Which of these figures is a concave polygon?

The length of EB is approximately 14.6 units when rounded to the nearest tenth.

To find the length of EB, we can use the property of similar triangles in this diagram. By looking at triangle DFE and triangle CFB, we can see that they are similar triangles.

Using the similarity ratio, we can set up the proportion:

DF / CF = DE / EB

Plugging in the given values, we have:

13.1 / 10.9 = 17.5 / EB

To find EB, we can cross-multiply and solve for EB:

13.1 * EB = 10.9 * 17.5

EB = (10.9 * 17.5) / 13.1

EB ≈ 14.6

Therefore, the length of EB is approximately 14.6 units when rounded to the nearest tenth.

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Answer:

  499.338 feet

Step-by-step explanation:

You want to know the distance traveled by an object in 25 seconds when its velocity is described by 20+5cos(t) feet per second.

The distance an object travels is the integral of its velocity. For the given velocity and time period, the distance is ...

  \(\displaystyle d=\int_0^{25}{v(t)}\,dt=\int_0^{25}{(20+5\cos(t))}\,dt=(20t+5\sin(t))|_0^{25}\\\\d=500+5\sin(25)\approx\boxed{499.338\quad\text{feet}}\)

The distance traveled in 25 seconds is 499.33 feet.

It is required to find the distance traveled in 25 seconds.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

We have to find the distance , we will integrate v(t) from 0 to 25 second.

Consider an object traveling at constant velocity v = k. Then, each second, it travels k feet, so after t seconds, the distance traveled is k*t.

Now, suppose its speed increases by 1 feet/sec . So, estimate for distance traveled after t seconds is

1 + 2 + 3 + 4 + ... + t = t(t+1)/2, or approximately 1/2 t^2.

According to given question we have

Given a velocity function v, the distance s is figured by taking the integral. In this case,

v = 20 + 5 cos(t)

s = 20t + 5 sin(t) from 0 to 25

= s(45)-s(0)

s(0) = 0

so, the distance is

s(25) = 20*25 + 5sin(25)

= 500 -0.661

=499.33 feet.

Therefore, the distance traveled in 25 seconds is 499.33 feet.

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Answer:

\((x-(3+\sqrt5))\) or \((x-3-\sqrt5)\) is a factor of the given polynomial.

Step-by-step explanation:

Let us learn the concept with an example first.

Let the polynomial be a quadratic function \(g(x)\).

\(g(x) = x^{2} -5x+6\)

The roots of \(g(x)\) are 2 and 3.

Putting \(x= 2\ in \ g(x)\)

\(2^2-5\times 2+6 = 4-10+6 =0\)

Putting \(x= 3\ in \ g(x)\)

\(3^2-5\times 3+6 = 9-15+6 =0\)

Putting x = 2 or x = 3, g(x) = 0 \(\therefore\) The roots of equation g(x) are 2 and 3.

Now, let us try to factorize g(x):

\(x^{2} -2x-3x+6\\\Rightarrow x(x -2)-3(x-2)\\\Rightarrow (x-3)(x-2)\)

so, the equation can be written as:

\(g(x) = x^{2} -5x+6=(x-3)(x-2)\) where 3 and 2 are the roots of equation.

The factors are (x-3) and (x-2).

\(\therefore\) for the polynomial f(x) which has roots \(3+\sqrt5\ and\ -6\) will have a factor:

\((x-(3+\sqrt5))\) or \((x-3-\sqrt5)\)

Volume of solid generated by revolving the region bounded by the graph is 3817.53 unit

A volume is created while a plane figure rotating about an axis or around any straight line situated on the same plane.

We apply definite integration to calculate the required volume.

we are given the equation y = 5x² and y =0, x= 3

volume is calculated by using the formula, V = ∫π y² dx

                                                                      V = ∫₀³π (5x²) ² dx

On the y-axis x = 0 so upper limit x = 3 and lower limit x= 0

                                                          V= π × 25/5 [x⁵] ³₀

                                                        V = 15.71 [3⁵- 0]

  hence, the volume of solid = 3817.53 unit

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The total value of the furniture sold by Joyce last week is A = $ 6,733.33

Given data ,

Let's call the value of the furniture Joyce sold "x".

She receives 10% commission on the first $1,200 of sales, which is $120:

Commission on first $1,200 = 0.1 * 1200 = 120

The remaining sales that she earns commission on is the difference between the total value of the furniture sold and the first $1,200:

Remaining sales = x - 1200

She earns 15% commission on the remaining sales, which is 0.15 times the remaining sales:

Commission on remaining sales = 0.15 * (x - 1200)

Her total earnings from commission last week was $950. So we can write an equation:

Commission on first $1,200 + Commission on remaining sales = $950

Substituting the expressions we found for the two commissions, we get:

120 + 0.15(x - 1200) = 950

120 + 0.15x - 180 = 950

On simplifying the equation , we get

0.15x - 60 = 950

0.15x = 1010

x = 6,733.33

Hence , the value of the furniture Joyce sold last week was $6,733.33

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Answer:

\(\frac{7}{24} \)

Step-by-step explanation:

Question : \(\frac{1}{6} +\frac{1}{8} \)

Answer :

\(\frac{1}{6} +\frac{1}{8} \)

\(\frac{1*8}{6*8} + \frac{1*6}{8*6} \)

\(\frac{8}{48} +\frac{6}{48} \)

\(\frac{14}{48} \)

Now to simplify the fraction divide both 2.

\(\frac{7}{24} \)

Hope this helps you :-)

Let me know if you have any other question :-)

According to the statement, the Ship must move at an average pace of 150 meters per hour.

The variable under examination is lessened when the gradient is "downhill" (negative). When used as a gauge of how well things are doing, "downhill" denotes a downward trend. Yet, if this indicates trouble or some other unpleasant quality, the situation is improving.

The chess player Carissa walks very, very slowly. She actually moves at speeds of 100 meters per hr upward, 150 meters per hr on flat terrain, and 200 meters every hour on downhill terrain.

Here,

Carissa traverses Boston on foot from a coffeehouse to a boba store before returning over the same path.

Total distance walked = 2 [200 + 100 + 150] = 900 meter

Total time = 2 [1 + 1 + 1] = 6 hour

Average speed is calculated as distance divided by time (900 / 6 = 150 m/s),

As a result, the needed Carissa average speed is 150 meters per hr.

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Answer:

21. 2x + 28

22. 18a - 17b

23. He flipped the numerator and denominator, 6.4 with 7.2 and he added the exponents instead of subtracting.

24. 8.8888888888889 × 10^{0}

Step-by-step explanation:

Answer:

22 1/2

Step-by-step explanation:

Main Answer: The total surface area of cylinder B is approximately 476.7  square units.

Supporting Question and Answer:

How is the surface area of a cylinder calculated?

The surface area of a cylinder is the sum of the areas of its curved surface and two circular bases. It can be calculated using the formula:

A = 2πrh + 2π\(r^{2}\)

where "r" is the radius of the circular base, "h" is the height of the cylinder, and π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter, approximately equal to 3.14159.

The first term, 2πrh, represents the area of the curved surface of the cylinder, while the second term, 2π\(r^{2}\), represents the combined area of the top and bottom circular bases.

Body of the Solution: Let the height and radius of cylinder A be "h" and "r" respectively. Then, the height and radius of cylinder B are "2h" and "R" respectively, since cylinder B has twice the height of cylinder A but the same radius.

The total surface area of a cylinder is given by the formula:

Area = 2πrh + 2π\(r^{2}\)

For cylinder A, we know that the surface area is 180, so we can substitute the values and solve for "r" as follows:

180 = 2πrh + 2π\(r^{2}\)

90 = πrh + π\(r^{2}\)

We can rearrange this equation to solve for r:

r² + rh - 90/π=0

Using the quAdratic formula,we get:

r = (-h ± √((h)² + 4(90/π)))/2

r = -h/2 ± √(h² + 4(90/π))/2

Now we have an expression for r in terms of h . We can use this expression to find the radius of cylinder B, since we know that cylinder B has twice the height of cylinder A.

R = 2r= -h ± √(h² + 4(90/π))

We can use this expression to find the surface area of cylinder B:

Surface area of cylinder B = 2πR² + 2πR(2h)

Surface area of cylinder B= 2π( -h ± √(h² + 4(90/π)))² + 4πh( -h± √(h² + 4(90/π)))

We can use the value we found for 2h using the quadratic formula in the expression to get:

Surface area of cylinder B = 476.7 square units (rounded to one decimal place)

Therefore, the total surface area of cylinder B is approximately 476.7  square units.

Final Answer: Therefore, the total surface area of cylinder B is approximately 476.7  square units.

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If you can buy 1 bunch of seedless green grapes for $2, then $18 we can buy 9 bunches.

The concept used here is a simple division to find out how many bunches of seedless green grapes can be purchased with a given amount of money.

In this case, we know the cost of one bunch of seedless green-grapes ($2) and we are given a total amount of money ($18) that we can spend on grapes. We can use division to find out how many bunches we can buy with that amount.

⇒ Number of bunches = ($18)/($2) per bunch,

⇒ Number of bunches = 9 bunches;

Therefore, with $18, you can buy 9 bunches of seedless green grapes.

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The square feet of paper that will cover the model is 56 ft squared.

The model above is a square base pyramid. Therefore, the square feet of papers he will need to cover the model is the surface area of the model.

Therefore,

surface area of the square base pyramid = A + 1 / 2 ps

where

Therefore,

p = 4 × 4 = 16 ft

s = 5 ft

A = 4² = 16 ft²

Therefore,

surface area of the square base pyramid = 16 + 1 / 2 × 16 × 5

surface area of the square base pyramid = 16 + 40

surface area of the square base pyramid = 56 ft²

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Equations to use:

x = biology

y = history

x + y = 445.

x - 45 = y

Step-by-step explanation:

hope you understand..........

The true statement about the equation that shows a number multiplied by 6. n x 6 is C. It is a multiple of 6.

A multiple in mathematics is the product of any number and an integer. In other words, for the quantities a and b, b is a multiple of an if b = na for some integer n known as the multiplier. If an is greater than zero, this means that b/a is an integer.

A composite number is one that can be formed by multiplying two smaller positive integers. It is a positive integer with at least one divisor other than 1 and itself.

A prime number is a natural number greater than one that cannot be calculated as the product of two smaller natural numbers. A composite number is a natural number greater than one that is not prime. 5 is prime, for example, because the only ways to write it as a product, 1 5 or 5 1, involve 5 itself.

In this case, the value will be a multiple of C. Therefore, the correct option is C.

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Complete questions

The equation shows a number multiplied by 6. n x 6

Which of these is true about the product?

It is always a composite number.

It is always a prime number.

It is a multiple of 6.

It is a factor of 6.

Answer:

4 lb/month

Step-by-step explanation:

loss of 144 lb in 36 months

144/36 = 4

Answer: 4 lb/month

The length of a 45° arc with a radius of 4 miles is approximately 3.14 miles, calculated using the formula for arc length.

To determine the length of a 45° arc given a radius of 4 miles, we can use the formula: Arc length = (angle measure / 360°) x 2πr, where r is the radius of the circle and π is a constant equal to approximately 3.14.

Substituting the given values into the formula, we get: Arc length = (45° / 360°) x 2π(4 mi)Arc length = (1/8) x 2π(4 mi)Arc length = (1/8) x 8π Arc length = π

The length of the 45° arc is approximately 3.14 miles.

Summary: To find the length of a 45° arc of a circle, we use the formula: Arc length = (angle measure / 360°) x 2πr. Given a radius of 4 miles, we can substitute the values into the formula to get the length of the 45° arc, which is approximately 3.14 miles.

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Answer:

7 to the 8th

Step-by-step explanation:

Answer: The probability of choosing an ace or a club is 16.

Step-by-step explanation:

Answer:

40% of £25.00 is 10

ypu answer should be £10

Step-by-step explanation:

The value of N that satisfies the following equation, 5!9!= 12N!, is 10.

Factorial notation (n!) means to multiply a series of descending natural numbers. Also stated in the problem that for positive integer n, the factorial notation n! represents the product of the integers from n to 1.

Take for example 6! which can be written as 6 x 5 x 4 x 3 x 2 x 1 = 720.

Given the equation 5!9!= 12N!, expand the factorial notation.

(5 x 4 x 3 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = (4 x 3) N!

N! = (5 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)

N! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

N = 10

Therefore, the value of N that satisfies the following equation, 5!9!= 12N!, is 10.

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Answer:

 C.No, because each lime will cost a bit more than 30¢, so 4 limes will cost a bit more than $1.20.Step-by-step explanation:

The unit price of the 8 limes is $0.25 per lime.

The given expression:

The selling price for 8 limes = $2.00

To find:

The unit price of the lime is calculated by dividing the total selling price by the total number of limes purchased.

\(unit \ price = \frac{total \ amount \ paid \ for \ 8 \ limes }{8 \ limes } \\\\unit \ price =\frac{\$ \ 2}{8 \ limes } \\\\unit \ price = (\frac{1}{4} ) \frac{\$}{lime} \\\\unit \ price = \$0.25 \ per \ lime\)

Thus, the unit price of the 8 limes is $0.25 per lime.

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Answer:

Last option

Step-by-step explanation:

\(-2(z + 3) - z = x - 4(z + 2)\)

\(x = -2(z + 3) - z + 4(z + 2)\)

\(x = -2z - 6 - z + 4z + 8\)

\(x = z + 2\)

Answer:

47

Step-by-step explanation:

Simplify the following:

-26 + 6 - -67

Hint: | Multiply -1 and -67 together.

-(-67) = 67:

-26 + 6 + 67

Hint: | Evaluate 6 + 67 using long addition.

| 1 |  

| 6 | 7

+ | | 6

| 7 | 3:

73 - 26

Hint: | Subtract 26 from 73.

| 6 | 13

| 7 | 3

- | 2 | 6

| 4 | 7:

Answer: 47

Based on the definition of  parallelogram, the conclusion about the quadrilateral is that: D. The quadrilateral is a parallelogram, because there are two pairs of equal slopes, and thus two pairs of parallel opposite sides.

If a quadrilateral is a parallelogram, the two pairs of opposite sides will be parallel to each other.

If two sides of a shape have the same slopes, it then means the shape is a parallelogram.

The quadrilateral that is given is said to have the following:

Two equal slopes of 5/4 and 5/4; and 2/5 and 2/5, this means the sides that have the same slope values are opposite to each other.

Since they are opposite to each other and they have the same slope, therefore, the conclusion about the described shape is: D. The quadrilateral is a parallelogram, because there are two pairs of equal slopes, and thus two pairs of parallel opposite sides.

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Answer:

Hope this helps lol !

Step-by-step explanation:

This is how to calculate net price. Start with the list price and add any taxes and other government-mandated charges. Then subtract any discounts, negotiated prices. The result you get will be the net price.

Answer:

b = 3

Step-by-step explanation:

Answer:

variable h is independent

The values of x for which f(x) = 7 are x = 61 and x = 21.

To find the values of x for which f(x) = 7, we can set up the equation and solve for x.

The given function is f(x) = 0.5|x - 41| - 3.

Setting f(x) equal to 7, we have:

0.5|x - 41| - 3 = 7.

First, let's isolate the absolute value term:

0.5|x - 41| = 7 + 3.

0.5|x - 41| = 10.

To remove the absolute value, we can consider two cases:

Case: (x - 41) is positive or zero:

0.5(x - 41) = 10.

Multiplying both sides by 2 to get rid of the fraction:

x - 41 = 20.

Adding 41 to both sides:

x = 61.

So x = 61 is a solution for this case.

Case: (x - 41) is negative:

0.5(-x + 41) = 10.

Multiplying both sides by 2:

-x + 41 = 20.

Subtracting 41 from both sides:

-x = -21.

Multiplying both sides by -1 to solve for x:

x = 21.

So x = 21 is a solution for this case.

Therefore, the values of x for which f(x) = 7 are x = 61 and x = 21.

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Answer:

26

Step-by-step explanation:

Answer:

A on edge

Step-by-step explanation:

I just took the test :3