write the integer as a product of two integers such that one of the factors is a perfect square
27

The length of the side DC is 10.099 units.

Similar triangles are those triangles whose corresponding sides are in the same ratio. And the corresponding angles measure the same. It is denoted by the ‘~’ symbol.

Given that DE is parallel to AB. Therefore, the two triangles, ΔCDE and ΔABC are similar to each other.

For a similar triangle, the ratio of the corresponding sides are in the same ratio, therefore, it can be written as,

DC/AC = DE/AB = CE/BC

Take the first two terms,

DC/AC = DE/AB

DC × AB = DE × AC

As the length of AB is the same as the length of DC,

DC × DC = DE × AC

DC² = 6 units × 17 units

DC² = 102 units²

DC = 10.099 units

Hence, the length of the side DC is 10.099 units.

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The complete question with the image of the triangle is mentioned below.

Question: In the diagram below, DE is parallel to AB. if the length of AB is the same as the length of DC, AC=17, and DE=6, find the length of DC.

The value of (2x^4+x^3-x^2+3)+(4x^4-2x^3-x^2+10x+2) is 6x⁴-x³-2x²+10x+5

Expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

Adding two expressions together requires to collect like terms. like terms are terms with similar variable. For example, in 2x²+6x+x² , x² and 2x² are like terms.

Therefore, 2x⁴+x³-x²+3 + 4x⁴-2x³-x²+10x+2 can be simplified as;

2x⁴+4x⁴+x³-2x³-x²-x²+10x+2+3

= 6x⁴-x³-2x²+10x+2

therefore, the value of 2x⁴+4x⁴+x³-2x³-x²-x²+10x+2 is 6x⁴-x³-2x²+10x+5.

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The percent error is 25%

The first step is to calculate the error

= 5 - 4

= 1

The percent error can be calculated as follows

= 1/4 × 100

= 0.25 × 100

= 25%

Hence the percent error is 25%

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Answer:

To fill in the blank, let's first expand the left-hand side of the equation:

(2d-5)(2d-4)

= 2d * 2d + 2d * (-4) -5 * 2d -5 * (-4) (using the distributive property)

= 4d^2 - 8d - 10d + 20

= 4d^2 - 18d + 20

Now, we can compare this with the right-hand side of the equation, which is 4d^2 + blank d + 20.

Comparing the coefficients of the like terms, we can see that the blank should be filled with -18, since the coefficient of d on the left-hand side is -18 (from -8d - 10d) and the coefficient of d on the right-hand side is blank.

So, the filled-in equation becomes:

(2d-5)(2d-4) = 4d^2 - 18d + 20

Brainlyest!?

Answer:

Step-by-step explanation:

(2d - 5) x (2d - 4)

= 4d^2 - 8d - 10d + 20

= 4d^2 - 18d + 20

Therefore Answer is -18.

The equation to find the total number of lessons is T = 6 + 12 = 18, and the ratio to find the total cost of the lessons is c:T = 72:18 or  4:1.

The equation to find the total number of lessons (T) can be written as:

T = number of salsa lessons + number of rumba lessons

Substituting the given values, we get:

T = 6 + 12 = 18

The ratio to find the total cost of the lessons (c) can be written as:

c = cost per lesson x total number of lessons

Substituting the given values, we get:

c = $4 x 18 = $72

Therefore, the equation to find the total number of lessons is T = 6 + 12 = 18, and the ratio to find the total cost of the lessons is c:T = 72:18 = 4:1.

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Step-by-step explanation:

distance / rate = time                s = plane speed    w = wind speed

Flying with wind       1053 / ( s+ w) = 1.75

                                   solve for s = 601.714 -w

Flying against wind  1053 / (s-w) = 2.75       sub in for s (above)

                                  1053 / ( 601.714 - w   -w )  = 2.75

                                          solve for w = 109.27 mi/hr  

sub this 'w'  into one of the equations to solve for 's'

          1053 / ( s + 109.273) = 1.75      shows   s = 492.44  mi/hr

The Dimensions of the tent are: Base of triangular face (b): 4.46 ft, Height of triangular face (0.5b): 2.23 ft, Length of tent (b + 1): 5.46 ft.

With two triangular bases and three rectangular sides, a triangular prism is a three-dimensional geometric form. The rectangular faces link the matching edges of the bases, which are connected by the parallel triangular bases. This produces a form with a triangular cross-section along the prism's length. The distance between the vertices of the triangle bases is referred to as the length, whereas the height of the prism is the perpendicular distance between the bases.

Given:

Volume of tent = [tex]63 ft^3[/tex]

Let's assume the base of the triangular face of the tent is "b" feet. The height of the triangular face is half of the base, so it would be "0.5b" feet.

The length of the tent is given to be 1 foot more than the base, so the length would be "b + 1" feet.

Mathematically, the volume of a triangular prism can be given by:

[tex]Volume = (1/2) * base * height * length[/tex]

Substituting the given values and rearranging the formula to solve for "b":

[tex]63 = (1/2) * b * (0.5b) * (b + 1)\\126 = b^2 * (0.5b) * (b + 1)\\0.5b^3 + 0.5b^2 - 126 = 0[/tex]

Solving this cubic equation, we get "b ≈ 4.46" (rounded to two decimal places).

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Answer:

1)   13    **Explained below **

2)   4    **Explained below **

3)   6

4)   8

5)   15

6)   2.64575    **Explained below **

Step-by-step explanation:

All 6 problems can be solved using the Pythagorean theorem using the following two rules

If x is the hypotenuse and a, b are the shorter sides then
[tex]x = \sqrt{a^2 + b^2}[/tex]

If x is one of the shorter sides and a (or b) is the other shorter side and c is the hypotenuse then

[tex]x = \sqrt{c^2 - a^2\\[/tex]  if a is the other shorter side

[tex]x = \sqrt{c^2 - b^2\\[/tex]  if b is the other shorter side

I will just demonstrate for  #1 , #2 and #6. You can figure out the reasoning behind the rest.

#1. x is the hypotenuse, 5 and 12 are legs(shorter sides)

[tex]x = \sqrt{5^2 + 12^2}\\\\x = \sqrt{25 + 144}\\\\x = \sqrt{169}\\\\x = 13\\\\[/tex]

# 2. x is one of the shorter sides (leg)

5 is the hypotenuse and 3 is the other shorter side

[tex]x = \sqrt{5^{2} - 3^{2}}\\\\x = \sqrt{5^{2} - 3^{2}}\\\\x = \sqrt{25 - 9}\\\\x = \sqrt{16}\\\\x = 4[/tex]

#6  hypotenuse is 4, short side = 3

[tex]x = \sqrt{4^{2} - 3^{2}}\\\\x = \sqrt{4^{2} - 3^{2}}\\\\x = \sqrt{16 - 9}\\\\x = \sqrt{7}\\\\x = 2.64575\\\\[/tex]

Answer:

140

Step-by-step explanation:

First you want to add up the numbers inside of the hexagon and set them equal to 720. Your starting equation should be 3x+240=720. Then your going to subtract 240 from each side giving you 3x=480. Next divide each side by 3 giving you x=160. Plug 160 in for x and you should get 160-20= 140.

Answer:

140

Step-by-step explanation:

First you want to add up the numbers inside of the hexagon and set them equal to 720. Your starting equation should be 3x+240=720. Then your going to subtract 240 from each side giving you 3x=480. Next divide each side by 3 giving you x=160. Plug 160 in for x and you should get 160-20= 140.

You have to apply the outside exponent to each piece inside the parentheses.

[tex]\begin{aligned}\left(2a^2\right)^3 &=(2)^3\cdot\left(a^2\right)^3\\[0.5em]&=8 a^6\end{aligned}[/tex]

You have to apply the outside exponent to each piece inside the parentheses.

[tex]\begin{aligned}\left(2a^2\right)^3 &=(2)^3\cdot\left(a^2\right)^3\\[0.5em]&=8 a^6\end{aligned}[/tex]

Part(A),

The percentage of friends who named Chocolate Chip is 18%.

Part(B),

We cannot determine that the most popular ice cream flavour for the general population is Pistachio and Vanilla based solely on the student's findings.

A bar chart is a graphical representation of data that uses bars of varying heights or lengths to represent the values of a set of data. The bars can be horizontal or vertical, and they are usually spaced equally apart to represent the categories or groups being compared.

Part A:

Let's say we choose the Chocolate Chip flavour. From the bar graph, we can see that 18% of the surveyed friends named Chocolate Chip as their favourite flavour. Therefore, the percentage of friends who named Chocolate Chip is 18%.

Part B:

We cannot determine that the most popular ice cream flavour for the general population is Pistachio and Vanilla based solely on the student's findings. The survey only represents a small sample size of the student's friends, and may not accurately reflect the preferences of the entire population. It is possible that the most popular flavour for the general population is different from what was found in the survey.

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Answer:

f = -15

Step-by-step explanation:

Use algebra to solve!

f/3 + 22 = 17

f/3 = 17 - 22 (bring 22 to the other side, this changes the sign from plus to minus)

f/3 = -5 {because 17-22 = (-5)}

f = (-5) (3) {to eliminate 3 from the denominator of f, you do the opposite of division which is multiplication, so -5 times 3}

therefore, f = -5

You can also check this answer by putting it back into the original equation, -15/3 is -5 and then -5 + 22 = 17.

Jake measured a hotel and made a scale drawing, the length of the room in the drawing is 24 inches.

If the scale of the drawing is 8 inches : 7 feet, this means that for every 8 inches in the drawing, there are 7 feet in real life.

To find out length of the room is in the drawing, we need to set up a proportion:

8 inches / 7 feet = x inches / 21 feet

where x is the length of the room in the drawing.

We can cross-multiply and solve for x:

8 inches × 21 feet = 7 feet × x inches

168 inches = 7 feet × x inches

Dividing both sides by 7, we get:

24 inches = x

Therefore, the length of the room in the drawing is 24 inches.

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A Organic shape is one that does not have an identifiable name. While still flat, 2-D enclosed areas, these shapes are more "freeform" and might resemble things that we see in nature.

Geometric shapes are well-defined, regular shapes described by mathematical formulas, including circles, squares, triangles, and rectangles. Symmetrical shapes exhibit mirror-like symmetry, like butterflies or snowflakes.

Organic shapes  appear in natural objects like leaves or rocks; they are flowing and curvilinear in form, with varying size, proportions, and contours. Organic shapes are free from strict rules and symmetry, often used in art.

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Answer:

Step-by-step explanation:

By the law of cosines, [tex](59.7)^2=52^2+41^2-2\cdot 52 \cdot 41 \cos(\angle R).[/tex]

Thus, after solving for [tex]\cos(\angle R)[/tex], we get [tex]\cos(\angle R) = 0.1925211.[/tex] So taking the inverse cosine then yields [tex]\boxed{\angle R = 1.377 \text{ rad}}.[/tex]

Answer:

Step-by-step explanation:

By the law of cosines, [tex](59.7)^2=52^2+41^2-2\cdot 52 \cdot 41 \cos(\angle R).[/tex]

Thus, after solving for [tex]\cos(\angle R)[/tex], we get [tex]\cos(\angle R) = 0.1925211.[/tex] So taking the inverse cosine then yields [tex]\boxed{\angle R = 1.377 \text{ rad}}.[/tex]

Answer:

scale factor = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

the side corresponding to WX is EH

the scale factor is the ratio of corresponding sides, image to original, so

scale factor = [tex]\frac{EH}{WX}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

The market's required rate of return for Samsung's common stock is 5.53%, rounded to two decimal points

What is meant by the rate of stock?

The rate of stock refers to the price at which a particular stock is being bought or sold in the stock market, which can vary based on supply and demand.

What is decimal?

A decimal is a number system that uses the base 10 and includes a decimal point to separate the integer part from the fractional part. It is commonly used in mathematics and everyday life for expressing fractions, percentages, and monetary values.

According to the given information

We can use the constant-growth dividend discount model to calculate the market's required rate of return for the stock. The model is:

Current stock price = Dividend next year / (Required rate of return - Dividend growth rate)

We know the current stock price is $216, the dividend next year is $1.14, and the dividend growth rate is 5%. We need to solve for the required rate of return.

216 = 1.14 / (r - 0.05)

Multiplying both sides by (r - 0.05), we get:

216(r - 0.05) = 1.14

Expanding the left side, we get:

216r - 10.8 = 1.14

Adding 10.8 to both sides, we get:

216r = 11.94

Dividing both sides by 216, we get:

r = 0.0553 or 5.53%

Therefore, the market's required rate of return for Samsung's common stock is 5.53%, rounded to two decimal points

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The market's required rate of return for Samsung's common stock is 5.53%, rounded to two decimal points

What is meant by the rate of stock?

The rate of stock refers to the price at which a particular stock is being bought or sold in the stock market, which can vary based on supply and demand.

What is decimal?

A decimal is a number system that uses the base 10 and includes a decimal point to separate the integer part from the fractional part. It is commonly used in mathematics and everyday life for expressing fractions, percentages, and monetary values.

According to the given information

We can use the constant-growth dividend discount model to calculate the market's required rate of return for the stock. The model is:

Current stock price = Dividend next year / (Required rate of return - Dividend growth rate)

We know the current stock price is $216, the dividend next year is $1.14, and the dividend growth rate is 5%. We need to solve for the required rate of return.

216 = 1.14 / (r - 0.05)

Multiplying both sides by (r - 0.05), we get:

216(r - 0.05) = 1.14

Expanding the left side, we get:

216r - 10.8 = 1.14

Adding 10.8 to both sides, we get:

216r = 11.94

Dividing both sides by 216, we get:

r = 0.0553 or 5.53%

Therefore, the market's required rate of return for Samsung's common stock is 5.53%, rounded to two decimal points

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Answer:

4,500.00 rupees

Step-by-step explanation:

Answer:

(a) 3581 N

(b) 6.1 kJ

(c) 4.5 kJ

(d) 74.6%

Step-by-step explanation:

(a) To lift the piano straight up, we need to counteract the force of gravity acting on it. The force required can be calculated using the formula F = mg, where F is the force, m is the mass of the piano, and g is the acceleration due to gravity. So, F = (230 kg) x (9.81 m/s^2) = 3581 N.

(b) The work done in lifting the piano is given by the formula W = Fd, where W is the work done, F is the force required to lift the piano, and d is the height to which the piano is lifted. So, W = (3581 N) x (1.7 m) = 6.1 kJ.

(c) Using a ramp reduces the force required to lift the piano. The force required can be calculated using the formula F = mg sinθ, where θ is the angle of inclination of the ramp. We are given that the force required is 300 N and the length of the ramp is 15 m. So, sinθ = F/mg = 300/(230 x 9.81) = 0.1416. Therefore, θ = sin^-1(0.1416) = 8.13 degrees. The work done using the ramp can be calculated using the formula W = Fd, where d is the height to which the piano is lifted. Using trigonometry, we can find that the height to which the piano is lifted is 1.53 m. So, W = (300 N) x (15 m) x sin 8.13 degrees = 4.5 kJ.

(d) The efficiency of the ramp is the ratio of the work output to the work input, expressed as a percentage. The work output is the same as the work done using the ramp, which is 4.5 kJ. The work input is the same as the work done when lifting the piano straight up, which is 6.1 kJ. So, the efficiency of the ramp is (4.5/6.1) x 100% = 74.6%.

Answer:

[tex] - 9 {g}^{3} + {g}^{2} + 10g - 5[/tex]

A recursive definition for the set S of ordered pairs of positive integers (a,b) where a is a factor of b can be given as follows:

1. The ordered pair (1, b) is in S for all positive integers b.

2. If a is a factor of b, then (a, b) is in S if and only if (a, b/a) is in S.

The first rule establishes the base case for the recursion, stating that (1, b) is in S for all b. The second rule provides the recursive step, stating that (a, b) is in S if and only if (a, b/a) is in S, where b/a is an integer division of b by a, and a is a factor of b. This recursive definition ensures that all pairs (a, b) in S have a as a factor of b.

The journal entry for the given information is below:

Journal entries:    

S.no. Accounts title andd explanations Debit $ Credit $

a. Accounts receivable   2500

Service revennue    2500

b. Cash account   2000

Service revenue    2000

c. Cash account   500

Unearned service revenue   500

d. Accounts receivabale  1500

Cash account    1500

e. Rent Payable   500

Cash account    500

f. Rent expenses   750

Rent payable    750

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Answer:

14 grams = 14,000 milligrams

Step-by-step explanation:

since multiply the grams by 1000 will convert it to milligrams

The area of the triangle is 22 miles square

From the question, we have the following parameters that can be used in our computation:

The triangle

Where we have

Base = 11 miles

Height = 4 miles

using the above as a guide, we have the following:

Area = 1/2 * Base * Heigt

substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 11 * 4

Evaluate

Area = 22 miles square

hence, the area is 22 miles square

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Step-by-step explanation:

a 1/15 for getting 0

b 2/14 for getting u

c 2/210 or 3/210

If P(A)= [tex]\frac{2}{3}[/tex], P(B) = [tex]\frac{1}{4}[/tex] and P(A and B)= [tex]\frac{2}{7}[/tex], then the events A and B are dependent.

By comparing the probability of events A and B intersection (P(A and B)) to the product of their individual probabilities (P(A) * P(B)), we can find out whether the events are independent or dependent.

Condition of independent events,

If P(A) * P(B) = P(A and B)

Condition of dependent events,

If P(A) * P(B) ≠ P(A and B)

Given,

P(A) = [tex]\frac{2}{3}[/tex]

P(B) = [tex]\frac{1}{4}[/tex]

P(A and B) = [tex]\frac{2}{7}[/tex]

Calculating P(A) * P(B) and compare it to P(A and B):

P(A) * P(B) = [tex]\frac{2}{3}[/tex] * [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{12}[/tex] = [tex]\frac{1}{6}[/tex]

Since P(A and B) ≠ P(A) * P(B), therefore events A and B are dependent.

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Answer:

x = 115°

Step-by-step explanation:

The interior angle adjacent to the 115° angle measures:

180° - 115° = 65°

x is an exterior angle, so x = 65° + 50°

x = 115°

Answer:

115

Step-by-step explanation:

X has to be supplementary to that adjacent angle, so first the angle next to the 115 has to be defined. 180-115 (as the must be supplementary) is 65. 65+ 50= 115, which should be x. The 2 opposite angles will equal the opposite outside angle. Hope this helps!