what is the slope of the line that passes through the points (2,0) and(32,-5)?

Additive inverse property of real numbers was used to transition from step 3 to step 4

The property of real numbers used to transition from Step 3 to Step 4 is the additive inverse property or the property of adding the opposite. The additive inverse property states that for any real number a, there exists an additive inverse -a, such that a + (-a) = 0. In other words, adding the opposite of a number results in the sum being zero.

In Step 3 of the given expression, we have "12 + (-12) + 6x." Notice that "-12" is the opposite of "12." To simplify this expression further, we can apply the additive inverse property by combining the positive and negative numbers.

Adding 12 and its additive inverse (-12) results in 0, according to the additive inverse property. So, in Step 4, we replace "12 + (-12)" with "0." By applying the additive inverse property, the expression simplifies to "0 + 6x," which can be further simplified to just "6x."

The use of the additive inverse property is crucial in algebraic simplifications as it allows us to eliminate terms that add up to zero. This property helps streamline calculations and reduce complex expressions to simpler forms.

Overall, the transition from Step 3 to Step 4 in the given expression utilizes the additive inverse property to eliminate the sum of opposite numbers and simplify the expression to its final form, which is "6x."

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The value of X is 3.25

Look at the attached picture

Hope it will help you

Good luck on your assignment

Ummm I think the answer is 9

The computation of the increased in salary is $500.

Here, we have,

Explanation:

Data provided in the question

Salary for the first year = $50,000

CPI increase during the year = 4%

Overstated inflation = 1% i.e. 5%

The computation of the increased in salary is shown below:

= Salary of the first year × inflation rate - salary of the first year × CPI increase during the year

= $50,000 × 5% - $50,000 × 4%

= $2,500 - $2,000

= $500

Hence, The computation of the increased in salary is $500.

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complete question:

Mark's wage contract specifies a $50,000 salary for the first year, and specifies a salary increase equal to the percentage increase in the CPI during the second year. The increase in the CPI during the year was 4.0%. If the CPI overstates inflation by 1.0% (that is, the actual price increase was 3% and not 4%), at the end of the first year Mark's salary increased by $________ more than it would have without the upward bias.

Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

Answer:

The line is parallel to y + x =3

=> y = -x+3

the slope = -1

passes (-12, 0)

the equation would be :

y-0 = -1(x+12)

y = -x -12 Y=-x+12

Turn into mx+b form.

Y=-x+3

Plug in (-12,0)

0=-12+b

b=12

y=-x+12

It is negative X, because the slope has to be the same since it is paralle

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

A is impossible.

the absolute value of something is always a positive number. the negative sign before it makes it an always negative number. so, this can never be equal to +5.

B is impossible for the same reasons.

the absolute value is always positive and can never be equal to -5.

C is impossible again for the same reasons.

the negative absolute value of x is always negative. subtracting 2 from that makes the result even more negative. this can never be equal to +5.

D is the only fitting option.

we have two extreme points x = -3 and x = 7.

putting them into the equation gives us for x = -3

-|-3 - 2| = -|-5| = -5 => correct

and for x = 7

-|7 - 2| = -|5| = -5 => correct

The correct answer is -|x - 2| = -5

The completed table is as follows:

x | y

8 | 0

9 | 3

36 | 6

8 | 2√2

8 | -2√2

To solve the equation x = y², we can substitute the values of x and find the corresponding values of y in the table.

Let's fill in the missing entries one by one:

For x = 9, we need to find y. Since x = y², we take the square root of both sides to solve for y. So, y = √9 = 3. Therefore, the corresponding value for y is 3.

For x = 36, again, we apply the square root operation to both sides, giving y = √36 = 6. Hence, the corresponding value for y is 6.

For y = 2√2, we need to find x. Squaring both sides of the equation, we have \(x = (2\sqrt2)^2 = 4 \times 2 = 8\). Therefore, the corresponding value for x is 8.

For y = -2√2, we follow the same process as in step 3. Squaring both sides, we get \(x = (-2\sqrt2)^2 = 4 \times 2 = 8\). So, the corresponding value for x is 8.

After filling in the missing entries, the completed table is as follows:

x | y

8 | 0

9 | 3

36 | 6

8 | 2√2

8 | -2√2

Please note that there can be multiple valid solutions for this equation, but this table provides one possible solution.

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Answer:

27.50(80) is 2,200

2,200-396-175-264= 1,365

I think this is how u do it correct me if I'm wrong

The given geometric sequence has the common ratio, r = -2/3, and the value of the 4th term, a₄ = -8/3.

A geometric sequence is a special series where every term is the product of the previous term and a common ratio.

The first term of a geometric sequence is represented as a, the common ratio as r, and the n-th term as aₙ, which is calculated as, aₙ = a.rⁿ⁻¹.

In the question, we are asked to find the common ratio and the 4th term of the geometric sequence, 9, -6, 4, ........

The first term of the sequence, a = 9.

The second term of the sequence, a₂ = -6.

By the formula of the n-th term, aₙ = a.rⁿ⁻¹, we can show that:

a₂ = a.r²⁻¹.

Substituting the values, we get:

-6 = 9(r²⁻¹),

or, r²⁻¹ = -6/9,

or, r = -2/3.

Thus, the common ratio of the given geometric sequence is -2/3.

The 4th term can be calculated using the formula of the n-th term, aₙ = a.rⁿ⁻¹ as:

a₄ = a.r⁴⁻¹ = a.r³.

Substituting the values, we get:

a₄ = 9(-2/3)³,

or, a₄ = 9.(-8/27),

or, a₄ = -8/3.

Thus, the 4th term of the given geometric sequence is -8/3.

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From the given information, we can formulate the following expression:

Money saved = initial savings + earnings

We know that Josie initially had $5 and that she earns $0.5 per chore, then we can rewrite the above equation, like this:

Money saved = $5 + $0.5x

We can call "y" to the money saved:

y = 5 + 0.5x, in this case, x is the number of chores that she completes.

In this case, we have a linear equation, then its slope is the number that is multiplied by the independent variable "x" that is 0.5, in this scenario the slope represents the pay that she receives for each chore.

The y-intercept is the number that is being added to the 0.5x term, that is $5, it is the initial amount of money saved by Josie, then that's what the y-intercept represents in this scenario.

In order to graph a linear equation we just need to find two points of the graph, then we join them with the line, we can specify the points of the line by replacing some values of x and then calculating the corresponding value of y, like this:

• When x equals 0

y = 5 + 0.5*0

y = 5 + 0

y = 5

Then, one point of the line is located at (0,5)

• When x equals 18

y = 5 + 0.5*18

y = 5 + 9

y = 14

Then, another point of the line is located at (18,9)

Now we can graph the line as follows:

Given:

Number of video players without defects out of 400 = 398

Let's predict the number of video players that will have defects out of 2000 video players.

To predict the number of video players that are likely to have no defects out of 2000 video players, we have:

Let's evaluate the expression:

Therefore, 1990 video players in the shipment are likely to have no defects.

ANSWER:

1990

The line of best fit for the data in this problem is given as follows:

y = -0.5x + 60.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

Two points on the scatter plot are given as follows:

(30, 45) and (60, 30).

When x increases by 30, y decays by 15, hence the slope m is given as follows:

m = -15/30

m = -0.5.

Hence:

y = -0.5x + b.

When x = 30, y = 45, hence the intercept b is obtained as follows:

45 = -15 + b

b = 60.

Thus the function is given as follows:

y = -0.5x + 60.

The data is given by the image presented at the end of the answer, and the problem asks for the line of best fit for the data.

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Answer:

7.85 units is your answer :)

Step-by-step explanation:

To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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The original price of the refrigerator was $400.

The statement "Julio bought a refrigerator on sale for $200 was one-half of the original price" can be translated into an algebraic equation as follows:

1/2x = 200

x represents the original price of the refrigerator.

This equation states that half of the original price is equal to $200 is the sale price that Julio paid.

To solve for x, we can multiply both sides of the equation by 2 gives us:

x = 2 × 200

x = 400

We can check this answer by verifying that half of $400 is indeed equal to $200 was the sale price that Julio paid.

We translated the verbal statement into an algebraic equation and solved for the unknown variable to find that the original price of the refrigerator was $400.

The phrase "Julio bought a refrigerator on sale for $200 was one-half of the original price" may be transformed into the following algebraic equation:

The initial cost of the refrigerator is 1/2x = 200x.

According to this calculation, Julio paid $200 for the item, which is equal to half of the original price.

By multiplying both sides of the equation by 2, we may find the value of x as follows:

x = 2 × 200 x

= 400

By confirming that half of $400 is actually equal to $200, which was the sale price paid by Julio, we can confirm this response.

The spoken statement was converted into an algebraic equation and the unknown variable was solved for in order to determine that the refrigerator's initial cost was $400.

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Answer:

12

Step-by-step explanation:

Simplify 3 log(x+7) by moving 3 inside the parentheses with 7.f(x)=log((x+7)3)−5

The value of the puzzle is 17

The value of the triangle :

Value of Circle :

Value of whole yellow square :

Value of half-yellow square :

Using the above information:

Triangle + Circle + half-square

10 + 5 + 2 = 17

Therefore, the solution to the puzzle is 17

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Answer:

80 degrees

Step-by-step explanation:

The amount all the angles in a triangle always add up to 180.

6x+4x+8x = 180

18x=180

x=10

The largest angle is 8x so 8*10 = 80

Answer:

Step-by-step explanation:

4. Nicole can make 7 quarts of lemonade with 10 cups of sugar.

If 3/4 cup of sugar is used to make 1 quart of lemonade and 10 cups of sugar are available, then you multiply 3 times 10 (when multiplying fractions, you only multiply with the numerator, not the denominator) which will give you 30.

Now, you can write it as 30/4. Using simple division, you find that 30/4 is 7.5 (or 7 and 1/2), and because we're trying to find how many full quarts we can make using 10 cups of sugar, your answer will be 7.

5. Each person will get 0.83 repeating (or 5/6) boxes of raisins.

In this problem, we have 6 people and we have to share 5 boxes of raisins among all of them. We know that each person can't get 1 because there would have to be 6 boxes (1 for each person), so we have a fraction (or decimal, depending on where you're at).

Dividing 5/6, you'll simply get 5/6 because you can't simply this any further, but if you were to write this as a fraction, you'd get 0.83 repeating (over the 3).

6. Each class will receive 30 boxes of cracker jacks.

We know that there are 153 boxes of cracker jacks available, and this needs to then be split among 5 different classes. So, to find the answer, we have to divide 153 by 5. In doing that, we get 30.6, but because we're trying to find the whole number that the classes will receive, as you can't get a fraction of a box (at least, I assume), then each class will get 30 with 3 boxes remaining.

Answer:150?

Step-by-step explanation:

Work Shown:

21/35 = (7*3)/(7*5) = 3/5

Answer:

x=-16 and X=16 beads "over" means divide

The coordinates of each points are:

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

We have,

The coordinates of each point are in an ordered form.

i.e

(x, y)

x is the x-axis value.

y is the y-axis value.

Thus,

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

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The function is:

To find the range in the domain 3 < x 8 we can replace the values of the extrems to sind it so:

for x = 3

for x= 8

So the only range between this numbers is:

3.1.1 The basic property of operations used is the commutative property of multiplication.

3.1.2 The basic property of operations used is the additive inverse property.

3.1.3 The basic property of operations used is the associative property of addition.

3.1.1 The basic property of operations used in this calculation is the commutative property of multiplication. It states that the order of the factors in a multiplication problem can be rearranged without changing the product. In this case, the numbers 25 and 4 were swapped, resulting in the same product of 100.

3.1.2 The basic property of operations used in this calculation is the additive inverse property. It states that for any number, there exists an additive inverse such that when the number and its additive inverse are added together, the result is zero. In this case, adding 412 and its additive inverse (-412) results in zero.

3.1.3 The basic property of operations used in this calculation is the associative property of addition. It states that the grouping of numbers being added does not affect the sum. In this case, the numbers 25, 37, 20, 5, 30, and 7 were regrouped to facilitate easier mental addition. By grouping 25 and 37, and then grouping 20, 5, 30, and 7, the final sum of 62 is obtained, which is the same as adding all the numbers together in the original order.

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The required solution is 5+39e.

What is arithmetic?

The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications

Given :

Write down the question as an algebra problem, with the unknown as X

The unknown is a number plus 5, so we write it as (X+5). The product is four times (X+5), so we write it as 39(X+5). Set it equal to e, as per the question, 5+39e

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Answer:

k

Step-by-step explanation: