Find the equation of the straight line passing through the point (0, 2) which is perpendicular to the line y = 1/4x + 5​.

Based on simple interest, the solution to the question is that his friend will ultimately owe Darrel $2,875.

A loan or investment's interest can be calculated using simple interest using the principal, interest rate, and duration of the transaction. Because it just considers the original principal and does not account for any compounded interest, it is known as "simple" interest.

Darrel will be indebted to his friend for the following sum if he lends him $2,500 and receives repayment with 15% simple interest after a year:

Interest = Principal x Rate x Time

Interest = $2,500 x 0.15 x 1

Interest = $375

Thus, the total sum his friend will be required to pay Darrel is:

Total amount = Principal + Interest

Total amount = $2,500 + $375

Total amount = $2,875

Thus, the total amount his friend owes Darrel is $2,875.

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Answer:

no

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

There are many ways to write an equation using 1/4 and 1000, depending on the context and what you are trying to express. Here are a few examples:

To find out what 1/4 of 1000 is, you can use the equation:

1/4 * 1000 = 250

This equation multiplies 1/4 (or 0.25) by 1000 to get the result of 250.

If you want to express a ratio between 1/4 and 1000, you can use the equation:

(1/4) : 1000 = x : 1

This equation sets up a proportion where x is the unknown value that represents the ratio between 1/4 and 1000. By cross-multiplying and solving for x, you can find the answer. For example:

(1/4) : 1000 = x : 1

1000x = 1/4

x = (1/4) / 1000

x = 0.00025

So the ratio of 1/4 to 1000 is 0.00025 to 1.

Another example of an equation using 1/4 and 1000 could be:

1/4 + 1000 = x

This equation adds 1/4 to 1000 to find the value of x. The result would be:

1/4 + 1000 = 1000.25

So x is equal to 1000.25.

a)she need 3.68 negative point , The new APR for Moira will be 3.25% + (3.68 x 0.135%) = 3.7452% because each negative point raises the APR by 0.135%.and the breakeven time for Moira's loan is 10 months

Breakeven time refers to the amount of time it takes for the savings from a particular action to equal the costs associated with that action. It is the point at which the benefits and costs are equal, and after which the benefits will begin to exceed the costs.

a. Moira has to buy 14,000/380,000 = 0.0368 or 3.68% in negative points to offset $14,000 in closing fees. The closing expenses are reduced by 1% of the principle for every negative point, therefore Moira has to buy 3.68/1 = 3.68 negative points.

b. The new APR for Moira will be 3.25% + (3.68 x 0.135%) = 3.7452% because each negative point raises the APR by 0.135%.

c.When the savings from buying the negative points equal the additional interest paid because of the higher APR, that is the breakeven point for Moira's loan. 3.68 x 380,000 x 1% = $14,040 is the savings from buying 3.68 negative points. The difference between the interest paid at the original APR of 3.25% and the interest paid at the new APR of 3.7452% represents the additional interest paid as a result of the higher APR. A 10-year, $380,000 mortgage at 3.25% would have a monthly payment of $3,680.97 according to an online mortgage calculator. During a period of ten years, interest payments total $73,276.23. A 10-year, $380,000 mortgage at 3.7452% has a $3,918.23 monthly payment. Throughout a ten-year period, interest was paid a total of $88,668.83. The additional interest paid as a result of the higher APR equals $15,392.60 ($88,668.83 x $73,276.23). The breakeven point is therefore $14,040/$15,392.60 = 0.910 or roughly 10 months.

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According to the given data the equation of the new function is (D) f(x) = 2x - 4.

An equation is a mathematical statement that indicates that two expressions are equal. It contains an equals sign "=" and may involve variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc.

If we translate the function h(x) = 2x - 9 up by 5 units, the new function f(x) will have the form:

f(x) = h(x) + 5

Substituting the definition of h(x) into this equation, we get:

f(x) = 2x - 9 + 5

Simplifying, we have:

f(x) = 2x - 4

Therefore, the equation of the new function is (D) f(x) = 2x - 4.

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Answer: -44

Step-by-step explanation:

[tex]2(4)^2 -4(7) -4(4)(7-4) = ?\\2(16) - 28 - 16(3) =\\32 - 28 -48 = -44[/tex]

Answer:

$2.50

Step-by-step explanation:

6% of $16.90 is $1.014

$16.90 + $1.014 is $17.914

14% of $17.914 is $2.50796

Which we then round down to $2.50

Hope this helps!

Answer:

Y + 3x = 10

Step-by-step explanation:

You need to know that Standard Form is: Ax + By = C

Y-4=-3x+6              Add 3x to both sides

Y - 4 + 3x = 6         Add 4 to both sides

Y + 3x = 10

Answer:

cosΘ = [tex]\frac{\sqrt{7} }{4}[/tex]

Step-by-step explanation:

using the identity

sin²x + cos²x = 1 ( subtract sin²x from both sides )

cos²x = 1 - sin²x ( take square root of both sides )

cosx = ± [tex]\sqrt{1-sin^2x}[/tex]

given

sinΘ = [tex]\frac{3}{4}[/tex] , then

cosΘ = ± [tex]\sqrt{1-(\frac{3}{4})^2 }[/tex]

         = ± [tex]\sqrt{1-\frac{9}{16} }[/tex]

         = ± [tex]\sqrt{\frac{16}{16}-\frac{9}{16} }[/tex]

         = ± [tex]\sqrt{\frac{7}{16} }[/tex]

         = ± [tex]\frac{\sqrt{7} }{\sqrt{16} }[/tex]

since Θ is in quadrant 1 , then cosΘ > 0

cosΘ = [tex]\frac{\sqrt{7} }{4}[/tex]

The value of x is 4

Similar triangles are triangles that have the same shape, but their sizes may vary. For two triangles to be similar, the corresponding angles must be equal.

Also the ratio corresponding sides are equal in similar triangles.

3/11 = x+5/6x+9

11(x+5) = 3( 6x+9)

11x+55 = 18x +27

collecting like terms

18x-11x = 55-27

7x = 28

x = 28/7

x = 4

therefore the value of x is 4

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The break-even points in terms of customers served = 14 customers

Charge per customer = 120

Let the Number of customers= n

So,

Income from serving n customers = 120n

Expenditure from serving n customers = Fixed cost + cost of preparation of meal per customer

= 1400 + 20n

For beak-even:

Income = Expenditure

Substituting values, we get:

120n = 1400 + 20n

So, we get:

100 n = 1400

So, we get:

n =1400/100

= 14

So,

The break-even points in terms of customers served = 14 customers

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The value of the side x is 4. 36

To determine the value, we need to know that there are six different trigonometric identities. They are;

From the information given, we have that;

the acute angle is 28 degrees and the obtuse angle is 126 degrees. The adjacent side of 28-degree angle is 8.2 and the opposite side is x.

Opposite side = x

Adjacent side = 8.2

Now, using the tangent identity;

tan 28 = x/8.2

multiply the values

x = 0. 5317(8.2)

multiply

x = 4. 36

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Answer:

The following objects would most likely weigh 2 kilograms:

The actual weight of each object may vary, but based on typical weights, any of these objects could weigh around 2 kilograms.

Required equation is $125 = $82 + x and the amount of money he still has to save to buy the bicycle is $43.

What is equation?

A statement that two expressions are equal. It typically contains one or more variables is called equation which are usually represented by letters, and it may also contain numbers and mathematical operations such as addition, subtraction, multiplication, and division.

Let x be the amount of money that Desmond still needs to save to buy the bicycle.

Since he has already saved $82, the total amount of money he needs to save,

Total cost of bicycle = Cost he has saved + Amount he still needs to save

$125 = $82 + x

We can solve for x by subtracting $82 from both sides:

$125 - $82 = x

Simplifying, we get:

$x = $43

Therefore, Desmond still needs to save $43 to buy the bicycle.

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Answer:

3 = equal

5 = equal

Step-by-step explanation:

3. both angles are alternate angles

5. both triangles are equal

Answer:

Step-by-step explanation:

Answer:To determine the possible scales of the map, we need to calculate the ratio of the distance on the map to the corresponding distance on the ground in the actual state. We can do this using the following formula:scale = distance on map ÷ distance on groundFirst, we need to convert the dimensions of Kansas from miles to inches using a common scale factor. Since 1 mile is equal to 63,360 inches, we have:Length of Kansas: 410 miles × 63,360 inches/mile = 25,984,600 inchesWidth of Kansas: 210 miles × 63,360 inches/mile = 13,315,200 inchesNow we can calculate the possible scales of the map based on the dimensions of the page in Jada's book, which is 5 inches by 8 inches:For the length of Kansas:scale = 5 inches ÷ (25,984,600 inches ÷ 2.54 cm/in) = 0.0000484scale = 8 inches ÷ (25,984,600 inches ÷ 2.54 cm/in) = 0.0000774For the width of Kansas:scale = 5 inches ÷ (13,315,200 inches ÷ 2.54 cm/in) = 0.0000962scale = 8 inches ÷ (13,315,200 inches ÷ 2.54 cm/in) = 0.0001539Therefore, the possible scales of the map are 1:20,655, and 1:10,326.

Let's call the number of minutes of calls "x".

For the first plan, the cost will be:

Cost = $18 + $0.15x

For the second plan, the cost will be:

Cost = $12 + $0.20x

To find the point at which the costs of the two plans are equal, we can set the two equations equal to each other and solve for x:

$18 + $0.15x = $12 + $0.20x

Subtracting $12 from both sides, we get:

$6 + $0.15x = $0.20x

Subtracting $0.15x from both sides, we get:

$6 = $0.05x

Dividing both sides by $0.05, we get:

x = 120

Therefore, if a customer makes more than 120 minutes of calls per month, the first plan with the $18 monthly fee and $0.15 per minute charge will be more cost-effective. If a customer makes less than 120 minutes of calls per month, the second plan with the $12 monthly fee and $0.20 per minute charge will be more cost-effective.

Answer:

120 minutes

Step-by-step explanation:

Let x be the number of minutes of calls made in a month.

For the first plan, the monthly cost is $18 + $0.15x.

For the second plan, the monthly cost is $12 + $0.20x.

To find the point where the costs are equal, we need to solve the equation:

18 + 0.15x = 12 + 0.20x

Subtracting 0.15x from both sides gives:

18 = 12 + 0.05x

Subtracting 12 from both sides gives:

6 = 0.05xDividing both sides by 0.05 gives:

x = 120

Therefore, the costs of the two plans will be equal for 120 minutes of calls.

Answer: 24 i am a expect

Answer:

-3

Step-by-step explanation:

First, -7 minus 8 is -15.

-15 divided by 5 is -3.

therefore, the simplified answer is -3.

The value of the logarithmic expression is:

log₅(5¹´²) = 1/2

Remember the two rules for logarithms:

logₐ(x) = ln(x)/ln(a)

ln(xⁿ) = n*ln(x)

Then we can rewrite the expression:

log₅(5¹´²) as:

ln(5¹´²)/ln(5)

Using the second rule we can take out the exponent to get:

ln(5¹´²)/ln(5) ]= (1/2)*ln(5)/ln(5) = 1/2

That is the value.

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50 miles would make the two choices equivalent in cost.

The following formula is used to determine a line's slope:

slope is equal to y2 - y1 / x2 - x1.

where the two points on the line are (x1, y1) and (x2, y2). The steepness or rate of change of the line is indicated by the slope. A line with a positive slope is increasing from left to right, whereas a line with a negative slope is dropping from left to right. An undefined slope denotes a vertical line, while a slope of zero denotes a horizontal line.

To determine the choice where the two miles are equivalent we take x as the number of miles:

For the first company:

Total cost = 25 + 0.8x

For the second company:

Total cost = 35 + 0.6x

Setting the equations as equal:

25 + 0.8x = 35 + 0.6x

0.2x = 10

x = 50

Hence, 50 miles would make the two choices equivalent in cost.

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Answer:

To rewrite the mixed number 9 2/5 as an improper fraction, we can multiply the whole number (9) by the denominator of the fraction (5) and add the numerator of the fraction (2), then write the result over the denominator:

9 2/5 = (9 × 5 + 2)/5 = 47/5

Therefore, 9 2/5 can be written as the improper fraction 47/5.

To find the equation of a line passing through a given point that is perpendicular to a given line, we need to follow these steps:

Find the slope of the given line by rearranging the equation into slope-intercept form y = mx + b, where m is the slope.

Find the slope of a line perpendicular to the given line by taking the negative reciprocal of the slope found in step 1.

Use the point-slope form y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope found in step 2, to write the equation of the perpendicular line.

Step 1: Find the slope of the given line 5x - 3y = 10

We can rearrange the equation into slope-intercept form by solving for y:

5x - 3y = 10

-3y = -5x + 10

y = (5/3)x - (10/3)

The slope of this line is 5/3.

Step 2: Find the slope of a line perpendicular to the given line

The slope of a line perpendicular to the given line is the negative reciprocal of 5/3:

m_perp = -3/5

Step 3: Use the point-slope form to write the equation of the perpendicular line passing through (-3, -7).

We plug in the values we found for the slope and the given point into the point-slope form:

y - y1 = m_perp(x - x1)

y - (-7) = (-3/5)(x - (-3))

Simplifying this equation, we get:

y + 7 = (-3/5)x - 9/5

Now we can rearrange this equation into slope-intercept form y = mx + b, where m is the slope and b is the y-intercept:

y = (-3/5)x - 44/5

Therefore, the equation of the line passing through the point (-3, -7) and perpendicular to the line 5x - 3y = 10 is y = (-3/5)x - 44/5.

Janet has 630 options to customize a car based on the given features.

How to solve the question?

To determine the number of ways Janet can customize a car, we need to multiply the number of choices she has for each feature. Therefore, the total number of ways Janet can customize a car can be calculated as:

10 car models x 7 exterior colors x 9 interior colors = 630

Thus, Janet has 630 options to customize a car based on the given features.

It's worth noting that this calculation assumes that each feature (car model, exterior color, and interior color) can be combined with any other feature, without any restrictions or dependencies. However, in reality, certain car models may not be available in certain exterior or interior colors, or there may be other restrictions on the customization options.

Additionally, there may be other features that Janet can customize, such as the type of engine, transmission, or other options. Therefore, the total number of customization options may be even greater than what we have calculated here.

In summary, based on the given information, Janet has 630 ways to customize a car, but in reality, the actual number of options may be more limited or varied depending on other factors.

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