directions: Find the distance between each pair of points
(-4, 6) and (3, -7)

Answer:

So from the general equation of line passing through two points is (y-y')=m(x-x') Where m is slope of the line and (x'y') be any any point out of these given two points. So, from the formula of slope m m (Y2 - Y1)/(x2-x1) So, m = 2-(-4)/(−2 − 1) m=-2 So equation of line will be (y-2)=-2(x+2) y-2=-2x-4 2x+y+2=0

Answer:

Step-by-step explanation:

(8 + 1)/(4 + 2)= 9/6 = 3/2

y + 1 = 3/2(x + 2)

y + 1 = 3/2x + 3

y = 3/2x + 2

Zoe travels 380 yards on foot from her home to the bus station. The distance between Zoe's home and the bus stop fluctuates from 250 yards to 410 yards when her distance from her home rises from 50 yards to 210 yards.

Distance is the measurement of the separation between two points. Since distance is a scalar quantity, it solely cares about its measurement or amount. Distance is measured and often stated in terms of meters in SI units (m).

Given,

zoe walks from her house to a bus stop that is 460 yards

and zoe's distance from her house increases from 50 yards to 210 yards,

So,

d1 = 460 yards - 50 yards

= 410 yards

d2 = 460 yards - 210 yards

= 250 yards

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Based on the linear function represented in the table, the expression to find the slope is a. StartFraction 9 minus 5 Over 4 minus 0 EndFraction.

The slope of a linear function can be found by the formula:
= (Y₂ - Y₁) / (X₂ - X₁)

From the table, we see that:

Y₂ = 9

Y₁ = 5

X₂ = 4

X₁ = 0

The slope is therefore:
= (9 - 5) / (4 - 0)

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Answer:

[tex]\textsf{1.} \quad f(x)+g(x) =8x^2+2x+3[/tex]

[tex]\textsf{2.} \quad f(x)-g(x)=-2x+1[/tex]

[tex]\textsf{3.} \quad h(x)+g(x)= 4x^2-x+5[/tex]

[tex]\textsf{4.} \quad h(x)-f(x)= -4x^2-3x+2[/tex]

[tex]\textsf{5.} \quad g(2)+f(x)= 4x^2+23[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=4x^2+2\\g(x)=4x^2+2x+1\\h(x)=-3x+4\end{cases}[/tex]

Function composition is an operation that takes two functions and produces a third function.

Question 1

Add function f(x) and function g(x) together:

[tex]\begin{aligned} \implies f(x)+g(x) & = (4x^2+2)+(4x^2+2x+1)\\& = 4x^2+2+4x^2+2x+1\\& = 4x^2+4x^2+2x+2+1\\& =8x^2+2x+3\end{aligned}[/tex]

Question 2

Subtract function g(x) from function f(x):

[tex]\begin{aligned} \implies f(x)-g(x) & = (4x^2+2)-(4x^2+2x+1)\\& = 4x^2+2-4x^2-2x-1\\& = 4x^2-4x^2-2x+2-1\\& =-2x+1\end{aligned}[/tex]

Question 3

Add function h(x) and function g(x) together:

[tex]\begin{aligned} \implies h(x)+g(x) & = (-3x+4)+(4x^2+2x+1)\\& = -3x+4+4x^2+2x+1\\& = 4x^2-3x+2x+4+1\\& = 4x^2-x+5\end{aligned}[/tex]

Question 4

Subtract function f(x) from function h(x):

[tex]\begin{aligned} \implies h(x)-f(x) & = (-3x+4)-(4x^2+2)\\ & = -3x+4-4x^2-2\\ & = -4x^2-3x+4-2\\ & = -4x^2-3x+2\end{aligned}[/tex]

Question 5

Add function g(x) when x = 2 to function f(x):

[tex]\begin{aligned} \implies g(2)+f(x) & = \left(4(2)^2+2(2)+1\right)+(4x^2+2)\\& = 4(4)+2(2)+1+4x^2+2\\& = 16+4+1+4x^2+2\\& = 4x^2+16+4+1+2\\& = 4x^2+23\end{aligned}[/tex]

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Notice the pattern:

10² = 100, so 10² - 9 = 91 with a digital sum of 9 + 1 = 10

10³ = 1000, so 10³ - 9 = 991 with a digital sum of 2•9 + 1 = 19

10⁴ = 10000, so 10⁴ - 9 = 9991 with a digital sum of 3•9 + 1 = 28

Then for an arbitrary power of 10, we have

[tex]10^n = 1\underbrace{00\ldots000}_{n\,\rm 0s} \implies 10^n - 1 = \underbrace{999\ldots99}_{n-1\,\rm9s}1 \\\\ \implies \text{digital sum} = 9(n-1)+1 = 9n - 8[/tex]

When [tex]n=51[/tex], the digital sum is 9•51 - 8 = 451.

(A) The distribution consists of two clusters and a gap, which best describes the distribution.

So, in the given situation the distribution consists of two clusters and a gap, which best describes the distribution.

Therefore, (A) the distribution consists of two clusters and a gap, which best describes the distribution.

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The complete question is given below:

The diameter, in centimeters (cm), of each tree in a random sample of trees in a forest was measured. The histogram shown summarizes the diameters.

Which of the following is the best description of the distribution?

A. The distribution consists of two clusters and a gap.

B. The distribution is approximately normal.

C. The distribution is symmetric with a skew to the right.

D. The distribution is skewed to the left.

E. The distribution is uniform.

Answer: compliment = (90-c)

supplementary = (180-c)

Step-by-step explanation:

Answer:

The result of decimal expansion of  [tex]8/15[/tex] is [tex]0.533[/tex].

Step-by-step explanation:

Hence the decimal expansion by simple division of [tex]8/15[/tex] is [tex]0.533[/tex].

Answer:

0.0015232292460015

I think you mean 2,626/4

Then it is  656.5

Step-by-step explanation:

What you wrote is probably not what you wanted the bottom is

Answer:

656 remainder of 2

Step-by-step explanation:

Step-by-step explanation:

Answer:

It is 0.4 and 40%

Step-by-step explanation:

Because if you divide 2 by 5 you get 0.4 and 0.4 is the same and 40% however, 4/100 is 0.04 or 4%

Answer:

0.4 and 40%

Step-by-step explanation:

0.4 and 40% can both be expressed as 2/5, however 4/100 cannot, as the simplified form of that is 1/25.

A compound inequality that represents the leg lengths of the cyclists the shop 18 ≤ 0.6x ≤ 26.

For the given question;

Let the cyclist's legs length be 'x'.

Then 0.6 times of cyclist's legs length will be 0.6x.

Now, the condition is;

The height ranging for the bikes is 18 inches and 26 inches.

It means the height of cyclist's legs length must be greater or equal to this value.

Thus,

18 ≤ 0.6x

And the maximum height of bike is 26 inch.

Thus, cyclist's legs length must be less than or equal to this length.

0.6x ≤ 26

Combining the two;

18 ≤ 0.6x ≤ 26 is the requires compounded inequality.

Thus, for, the value of x such that the range of the leg length lies between the 18 and 26 including both, the bike is provided otherwise NOT.

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Based on the given parameters, the quotient of 21.64 and 0.4 is 54.1

The quotient of numbers involves dividing a number by another i.e. the division problem

A division problem is an expression or an equation that involves the quotients of numbers or polynomials i.e. the quotient of two numbers

The numbers in the question are given as

21.64 and 0.4

The above numbers are decimal numbers, and the quotients can be calculated using a calculator

Express the above numbers as quotient of two numbers

So, we have

21.64/0.4

Next, we solve the above expression using a calculator

Using a calculator, we have the following equation

21.64/0.4 = 54.1

The above means that the quotient of 21.64 and 0.4 is 54.1

Hence, the required quotient of 21.64 and 0.4 is 54.1

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the composition of functions gives:

g(f(0)) = -6

Here we have the two functions:

f(x) = 3(x - 7)/4

g(x) = 2x  - 1

The problem in the answer is in the third step, where the distribution is done incorrectly.

g(f(x)) = 3*( (2x - 1) - 7)/4

g(f(x)) = 3*( 2x - 8)/4

g(f(x)) = ( 6x - 24)/4

Evaluating in x = 0 we get:

g(f(0)) = ( 6*0 - 24)/4 = -24/4 = -6

That is the solution of the composition of functions.

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Answer:

The mistake is in the third step

Wayne's Actual ACT score is 19.2 where mean is 21, standard deviation is 5 and the Z - score is -0.6.

Standard Deviation:

Standard deviation is  a measure of the dispersion of a set of numerical values from their mean.

The general form of the standard deviation is,

[tex]SD=\sqrt{\frac{\sum (x_i-\bar{x})}{n} }[/tex]

where

xi is each value in the data set,

x-bar is the mean, and

n is the number of values in the data set.

Given,

Mean = 21.

Standard deviation = 5

Wayne's standardized score on the act = −0.6 .

Here we need to find the Wayne's Actual ACT score.

Let x be the Wayne's Actual ACT score.

So,
=> z-score = (x - mean)/SD

Apply the values on it,

=> -0.6 = (x - 21) / 3

=> -1.8 = x - 21

=> x = 21 - 1.8

=> x = 19.2

Therefore, Wayne's Actual ACT score is 19.2

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The solutions to the given equation containing absolute value term |3x-7| - 7 = x are 0 and 7.

Given the equation in question;

|3x-7| - 7 = x

First, add 7 to both sides.

|3x-7| - 7 + 7 = x + 7

|3x-7|  = x + 7

Next, remove the absolute value term, this creates a ± on the right side of the question.

|3x-7|  = x + 7

3x-7  = ±( x + 7 )

The complete solution is the result of both the negative and positive portions of the solution.

For the first solution, use the positive of ±.

3x-7  = ( x + 7 )

3x - 7  =  x + 7  

3x - x = 7 + 7

2x = 14

x - 14/2

x = 7

For the second solution, use the negative of ±.

3x-7  = -( x + 7 )

3x-7  = -x - 7

3x + x = -7 + 7

4x = 0

x = 0/4

x = 0

Therefore, the solutions to the given equation containing absolute value term |3x-7| - 7 = x are 0 and 7.

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The simplified expression of 6(d - 6f) -6f- 3(-7f + 8d) is - 18d- 21f

The expression is given as

6(d - 6f) -6f- 3(-7f + 8d)

Expand the brackets

6(d - 6f) -6f- 3(-7f + 8d) = 6d - 36f - 6f + 21f - 24d

Collect the like terms

6(d - 6f) -6f- 3(-7f + 8d) = 6d  - 24d- 36f - 6f + 21f

Evaluate the like terms

6(d - 6f) -6f- 3(-7f + 8d) = - 18d- 21f

Hence, the simplified expression of 6(d - 6f) -6f- 3(-7f + 8d) is - 18d- 21f

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Answer:

x = 19

z = 64

Step-by-step explanation:

Angles (11x - 93)° and 116° are vertical angles, so their measures are equal.

11x - 93 = 116

11x = 209

x = 19

Angles z° and 116° are a linear pair, so they are supplementary, and their measures have a sum of 180°

z + 116 = 180

z = 64

As the x-values approach negative infinity, the function's values approach positive infinity, which is the right assertion regarding the graph's final behavior. The right answer is D.

A function in mathematics is an expression, rule, or law that determines the relationship between two variables, one of which is independent, and the other of which is dependent (the dependent variable). Functions can be found everywhere in mathematics, and they are essential for building physical connections in the sciences.

According to given information;

In light of the available data, the graph in the question depicts a function. The graph reveals the conclusions listed below:

At x=0, the function's value is 0.

The value of the function is 0 at x=0.

The function has a minimum value at x=2.4.

As the value of x reaches negative infinity, the function tends to positive infinity because it is open upwards.

As the value of x reaches positive infinity, the function tends to positive infinity because it is open upwards.

From the above conclusions, it can be said that "as the x-values go to negative infinity, the function's values go to positive infinity".

Therefore, option D is correct.

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Answer:

44

Step-by-step explanation:

4 * 2 + 3 * 4 = 44

Answer: the answer is 20

m2 + 3m when m =4

4x2=8

3x4=12

8+12=20

Answer:

If you add up all those hours that makes 6.5 hours

Answer:7.5

Step-by-step explanation:

Just add them

Tony have to get to pay $187.5.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

There are two cases in Unitary Method

Let's start with finding the price of one ice cream. Divide the entire cost of ice cream by the total number of ice creams to get at that. A single ice cream will cost you 125 divided by the amount of ice creams, or 25 cents. Consequently, 1 ice cream costs $25.

Step 2: To calculate the price of three ice creams, multiply the price of one ice cream by the quantity. Cost of 1 ice cream x number of ice creams = 25 x 3 = $75 is the price of 3 ice creams. The final cost is $75, which is the price of three ice creams.

Given:

For 1 1/2 or 3/2 hours tony charges = $37.50

For 1 hour tony charges = 37.50 * 2/3

                                        = 12.5 * 2

                                        = $25

Now, for 7 1/2 hours tony charges

= 15/2 * 25

= $187.5

Hence, tony charges $187.50 for tutoring 7 1/2 hours.

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Total 330 four-digit numbers can be formed if the number is odd and greater than 6000.

Let's tackle the problem in three steps.

First, take into account the numbers with "6" as the first digit on the left.

Then take the first eight digits of the numbers as the leftmost digit.

Last but not least, we'll use the numbers that begin with "7" as the leftmost digit.

1. As the leftmost digit, think of the numbers that begin with "6."

Any one of the final four odd digits—1, 3, 5, or 7—is acceptable (and recommended).

You are given four options.

You can use any of the remaining 8-1-1 = 6 digits for the second and third digit.

In all, it gives you 4×6×5  = 120 choices/numbers.

2.  Consider  the leftmost digit as the number starting with "6."

You have 120 more options/numbers using the same logic and analysis.

Everything is going well thus far, and you only need 120 + 120 = 240 numbers.

3.  Consider the numbers starting with "7" as leftmost digit.

Any of the final three odd digits—1, 3, and 5—may (and ought to) be used.

You have three options.

Any of the remaining 8-1-1 = 6 digits can be used for the second and third digit.

In all, it gives you 3×6×5  = 90 choices/numbers.

4. You have 120 + 120 + 90 = 330 numbers/options when everything is added up.

Hence we get 330 choices to create four digit numbers.

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Your question is incomplete. Please find the missing content below.

A four-digit number is formed using four of the eight digits 1, 2, 3, 4, 5, 6, 7, 8. No digit can be used more than once. Find how many different four-digit numbers can be formed if the number is odd and greater than 6000.

Asking questions, formulating a hypothesis, testing the hypothesis, drawing conclusions, and reporting the results are steps in the: scientific method.

Scientific method refers to a process that has been the hallmark of natural science since the 17th century and entails systematic observation, measurement, and experiment as well as the creation, examination, and change of hypotheses.

Now,

Hence, Asking questions, formulating a hypothesis, testing the hypothesis, drawing conclusions, and reporting the results are steps in the: scientific method.

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Answer:

I think that's the answer heh

Step-by-step explanation:

–3 [(8a−6a² + 9)+ (−10a−8+8a²)]

=−3−[8a−6a² + 9+ −10a− 8 + 8a²]

=−3−[(8a − 10a) + (−6a² + 8a² ) + (9 − 8)]

=−3−[−2a + 2a² +1]

=−3 + 2a − 2a² −1

= +2a − 2a² −4

=−2a² + 2a −4

Answer:

No Solution

Step-by-step explanation:

13+6h= -11+6h

Bring 6h over to the left side of the equation and subtract it from the other 6h. You have to subtract because it's a positive number, and you must do the opposite operation.

6 - 6 = 0, so there are no solutions. Once h is proven to be 0, you can't do anything else.

Hopefully this helps!

If a chip is randomly drawn from the bag, the probability it will be a red or a blue one is P(red or blue) = 10/19.

Probability of an event A is the number of event A divided by all possible outcomes. Mathematically,

P(A) = n(A)/n(S)

where:

n(A) = number of event A

n(S) = number of all possible outcomes or sample space.

Suppose A and B are independent outcomes, then:

P(A or B) = P(A) + P(B)

In the given problem:

Number of chips:

Blue = 3

Red = 7

Yellow = 4

Green = 5

Total chips = 3 + 7 + 4 + 5 = 19

If a chip is randomly drawn, the probability it will be a red one is:

P(red) = 7/19

Similarly,

P(blue) = 3/19

Using the probability formula for independent outcomes:

P(red or blue) = P(red) + P(blue)

                      = 7/19 + 3/19 = 10/19

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It will take 27 minutes for all the kids to have gone home

The given parameters are:

9 kids every 3 minutes

This can be represented as

9 kids = 3 minutes

Let the time spent by 81 kids be x

So, we have the following equation

81 kids = x

Rewrite the parameters as

9 kids = 3 minutes

81 kids = x

Cross multiply in the above equation

So, we have:

9 * x = 3* 81

Divide both sides by 9

x = 3 * 9

Evaluate

x = 27

Hence, it will take 27 minutes for all the kids to have gone home

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Answer:

Scale factor = 1/2

Explanation below

Explanation belowHope this helps :)

Step-by-step explanation:

If the second figure is turned correctly then all the numbers will correspond.

10 × 1/2 = 5

6 × 1/2 = 3

8 × 1/2 = 4