, and "relative speed" is the speed at which Mrs. Reed is gaining on Mr. Reed, which is the difference between their speeds:

relative speed = 80 mph - 40 mph

relative speed = 40 mph

So, the time it will take for Mrs. Reed to catch up to Mr. Reed can be calculated as:

Therefore, it will take Mrs. Reed 3 hours to catch up to Mr. Reed.

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The response to the given question would be that Hence, 2 is the proportionality constant between y and x.

Partnerships that have the same ratio across time are said to be proportional. For instance, how many trees there are in an orchard and how many apples there are in a harvest of apples are determined by the average number of apples per tree. Proportional in mathematics refers to a linear connection between two numbers or variables. As the first quantity doubles, so does the other. When one of the variables drops to 1/100th of its previous value, the other also decreases. When two quantities are proportional, it means that as one rises, the other rises as well, and the ratio between the two quantities stays the same at all levels. As an example, consider the diameter and circumference of a circle.  

We must calculate the ratio of the change in y to the change in x in order to discover the constant of proportionality between two variables, x and y. The slope of the line that depicts the connection between x and y is another name for this.

The slope of the line, which is the change in y divided by the change in x, is therefore equal to the constant of proportionality between y and x. As we can see from the graph, y grows by 2 units for every unit rise in x. Hence, the line's slope is 2/1, or only 2.

Hence, 2 is the proportionality constant between y and x.

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The formula for the exponential function passing through the points (-2,768) and (2, 3) is:

[tex]y = 48 \times ((3/768)^{1/4})^x[/tex]

We have,

To find a formula for the exponential function passing through the points (-2, 768) and (2, 3), we can use the general form of an exponential function: y = a x [tex]b^x[/tex], where "a" is the initial value or y-intercept, and "b" is the base of the exponential function.

Let's start with the first point (-2, 768).

Plugging in the values, we have:

768 = a x [tex]b^{-2}[/tex]

Next, let's consider the second point (2, 3).

Plugging in the values, we have:

3 = a x b²

Now we have a system of equations:

768 = a x [tex]b^{-2}[/tex]

3 = a x b²

To solve this system, we can divide the second equation by the first equation:

3/768 = (a x b²) / (a x [tex]b^{-2}[/tex])

Simplifying further:

3/768 = [tex]b^4[/tex]

Taking the fourth root of both sides:

[tex](b^4)^{1/4} = (3/768)^{1/4}\\b = (3/768)^{1/4}[/tex]

Now we can substitute the value of b back into either of the original equations to solve for a.

Let's use the first equation:

[tex]768 = a \times b^{-2}[/tex]

Substituting [tex]b = (3/768)^{1/4}:[/tex]

[tex]768 = a \times ((3/768)^{1/4})^{-2}[/tex]

Simplifying:

[tex]768 = a \times (3/768)^{-1/2}[/tex]

Now, we can simplify the right-hand side:

[tex]768 = a \tmes (768/3)^{1/2}[/tex]

Simplifying further:

[tex]768 = a \times (256)^{1/2}[/tex]

Taking the square root of 256:

768 = a x 16

Solving for a:

a = 768 / 16 = 48

Therefore,

The formula for the exponential function passing through the points (-2,768) and (2, 3) is:

[tex]y = 48 \times ((3/768)^{1/4})^x[/tex]

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Step-by-step explanation:

1) geometric

2) arithmetic

3) neither

4) geometric

5) neither

6) arithmetic

you can this by usin their formulas or

you see if it has common difference which is for arithmetic sequence or you find the common ratio which is geometric sequence.

Answer: LCM is 72. GCF is 6.

Answer:

jimmy has 12 candy bars left

Step-by-step explanation:

28-7-9=12

Answer:

Jimmy has 12 candy bars.

Step-by-step explanation:

Subtract 28 from 7.
=21

21-9=12.
Jimmy has 12 candy bars left if he eats 7 and his mom takes 9.

The linear equation y = 3x - 7 has a data that is correlated because it has a linear relationship and we cannot determine if there's a causation between x and y

A. y causes a. is not applicable in this case, as there is no variable named "a" in the equation.

B. The equation y = 3x - 7 represents a linear relationship between two variables, x and y. As the equation has a slope of 3, it indicates that as the value of x increases by 1, the value of y increases by 3. Therefore, the data are correlated positively.

C. This is incorrect. As mentioned in B, the equation represents a linear relationship between two variables, x and y, which are positively correlated.

D. This is correct. Although the equation represents a linear relationship between x and y, it does not imply causation. It is possible that x causes y, y causes x, or some other variable or variables may be influencing both x and y. Therefore, we cannot determine if there is causation between x and y based on the equation y = 3x - 7 alone

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The quadratic formula multiplied by π divided by x is: π(-b ± √(b² - 4ac)) / (2ax).

The quadratic formula is used to solve quadratic equations, and is given by: x = (-b ± √(b² - 4ac)) / 2a.

Pi otherwise denoted by the symbol π in real terms is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14159, although its decimal representation goes on infinitely without repeating.

Since the rational objective of every mathematical expression or problem is to simplify, we  will leave Pi in it's symbolic form - π.

Thus, multiplying quadratic formula by π and dividing by x, we get:

π(-b ± √(b² - 4ac)) / (2ax)

Therefore, the quadratic formula multiplied by π divided by x is:

π(-b ± √(b² - 4ac)) / (2ax).


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Answer:  π(-b ± √(b² - 4ac)) / (2ax)

Step-by-step explanation:

take the standard quadratic formula and plug in pi and x and you get you answer hope this helps