Suppose that the function fis defined, for all real numbers, as follows.
-2 if x #2
4 if x = 2
Find f(-1), f(2), and f(5).
f(-1) =
f(2) =
ƒ (5) =

Answer:

It looke like the point given is (1,2) and the slope is 3

Point slope form: y - 2 = 3(x -1)

Slope Intercept form: y = [tex]\frac{-1}{3}[/tex]x + 1

Step-by-step explanation:

Point slope  As they name implies, you need a point and a slope.  The picture is a little hard to read, but it looks like the point plotted is (1,2)  The slope is the change in y over the change in x.  It looks like from that point to get back on the line only using horizontal and vertical moves, we would move up three and 1 to the right to get back on the line at point (2,5).

The point slope form of a line is:

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])    Plug in 2 for [tex]y_{1}[/tex] and 1 for [tex]x_{1}[/tex] amd 3 for m

y = 2 = 3( (x-1)

Slope intercept form:  As the names implies we need a slope and a yi-intercept.

The slope is [tex]\frac{-1}{3}[/tex].  Select a point on the line.  If you can only move veritacl and horizontal.  You  would move down 1 unit and three units to the right.  The y intercept is where the line crosses the y axis.  In this case 1

y = [tex]\frac{-1}{3} x + 1[/tex]

The present value of an annuity is $736.01

We know that the formula for Present Value of Annuity:

PV = P * [1 - (1 + r)^(-n)]/r

where, PV = present value of an ordinary annuity

P = value of each payment

r = interest rate per period

n = number of periods

From given data:

P = $100, n = 10 and r = 0.06

So, the present value would be,

PV = 100 * [1 - (1 + 0.06)^(-10)]/0.06

PV = 100 * 7.3601

PV = $736.01

Therefore, the present value of an annuity is $736.01

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Answer:

Step-by-step explanation:

1=205

2=63

3=45

4=5

The number of kilometers that Brett and Julian would have run at the 3 / 5 point are:

Brett is running the 5k race at the Memorial Day race which means that when he runs 3 / 5 of the race, he would have ran a total of :
= Distance on Brett's race x Proportion ran

= 5 x 3 / 5

= 15 / 3

= 3 km

Julian on the other hand, is in the 10 k race which means that when they get to 3 / 5 of the race, they would have ran:

= 10 x 3 / 5

= 30 / 5

= 6 km

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The speed of the wave is 2 m/s.

Given,

Time taken by wave to travel back and forth=25 seconds

Length of the pool = 25 meters

As given, the wave travels the length of pool and returns back then,

distance covered by wave is twice the length of pool i.e. [tex]2*25=50[/tex] meters

To find speed of the wave, use formula

[tex]Speed=\frac{Distance covered }{time taken}\\\\Speed=\frac{50}{25} \\\\Speed=2 m/s[/tex]

Thus, the speed of the wave is 2 meter/sec.

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According to the sum of the given supplementary angles, we find out that the value of x is 30.

It is given that ∠A and ∠B are supplementary where,

∠A = (4x + 30)° and,

∠B = (2x - 30)°

We have to find out the value of x.

We know that two supplementary angles add up to 180°.

Since ∠A and ∠B are supplementary angles, therefore

∠A + ∠B = 180°

=> (4x + 30) + (2x - 30) = 180°

=> 6x = 180°

=> x = 30

Thus, for the given supplementary angles, the value of x is 30.

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**According to the sum of the given supplementary angles, we find out that the value of x is 30.

It is given that ∠A and ∠B are supplementary where,

∠A = (4x + 30)° and,

∠B = (2x - 30)°

We have to find out the value of x.

We know that two supplementary angles add up to 180°.

Since ∠A and ∠B are supplementary angles, therefore

∠A + ∠B = 180°

=> (4x + 30) + (2x - 30) = 180°

=> 6x = 180°

=> x = 30 **

1) The scatter plot at the right most likely represents the number of siblings a person has and the person’s GPA.

2) The most reasonable estimate of the gallons of gas in a tank if it has been 3 days since filling up is; 17 gallons

1) Scatter plots are defined as the graphs that present the particular relationship between two variables in a data-set.

A scatter plot is also defined as a chart type that is usually used to observe and visually display the relationship between variables.

From the given scatter plot, we can say that the scatter plot at the right would most likely be used to represent the number of siblings a person has and the person’s GPA.

2) From the given scatter plot, we can see that the x-axis shows the number of days left since filling up while the y-axis represents the gallons of gas.

Now, we want to find out the most reasonable estimate of the gallons of gas in a tank if it has been 3 days since filling up. We will trace 3 on the x-axis and the corresponding value on the y-axis would be approximately 17 gallons.

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Answer:

choose 2nd option

Step-by-step explanation:

The value of the equation (2a^2 +a + 3) divided by (a - 1) is 2a + 3.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, the equation is illustrated as:

(2a² +a - 3) divided by (a - 1). This will be

(2a² +a - 3) / (a - 1)

It should be noted that (2a² +a + 3) will be:

(2a² +a + 3)

= 2a² - 2a + 3a - 3

= 2a(a - 1) + 3(a - 1)

= (2a + 3)(a - 1)

This will be:

= (2a + 3)(a - 1) / (a - 1)

= 2a + 3

The value is 2a + 3.

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Complete question

(2a^2 +a - 3) divided by (a - 1)

The width of the original rectangular slate is 14 inches.

A rectangle is an object that has four sides. The opposite sides are of equal length. A rectangle has two diagonals that are of equal length that bisect each other at right angles.

The area of a rectangle = length x width

Area of the new rectangular slate = (16 - 2) x (w - 2) = (16 x w) - 56

Area of the new rectangular slate = 14 x (w - 2) = 16w - 56

Area of the new rectangular slate = 14w - 28 = 16w - 56

In order to determine the value of w, take the following steps:

Combine similar terms together: 56 - 28 = 16w - 14w

Add similar terms together: 28 = 2w

Divide both sides of the equation by 2 : w = 28 / 2

w = 14

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Answer:

4/8 and 8/16

Step-by-step explanation:

Multiply 1/2 and 3/4 to find a common fraction between them (4/8) then multiply that fraction by any number greater than 1 to find another fraction equivalent

The customer will rent 4 bikes per dollar

Keller's bike deal with renting of bikes

At the Keller's bike rentals it costs $16 to rent a bike for 4 hours

Therefore the number of bikes per dollar can be calculated as follows

16= 4

x= 1

Cross multiply

4x= 16

x= 16/4

x= 4

Hence it costs a customer 1 dollar to get 4 bikes

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The equation that represents the cost, y, and the number of bagels, x is D. y=1.25x

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It should be noted that 1 dozen = 12

The equation the represents the information will be:

y = (15/12) × x

y = 1.25 × x

y = 1.25x

where x = number of bagels

The equation is y = 1.2x.

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The other points (7.3, 2.2) are on a line that includes points (-5, 4) and (4, 1).

What is the equation of a line?

The equation of a line is written as axe + by + c = 0, which is its conventional form. In this equation, the variables x and y are the constant term, while the coefficients a and b are the coefficients. It is a first-order equation with the variables x and y.

Slope using the formula:

[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

We have two points, (-5, 4) and (4, 1).

m = (1 - 4) ÷ (4 - (-5))

m = −1/3

m = -0.3

Line Equations with Slope : y - y1 = m(x - x1)

Using the coordinates of one of the points on the line, insert the values in the x1 and y1 spots to get an equation of a line in point-slope form.

Let's use a point from the original example above  (4, 1). and the slope we calculated as -0.3. Put those values in the point-slope format to get an equation of that line in the point-slope form:

y - 1 = -0.3(x - 4)

y = -0.3x + 2.2

Using the equation y = -0.3x + 2.2, set x=0 to find the y-intercept.

y = -0.3(0) + 2.2

y = 2.2

The y-intercept is 2.2

Using the equation y = -0.3x + 2.2, set y=0 to find the x-intercept.

0 = 3x - 6

0 = -0.3x + 2.2

0.3x  = 2.2

x = 7.3

The x-intercept is 7.3.

Hence, the other points (7.3, 2.2) are on a line that includes the points (-5, 4) and (4, 1).

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Answer:

Avi

$21.61

Step-by-step explanation:

I = Prt

Sari: I = Prt = $1230 × 0.045 × 4 = $221.40

Avi: I = Prt = $1105 × 0.055 × 4 = $243.01

$243.01 - $221.40 = $21.61

Answer:

Avi

$21.61

Answer:

Step-by-step explanation:

You have segment RT of length 77 with point S on it dividing it into segments RS=6y+3 and ST=5y+8. You want to know the value of y and the lengths of segments RS and ST.

The segment sum theorem tells you the whole is the sum of the parts:

  RS +ST = RT

  (6y +3) +(5y +8) = 77 . . . . . use given values

  11y +11 = 77 . . . . . . . . . . . . collect terms

  y +1 = 7 . . . . . . . . . . . . . . . divide by 11

  y = 6 . . . . . . . . . . . . . . . . . subtract 1

The lengths of the parts are ...

  RS = 6y +3 = 6(6) +3 = 39

  ST = 5y +8 = 5(6) +8 = 38

The value of m is equal to 7√5 using the Pythagoras' theorem.

What is are Right Angled Triangle?

According to the definition of a right triangle, if one of the triangle's angles is a right angle (90°), the triangle is referred to as a right-angled triangle or just a right triangle. Triangle ABC is a right triangle in the example image, and its components are the base, altitude, and hypotenuse. Here, the base is represented by AB, the altitude by AC, and the hypotenuse by BC. The largest side and side opposite to the right angle of a right triangle, the hypotenuse, is the side that needs to be considered.

The sum of any two sides of a triangle's three sides is always more than the sum of its third side, making it a regular polygon. A triangle only possesses this quality.

In the figure

From Pythagoras' theorem, we have, h² = p²+b²

Now we can write 3 equations from the figure i.e

m²=7²+n²

m²=35²-x²

x²=n²+28²

So we have m²=35²-n²-28²

⇒m²=35²-28²-m²+7²

⇒2m²=35²-28²+7²

⇒2m²= 490

⇒m²= 490/2

⇒m= 7√5

Hence, the value of m in the figure is 7√5

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The equation if a=4 represents the number of people who can go to the park is 8.75 + 26.50a = C.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

a formula that expresses the connection between two expressions on each side of a sign.

Typically, it has a single variable and an equal sign.

Like this: 2x - 4 = 2.

In the above example, the variable x exists.

So, the equation represents the number of people who can go to the park:

The total budget is $114.75.

Parking costs $8.75.

The cost of a ticket per person is $26.50.

So form the equation:

Let, a be the number of people and C be the total cost.

8.75 + 26.50a = C

Now, let a be 4.

8.75 + 26.50a = C

8.75 + 26.50(4) = C

8.75 + 106 = C

114.75 = C

Therefore, the equation if a=4 represents the number of people who can go to the park is 8.75 + 26.50a = C.

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The measure of angle CDE ( ∠CDE) is 55°. The correct option is the first option  55°

From the question, we are to determine the measure of angle CDE.

From one of the circle theorems, we have that

"The measure of the angle formed by two tangents that intersect at a point outside a circle is equal to one-half the positive difference of the measures of the intercepted arcs"

Thus,

m ∠CDE = 1/2(measure of arc CBE - measure of arc CE)

From the given information,

Measure of arc CE = 125°

Then,

Measure of arc CBE = 360° - 125°

Measure of arc CBE = 235°

Therefore,

m ∠CDE = 1/2(235° - 125°)

m ∠CDE = 1/2(110°)

m ∠CDE = 55°

Hence, the measure of ∠CDE is 55°

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Answer:

Guys this answer is wrong

Step-by-step explanation:
when you are coming from the center point of the circle it mirrors the arc wich is 125 degrees
But when we are trying to figure out the angle which is CDE its always half of the arc of the circle
So you would do 125/2
wich gives you 62.5
therefore your answer is 62.5
No hate to the other guy but plsssss make sure you read the question before answering

The probability that at least one envelope is red envelope is 2/7.

Given:

A collection of envelopes consisting of two red envelopes three blue envelopes one green envelope and one yellow envelope if two envelopes are selected at random with replacement.

Total = 2 + 3 + 1 + 1

= 5 + 2

= 7

Number of possible outcomes = 7

Number of favorable outcomes = 2

Probability that at least one envelope is red envelope is = 2/7

= 0.2857

Therefore the probability that at least one envelope is red envelope is 2/7.

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Answer: 1- 26%

Step-by-step explanation:

just divide 100 by 100 and remove the % sign :)

The component form of the vector that translates C to D is <7, -3>

A translation is a movement in a straight line.

In order to determine the component form of the vector that translates C to D, we have to subtract the coordinate values of point C from the coordinate values of the image C:  

(x, y) = D - C  

The movement from C to D on the x-axis is 7 units to the right (positive 7) while movement on the y-axis is 3 units down (negative -3). Thus:

(x, y)  = (7, -3)

In vector form, <x, y> = <7, -3>

Therefore, the vector that translates C to D is <7, -3>

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Answer:

I think 72,000 because since the weightlifter is lifting 72 and it is kg. It is turned into grams. multiplied by 1000 so 72000

Using the given information, the length of LM is and the length of LN is 12

From the question, we are to determine the length of LM and LN.

From the given information,

M is the midpoint of LN

Therefore,

LM = MN

Also,

From the given information,

LM = 3x

MN = 2x + 2

Thus,

3x = 2x + 2

Solving for x

3x = 2x + 2

3x - 2x = 2

x = 2

Then,

Substitute the value of x in the equation

LM = 3x

LM = 3(2)

LM = 6

Also,

LN = LM + MN

LN = 3x + 2x + 2

LN = 5x + 2

Substitute the value of x

LN = 5(2) + 2

LN = 10 + 2

LN = 12

Hence, the value of LM is 6 and the value of LN is 12

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A graph of the given set of functions has been plotted and shown in the image attached below.

In Mathematics, a function simply refers to a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable to an output variable.

In Mathematics, a graph is a type of chart that is typically used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).

By critically observing the graph of this set of functions (see attachment), we can reasonably infer and logically deduce that they both represent parallel lines, with function f(x) being transformed to produce function h(x).

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The estimates for the number of transistors per IC, using an exponential function, are given as follows:

The format of an exponential function is presented as follows:

[tex]y = ab^\frac{x}{n}[/tex]

In which the parameters of the function are listed as follows:

Moore's Law states that the number of transistors per IC doubles every two years, hence the values of parameters b and n both have values of two, hence:

b = 2, n = 2.

The number of transistors per IC in the reference year of 1972 was of 4000, hence the initial value is of:

a = 4000.

Then the exponential function is:

[tex]y = 4000(2)^{\frac{x}{2}}[/tex]

2012 is 2012 - 1972 = 40 years after 1972, hence the estimate is given as follows:

[tex]y = 4000(2)^{\frac{40}{2}} = 4,194,304,000[/tex]

2040 is 68 years after 1972, hence hence the estimate is given as follows:

[tex]y = 4000(2)^{\frac{68}{2}} = 6.87 \times 10^{13}[/tex]

The chart is given by the image at the end of the answer.

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