Given that the two triangles are similar find the unknowns length of the side labeled in

The reduced ratio form of 13 nickels to 43 dimes is 13/86.

What is a ratio?

a ratio let us know that how many times one number contains another number.

We are given 13 nickels and 43 dimes.

We know that 1 dime equal to 2 nickels.

Hence 43 dimes equals 86 nickels.

Now we find the ratio of the 2.

Which will be [tex]\frac{13}{86}[/tex]

Hence the reduced ratio form is 13/86.

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A kite has reflective symmetry but not rotational symmetry.

In common parlance, the term "symmetry" describes a sense of lovely proportion and balance. A more exact meaning of "symmetry" can be found in mathematics, where it typically refers to an object that is unaffected by certain transformations like translation, reflection, rotation, or scaling. Symmetry in mathematics means that when one shape is moved, rotated, or flipped, it looks exactly like the other shape. When something is identical on all sides, it is said to be symmetrical. If a center dividing line (also known as a mirror line) can be drawn on a shape to demonstrate that both of its sides are identical, then the shape is said to be symmetrical.

Given,

A kite has reflective symmetry but not rotational symmetry.

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Since the yearly tax is calculated as $3 per $100 of assessed value, which is 3/4 of $56,000 , the yearly tax on this property can be calculated as: $56,000*3/4*$3/$100 = $ 1260. The answer is option C.

First, let's calculate the total number of items:

The ratio of books to marbles is calculated by dividing the number of books by the number of marbles:

The ratio of DVD's to the total number of items is:

The percentage of dvd's from the total is:

Answer:

It's already in its simplest form.

Step-by-step explanation:

I'm writing a book/document on this topic but it's not finished. I suspect there is an error in this question because it's practically impossible to factorise it into integers.

The quadratic polynomial in the numerator has imaginary roots because 5 squared is less than 20 times 4.

ax² + bx + c;

if ( b² < 4ac ) { 'solution is imaginary' }

The quadratic equation will explain the above.

The given expression is

We would apply the rule of indices or exponent which is expressed as

Diagram 1.

Strategy 1.

If we add all the areas together we get:

Diagram 2.

Strategy 2.

If we add all the areas together we get:

We can see that we got the same answer: Total area = 7843 quare units

The strategies are similar because they are dividing the total area into smaller ones and then add them together.

However, they are different in that diagram 1 has more areas that are smaller compared to diagram 2. Also, the divisions in diagram 1 are designed to make multiplications easier compared to diagram 2.

We are to solve for x in all the equations and select the ones that occur more than one solution.

Hence,

Next,

Next,

Next,

Next,

Lastly,

Hence, the numbers that represent solutions to more than one of the six equations are

[tex]\angle J = 90^{\circ}\\\\\cos (\angle K)=\frac{5}{23} \implies \angle K=\arccos(5/23)\\\\\sin (\angle I)=\frac{5}{23} \implies \angle I=\arcsin(5/23)[/tex]

As you can see the options A and B are decreasing, D is constant, therefore, the only increasing relationship is the option C

ANSWER and EXPLANATION

We have that the 1 - 5th terms of the sequence are:

2/3, 1, 3/2, 9/4 and 27/8

To plot the graph of this sequence, we have:

=> on the x axis, the term number (i.e. n = 1, 2, 3, 4, 5)

=> on the y axis, the term(i.e. a(n) 2/3, 1, 3/2, 9/4, 27/8)

We will plot the graph of n versus a(n).

That is:

That is the graph.

Answer: 45,000 ÷ 900=50

Step-by-step explanation:

After solving the given polynomial (7x³ + 21x² - 63x = 0), the value of x are (x = 0) and {x = [(-3 ± 3√5)/2]}

So, 7x³ + 21x² - 63x = 0:

Now, solve for x as follows:

Zero factor principal, if ab = 0, then a = 0 and b = 0.

Now, x² + 3x - 9 = 0:

Therefore, after solving the given polynomial (7x³ + 21x² - 63x = 0), the value of x are (x = 0) and {x = [(-3 ± 3√5)/2]}

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We are given the following inequality

Let us first convert the inequality into slope-intercept form

Comparing this inequality with the standard slope-intercept form we see that

Slope = -3 and y-intercept = 4

So the graph of the inequality is

The area left to the red line represents the solution of the inequality.

Now we need to check if the point (1, 1) lies left to the red line.

We can clearly see that point (1, 1) is just left to the red line hence it is a solution.

Therefore, it is true.

The average monthly expenses for Bill's utilities is $266.67.

It is given in the question that:-

Expenditure in December by Bill = $ 234.45

Expenditure in January by Bill = $ 281.23

Expenditure in February by Bill = $ 284.33

We have to find the average monthly expenses for Bill's utilities.

We know that,

Average monthly expense for utilities = (Expenditure in December + Expenditure in January + Expenditure in February)/3

Hence, using the data given in the question, we can write,

Average monthly expense for utilities = (234.45 + 281.23 + 284.33)/3

Average monthly expense for utilities = 800.01/3 =  $266.67

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Answer

(-12, -8) after R270°.D¼ becomes (-2, 3)

Explanation

The first operation represented by R270° indicates a rotation of 270° counterclockwise about the origin.

When a rotation of 270° counterclockwise about the origin is done on some coordinate, A (x, y), it transforms this coordinates into A' (y, -x). That is, we switch y and x, then add negative sign to x.

Then, the second operation, D¼ represents a dilation of the coordinate about the origin by a scale factor of ¼ given.

The coordinates to start with is (-12, -8)

R270° changes A (x, y) into A' (y, -x)

So,

(-12, -8) = (-8, 12)

Then, the second operation dilates the new coordinates obtained after the first operation by ¼

D¼ changes A (x, y) into A' (¼x, ¼y)

So,

(-8, 12) = [¼(-8), ¼(12)] = (-2, 3)

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Recall that the y-intercept of a graph is the point where the graph intersects the y-axis.

From the given graph we get that the line intersects the y-axis at (0,2).

Answer: Option C.

The correct statement is the relationship is proportional because the ratio of the area to the cost is constant.

The first step is to determine if the ratio of the area of the carpet and its cost is proportional. The ratio is proportional, if the ratio is constant for all the areas and costs provided in the question. The ratio can be determined by dividing cost by the area.

Ratio = cost / area

750 / 500 = 1.50

1500 / 1000 = 1.50

2,250 / 1500 = 1.50

3000 / 2000 = 1.50

Since the ratios are constant, the relationship is proportional.

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The correct statement is the relationship is proportional because the ratio of the area to the cost is constant. Is the relationship proportional?The first step is to determine if the ratio of the area of the carpet and its cost is proportional. The ratio is proportional, if the ratio is constant for all the areas and costs provided in the question. The ratio can be determined by dividing cost by the area. Ratio = cost / area 750 / 500 = 1.50 1500 / 1000 = 1.502,250 / 1500 = 1.503000 / 2000 = 1.50 Since the ratios are constant, the relationship is proportional.

Karen will run more than 28

Answer:

Explanation:

Let's define each of the given types of numbers;

*Whole numbers are a set of all positive integers including 0. E.g 0, 1, 2,

*Integers

Derivative and Maximum Value of a Function

The critical points of a function are those where the first derivative is zero or does not exist.

Out of those points, we may find local maxima or minima or none of them.

One example of a function with a derivative that does not exist is:

This function has a local maximum at x=0 where the derivative does not exist.

The graph of this function is shown below:

Solution:

Given:

The right triangle can be sketched as shown below;

To get the distance between the building and the base of the ladder, we use the Pythagoras theorem since it is a right triangle.

Hence,

Therefore, the distance between the building and the base of the ladder in feet is 6 feet.

Given: a quadratic function with vertex (2,3) opening upward .

Find: the given statement is true or false.

Explanation: if parabola has a vertex at (2,3) and opens upward, it has one real solution., (2,3) will be a lowest point. The vertex will be at lowest point, it will be minimum.

that means graph has no one real solution. hence it will never going to intersect. so this statement is false.

Final answer: the given statement is FALSE.

for:

Divide both sides by 5:

Factor:

The factors of -20 which sum to 1, are -4 and 5 so:

So:

Since a negative year wouldn't make any sense:

Therefore, the company revenue will be $730 for the year:

Answer:

2002

Answer

The rate of change of both functions is 2.

Explanation

To know the statement that best compares the rate of change of the two functions, we need to first calculate the rate of change for each function.

Rate of change of function A

Using x₁ = 7, y₁ = 14, x₂ = 8 and y₂ = 16

Rate of change = Δy/Δx

Δy = (y₂ - y₁) = 16 - 14 = 2

Δx = (x₂ - x₁) = 8 - 7 = 1

⇒ Rate of change = 2/1 = 2

Rate of change of function B

From the graph

Using coordinate x₁ = 2, y₁ = 4, x₂ = 3 and y₂ = 6

Rate of change = Δy/Δx

Δy = (y₂ - y₁) = 6 - 4 = 2

Δx = (x₂ - x₁) = 3 - 2 = 1

⇒ Rate of change = 2/1 = 2

Since the rate of both functions are the same (2), then the statement that best compares the rate of change of the two functions in the options given is "The rate of change of both functions is 2"

Solution:

Given a cosine function graph;

The general cosine function is

Where

From the graph,

The midline is y = 1

The amplitude, A, is

The amplitude, A is 3

Where,

The phase shift, C = 0, and the vertical, D, is 1

Thus, the equation of the graph is

The graph is shown below

Hence, the equation is

As per the distance formula, it take 1 hour of time for Sean to catch up to Gina.

Distance formula:

The equation that relates the distance, rate, and time is

d  =  rt

Where d represents the distance traveled, r represents the rate, and t represents the time.

Given,

Gina left home, riding her bicycle at a rate of 25 miles per hour. Sean left 1 hour later, riding at a rate of 30 miles per hour.

Here we need to find the time take by Sean to catch up Gina.

Let us consider x be the time when Gina left the home.

Then, Sean left 1 hour later from her time.

So, it can be written as,

=> x + 1

As the Distance traveled is the same, the ratio of Speed in case 1 to the Speed in case 2 will be the inverse of the Time taken in both cases.

Therefore, the ratio of Speed in both cases

=> 25 : 30

=> 25/30

=> 5/6

Therefore, it can be written as,

x/x+1 = 5/6

When we cross multiply them, then we get,

5x + 5 = 6x

x = 5.

If Gina left at the time of 5, then Sean left at the time of 6.

So, it take 1 hour for Sean to catch up to Gina.

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This is a compound interest question and we have been given:

Principal (P) = $24000

Rate (r) = 7.25%

Years (t) = 10

However, we are told this value is compounded continuously. This means that for every infinitesimal time period, the value keeps being compounded.

The formula for finding the compound interest is:

But because the compounding period is continuous and therefore, infinitesimal,

This is similar to the general formula for Euler's number (e) which is:

Thus, we can re-write the Amount formula in terms of e:

Therefore, we can find the amount of money in the account after 10 years:

Therefore the amount after compounding continuously for 10 years is:

$49553.55

step 1

Find the equation of the line First Company

y=100.25x+6,500

where

y is the total charge

x is the number of ton of sugar

Second Company

y=225.75x+4,492

Part a)

Equate both equations

100.25x+6.500=225.75x+4,492

solve for x

225.75x-100.25x=6,500-4,492

125.50x=2,008

x=16

Part b) For x=16 ton

substitute the value of x in any of the two equations (the result is the same)

y=100.25(16)+6,500

y=$8,104