Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms. 2 similar right triangles. Triangle 1 has side length 12, hypotenuse 15, and blank side. Triangle 2 has side length 4, hypotenuse 5, and blank side. a. StartFraction 4 Over 15 EndFraction = StartFraction 5 Over 12 EndFraction = StartFraction 4 Over 15 EndFraction b. StartFraction 4 Over 5 EndFraction = StartFraction 12 Over 15 EndFraction = StartFraction 4 Over 5 EndFraction c. StartFraction 4 Over 12 EndFraction = StartFraction 5 Over 15 EndFraction = StartFraction 1 Over 3 EndFraction d. StartFraction 5 Over 4 EndFraction = StartFraction 15 Over 12 EndFraction = StartFraction 5 Over 4 EndFraction

The proof that ΔABC ≅ ΔDCB (congruent) in a parallelogram is because they are alternate interior angles.

If AABC is a parallelogram, then AB and AC are parallel. Therefore, angle BAC is equal to angle BDC since they are alternate interior angles.

Similarly, angle ABC is equal to angle ADC since they are also alternate interior angles.

Now, using the angle-angle-side (AAS) postulate to show that ΔABC and ΔDCB are congruent.

Since angle BAC = angle BDC and angle ABC = angle ADC, angle A = angle D, angle B = angle C, and side AB = side DC.

Therefore, ΔABC ≅ ΔDCB.

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Image transcribed:

8. Prove ΔABC≅ΔDCB (parallelogram)

You need to cut  [tex]\frac{7} {10}[/tex] minutes from the song for it to be exactly 3 1/2 minutes.

The unitary technique can be used tο calculate the value οf a single unit frοm the values οf multiple units and the value οf multiple units frοm the values οf single units.

This methοd is frequently emplοyed in math calculatiοns. Yοu can use this methοd tο sοlve issues cοncerning ratiο and prοpοrtiοn, algebra, geοmetry, etc.

The amount of time needed to cut is the difference between these two mixed fraction:

[tex]$ \Rightarrow 4 \frac{1}{5} - 3 \frac{1}{2}[/tex]

[tex]$ \Rightarrow \frac{21}{5} - \frac{7}{2}[/tex]

The LCM of 5 and 2 is 10

[tex]$ \Rightarrow \frac{42- 35} {10}[/tex]

[tex]$ \Rightarrow \frac{7} {10}[/tex]

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Complete question:

You plan to enter a song writing contest. Your song must be exactly 3 1/2 minutes long. You have a song that lasts for 4 1/5 minutes. How many minutes do you need to cut from the song?

Answer:

To solve for x, we can start by cross-multiplying the equation to eliminate the denominators:

(a+bx)(c+d) = (c+dx)(a+b)

Expanding the terms on both sides:

ac + adx + bc + bdx^2 = ac + abx + cdx + bd

Simplifying and rearranging the terms:

adx + bdx^2 - abx - cdx = bd - ac

dx(ad - ab - c) = bd - ac

Now, since we know that cb=ad, we can substitute ad=cb into the equation:

dx(cb - ab - c) = bd - ac

dx(cb - ab - c) = b(cd - ac)

x = b(cd - ac)/(d(cb - ab - c))

Therefore, the solution for x is:

x = b(cd - ac)/(d(cb - ab - c))

The domain of f(x) is (-∞, -7) ∪ (-7, -3) ∪ (-3, ∞).

What is the domain of function?

The function f(x) is defined as:

f(x) = 1/√((3+X)(7+X))

For f(x) to be defined, the expression under the square root must be positive. Therefore, we need to find the values of x that make (3+x)(7+x) positive.

We can use a sign analysis to determine the signs of (3+x) and (7+x) for different intervals of x:

When x < -7, both (3+x) and (7+x) are negative, so their product is positive.

When -7 < x < -3, (3+x) is negative and (7+x) is positive, so their product is negative.

When -3 < x < -7, (3+x) is positive and (7+x) is negative, so their product is negative.

When x > -3, both (3+x) and (7+x) are positive, so their product is positive.

Therefore, the expression (3+x)(7+x) is positive when x < -7 or x > -3.

However, we also need to consider the denominator of f(x), which cannot be zero. Therefore, we need to exclude any values of x that make the denominator equal to zero. The denominator is equal to zero when:

(3+x)(7+x) = 0

This occurs when x = -3 or x = -7.

Therefore, the domain of f(x) is all real numbers except -3 and -7, or:

x < -7 or -7 < x < -3 or x > -3

In interval notation, the domain of f(x) is (-∞, -7) ∪ (-7, -3) ∪ (-3, ∞).

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The quadratic equation on the graph can be written as:

y = x² + 6x + 8

Remember that a quadratic equation whose vertex is (h,k) and the leading coefficient is a, can be written as:

y = a*(x - h)² + k

Here we can see that the vertex is at (-3, -1), replacing that we will get:

y = a*(x + 3)² - 1

Now we can also see that it passes through the point (-2, 0), replacing these values we will get:

0 = a*(-2 + 3)² - 1

0 = a - 1

1 = a

Then the quadratic is:

y  = (x + 3)² - 1

Expanding that we get:

y = x² + 6x + 9 - 1

y = x² + 6x + 8

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The inequality for the provided sentence is (x+9)/(-4) >-2, and x>-1 is the obtained inequality's solution.

In mathematics, inequality is a concept that describes a relationship between two values. It is commonly expressed using symbols such as ">", "<", "≥", "≤", or "≠", and can be used to compare two numbers, variables, expressions, or sets. Inequality can be used to describe a range of values, such as "x is greater than 0 but less than 10", or "x is not equal to 0". Inequality is an important concept in mathematics, and it is used in many areas, such as problem solving, analysis, and statistics.

Given that, a maximum of -2 results when a number multiplied by 9 and split by -4.

Let x be the unknowable integer.

x+9 is the result of adding 9 to an integer.

Divided by -4, the outcome is (x+9)/.(-4)

Up to a limit of -2

(x+9)/(-4) >-2

On both sides of the discrepancy, multiply -4 to get

x+9>8

Subtract  9 on both the sides of inequality, we get

x>-1

Therefore, the inequality for the given phrase is (x+9)/(-4) >-2 and the solution for the inequality obtained is x>-1.

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Answer:

Supplementary Angles: The angles 1 & 2 are supplementary angles, as, when combined together, their total angle measurement is 180°, or a straight line. Supplementary angles, by definition, is either two angles in which, when combined, the sum is equal to 180°.

Adjacent Angles: The angles 1 & 2 are adjacent angles, as they share a common side and vertex. Vertexes, by definition is the corner point.

Why it is not:

Complementary Angles: Complementary angles suggest that, when two angles are combined together, their total angle measurements is 90°, or it creates a right angle. In this case, the total measurements of the combination of ∠1 & ∠2 is a straight line, or 180°. Therefore, complementary angles is not your answer.

Vertical Angles: Vertical angles suggest that, when there are two angles, they are directly opposite of each other. Vertical angles would share the same angle measurements.

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Answer:

Step-by-step explanation:

To solve this problem, we need to calculate the present value of the cash flows in both cases - the case where the payments are made at the beginning of each year and the case where the payments are made at the end of each year - and compare the two values.

First, let's calculate the present value of the cash flows when payments are made at the end of each year. We can use the formula for the present value of an ordinary annuity:

PV = PMT x [(1 - (1 / (1 + r)n)) / r]

where PV is the present value, PMT is the payment amount, r is the discount rate, and n is the number of periods.

In this case, PMT = R15 000, r = 9%, and n = 13. Plugging in these values, we get:

PV = R15 000 x [(1 - (1 / (1 + 0.09)^13)) / 0.09] = R141,798.06

Now let's calculate the present value of the cash flows when payments are made at the beginning of each year. To do this, we can use the formula for the present value of an annuity due:

PV = PMT x [(1 - (1 / (1 + r)n)) / r] x (1 + r)

where PV is the present value, PMT is the payment amount, r is the discount rate, n is the number of periods, and (1 + r) adjusts the formula for the fact that payments are being made at the beginning of each year.

In this case, PMT = R15 000, r = 9%, and n = 13. Plugging in these values, we get:

PV = R15 000 x [(1 - (1 / (1 + 0.09)^13)) / 0.09] x (1 + 0.09) = R153,094.97

So the present value of the cash flows when payments are made at the beginning of each year is R153,094.97, and the present value of the cash flows when payments are made at the end of each year is R141,798.06. Therefore, the difference in present value is:

R153,094.97 - R141,798.06 = R11,296.91

So, receiving the payments at the beginning rather than at the end of each year would result in a present value that is R11,296.91 higher.

AB has a length of 15, angle A is approximately 36.87 degrees and angle B is approximately 53.13 degrees.

We can use the Pythagorean theorem to find the length of AB:

AB² = AC² + BC²

AB² = 9² + 12²

AB² = 81 + 144

AB² = 225

AB = √225

AB = 15

So, AB has a length of 15.

To find angle A, we can use the inverse tangent function:

tan(A) = opposite/adjacent = AC/BC = 9/12 = 3/4

A = tan⁻¹(3/4) ≈ 36.87°

So, angle A is approximately 36.87 degrees.

To find angle B, we can use the fact that the three angles in any triangle add up to 180 degrees:

B = 90 - A = 90 - 36.87 ≈ 53.13°

So, angle B is approximately 53.13 degrees.

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Answer:

least common denominator = 18

Step-by-step explanation:

Because the function is one-to-one we know that it is invertible, from that we conclude:

If a function is one-to-one, then the function is invertible in its domain, if we define f⁻¹(x) as the inverse, then we can define two relations:

f( f⁻¹(x)) = x

And that if:

f(x)= y

then:

f⁻¹(y) = x

Here we know that:

f(0) = 7

Then the inverse evaluated in 7 must give 0, this is:

f⁻¹(7) = 0

And the second expression is:

( f(0) )⁻¹

This is not an inverse function, this is the inverse of the function evaluated in 0, then we will get:

( f(0) )⁻¹ = ( 7 )⁻¹ = 1/7.

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Answer: To find the points where the two skaters might collide, we need to find the values of x and y that satisfy both equations:

y = -3x + 8

y = -2x^2 + 7x

We can set the two equations equal to each other and solve for x:

-3x + 8 = -2x^2 + 7x

This simplifies to:

2x^2 - 10x + 8 = 0

Dividing both sides by 2, we get:

x^2 - 5x + 4 = 0

Factoring the left side, we get:

(x - 1)(x - 4) = 0

So the solutions for x are x = 1 and x = 4.

To find the corresponding values of y, we can substitute these values of x into either equation. Let's use y = -3x + 8:

When x = 1, y = -3(1) + 8 = 5

When x = 4, y = -3(4) + 8 = -4

Therefore, the two skaters might collide at the points (1, 5) and (4, -4).

Step-by-step explanation:

The number of solutions to the system of equation; y = x and y = x - 7 are;

There are no solution to the equation system

A solution is a set of the variable values in the equation system that make the system true at the same time.

The equations are;

y = x and y = x - 7

Whereby the right hand side of both equations are equated, we get;

x = x - 7

Subtracting x from both sides, we get;

x - x = x - 7 - x = -7

0 = -7

Geometrically, the meaning of the equations is that the two lines representing the two equations do not intersect, and are parallel lines. This is shown by the slopes (the coefficient of x) of the two equations, which are the same (The slope is 1 in each equation)

The y-intercepts of the equations are however different (0 and -7), therefore, the two equations represent parallel lines with different y-intercepts

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Step-by-step explanation:

y = x^2 / z      now triple x and z

y = (3x)^2 / 3z = 9x^2 / 3z = 3 * x^2 / z  <==== this is 3 times the original

    y is tripled

A sliced cylinder's cross section can be any shape that can be formed by intersecting a cylinder with a plane.

The shape of a sliced cylinder's cross section is determined by the angle and position of the slice.

If the slice is made parallel to the cylinder's base, the cross section is a circle.

If the slice is made at an angle to the cylinder's base, the cross section is an ellipse.

If the slice is made perpendicular to the cylinder's base, the cross section is a rectangle.

In general, a sliced cylinder's cross section can be any shape formed by intersecting a cylinder with a plane.

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To find the range of a data set from a box and whisker plot, you can use the whiskers of the plot. The whiskers represent the minimum and maximum values of the data set, so the range can be calculated by subtracting the minimum value from the maximum value.

A whisker plot, also known as a box and whisker plot, is a graphical representation of the distribution of a set of data. It displays a summary of the minimum, maximum, median, and quartiles of the data set.

A typical whisker plot consists of a rectangular box with a vertical line inside, which represents the median of the data set. The lower and upper edges of the box represent the first and third quartiles, respectively. The length of the box thus represents the interquartile range (IQR), which is a measure of the spread of the middle 50% of the data.

In statistics, the range of a data set can be found from a box and whisker plot by looking at the endpoints of the whiskers.

The whiskers in a box and whisker plot extend from the box to the smallest and largest data points within a certain range of the median. The range of the data set is simply the difference between the smallest and largest data points.

To find the range of the data set from a box and whisker plot, simply identify the endpoints of the whiskers and find the difference between them. Note that the whiskers may be labeled with the actual values of the data points or labeled with a multiple of the interquartile range (IQR), which is the distance between the first and third quartiles of the data set.

It's worth noting that the range is a very basic measure of the spread or dispersion of a data set and is sensitive to outliers. Other measures of spread, such as the interquartile range, variance, or standard deviation, may provide more robust and informative summaries of the data.

Hence, the method to plot whiskers in a data range is provided.

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Answer:25% interest or $5,000

5\100= .05

.05 / 20= .0025

5,000/1,000=0.5

0.5 / 20=.25

Step-by-step explanation:

Answer:

Step-by-step explanation:

To determine the implied interest rate in this scenario, we can use the concept of present value (PV) and future value (FV).

If Jochebed decides to pay the full amount of R20 000 cash right now, then the PV is R20 000 and the FV is also R20 000. Therefore, the implied interest rate on this option is 0%.

If Jochebed decides to pay in five annual installments of R5 000 each, then the PV of the land is equal to the sum of the present values of each installment. Using the formula for present value of an annuity, we can calculate the PV as:

PV = R5 000 x ((1 - (1 + r)^-5) / r)

where r is the implied interest rate. Solving for r, we get:

r = 7.18%

Therefore, the implied interest rate on the installment plan is 7.18%.

The experimental probability that the next train to arrive at Danville Station will be on time is 3/4 or 0.75.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The experimental probability of the next train to arrive at Danville Station being on time is given by the number of on-time trains divided by the total number of trains that arrived -

experimental probability = number of on-time trains / total number of trains

From the information given, we know that out of the last 20 trains to arrive, 15 were on time. Therefore -

number of on-time trains = 15

total number of trains = 20

Substituting these values into the equation, we get -

experimental probability = 15 / 20

Simplifying the fraction, we get -

experimental probability = 3/4

Therefore, the experimental probability value is obtained to be 3/4 or 0.75.

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To determine the profit earned from selling 250 shares worth $4.50 each with a 7% fee charged by the stock broker, we need to calculate the total revenue earned and the total cost incurred.

Total revenue earned from selling 250 shares at $4.50 per share:

Revenue = 250 x $4.50 = $1,125

Total cost incurred for buying and selling the shares, including the 7% fee charged by the broker:

Cost = 2 x 250 x $4.50 x 0.07 = $157.50

Here, we are multiplying the number of shares (250) by the price per share ($4.50) to get the total value of the shares. Then we multiply this by 2, since we need to account for both the buying and selling transactions, and then multiply by the broker fee rate of 7% (0.07) to get the total cost incurred.

Therefore, the profit earned from the sale of 250 shares is:

Profit = Revenue - Cost

Profit = $1,125 - $157.50

Profit = $967.50

Hence, the profit earned from selling 250 shares worth $4.50 each with a 7% fee charged by the stock broker is $967.50.

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Answer:

A fraction tells you how many parts of a whole there are. When we find a fraction of an amount, we are working out how much that 'part' is worth within the whole. You can see fractions of amounts all around us

Step-by-step explanation:

i may be wrong but I tried

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Step-by-step explanation:

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the probability of rolling a 6 and a 4 is 1/36 or 2.78%.

The probability of rolling a 6 and a 4 is calculated by taking the number of outcomes that would result in rolling a 6 and a 4 divided by the total number of possible outcomes. To calculate the probability of rolling a 6 and a 4 on a standard six-sided die, we first need to determine the number of outcomes that would result in rolling a 6 and a 4. There is only one way to roll a 6 and a 4 in that order, since each roll is independent of the other and the order matters.There is only one possible outcome that would result in rolling a 6 and a 4 (6,4). There are a total of 36 possible outcomes when rolling two six-sided cubes (6x6). Therefore, the probability of rolling a 6 and a 4 is 1/36 or 2.78%.

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The aforementioned equations have the following solutions: x = 0, x = 3. And the right response is B) x = 0, x = 3.

Replace the equation's variable with the given integer. The expressions on both sides of the issue should ideally be made simpler. Check the accuracy of the derived equation.

We must rearrange the terms to obtain a quadratic equation in standard form in order to solve the problem x2 - 2x = x:

x² - 2x - x = 0

x² - 3x = 0

Now we can factor out x:

x(x - 3) = 0

When x = 0 or x - 3 = 0, the equation is true. Hence, the equation's answers are x² - 2x = x are x = 0 and x = 3.

We can enter these answers into the initial equation and determine whether they satisfy it to verify that they work:

f(0) = 0² - 2(0) = 0

g(0) = 0

So, x = 0 is a solution.

f(3) = 3² - 2(3) = 3

g(3) = 3

So, x = 3 is also a solution.

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Question:

Given the function f(x) = x² - 2x and g(x) = x what is the solution for the equation x² - 2x = x?

A) X= 1, x = 3

B) x = 0, x = 3

C) x=-1,x=0

D) x = 0, x = 1

Answer:

This isn't a reasonable scale

Step-by-step explanation:

Using the scale 1 in. = 4 in., the width of the scaled down painting will be:

48 in. ÷ 4 = 12 in.

And the height of the scaled down painting will be:

120 in. ÷ 4 = 30 in.

So the scaled down painting will be 12 in. wide and 30 in. tall. Since Sarah's paper is 12 in. wide and 24 in. tall, the scaled down painting will fit within the paper's width but will be taller than the paper.

Therefore, the scale is not reasonable because the scaled down painting will not fit within the dimensions of Sarah's paper.

Answer:

19.2 ft

Step-by-step explanation:

Let x be the number of pounds needed for 6035 square feet.

We can set up a proportion between the pounds of grass seed and the square feet covered:

5 pounds / 355 square feet = x pounds / 6035 square feet

To solve for x, we can cross-multiply and simplify:

5 pounds * 6035 square feet = 355 square feet * x pounds

30175 = 355x

x = 30175 / 355

x ≈ 85.07

Therefore, approximately 85.07 pounds of grass seed are needed for 6035 square feet

Answer:

Step-by-step explanation:

It will take 50 minutes for the turtle and snail to meet.

because they are all moving at feet per minute we can create a formula

total feet = (turtle feet per minute) + (snail feet per minute)

300 = 5m +1m

combine like terms

300 = 6m

divide both sides by 6

50=m

Answer:

See below.

Step-by-step explanation:

Let's denote the distance the turtle walks by x. Then the distance the snail crawls would be 300 − x.

We can now set up an equation to represent the situation. Since distance = rate × time, we have

x/5 = (300 - x)/1

Solving for x, we get

x = 250

So the turtle walks 250 feet before meeting the snail, and the snail crawls the remaining 50 feet.

To find the time it takes for them to meet, we can use either of the two distances and its corresponding rate:

time = distance/rate

For example, using the turtle's distance

time = 250/5 = 50 minutes

Therefore, it takes 50 minutes for the turtle and the snail to meet.

Okay so hopefully. I got the equation right. But I believe this is it