What are the tests for parallel and perpendicular lines?

The expression used to calculate the sale price is given as follows:

S(p) = 0.65p.

The expression used to calculate the sale price is obtained applying the proportions in the context of the problem.

The price was 35% off, meaning that there was a discount of 35%, meaning that a percentage of 100 - 35 = 65% of the total price was paid, hence the expression used to calculate the sale price is given as follows:

S(p) = 0.65p.

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By using a system of equations of two variables we concluded that the first number was 6

Let the numbers be x and y and their sum gives z

The equation for the sum of 2 numbers:

                                             x + y = z    -(1)

We know, z = 30 and y = 4 times x = 4x

Putting values of y and z in equation (1), we get

                                             x + 4x = 30

Solving for x, we get

                                                  5x = 30

                                         x = 30/5 = 6

To get the value of y, put the value of x in y = 4x and we get

                                          y = 4 x 6 = 24

So the real equation was

                                              6 + 24 = 30

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The number of seconds does the firework hit the ground is 3 seconds

From the information given, we have the quadratic function;

y = -16x² + 32x + 48

To determine the value of x , let's reduce the expression, we get;

-2x² + 4x + 6

Now, let's factorize the terms

Multiply the coefficient by the constant and find the pair factors

-2x² + 6x - 2x + 6

Factorize in pairs, we get;

-2x(x -3) - 2(x -3)

Then, we have the expressions

-2x - 2 = 0

solve for x

x = -1

x - 3 = 0

x = 3

Hence, the value is 3 seconds

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Answer:

3

Step-by-step explanation:

i took the test

Answer:

8π

Step-by-step explanation:

The period of a function f(x)  is the x-distance between two repeating points of the function

Looking at the function graph given we see that the function reaches a peak value(called amplitude) at x = -6π and then again reaches this value at x = 2π

So the x-distance is 2π - (-6π) = 2π + 6π = 8π

From 2π, the function reaches its maximum value again at 10π giving the period once again as 10π - 2π = 8π

Answer:

It would be 3.765 pounds. You have to do 7.53 x 10 to the -10= 0.000000000753. Then do 0.000000000753 x 5 billion to get 3.765.

Step-by-step explanation:

The equation shows how to find the length of each piece is L = R / N and the length of each piece is 1.5 feet.

To find the length of each piece, we can use the following equation:

Length of each piece = Total length of the ribbon / Number of pieces

In mathematical terms, we can represent this equation as:

L = R / N

Where,

L is the length of each piece

R is the total length of the ribbon (66 feet in this case)

N is the number of pieces (44 in this case)

In this problem, we are given a 66-foot ribbon and we are asked to cut it into 44 equal pieces. We need to find out the length of each piece.

Using this equation, we can easily find the length of each piece:

L = 66 / 44

L = 1.5 feet

Therefore, each piece of the ribbon is 1.5 feet long.

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Answer:

x=15°

∡Q= 75°

Step-by-step explanation:

supplementary angles means the sum of the angles =180°

so, 5x+105°=180°

5x=75°

x=15°

∡Q= 75°

The value of the function f(a + 1) - f(a) is 2a - 2

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

In the given problem;

f(x) = x² - 3x

f(a + 1) - f(a) = ?

f(a + 1) = a² - a - 2

f(a) = a² - 3a

f(a + 1) - f(a) = a² - a - 2 -(a² - 3a)

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

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The intercepts of the line are x intercept: (4.3,0) y-intercept: (0,-13)​

From the question, we have the following parameters that can be used in our computation:

y+1=3(x − 4)

To calculate the x-intercept, we set y to 0

So, we have the following representation

0+1=3(x − 4)

This gives

x - 4 = 1/3

So, we have

x = 4.33

To calculate the y-intercept, we set x to 0

So, we have the following representation

y + 1 = 3(0 − 4)

This gives

y + 1 = -12

So, we have

y = -13

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If the ratio of cars to trucks on the lot is 11 to 33 and there are currently 51 trucks for sale, then there are 17 cars for sale

The ratio of cars to truck on the lot = 11 : 33

Total number of trucks for sale = 51 truck

Consider the number of cars for sale = x

Then the ratios will be

11/33 = x / 51

Cross multiply the terms in the equation

33x = 51 × 11

33x = 561

Move 33 to the right hand side of the equation

x = 561 / 33

Divide the terms

x = 17

Therefore, the number of cars does the dealer have for sale is 17

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Null hypothesis: Proportion of residents favoring annexation <= 72%. Alternative hypothesis: Proportion of residents favoring annexation > 72%

The null hypothesis is that the proportion of residents who favor annexation is equal to or less than 72%. The alternative hypothesis is that the proportion of residents who favor annexation is greater than 72%.

To determine if there is sufficient evidence to support the mayor's claim, a hypothesis test should be performed. A common approach is to use a one-sample proportion test. This test compares the proportion of residents who favor annexation in a sample to the hypothesized proportion of 0.72.

Assuming a significance level of 0.05, if the p-value is less than 0.05, then there is sufficient evidence to reject the null hypothesis and conclude that the proportion of residents who favor annexation is greater than 72%.

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The type of sampling that Huw is using is called Convenience Sampling.

Explanation:

Convenience sampling is a non-probability sampling technique where the sample is selected based on ease of access and availability. In Huw's case, he is administering the questionnaire to people who happen to be in the town centre, which is convenient for him. The sample is not selected randomly, and therefore does not accurately represent the population as a whole. Convenience sampling is often used in quick, informal surveys where the researcher does not have the resources or time to conduct a more rigorous, randomized sampling method.

Answer:

7

Step-by-step explanation:

about 45 of every 300 apples picked at the Newbury apple orchard are rotten, if 3560 apples were picked one week, about 534 many apples were rotten. We drew this answer with the help of algebra,

45/300 = x/3560

x = 3560*(45/300) = 534

At the same rate, about 534 rotten apples can be expected in the week's pickings.

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions. In algebra, we use numbers like 2, −7, 0.068 etc., which have a definite or fixed value. In algebra we use variables like x, y, and z along with numbers.

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The given equations having infinitely many solutions.

What is Solutions of system of equation?

A solution to a system of equations is a collection of variable values that satisfy all of the equations at the same time. To solve a system of equations, one must determine all of the sets of variable values that compose the system's solutions.

The solution to the system of equations y = -2x + 1 and 4x + 2y = -1 can be determined graphically by plotting both equations on the same set of axes and finding the points of intersection.

If there is exactly one point of intersection, then that point represents the unique solution to the system. If there are no points of intersection, then the system has no solution. If there are infinitely many points of intersection, then the system has infinitely many solutions.

Based on the information you provided, the system has two points of intersection: (0, -3) and (-3, 0). This means that the system has two solutions, and the solution set is the set of all points on the line that passes through these two points.

Therefore, The given equations having infinitely many solutions.

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Answer:

Step-by-step explanation:

To build a sequence, you have to create a rule. For example, if the rule is +2, then you add 2 to 10 to get 12, and then you add 2 to 12 to get 14, and so on. Your sequence would then be 10, 12, 14, 16, 18.

The probability that all four of the selected bolts are torqued to the proper limit is approximately 0.28.

To calculate the probability that all four of the selected bolts are torqued to the proper limit, we need to find the number of combinations of 4 bolts out of 20 that have been torqued to the proper limit.

Let's call the number of proper bolts n = 20 - 5 = 15.

The number of combinations of 4 proper bolts out of 15 is given by the binomial coefficient nCk, where n is the number of bolts and k is the number of bolts selected.

nCk = n! / (k! (n - k)!).

So, the number of combinations of 4 proper bolts out of 15 is:

15C4 = 15! / (4! (15 - 4)!) = 15! / (4! 11!) = 1365.

Therefore, the probability of selecting all 4 proper bolts out of 20 is:

P = number of combinations of 4 proper bolts / number of combinations of 4 bolts = 1365 / 20C4 = 1365 / 4845 = 0.28

So, the probability that all four of the selected bolts are torqued to the proper limit is approximately 0.28.

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Answer:

Point (-3, 3) is not a solution to the system of equations

2y+x=3

y=x+0

Step-by-step explanation:

2y + x = 3

y = x + 0

2(3) + (-3) = 3

6 - 3 = 3

3 = 3

The point works in the first equation.

3 = -3 + 0

3 = -3

The point does not work in the second equation.

Answer:

The value of z is 58    

Step-by-step explanation:

The mean is the average of a set of numbers.  Mean = (sum of the numbers)/(the number of numbers).

We are told that the mean of x+y+z is = 55.  

We can wriote this as:

 55 = (x+y+z)/3

We learn that x+y = 107.  So lets enter that number for x + y:

 55 = (x+y+z)/3

55 = ((x+y)+z)/3    

55 = ((107)+z)/3           [Substitution]

55 = (107+z)/3

165 = 107+z               [Multiply both sides by 3]

z = 58                       [Simplify]

CHECK:

Is the mean of x, y, and z 55?

55 = (x+y+z)/3  ?

55 = ((107)+z)/3 ?   [Since we know x+y = 107]

55 = ((107)+58)/3 ?  [Since z=58]

55 = (165)/3)  ?

55 = 55  YES  The value of z is 58    

Answer:

12.2 pints

Step-by-step explanation:

In all means add.  Add the two decimals together.

4.8 + 7.4

12.2 pints

The number of many different outfits Sophia has to choose from should be 16.

What is arithmetic?

Mathematical arithmetic is the study of the properties of the standard operations on numbers, such as addition, subtraction, multiplication, division, exponentiation, and root extraction.

Here, we have

Given: Sophia is trying to pick out an outfit for the first day of school. She can choose from 2 pairs of pants, 2 t-shirts, and 4 pairs of shoes.

She can choose from 2 pairs of pants, 2 t-shirts, and 4 pairs of shoes.

So here the number of distinct outfits should be like

= 2 × 4 × 2

= 16

Hence, the number of many different outfits Sophia has to choose from should be 16.

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Answer:16

Step-by-step explanation:Total outcomes

=

Total outcomes=

2‾

pants

×

2‾

t-shirts

×

4‾

shoes

pants

2

​

​

×

t-shirts

2

​

​

×

shoes

4

​

​

Fundamental counting principle

=

=

16

The secret number is 564 as we solve it by given question.

jack's favorite number is 836 so here we have number 836 and

jill subtracts a secret number from 836 and her answer is the smallest possible combination of all the digits from jack's favorite number

so here we have a number 836

let we subtract x from 836 to get a number which is smallest number by using 836

the number which we can make by using these 3 degits are

368, 386, 638, 683, 836, 863 anf from all these numbers the smallest number which can be using 836 is 368

as given in question we have 836 and we will subtract x and get 368 so

836 - x = 368

x = 836 - 368

x = 564

the secrets number is 564.

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Answer:  Choice D

Explanation:

The notation [tex]-\infty < \text{x} < \infty[/tex] says x is anything between negative infinity and positive infinity. Basically x is any real number. This is because the curve stretches forever to the left and right. Any number can be the x input.

After unit conversion of 24 in./s into ft/min the value will be 120

To measure and compare various things we use one term which is known as a unit. When all of the measuring units are the same, comparison is simple. Depending on their intended usage, different units can be categorized.

For example, for  length measurement we use units like:- meter, centimeter, inch, miles.

Given that,

A rate = 24 in./s

The value of rate in ft./min. = ?

It is known that,

1 feet = 12 inches

And 1 minute = 60 second

So,

1 inches = 1/12 feet

1 second  = 1/60 minute

⇒ 24 in./s

⇒  24 ((1/12)ft / (1/60)sec)

⇒ 24 × 60/12

⇒ 24 x 5

⇒ 120

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The updated positions are (5, -6) + (-2, 10) = (3, 4)

A vector is a mathematical concept that has both magnitude and direction. The vector's size is determined by size. An arrow-depicted line serves as this representation. The vector's magnitude is represented by the line's length, and its direction is shown by the arrow. additionally referred to as geometric, Euclidean, spatial, or just "vectors."

You can add the components of the vector to the corresponding components of the point to translate point (5, -6) based on vector V:(-2,10).

The updated positions are (5, -6) + (-2, 10) = (3, 4)

Thus, the translated message is (3, 4).

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