If two methods agree perfectly in a method comparison study, the slope equals ________ and the y-intercept equals ________.
a. 0.0, 1.0
b. 1.0, 0.0
c. 1.0, 1.0
d. 0.0, 0.0
e. 0.5, 0.5

Answer: right

Step-by-step explanation:

[tex]-499 > -500[/tex], and larger numbers are to the right of numbers smaller than them on the number line.

Answer:

The box is 8 feet long.

Step-by-step explanation:

1 inch = 2 feet.

Multiply 4 by 2.

4×2=8

I multiplied 4 by 2 because 1-inch equals 2 feet, which means if we multiply both terms by 4, you will get 4 inch = 8 feet.

Hope this helps!

Answer:

26

Explanation:

[tex]\int\limits^{25}_{-1} {e^{x-[x]}} \, dx[/tex]

simplify

[tex]\int\limits^{25}_{-1} {e^{0} \, dx[/tex]

any variable to the power 0 is 1

[tex]\int\limits^{25}_{-1} 1 \, dx[/tex]

integrating 1 gives x

[tex]\left[ \:x \: \right]^{25}_{-1}[/tex]

apply limits

[tex]25 - (-1)[/tex]

add terms

[tex]26[/tex]

[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}e^{x-[x]}dx[/tex]

[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}e^{x-x}dx[/tex]

[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}e^0dx[/tex]

[tex]\\ \rm\hookrightarrow \displaystyle\int\limits_{-1}^{25}dx[/tex]

[tex]\\ \rm\hookrightarrow \left[x\right]_{-1}^{25}[/tex]

[tex]\\ \rm\hookrightarrow 25-(-1)[/tex]

[tex]\\ \rm\hookrightarrow 25+1[/tex]

[tex]\\ \rm\hookrightarrow 26[/tex]

Answer:

288pi in^3 , which is 904.78 in^3 to nearest hundredth.

Step-by-step explanation:

V = 4/3 pi r^3

  = 4/3 pi * 6*3

   = 288pi in^3

   = 904.7786842 in^3

The equation of the graphed parabola is y=a[tex](x+3)^{2}[/tex]-4.

Given that parabola is plotted, concave up , with vertex located at coordinates (-3,-4).

We are required to find the equation of the graphed parabola.

The equation of a quadratic function of vertex (h,k) is given by:

y=a[tex](x-h)^{2}[/tex]+k

In the above equation a is the leading coefficient.

We have been given point (-3,-4).

We have to just put the value of h=-3 and k=-4 and the required equation will be as under:

y=a[tex](x+3)^{2}[/tex]-4

Hence the equation of the parabola which is plotted, concave up, with vertex located at coordinates (-3,-4) is y=a[tex](x+3)^{2}[/tex]-4.

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Maximum value = 880/3.

Maximizing the objective function in the LP model means that the value occurs in an acceptable set of decisions. Linear programming refers to selecting the best alternative from the available alternatives that can represent the objective and constraint functions as linear mathematical functions.

As mentioned above, the equation is an example of a constraint. You can use this to think about what it means to solve equations and inequalities. For example, solving 3x + 4 = 10 yields x = 2. This is an easy way to express the same constraints.

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Question 4

1) [tex]\overline{AC} \cong \overline{AE}, \overline{AB} \cong \overline{AD}[/tex] (given)

2) [tex]\angle A \cong \angle A[/tex] (reflexive property)

3) [tex]\triangle ABC \cong \triangle ADC[/tex] (SAS)

Question 5

3) [tex]\angle ABC \cong \angle DCB[/tex] (all right angles are congruent)

4) [tex]\overline{AC} \cong \overline{AC}[/tex] (reflexive property)

5) [tex]\triangle ABC \cong \triangle DCB[/tex] (AAS)

Answer:

y =- [tex]\frac{1}{4}[/tex]x - 1

Step-by-step explanation:

You are asked to give the equation of the line in slope intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

Y-intercept is the point where the graph intersects the y-axis at point (b, 0). The graph seems to cross the y-axis at (-1, 0), so the b value is -1.

Slope is rise over run. Looking at the graph, it goes down 1 unit every 4 units to the right, so the slope is -1/4.

Answer:

Below in bold.

Step-by-step explanation:

The slope is -1/4 and y-intercept is -1

y = -1/4x - 1

The answer choice which best fits the function described in the task content is; Choice A; time(length).

It follows from the task content that the function takes the length of a race and returns the time needed to complete it.

On this note, it follows that the time taken is a function of the length of the race.

Hence, the appropriate name of the function is; Choice A.

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Answer:

23

Step-by-step explanation:

small brain

The slope of a line shows the distance of that line. This means it tells us how far the line moves each time you move over one unit on the x-axis for that line.

The slope of a line can be defined a number that describes the direction and steepness of the line.

It is also known as gradient

It is denoted by the letter 'm'

Thus, the slope of a line shows the distance of that line. This means it tells us how far the line moves each time you move over one unit on the x-axis for that line.

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Using the given table:

a) the average rate of change is 32.5 jobs/year.

b) the average rate of change is 12.5 jobs/year.

For a function f(x), the average rate of change on an interval [a, b] is:

[tex]\frac{f(b) - f(a)}{b - a}[/tex]

a) The average rate of change between 1997 and 1999 is:

[tex]A = \frac{695 - 630}{1999 - 1997} = 32.5[/tex]

So the average rate of change is 32.5 jobs/year.

b) Now the interval is 1999 to 2001.

The rate this time is:

[tex]A ' = \frac{720 - 695}{2001 - 1999} = 12.5[/tex]

So the average rate of change is 12.5 jobs/year.

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Answer:

25%

Step-by-step explanation:

When you simple 6 out of 24 you get a quarter.

A quarter us equivalent to 25%

Answer:

sum

Step-by-step explanation:

example

2+3=5

Considering the surface area of the spherical ballon, it will take 7 seconds for the the balloon to fully inflate.

The surface area of a sphere of radius r is given by:

[tex]S = 4\pi r^2[/tex]

In this problem, the surface area is of [tex]784\pi[/tex] cm², hence the radius in cm is found as follows:

[tex]784\pi = 4\pi r^2[/tex]

[tex]4r^2 = 784[/tex]

[tex]r^2 = \frac{784}{4}[/tex]

[tex]r^2 = 196[/tex]

[tex]r = \sqrt{196}[/tex]

r = 14 cm.

The radius start at 0 cm, inflating at a rate of 2 cm/s, hence it will take 7 seconds for the the balloon to fully inflate, as 14 cm/(2 cm/s) = 7 s.

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The equation of distance traveled by the car is d(t) = 60 · t, for t ≥ 0.

In accordance with the statement, car travels in a straight line at constant speed. The distance traveled (d), in miles, is equal to the product of the speed (v), in miles per hour, and time (t), in hours:

d(t) = v · t     (1)

If we know that v = 60 mi/h, then the equation of distance traveled by the car is d(t) = 60 · t, for t ≥ 0.

The statement is incomplete and complete form cannot be found. Then, we decided to complete the statement by asking for the equation that describes the distance of the car.

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The tiger population loses 3/5 of its size every 2.94 decades

The given equation is:

[tex]N(t)=710(\frac{8}{125} )^t[/tex]

Find the derivative of the given function

[tex]\frac{dN}{dt} =710(0.064)^tln(0.064)\\\\\frac{dN}{dt} =-1951.7(0.064)^t[/tex]

When the tiger loses 3/5 of its population

dN/dt = 3/5

Solve for t

[tex]\frac{3}{5} =-1951.7(0.064)^t\\\\-0.0003=(0.064)^t[/tex]

Take the natural logarithm of both sides

[tex]ln(-0.0003)=t(ln0.064)\\\\-8.087=-2.75t\\\\t=\frac{-8.087}{-2.75} \\\\t=2.94[/tex]

The tiger population loses 3/5 of its size every 2.94 decades

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Answer:

it depends.

Step-by-step explanation:

A perfect square is a number that can be expressed as the product of an interger by itself or as the second exponent of an interger. For example, 25 is a perfect square because it is the product of interger 5 by itself, 5 × 5 =25.

The root of the polynomial function x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12 is -3, -2 and 3

The graph that completes the question is added as an attachment

The polynomial function is given as:

x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12

From the attached graph, we have the following highlight:

The curves of both equations intersect at

x = -3, x = -2 and x = 3

This means that the root of the polynomial function is -3, -2 and 3

Hence, the root of the polynomial function x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12 is -3, -2 and 3

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Complete question

Carlos graphed the system of equations that can be used to solve x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12

What are the roots of the polynomial equation?

A) –3, –2, 3

B) –3, 2

C) 18, 32

D) 18, 32, 66

Answer:

11

Step-by-step explanation:

if the some of a number is an restrocal is 122 upon 11 find the integers value of x let the number bees two values of x i e 11 and 1 upon 11 are possible hence required in future value of x is 11

The largest interval of x-values where the function is increasing is (-1, 1)

The table of values is added as an attachment

From the table, the function f(x) decreases from x = -3 to x = -1 and x = 1 and x = 2

So, we make use of the intervals

x = -1, 0 and 1

From the table,

From x = -1 to 0, the change is 3

From x =  0 to 1, the change is 3

From x =  -1 to 1, the change is 6

Using the above highlights, the largest increasing interval is (-1, 1)

Hence, the largest interval of x-values where the function is increasing is (-1, 1)

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The solution to the system of equations is the point ( -1, 9 ).

What is the solution to a system of linear equations?

If you have a system of equations that contains two equations with the same two unknown variables, then the solution to that system is the ordered pair that makes both equations true at the same time.

The system of equations

y = -3x + 6 ...................(1)

y = 9 .................(2)

Substitute equation (2)  in equation

9 = -3x + 6

subtract  both sides

9 - 6 = -3x + 6 - 6

3 = -3x

Divide by  -3 both sides

  x = -1

the solution is the point ( -1, 9 )

Therefore,the solution to the system of equations is the point ( -1, 9 ).

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The complete question is -

Y = –3x + 6  y = 9 what is the solution to the system of equations? (–21, 9) (9, –21) (–1, 9) (9, –1)

Answer:

c

Step-by-step explanation:

What is the solution to the system of equations?

(–21, 9)

(9, –21)

(–1, 9)

(9, –1)

The correct option is (c) h = 10sin(π15t)+35.

The equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds is  h = 10sin(π15t)+35.

The blades of a turbine, which resemble propellers and function much like an airplane wing, capture the wind's energy.

A pocket of low-pressure air develops on one side of the blade when the wind blows. The blade is subsequently drawn toward the low-pressure air pocket, which turns the rotor.

Calculation for the equation of the model height-

Let's now review each choice individually and select the best one.

The blade is horizontal at time t = 0. As a result, h = 35 at t = 0 is valid for all of the possibilities in this situation.

They accomplish two spins in a minute. The blades will so complete one rotation in 30 seconds. and they will complete a quarter rotation in 15/2 seconds. Because of this, the blade will be vertically up from time t = 0 to t = 15/2. Its height in this instance should be 35 + 10 = 45 ft. Let's now examine the available possibilities.

If we put t=15/2 in the options

Option (a) gives h = 25

Option (b) gives h = -10sin(15/2) + 35

Option (c) gives h = 45

Option (d) gives h = 10sin(15/2) + 35

Therefore, the correct equation is given in option c.

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The complete question is -

The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds? Assume that the blade is pointing to the right, parallel to the ground at t = 0 seconds, and that the windmill turns counterclockwise at a constant rate.

a) h = −10sin(π15t)+35  

b) h = −10sin(πt)+35

c) h = 10sin(π15t)+35

d) h = 10sin(πt)+35

The number of blue balls that are needed to balance four green, two yellow and two white balls is 16 blue balls.

Green(g)

Blue (b)

Yellow (y)

White (w)

First step is to formula an equation

3g=6b

g=2b

2y=5b

y=5/2b

4w=6b

w=3/2b

Second step is to substitute

4g+2y+2w

=4(2b)+2(5/2b)+2(3/2b)

=8b+5b+3b

=16b

Therefore 16 blue balls are needed.

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Bob is 2 years older than Carol and the reverse of Carol's age is 3 times Bob's age, which makes Bob's to be 17 years.

Let 1B represent Bob's age and let 1C represent Carol's age, we can write the following equations;

Reversing Carol's age gives;

The multiples of 3 that have the form X1 have 7 as the rightmost number.

Given that 1B is a teenager, we have;

When;

The reverse of Carol's age is therefore;

Therefore, from the given description, Bob's age 1B = 17 years

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Answer:

Step-by-step explanation:

A Geometric sequence can be used:

To Model this sequence you need to use this formula

A (subscript n) = Ar(n-1)

a = value of the first term

n = the # of the term you want to find (For example, if you want to find the term number 3, it is 12)

r = the common ratio, this is obtained by dividing the second term in the sequence by the first.

So the value of r is = 2/3 because 27 times 2/3 = 18 which is the second term

n = 4 since you want to find the 4th term in the sequence

Plug it in and the results are

4th term = 27(2/3)^(4-1)  = 8

The answer is 8

The solution to the expression [tex]\frac{x^2+7x+12}{x-3} .\frac{x^2-6x+9}{2x^2-18}[/tex] gives (x + 4)/2

An equation is an expression that shows the relationship between two or more number and variables.

[tex]\frac{x^2+7x+12}{x-3} .\frac{x^2-6x+9}{2x^2-18} \\\\=\frac{(x +3)(x +4)}{x-3} .\frac{(x-3)(x-3)}{2(x+3)(x-3)} =\frac{x+4}{2}[/tex]

The solution to the expression [tex]\frac{x^2+7x+12}{x-3} .\frac{x^2-6x+9}{2x^2-18}[/tex] gives (x + 4)/2

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Answer:

3x+2=2190

3x=2190-2

3x=2188

x=2188÷3

x=729

Answer:

10 eggs

Step-by-step explanation:

We need to work out the price per unit :

12 eggs = rs 192

1 egg = rs 192÷12

1 egg = rs 16

? egg = rs 160

16×? = 160

? = 160÷16

? = 10

So our final answer will be 10 eggs

Answer:

10

Step-by-step explanation: