7. Find the slope and y-intercept of the line.
y = 2x + 5

A) 5; 2.

B) 2; 5

C) 1/2;1/5

D) -1/2;-1/5

Answer:

OC. $57.28

Step-by-step explanation:

It depends on how much she sells them for.

Let's say Anne sells them for $x.

Then her profit is:

8x-(8*7.16)

=8x-57.28

To make a minimum to at least make even is $57.28 and sell for $7.16 a piece.

Anne makes a profit of $57.28 on the sale of these 8 canvases. which is the correct answer would be option (C).

The profit is equal to the difference between the selling price and the original cost price.

Anne purchases art supplies for her business from a wholesaler. She spends $7.16 on eight 16 by 20-inch canvases.

To calculate the profit that Anne makes on the sale of these 8 canvases, you need to know the price at which she sells them and the cost of buying them from the wholesaler. If the cost of each canvas is $7.16 and she buys 8 of them, the total cost of the canvases is :

⇒ 8 × $7.16

Apply the multiplication operation and we get

⇒ $57.28.

Therefore, she makes a profit of $57.28 on the sale of these 8 canvases.

Hence, the correct answer would be an option (C).

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Answer: $58,088.57

Step-by-step explanation:

The investment is compounded weekly so you need to change the parameters of the equation to a weekly figure:

Interest rate is yearly so:

= 3.75%/52

= 3.75/52% per week

Number of periods is 4 years so:

= 4 * 52

= 208 weeks

Future value in 4 years is:

= 50,000 * ( 1 + 3.75/52%)²⁰⁸

= $58,088.57

a) The actual distance between towns K and L is: 100 km

b) As shown in the attached file

c) The bearing of town L from town K is 117 degrees.

The scale of the map is given as:

1 cm to represent 50 km

Now, when we measure the distance between K and L on the map, we see that it gives us a distance of 2 cm.

Using the scale of 1 cm: 50 km, we can say that:

Actual distance between towns K and L = (2 * 50)/1 = 100 km

b) Using a compass and it’s 3cm aiming down {South} as seen in the attached photo. Then a line was drawn aiming {South} with a ruler. On the end of the line the (x) point was put there to get the mark.

c) Measuring the angle gives the bearing of town L from town K which is 117 degrees.

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Answer:

64

Step-by-step explanation:

diy

Answer:

-120

Step-by-step explanation:

Parentheses first: 2-10= (-8)

Then Add: 8+7=15

Then Multiply: 15 x (-8) = (-120)

Answer:

a

Step-by-step explanation:

In this scenario, asset a and asset b are both expected to make a single guaranteed payment of $100 in one year. However, the current prices of the assets are different, with asset a priced at $85 and asset b priced at $95. This raises the question of which asset is a better investment, taking into account both the expected payment and the current price.

One way to compare the assets is to calculate the expected return on investment (ROI) for each asset. The expected ROI is calculated by dividing the expected payment by the current price, and multiplying by 100 to express the result as a percentage. Using this approach, we can calculate the expected ROI for asset a as 100/85 * 100 = 117.65% and the expected ROI for asset b as 100/95 * 100 = 105.26%.

Based on this calculation, asset a has a higher expected ROI than asset b. This suggests that, all else being equal, asset a is a better investment than asset b. However, it's important to note that this calculation assumes that the expected payments are guaranteed and that there are no additional factors that may impact the value of the assets, such as changes in interest rates or inflation. Therefore, it's important to consider all relevant factors before making an investment decision.

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The unknown value in the table using the constant of proportionality is; 96

The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant.

We are given the coordinates;

(12, 42), (18, 63), (40, y)

where x-values represents time in seconds and y-values represents number of pencils that were produced.

To find the constant of proportionality is as good as finding the slope between two consecutive points as;

m = (63 - 18)/(42 - 12)

m = (45/30)

m = 1.5

Thus to find the unknown value y, we will use the formula;

(y - y1)/x - x1) = m

So we will use the coordinates; (18, 63), (40, y)

Plugging them into the formula above will result in;

(y - 63)/(40 - 18) = 1.5

y - 63 = 1.5 * 22

y - 63 = 33

y = 33 + 63

y = 96

Thus, we can conclude that using the constant of proportionality, the number of pencils that were produced after a time of 40 seconds is 96 pencils.

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The work done by the winch in winding up the entire chain is 6250 ft·lb

Work is the product force applied times displacement in the direction of force applied.

Given Parameters,

The weight of the chain is 5 pounds per foot

The Height of the chain = 50 foot

So, (5 lb/ft)(50 ft) = 250 lb

The center of mass of the hanging chain is its midpoint, 50/2 = 25 ft below the winch.Lifting the center of mass 15 feet to the winch requires the same amount of work as winding the chain:

(250 lb)(25 ft) = 6250 ft·lb

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Answer:

grtestdrugyiytfrx

Step-by-step explanation:

Answer:

all that I know is he eats alot of carbs

Step-by-step explanation:

sheesh, those calories are gonna add up quickly

Answer:

18.75

Step-by-step explanation:

75 is the 100% price. If you divide 75 by two you will get the 50% price. Which is 37.5. If you divide that by two you will get the 25% price which is 18.75

Answer:

A. F'G' = 3 & G'H' = 5.

Step-by-step explanation:

Translations of any shape will not change the side lengths and will be congruent to the original shape.

56/120

Step-by-step explanation:

The body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.

Let the body mass of the man be x kg.

The first child's body mass is five-sixths of their father's body mass:

Body mass of the first child = (5/6) * x

= 5x/6 kg.

The second child's body mass is four-fifths of their father's body mass:

Body mass of the second child = (4/5) * x

= 4x/5 kg.

Therefore, the body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

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Both statements are false because the sum of two angles does not equal the sum of their cosines or sines.

Statement 53 is false. This is because the sum of two angles does not equal the sum of their cosines. The correct equation for the sum of two angles in terms of their cosines is:

\( \cos \left(30^{\circ}+60^{\circ}\right)=\cos 30^{\circ} \cos 60^{\circ} - \sin 30^{\circ} \sin 60^{\circ} \)

Using this equation, we can calculate the correct value of the cosine of the sum of the two angles:

\( \cos \left(30^{\circ}+60^{\circ}\right)=\cos 30^{\circ} \cos 60^{\circ} - \sin 30^{\circ} \sin 60^{\circ} \)
\( \cos 90^{\circ}=\frac{\sqrt{3}}{2} \cdot \frac{1}{2} - \frac{1}{2} \cdot \frac{\sqrt{3}}{2} \)
\( \cos 90^{\circ}=0 \)

Statement 54 is also false. This is because the sum of two angles does not equal the sum of their sines. The correct equation for the sum of two angles in terms of their sines is:

\( \sin \left(30^{\circ}+60^{\circ}\right)=\sin 30^{\circ} \cos 60^{\circ} + \cos 30^{\circ} \sin 60^{\circ} \)

Using this equation, we can calculate the correct value of the sine of the sum of the two angles:

\( \sin \left(30^{\circ}+60^{\circ}\right)=\sin 30^{\circ} \cos 60^{\circ} + \cos 30^{\circ} \sin 60^{\circ} \)
\( \sin 90^{\circ}=\frac{1}{2} \cdot \frac{1}{2} + \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2} \)
\( \sin 90^{\circ}=1 \)

In conclusion, both statements are false because the sum of two angles does not equal the sum of their cosines or sines. The correct equations for the sum of two angles in terms of their cosines and sines are shown above.

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Answer:

y≤4

Step-by-step explanation:

Hope this helped C:

By algebra properties, the rational equation 1 / [1 / (x + 2) + 1 / (x + 3)] is equivalent to the rational expression (x² + 5 · x + 6) / (2 · x + 5). (Correct choice: B)

In this problem we find a rational equation, whose simplified form has to be found by means of algebra properties. First, write the entire expression:

1 / [1 / (x + 2) + 1 / (x + 3)]

Second, expand the denominator by addition of fractions with distinct denominator:

1 / [[(x + 3) + (x + 2)] / [(x + 2) · (x + 3)]]

Third, use division of fractions:

[(x + 2) · (x + 3)] / [(x + 3) + (x + 2)]

Fourth, simplify both numerator and denominator:

(x² + 5 · x + 6) / (2 · x + 5)

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Answer:

To divide one fraction by another one, flip numerator and denominator of the second one, and then multiply the two fractions. The flipped-over fraction is called the multiplicative inverse or reciprocal.

Step-by-step explanation:

The answer is Reciprocal

I hope this helps you :)

Step-by-step explanation:

When we flip a fraction we form it's reciprocal, the use of reciprocal is generally used for division of fractions ,Hope this helps....

When a consumer's budget increases, the budget line shifts to the right, allowing the consumer to reach a higher level of consumption. Therefore, the correct answer is A. right; higher

When a consumer's budget increases, it means they have more money available to spend on goods and services. This increase in budget causes the budget line, which represents the different combinations of goods a consumer can afford, to shift. The budget line shows the maximum amount of goods that can be purchased with the given budget and prices.

When the budget line shifts to the right, it indicates that the consumer can now afford to purchase more goods than before. This means that the consumer can reach a higher level of consumption because they have more options available to them within their budget constraint. They can either purchase more of the same goods or allocate their budget towards different goods and increase their overall consumption.

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Answer:

To create a perfect square of given expression,

On solving the above expression we get,

we have that,

To create a perfect square: add ( half the coefficient of the x- term )²

Coefficient of x term is 3

half the coefficient of the x- term is 1.5

( half the coefficient of the x- term )² is 2.25

Add 2.25 to the quadratic expression inside the bracket, we get,

In general, we adding 11.25 (that is, 2.25x5=11.25) to the given expression.

we get,

Multiply 5 to the above equation, we get

Based on the above calculation, we adding 11.25 and multiplying the expression by 5 in order to create a perfect square.

Adding 11.25 and multiplying the expression by 5 in order to create a perfect square.

Answer:

24 will be the maximum value of this graph

Answer: the maximum value is 24 vertical and 20 horizontal

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

To find the constant

take the coefficient of x

10

divide by 2

10/2 =5

Square it

5^2 =25

Add this

x^2 +10x+25

Answer:

40% I believe

Step-by-step explanation:

I searched it up

a) The Probability is (26C4 * 26C4) / 52C8. b) The Probability (at least two of a kind) is 1 - (13C8 * 4^8) / 52C8.

a) To find the probability of getting half red and half black cards from a hand of 8 cards, we need to calculate the number of favorable outcomes and divide it by the total possible outcomes.

Favorable outcomes: Choose 4 red cards (26C4) and 4 black cards (26C4).
Total possible outcomes: Choose any 8 cards from a 52-card deck (52C8).

Probability = (26C4 * 26C4) / 52C8

b) The probability of not having at least two of a kind is getting all distinct cards (13 ranks). So, we can calculate the complement and subtract it from 1.

Favorable outcomes (no two of a kind): Choose 8 distinct ranks (13C8) and 1 suit for each (4^8).
Total possible outcomes: Same as before, 52C8.

Probability (at least two of a kind) = 1 - (13C8 * 4^8) / 52C8

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The given identity is [1/(sinu cosu)] - (cosu/sinu) = tanu, this identity can be verified by multiplying the numerator and denominator by cos u * sin u.

Given identity is [1/(sinu cosu)] - (cosu/sinu) = tanu. To prove this identity, we need to manipulate the left-hand side of the equation until it matches the right-hand side of the equation. The first step is to convert everything to a common denominator:

[(1/sinu cosu) * sinu/sinu] - (cosu/sinu * cosu/cosu) = tanu(sinu cosu)

Multiplying out the denominators gives us:

(1/sinu) - (cos²u/sin²u) = tanu(sinu cosu)

Multiplying the numerator and denominator of the first fraction by cos u * sin u gives us:

cosu * cosu * sinu * sinu / (cosu * sinu) - cosu * cosu / (sinu * sinu) = sinu / cosu

Multiplying out the terms on the left-hand side gives us:

(cos²u - 1) / sinu = sinu / cosu

Next, we can simplify the left-hand side by using the identity cos²u - 1 = - sin²u:-

sin²u / sinu = sinu / cosu

Multiplying both sides by -1 gives us:

sinu / sin²u = - sinu / cosu

Simplifying the right-hand side gives us:- tanu

Finally, we can take the negative of both sides to get our final answer:[1/(sinu cosu)] - (cosu/sinu) = tanu.

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A root of a transformed equation that is not the root of the original equation because it was excluded from the original equation's domain is known as an extraneous solution.

What are extraneous solutions?

A "false" solution to an equation is known as an extraneous solution. Even if we appeared to follow sound procedures when solving the equation, an extraneous solution did not fulfill the original equation.

So,

When we solve an equation, an extraneous solution is a result that does not fulfill the equation. As an illustration, if we square both sides of the equation x = -1, we obtain the value x = 1, which does not satisfy the original equation, indicating that x = 1 is an extraneous solution.

when we wanted to solve the equation √x = -1.  After squaring both sides, we get a value of x = 1.

When we substitute x = 1 into the original equation, we get:

x = -1  [original equation]

√1 = -1  [substitute x = 1]

1 = -1  [this is not true]

Hence,

This equation is called an extraneous solution.

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Answer:

5

Step-by-step explanation:

We know that the area of the rectangle is equal to the perimeter of the triangle

S (rectangle) = (x + 8) × (2x - 1)

P (triangle) = (5x - 1) + (6x + 8) + (8x + 15)

Now we can form an equation:

(x + 8) × (2x - 1) = (5x - 1) + (6x + 8) + (8x + 15)

\( {2x}^{2} - x + 16x - 8 = 5x - 1 + 6x + 8 + 8x + 15\)

\(2 {x}^{2} - 4x - 30 = 0\)

\(d = {b}^{2} - 4 \times a \times c = ({ - 4})^{2} - 4 \times 2 \times ( - 30) = 16 + 240 = 256 > 0\)

\(x1 = \frac{ - b - \sqrt{d} }{2 \times a} = \frac{4 - 16}{4} = \frac{ - 12}{4} = - 3\)

-3 is a negative number and we cannot use it, since x must be a natural number

\(x2 = \frac{ - b + \sqrt{d} }{2 \times a} = \frac{4 + 16}{4} = \frac{20}{4} = 5\)

Using Richardson extrapolation, the computed first derivative of f(x) at x = 2 is approximately -0.052.

The absolute error with respect to the true solution is 22.348.

To compute the accuracy gain using Richardson extrapolation, we'll use the central difference formula for the first derivative, which is given by:

f'(x) = [f(x + h) - f(x - h)] / (2h)

h₁= 0.02 and h₂ = 0.03, and then apply Richardson extrapolation.

Calculate the derivative using h₁ = 0.02

x = 2

h₁ = 0.02

f(x + h₁) = f(2 + 0.02) = f(2.02) = 5sin(10 × 2.02) + (2.02)³ - 2(2.02)² - 6(2.02) + 10

= 5sin(20.2) + 8.120808 - 8.162808 - 12.12 + 10

= -3.5799

f(x -h₁) = f(2 - 0.02) = f(1.98)

= 5sin(19.8) + 7.783608 - 7.844808 - 11.88 + 10

= -3.4758

f'(x) = [-3.5799 - (-3.4758)] / (2 × 0.02)

= -0.052

Calculate the derivative using h₂ = 0.03

x = 2

h₂  = 0.03

f(x + h₂ ) = f(2 + 0.03) = f(2.03) = 5sin(10 × 2.03) + (2.03)³ - 2(2.03)² - 6(2.03) + 10

= -3.5998

f(x - h₂) = f(2 - 0.03) = f(1.97)

= -3.3943

f'(x) = [-3.5998 - (-3.3943)] / (2 × 0.03)

= -0.052

Richardson extrapolation is given by the formula:

\(f'(x) = (2^p \times f'(x, h_2) - f'(x, h_1)) / (2^p - 1)\)

Here, p is the order of the method. Since we're using the central difference formula, which is second-order accurate, p = 2.

f'(x) = (2² × -0.052 - (-0.052)) / (2² - 1)

= (4 × -0.052 + 0.052) / 3

= -0.052

Therefore, using Richardson extrapolation, the first derivative of f(x) at x = 2 is approximately -0.052.

To compute the absolute error with respect to the true solution, we need to find the true derivative of f(x) and evaluate it at x = 2.

f(x) = 5sin(10x) + x³ - 2x² - 6x + 10

f'(x) = 50cos(10x) + 3x² - 4x - 6

f'(2) = 50cos(20) + 3(2)^2 - 4(2) - 6

= 50(-0.408) + 12 - 8 - 6

= -22.4

Absolute error = |(-22.4) - (-0.052)|

= |-22.4 + 0.052|

= 22.348

Therefore, the absolute error with respect to the true solution is  22.348.

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