I need this answered CORRECTLY because my grade relies on it and this is the last attempt I get. Please help me out here!

Length of DF is 24cm.

If one figure may be produced from the other by a single transformation, or by a series of transformations, such as translations, reflections, rotations, and/or dilations, then and only then are two figures said to be similar. When there is a similarity transformation, the transformed image has the same shape as the original. There will always be similar varieties of triangles, quadrilaterals, and polygons. For instance, squares and equilateral triangles are both similar shapes. We know the lengths of comparable sides are proportional if two polygons resemble one another.

Given,

Two triangles are similar,

DF = AC (3)

DF = 8(3)

DF = 24

Length of DF is 24cm.

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Answer:

50%

Step-by-step explanation:

He sold it for Rs 15 each. What is his profit percent? CP of 1 pen = 120/12= 10 SP of 1 pen = 15 Profit = 5 P % = (p/CP)*100=(5/10) x 100 = 50%.

-3x + 14 = 4x - 7

Answer:

x = 3

Step-by-step explanation:

-3x + 14 = 4x - 7

+7                  +7

-3x + 21 = 4x

+3x         +3x

21 = 7x

21 / 7     7x / 7

3 = x

Check:

-3x + 14 = 4x - 7

-3 x 3 + 14 = 4 x 3 - 7

-9 + 14 = 12 - 7

5 = 5

x = 3

Answer:c

Step-by-step explanation:

Answer: Solving x2 - 4x - 7 = 0 by completing the square, the solutions are x = ±√11 + 2.

Step-by-step explanation:

7) The given distribution of data is:

19, 17, 18, 21, 14, 17, 16, 22, 14, 22, 16

This can be rearranged as:

14, 14, 16, 16, 17, 17, 18, 19, 21, 22, 22

The frequency distribution table is drawn below

The dot plot is drawn right after the frequency table

Answer:

1,2, and 4

Step-by-step explanation:

I attached a picture with the graph

y= -4 is a straight horizontal line (red line) and  

y≤10 will give a horizontal line passing trough y=10 (blue line)

the solution is all points under and on the line  y=10

1, 2, and 4 are part of the solution set

(the blue area is the solution of the system of equations)

Answer:

( - 2, 7 )

Step-by-step explanation:

Answer:

25.7 in

Step-by-step explanation:

perimeter = 1/2(2)πr + 10 = 15.7 + 10 = 25.7 in

Answer:

the answer is d

Hope This Helps!!!

Answer:

Step-by-step explanation:

1.02 represents:

It is a 2% growth

Correct choice is (4)

Answer:

318+954

Step-by-step explanation:

divide 1272 by 2 to get what they would cost if they were the same amount then divide that by 2 to get 318 times that by 3 to get 954 and add 318 to get 1272

The required cost of the couch and coffee table is $848 and $424 respectively.

Given that,
A couch and coffee table cost a total of $1272. The cost of the couch is two times the cost of the coffee table.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
let the cost of the coffee table be x,
Now the cost of the couch  = 2x
According to the question,
2x + x = 1272
x = 424
now,
Cost of the couch = 424 [2] = 848

Thus, the required cost of the couch and coffee table is $848 and $424 respectively.

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Answer:

To solve the equation 2(4x - 1) = -10(x - 3) + 4, we can follow these steps:

Step 1: Distribute the 2 on the left side of the equation:

8x - 2 = -10x + 6 + 4

Explanation: When we distribute the 2, we get 2 * 4x - 2 * 1, which simplifies to 8x - 2.

Step 2: Combine like terms on both sides of the equation:

8x - 10x = 6 + 4 - 2

-2x = 8

Explanation: On the left side of the equation, we have 8x - 10x, which simplifies to -2x. On the right side of the equation, we have 6 + 4 - 2, which simplifies to 8.

Step 3: Divide both sides of the equation by -2 to solve for x:

x = -4

Explanation: When we divide both sides of the equation by -2, we get -2x / -2 = 8 / -2, which simplifies to x = -4.

Therefore, the solution to the equation is x = -4.

To solve the equation 2(4x - 1) = -10(x - 3) + 4,we can follow these steps:

Distribute the 2 on the left side of the equation:

8x - 2 = -10x + 6 + 4

When we distribute the 2, we get 2 * 4x - 2 * 1, which simplifies to 8x - 2.

Combine like terms on both sides of the equation:

8x - 10x = 6 + 4 - 2

-2x = 8

On the left side of the equation, we have 8x - 10x, which simplifies to -2x. On the right side of the equation, we have 6 + 4 - 2, which simplifies to 8.

Divide both sides of the equation by -2 to solve for x:

x = -4

When we divide both sides of the equation by -2, we get -2x / -2 = 8 / -2, which simplifies to x = -4.

Therefore, the solution to the equation is x = -4.

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Answer:

39

Step-by-step explanation:

2×4²+7
2×16+7

32+7=39

(brainlist ty)

The income that's made based on the equation when 1 comb is sold is $0.5.

From the information given, the equation is given as y = x/2. In this case, it was illustrated that the income is depicted based on the combs sold.

Therefore, the income by selling 1 comb will be:

y = 1/2

y = $0.5

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Answer:

C

Step-by-step explanation:

negative four raised to the sixth power divided by negative four raised to the fourth power

because  negative four raised to the fourth power divided by negative four raised to the second power = negative four raised to the second power

negative four raised to the sixth power divided by negative four raised to the fourth power also = negative four raised to the second power

The answer is A: negative four raised to the second power divided by negative four raised to the fourth power. This is obtained by applying the rules of exponents, specifically, when dividing with the same base, subtract the exponents.

This question pertains to exponents division rules. According to the rule of Power of a Power in exponents, when you divide expressions with the same base, you subtract the exponents. So if you have negative four raised to the fourth power (-4⁴) and you want to divide it by negative four raised to the second power (-4²), you subtract 2 from 4 to get an exponent of 2. This results in a negative four raised to the second power (-4²). So, the correct option from the given choices in your question is A: negative four raised to the second power divided by negative four raised to the fourth power.

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Answer: 4 blue chips (brochure), 6 yellow chips (news article), and 10 red chips (computer presentation).

Step-by-step explanation: If you have 20 colored chips, then 20% of the people that chose the brochure will be 20% of 20 of the chips. That is 20 * 0.2 = 4. Now, to find how to model the people who chose the news article, it will be 30% of the 20 chips. That is 20 * 0.3 = 6. Thus, 6 chips can be modeled for the news articles. Lastly, we add 6 + 4 and that is 10. The rest is another ten out of the 20. Thus, we can use 10 red chips to model the computer presentation.

The teacher should use 4 blue chips for the making a brochure option, 6 yellow chips for the writing a news article option, and 10 red chips for the designing a computer presentation option.

A division is a process of splitting a specific amount into equal parts.

To model this situation using colored chips, we can use the following approach:

Divide the total number of chips (20) into five equal parts, each representing 20% of the total number of students.

For the making a brochure option, use four blue chips to represent the 20% of students who choose this option.

For the writing a news article option, use six yellow chips to represent the 30% of students who choose this option.

For the designing a computer presentation option, use ten red chips to represent the remaining 50% of students who choose this option.

So, the teacher should use 4 blue chips for the making a brochure option, 6 yellow chips for the writing a news article option, and 10 red chips for the designing a computer presentation option.

Hence,  the teacher should use 4 blue chips for the making a brochure option, 6 yellow chips for the writing a news article option, and 10 red chips for the designing a computer presentation option.

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The series diverges with an integral of 1/ln(16) and the series converges with an integral of 1/4 and a sum of 1/2.

We can use the integral test to determine the convergence of the series ∑n=1∞ 1/6n. The integral of the function f(x) = 1/6x is:

\(∫f(x) dx = (1/6) ln(x) + C\)

Using the limits of integration from 1 to ∞, we get:

∫1∞ f(x) dx = (1/6) ln(∞) - (1/6) ln(1) = ∞

Since the integral diverges, the series also diverges.

We can use the integral test to determine the convergence of the series ∑n=1∞ \((n+4)/(n^2+8n+4\)). The integral of the function f(x) = \((x+4)/(x^2+8x+4)\) is:

∫f(x) dx = (1/2) ln(x^2 + 8x + 4) + 3 ln|x + 4| + C

Using the limits of integration from 1 to ∞, we get:

∫1∞ f(x) dx = (1/2) ln(∞) + 3 ln(∞ + 4) - (1/2) ln(13) - 3 ln(5) = ∞

Since the integral diverges, the series also diverges.

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The solution to the given differential equation is: x⁷ cos y = y + C

where C is the constant of integration

To solve the given differential equation:

\(\[7x^6\cos y dx - dy = 0\]\)

We can separate the variables and integrate both sides.

Separating variables, we can write the equation as:

\(\[7x^6\cos y dx = dy\]\)

Now, we can integrate both sides with respect to their respective variables:

\(\[\int 7x^6\cos y dx = \int dy\]\)

Integrating the left side:

\(\[\int 7x^6\cos y dx = 7 \int x^6 \cos y dx\]\)

To integrate \(\(x^6 \cos y\)\)with respect to x, we can use integration by parts.

Let's take u = x⁶ and \(\(dv = \cos y dx\)\).

Differentiating u with respect to \(\(x\) gives \(du = 6x^5 dx\).\)

Integrating dv with respect to x gives \(\(v = \int \cos y dx = \cos y \cdot x\).\)

Applying the integration by parts formula:

\(\[\int x^6 \cos y dx = u \cdot v - \int v \cdot du\]\)

Substituting the values:

\(\[\int x^6 \cos y dx = x^6 \cdot \cos y \cdot x - \int (\cos y \cdot x) \cdot (6x^5 dx)\]\)

Simplifying:

\(\[\int x^6 \cos y dx = x^7 \cos y - 6 \int x^6 \cos y dx\]\)

Moving the integral term to the left side:

\(\[7 \int x^6 \cos y dx = x^7 \cos y\]\)

Dividing both sides by 7:

\(\[\int x^6 \cos y dx = \frac{x^7 \cos y}{7}\]\)

Now, substituting this result back into our original equation:

\(\[7 \int x^6 \cos y dx = dy\]\)

\(\[\frac{7x^7 \cos y}{7} = dy\)

Simplifying:

x⁷ cos y = dy

Finally, the solution to the given differential equation is:

x⁷ cos y = y + C

where C is the constant of integration.

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If you spend $100 at a store such as Sam's Club or Costco, you would save $20 compared to shopping elsewhere.

However, since you would also have to pay the annual membership fee of approximately $40, you would actually lose $20 ($20 saved - $40 membership fee). Therefore, in this scenario, you would not come out ahead and would actually be better off not having a membership and paying full price elsewhere.
Hi! Based on the information provided, if you spend $100 in one year at a store like Sam's Club or Costco with a $40 annual membership fee, you can save $20 for every $100 spent compared to shopping elsewhere.

In this scenario, you would save $20 from the $100 spent. However, you also have to account for the $40 membership fee. So, your net savings would be:

$20 (savings) - $40 (membership fee) = -$20

Since the result is negative, you would actually lose $20 compared to not having a membership and paying full price at another store. To come out ahead, you would need to spend more than the break-even point, which is calculated as:

Membership fee / Savings per $100 = Break-even spending
$40 / $20 = $200

So, you would need to spend at least $200 in a year at the membership store to start saving money compared to shopping elsewhere.

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The quotient of a number and its reciprocal is the square of that number.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

here,

let the number be x and its reciprocal is 1 / x.
now,
the quotient of the x and 1 / is,
= x ÷ 1 /x
= x * x
= x²
So,
9 ÷ 1 / 9 = 81
2 / 3 ÷ 3 / 2 = 4 / 9
1 / 7 ÷ 7 = 1 / 49

Thus, the quotient of a number and its reciprocal is the square of that number.

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An inequality for this situation "A cruise ship can carry at most 3500 passengers." is x ≤ 3,500.

A graph of the inequality x ≤ 3,500 is shown in the image attached below.

What is an inequality?

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Note: At most simply refers to less than or equal to (≤) in Mathematics.

Since the cruise ship can only carry at most 3500 passengers, an inequality that models this situation is given by;

x ≤ 3,500

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Answer:

72

Step-by-step explanation:

Given that 2x + 3y = 12 , then

(2x + 3y)² = 12² = 144 ← distribute left side using FOIL

4x² + 12xy + 9y² = 144 ( subtract 12xy from both sides )

4x² + 9y² = 144 - 12xy = 144 - 12(6) = 144 - 72 = 72

The equation of a given situation:

                  2x - 157 = 755

Dave Winfield has 465 home runs.

Hank Aaron has 157 runs fewer than twice the runs that Dave Winfield has.

Hank Aaron hits 755 home runs.

Assume that Dave Winfield has X runs.

The equation is 2x - 157 = 755 --------------------------- (1)

solving the equation (1),

    2x - 157 = 755

⇒ 2x = 755 + 157

⇒ 2x = 912

⇒ x = 456

∴ Dave Winfield has 465 home runs.

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Step-by-step explanation:

(u - 9) - 8

the difference of u and 9 = (u - 9)

8 fewer than that means to subtract 8 from the difference result.

Answer:

13, or 13.1

Step-by-step explanation:

For this problem, we have a Right Triangle. We should use the Tangent of 54°.

\(Tangent \ = \ \frac{Opposite \ Side}{Adjacent \ Side}\)

(Use a Calculator to find x)

Tan(54°) = \(\frac{18}{x}\)

Divide 18 by Tan(54°):

\(\frac{18}{tan(54)}\) ≈ \(13 \ or \ 13.1 \ (tenths \ place)\)

x ≈ 13, 13.1

Suppose AB = AC, where B and C are nx p matrices and A is invertible and this is not true when A is not invertible.

From the assumptions ,Since it is given that AB = AC, divide both sides by matrix A.  So, correct option is B.

An equivalent equation to AB = AC using A^- 1 such that, when it is simplified, the resulting equation will simplify to B = C is B = C(A^-1)

If AB = AC and A is invertible, then we can multiply both sides by A^-1 to get A^-1(AB) = A^-1(AC), which simplifies to B = C. This is true only when A is invertible, because if A is not invertible, then A^-1 does not exist and we cannot perform this operation.

From the assumption that AB = AC and A is invertible, we can deduce that we can cancel out A from both sides of the equation by multiplying both sides by A^-1. This gives us B = C, which shows that B and C are equal. So, correct option is B.

To write an equivalent equation to AB = AC using A^-1, we can multiply both sides by A^-1 on the right. This gives us AB(A^-1) = AC(A^-1), which simplifies to B = C(A^-1).

Then, we can multiply both sides by A to get BA = CA, and from the previous step we know that C(A^-1) = B. Thus, we have shown that BA = CA implies B = C, which proves that B = C if AB = AC and A is invertible.

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Step-by-step explanation:

just breathe and read it carefully. no need for panic. all you need is common sense, nothing fancy.

the tools and definitions to use are given in the description. we only need to use them.

the height of the point of view is 44 + 6 = 50 ft (because the eyes are again 6 ft above the top of the hill, and we are dealing with what the eyes can see).

so, the seeable distance D in miles is then

D = sqrt(2×50) = sqrt(100) = 10 miles

she will be able to see approximately 10 miles to the horizon.

Answer:

Volume

Step-by-step explanation:

Answer:

Volume

Step-by-step explanation:

Answer:

It will make 4 90° turns, because each 1/4 turn or 15 minutes is 90°.