A student added the rational expressions as follows:
Problem:
Work:
5x
+
x+7
5x
+
x+7
Solution:
7
x
7(7)
x+7
5x+49
x+7
Describe and correct the error the student made. Solve the problem correctly.

Answer:

1039.23 square inches

Step-by-step explanation:

                      a = 20 inches

    [tex]\sf \boxed{\text{\bf Area of regular hexagon = $\dfrac{3\sqrt{3}}{2}a^2$}}[/tex]

                                                   [tex]= \dfrac{3\sqrt{3}}{2}*20*20\\\\= 3\sqrt{3}*200\\\\= 1039.23 \ inches^2[/tex]

Answer:

volume = 290m

Step-by-step explanation:

box 1

[tex]vol= lwh\\=3*5*6\\=90m[/tex]

box 2

[tex]vol=lwh\\=8*5*5\\=200m[/tex]

total volume = 90+200 =290m

The correct coordinates of the center of dilation are (2.8, 3.8).

What is dilation?

In geometry, dilation is a transformation that changes the size of an object. When a figure is dilated, each point of the original figure is moved away from or toward the center of dilation.

Dylan's claim is incorrect because the center of dilation is not necessarily located on the line segment PP'.

To find the center of dilation, we need to locate the image point of a known point after dilation.

Let's consider a point Q on the same line as PP', but on the other side of P', such that PQ = 1 unit. After dilation with a scale factor of 4, the image of Q will be on the line passing through P and P'. Let's denote this image point by Q'.

Since PQ : P'Q' = 1 : 4, the distance from P to Q' is 4 units. Similarly, since PP' : PQ' = 1 : 5, the distance from P to Q' is 5 times the distance from P to P'. Thus, the distance from P to P' is 1 unit and the distance from P to Q' is 5 units.

Therefore, the center of dilation is located on the line passing through P and Q', and is 4 units away from P and 1 unit away from Q'.

Using the midpoint formula, we can find the coordinates of the center of dilation:

[tex]x &= \frac{1}{2}(4.8 + 0.8)[/tex]

[tex]&= 2.8[/tex]

[tex]y &= \frac{1}{2}(3.2 + 4.4)[/tex]

[tex]&= 3.8[/tex]

Thus, the correct coordinates of the center of dilation are (2.8, 3.8).

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Mr. Brust is standing at a height of approximately 90.6 feet in the tree. When they shoot him, he will fall from this height.

Let's break down the problem and solve it step by step.

First, we'll find the height from which Mr. Brust falls, and then we'll find the total distance he falls considering the tree's height and the height of the shed.

Find the height of the tree where Mr. Brust is standing:

We can use the tangent function to find the height of the tree above the shed where Mr. Brust is hiding.

tan(θ) = opposite/adjacent

We know the angle of elevation (θ) is 65°, and the tree is 40 feet in front of the shed. So, we have:

tan(65°) = height_above_shed / 40 ft

height_above_shed = 40 ft * tan(65°)

Using a calculator, we find:

height_above_shed ≈ 40 ft * 2.14 ≈ 85.6 ft

Find the total height of the tree where Mr. Brust is standing:

Since Mr. Kelly and Mr. Sullivan are 5 feet off the ground, we need to add this height to the height_above_shed we just calculated:

total_height = height_above_shed + height_of_shed

total_height = 85.6 ft + 5 ft = 90.6 ft

So, Mr. Brust is standing at a height of approximately 90.6 feet in the tree. When they shoot him, he will fall from this height.

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The specified central angle is 170 degrees since the figure is 17/36 of a full circle.

A central angle is an angle with endpoints on the perimeter and a vertex in the centre of a circle. An arc is defined by the angle in the centre of a circle.

Since the figure represents 17/36 of a full circle, the central angle that it subtends is also equal to 17/36 of 360 degrees (the measure of a full circle).

We can calculate this as follows:

Central angle = (17/36) x 360 degrees

Central angle = 17 x 10 degrees

Central angle = 170 degrees

Therefore, the measure of the marked central angle is 170 degrees.

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Answer:

Step-by-step explanation:

To find:-

Answer:-

As we know that the measure of complete angle about any point is 360° = 2π rad .

Also we are given that the given circle is 17/36 of full circle. So the angle substended too be will be equal to 17/36 of the complete angle.

So that , we have;

==> Angle = 17/36 * 360°

==> Angle = 170°

Hence the value of central angle is 170° .

The perimeter of the figure is approximately 63.6 meters, since the lengths of all the sides add up to the figure's perimeter.

Perimeter is the total length of the boundary of a closed 2-dimensional shape. In other words, it is the distance around the edge of a shape. The perimeter is usually measured in units such as meters, centimeters, feet, or inches depending on the measurement system used. The perimeter can be calculated by adding up the lengths of all the sides of the shape.

Since opposite sides of a parallelogram are equal in length, the length of the straight side of the first parallelogram is:

Length of first parallelogram = 9m

Similarly, the length of the straight side of the second parallelogram is:

Length of second parallelogram = 11m

Now, let's find the length of the straight side of the semicircle segment. We are given that the other side of each parallelogram gets half of the diameter, which is 17m. Therefore, the length of the straight side of the semicircle segment is:

Length of semicircle segment = 17m / 2 = 8.5m

The lengths of all the sides add up to the figure's perimeter. Let's use P to represent the perimeter. Then:

P = 2 (parallelogram length) + semicircle length

When we replace the values we discovered earlier, we obtain:

P = 2(9m + 11m) + π(17m)/2

= 38m + 8.5πm

≈ 63.6m (using π ≈ 3.14)

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Answer: 64°

Step-by-step explanation:

Had this problem and got it right

The volume of the second cylinder is 90 square feet.

Here we know that a cylinder whose height is 1 ft has a volume of 10 ft², remember that the volume for a cylinder of radius R and height H is:

V =pi*R²*H

Where p = 3.14

Then the radius here is:

10 = 3.14*R²*1

√(10/3.14) = R

If we triple the diameter we also triple the radius, then the volume of the other cylinder will be:

V = 3.14*(3*√(10/3.14))²*1

V = 90

The volume is 90 square feet.

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To describe the transformation of the graph of function f(x) onto the graph of function g(x), we can compare the two functions and identify the changes that have been made.

First, note that f(x) and g(x) have different denominators: x-1 for f(x) and x+2 for g(x). This means that the graphs of f(x) and g(x) will have vertical asymptotes at x=1 and x=-2, respectively.

Next, we can see that g(x) is a transformation of f(x) because it is obtained by applying one or more transformations to f(x). Specifically, we can identify the following transformations:

Horizontal shift to the left by 3 units: f(x) is shifted 3 units to the right to get g(x). This is because g(x) has x+2 in the denominator, which is equivalent to f(x) with x-(-2) = x+2 in the denominator. So g(x) is equivalent to f(x) shifted 3 units to the left.

Vertical shift upwards by 4 units: The entire graph of f(x) is shifted 4 units upwards to get the graph of g(x). This is because the constant term 4 is added to g(x) but not present in f(x).

Vertical compression: The vertical scale of the graph of g(x) is compressed compared to the graph of f(x). This is because the size of the denominator is increasing for g(x) relative to f(x), so the graph will appear "squeezed" vertically.

Therefore, the transformation of the graph of function f(x) onto the graph of function g(x) involves a horizontal shift to the left by 3 units, a vertical shift upwards by 4 units, and a vertical compression.

Answer:

Yes, there is a linear relationship between height and volume.

V = (12π)h. 12π is a constant.

If you rewrite this as y = (12π)x and graph it, you will notice that the graph is a line which goes through the origin.

Answer:

y = 5/6x + 1/6

Step-by-step explanation:

m = 5/6, x = 7, y = 6

y = mx + b

6 = 5/6(7) + b

b = 6 - 35/6

b = 36/6 - 35/6 = 1/6

y = 5/6x + 1/6

Answer:

Below

Step-by-step explanation:

Here is another way:

 Start with point ( 7,6)   slope ( m= 5/6)  form :

    (y-6) = 5/6 ( x-7)     expand

    y-6 = 5/6 x -  35/6     add 6 to both sides

       y = 5/6 x + 1/6     Done.

The height and slant height of the cone is 7.64 inches and 9.38 inches respectively.

What is volume of cone ?

The volume of a cone is the amount of space occupied by the cone and is given by the formula:

[tex]Volume of a cone = (1/3) * pi * r^2 * h[/tex]

where pi is the mathematical constant approximately equal to 3.14, r is the radius of the circular base of the cone, and h is the height of the cone.
The formula for the volume of a cone can be derived by using calculus or by dividing the cone into a series of infinitesimally thin circular disks, calculating the volume of each disk, and summing up the volumes to obtain the total volume of the cone

According to the question:
To solve this problem, we need to use the formulas for the volume and surface area of a cone:

[tex]Volume of a cone = (1/3) * pi * r^2 * h[/tex]

Surface area of a cone = [tex]pi * r * (r + \sqrt{h^2 + r^2})[/tex]

where r is the radius of the base, h is the height, and pi is a mathematical constant approximately equal to 3.14.

First, we need to find the radius of the cone. The diameter is 10 inches, so the radius is half of that, or 5 inches.

The volume of the cone is given as 300 cubic inches. We can plug in the values we know and solve for the height:

[tex]300 = (1/3) * pi * 5^2 * h[/tex]

[tex]h = 300 / ((1/3) * pi * 5^2)[/tex]

[tex]h \approx 7.64 inches[/tex]

So the height of the cone is approximately 7.64 inches.

Next, we can use the Pythagorean theorem to find the slant height of the cone.

[tex]slant height^2 = radius^2 + height^2[/tex]

[tex]slant height^2 = 5^2 + 7.64^2[/tex]

[tex]slant height \approx 9.38 inches[/tex]

So the slant height of the cone is approximately 9.38 inches.

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Answer:32+ 1.21

Step-by-step explanation:

if you really want an awser you would take all the nubers and sfhgkjfqipjghwpkrejvhbwptijgbqkejnvwpigtnjuvrepiufgnjwrekjbhartio

Step-by-step explanation:

(a) If the order of the choices is relevant, we can choose the first object in 5 ways, and the second object in 4 ways (since we cannot choose the same object again). Therefore, the total number of ways to choose 2 objects without replacement and with order being relevant is:

5 x 4 = 20 ways

(b) If the order of the choices is not relevant, we need to use the combination formula, which is:

nCk = n! / (k! * (n-k)!)

where n is the total number of objects, and k is the number of objects we want to choose.

In this case, we want to choose 2 objects out of 5, so n = 5 and k = 2. Therefore, the number of ways to choose 2 objects without replacement and with order not being relevant is:

5C2 = 5! / (2! * (5-2)!) = 10 ways

Therefore, there are 20 ways to choose 2 objects without replacement and with order being relevant, and 10 ways to choose 2 objects without replacement and with order not being relevant.

The sum of x and 2 is equal to x + 2.

Value in math is the numerical representation of a quantity or expression. It can also be defined as an amount or a numerical representation of a quantity that is assigned to a variable or a constant in a mathematical expression. Value can be expressed in various forms, such as decimal, fraction, and scientific notation. Value is also used to calculate the result of an equation or a problem. Value is a fundamental concept in mathematics, and it is used to measure and compare different quantities.

This equation can be used to calculate the sum of any two numbers, x and 2. For example, if x is equal to 5, then the sum of x and 2 is equal to 5 + 2, which is equal to 7. Similarly, if x is equal to 10, then the sum of x and 2 is equal to 10 + 2, which is equal to 12. Therefore, the sum of x and 2 depends on the value of x.

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Expression equivalent to 5x - 4 are 5(x - 4/5), 5x - 20/5, 10x/2 - 8/2 and 3(5x/3) - 4

To create an expression equivalent to 5x - 4, we need to use arithmetic operations such as addition, subtraction, multiplication, and division, along with numbers and variables. The goal is to manipulate the numbers and variables in a way that results in the same value as 5x - 4.

Here are some examples of how we can do this:

5(x - 4/5)

In this expression, we start with x and subtract 4/5 from it. Then we multiply the result by 5. This is equivalent to distributing the 5 to x and -4/5, which gives us 5x - 4.

5x - 20/5

Here, we simply subtract 20/5 (which simplifies to 4) from 5x. This gives us 5x - 4.

(25x - 20)/5

In this expression, we start with 25x and subtract 20 from it. Then we divide the result by 5. This is equivalent to simplifying the expression to 5x - 4.

10x/2 - 8/2

This expression might look a bit different, but it's still equivalent to 5x - 4. Here, we start with 10x and divide it by 2, which gives us 5x. Then we subtract 8/2 (which simplifies to 4) from it, giving us 5x - 4.

3(5x/3) - 4

In this expression, we start with 5x and divide it by 3. Then we multiply the result by 3, which gives us 5x. Finally, we subtract 4 from it, giving us 5x - 4.

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Answer: The building is approximately 16.6 feet tall.

Step-by-step explanation:

Use Pythagorean theorem (a²+b²=c²) to solve this.

We know that the ladder is 26 feet long so that would be our hypotenuse (c²). and the distance between the ladder and the building is 20 feet. So, this is the base. The remaining side is x.

Your equation would be: 20²+x²=26²

subtract 20² from 26² --> 276=x²

then take the square root --> 16.6=x

Answer: D. 2/3

Step-by-step explanation:

If it is 1/5 of an hour, we times it by 5, to get full hour, right?

So, we also do ×5 for the acre of land, so we can get the amount of acres in a full 1 hour.

5 is the same as 5/1 as a fraction

1/5 × 5 = 5/5 ......1 hour

2/15 × 5/1 = 10/15

So we get, 10/15 acre of land cleared in 1 hour

We simplify 10/15,

Which becomes,

2/3.

In conclusion, this is the working out =

2/15 × 5 = 10/15 = 2/3

Answer:

Step-by-step explanation:

To find the value of t, we can use the information given about the temperature at two different elevations and use the formula for a linear equation.

Let's assume that the temperature decreases by tº Fahrenheit for every additional 100 feet above sea level, where t is the constant we want to find.

Then, using the two points given:

- (8000, 65) where 65 is the temperature in Fahrenheit at 8000 feet above sea level

- (10,500, 15) where 15 is the temperature in Fahrenheit at 10,500 feet above sea level.

We can calculate the slope of the line connecting these two points:

slope = (15 - 65) / (10,500 - 8,000) = -25

The slope of the line represents the amount that the temperature decreases per unit increase in elevation. In this case, we've found that the temperature decreases by 25 Fahrenheit for each increase in elevation of 1000 feet.

To find the value of t, we need to express the slope in terms of the decrease in temperature per 100 feet of elevation. We can do this by dividing the slope by 10:

t = slope / 10 = -2.5

Therefore, the value of t is -2.5.

Answer:

Thank you for your kind words and concern. I appreciate your offer to listen and support others. I think it's important for people to know that they can reach out for help when they're struggling and that there are resources available to them. And as for something that made me happy, I always appreciate it when people show kindness and empathy towards others, and when they're able to make a positive impact in the world.

Answer:hi tysm your literally the person everyone needs in there life and your so kind for that

Step-by-step explanation:

Today me and my friend went to the park with my brother and we got snowcones and played for a while then I got home and took a refreshing nap!

Answer:

64.58

Step-by-step explanation:

1 meter is 3.28084 so 3 meters is 9.84252 because you multiply it by 3 or add them to each other 3 times. 2 meters is 6.56168 because you multiply it by 2 or add them to each other. now that you have 6.56168 and 9.84252 multiply them with each other and you get 64.5834666336 but it was said to round to nearest hundredth so since the 3 in front of the 8 is not a 5 and above the answer is 64.58 and not 64.89

Answer:

2 real zeros at x = - 2 , x = 1

Step-by-step explanation:

f(x) = x² + x - 2

to find the zeros let f(x) = 0 , that is

x² + x - 2 = 0 ← in standard form

(x + 2)(x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x + 1 = 0 ⇒ x = - 1

there are 2 real zeros , x = - 2 and x = 1

Three points on the graph: (4, 0), (13, 5), (28, 8)

What is function ?

Function can be defined in which it relates an input to output.

Function 1: y = [tex](x+2) ^{1/3}[/tex] - 1

Domain: x ≥ -2

Range: y ≥ -1

x-intercept: There is no x-intercept.

y-intercept: (0, -1)

Transformation: The cube root function is shifted 2 units to the left and 1 unit down.

Three points on the graph: (-2, -1), (-1, 0), (6, 1)

Function 2: y = 3[tex](x - 4)^{1/3}[/tex] + 2

Domain: x ≥ 4

Range: y ≥ 2

x-intercept: (4, 0)

y-intercept: There is no y-intercept.

Transformation: The cube root function is shifted 4 units to the right, vertically stretched by a factor of 3, and shifted 2 units up.

Therefore, Three points on the graph: (4, 0), (13, 5), (28, 8)

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It should be noted that to use the diagram to figure out how many 2/5-ounce doses Zoe has, she can divide the 7/3-ounce amount into equal parts of 2/5 ounce.

One way to do this is to divide 2/5 by 1/5 to get the number of 1/5-ounce portions that make up a 2/5-ounce dose, which is 2. Then, divide 7/3 by 2/5 to get the total number of 2/5-ounce doses she has.

So, using the diagram, Zoe can count the number of 1/5-ounce portions she has, and then divide that number by 2 to find out how many 2/5-ounce doses she has.

Alternatively, Zoe could redraw the diagram to show 2/5-ounce portions instead of 1/5-ounce portions, and then count the number of 2/5-ounce portions she has. She would need to divide the original diagram into equal parts of 2/5 ounce by drawing lines to divide each square into two parts. Then she can count the number of squares that represent a 2/5-ounce dose.

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The number of runners who are expected to finish the race, given the probability of finishing and the number who registered is 1, 375 runners.

The probability of a runner finishing the race is 11/12. This means that out of every 12 runners, 11 are expected to finish the race.

We know that 11 out of 12 runners are expected to finish the race, so we can write:

11/12 = x/1,500

11 × 1,500 = 12 × x

16,500 = 12x

x ≈ 1,375

Therefore, approximately 1375 runners are expected to finish the race out of 1500 runners.

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The side lengths of such a triangle with a leg length of 5 and angles of 45, 45, and 90 are not listed in any of the options.

The right angle is established when 2 straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol is used to indicate a right angle.

For the given question:

Triangle with degree angles - 45-45-90

It means two legs are of same length 5 units.

Then, hypotenuse H will be:

H² = 5² + 5²

H² = 25 + 25

H² = 50

H = 5√2

Thus, the correct third side of the triangle will be 5√2.

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The no of people take more than 19 mins are above 50%

1. Break it down: Divide the topic into smaller subtopics or concepts. This can make it easier to understand and digest each piece of information.
2. Research: Look up definitions, explanations, or examples related to the terms or concepts you're trying to understand. This can help clarify any confusion or uncertainty.
3. Take notes: Write down important information, key points, or definitions as you research. This can help you remember and better understand the material.
4. Ask questions: If you're still unsure about certain aspects, don't hesitate to ask for help or clarification from a teacher, tutor, or friend.
5. Practice: Apply what you've learned to related problems or questions. Practicing can help reinforce your understanding

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the answer is m + n = 24 + 55 = 79.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

There are two ways this can happen: either he selects an apple first and then an orange, or he selects an orange first and then an apple. We can compute the probability of each of these events separately and then add them together.

First, let's consider the probability that Preston selects an apple first and then an orange. The probability of selecting an apple first is 4/11, and then the probability of selecting an orange from the remaining 10 fruits (which includes 3 apples and 6 oranges) is 6/10. So the probability of this event is (4/11) * (6/10) = 24/110.

This can be simplified by dividing the numerator and denominator by 2:

48/110 = 24/55

So the probability that Preston selects an apple and an orange is 24/55. Therefore, the answer is m + n = 24 + 55 = 79.

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