a) Find the function algebraically. Show yourwork!b) Where is the asymptote on the graph of thisfunction? Give as an equation.c) What is the domain and range of thisfunction?Domain:Range:

Answer:x=32°

y=35°

Step-by-step explanation:

23°+32°+y=90°

55°+y=90°

y=35°

35°+23°+x=90°

58°+x=90°

x=32°

Answer:

Angle AOE = angle FOB = 32° (vertically opposite angles)

x = 32°

Since GH is a straight line, angle COH = angle COG = 90°

Angle BOD = angle COA = y° (vertically opposite angles)

y = 90-32-23 = 35°

Answer:

it is often known as the unequal variance t test. It assumes that both groups of data are drawn from Gaussian populations, but does not assume that their standard deviations are the same.

Answer: B and D.

Step-by-step explanation:

1) Find 40% as a decimal

100% = 1

40% = 0.4

2) It's -40% of its total value. So minus its value time 40%.

p - 0.4p

3) Simplify

0.6p

A) 0.4p not equal 0.6p X

B) 0.6p = 0.6p

C) p - 0.4 not equal 0.6p X

D) p-0.4p = 0.6p

Answer:

2(x-2)

Step-by-step explanation: distribute, add the numbers, common factor

We will have that some of the principles that geometry works with, that are present in the image are:

Length, Area, Volume, Surfaces, Angles & Curves.

All solutions to the cubic equation, 4•x³ + 16•x² + 28•x = 0, are presented as follows;

0, -2 + i•√(3), -2 - i•√(3), which is the option;

The solutions of a cubic function are given by the values at which the graph intersects the horizontal axis.

First Part

The graph showing the shaded region of the inequality is left out

Second part;

The given equation can be presented as follows;

4•x³ + 16•x² + 28•x = 0

Required;

To find all the solutions of the equation

Solution;

The solutions of the equation are given by the locations on the graph where the equation intersects the x–axis, which are therefore, the points where the function is equal to 0

The equation 4•x³ + 16•x² + 28•x = 0 can therefore be used to find the solution as follows;

4•x³ + 16•x² + 28•x = 0

x•(4•x² + 16•x + 28) = 0

x•(4)•(x² + 4•x + 7) = 0

x•(x² + 4•x + 7) = 0 ÷ (4) = 0

x•(x² + 4•x + 7) = 0

Which by the multiplicative identity of 0, gives;

Therefore;

x = 0 is a solution to the equation

The other solutions are found from the quadratic equation, x² + 4•x + 7 = 0, using the quadratic formula that gives the solution to the general quadratic equation, a•x² + b•x + c = 0, as follows;

[tex] \displaystyle{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4 \times a \times c } }{2 \times a }}[/tex]

Comparing the general form of the quadratic equation to the quadratic equation from the question;

a•x² + b•x + c = 0

x² + 4•x + 7 = 0

Gives;

a = 1

b = 4

c = 7

Plugging in the above values of a, b, and c, we get;

[tex] \displaystyle{x = \frac{ - 4 \pm \sqrt{ {4}^{2} - 4 \times 1 \times 7 } }{2 \times 1} = \frac{ - 4 \pm 2 \cdot\sqrt{ - 3} }{2} }[/tex]

Which gives;

x = -2 ± √(-3) = -2 ± i•√(3)

The other solutions are therefore;

The solutions of the equation, 4•x³ + 16•x² + 28•x = 0, are therefore;

x = 0, x = -2+i•√(3), and x = -2 - i•√(3)

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The total life expectancy of the kid is 45.5 years.

rate of increase of life expectancy = 1.5 years per day

The rate of reduction of life expectancy = 0.5 years per day

37 days will mean ((7x5)+2), i.e., 5 complete weeks and 2 extra days.

Let the 2 extra days be Tuesday and Wednesday, now the 5 complete weeks will start from Thursday and after 37 days, the day will be Wednesday.

In this duration 5 Sundays will come on which the kid falls ill, so the reduction in life expectancy will be: 0.5 x 5= 2.5 years.

The remaining days will be: 37 - 5 = 32

So, the increase in life expectancy will be: 1.5 x 32= 48 years.

Thus, the total life expectancy of the kid is found to be : (48-2.5)years=45.5 years.

What are linear equations?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where y and x are the variables.

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Answer:6/7

Step-by-step explanation:

Answer:

162/189

Step-by-step explanation:

Divide by 2...................

Answer:

$15 × .8 = $12

$12 × .75 = $9

Answer: Domain: [-4,infinity)

Range: (-infinity,6]

f(-1) is 3

Step-by-step explanation:

Answer: Domain: [tex]x\geq -4[/tex]

Range: [tex]y\leq 6[/tex]

f(-1) = 3

Step-by-step explanation:

(-4,6) and (0,2) are both points on the line, so the equation of the line is

y = -x + 2

1 + 2 = 3

He drove for 2.3 hours.

The speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity. 

A body's speed is the amount of distance it travels in one unit of time.

Therefore, the SI Unit for speed is the meter per second, abbreviated as m/s 

Formula

Speed = [tex]\frac{distance}{time }[/tex]

Time = [tex]\frac{distance}{speed}[/tex]

Given Data

Distance = 161km

Speed = 70km

Putting values in the formula

Time = [tex]\frac{161}{70}[/tex]

Time = 2.3

He drove for 2.3 hours.

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It is better to buy 1 liter of soda for $1 compare to 1 gallon of soda for $4  .

As given in the question,

1 liter of soda for $1                    ____(1)

1 gallon of soda for $4

Relation between gallons and liters is given by:

1 gallon is equal to 3.785 liters

1 gallon of soda = $4

⇒ 3.785 liter = $4

⇒ 1 liter = $ ( 4 / 3.785 )

⇒ 1 liter = $ 1.056                _____(2)

From (1) and (2)

$1.056 > $1

It shows $1.056 is little bit higher than $1.

Therefore, it is better to buy 1 liter of soda for $1 compare to 1 gallon of soda for $4 .

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Answer:

13

Step-by-step explanation:

The equation for the perpendicular bisector of the line segment whose endpoints are (-2, 4) and (-8,-6) is 3x + 5y + 20 = 0.

Given:

Endpoints of the line segment are (-2, 4) and (-8,-6).

Midpoint of the line segment = ( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )

                                                 = [tex]\frac{-2 +(-8) }{2}[/tex] , [tex]\frac{4 +(-6) }{2}[/tex]

                                                =( [tex]\frac{-10}{2}[/tex] , [tex]\frac{-2}{2}[/tex] ) = (-5, -1)

Slope of the line segment =  [tex]\frac{y_{2} - y_{1} }{x_{2} -x_{1} }[/tex]

                                            = [tex]\frac{(-6) - 4 }{(-8) - (-2) }[/tex]

                                            = [tex]\frac{-10}{-6}[/tex] = [tex]\frac{5}{3}[/tex]

The line perpendicular to the line segment will have a slope of the negative reciprocal of the line segment which is -3/5.

Therefore, the perpendicular bisector passes through (-5,-1) and has a slope of -3/5.

Equation of the line will be,

y - y₁ = m(x - x₁)

⇒ y - (-1) = -3/5(x -(-5))

⇒ 5( y + 1) = -3(x + 5)

⇒ 5y + 5 = -3x - 15

⇒ 3x + 5y + 20 = 0

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you get he common ratio by dividing a term by the previous term

so,

15/-5 = -3

common ratio = -3

Geometric seuqence has a general term of:

Wher

r is common ratio

a is first term

Given,

a = -5

r = -3

We have:

12th term is basically n = 12

So, we have:

If this is an arithmetic sequence, each of the terms will have a common difference. Let's check.

As we can see, each of the terms does not have a common difference. The first one is -18 while the other one is -126. Therefore, this is not an arithmetic sequence.

Now, let's check if this is a geometric sequence. If it is, each of the terms will have a common ratio.

As we can see, each of the terms has a common ratio which is 1/7. Therefore, 147, 21, 3 is a geometric sequence and the common ratio is equal to 7.

The perimeter of the isosceles triangle whose base is 6 cm and two equal sides are 7.5 cm is 21 centi-meters.

What is isosceles triangle?

An isosceles triangle in geometry is one with at least two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception. The isosceles right triangle, the golden triangle, the faces of bipyramids, and some Catalan solids are all examples of isosceles triangles.

To calculate the perimeter of isosceles triangle, we use equation:

Perimeter = Base + 2(Two equal side)

Perimeter = 6 + 2(7.5)

Perimeter = 21 cm

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Given:

The quadratic equation ,

The solution of the given quadratic equation can be obtained as,

Hence, the solutions are,

Let the total marks are 100.

And Bradely got 66% marks.

So the marks of Bradely are:

And Zevel got one third of Bradely's marks so:

Answer:

y = 1/2x + 1/2

Step-by-step explanation:

I'm going to give me answer is gradient/slope form :

To work out the gradient we make a triangle from the line and do :

change in y / change in x

You should get 1/2

Now we have y=1/2x + c

to work out c we substitute a point from the line and solve for c :

Point (1 , 1)

1 = 1/2(1) + c

1 = 1/2 + c

c = 1/2

So our final answer is y = 1/2x + 1/2

Hope this helped and have a good day

Answer:

basically the even twill not happen as the probability of that is 0

Using the concept of the slope of a linear function, it is found that:

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

For this problem, we have that Pool B starts with significantly less water than Pool A, but their volumes get closer, meaning that Pool B fills faster and has a higher slope, that is, it fills more gallons per minute into the pool.

The information above it what we use to complete the statements.

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SOLUTION:

Step 1:

In this question, we are given the following:

Jason is putting crown molding in his master bedroom. The length of the room is 22 feet, and the width is 20 feet.

How much crown molding will Jason need if he wants to have 20% extra in case of mistakes or damage?

Step 2:

The details of the solution are as follows:

Then, we need to calculate 20% increase of 84 feet, we have that:

CONCLUSION:

The final answer is:

The probability that a 3 will be rolled would be 0.125 and the expected number of 6's roll would be 68.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

The events' estimated probabilities are as follows, according to the exponential probability theory:

P(3) = 0. 125

P(6 in 500 rolls) = 68 rolls

Number of times event occurs / number of trials

A number of attempts = sum of frequency:

(12+35+11+23+7+12) = 88

So the probability that a 3 will be rolled as

⇒ number of 3's / number of attempts

⇒ 11/88 = 0.125

The number of 6's probable in 500 rolls

⇒ (12 /88) × 500

⇒ 68.18 = 68

Therefore, the expected number of 6's roll would be 68.

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Answer:

Part A is Figure D

Part B is 3 units left

Given:

A table with the given values of the function y=g(x).

To find the function that represents g(x), we substitute a value of x into the given options.

For:

g(x =3+2x:,:

Let x=3

Based on the given table, the value g(x) is 24 when x=3. So g(x)=3+2x is not the function that represents g(x).

For

The value of g(x) =18 when x=3, so this is not the function.

For g(x)=3x^2:

Hence, this is not the function as well.

For g(x)=3(2)^x:

We can notice that when x=3, the value of g(x) =24 which is the same as the value of g(x) in the given table.

To double check this, we plug in the other values of x.

Therefore, the answer is:

Answer:

First number: 21

Second number: 84

Third number: 30

21 times 4 = 84 which checks out.

30 - 21 = 9 which also checks out

21 + 84 + 30 = 135 so they are correct!

Step-by-step explanation:

Hope it helps! =D

Ben must bowl 130 in his third game so that the average will be of at least 160.

Given that, Ben bowled 157 and 193 in his first two games. So, we have to calculate the average of his third bowl to have an average of at least 160.

Let the average of third bowl be x.

The average is known as the arithmetic mean which is the sum of all numbers in a collection, divided by the count of the numbers present in the collection. In other words, the average is the ratio of the sum of all given observations to the total number of observations. Hence, the average formula is:

Average = Sum of the Observations/Number of Observations

160 = 157+193+x/3

⇒ 160×3 = 157+193+x

⇒ 480 = 350+x

⇒ 480-350 = x

⇒  130 = x

Therefore, Ben must bowl 130 in his third game so that the average will be of at least 160.

Hence, 130 is the required answer.

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