How many solutions does the system have? { y = − 7 x + 8 y = − 7 x − 8 ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ ​ y=−7x+8 y=−7x−8 ​

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

The impact on Carns Company's income from eliminating the Small Tools Division would be a decrease of $1,209,000.

To determine the impact on Carns Company's income from eliminating the Small Tools Division, we need to consider the avoidable costs associated with the division.

The avoidable costs include all of the variable costs of the division and a portion of the fixed costs that are specifically related to the Small Tools Division. In this case, the variable costs of the division are $1,295,000, and $119,000 of the fixed costs are avoidable.

To calculate the impact on income, we subtract the avoidable costs from the loss reported by the division:

Impact on income = Loss - Avoidable costs

Impact on income = $205,000 - ($1,295,000 + $119,000)

Impact on income = $205,000 - $1,414,000

Impact on income = -$1,209,000

The negative sign indicates a decrease in income.

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Answer:

50 yards

Step-by-step explanation:

1 feet = 0.333333 yards

150 feet * 0.333333 yards / 1 feet = 50 yards

Step-by-step explanation:

points on the line: (4, -2) & (-5, 3)

gradient of the line = -5/9

general equation for all straight lines: y = mx + c

substitute one coordinate and the gradient into the equation. 3 = (-5/9)(-5) + c

therefore, c = 2/9

so the general equation is y = (-5/9)x + 2/9

Answer:

x=10

Step-by-step explanation:

Step 1: Add x to both sides

Step 2: Subtract 2 from both sides.

Step 3: Multiply both sides by 2.

If she gave two to each of her friends. She only has 8 remaining balls. so she has a total of 16 friends.

What is division in mathematics?

In mathematics, division is the process of dividing a number into equal parts and determining how many equal parts can be made. For instance, dividing 15 by 3 means dividing 15 into three equal groups of five. The symbol " or sometimes '/' represents division.

Sumalee won a total of 40 super bouncy balls.

then she gave two balls to each of her friends.

So she can distribute the balls to = 40/2

                                                       = 20 friends.

But after the distribution, she remained with 8 balls.

Now the number of balls will be = 40 - 8 = 32 balls.

and she can distribute 32 balls to = 32/2

                                                        = 16 friends.

Hence, If she gave two to each of her friends. She only has 8 remaining balls. so she has a total of 16 friends.

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The area of a triangle is 20 inches².

The area of a triangle:

The area of a triangle is equal to half the product of the base and its height.

The formula for the area of a triangle = 1/2 × base × height

Here the base = 10 inches

height = 4 inches

Area = 1/2 × 10 × 4

       = 10×2

       = 20 inches²

Therefore the area of a triangle is 20 inches².

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Answer:

Fruit mass = 63.2 g

Biscuit mass = 94.8 g

Step-by-step explanation:

Since the ratio of fruit mass to biscuit mass is 2:3, the fraction of fruit mass to the total of fruit and biscuit mass is 2/5 and the fraction of biscuit mass to the total of fruit and biscuit mass is 3/5.

For Monkey A, the total of fruit and biscuit mass is 73 g, which means that the fraction of fruit mass is 2/5 × 73 g = 29.2 g and the fraction of biscuit mass is 3/5 × 73 g = 43.8 g. Therefore, the values for fruit mass and biscuit mass are:

Fruit mass = 29.2 g

Biscuit mass = 43.8 g

For Monkey B, the total of fruit and biscuit mass is 73 + 85 = 158 g, which means that the fraction of fruit mass is 2/5 × 158 g = 63.2 g and the fraction of biscuit mass is 3/5 × 158 g = 94.8 g. Therefore, the values for fruit mass and biscuit mass are:

Fruit mass = 63.2 g

Biscuit mass = 94.8 g

To identify the correct weight to the nearest 1/8 pound, you need to have a weight measurement that is divisible by 1/8 pound. If you have a weight that is not divisible by 1/8 pound, then you need to round it to the nearest 1/8 pound.

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By following this rounding method, you can determine the correct weight to the nearest 1/8 pound based on the specific weight measurement provided.

To identify the correct weight to the nearest 1/8 pound, we need a specific weight or measurement to work with.

Once we have that information, we can apply the rounding method.

When rounding to the nearest 1/8 pound, we look at the digit immediately after the 1/8 pound mark, which is 0.125 pounds.

If this digit is 4 or less, we round down, and if it is 5 or greater, we round up.

For example, let's say we have a weight of 15.6 pounds. The digit after the 1/8 pound mark is 6, which is greater than 4.

Therefore, we round up, and the weight to the nearest 1/8 pound is 15.75 pounds.

On the other hand, if we have a weight of 12.3 pounds, the digit after the 1/8 pound mark is 3, which is less than 4.

Thus, we round down, and the weight to the nearest 1/8 pound is 12.25 pounds.

Similarly, if the weight is 22.7 pounds, the digit in the thousandth place is 7. Since 7 is greater than 4, we round up.

The 1/8 pound measurement is 0.125 pounds, so rounding up gives us 22.875 pounds.

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Answer:

x=2

Step-by-step explanation:

Add

6

and

3

.

4

x

+

9

=

17

Move all terms not containing

x

4

x

=

8

Divide each term by

4

and simplify.

x

=

2

Answer:

2

Step-by-step explanation:

4X + 6 + 3 = 17

add all the whole numbers together

6+3=9

going back to the problem, it'll look like this

4X + 9 = 17

subract 9 from itself and 17

4X + 9 = 17

     - 9    -9

------------------

4x         = 8

----           ---          divide 4 from both sides

4              4

X = 2

Answer:

79.5

Step-by-step explanation:

The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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Answer:

38 percent of the Cocoa is produced in the ivory coast, with thousands being produced in Ghana, so Ghana is the main production rate of the cocoa, with the ivory coast producing less than half.

Step-by-step explanation:

Answer:

990 very simple you could use a calculator next time

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

To solve the equation 1/x-1 = |x-2| using three iterations of successive approximation, we will start with an initial guess and refine it using an iterative process.

Given that the equation involves absolute value, we will consider two cases:

Case 1: x - 2 ≥ 0

In this case, |x-2| simplifies to x-2, and the equation becomes 1/(x-1) = x-2.

Case 2: x - 2 < 0

In this case, |x-2| simplifies to -(x-2), and the equation becomes 1/(x-1) = -(x-2).

Now, let's perform the successive approximation:

Iteration 1:

Let's start with an initial guess, x = 2.

Case 1: When x - 2 ≥ 0,

1/(2-1) = 2-2,

1/1 = 0,

which is not true.

Case 2: When x - 2 < 0,

1/(2-1) = -(2-2),

1/1 = 0,

which is not true.

Since our initial guess did not satisfy the equation in either case, we need to choose a different initial guess.

Iteration 2:

Let's try x = 3.

Case 1: When x - 2 ≥ 0,

1/(3-1) = 3-2,

1/2 = 1,

which is not true.

Case 2: When x - 2 < 0,

1/(3-1) = -(3-2),

1/2 = -1,

which is not true.

Again, our guess did not satisfy the equation in either case.

Iteration 3:

Let's try x = 2.5.

Case 1: When x - 2 ≥ 0,

1/(2.5-1) = 2.5-2,

1/1.5 = 0.5,

which is true.

Case 2: When x - 2 < 0,

1/(2.5-1) = -(2.5-2),

1/1.5 = -0.5,

which is not true.

Our guess of x = 2.5 satisfies the equation in Case 1.

Therefore, the approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

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Answer:

1,250

Step-by-step explanation:

5 to the 4 power is 50,and 5 to the 2 power is 25 and then Multiply them and that should be your answer

Answer:

Cos z is 28/35

Step-by-step explanation:

Answer: first blank is (3)

second blank is (-2)

Step-by-step explanation:

edge 2020

The inverse function of f (x) = 1/3x - 2 is f⁻¹(x) = 3(x + 2), the value of a is 3, and the value of x-intercept is x = -2.

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

Given:

f (x) = 1/3x - 2

Find its inverse as shown below,

Add 2 to x and then divide by 1/3 as shown below,

f⁻¹(x) = (x + 2) / 1/3

f⁻¹(x) = 3(x + 2)

compare with f⁻¹(x) = a (x + 2)

a = 3

Calculate the x-intercept by putting f(x) = 0

0 = x + 2

x = -2

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The value of y in the triangle is 2√10 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

The value of y can be found using the similar triangle ratios as follows:

Hence,

8 / y = y / 5

cross multiply

y² = 8 × 5

y²= 40

square root both sides of the equation

y = √40

Therefore,

y = 2√10 units

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Answer:

{7, 9}

(Numbers from 1 to 10 equal to or greater than 7 are 7 and 9)

Step-by-step explanation:

We have to find the set of whole number greater than and equal to 7 from 1 to 10,

Now, From 1 to 10, the odd numbers are, 1,3,5,7,9,

And of these, 7 and 9 are equal to or greater than 7

So, we get the set,

{7, 9}

Answer:

70,438.20

Step-by-step explanation:

To calculate the future value you use the following formula

FV=PV(1+i)^n

Plug in our numbers and get

FV=42000(1+.09)^6

42000*1.09^6=70,438.20

the length of the rope is approximately 11.9 feet.

What is right angle triangle?

The term "right-angled triangle" refers to any triangle with an internal angle that is either a right angle or 90 degrees in value. The right triangle or the 90-degree triangle are other names for this triangle because of this. Right triangles have "opposite" and "adjacent" sides, which refer to the sides that are across from and next to respective angles, respectively. When a right triangle is formed, the hypotenuse is its longest side.

We can consider the flagpole, the ground, and the rope as forming a right triangle. The angle between the flagpole and the rope is 90 degrees, and the angle between the rope and the ground is 35 degrees. Therefore, the angle between the flagpole and the ground is 90 - 35 = 55 degrees.

Let's call the length of the rope "r". We can use the trigonometric function tangent to find r:

tan(35°) = opposite/adjacent = r/20

Multiplying both sides by 20, we get:

r = 20 tan(35°)

Using a calculator, we get:

r ≈ 11.9 feet

Therefore, the length of the rope is approximately 11.9 feet.

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Answer:

4^8

Step-by-step explanation:

keep base (which is 4) and add exponents when multiplying

Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

Answer:

-7≤y≤2

Step-by-step explanation:

The range measures the highest and lowest numbers up and down on the y-axis for a line. In order to determine range, start with the smallest number (the farthest place the line touches going down) then write less than or equal to. This is because the two dots are closed, meaning they include what the line touches. Afterward, add another less than or equal to, and then add the biggest number (the highest place the line touches going up). The range basically gives you your boundaries, and tells you how high or low the line you are describing is. And after that, you're done!

I hope this helps :)

Answer:

5

Step-by-step explanation:

22-2x ... (equation-1)

(x=-5)

Substituting the value of x in equation 1

22-2(x-5)

20(x-5)

20x-100

20x=100

x=100/20

x=5

Hope it helps

Answer:

142

38

Step-by-step explanation: