How does your current (or future) employment affect your Social Security or Medicare benefits?

Using the formula of speed, the speed of first trains is 45 mph and the speed of second train is 60 mph.

In the given question, we have to find the speed of each.

Two trains going in opposite directions leave at the same time.

One train tavels 15 mph faster than the other.

In 6 hours the trains are 630 miles apart.

Let the speed of the first vehicle be s mph, then according to the question, the speed of the second vehicle would be (s+15) mph.

Let the first vehicle covers the distance D(1) and the second one D(2) in the prescribed time.

So, find the distance covered by the first vehicle in 6 hours by using the formula

Distance = Speed × Time

So the distance D(1) is;

D(1) = s*6

D(1) = 6s

So the distance D(2) is;

D(2) = (s+15)*6

D(2) = 6s+90

Since, after 6 hours both the vehicles are at the distance 630 miles. So, the sum of the two distances D(1) and D(2) will be equal to 630.

D(1)+D(2) = 630

Puttimg the value of D(1) and D(2)

6s+6s+90=630

Simplifying

12s+90=630

Subtract 90 on both side we get

12s=540

Divide by 12 on both side we get

s=45 mph

So the value of speed of the faster vehicle

s+15 = 45+15

s+15 = 60 mph

Hence, the speed of first train is 45 mph and the speed of second train is 60 mph.

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The answer is ∠BED by vertical angles theorem.

Answer:

B

Step-by-step explanation:

∠AEB and ∠CED are congruent  

by the Vertical Angles Theorem

∠AEC and ∠

BED

are congruent by the Vertical Angles Theorem.

Question 1: The item not included in the cost of merchandise inventory is "Purchase discounts."

2: The total cost of the merchandise is $3,332.00.

5: The company's gross margin and operating expenses, are $211,000 and $191,720.

Merchandise inventory expenses normally consist of the price paid for the inventory, deductions from the purchase price resulting from purchase returns and allowances, and freight expenses paid by the purchaser.

Although purchase discounts reduce the cost of merchandise inventory, they are not considered part of it. Instead, they are treated as a distinct discount in the accounting records.

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Answer: The new price of the rice in March 2023 was $180.

Step-by-step explanation:

> 20% of $150 is 0.20 ($150) = $30

> The price of the rice increased by $30, so the new price is:

> $150 + $30 = $180

Therefore, the new price of the rice in March 2023 was $180.

Answer:

-6/9 = -2/3 (C)

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

Plug in x for 1

Y=-4(1)+10

Y=-4+10

Y=6

Answer:

y = 3/-2x + 3

Step-by-step explanation:

y is the y value

3/-2 is the slope

x is the x value

3 is the y intercept

Answer:

y = - \(\frac{3}{2}\) x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2, 0 ) and (x₂, y₂ ) = (0, 3 )

m = \(\frac{3-0}{0-2}\) = \(\frac{3}{-2}\) = - \(\frac{3}{2}\)

The line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = - \(\frac{3}{2}\) x + 3 ← equation of line

Answer:

19.6x24=470.4

Step-by-step explanation:

The future value (A) is approximately 5610.2 for the given investment and annu $4000 for 5 years at 7% compounded annually

To find the compound amount and compound interest rate for the given investment, we can use the formula for compound interest:

(a) The compound amount in the account after 5 years can be calculated using the formula:

A = P(1 + r/n)^(nt)

Where A is the compound amount, P is the principal (initial investment), r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Given that the principal (P) is $4000, the interest rate ® is 7%, and the interest is compounded annually (n = 1), and the investment is for 5 years (t = 5), we can plug these values into the formula:

A = 4000(1 + 0.07/1)^(1*5)

A = 4000(1 + 0.07/1)^(1*5)

= 4000(1 + 0.07)^(5)

= 4000(1.07)^(5)

≈ 4000(1.402551)

≈ 5610.20

Therefore, the future value (A) is approximately 5610.2

Calculating this expression will give us the compound amount after 5 years.

(b) The compound interest earned can be calculated by subtracting the principal from the compound amount:

Compound interest = Compound amount – Principa

This will give us the total interest earned over the 5-year period.

By evaluating the expressions in (a) and (b), we can determine the compound amount and the compound interest earned for the given investment.

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Answer:

(5,3)

Step-by-step explanation:

I took the test and go it right!

The coordinate point for D is (5, 3). Therefore, option C is the correct answer.

A rhombus can be defined as a special parallelogram as it fulfills the requirements of a parallelogram, i.e. a quadrilateral with two pairs of parallel sides. In addition to this, a rhombus has all four sides equal just like a square. That is why it is also known as a tilted square. Look at the image below to understand the relationship of rhombus shape with parallelogram and square.

Given that, Point A (2,2), Point B (3,4) and Point C (4,1)

The coordinate point for D that would make ABDC a rhombus.

So, the coordinate point for D is (5, 3).

Therefore, option C is the correct answer.

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Answer:

y = \(\frac{5}{2}\) x - 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = \(\frac{5}{2}\) , thus

y = \(\frac{5}{2}\) x + c ← is the partial equation

To find c substitute (2, 0) into the partial equation

0 = 5 + c ⇒ c = 0 - 5

y = \(\frac{5}{2}\) x - 5 ← equation of line

The equation of the line is the way of represent the line by the given point in the coordinate plane and the its slope.. Thus the equation of the line with point (2,0) and slope 5/2 is,

\(y=\dfrac{5}{2} x-2\)

Given information;

The point of the line through which the line passes are (2,0).

The slope of the line is 5/2.

The equation of the line is the way of represent the line by the given point in the coordinate plane and the its slope.

The standard form of the equation of the line for point and slope can be given as,

\((y-y_1)=m(x-x_1)\)

Put the values,

\((y-0)=\dfrac{5}{2} (x-2)\)

Solve it further;

\(y=\dfrac{5}{2} x-2\)

Thus the equation of the line with point (2,0) and slope 5/2 is,

\(y=\dfrac{5}{2} x-2\)

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Answer:

A. B is correct

B. A is correct

C. B is correct

Step-by-step explanation:

Area of triangle: A = 1/2bh

A. Area of each triangle: A = 1/2 x 11.5 x 12 = 69

Total surface areas = 4(area of triangle) + area of square = 4(69) + 12^2 = 420

So A is incorrect and B is correct

B. Area of triangle: A = 1/2 x 13.9 x 16 = 111.2

Surface area = 4(area of triangle) = 4(111.2) = 444.8

So A is correct and B is incorrect

C. Area of triangle with base of 10: A = 1/2 x 10 x 7 = 35

Area of triangle with base of 8.1: A = 1/2 x 8.1 x 16 = 64.8

Total surface areas = 2(area of triangle base of 10) + 2(area of triangle base of 8.1) + area of rectangle = 2(35) + 2(64.8) + (10x8.1) = 280.6

So A is incorrect and B is correct.

The work done in pumping water out over the top edge to empty the tank is approximately 9984 foot-pounds, rounded to one decimal place.

To calculate the work done in pumping water out of the tank, we will use the formula:

Work = weight of water × height to be lifted

First, let's find the volume of the tank:

Next, find the total weight of the water in the tank:

Since the height of the tank is 4 feet, and we need to pump the water over the top edge, we can assume the average height the water needs to be lifted is half the height of the tank, which is 2 feet.

Now, we can calculate the work done:

So, the work done in pumping water out over the top edge to empty the tank is approximately 9984 foot-pounds, rounded to one decimal place. Here is the visualization:

_______

|       |

|       | 4 feet

|       |

|_______|

  5 feet

|\

| \

h  \

|___\____

    5 feet

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Answer:

y = 5x - 3, so M = 5 and C = -3.

Answer:

your anwser is 1085

Step-by-step explanation:

Answer:

Area of his yard = 19680ft²

Fertilizer needed = 590.4 ounces

Step-by-step explanation:

Step 1 Find the area of his lawn

The question states that his lawn is a rectangle that measures 240 feet by 82 feet

To find the area of a rectangle we simply multiply the side lengths

Hence, area of his yard = 240 * 82 = 19680ft²

Step 2 find amount of fertilizer needed.

The question states that .03 ounces is used per square foot.

So to find the amount of fertilizer needed simply multiply total area by amount used per square foot.

19680 * .03 = 590.4

So we can conclude that John will need 590.4 ounces of fertilizer

Answer:

you have 48

Step-by-step explanation:

15x2=30

9x2=18

18+30=48

Answer: 45

Step-by-step explanation:

Answer:

s = 5\(\sqrt{6}\)

Step-by-step explanation:

using the cosine ratio in the right triangle and the exact value

cos30° = \(\frac{\sqrt{3} }{2}\) , then

cos30° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{s}{10\sqrt{2} }\) = \(\frac{\sqrt{3} }{2}\) ( cross- multiply )

2s = 10\(\sqrt{2}\) × \(\sqrt{3}\) = 10\(\sqrt{6}\) ( divide both sides by 2 )

s = 5\(\sqrt{6}\)

Answer:i think its 115 degres

Step-by-step explanation:

Answer:

h‐¹(x)= (x-1)/3

To do this switch the x and y variables in this case it would be x=3y+1 and rearrange to get the y alone

gh‐¹(7)=(x-1)/9=(7-1)/9=2/3

For this section substitutethe x in the g(x) equation with h-¹(x) and then simplify to get your final expression then substitute 7 in place of x to get your integer answer

Hope it's clear, cheers!

Circle O is represented by the equation (x+7)² + (y + 7)² = 16. The length of the radius of Circle O is 4.

The equation of Circle O, (x+7)² + (y+7)² = 16, is in the standard form of a circle equation: (x - h)² + (y - k)² = r². Comparing it to the given equation, we can determine the values of h, k, and r.

In the given equation:

Center coordinates: (-7, -7) → h = -7, k = -7

Radius squared: 16 → r² = 16

To find the length of the radius, we need to take the square root of r²:

r = √(16)

Calculating the square root, we get:

r = 4

Therefore, the length of the radius of Circle O is 4.

Looking at the answer options, we see that the correct answer is Option B which is equal to 4.

The equation of a circle in the standard form (x - h)² + (y - k)² = r² represents a circle with center (h, k) and radius r. By comparing the given equation to the standard form, we can extract the values of h, k, and r. Taking the square root of r² gives us the length of the radius, which in this case is 4.

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The equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

To find the equation of the line perpendicular to the tangent to the curve at (2,1), we need to first find the slope of the tangent line at that point.

The derivative of y=x^3-4x+1 is y'=3x^2-4, so the slope of the tangent line at (2,1) is y'(2) = 3(2)^2-4 = 8.

Since we want the line perpendicular to the tangent, we know that its slope will be the negative reciprocal of the tangent's slope. Therefore, the slope of the line we're looking for is -1/8.

Next, we use the point-slope form of the equation of a line to write the equation of the line with the slope we found and passing through the point (2,1):

y - 1 = (-1/8)(x - 2)

Simplifying and putting the equation in slope-intercept form:

y = (-1/8)x + 9/8

Therefore, the equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

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Answer:

(x+4)(x+8)

Step-by-step explanation:

Factor x²+12x+32 using the AC method.

Explanation:

Let's say 5 people get a lunch platter. The cost would be 7*5 = 35 dollars.

Or if 3 people got the lunch platter, then it would be 7*3 = 21 dollars

In general, the cost is 7p dollars where p is a placeholder for a whole number. So that's how we end up with c = 7p

If it is one platter per person, the following will be true,

Answer:

c = 7p

Step-by-step explanation:

    This is because every time someone buys a platter, it adds $7 to the total cost

-> If two people buy a platter, it is 7 + 7, aka 7 *2

-> If three, it is 7 + 7 + 7 aka 7 * 3

    Using this pattern, we can see that the total cost will be 7 times the number of people there.

We can put this into an equation by doing:

c = 7p

,The matrix P is an orthogonal projector since it satisfies the conditions of being a projection matrix and an orthogonal matrix. The range of P is the two-dimensional subspace spanned by the columns of P, which are the vectors v1 and v2.

Multiplication is a mathematical operation that involves combining two or more quantities to obtain a product. It is represented by the symbol "×" or "*", and is used to find the total value of a given quantity when it is multiplied by another quantity.

To prove that P is an orthogonal projector, we need to show that it satisfies two conditions: (1) P is a projection matrix, and (2) P is an orthogonal matrix.

First, we will show that P is a projection matrix. To do this, we need to show that \(P^2 = P\). We have:

\(P^2 = (v1v1^T + v2v2^T)(v1v1^T + v2v2^T)\\= v1v1^Tv1v1^T + v1v1^Tv2v2^T + v2v2^Tv1v1^T + v2v2^Tv2v2^T\\= v1(v1^Tv1)v1^T + v1(v2^Tv1)v2^T + v2(v1^Tv2)v1^T + v2(v2^Tv2)v2^T\\= v1v1^T + v2v2^T\\= P\)

Therefore, P is a projection matrix.

Next, we will show that P is an orthogonal matrix. To do this, we need to show that\(P^T = P^-1\). We have:

\(P^T = (v1v1^T + v2v2^T)^T\\= v1v1^T + v2v2^T\\= P\)

Also, since P is a projection matrix, its range is the subspace spanned by its columns. The columns of P are v1 and v2, which form an orthonormal basis for a two-dimensional subspace of R^n. Therefore, the range of P is this subspace.

In conclusion, we have shown that P is an orthogonal projector, and its range is the two-dimensional subspace spanned by v1 and v2.

Therefore,The matrix P is an orthogonal projector since it satisfies the conditions of being a projection matrix and an orthogonal matrix. The range of P is the two-dimensional subspace spanned by the columns of P, which are the vectors v1 and v2.

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Answer:

34.8°

Step-by-step explanation:

90-55.2=34.8

Hope this helps:)

If p > 5 is prime and p is divided by 10, then the remainders are 1, 3, 7, or 9

The given information, we know that p is a prime number greater than 5, and that p is divided by 10. This means that p must end in either 0 or 5. since those are the only digits that allow for a number to be divisible by 10.

However, we also know that p is prime, which means it cannot be divisible by any number other than 1 and itself. This rules out the possibility of p ending in 0. since any number ending in 0 is divisible by 10 (and therefore not prime).

Therefore, p must end in 5. This means that p can be written in the form:

p = 10n + 5

where n is some integer. Now, let's consider what happens when we divide p by 10:

p/10 = (10n + 5)/10 = n + 0.5

Since p/10 is not an integer (it has a decimal component of 0.5), we know that p cannot be evenly divided by 10. Therefore, when p is divided by 10, there must be a remainder.

To determine what possible remainders there could be, we can look at the possible values for the last digit of p. Since p ends in 5, the last digit can only be 1, 3, 7, or 9 (since these are the only digits that, when multiplied by 5 and added to 10n, result in a number ending in 5).

Therefore, if p > 5 is prime and p is divided by 10, the remainder must be either 1, 3, 7, or 9.

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