Simplify using exponent B-³

Data:

• Distance ( ,D ,)= 144 miles

• Time ( ,t ,) = 4 hours

• Speed of Ahmed (,A,): unknown

• Speed of Blake (,B,): unknown

• Formula of speed:

Procedure:

• As Blake travels 8 mph faster than Ahmed

Since they are traveling towards each other, we can add up their speeds as follows:

Using the distance formula, we can find the speed:

To know the speed of Blake:

Answer:

• Blake = 292 mph

• Ahmed = 284 mph

STEP-BY-STEP EXPLANATION:

What to do? Convert percentage to fraction

Given parameter

0.0032%

Recall that two figures are similar if their corresponding angles have the same measure.

Therefore, if we reduce or increment the measurement of each angle, the resulting figure will not be similar to the original figure.

Now, notice that increasing the length of the sides of a polygon does not necessarily result in a similar figure, for example:

Now, recall that translations, rotations, reflections, and dilations result in similar figures.

Answer: Third and last options.

The dimensions of the rectangle are L=10in, B=5in

A rectangle includes everything listed below:

Your polygon's four sides must be two congruent pairings in order to have two pairs of parallel sides. The length of the left and right sides, as well as the base and top, will be equal.

let width of rectangle be x, then length will be

B=5+x

given area of rectangle

A=50in²

area = length×width

A=L×B

50 = x×(5+x)

50=5x+x²

x²+5x-50=0

x²+10x-5x-50=0

x(x+10)-5(x+10)=0

x=-10 or x=5

since x=-10 is not possible

therefore, x=5

Length(L)=5+5=10in

Width(B) = 5in

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The length , width and height of a box with volume 125 cubic centimeters will be

1, 5 and 25.

The volume of a box can be calculated by multiplying its length, width, and height.

here given volume = 125

V = l x w x h

125 = l x w x h

l, w, h is the factors of 125

To find the common factors, we must first list the factors of each of the given numbers.

since 125 is  composite number, it will have more than two factors.

125 → 1, 5, 25 and 125.

The factors of 125 is 1, 5, 25,125

here 125 cannot consider as length since volume is 125 other sides cannot be 0.

so the length, width, height can be 1 , 5, 25.

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Answer: i believe its 0.46 im not for sure though

Step-by-step explanation:

1)  A number that is divided by 5, with the result as 50 less than if the number had been divided by 6 is; -1500

2) If both turtles survive until then, the number of years from today that the older turtle's age would be 3 times that of the younger turtle is; 146 years

1) Let the number be x. We are told that it is divided by 5, and the result is 50 less than if the number had been divided by 6. Thus, we have;

(x/6) - (x/5) = 50

Multiply through by 30 to get;

5x - 6x = 1500

-x = 1500

x = -1500

2) Let the older turtle be x and the younger one be y.

Today, the older turtle's age is 11 times that of the younger turtle. Thus;

Todays age;

Older turtle = 11y years

Younger turtle = y years

In 24 years, the older turtle's age will only be 7 times that of the younger turtle. Thus;

11y + 24 = 7(y + 24)

11y + 24 = 7y + 168

11y - 7y = 168 - 24

4y = 144

y = 144/4

y = 36

Thus;

Age of older turtle today = 11 * 36 = 396 years

Age of younger turtle today = 36 years

Thus, for older turtle to be thrice the age of younger turtle, then;

3(36 + t) = 396 + t

108 + 3t = 396 + t

2t = 292

t = 292/2

t = 146 years

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A linear equation has a constant slope.

For every step increase in x, there needs to be another step increase in y.

From the table,

x decreases by 2 units

y doesn't decrease by the same unit

So, this cannot be linear relationship.

To see whether it is quadratic or exponential, we graph the (x,y) points and see the general shape of the curve by connecting the points in a smooth curve.

The graph is shown below:

From seeing the graph, it is quite evident that the tabular relationship represents a quadratic function.

Thus, the correct answer is:

Area of Sector.

The area of a sector is given by the formula below:

Substituting these values into the formula above, we get

Thus, the correct answer is 46.5 square meters.

8/9 - 1/3

To subtract these two fractions, first find a common denominator.

The common denominator will be the

least common multiple for the two denominators.

In this case, the least common multiple of 9 and 3 is 9.

So to subtract, a denominator of 9 is needed in each fraction.

8/9 already has 9 in the denominator so it stays the same.

To get a 9 in the denominator of 1/3, multiply top and bottom by 3.

This gives us 3/9.

So we have 8/9 - 3/9 which is 5/9.

#7777

Answer:

180

Step-by-step explanation:

So, in the first 4 games, they score 10 points. If this continues to happen in the remaining 18 games, it would be 180.

             10 x 18 = 180.

Answer:

11.34 m³

Explanation:

The volume of a right rectangular prism can be calculated as:

So, replacing the height by 3.6 m, the length by 2.1 m, and the width by 1.5m, we get:

Therefore, the volume of the prism is 11.34 m³

we have the equation

A=bh

solve for h

that means -----> isolate the variable h

so

step 1

Divide both sides by b

A/b=bh/b

simplify

A/b=h

rewrite

If the full-time year-round median salary for U.S. men in 2010 was $42,600. The​ full-time year-round median salary for U.S. men in 2010 was 121% of the​ full-time year-round median salary for U.S. women in 2010.

Using this formula

Median salary percentage = 2010 Median salary in US men / 2010 Median salary in US women

Let plug in the formula

Median salary percentage = $42,500 / $35,000

Median salary percentage = 1.2143 × 100

Median salary percentage = 121.43%

Median salary percentage = 121% (Approximately)

Therefore median salary for men in 2010 was 121% of  median salary for  women in 2010.

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Solving an Equation

We are given the equation:

The first step is to multiply the constants by the binomials in parentheses:

This step was correctly done by Jose.

The second step is to 'pass' the 4x from the right side of the equation to the left by adding 4x on both sides:

This step was also correct.

Now we must 'pass' 15 to the right by subtracting 15:

And here we find the first error. Jose subtracted 15-20 instead of 20-15 and erroneously got -5.

Answer: First error in step 3

K (5 * 3)

K * 15

15K

The answer is 15K based on the information available. I asked the student twice if he has more details about this exercise but he become unresponsive.

Hope that this is the answer to the actual exercise.

Closing the session.

The teammates are 15 but 6 of them do not want the photo, so the number of the teammates who wants the photo is 15 - 6.

Now, each photo cost $2 adn the number of photo is equal to the number of teammates who wants the photo which is (15-6), so the expression for the total cost is:

We have to multiply the cost of each photo for the number of photo Greta will buy.

The order of the numbers from lowest to highest is 4.68 × 10⁻⁶,  8.34 × 10⁻², 1.2  × 10⁷, 3.24 × 10⁹ and  5.48  × 10⁹

The given numbers are expressed in standard form. Standard form is a way of writing numbers as a power 10 e.g 100 = 1 × 10² and 0.01 = 1 × 10⁻².

So converting the numbers back to ordinary numbers will be useful.

To do this, we will multiply or divide the powers of 10 with the decimal numbers.

We will multiply if the power is positive e.g 2.4 x 10² = 2.4 x 100 = 240 and divide if the power is negative  2.4 x 10⁻² = 2.4/100 = 0.024

3.24 × 10⁹  = 3.24 x 1000,000,000 =  3240000000

4.68 × 10⁻⁶ = 4.68 / 1000000 = 0.00000468

5.48  × 10⁹ = 5480000000

8.34 × 10⁻² = 8.34/100 = 0.0834

1.2  × 10⁷ = 12000000

Therefore, arranging from lowest to highest. We have:

4.68 × 10⁻⁶,   8.34 × 10⁻², 1.2  × 10⁷, 3.24 × 10⁹ and  5.48  × 10⁹

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The domain of the functions F(x)=|x|, g(x)=x+9, f o g is x ∈ R the functions exist for all real numbers.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The function f(x):

f(x) = |x|

The domain of the function is:

x ∈ R

g(x) = x + 9

The domain of the function:

x ∈ R

f o g = f(g(x)) = |x + 9|

The domain of the function f o g is x ∈ R

Thus, the domain of the functions F(x)=|x|, g(x)=x+9, f o g is x ∈ R the functions exist for all real numbers.

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The solution for the given system of equations, y = [tex]\frac{-1}{2}[/tex]x + 5 and y = 3x - 2 is (2,4) and the graph is attached below

The system of equations is a set of equations consist the same variables. If the given equation are all linear then, it is the system of linear equation.

To solve such system, it is required to figure out the variable values that can solve all the equations involved in the system.

For the given system of equation the variable value is x.

So,  [tex]\frac{-1}{2}[/tex]x + 5  = 3x - 2

2 + 5 = 3x + [tex]\frac{x}{2}[/tex]

7 = x ([tex]\frac{6+1}{2}[/tex]) = [tex]\frac{7x}{2}[/tex]

x = 2

Now apply the obtained value of x in either of the equations:

y = 3x - 2

y = 6 - 2

y = 4

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Answer:

89%

Step-by-step explanation:

Answer:

Step-by-step explanation:

We have the following points:

A(-11, -3) and B(-2,5)

The distance between AB is:

C(7,1) and D(x, 9)

the value of x is -2

Given:

When two negetive sign comes together it becomes positive.

Thus, the final answer is 21.

Answer:

It would be, Yes, No, Yes, Yes.

Hope this helps!

Solution

Step 1

Two lines are perpendicular if the product of their slope = -1

Step 2

Step 2

Slope-intercept format is represented by the following expression:

Then to rewrite it, we need to isolate the variable y, using inverse operations to solve equations:

In any equation in math, the most basic thing is the the fact that both expressions on either side of the equality sign are of the same value. This means -35 and 5b (in number 1) are of the same value. Therefore, whatever you do to the one on the left, you must likewise do to the one on the right. That is, if you have to add 10 to the one on the left, you must simultaneously add 10 to the one on the right. Hence, number 1 is solved as follows;

(1) -35 = 5b

To eliminate the 5 and isolate the b variable, divide both sides by 5

-35/5 = 5b/5

- 7 = b

(2) x - 6 = - 26

Add 6 to both sides of the equation;

x - 6 + 6 = - 26 + 6

x = - 20

(3) 130 = 13b

Divide both sides of the equation by 13

130/13 = 13b/13

10 = b

(4) 19 = 16 + m

Subtract 16 from both sides of the equation

19 - 16 = 16 - 16 + m

3 = m

(5) a + 15 = 11

Subtract 15 from both sides of the equation

a + 15 - 15 = 11 - 15

a = - 4

(6) p - 8 = - 8

Add 8 to both sides of the equation

p - 8 + 8 = - 8 + 8

p = 0

(7) - 17 + x = - 24

Add 17 to both sides of the equation

- 17 + 17 + x = - 24 + 17

x = - 7

(8) 4 + n = 13

Subtract 4 from both sides of the equation

4 - 4 + n = 13 - 4

n = 9

(9) - 3x = 0

Divide both sides of the equation by - 3

- 3x/-3 = 0/-3

x = 0

(10) 0.6 = m - 0.8

Add 0.8 to both sides of the equation

0.6 + 0.8 = m - 0.8 + 0.8

1.4 = m

(11) x - 5.3 = 1.27

Add 5.3 to both sides of the equation

x - 5.3 + 5.3 = 1.27 + 5.3

x = 6.57

Marcus have 44 CDs, Sherry have 34 CDs and Kristen have 22 CDs.

Let us assume that Kristen has x numbers of CD's.

According to the provided situation,

Marcus have twice the number of CDs as Kristen.

Number of CDs of Marcus = 2x

The number of CDs of Sherry is 12 more than the CDs of Kristen

Number of CDs of of Sherry = 12 + x

Total number of CDs combined are 100.

So, we can write,

x + 2x + (12 + x) = 100

4x + 12 = 100

Any equation with the highest degree of variable as one, just like the above equation is called Linear Equation.

Further solving the Equation,

4x + 12 = 100

4x = 88

x = 22

The number of CDs that Kristen has is 22.

The number of CDs that Marcus have is 2(22).

The number of CDs Marcus gas is 44.

The number of CDs Sherry has is (12 + x) which is equal to 34.

The number of CDs Kristen, Marcus and Sherry have is 22, 44 and 34 respectively.

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Answer:

16 batches of cookies

Step-by-step explanation:

First, I converted the fraction (1/2) to a decimal (.5). Then I divided 4 by .5 and got 8. Next, multiply 8 by 2 and we get 16, which means we can make 16 batches of cookies.

4 ÷ .5 = 8
8 × 2 = 16

Answer:

f(x) = x^4

Step-by-step explanation:

h(x) = f(g(x)) = (x - 2)^4

g(x) = x - 2

h(x) = f(g(x)) = (g(x))^4

f(x) = x^4