Can someone please help I need a clear explanation on how to solve this equation.
At Avery Middle School, 273 students responded to a survey asking whether a Bulldog, a Lion, or a Tiger should be the new school mascot. Four times as many students chose Bulldog as chose Tiger. Twice as many students chose Lion as chose Tiger. How many students chose Lion?

The area of the rectangle is  567 cm².

Perimeter = 2(6w + w) = 126

6w + w = 126/2

7w = 63

w = 9 cm

Length = 6 x 9 = 63

Area = length x width

63 x 9 = 567 cm²

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Answer:d. 147.00

Step-by-step explanation:

Area of sequins required is equal to the area of the rectangle.

Length of rectangle is 10cm and width is 21 cm.

Area of rectangle = length x width.

                               = 10 x21 =210 square cm.

Cost of sequins = 210x0.70= $147.00.

Option d $147.00 is the right answer.

Answer:

The correct option is C. 120°

Step-by-step explanation:

For better explanation of the answer see the attached figure :

Since, Angle formed at the center is equal to the angle measure of its opposite arc

⇒ ∠AOD = 104°

Also, The angle formed in the segment is half the angle formed at the center of the circle

⇒ ∠DOB = 2 × ∠BAD

⇒ ∠DOB = 2 × 68°

⇒ ∠DOB = 136°

Now, ∠AOB = 360 - ∠BOD + ∠AOD

⇒ ∠AOB = 360 - 136 - 104

⇒ ∠AOB = 120°

Now, Angle formed at the center is equal to the angle measure of its opposite arc

⇒ b = ∠AOB

⇒ b = 101°

Hence, the correct option is C. 120°

To determine which shapes are similar to shape A, we must evaluate the pattern, repetition, and geometrical structure, while understanding the differences in geometrical and organic forms.

When identifying shapes similar to shape A, we must look at the pattern and repetition of the figures while noting the differences. Shapes that are similar will have proportionally equivalent angles and sides, despite potential differences in size. We analyze the given shapes by comparing their properties such as angles, sides, and overall geometrical structure.

In a more complex composition, identifying positive and negative shapes can be challenging due to the presence of implied shapes that are created by the arrangement of other shapes or colors around them. Therefore, an in-depth inspection is needed to determine similarity.

Lastly, it is necessary to understand that shapes can be geometric, like circles and squares, or organic, which are more freeform and less regular. When comparing shapes to shape A, recall that similar shapes must relate in the ways mentioned, despite their geometric or organic nature.

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

                     2*x^2-3*x-(2)=0 

 2.1     Factoring  2x2-3x-2 

The first term is,  2x2  its coefficient is  2 .
The middle term is,  -3x  its coefficient is  -3 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -2 = -4 

Step-2 : Find two factors of  -4  whose sum equals the coefficient of the middle term, which is   -3 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  1 
                     2x2 - 4x + 1x - 2

Step-4 : Add up the first 2 terms, pulling out like factors :
                    2x • (x-2)
              Add up the last 2 terms, pulling out common factors :
                     1 • (x-2)
Step-5 : Add up the four terms of step 4 :
                    (2x+1)  •  (x-2)
             Which is the desired factorization

To find the radian measure between adjacent spokes of a wheel, you divide 2π by the number of spokes. In this case, the wheel has 22 spokes, leading to a radian measure of approximately 0.286 radians for the angle between adjacent spokes.

The topic of the question pertains to geometry and radian measures. In a full circle, there are 2π radians. If a wheel has 22 spokes, each spoke defines a section of the circle equally. So, you would divide 2π by 22 to determine the measure, in radians, of the central angle formed by adjacent pairs of spokes.

Step-by-step calculation: The formula for calculating this is 2π/n, where n is the number of sections (or spokes). Therefore, the radian measurement of the angle between adjacent spokes would be 2π/22 = 0.286 radians when rounded up.

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Answer: 1, 2, 5, and 10

Step-by-step explanation: To find the factors of 10, begin by dividing 10 by 1 which gives us 10. This tells us that 1 and 10 are factors of 10. Next, divide 10 by 2 which gives us 5. This tells us that 2 and 5 are also factors of 10. Next, divide 10 by 3. Notice that 10 doesn't divide evenly by 3 so 3 is not a factor of 10. Next, divide 10 by 4. Since 10 doesn't divide evenly by 4, then 4 is not a factor of 10. Next, divide 10 by 5 which gives us 2. This tells us that 5 and 2 are factors of 10 but notice that we already know that 5 and 2 are factors of 10. This means that 5 and 2 are repeat factors.

There is no need to repeat factors that we already know. In fact, as we are writing the factors of a number, it's important to understand that once we hit repeat factors, all other factors that we try will also repeat.

So here, dividing by anything greater than 5 will give us factors that we already know so we can stop here.

This means that the factors of 10 are 1, 2, 5, and 10.

Answer:

The train travels 268 miles in 1 hour. It would take 2.0896 hours to travel between the cities.

Step-by-step explanation:

Consider the provided information.

The shanghai maglev traveling about 2144 miles in 8 hours.

This can be written as:

2144 miles = 8 hours

Divide both sides by 8.

2144/8 miles = 8/8 hours

268 miles = 1 hours

Thus, the train travels 268 miles in 1 hour.

The distance between Columbus Ohio and new York city is about 560 miles. We need to find how many hours would it take the train to travel between the cities.

268 miles = 1 hours

Divide both the sides by 268.

1 miles = 1/268 hours

Now multiply both sides by 560.

560 miles = 560/268 hours

560 miles = 2.0896 hours

Hence, it would take 2.0896 hours to travel between the cities.

It takes approximately 12.47 minutes for light from the Sun to reach the Earth.

To find out how many minutes it takes for light from the Sun to reach the Earth, we can divide the distance from the Earth to the Sun by the distance light travels in 1 minute.

First, let's convert the distance from miles to kilometers. 1 mile is approximately 1.60934 kilometers, so the distance from the Earth to the Sun is approximately 1.496 × 108 kilometers.

Now, we divide this distance by the distance light travels in 1 minute: 1.496 × 108 kilometers / 1.2 × 107 kilometers per minute = 12.47 minutes.

Therefore, it takes approximately 12.47 minutes for light from the Sun to reach the Earth.

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Bills father weight is 76 kilograms.

Here,

Bills weight is 48 kilograms. This is 10 grams more than one half his fathers weight.

We have to find, Bills father weight.

What is Linear expression?

Linear Equations deal with Equations with linear expression in one or two variables . Such Equations are known as Linear Equations.

Now,

Let Bills father weight is x kilograms.

According to given condition,

Bills weight is 48 kilograms. This is 10 grams more than one half his fathers weight.

⇒ [tex]\frac{x}{2} + 10 = 48[/tex]

⇒ [tex]\frac{x}{2} = 48 - 10[/tex]

⇒ [tex]\frac{x}{2} = 38[/tex]

⇒ [tex]x = 76[/tex]

Hence, Bills father weight is 76 kilograms.

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To solve this problem, we can set up an equation using the amount invested at each rate. Solving the equation will give us the amount invested at 8% and 7%.

To solve this problem, let's assume that the amount invested at 8% is x dollars. Therefore, the amount invested at 7% would be (23000 - x) dollars. Now we can set up an equation to represent the given information:

0.08x + 0.07(23000 - x) = 1800

Solving this equation will give us the amount invested at each rate.

0.08x + 0.07(23000 - x) = 1800

0.08x + 1610 - 0.07x = 1800

0.01x = 1800 - 1610

0.01x = 190

x = 190 / 0.01

x = 19000

Therefore, $19000 is invested at 8% and $4000 (23000 - 19000) is invested at 7%.

To solve the problem, set up a system of equations using x and y as variables to represent the amounts invested at 8% and 7%. Solve the system to find x and y. The amount invested at 8% is $19,000 and the amount invested at 7% is $4,000.

To solve this problem, we can set up a system of equations. Let x represent the amount invested at 8% and y represent the amount invested at 7%. The total amount invested is $23,000, so we have the equation x + y = 23,000. The total return is $1,800, so we have the equation 0.08x + 0.07y = 1,800. We can solve this system of equations to find the values of x and y.

By substitution, we can solve for x:

x + y = 23,000

x = 23,000 - y

Substituting this into the second equation:

0.08(23,000 - y) + 0.07y = 1,800

1,840 - 0.08y + 0.07y = 1,800

-0.01y = -40

y = 4,000

Substituting the value of y back into the first equation, we can find x:

x + 4,000 = 23,000

x = 19,000

So, $19,000 was invested at 8% and $4,000 was invested at 7%.

when x =1 , y = 3

 when x = 3, y =27

27-3 = 24

3-1 = 2

24/2 = 12

 rate of change = 12