Find the equation for the linear function that passes through the points (−5,−4) and (5,2). Answers must use whole numbers and/or fractions, not decimals.

Use the line tool below to plot the two points.


State the slope between the points as a reduced fraction.

State the y-intercept of the linear function.

State the linear function

Answer:

[tex](6,17)[/tex]

Step-by-step explanation:

we know that

In this problem

The gate hinges must be placed at the mid-point of the fence.

The formula to calculate the midpoint between two points is

[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

we have

[tex]A(4,12),B(8,22)[/tex]

substitute the values in the formula

[tex]M(\frac{4+8}{2},\frac{12+22}{2})[/tex]

[tex]M(6,17)[/tex]

Answer: (6,17)

Step-by-step explanation: Plato and Edmentum

Answer:

C)

Step-by-step explanation:

To find area, You use the equation (Length × Width). If you need to find the perimeter By using the Area, You need to Divide one of the Equal Sides, since it is a square you can use either length or width, So Since it is a square, You Can also use the Square Root method. Square root is basically Dividing the number by the number it was multiplied by.

EX:

9 × 9 = 81

because

81 ÷ 9 = 9

So, If both the Length and width are 9, You add them together to get eighteen. Though since it's a square, You Can't only Count The Half of the Shape, So you multiply that by two, Leaving you with 36

Answer: C) 36 ft

To solve this equation, we need to fin out how long each side is. To do this, find the square root of 81, since it is a perfect square.

[tex]\sqrt{81 ft} = 9 ft[/tex]

So now we know that each side is 9 feet, we need to find the perimeter of the square using these dimensions.

9 ft · 4 sides = 36 ft of fencing

Therefore, Ariel needs 36 ft of fencing for her garden.

Answer:

D. y> 1

The shaded area on the graph is y>1 but since the line is solid it is also equal to 1.

Answer:

y ≥ 1

Step-by-step explanation:

The given line is a horizontal line.

The equation of a horizontal line is y = a, where "a" is a constant.

Here the horizontal drawn at y = 1.

Therefore, the equation of line is y = 1

The solution is shaded above the line, therefore, it is y > 1

The line is a solid, therefore, the inequality that represents the solution is y ≥ 1

Answer: D) y ≥ 1

Answer:

6

Step-by-step explanation:

I took the same test

Answer:

he would have 10 roses left

Step-by-step explanation:

12-5=7-2=5

5+9=14-4=10

Answer:

-[tex]\sqrt{5}[/tex]

Step-by-step explanation:

A root with square root or under root is only obtained when we take the square root of both sides. Remember that when we take a square root, there are two possible answers:

For example, for the equation:

[tex]x^{2}=3[/tex]

If we take the square root of both sides, the answers will be:

[tex]x=\sqrt{3} \text{ or } x= -\sqrt{3}[/tex]

Only getting one solution with square root is not possible. Solutions with square root always occur in pairs.

For given case, the roots are 6 and [tex]\sqrt{5}[/tex]. Therefore, the 3rd root of the polynomial function f(x) had to be -[tex]\sqrt{5}[/tex]

It seems you made error while writing option B, it should be - square root of 5.

Answer:

B

Step-by-step explanation:

Answer:

Inverse of a function

Step-by-step explanation:

If the x- and y-values in each pair of a set of ordered pairs are interchanged, the resulting set of ordered pairs is known as the inverse of a function.

For example, given the following function:

y = 2x

If x=0 → y= 0

If x=1 → y= 2

If x=2 → y= 4

Now, if we find the inverse of the function:  

y = 2x → x = 2y → y = x/2

Now:

If x=0 → y= 0

If x=2 → y= 1

If x=4 → y= 2

Comparing both cases, you will notice that the ordered pairs are effectively interchanged.

The resulting set of ordered pairs formed by interchanging the x- and y-values in each pair is known as the inverse of the original set.

If the x- and y-values in each pair of a set of ordered pairs are interchanged, the resulting set of ordered pairs is known as the inverse of the original set. In mathematics, an ordered pair is a pair of objects written in a specific order, typically as (x,y). If you switch the positions of the elements to form (y,x), you create an ordered pair that represents the inverse relationship. This is particularly relevant in the context of functions and relations on a Cartesian coordinate system. The concept of ordered pairs is fundamental to understanding mappings and the domain and range of relations.

For example, if you have an ordered pair representing a function, such as (3,4), its inverse would be (4,3). This reflects a new relationship where the original output is now the input and vice versa. The set of all such inverted pairs from a function forms the inverse function, provided that each y value is associated with only one x value (the function is one-to-one).

A relation where the ordering of elements matters contrasts with a set where the order does not affect the identity of the set. Hence, achieving an inverse relationship by switching the ordered pairs is a useful tool in mathematical problem-solving and analysis.

Answer:

c = 6t + 19.60

Step-by-step explanation:

   Let t = the time in hours for which Beth rented the bike. Then  

       6t = the rental cost for the bike and

$19.60 = the up-front cost

The expression for the total cost (c) is

c = 6t + 19.60

The expression for the total cost is C = 19.60 + 6t. According to the given statements, time t is the variable term.

An expression is the combination of variables, coefficients, and constants. These are separated by operators like addition or subtraction. Each combination is called a term.

Given that,

Beth rented a bike from Julia's Bikes.

It cost $19.60 plus $6 per hour.

So, here the variable is time because as the time increases the cost also increases.

Consider time = t and the total cost = C

Then, the expression that represents the given statements is

C = 19.60 + 6t

∴ The expression is C = 19.60 + 6t.

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Answer:

The correct answer is A. Aimee's graph is correct because the ratio [tex]\frac{2}{3} :1[/tex] is equal to 2:3, which her graph shows in each point.

Step-by-step explanation:

We are given that Aimee noticed her plant grew 2/3 of an inch every week since it sprouted and a graph is drawn to show the plant growth.

We are to determine whether which of the given statements is correct.

The ratio [tex]\frac{2}{3} :1[/tex] is basically equal to 2:3. Therefore, the graph is correct as it shows the same ratio at each point.

For the points (6, 4) and (3, 2) = [tex]\frac{4-2}{6-3} =\frac{2}{3}[/tex]

Answer:

-1.9, -1.8, and -1.7 (answers will vary)

Step-by-step explanation:

Since you have to pick a rational number that is between -2 and -1 there is an infinite options you can choose from. A rational number is a number that can be written as a fraction so you could choose a number like -1.0000000000000000000000001 and 1.999999999999999999999999.

Answer:

Option A 0.496

Step-by-step explanation:

we know that

The approximate average rate of change is equal to

[tex]\frac{f(8)-f(3)}{8-3}[/tex]

[tex]\frac{f(8)-f(3)}{5}[/tex]

we have

[tex]f(x)=0.01(2^{x})[/tex]

Find f(8)

For x=8

[tex]f(8)=0.01(2^{8})=2.56[/tex]

Find f(3)

For x=3

[tex]f(8)=0.01(2^{3})=0.08[/tex]

Find the approximate average rate of change

[tex]\frac{f(8)-f(3)}{5}[/tex]

substitute

[tex]\frac{2.56-0.08}{5}=0.496[/tex]

Answer: A, 0.496

Step-by-step explanation:

To find the difference, you need to raise the base, 2, to each number since x represents the days.

Raise 2 to the power of 3:

2^3 = 8

multiply by 0.01

0.01 * 8 = 0.08

That is the growth of day three.

Now do the same with the 8

Raise 2 to the power of 8

2^8 = 256

Now multiply that by 0.01

0.01 * 256 = 2.56

Now use this formula: f(b) - f(a)/b - a

2.56 - 0.08/8 - 3

Subtract 0.08 from 2.56

2.56 - 0.08 = 2.48

Subtract 3 from 8

8 - 3 = 5

Now divide: 2.48/5 = 0.496

0.496 is the average rate of change between day 3 and day 8. Also I got 100 on the test so I know the answer :))

Are you sure that one of the variables is v and not y?

v+4= -2(x-1)

Since you posted v, I will use v in place of y.

v + 4 = -2x + 2

v = -2x + 2 - 4

v = -2x - 2

Done!

Answer:

The red point (-4 , -6)

Step-by-step explanation:

* Lets revise the complex number

- The complex number z = a + bi, where a is the real part and b is the

  imaginary part

- The real part represented by the x-axis and the imaginary part

  represented by the y-axis

- The value of i is √(-1)

- The complex conjugate of a complex number is the number with an

 equal real part and an imaginary part equal in magnitude but opposite

 in sign

- Ex: the conjugate of a + bi is a - bi

* Lets solve the problem

∵ A is an complex number

∵ The x-coordinate of A is -4 and the y-coordinate of it is 6

∵ The x-axis is the real axis and y-axis is the imaginary axis

∴ A = -4 + 6i

∵ The conjugate numbers are equal in real part and the imaginary

  part equal in magnitude and different in sign

∴ The conjugate of A = -4 - 6i

- From the graph The red point (-4 , -6) represents the complex

 conjugate of point A

Answer:

See below in bold,.

Step-by-step explanation:

There are 30-17 = 13 boys in the class.

a.  Prob(First is a boy ) = 13/30 and Prob( second is a boy = 12/29).

As these 2 events are independent:

Prob( 2 boys being picked) = 13/30 * 12/29 =  26/145 or 0.179 to the nearest thousandth.

b. By a similar method to a:

Prob ( 2 girls being picked) =  17/30 * 16/29 = 136/435 = 0.313 to the nearest thousandth.

c.  Prob (First student is a boy and second is a girl) =  13/30 * 17/29 = 221/870.

Prob ( first student is a girl and second is a boy)  = 17/30 * 13/29 = 221/870

These 2 events are not independent so they are added:

Prob( one of the students is a boy)  = 2 (221/870 =  221/435 = 0.508 to the nearest thousandth.

Answer: Answer should be 882.

Step-by-step explanation:

5% =0.05

840*0.05=42

840+42=882

We will have a total of 882 employees.

The percentage is defined as a ratio expressed as a fraction of 100.

For example, If Misha obtained a score of 67% on her exam, that corresponds to 67 out of 100. It is expressed as 67/100 in fractional form and as 67:100 in ratio form.

Last year at this time we had 840 employees.

Since that time our staff has increased by 5%.

We have to determine the employees will we have in total

The total employees = 840 + 5% of 840

The total employees = 840 + 0.05 × 840

The total employees = 840 + 42

The total employees = 882

Hence, there are 882 employees will we have in total.

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Answer:

40

Step-by-step explanation:

There are 3 red bars

It states we have 24 red notebooks

24/3 = 8

Each bar represents 8 notebooks

We have 5 gold  bars

5*8 = 40

We have 40 gold notebooks

Answer:

40

Step-by-step explanation:

There are 5 gold books for every 3 red books.

You are trying to find the ratio of "x" gold books to 24 red books.

First, divide 24 with 3:

24/3 = 8

The questioner multiply 8 to the ratio's denominator. To solve completely, what you do to the denominator of the fraction, you must do to the numerator. Multiply:

5 x 8 = 40

40 gold notebooks is your answer, making the ratio 40 gold : 24 red.

~

Answer:

[tex]y-5=\frac{-1}{2}(x+2)[/tex] point-slope form

[tex]y=\frac{-1}{2}x+4[/tex]  slope-intercept form

Step-by-step explanation:

The slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

The slopes of perpendicular lines are opposite reciprocals.

The slope of y=2x-5 is 2.

So we are looking for a line perpendicular to y=2x-5 which means we first to the take the opposite reciprocal of it's slope giving us:

opposite reciprocal of (2) is opposite (1/2)=-1/2.

So the slope of the line we are looking for is -1/2.

This means are equation for our line is in this form:

[tex]y=\frac{-1}{2}x+b[/tex]

To find b we will use a point (x,y) that is on our line.

We are given a point (x,y)=(-2,5).

Plug this into our equation:

[tex]5=\frac{-1}{2}(-2)+b[/tex]

[tex]5=1+b[/tex]

Subtract 1 on both sides:

[tex]4=b[/tex]

So the equation for our line that we are looking for is:

[tex]y=\frac{-1}{2}x+4[/tex]  (slope-intercept form).

You could also go for point-slope form [tex]y-y_1=m(x-x_1)[/tex] where m is the slope and [tex](x_1,y_1)[/tex] is a point on the line.

We have m=-1/2 and (x1,y1)=(-2,5) so our equation in point slope-form is:

 [tex]y-5=\frac{-1}{2}(x-(-2))[/tex]

Simplifying just a hair:

[tex]y-5=\frac{-1}{2}(x+2)[/tex].

Answer:

[tex]RS\ 8,748[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

step 1

Find the rate of interest

in this problem we have

[tex]t=8\ years\\ P=RS\ 3,560\\ A=RS\ 4,272\\r=?[/tex]

substitute in the formula above

[tex]4,272=3,560(1+8r)[/tex]

solve for r

[tex]8r=(4,272/3,560)-1[/tex]

[tex]r=[(4,272/3,560)-1]/8[/tex]

[tex]r=0.025[/tex]

convert to percentage

[tex]r=0.025*100=2.5\%[/tex]

step 2

What will be the simple interest on Rs 6480 in 14 years at the same rate of interest?

we have

[tex]t=14\ years\\ P=RS\ 6,480\\ A=?\\r=0.025[/tex]

substitute in the formula above

[tex]A=6,480(1+0.025*14)[/tex]

[tex]A=6,480(1+0.35)[/tex]

[tex]A=RS\ 8,748[/tex]

Answer:

The correct option is D) (5x − 2)(2x − 3).

Step-by-step explanation:

Consider the provided expression.

[tex]10x^2-19x+6[/tex]

Where x is time in minutes.

We need to find the appropriate form of the expression that would reveal the time in minutes when the trough is empty.

When the trough is empty the whole expression becomes equal to 0.

Substitute the whole expression equal to 0 and solve for x that will gives us the required expression.

[tex]10x^2-19x+6=0[/tex]

[tex]10x^2-15x-4x+6=0[/tex]

[tex]5x(2x-3)-2(2x-3)=0[/tex]

[tex](5x-2)(2x-3)=0[/tex]

Now consider the provided option.

By comparison the required expression is D) (5x − 2)(2x − 3).

Hence, the correct option is D) (5x − 2)(2x − 3).

Answer:

The correct answer is D

Step-by-step explanation:

System of equations have infinitely many solution for x and y.

We have to given that,

System of equation are,

3x + 2y = 12

12x + 8y = 48

We can use the elimination method to solve,

System of equation are,

3x + 2y = 12  .. (i)

12x + 8y = 48  .. (ii)

Multiply by 4 in (i) and subtract from (ii);

12x + 8y - 12x - 8y  = 48 - 48

0 = 0

Hence, System of equations have infinitely many solution for x and y.

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Answer:

0, 17

3 1/2, 5

-3 1/2, -12

0, 17

Answer:

17

Step-by-step explanation:

First label the 2 points.

A = (3, 1/2, 5), B = (3, 1/2, -12)

Then calculate the vector from A to B:

[tex]\vect{AB} = (0, 0, -17)[/tex]

And then calculate it's length by the formula:

[tex]||\vect{a}|| = \sqrt{x^2 + y^2 + z^2}[/tex], where x, y, z are the coordinates related to the vector.

[tex]||\vect{AB}|| = \sqrt{0^2 + 0^2 + (-17)^2} = \sqrt{(-17)^2} = |17| = 17[/tex]

The coefficient of x needs to be 2.

The current coefficient is 2/5.

To eliminate the 5 in the denominator, we can multiply the equation by 5.

We get

[tex]2x + 30y = - 50[/tex]

Now, to solve the equations, all we need to do is add them.

Hope this helps!

Answer:

56.4 miles

Step-by-step explanation:

4228/75 = 56.37333333

Answer:

Answer is all real numbers.

<~~~~~~~~~~~~~~~~~~~~~~~~~~~~~>

---------(-3)---------------------(6)-------------

Step-by-step explanation:

6b<36

Divide both sides by 6:

b<6

or

2b+12>6

Subtract 12 on both sides:

2b>-6

Divide both sides by 2:

b>-3

So we want to graph b<6 or b>-3:

               o~~~~~~~~~~~~~~~~~~~~~~~~~~ b>-3

~~~~~~~~~~~~~~~~~~~~~~~~o                        b<6

_______(-3)____________(6)___________

So again "or" is a key word! Or means wherever you see shading for either inequality then that is a solution to the compound inequality.  You see shading everywhere so the answer is all real numbers.

<~~~~~~~~~~~~~~~~~~~~~~~~~~~~~>

---------(-3)---------------------(6)-------------

Answer:

All real numbers [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

First we solve the following inequality

[tex]6b < 36[/tex]

Divide by 6 both sides of the inequality

[tex]b<\frac{36}{6}\\\\b<6[/tex]

The set of solutions is:

[tex](-\infty, 6)[/tex]

Now we solve the following inequality

[tex]2b + 12 > 6[/tex]

Subtract 12 on both sides of the inequality

[tex]2b + 12-12 > 6-12[/tex]

[tex]2b> -6[/tex]

Divide by 2 on both sides of the inequality

[tex]\frac{2}{2}b> -\frac{6}{2}[/tex]

[tex]b> -3[/tex]

The set of solutions is:

[tex](-3, \infty)[/tex]

Finally, the set of solutions for composite inequality is:

[tex](-\infty, 6)[/tex]  ∪ [tex](-3, \infty)[/tex]

This is: All real numbers [tex](-\infty, \infty)[/tex]

Answer:

34.24 cm²

Step-by-step explanation:

You first need to find the area of the circle.

4 is radius. r*r*3.14=50.24

Now the triangle is 4*4=16.

50.24-16= 34.24

Answer:

B.

Step-by-step explanation:

The area of the shaded region will be the area of the circle minus the area of the triangle inside the circle. Then:

The circle has radius 4 cm (distance from the center to the edge of the circle), so the area of the circle is

[tex]A=\pi r^2 = 3.14(4cm)^2 = 3.14(16cm^2) = 50.24 cm^2.[/tex]

Now, the area of the triangle is

[tex]A_2 = \frac{b*h}{2}[/tex].

The base of the triangle is the diameter of the circle (as you can see in the image) and the height is the radius of the circle. Then the are of the triangle is

[tex]A_2 = \frac{8*4}{2} = \frac{32}{2} = 16cm^2[/tex].

Finally, the shaded area is [tex]A-A_2 = 50.24-16 = 34.24 cm^2[/tex].

Answer:

The slope is 14/1, meaning you rise 14, then run 1. This is a steep slope.

Step-by-step explanation:

The slope equation is y=mx+b. The "m" in the equation is equal to the slope. In your case, 14 takes the place of the "m", making it the slope.

The slope of the equation y = 14x + 10 is 14, which means the line has a positive slope, indicating a rise of 14 units in y for each unit increase in x. The y-intercept of the line is 10.

The equation given is y = 14x + 10. To understand the slope of this linear equation, we can refer to the formula y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the number 14 is the coefficient of x, which means the slope of the line is 14. This indicates that for each unit increase in x, the value of y will increase by 14 units. Therefore, the line represented by this equation has a positive slope, which tells us that as x increases, y also increases at a constant rate. The slope is important in many fields, including economics, as it measures the relationship between two variables.

The y-intercept is the point where the line crosses the y-axis, which occurs when x equals 0. In our equation, the y-intercept is 10, indicating that the line crosses the y-axis at the point (0, 10).

Answer:

-7 + a = 37

Step-by-step explanation:

The value of 'a' is 44 and the equation for the statement "The sum of -7 and a is equal to 37" is -7 + a = 37

Let's start by writing the equation for the given statement:

-7 + a = 37

To find the value of 'a', we need to isolate 'a' on one side of the equation. We can do this by performing inverse operations. The inverse of subtracting 7 is adding 7. So, we will add 7 to both sides of the equation:

-7 + a + 7 = 37 + 7

On the left side, the -7 and +7 cancel out, leaving us with:

a = 44

Therefore, the value of 'a' that satisfies the given equation is 44.

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Answer:

A plane figure with 4 sides is called a quadrilateral.

A quadrilateral is a plane figure bounded by four straight lines in mathematics.

Plane figure bounded by four straight lines: In mathematics, a quadrilateral is a plane figure bounded by four straight lines. Examples of quadrilaterals include squares, rectangles, parallelograms, and trapezoids.

Answer:

Step-by-step explanation:

Unit vector is a vector with mangnitue 1 and we can find out the magnitude of the vector [tex]u = (x , y)[/tex] with the following formula

[tex]magnitude = \sqrt{x^{2}+y^{2}}[/tex]

So in the given options whichever vector has magnitude 1 it will be a unit vector.

So if we put the values in the above mentioned formula

1.Magnitude of option A is not 1 so it is not a unit vector

2.Magnitude of option B is  1 so it is a unit vector

3.Magnitude of option C is  1 so it is a unit vector

4.Magnitude of option D is not 1 so it is not a unit vector

A unit vector is of length 1 and is used to represent the positive direction on an axis in a Cartesian system. In mathematics, the i, j, and k unit vectors denote the positive directions on the X, Y, and Z axes, respectively. The magnitudes of all unit vectors are one, and they are crucial in representing directions in space.

In mathematics, a unit vector is a vector of length 1. The unit vectors in a Cartesian system are typically denoted as i, j, and k. Unit vector i signifies the positive direction on the X-axis, while unit vector j represents the positive direction on the Y-axis. In three-dimensional space, unit vector k denotes the positive direction on the Z-axis.

For example, Consider any vector A in a Cartesian coordinate system (figure 2.16). The scalar x-component of vector A is its dot product with the unit vector i, while the scalar y-component of that vector is its dot product with the unit vector j. This approach effectively expresses A in terms of the unit vectors of the axes. By their very definition, these unit vectors are dimensionless, such as their direction allows precise representations of vectors in space.

In summary, unit vectors essentially establish the directions for the system of coordinates in question. These vectors assist in expressing the direction of physical entities, such as the projection of vector A onto the x-axis or the y-axis. The magnitudes of these unit vectors are always one, so their principal significance comes from the directions they represent.

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