Two cars leave the same location traveling in opposite directions. One car leaves at 3:00 p.m. traveling at an average rate of 55 miles per hour. The other car leaves at 4:00 p.m. traveling at an average rate of 75 miles per hour. Let x represent the number of hours after the first car leaves. How many hours after the first car leaves will the two cars be 380 miles apart?

Enter an equation that can be used to solve this problem in the first box. Solve for x and enter the number of hours in the second box.

Equation:
x =

The equation which is not necessarily true is that G'H' = 8 units.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

A formula known as an equation uses the same sign to denote the equality of two expressions.

In another word, the equation must be constrained with some constraint.

Given that a polygon of GHIJ translates 8 units to the left to form polygon G 'H 'I 'J ' in the option it is necessary because GH is a side and G'H' will still be a side so they will be the same.

In option b G'G will be  8 units because the entire figure has shifted towards the left.

And the correct answer will be that G'H' = 8 units which are not true.

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Answer:

59 ft

Step-by-step explanation:

Given;

Then Darren's plane must have flown (2 × 20ft) = 40 ft

Amanda's plane would have flown (40ft + 19ft) = 59 ft

Amanda's plane flew 59 ft far.

The distance of the paper plane thrown by Amanda is given by the equation A = 59 feet

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the distance of the paper plane thrown by Amanda be A

Now , the equation will be

The distance of the paper plane thrown by Rachel R = 20 feet

The distance of the paper plane thrown by Darren D = 2 x distance of the paper plane thrown by Rachel R

Substituting the values in the equation , we get

The distance of the paper plane thrown by Darren D = 40 feet

And , Amanda plane flew 19 ft farther than Darren plane Darren plane

Substituting the values in the equation , we get

The distance of the paper plane thrown by Amanda A = 19 + distance of the paper plane thrown by Darren D

On simplifying the equation , we get

The distance of the paper plane thrown by Amanda A = 19 + 40

The distance of the paper plane thrown by Amanda A = 59 feet

Hence , the distance is 59 feet

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To convert 680% to a fraction, write it as 680/100 and simplify to 34/5. This improper fraction can also be written as the mixed number 6 [tex]\frac{4}{5}[/tex].

To convert 680% to a fraction or mixed number, follow these steps:

First, write the percent as a fraction with a denominator of 100. So, 680% becomes 680/100.

Next, simplify the fraction by finding the greatest common divisor (GCD) of 680 and 100. The GCD of 680 and 100 is 20.

Divide both the numerator and the denominator by their GCD:
680 ÷ 20 = 34
100 ÷ 20 = 5
So, 680/100 simplifies to 34/5.

Finally, convert the improper fraction to a mixed number. To do this, divide the numerator by the denominator:
34 ÷ 5 = 6 (with a remainder of 4).
This gives us the mixed number 6 [tex]\frac{4}{5}[/tex].

Therefore, 680% as a fraction is 34/5 and as a mixed number is 6 [tex]\frac{4}{5}[/tex].

Answer:

The decay factor is 0.88.

Step-by-step explanation:

The general form of an exponential decay function is

[tex]f(x)=ab^x[/tex]

Where, a is initial value and b is decay factor.

It is given a new truck that sells for $29,000 depreciates (decreases in value) 12% each year.

The initial value is $29,000 and decay factor is

[tex]1-r=1-\frac{12}{100}=1-0.12=0.88[/tex]

The exponential function is

[tex]f(x)=29000(0.88)^x[/tex]

Therefore the decay factor is 0.88.

The decay factor b for the truck, which depreciates 12% each year, is 0.88.

The decay factor, b, for the truck's depreciation can be calculated using the formula for exponential decay:

b = 1 - r

where r is the annual depreciation rate. In this case, the annual depreciation rate is given as 12%, or 0.12 in decimal form.

Now, let's calculate the decay factor:

b = 1 - 0.12

b = 0.88

So, the decay factor for the truck's depreciation is 0.88.

The decay factor is used to calculate the value of the truck after n years by raising b to the power of n and multiplying it by the initial value of the truck. The formula for the value of the truck after n years is:

[tex]\[ V(n) = P \cdot b^n \][/tex]

where P is the initial price of the truck, b is the decay factor, and n is the number of years.

In this case, the initial price P is $29,000, and the decay factor b is 0.88. If we want to find the value of the truck after, say, 5 years, we would use the formula:

[tex]\[ V(5) = 29000 \cdot (0.88)^5 \][/tex]

However, the question only asks for the decay factor, which we have already determined to be 0.88.

A bar graph would be the best way to summarize this information for display the data.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Andrea surveyed her classmates asking what type of pets they have.

Hence To show this on graph bar graph would be the best way to summarize this information for display the data.

Because, Bar graphs show comparisons between distinct categories and display changes over time.

Thus, A bar graph would be the best way to summarize this information for display the data.

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Answer:

Option A - Non-linear              

Step-by-step explanation:

Given : Graph the function by the table.

x           y

1          12.3

2         19.6

3         26.6

4         34.2

5         41.5

To find : Is the function linear or nonlinear?

Solution :

The function is linear when there slopes are equal.

So, we find the slope of the points.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Taking point, [tex](x_1,y_1)=(1,12.3)[/tex] and [tex](x_2,y_2)=(2,19.6)[/tex]

[tex]m=\frac{19.6-12.3}{2-1}[/tex]

[tex]m=\frac{7.3}{1}[/tex]

[tex]m=7.3[/tex]

Taking point, [tex](x_1,y_1)=(2,19.6)[/tex] and [tex](x_2,y_2)=(3,26.6)[/tex]

[tex]m=\frac{26.6-19.6}{3-2}[/tex]

[tex]m=\frac{7}{1}[/tex]

[tex]m=7[/tex]

We have seen that slope between points are not equal.

Therefore, The given points are non-linear.

So, Option A is correct.

Answer:

false

Step-by-step explanation:

y=2x-3 is the equation of line that includes the point (6, 3) has a slope of 2

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

We need to find the equation of line that includes the point (6, 3) has a slope of 2.

y minus y one equal to m time of x minus x one.

(y-y₁)=m(x-x₁)

x₁=6,y₁=3 and m is 2

y-3=2(x-3)

Apply distributive property on right hand side.

y-3=2x-6

Shift -3 to the RHS side

y=2x-6+3

y=2x-3

Hence y=2x-3 is the equation of line that includes the point (6, 3) has a slope of 2

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To get an A, David must score at least 85 on the last test.

David has taken three tests so far, with scores of 89, 92, and 95. To find out what score he needs on the last test to achieve a total of at least 360 points, we first calculate the total points he has accumulated from the first three tests:

[tex]\[ 89 + 92 + 95 = 276 \][/tex]

Now, we subtract this total from the minimum total points required for an A:

Therefore, David needs to score at least 84 points on the last test to reach a total of 360 points. However, since test scores are whole numbers, we round up to the nearest whole number that David can actually achieve on the test. Thus, David needs to score at least 85 on the last test to ensure he gets an A.

Answer:

40 farms

Step-by-step explanation:

Given :

A mango farm contains 1250 mango trees.

Each tree produces an average of 160 mangoes .

To Find : No. of mango farms needed to produce 8,000,000 mangoes .

Solution :

1 farm contains 1250 mango trees

Each tree produces an average of 160 mangoes .

1250 trees produces mangoes = 1250 *160 = 200000.

⇒ 1 farm produces 200000 mangoes

Now to calculate  mango farms are needed to produce 8,000,000 mangoes .

No. of Farm produces 200000 mangoes = 1

So, farms needed to produce  8,000,000 mangoes  = 8000000/200000 = 40 farms.

Thus 40 farms are required to produce 8,000,000 mangoes during the summer.

Final answer:

To find out how many pounds of untrimmed celery is needed to get 8 pounds of trimmed celery with a 75% yield, we divide the required trimmed weight by the yield percentage as a decimal. The calculation is 8 divided by 0.75, which equals approximately 10.67 pounds of untrimmed celery.

Explanation:

To determine the amount of untrimmed celery needed when a recipe requires 8 pounds of trimmed celery with a 75% yield, we use the yield percentage to find out how much the weight reduces during trimming. Yield percentage tells us how much of the original, or untrimmed, product remains after trimming. In this case, a 75% yield means that 75% of the untrimmed celery's weight will be left after trimming.

To find the amount of untrimmed celery, we set up the equation using the yield percentage (Y) of the untrimmed weight (U) that will result in the desired trimmed weight (T). The equation is T = U * Y/100. We can rearrange the equation to solve for U using the given values. So U = T / (Y/100), which gives us U = 8 / (75/100), resulting in U = 8 / 0.75.

After completing the division, we find that U equals 10.67. This means we need approximately 10.67 pounds of untrimmed celery to get 8 pounds of trimmed celery. Always remember to round according to the context, in most recipes a little more celery wouldn't be a problem, but it depends on the precision needed for the specific recipe.

The equation of the line is y + 2 = −3 (x − 1). The correct option is C.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The points from which the line passes are ( 0,1) and (1,-2). The slope of the line will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -2 - 1 ) / ( 1 )

Slope = -3

The equation of the line will be written as,

y - y₁ = m ( x - x₁ )

y +2 = -3 ( x - 1 )

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The answer is -π

If you add π + (-π), you get 0 which is a rational number.

Adding 2 only results in changing the 3.14... to a 5.14... which is still an irrational number.

Adding 1/π only results in adding 1/3.14... to π which equals 3.45... which is still an irrational number.

Adding 0 doesn't change the original value at all so its still an irrational number.

Therefore, -π is the only logical answer.

Best of Luck!

Answer:

- pi

Step-by-step explanation:

Pi is an irrational number. We need to add an equal and opposite irrational number to get a rational number. pi +-pi = 0

That is rational

Adding anything else will still leave us with pi in our answer which is irrational

2+pi  

1/pi + pi =

0+pi

All have pi in the answer