8. Two functions are shown below.
f(x) = 3(2)*
g(x) = 6x
What is the sum of the x-values where f(x) = g(x)?
(Hint: Sum-add. They are equal where they cross/intersect.)
A. 1
B. 3
C. 5
D. 18

Answer:

  41.12 square units

Step-by-step explanation:

You want the area of the attached figure showing a triangle of height 4 atop a semicircle of diameter 8.

The area of a triangle is given by ...

  A = 1/2bh

where b is the base and h is the height.

The area of a semicircle is given by ...

  A = (π/2)r²

where r is the radius, half the diameter.

The figure shows a triangle with a base of 8 units and a height of 4 units. Its area is ...

  A = 1/2(8)(4) = 8·2 = 16

The semicircle has a radius of 4, so its area is ...

  A = π/2(4²) = 8π ≈ 25.12

Then the total area of the figure is ...

  triangle area + semicircle area = 16 +25.12 = 41.12 square units

__

Additional comment

Since the triangle and the semicircle have the same width, we can sum the "equivalent" heights of each and consider the result as a rectangle. You are familiar with the fact that a triangle has half the area of a rectangle the same height, so a triangle of height 4 is equivalent to a rectangle of height 4/2 = 2.

Similarly, the equivalent height of the semicircle can be found to be π/4 times its radius. Here, the radius is 4 units, so the semicircle of diameter 8 is equivalent to a rectangle 8 units by 4(π/4) = π units.

This means the entire figure is equivalent to a rectangle 8 units wide and (2+π) units high. That is the calculation shown in the attachment.

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A graph that uses images to symbolize the data that appears on the graph is known as a pictograph.

A pictograph is a type of chart that represents data using images or symbols. Each symbol on the pictograph represents a specific quantity, and the quantity is determined by the number of times the symbol appears on the chart. Pictographs are used to present data in a visually appealing and easy-to-understand manner, especially when the data is complex or there are multiple variables involved. Pictographs can be useful for a wide range of applications, from presenting sales figures to illustrating demographic information. They are often used in advertising, marketing, and educational materials to make data more engaging and memorable.

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In this problem, we have two circles with different radii and central angles defining arcs with specific lengths. We are asked to compare the measures of the two central angles.

Recall that the length of an arc (arc length) can be calculated using the formula: Arc Length = Radius × Central Angle (in radians). To compare the measures of the central angles, we'll first rearrange the formula to solve for the central angle: Central Angle = Arc Length / Radius.
For the first circle with radius 16 units and an arc length, let's denote the central angle as θ₁. Thus, θ₁ = Arc Length₁ / 16.
For the second circle with radius 5 units and an arc length, let's denote the central angle as θ₂. Therefore, θ₂ = Arc Length₂ / 5.
To compare the central angles θ₁ and θ₂, we can use the ratios of the respective arc lengths and radii. If the ratio of Arc Length₁ to Arc Length₂ is the same as the ratio of 16 to 5, then the central angles are equal. If the ratio is greater, then θ₁ is greater than θ₂, and if the ratio is smaller, then θ₁ is smaller than θ₂.
Without the specific arc lengths, we cannot determine the exact relationship between the central angles, but this method can be used to compare them once the arc lengths are provided.
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The spheres into groups and testing the groups against each other The false Sphere,Now our findings to the king and claim our reward.

To  identifying a false sphere using a balance with only two uses can be approached by dividing the spheres into groups and testing the groups against each other. Here's one possible solution to the problem:

First, divide the spheres into three groups of three, three, and two spheres each. Weigh the two smaller groups against each other on the balance. If they balance, then the false sphere must be in the larger group of three.

Next, take any two spheres from the larger group and weigh them against two spheres from one of the smaller groups. If they balance, then the false sphere must be the remaining sphere in the larger group. If they don't balance, then the false sphere must be one of the spheres being weighed.

Finally, take the two spheres that didn't balance and weigh them against each other. Whichever one is lighter is the false sphere.

Using this method, we have used the balance twice and identified the false sphere. Now, we just need to present our findings to the king and claim our reward.

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The time it takes for the diver to reach the water is 1.7 seconds.

To find the time it takes for the diver to reach the water, we need to determine when the height of the diver, as modeled by the function

h(x) = -16x² + 6x + 36, becomes 0.

So, h(x)= 0

-16x² + 6x + 36 = 0

We can either factor the equation or use the quadratic formula to find the solutions. Let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

x = (-6 ± √(36 + 2304)) / (-32)

x = (-6 ± √2340) / (-32)

x ≈ (-6 ± 48.38) / (-32)

This gives us two possible solutions:

x ≈ (-6 + 48.38) / (-32) ≈ 42.38 / (-32) ≈ -1.32

x ≈ (-6 - 48.38) / (-32) ≈ -54.38 / (-32) ≈ 1.7

Since time cannot be negative in this context, the time it takes for the diver to reach the water is 1.7 seconds.

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The triangle drawn on the grid using the scaled dimensions is attached

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

Base = 10 meters

Height = 15 meters

The scale is given as

1 unit represents 2 meters

When represented on the grid, we have

Base = 10/2 units

Height = 15/2 units

Evaluate

Base = 5 units

Height = 7.5 units

Next, we draw the triangle on the grid using the above dimensions

See attachment for the triangle

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Answer:

1. Yes, 90+45+45=180

2. Yes, adds to 180

3. No

4. No

Step-by-step explanation:

Answer:

They eat 2 pounds in one week

Step-by-step explanation:

Lets write down what we know:

Zeus eats: 1/2

Shiva eats: 1

Apollo eats: Same amount as Zeus, 1/2.

How many do they eat in one week?

In order to answer this question, we just need to add all of our numbers together.

[tex]\frac{1}{2}+\frac{1}{2}+1[/tex]

Add the halves together. 1/2 + 1/2 = 1

[tex]1+1[/tex]

Add the 1s

[tex]2[/tex]

They eat 2 pounds in one week

Answer:

The answer is Multiplication.

Step-by-step explanation:

The coefficient of the x term in f(x) is 2, and the coefficient of the x term in g(x) is 2. When we add or subtract the two functions, the coefficient of the x term remains 2. However, when we multiply the two functions, the coefficient of the x term becomes 4. Therefore, multiplication results in the largest coefficient on the x term.

Here is the solution for each of the operations:

Addition: f(x) + g(x) = (2x −1) + (2x + 4) = 4x + 3

Subtraction: f(x) - g(x) = (2x −1) - (2x + 4) = -5

Multiplication: f(x) * g(x) = (2x −1) * (2x + 4) = 4x^2 + 6x - 4

As you can see, the coefficient of the x term in f(x) * g(x) is 4, which is larger than the coefficients of the x terms in f(x) + g(x) and f(x) - g(x). Therefore, multiplication results in the largest coefficient on the x term.

Answer:

The answer is -0.75

Step-by-step explanation:

7/12-5/6+1/8-5/8

find Lcm of 12 and 8 is 24

7/12-5/6+1/8-5/8

-------------------------

24

2(7)-4(5)+3(1)-3(5)

-------------------------

24

14-20+3-15

-----------------

24

= -18

-----

24

=-3/4

= -0.75

The maximum number of hikers who could have walked between 7 and 18 miles is 7.

To determine the minimum and maximum number of hikers who could have walked between 7 miles and 18 miles, we need to analyze the given frequency distribution. Let's break it down step by step.

a) Minimum number of hikers: To find the minimum number of hikers who could have walked between 7 miles and 18 miles, we need to consider the minimum values of each interval.

Looking at the table, we see that the 7-mile distance falls into the second interval (5 < x ≤ 10), which has a frequency of 3. Therefore, a minimum of 3 hikers could have walked 7 miles.

Similarly, the 18-mile distance falls into the third interval (10 < x ≤ 15), which has a frequency of 8. Therefore, a minimum of 8 hikers could have walked 18 miles.

Since we are interested in the number of hikers who walked between 7 and 18 miles, we take the maximum value of the two intervals: 8.

Therefore, the minimum number of hikers who could have walked between 7 and 18 miles is 8.

b) Maximum number of hikers: To find the maximum number of hikers who could have walked between 7 miles and 18 miles, we need to consider the maximum values of each interval.

Looking at the table, we see that the 7-mile distance falls into the third interval (5 < x ≤ 10), which has a frequency of 8. Therefore, a maximum of 8 hikers could have walked 7 miles.

Similarly, the 18-mile distance falls into the fourth interval (10 < x ≤ 15), which has a frequency of 7. Therefore, a maximum of 7 hikers could have walked 18 miles.

Since we are interested in the number of hikers who walked between 7 and 18 miles, we take the minimum value of the two intervals: 7.

Therefore, the maximum number of hikers who could have walked between 7 and 18 miles is 7.

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To eliminate one of the variables by adding a multiple of one equation to the other, you should multiply the equation containing the variable you want to eliminate by a suitable multiplier.

Let's assume you want to eliminate the variable y. In this case, you should multiply the equation containing y by a multiplier that will make the coefficient of y in one equation equal to the negative coefficient of y in the other equation. This will ensure that when you add the two equations, the y terms will cancel out.

For example, if the equation you want to eliminate y from is 2x + 3y = 7, and the other equation is 4x + 5y = 9, you would multiply the first equation by -5 and the second equation by 3 to obtain:

-5(2x + 3y) = -5(7) (equation 1 multiplied by -5)

3(4x + 5y) = 3(9) (equation 2 multiplied by 3)

This will result in:

-10x - 15y = -35 (equation 1 after multiplication)

12x + 15y = 27 (equation 2 after multiplication)

Now, when you add the two equations, the y terms will cancel out, and you can solve for the remaining variable x.

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Answer:

Expression 1: 3y+x+52+(2x-60)+(x+15)+52=360

Expression 2: 4x+3y+59=360 or if you want just "x"'s and "y"'s on one side, you would do 4x+3y=301

Step-by-step explanation:

Expression 1:  Add up all the angles to get expression 1.

Expression 2: Combine like terms.

Hope this helps! :)

Answer:

1: 3y+x+52+(2x-60)+(x+15)+52=360

2: 24x+3y+59=360

Step-by-step explanation:

The number of sides of the polygon will be 6.

In any closed polygon, the number of sides is equal to the number of interior angles.

Let the number of sides is n in the given polygon.

Sum of angles = 90° + 126° × (n - 1)

The sum of angles is given as, 180(n - 2)

90° + 126° × (n - 1) = 180(n - 2)

90 + 126n - 126 = 180n - 360

180n - 126n = 90 - 126 + 360

54n = 324

n = 6

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The value of x in the trapezoid that is shown above is calculated as:

x = 101°.

The trapezoid in the image shown is an isosceles trapezoid because the two lower base angles are indicated to be congruent to each other, therefore, any of the lower base angle and upper base angle would be supplementary or have a sum of 180 degrees when added together.

Given that angle A and angle D are congruent, therefore:

m<A = 79 degrees.

m<A + m<B = 180 [supplementary angles]

79 + x = 180

x = 180 - 79

x = 101°

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1. We can buy 15 cans of green beans for $10.

2. The jet could fly 959 miles in 7 hours at same speed.

3. Its take 4 days for the car manufacturer to produce 800 cars.

A proportion refers to an equation in which two ratios are set equal to each other.

To get how many cans of green beans you can buy for $10, we will set up a proportion:

9 cans / $6 = x cans / $10

By cross-multiplying, we get:

9*($10) = 6x

90 = 6x

x = 90 / 6

x = 15.

2. To get distance the jet can fly in 7 hours, we will use [tex]Distance = rate * time[/tex]

Rate = Distance / Time

Rate = 548 miles / 4 hours

Rate = 137 miles per hour

Now we will it to get how far the jet could fly in 7 hours:

Distance = Rate × Time

Distance = 137 miles per hour × 7 hours

Distance = 959 miles.

3. We will set up a proiportion.

1400 cars / 1 week = 800 cars / x days

To solve for x, we cross-multiply and divide

1400 * x = 800 * 7

1400x = 5600

x = 5600 / 1400

x = 4.

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Suppose Sipho has x marbles. According to the given information, Mark has 3 times more marbles than Sipho, so Mark has 3 times more marbles.

If Mark gives Sipho 17 marbles, Mark will be left with (3x - 17) marbles. And this will be twice as many Sipho particles, i.e. x.

Therefore, we can write the equation:

3x - 17 = 2x

To solve x, we subtract 2x on both sides of the equation:

3x - 2x - 17 = 0

Simplify the equation:

x - 17 = 0

Added 17 to both sides:

x = 17

So Sipho has 17 marbles. Since Mark has 3 times as many marbles as Sipho, Mark has 3 * 17 = 51 marbles.

So Sipho has 17 marbles and Mark has 51 marbles. 

it will be 26 cm as diagonals bisect each other

Janet had 10 5/6 leftover birthday cakes in her deli at the end of the week. To determine how many remained after the donation, we need to subtract the number of cakes donated from the initial quantity.

To subtract fractions, we need to have a common denominator. The common denominator of 6 and 3 is 6, so we convert the fractions to have a denominator of 6.

10 5/6 can be written as (10 * 6 + 5) / 6 = 65/6.

5 2/3 can be written as (5 * 3 + 2) / 3 = 17/3.

Subtracting 17/3 from 65/6, we need to find a common denominator of 6 and multiply the numerators accordingly.

(65/6) - (17/3) = (65/6) - (34/6) = 31/6.

Therefore, 31/6 birthday cakes remained at Janet's deli at the end of the week, which can be simplified to 5 1/6 cakes.

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Answer:

126 sq metres

Step-by-step explanation:

area of triangle = 0.5 X base length X height

surface area = base square + 4 (triangles)

= (6X6) + 4(0.5 X 6 X 7.5)

= 36 + 4(22.5)

= 36 + 90

= 126 (sq metres)

when X = 3, Ŷ equals 4,601. The correct answer is (c) 4,601.

If the least squares regression equation is Ŷ = 1,202 + 1,133X, we can find the value of Ŷ when X = 3 by substituting X = 3 into the equation and solving for Ŷ:

Ŷ = 1,202 + 1,133(3)

Ŷ = 1,202 + 3,399

Ŷ = 4,601

what is equation?

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two sides separated by an equals sign (=). The expressions on either side of the equals sign can be numbers, variables, or combinations of both, connected by arithmetic operations such as addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, logarithms, and trigonometric functions.

An equation can be either true or false, depending on the values of the variables and constants involved. Equations are used in a wide variety of mathematical contexts, from basic arithmetic to advanced calculus, physics, and engineering.

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Answer:

36 π and 12 π respectively.

Step-by-step explanation:

To find the area of a circle, we do πr^2. For circumference, we do 2πr, where r is the radius. Since we know the diameter of this circle is 12, and we know the radius is half the diameter, then:

12/2 = 6 = r

knowing r, we can find out the area and the circumference. The area is:

πr^2 = π 6^2, so it is 36π for the area. The circumference is:
2πr = 2 π 6 = 12π.

The amount of money that Emma would have in her account after 30 weeks is $200.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided above, a linear equation that models the amount of money Emma has in her savings account is given by;

y = mx + c

y = 5x + 50

By substituting the given parameter (x = 30 weeks), we have the following:

y = 5(30) + 50

y = $200

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Using the slope-intercept form of the linear equation, the amount in her account after 30 weeks is $200

An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has a variable whose exponent is more than 1.

In this problem, we are given an equation in the slope- intercept form and which is represented as y = mx + c

In the given equation;

y = 5x + 50

The amount in her account after 30 weeks is calculated as;

y = 5(30) + 50

y = 200

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The margin of error for the confidence interval for the population proportion, with a 95% confidence level, is approximately 0.0513 (or 5.13%).

To find the margin of error for the confidence interval for the population proportion, we can use the formula:

Margin of Error = Z * sqrt((p * (1 - p)) / n)

Where:

Z is the critical value for the desired confidence level (95% confidence level corresponds to a Z-value of approximately 1.96)

p is the sample proportion (54/240 in this case)

n is the sample size (240 in this case)

Plugging in the values, we have:

Margin of Error = 1.96 * sqrt((54/240 * (1 - 54/240)) / 240)

Calculating this expression, we find:

Margin of Error ≈ 0.0513

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The answer is correct, we can plot both triangles on a Coordinate plane and visually inspect the result. If we plot triangle ABC with vertices A(-3, 3), B(0, 4), and C(-3, 0), and then plot the image triangle A'B'C' with vertices A'(-3, -1), B'(0, 0), and C'(-3, -4), we can see that the image is a translation of the original triangle down by 4 units.

To determine the coordinates of the vertices of the image of triangle ABC after being translated 4 units down, we need to subtract 4 from the y-coordinates of each vertex. This is because a translation is a type of transformation that moves each point of a figure a certain distance in a certain direction.

So, starting with the preimage of triangle ABC with vertices at A(-3, 3), B(0, 4), and C(-3, 0), we can find the image by subtracting 4 from the y-coordinates:

A'(-3, 3 - 4) = A'(-3, -1)

B'(0, 4 - 4) = B'(0, 0)

C'(-3, 0 - 4) = C'(-3, -4)

Therefore, the coordinates of the vertices for the image after the translation are A'(-3, -1), B'(0, 0), and C'(-3, -4).

So, the correct option is A) A′(−3, −1), B′(0, 0), C′(−3, −4).

To check if the answer is correct, we can plot both triangles on a coordinate plane and visually inspect the result. If we plot triangle ABC with vertices A(-3, 3), B(0, 4), and C(-3, 0), and then plot the image triangle A'B'C' with vertices A'(-3, -1), B'(0, 0), and C'(-3, -4), we can see that the image is a translation of the original triangle down by 4 units.

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The area of the circle with a Diameter of 36 inches,  π = 3.14, is 1017.36 square inches.

The surface area of one mini muffin and multiply it by 6. The surface area of a cylindrical mini muffin can be calculated as 28 and 2/7 square inches. Multiplying by 6, we get a total of 169 and 1/7 square inches. Approximating the answer, we get 169 and 1/7 169.14 square inches.  the correct answer is 169 and 1/7 square inches.      

The area of the enlarged map, we need to scale up the dimensions of the state of Colorado by the scale factor of 2.5.

The length of the enlarged map would be 4 cm * 2.5 = 10 cm.

The width of the enlarged map would be 3 cm * 2.5 = 7.5 cm.

Area = length * width

Area = 10 cm * 7.5 cm

Area = 75 cm²

Therefore, the area of the enlarged map is 75 cm².

The area of a circle can be calculated using the formula:

Area = π * (radius)^2

the diameter of the circle is 36 inches, we can find the radius by dividing the diameter by 2:

Radius = 36 inches / 2 = 18 inches

Now, we can calculate the area using π = 3.14:

Area = 3.14 * (18 inches)^2

    = 3.14 * 324 square inches

    = 1017.36 square inches

the area of the circle with a diameter of 36 inches, using π = 3.14, is 1017.36 square inches.

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This means the confidence interval for the population mean is approximately (21.135, 23.665).

To construct a confidence interval for the population mean, we can use the formula:

CI =  ± Z * (σ/√n)

Where:

is the sample mean (22.4),

Z is the Z-score corresponding to the desired confidence level (98% corresponds to a Z-score of approximately 2.33),

σ is the population standard deviation (3.8), and

n is the sample size (49).

Plugging in the values, we have:

CI = 22.4 ± 2.33 * (3.8/√49)

Calculating this expression will give us the confidence interval for the population mean. Evaluating the expression, we find:

CI ≈ 22.4 ± 2.33 * 0.543

Simplifying further, we get:

CI ≈ 22.4 ± 1.265

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The two rational and irrational number that can be found between 2.37 and 2.41 would be given below;

Rational numbers= 2.38 and 2.4.

Irrational numbers = √2 + 2.37 and √3+2.37

A rational number can be defined as the type of number that can be written as the ratio of two integers or any number that can be written as a fraction, where both the numerator (the top number) and the denominator (the bottom number) are integers, and the denominator is not equal to zero.

Therefore,Rational numbers between 2.37 and 2.41 = 2.38 and 2.4.

An irrational number is defined as the number that is a real number that cannot be expressed as a ratio of integers; for example,

Therefore that Irrational numbers between 2.37 and 2.41 = √2 + 2.37 and √3+2.37

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