Which expression is equivalent to |8|+|-7|?

Answer:

  addition property of equality

Step-by-step explanation:

You want the justification for step 1 in the solution process for -22 - x = 14 + 6x.

No solution process steps are shown, but we can speculate what they might be.

The goal is to separate constant terms and variable terms. This can be done several ways, but generally consists of adding the same thing to both sides of the equation.

Often, you're told to collect the variable terms first. Some prefer to do that so the variable terms are on the left side of the equal sign. Others prefer to do that so the result has a positive coefficient for the variable term. Taking the latter tack, we want to add x (the opposite of -x) to both sides of the equation:

  -22 -x +x = 14 +6x +x . . . . . x added to both sides

  -22 = 14 +7x . . . . . . . simplified

The justification for this step is the addition property of equality. That property allows you to add the same thing to both sides of an equation without changing the values of the variables.

__

Additional comment

Step 2 would be to add -14 to both sides, giving you ...

  -36 = 7x . . . . . . . . add -14; addition property of equality

If you like, you can do both of these additions in one step:

  -22 -x +(x -14) = 14 +6x +(x -14) . . . add(x -14); addition property of equality

  -36 = 7x . . . . . . simplified

Step 3 is to divide by the coefficient of the variable.

  -36/7 = (7x)/7 . . . . division property of equality

  -5 1/7 = x . . . . . . . simplified. This is the solution.

The usual procedure takes 3 steps, so this is called a "3-step equation."

Note that we choose for the variable coefficient to be positive, because we judge arithmetic with positive numbers to be less error-prone. If you collect the variable terms on the left, you get ...

   -7x = 36

so have to divide by -7. This should not be an issue if you're careful with your arithmetic, but many find dealing with negative numbers to be a challenge.

Answer:

Thus, the equation of line for point (-1, 2)  is y = x + 3.

Step-by-step explanation:

Answer:

The equation of the line is y = x + 3.

Step-by-step explanation:

A line that is parallel to y=x+4 and passes through the point (-1,2) will have the same slope as y=x+4. The slope of y=x+4 is 1, so the equation of the line will be in the form y = mx + b, where m=1. To find b, we can plug in x = -1 and y = 2 into the equation and solve for b.

y = mx + b

y = 1 * -1 + b

y = -1 + b

b = y + 1

b = 2 + 1

b = 3

Answer:   SSS

Step-by-step explanation:

SSS congruence postulate: If all the three sides of one triangle are equivalent to the corresponding three sides of the another triangle, then the two triangles are congruent.

In the given figure, we have

ΔPQR and ΔPQS such that

PQ = PQ      [common]

PR= PS         [Given]

RQ = QS      [Given]

By SSS congruence postulate,

ΔPQR ≅ΔPQS

So, the right choice : "SSS"

Answer: 15.77

Step-by-step explanation: We know that Milans car had 19.57 gallons of fuel, so I subtracted 19.57 - 3.8 to get my answer.

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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The answer is B 0.3 because its 3/10 and all of the others is lesss

The sample of given data is Sample 1: 1, 2, 3, 4, 5 Sample 2: 6, 7, 8, 9, 10

b)Sample 1: 1, 2, 3, 4, 5 Sample 2: 6, 7, 8, 9, 10

(a) An example of data with SS(between) = 0 and SS(within) > 0 could be the following:

Sample 1: 1, 2, 3, 4, 5

Sample 2: 6, 7, 8, 9, 10

Sample 3: 11, 12, 13, 14, 15

In this example, the means of each sample are all different from each other, but the grand mean (8) is equal to the mean of each sample. Therefore, there is no variability between the means of the samples, resulting in SS(between) = 0. However, there is still variability within each sample, resulting in SS(within) > 0.

(b) An example of data with SS(between) > 0 and SS(within) = 0 could be the following:

Sample 1: 1, 2, 3, 4, 5

Sample 2: 6, 7, 8, 9, 10

Sample 3: 11, 12, 13, 14, 15

In this example, the means of each sample are all the same (8), but the values within each sample are all different from each other. Therefore, there is variability between the means of the samples, resulting in SS(between) > 0. However, there is no variability within each sample, resulting in SS(within) = 0.

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The round trip distance in miles from city 1 to city 3 is given as follows:

30 miles.

The matrix corresponding to the distances between each of the cities is given by the image presented at the end of the answer.

Looking at row 1, column 3, we have that the distance from city 1 to city 3 is of 15 miles.

For the round trip distance, we have to go back from city 3 to city 1, more 15 miles, hence the distance is given as follows:

2 x 15 = 30 miles.

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Answer:

Step-by-step explanation:

To find the height of the sandbox, we can use the formula for the volume of a rectangular prism: V = l × w × h, where V is the volume, l is the length, w is the width, and h is the height.

We know that the volume of the sandbox is 32,188.04 in³, the length is 59.3 inches, and the width is 59 inches. We can plug in these values and solve for the height:

32,188.04 in³ = 59.3 in × 59 in × h

Dividing both sides by (59.3 * 59) inches gives:

h = 32,188.04 in³ / (59.3 in × 59 in) h ≈ 9.2 inches

Therefore, the height needed to reach the desired volume is approximately 9.2 inches.

Answer: 9.2 inches.

Step-by-step explanation:

Volume is l x w x h

We know that 59.3 x 59 = 3498.7

Then, to find what we need to multiply 3498.7 by, we do 32,188.04 (the desired volume) divided by 3498.7 which gets us 9.2

To check our work, we do 3498.7 x 9.2, which equals 32,188.04

Hope I could help!

Based on the data, the estimated number of lemon candies in the bag of 100 assorted candies is about 19.

In mathematics, proportion refers to the relationship between two quantities that are equivalent or have a constant ratio. It is usually expressed as a fraction or a ratio. For example, if a recipe calls for 2 cups of flour and 1 cup of water, the proportion of flour to water is 2:1 or 2/1. Proportions are used in a variety of mathematical and real-world situations, such as solving problems involving ratios, rates, and percentages.

In the given question,

We can use a simple proportion to estimate the number of lemon candies in the bag. We know that Ridgette handed out a total of 6 lemon candies out of a total of candies. Therefore, the proportion of lemon candies in the bag is:

6/total candies = number of lemon candies/100

We can cross-multiply to solve for the number of lemon candies:

number of lemon candies = 6 x 100 / total candies

We can also use the information about the other flavors to estimate the total number of candies in the bag. The total number of candies is:

total candies = lemon + orange + grape + cherry

Using the information from the table, we can estimate the total number of candies:

total candies = 6 + 5 + 8 + 13 = 32

Therefore, the estimated number of lemon candies in the bag is:

number of lemon candies = 6 x 100 / 32 = 18.75

We can round this to the nearest whole number to estimate that there were about 19 lemon candies in the bag of 100 assorted candies.

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The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of periods is given as follows:

5 + 6 + 4 = 15.

The frequency of each class is given as follows:

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Given:-

The denominator of a fraction is one more than three times and if 8 is added to the neumerator and the demominator then the solution is 1/2.

To find the equation.

So now the given fraction is,

So now we add. so we get,

So now we get,

So this is the required solution.

Answer:

2×2×7=28

Step-by-step explanation:

28÷2=14

14÷2=7

Prime numbers 2, 2, and 7 make 28

The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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In order for the relationship zyx ~ wvu to be correct, the following conditions must be true:

Corresponding angles are congruent: The angles formed by matching vertices should have the same measures in both triangles. This ensures that the corresponding angles are equivalent.

Corresponding sides are proportional: The lengths of the sides that connect the corresponding vertices of the triangles should have a consistent ratio. This implies that the corresponding sides are proportional to each other.

These conditions are based on the definition of similarity between two triangles. If both the corresponding angles are congruent and the corresponding sides are proportional, then the triangles zyx and wvu are considered similar (denoted by ~).

Therefore, in order for zyx ~ wvu to be correct, the congruence of corresponding angles and the proportionality of corresponding sides must hold true.

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Answer:

Option 2: 1 teaspoon of baking soda per 1 cup of flour

Option 3: ½ teaspoon of salt per 1 teaspoon of baking soda

Step-by-step explanation:

The recipe has 3 ingredients mixed in the following ratio =>

½ of a cup of flour : ½ of a teaspoon of baking soda : ¼ of teaspoon of salt

Let's analyse each given options to see which rate is correct or not using the above ratio that makes a recipe:

Option 1 => 2 teaspoon of salt : 1 teaspoon of baking soda.

¼ salt : ½ baking soda

2 salt : x baking soda

Thus, ¼ / ½ = ²/x

Cross multiply

¼*x = ½*2

x/4 = 1

x = 4

Therefore, 2 teaspoon of salt will need 4 teaspoon of baking soda not 1.

Option 2 => 1 teaspoon of baking soda : 1 cup of floor.

½ baking soda : ½ flour

1 baking soda : x flour

Thus, ½ / ½ = ¹/x

Cross multiply

½*x = ½*1

x/2 = ½

Multiply both sides by 2

x = ½*2

x = 1

Therefore, 1 teaspoon of baking soda will need 1 cup of floor. This is correct.

Option 3 => ½ teaspoon of salt : 1 teaspoon of baking soda.

¼ salt : ½ baking soda

½ salt : x baking soda

Thus, ¼ / ½ = ½/x

Cross multiply

¼*x = ½*½

x/4 = ¼

Multiply both sides by 4

x = ¼*4

x = 1

Therefore, ½ teaspoon of salt will need 1 teaspoon of baking soda. This is correct.

Option 4 => 1 teaspoon of baking soda : 2 teaspoon of salt.

½ baking soda : ¼ salt

1 baking soda : x salt

Thus, ½ / ¼ = 1/x

Cross multiply

½*x = ¼*1

x/2 = ¼

Multiply both sides by2

x = ¼*2

x = ½

Therefore, 1 teaspoon of baking soda will need ½ teaspoon of salt not 2.

Option 5 => 2 teaspoon of salt : 1 cup of flour

¼ salt : ½ flour

2 salt : x flour

Thus, ¼ / ½ = ²/x

Cross multiply

¼*x = ½*2

x/4 = 1

x = 4

Therefore, 2 teaspoon of salt will need 4 cup of flour not 1.

The correct options are option 2 and option 3.

Answer:

x = -5/3y + 15

Step-by-step explanation:

Step 1: Subtract -5y from both sides.

3x+5y+−5y=45+−5y

3x=−5y+45

Step 2: Divide both sides by 3.

3x divided by 3 = −5y+45 divided by 3

x = -5/3y + 15

Hope this helps you

80

9 to 1 is equivalent to 72 to 8 and 72+8=80

Answer:

which one substitution or elimination

Step-by-step explanation:

Substitution: (-1,-3 )

Elimination: (-1,-3)

i hope this helps you :)

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Answer:

3(x+2) = 27.

Step-by-step explanation:

Subtracting 6 from both sides of the equation, we get:

3x + 6 - 6 = 27 - 6

Simplifying:

3x = 21

Dividing both sides by 3:

x = 7

So the equation equivalent to 3x+6=27 is:

3(x+2) = 3(7+2) = 3(9) = 27

Therefore, the answer is 3(x+2) = 27.

The Volume of the box is 3.75in³

The volume of the box is dependent on the volume of the cube in it.

To obtain the volume of a cube, we use the relation, V = s³

s = side of the cube

Volume = 0.5³ = 0.125 in³

Number of cubes in box = 30

Volume of each cube × Number of cubes

0.125 × 30 = 3.75 in³

Hence, the volume of the box is 3.75in³

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\(0.0008 = 8 \times 10 {}^{ - 4} \\ \\ \frac{8 \times 10 {}^{ - 4} }{2 \times 10 {}^{ - 6} } \\ \\ 4 \times 10 {}^{6 - 4} \\ \\ 4\times 10^2\)

Using the concept of addition of numbers, he made a deposit of $887

The addition is the term used to describe adding two or more numbers together. The addition is denoted using the plus sign ‘+‘ such as the addition of any number.

In this problem, to determine how much he has in his account, we may simply sum every deposit he made in the account.

The amount he has in his account is ;

40 + 50 + 35 + 8(50) + 12(20) + 22(1) + 100 = 125 + 400 + 240 + 22 + 100

This total amount after summing everything up will be $887

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The completed list of numbers would be: 1, 1, 1, 2, 1, 4, 1, 2

By examining the given list of numbers 1, 1, 1, 2, 1, 4, 1, we can observe a pattern emerging.

The pattern seems to involve alternating sequences. The first sequence is the number 1 repeated three times (1, 1, 1). The second sequence is a number that follows the pattern of increasing by 1 each time (2). The third sequence is the number 1 repeated once (1). The fourth sequence is a number that follows the pattern of doubling each time (4). This pattern of alternating sequences continues.

Based on this pattern, we can predict that the next number in the sequence will follow the alternating sequence pattern. Since the last number in the sequence is 1, the next sequence will involve a number that follows the pattern of increasing by 1. Therefore, the next number in the sequence would be:

1 + 1 = 2

Hence, based on the observed pattern, the next number in the sequence is 2.

Therefore, the completed list of numbers would be:

1, 1, 1, 2, 1, 4, 1, 2

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Answer:

37

Step-by-step explanation:

x=-4

=2(5-(-4)2+1

=2(5+4)2+1

=2(9)2+1

=18(2)+1

=36+1

=37

Answer:

 \(\lim_{x \to\frac{\pi }{4} } (3x-tanx)\) =  \(3(\frac{\pi }{4} )\)

Step-by-step explanation:

Explanation:-

Given that

         \(\lim_{x \to\frac{\pi }{4} } (3x-tanx)\)

  =  \(\lim_{x \to\frac{\pi }{4} } (3x) - \lim_{x \to\frac{\pi }{4} } tanx)\)

 = \(3(\frac{\pi }{4} )+tan(\frac{\pi }{4} )\)

=  \(3(\frac{\pi }{4} )+ 1 )\)

=  \(3(\frac{\pi }{4} )\)

Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

Answer:

First blank is 4, second blank is 0

Step-by-step explanation:

divide it :)

Answer:

Yellow box #1=0

Yellow box #1=4

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

A division is a process of splitting a specific amount into equal parts.

We have to find 3x³-2x²+7x+9 divided by x²-3x

3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.

The steps to solve this are given below.

Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next digit of the dividend (if present).

Step 5: Repeat the same process.

Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

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