O GRAPHS AND FUNCTIONSFinding a difference quotient for a linear or quadratic function

We have that approximately, the distance from Saturn to Jupiter is:

and the distance from Jupiter to Mars approximately is:

then, the total distance traveled would be the sum of these two quantities:

therefore the total distance is 7.98x10^8 miles

The perimeter of a figure is found adding the length of all its sides.

In this case, the perimeter is:

P = (x + 6) + (3x - 2) + (x- 3) + (x+ 2) + (x) + (x + 5)

P = (x +3x + x +x + x + x) + (6 - 2 -3 +2 + 5)

P = 8x + 8

Answer:

solution:

Here,3[ 2^(x-3) ] = 384

or,     2^(x-3)       =  ( 384 /3 )

or,     2^(x-3)       =  128

or,     2^(x-3)       =  2^(7)

or,     x                =  7+3

We know that they lots of $450.

If they want to share the loss equally, we just have to divide the amount by 9 owners.

Remember that losses are represented by negative numbers.

Answer:

The answer is 5

Step-by-step explanation:

( 4k+2 ) / 10 = x

( 4(12) + 2 ) / 10 = x

( 48 + 2 ) / 10 = x

50 / 10 = x

x = 5

The co ordinates of the point B is (12, 12)

Given,

The co ordinates:

Point C = (6, 9)

Point A = (4, 8)

Point B = (x, y)

AC : CB(m : n) = 1 : 3

We have to find the co ordinates of point B.

Lets use the formula to find the coordinates of point C.

C = 1 / (m + n) × (mx₂ + nx₁, my₂ + ny₁)

Where,

C = (6, 9)

m = 1

n = 3

x₁ = 4

x₂ = x

y₁ = 8

y₂ = y

So,

(6, 9) = 1 / (1 + 3) × ((1 × x) + (3 × 4), (1 × y) + (3 × 8))

(6, 9) = 1/4 × (x + 12, y + 24)

(6 × 4, 9 × 4) = (x + 12, y + 24)

(24, 36) = (x + 12, y + 24)

Lets evaluate:

x + 12 = 24 and y + 24 = 36

Solve for x,

x + 12 = 24

Add -12 to both sides

x + 12 - 12 = 24 - 12

We get,

x = 12

Now solve for y,

y + 24 = 36

Add -24 to both sides

y + 24 - 24 = 36 - 24

We get,

y = 12

That is, the co ordinates of the point B is (12, 12)

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Based on the data of the table, you can notice that the following function f(x):

f(x) = x + 4

represents the relation in between the values of the columns of the table.

For instance, you have:

f(3) = 3 + 4 = 7

f(4) = 4 + 4 = 8

f(5) = 5 + 4 = 9

f(6) = 6 + 4 = 10

Answer

The statement that does not represent an expression are 4 + x = 12 and x^2 = 24 which are option B and C respectively

Explanation:

An expression is a set of term combined using the operators +, - /

From the option given

8+ x - 7 this can be further expressed as

8 + x - 7

x + 8 - 7

x - 1

The only expression in the option are x - 1, and 5

4 + X = 12 is an equation. This is because it is a combination of two expressions that are equal to each other

x^2 = 24 is also an equation

Therefore, the statement that does not represent an expression are 4 + x = 12 and x^2 = 24 which are option B and C respectively

Answer:

108°

Step-by-step explanation:

[tex]m\angle 3=72^{\circ}[/tex] (corresponding angles)

[tex]m\angle 1=108^{\circ}[/tex] (linear pair)

13 water stations will be placed every 400 meters of a 5 kilometer.

Given: Water stations will be placed ; every 400 meters

Also the total distance = 5 km = 5000 meters

Thus if a water station is supposed to be kept at every 400 meter distance then that means we can find out this distance by using unitary method

this means by using unitary method we get;

Number of water stations needed is = 5000 divided by 400

12.5 = 13 water stations would be required.

Thus 13 water stations will be placed every 400 meters of a 5 kilometer.

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The rate of the claims paid expressed as a percent is 86.67%.

Out of the 4,500 prescription claim submissions, it has been stated that the insurance company covers 3,900 prescription claims in full.

We must determine what percentage of 4,500 is 3,900 in order to solve the presented problem.

Percent of the claims paid = 3,900 / 4,500 x 100

Percent of the claims paid = 0.8666666 × 100

Percent of the claims paid 86.66666%

Percent of the claims paid = 86.67%

As a result, 86.67% would be the rate of claims paid represented as a percentage.

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We have the following function given:

x f(y)

-2 -8

-1 -3

0 -2

1 4

2 1

3 3

And we can see that the minimum of the function is for the lowest f(y) value on this case -8

And the closest pair to this local minimum is:

A. (-1,3)

The probability of doing all questions correct is 1/3.

So, the probability to get all questions correct:

Probability formula: P(E) = Favourable outcomes/Total outcomes

Then,

Now, find the probability by putting the values as follows:

Therefore, the probability of doing all questions correct is 1/3.

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The correct question is given below:

Your stats test has five multiple-choice questions, each having four possible answers with one correct answer per question. If you completely guess (which you would never do), what is the probability (in decimal form) that each of the following will happen? Show your work.

A) Get all of the questions correct

1) Let's write the inequality and solve it

w+3≥-22 Subtracting 3 from both sides

w ≥ -22 -3

w ≥ -25

2) Now let's write the solution as an interval. Considering that the solution is a set for all values greater than or equal to -25 for w. Including the -25 (closed) up to infinite (open).

When we talk of rigid transformation, we refer to transformation that occurs, and the size of the shape is not affected. Of the three options, dilation is the only sort of transformation that affects the size of the object.

DILATION

Let's use some examples where we have order of operations and also there are negative numbers and signs involved:

Let's evaluate the following:

(-4) x 5 + (-6)

So order of operations tells us to first take care of the multiplications and after that, deal with the additions or subtractions.

So the multiplication goes first here:

(-4) times 5 = - 20

Recall that a positive number times a negative number gives alwasy a negative number. So negative times positive gives the negative sign to the multiplication, and then, once the sign is taken care of, you multiply the numbers (4 x 5 = 20)

Next, we do the indicated addition

-20 + (-6) = -20 - 6 = -26

weher again we use the property that the + times the - inside the parenthesis gives a minus. ad we finalize by doing -20 - 6 = -26 (combining of two negative numbers).

Another example:

(8 + (-5)) x (-8)

So we first work on solving what is inside the first parenthesis :

8 + (-5) this is 8 - 5 (as we did before, the plus outside the parenthesis where -5 is, results in a minus sign as it multiplies the "-" that is shown ahead of 5.

So, inside this parenthesis we get: 8 - 5 = 3

Now we are left to multiply 3 times (-8)

This is a product of a positive number (3) times a negative number (-8). Again, do the rule for product of the signs (positive times negative equals negative) , ad then the product of the numbers: 3 x 8 = 24

so the answer is - 24

Another example:

(-9) x ((-10)+ 10)

We need to start by solving the operation indicated inside the parenthesis:

(-10) + 10 This is the same as: - 10 + 10 = 0

Now, whenwe use this result in the full expression, we get:

(-9) x 0 = 0 SInce any number multiplied times zero is zero.

The area, A, of a rectangle with dimensions l and b is given by:

A = l times b

Therefore the total area of the two opposite and congruent rectangular sides with

the dimension 6 by 5 is:

The total area of the two opposite and congruent rectangular sides with

the dimension 6 by 7 is:

One observation (210) given a test at the end of the movie to measure their recall is an outlier because it is above the fence above, as can be seen.

Data should first be arranged as follows in ascending order:

10, 22, 26, 27, 28, 31, 35, 40, 49, 57, 58, 61, 61, 62, 86, 86, 87, 88, 92, 97, 101, 210

There are n = 22 observations. Here n is even. Hence median is the mean of the middle two observations.

Median = (11 + 12) th observation /2 = (58 + 61)/2 = 59.5

We now divide the ordered data equally into two halves. Therefore, there are 11 observations in the lower section and 11 observations in the upper part.

The first quartile now corresponds to the median of the lower half.

Q1 = [(11 + 1)/2] the observation = 6th observation = 31

The third quartile represents the upper half part's median.

Q3 = [(11 + 1)/2] the observation = 6th observation = 87

IQR = Q3 - Q1 = 87 - 31 = 56

Lower fence = Q1 - 1.5 × IQR = 31 - 1.5 × 56 = -53

Upper fence = Q3 + 1.5 × IQR = 87 + 1.5 × 56 = 171

One observation (210) is an outlier since it is above the upper fence, as can be seen.

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a) 7 - 5 = 12

2 = 12 This is not a solution

b) 5 + 7 = 12

12 = 12 This is a solution

c) 7 + 12 = 19

19 = 19 This is a solution

d) x - 5 = -12

7 - 5 = -12

2 = -12 This is not a solution

The complete table describing the probability distribution of X is:

x        |      P(x)    

0             0.027

1               0.189

2              0.441

3               0.343

The values of the random variable X are given and the corresponding probabilities are to be found.

The probability distribution is binomial.

That is, P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ, where p is the probability of success of X in n trials.

So here values of x are given.

From the table, it is clear that p = 0.7

and  1-p = 0.3

Number of trials, n = maximum number of x = 3

Now consider each x.

When x = 2,

P(X = 2) = P( getting 2 tails out of 3 flips)

             = P(TTH or THT or HTT)

             = P(TTH) +P(THT) +P(HTT)  [since each of them are independent events]

             = ³C₂ p²(1-p)³⁻²

             = 3 (0.7)²(0.3)

             = 0.441

When x = 3,

P(X = 3) = P( getting 3 tails out of 3 flips)

             = P(TTT)

             = ³C₃ p³(1-p)³⁻³

             = 1 (0.7)³(0.3)⁰

             = 0.343

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By comparing both polygons, we can tell that they are not the same polygon, since one of the sides has length 11 in one trapezoid and 12 in the other. So, this polygons are similar. We notice that the variables X and Y are part of the angles. In polygons that are similar, the measure of the homologous angles are equal. By homologous we mean angles that are located at the same place in both figures. To determine the homologous angles, we should have both figures drawn in the same orientation. To do so, we will flip the trapezoid on the left, so its orientation matches the one fromt the right. I picture of this flipping would be

From this picture, by comparing it to the other polygon, we determine that the angle EDC is homologous to the angle UTS. So, their measure should be the same. So, we get the following equation

By adding 37 on both sides and subtracting y on both sides, we get

This implies that y = 39°.

By doing the same procedure, we find that the angles URS and CBE are homologous. So their measures are equal and we get the equation

Then, by subtracting 13 on both sides

If we divide both sides by 2 we get

So x = 19°.

The range is the difference between the greatest and the smallest number, so it is 32 - 16 = 16.

start by writing in the form

where you already have the slope and you must find b, which is the y-intercept

use the point given (-5,-3) to find b

The simplified form of expression  4(126) + 76 - 10 is 6 (100 - 5).

A mathematical expression is a sentence that contains a minimum of two numbers or variables and at least one mathematical operation. Let's learn how to write expressions.

A number is 6 more than half of another number, and that other number is called x. In a mathematical expression, this statement is represented as x/2 + 6. Complex puzzles can be solved using mathematical expressions.

We have been asked to simply the expression

4(126) + 76 - 10

= 4(60 + 66) + 66

= 4(60) + 4(66) + 66

= 4(60) + 5(66)

= 4(60) + 5( 60 + 6)

= 4(60) + 5(60) +5(6)

= 60(4+5) + 6(5)

= 60(9) + 6(5)

= 6(90 + 5)

= 6(95)    

= 6 (100 - 5) simplified form

= 600 - 30

= 570

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Answer:

15

Step-by-step explanation:

5/2=2.5

35/2.5=15

Step-by-step explanation:

To make 5 batches of cookies, 10 cups of flour are required.

To make 1 batch of cookies:

10 cups ÷ 5 cups = 2 cups of flour

Answer:

she has left 28 unsolved problem or whatever it is

Step-by-step explanation:

48:12=4

4x7=27

In order to determine the weighs of the boxes, name x as the larger box and y as the smaller one.

Then, based on the given situation, you can write the following equations:

3x + 2y = 86

8x + 4y = 209

Solve the previous system of equations as follow:

Multiply the first equation by -2 and add the result to the second equation:

(3x + 2y = 86)(-2)

-6x - 4y = -172

8x + 4y = 209

-6x - 4y = -172

2x = 37

Solve the previous equation for x by dividing by 2 both sides:

x = 37/2

x = 18.5

Next, replace the previous value of x into any of the equations of the system, for instance, into the first equation, and solve for y:

3x + 2y = 86

3(18.5) + 2y = 86

55.5 + 2y = 86

2y = 86 - 55.5

2y = 30.5

y = 30.5/2

y = 15.25

Hence, the weighs of the boxes are:

larger box = 18.5 kg

smaller box = 15.25 kg

Answer:

C. (5, 5)

Step-by-step explanation:

To do this, you take each coordinate and perform the function that is shown in the translation.

So for (x-2, y+3),

you are going to take the x value of the coordinate you are given:

(7,2) and subtract 2, and then take the y value of (7,2) and add 3.

(7 - 2, 2 + 3)

Then solve this:

(5, 5)

To calculate the 60% of 90, we need to understand what means 60% in terms of fractions. Converting a percentage into a fraction has a simple method: Dividing the percentage by 100. So 60% in fraction form is just

Now, to solve the problem, we only need to multiply our number 90 by this fraction; it gives us

Thus the 60% of 90 is 54.