Which is true of the slopes of parallel lines

Answer:

x=7

Step-by-step explanation:

The two triangles are congruent so the equation is

9x-15=7x-1

9x-7x=15-1

2x=14

x=7

Answer:

x=7

Step-by-step explanation:

9x-15=7x-1

Answer:

Step-by-step explanation:

Which of the following angles have equal measure when a pair of parallel lines is crossed by a transversal?

When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles . When the lines are parallel, the corresponding angles are congruent .

Answer:

12.5 cents per box

Step-by-step explanation:

First, find the price difference of the cases.

11.99 - 10.49 = $1.50

We want to find the money saved per box so divide $1.50 by 12.

1.50/12 = 12.5 cents

Answer:

x=90 y=33

Step-by-step explanation:

similar, so you can reflect x and y across, and x is altitude so x=90

90+y+47=180

90+y=123

y=33

Answer:

288xy

Step-by-step explanation:

First, you multiply 12 by 24 and you get 288. Next, you can't forget the variables, so you add those to the end and get, 288xy.

Answer:

B. 7−10; 11−14; 15−18; 19−22

Step-by-step explanation:

Answer: is the same as asking "How much is 25 divided by 2?" Thus, the answer can be calculated as follows: 25/2 = 12.5. "How many times does 2 go into 25?" is also the same as asking "What (x) do you multiply by 2 to get 25?" We solve the problem with an easy algebra equation:

2(x) = 25

x = 12.5

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

=2.5(6*4)/6

=2.5*4(6 and 6 gets cancel)

=10

The slope of the tangent line to the curve defined by 9xy + xy = 10 at the point (1, 1) is -1.

To find the slope of the tangent line to the curve defined by the equation 9xy + xy = 10 at the point (1, 1), we can use implicit differentiation.

Let's start by differentiating both sides of the equation with respect to x.

Differentiating the left side of the equation:

d/dx(9xy + xy) = d/dx(10)

Using the product rule for differentiation, we differentiate each term separately:

d/dx(9xy) + d/dx(xy) = 0

Now, let's calculate the derivatives of each term:

For the first term, 9xy:

Using the product rule, we have:

d/dx(9xy) = 9y * dx/dx + 9x * dy/dx

= 9y + 9x * dy/dx

For the second term, xy:

Using the product rule again, we have:

d/dx(xy) = y * dx/dx + x * dy/dx

= y + x * dy/dx

Substituting these results back into our equation, we get:

9y + 9x * dy/dx + y + x * dy/dx = 0

Combining like terms, we have:

10y + 10x * dy/dx = 0

Now, let's find the value of dy/dx at the point (1, 1). We substitute x = 1 and y = 1 into the equation:

10(1) + 10(1) * dy/dx = 0

Simplifying further:

10 + 10 * dy/dx = 0

Dividing both sides by 10:

1 + dy/dx = 0

Finally, subtracting 1 from both sides:

dy/dx = -1

Therefore, the slope of the tangent line to the curve defined by 9xy + xy = 10 at the point (1, 1) is -1.

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The even integers are 10,12 and 14.

Concept:  An integer is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.

Let x,x+2,x+4 be the least, middle and greatest integer respectively.

According to the question,

15< x+x+2+x+4< 21

(3x+6)/2> 15      and    (3x+6)/2< 21

30< 3x+6                      3x+6> 42

24<3x                            3x<36

8<x                                x>12

x=10

x+2=12

x+4=14

Hence, The even integers are 10,12 and 14.

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Therefore, 10/12 cups of fruit are required for the dish, which can be expressed as 5/6 cups.

An element of a whole is a portion. The number is represented mathematically as a fraction, where the numerator and denominator are split. Both are numbers in a straightforward fraction. A fraction appears in the sum or base of a complicated fraction. The numerator of a perfect proportion is smaller than the denominator.

Based on the given conditions, formulate: \(\frac{2}{4} +\frac{1}{3}\)

Cross out the common factor: \(\frac{1}{2}+\frac{1}{3}\)

Rewrite fractions using the Least Common Denominator: \(\frac{3+2}{6}\)

Calculate the sum or difference: \(\frac{5}{6}\)

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The probability that the sample average is more than 8.47 is 0.4406 if the pH level of the reservoir is ok

To calculate this, we will use a standard normal distribution table and the Z-score formula.

First, we need to calculate the Z-score for the sample average of 8.47. This is done by using the Z-score formula:

Z-score = (x - mean)/standard deviation

where x is the sample average, mean is the average of all samples, and standard deviation is the standard deviation of all samples.


In this case, the Z-score is:

Z-score = (8.47 - 8.50)/0.22 = -0.14


Then, we need to look up the Z-score in a standard normal distribution table. The probability of the sample average being more than 8.47 is equal to 1 minus the Z-score probability. So, in this case, the probability of the sample average being more than 8.47 is equal to 1 - 0.5594 = 0.4406.

Therefore, the probability that the sample average is more than 8.47 is 0.4406 if the pH level of the reservoir is ok.

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Answer:

\(x = 26.25\) inches

Step-by-step explanation:

Since we know the triangles are similar, we can simply set up ratios to find the length of side length 'x'.

\(\frac{15.75}{x} = \frac{9}{15}\)

Cross multiply:

\(236.25 = 9x\)

Divide both sides by '9' to solve for 'x':

\(\frac{236.25}{9} = \frac{9x}{9}\)

\(x = 26.25\)

Therefore, side length 'x' equals 26.25 in.

Based on the information, it noted that the brass section has more possible arrangement.

It should be noted that a factor pair simply means the set of two factors that when multiplied will able to give a particular product.

It should be noted that from the information, thr woodwinds section of the marching band has 38 members.

This can be written as:

38 = 1 × 38

38 = 2 × 19

These are 4 possible arrangement. These are 1 row of 38, 38 rows of 1. 2 rows of 19 and 19 rows of 2. On the brass section, there are 8 arrangements.

Therefore, the possible arrangement for the brass section is more.

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Answer:

10

Step-by-step explanation:

\(1. \: \frac{56}{8} + 3 \\ 2. \: 7 + 3 \\ 3. \: 10\)

According to the given statement The faster computer will take 2 minutes to send out the company's email on its own.

To solve this problem, let's assign variables to the given information. Let "x" represent the time it takes the slower computer to send out the company's email on its own, and let "y" represent the time it takes both computers working together to send out the email.

According to the problem, it takes two computers "y" minutes to send out the email, and it takes the slower computer "x" minutes to do the job on its own.

Since the two computers are working together, we can set up the following equation: 1/x + 1/y = 1/t, where "t" represents the time it takes the faster computer to do the job on its own.

Substituting the given values into the equation, we have: 1/x + 1/y = 1/2y

To find the value of "t", we need to solve for "y" in terms of "x". Multiply both sides of the equation by 2xy to eliminate the denominators:

2y + 2x = xy

Rearranging the equation, we get:

xy - 2y - 2x = 0

Now, let's factor the equation:

y(x - 2) - 2(x - 2) = 0

Simplifying further:

(x - 2)(y - 2) = 0

Since we are looking for the time it takes the faster computer to do the job on its own, we disregard the solution (y - 2) = 0, which gives us y = 2.

Therefore, the faster computer will take 2 minutes to send out the company's email on its own.

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Answer:

\(\boxed{\sf n= \dfrac{2}{5} ,\: n=1}\)

Step-by-step explanation:

\(\rightarrow 5n^2 = 7n -2\)

\(\rightarrow 5n^2 - 7n +2=0\)

\(\rightarrow 5n^2 - 5n -2n+2=0\)

\(\rightarrow 5n(n - 1) -2(n-1)=0\)

\(\rightarrow (5n-2)(n-1)=0\)

\(\rightarrow 5n-2= 0,\: n-1=0\)

\(\rightarrow 5n= 2,\: n=1\)

\(\rightarrow n= \dfrac{2}{5} ,\: n=1\)

Step-by-step explanation:

\(\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= \dfrac{2}{5} \:or~ n=1}\)

By Using the table to work out the values of a , b , c , and d. X y = 2 x + 1 − 3 a − 2 − 3 − 1 b 0 1 1 c 2 d a = b = c = d =

Therefore, The solutions are : a = -3, b = 0, c = 6, d = 9

Equation:

In mathematics, an equation is an expression that indicates equality of two expressions by connecting them with the equal sign = . The word "equation" and related words in other languages ​​can have slightly different meanings. For example, in French an equation is defined as containing one or more variables, whereas in English a well-formed formula consisting of two expressions connected by an equal sign is an equation.

Given:

This table;

x             y = 3x+3

-3                -6

-2                 a

-1                  b

0                 3

1                  c

2                 d

To Find:

Values of a, b, c and d

Consider the 2nd row,

x = -2, y = a

Putting the values in the equation,

we get,

   a = 3(-2) + 3

⇒ a = -3

Consider the 3rd row,

x = -1, y = b

Putting the values in the equation,

we get,

   b = 3(-1) + 3

⇒ b = 0

Consider the 5th row,

x = 1, y = c

Putting the values in the equation,

   c = 3(1) + 3

⇒ c = 6

Consider the 6th row,

x = 2, y = d

   d = 3(2) + 3

⇒ d = 9

The final answer is,

a = -3, b = 0, c = 6, d = 9.

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Answer:

Step-by-step explanation:2+2

A set of treatment and control groups for a retrospective study on the effects of endocrine disruptors on humans a group of children with mothers exposed to PCBs during pregnancy and a group of children who were exposed to DDT after they were born (option c).

In a retrospective study, researchers investigate the effects of endocrine disruptors on humans by analyzing past data and observing correlations. To ensure reliable findings, it is crucial to establish appropriate treatment and control groups. These groups are designed to compare individuals who have been exposed to different levels or types of endocrine disruptors, allowing researchers to assess the effects accurately. Let's explore the potential treatment and control groups for such a study.

A group of children with mothers exposed to PCBs during pregnancy and a group of children who were exposed to DDT after they were born:

In this case, the treatment group would consist of children whose mothers were exposed to PCBs during pregnancy. The control group, on the other hand, would include children who were exposed to DDT after birth. PCBs and DDT are both endocrine disruptors, but by comparing these two groups, researchers can examine the effects of prenatal exposure (PCBs) versus postnatal exposure (DDT).

Hence the correct option is (c).

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Complete Question

Which could be a set of treatment and control groups for a retrospective study on the effects of endocrine disruptors on humans?

(a) A group of farmers that are planning to spray crops with atrazine and a group of farmers that are planning to use organic pesticides,

(b) A group of construction workers that have been exposed to asbestos and a group of construction workers that have been exposed to PCBs,

(c) A group of children with mothers exposed to PCBs during pregnancy and a group of children who were exposed to DDT after they were born,

(d) Members of a town that was downwind of a commercial farm that sprayed pesticides and members of a town that was downwind of an organic farm,

(e) Humans raised when DDT was used and humans raised after DDT was no longer used.

(a) The set of integers less than 100:

This set is finite because it contains a finite number of integers, specifically 99 integers (-99 to 0, and 1 to 99).

(b) The set of integers that are multiples of 7:

This set is countably infinite. To exhibit a bijection between this set and the natural numbers, we can define a function f: N -> Z, where N is the set of natural numbers and Z is the set of integers. The function f(n) = 7n is a valid bijection.

To show that f is well-defined, we need to demonstrate that each natural number n corresponds to a unique integer that is a multiple of 7. Since every natural number can be multiplied by 7 to obtain a unique multiple of 7, this function is well-defined.

To prove that f is a bijection, we need to show both injectivity and surjectivity.

Injectivity: Let's assume f(m) = f(n), where m and n are natural numbers. If f(m) = f(n), it means that 7m = 7n. Dividing both sides of the equation by 7, we get m = n. Therefore, f is injective.

Surjectivity: For any integer x that is a multiple of 7, we can find a natural number n such that f(n) = x. Specifically, if x = 7n, then f(n) = 7n = x. Thus, f is surjective.

Since f is both injective and surjective, it is a bijection between the natural numbers and the set of integers that are multiples of 7.

(c) The set of odd negative integers:

This set is countably infinite. To exhibit a bijection between this set and the natural numbers, we can define a function g: N -> Z, where N is the set of natural numbers and Z is the set of integers. The function g(n) = -2n - 1 is a valid bijection.

To show that g is well-defined, we need to demonstrate that each natural number n corresponds to a unique odd negative integer. By plugging in natural numbers into the function g, we obtain a unique odd negative integer. Therefore, g is well-defined.

To prove that g is a bijection, we need to show both injectivity and surjectivity.

Injectivity: Let's assume g(m) = g(n), where m and n are natural numbers. If g(m) = g(n), it means that -2m - 1 = -2n - 1. Rearranging the equation, we get -2m = -2n, and dividing both sides by -2, we have m = n. Thus, g is injective.

Surjectivity: For any odd negative integer x, we can find a natural number n such that g(n) = x. Specifically, if x = -2n - 1, then g(n) = -2n - 1 = x. Therefore, g is surjective.

Since g is both injective and surjective, it is a bijection between the natural numbers and the set of odd negative integers.

(d) The set A x Z₀, where A = {2, 3}:

This set is countably infinite. To exhibit a bijection between this set and the natural numbers, we can define a function h: N -> A x Z₀, where N is the set of natural numbers.

To describe the function, we can use the method of interleaving. We can construct a sequence of pairs (a, b) such that a ∈ A and b ∈ Z₀ by interleaving the elements of A and the

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Answer:

a Car rents a compact car for $24.95 per day plus $0.23 per mile. Cargo Rent a Car rents a compact car for $ 22.95 per day plus $0.31

Step-by-step explanation:

because its plus

25 miles

Step-by-step explanation:

Answer:

y = 15

Step-by-step explanation:

It is given that y = kx (Note the green colored text).

Plug in the corresponding numbers to the corresponding variables:

x = 5 ; k = 3 ; y

y = kx

y = (3)(5)

Simplify by multiplying 3 with 5:

y = 3 * 5

y = 15.

15 is your answer for y:

~

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Answer:

a = 2

Step-by-step explanation:

Note that a point uses (x , y).

y = 1

x = a

Plug in 1 for y in the equation, and a for x:

y = 3x - 5

1 = 3a - 5

Isolate the variable, a. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First add 5 to both sides:

1 (+5) = 3a - 5 (+5)

1 + 5 = 3a

6 = 3a

Next, divide 3 from both sides:

(6)/3 = (3a)/3

a = 6/3

a = 2

2 is your value for a.

~

Therefore, the series does not satisfy the necessary condition for convergence, which states that the terms should approach zero.

To determine whether the series converges or diverges, we need to examine the behavior of the terms as the series progresses. Let's analyze the given series:

=2/5 - 2/6 + 2/7 - 2/8 + 2/9

We can rewrite the series by grouping the terms:

=(2/5 - 2/6) + (2/7 - 2/8) + 2/9

To determine the convergence or divergence of the series, we need to evaluate the limit of the terms as the series progresses.

Term 1: 2/5 - 2/6

= (12 - 10)/30

= 2/30

= 1/15

Term 2: 2/7 - 2/8

= (16 - 14)/56

= 2/56

= 1/28

Term 3: 2/9

As we can see, the terms are positive and decreasing as the series progresses. However, the terms do not approach zero.

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By finding the proportional relation between x and y, we will see that when x = 16, we have y = 32.

If y varies directly with x, then we can write the relation as:

y = k*x

Where k is the constant of proportionality.

First, we know that when x = 4, we have y = 8, replacing that we get:

8 = k*4

Solving for k, we get:

k = 8/4 = 2.

Then the relation between x and y is:

y = 2*x

When x = 16, we have:

y = 2*16 = 32

Then the correct option is a.

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Answer:

Median: 48

Range: 18

Step-by-step explanation:

The range: is calculated by subtracting the lowest value from the highest value

The median: Arrange the data points from smallest to largest. If the number of data points is odd, the median is the middle data point in the list. If the number of data points is even, the median is the average of the two middle data points in the list.