Ms. Martina filled her truck's gas tank with
28.7 gallons of gas. If she drove 100 miles
on the same tank of gas, how much gas did
she use per mile?​

Answer:

[tex]y=\frac{3}{4}-1[/tex]  and   [tex]y=-\frac{4}{3}+9[/tex]

Step-by-step explanation:

step 1

Find the equation of the blue line

take the points

(0,-1) and (8,5) from the graph

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{5+1}{8-0}[/tex]

[tex]m=\frac{6}{8}[/tex]

simplify

[tex]m=\frac{3}{4}[/tex]

Find the equation of the line in slope intercept form

[tex]y=mx+b[/tex]

we have

[tex]m=\frac{3}{4}[/tex]

[tex]b=-1[/tex] ---> see the graph

substitute the given values

[tex]y=\frac{3}{4}-1[/tex]

step 2

Find the equation of the black line

take the points

(0,9) and (3,5) from the graph

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{5-9}{3-0}[/tex]

[tex]m=-\frac{4}{3}[/tex]

Find the equation of the line in slope intercept form

[tex]y=mx+b[/tex]

we have

[tex]m=-\frac{4}{3}[/tex]

[tex]b=9[/tex] ---> see the graph

substitute the given values

[tex]y=-\frac{4}{3}+9[/tex]

therefore

The system of equations is

[tex]y=\frac{3}{4}-1[/tex]  and   [tex]y=-\frac{4}{3}+9[/tex]

The equations of the blue and black lines are y = 3/4x - 1 and y = -4/3x + 9, respectively, based on their respective slopes and given points.

To find the equations of the blue and black lines, we start by determining their slopes using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on each line.

For the blue line:

Points: (0, -1) and (8, 5)

m = (5 - (-1)) / (8 - 0) = 6/8 = 3/4

Now, using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we substitute the slope m = 3/4 and the given point (0, -1):

y = 3/4x - 1

For the black line:

Points: (0, 9) and (3, 5)

m = (5 - 9) / (3 - 0) = -4/3

Substituting the slope m = -4/3 and the given point (0, 9) into the slope-intercept form, we get:

y = -4/3x + 9

Therefore, the system of equations representing the blue and black lines is:

y = 3/4x - 1

y = -4/3x + 9

The question probable may be:

Write  system of equations could be used to solve for the point of intersection of the lines on the graph?

Answer:

%75

Step-by-step explanation:

30/40 is equal to 0.75

0.75 is also %75

Answer:  %75

Answer:

part a) 13 scoops

part b) 3 scoops

Step-by-step explanation:

1) so we know that the volume of the sink is 660pi in^3

we have to divide this with the volume of each cup to find out the number of scoops it takes to get all the water out.

since we are dividing, I don't like leaving answers in terms of pi so

660*pi= 2073.45115137

formula for volume of cylinder(diameter) [tex]pi(\frac{d}{2} )^2 h[/tex]

pi*(5/2)^2*h=157.079632679

so

2073.45115137/157.079632679= 13.2 - for cup 1

for cup 2:

pi*(10/2)^2*8= 628.318530718

so

2073.45115137/628.318530718= 3.3- for cup 2

Hope this helps!

Work Shown:

i = P*r*t

157.50 = 2250*r*7 ... plug in given values

157.50 = 2250*7*r

157.50 = 15750r

15750r = 157.50

r = 157.50/15750 ... divide both sides by 15750

r = 0.01

The interest rate is 1%

To go from 0.01 to 1%, you move the decimal point 2 spots to the right.

Alternatively, you would multiply by 100.

Answer:7%

Step-by-step explanation:

Answer:

a- 16/100

b- 1/6

c- not sure

Step-by-step explanation:

Answer:

106 gal

Step-by-step explanation:

step 1

Find the area of the path

we know that

The area of the path is given by the formula

[tex]A=\pi r_2^{2} -\pi r_1^{2}[/tex]

[tex]A=\pi [r_2^{2} -r_1^{2}][/tex]

where

r_2 is the radius of the pool plus the width of the path

r_1 is the radius of the pool

we have

[tex]r_1=22/2=11\ yd[/tex] ---> the radius is half the diameter

[tex]r_2=11+6=17\ yd[/tex]

substitute

[tex]A=\pi [17^{2}-11^{2}][/tex]

[tex]A=168\pi\ yd^2[/tex]

assume

[tex]\pi =3.14[/tex]

[tex]A=168(3.14)=527.52\ yd^2[/tex]

step 2

Find the gallons of coating needed

Divide the area of the path by 5

so

[tex]527.52/5=105.5\ gal[/tex]

Round up

therefore

106 gal

To calculate how many gallons of coating are needed, we find the area of the path by subtracting the area of the pool from the total area covered. This equals to 527.52 yd². As each gallon of coating covers 5 yd², we need 105.504 gallons. However, since the paint is sold in whole gallons, we round it up to 106 gallons.

To determine how many gallons of coating are needed, we first need to calculate the area of the ring-shaped path around the pool.

The pool is a circle with a diameter of 22 yd, so its radius is 11 yd. The path is around this pool and has a width of 6 yd. Therefore, the outer radius of the path is 11yd (radius of pool) + 6yd (width of path)=17 yd. The area of a circle is given by the formula πr² where r is the radius and π is a constant, approximately equal to 3.14.

So, the area of the outer circle is 3.14 × (17 yd)² = 907.46 square yards, and the area of the inner circle (pool) is 3.14× (11 yd)² = 379.94 square yards. The area of the path is the difference of those two areas, 907.46 yd² - 379.94 yd² = 527.52 yd².

Since one gallon of the coating can cover 5 sq yd, the number of gallons required is the total area divided by the area that one gallon can cover, which is 527.52 yd² / 5 yd²/gallon = 105.504 gallons. Since paint comes in whole gallons, you'll need to round up to the next whole number, which is 106 gallons.

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Answer: They will travel about 131.18 yards.

Step-by-step explanation:

Given : A football field is 120 yards long by 53 yards wide.

We know that a football field is rectangular in shape.

Each interior angle in a rectangle is a right angle.

Then, by Pythagoras theorem, we have

(Diagonal)² = (Length)² + (Width)²

If a player runs diagonally from one corner to the opposite corner, then the length of the diagonal is given by :-

[tex](\text{Diagonal})=\sqrt{(120)^2+(53)^2}\\\\\Rightarrow\ (\text{Diagonal})=\sqrt{14400+2809}\\\\\Rightarrow\ (\text{Diagonal})=\sqrt{17209}\\\\\Rightarrow\ (\text{Diagonal})=131.183078177\approx131.18\text{ yards}[/tex]

Hence, they will travel about 131.18 yards.

Final answer:

The distance a player would travel running diagonally across a football field that is 120 yards long and 53 yards wide is approximately 131.183 yards.

Explanation:

The student asked about the distance a player would travel if they ran diagonally from one corner to the opposite corner of a football field that is 120 yards long and 53 yards wide.

To solve this, we need to apply the Pythagorean theorem in which the length and width of the football field will be the legs of the right triangle and the diagonal the player runs will be the hypotenuse.

The formula for the Pythagorean theorem is a² + b² = c², where a and b are the lengths of the legs and c is the length of the hypotenuse.

Therefore, the calculation will be as follows:

(120 yd)² + (53 yd)² = c².

Simplifying,

14400 yd² + 2809 yd² = c².

Adding these together gives us 17209 yd², and taking the square root of that gives us the length of the diagonal, which is the distance the player will travel.

Thus, c = √17209 yd2 ≈ 131.183 yards.

Step-by-step explanation:

[tex]\large\text{Hey there!}[/tex]

[tex]\mathsf{The\ sphere\ formula\ is: \dfrac{4}{3}\pi\times r^3}[/tex]

[tex]\mathsf{Now, that\ we\ have\ our\ formula\ let's\ solve\ for\ the\ equation}[/tex]

[tex]\mathsf{So,\ first\ \bf{\underline{DIVIDE}}}\mathsf{\ both\ of\ your\ sides\ by\ \pi}[/tex]

[tex]\mathsf{\dfrac{4}{3}r^3=972}\\\\\rightarrow\ \mathsf{r^3=972\times\dfrac{3}{4}}\\\\\mathsf{972\times\dfrac{3}{4}=729}\\\\\mathsf{\rightarrow\ r^3=729}[/tex]

[tex]\mathsf{\sqrt[\mathsf{3}]{\mathsf{729}} = 81}\\\\\mathsf{\sqrt{81}=81\div9=9}\\\\\mathsf{\sqrt{81}=9}\\\\\mathsf{r=9}[/tex]

[tex]\boxed{\boxed{\mathsf{\bf{Answer: \boxed{\mathsf{radius = \bf{9}}}}}}}\checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]

Answer:5

Step-by-step explanation:

Answer:

102

Step-by-step explanation:

To find the range of a set of data, you have to put all of the values in order from smallest to largest. Then you subtract the smallest and largest value to find your answer.

199 - 97 = 102

B. False

There are cases where this is not true, but if you want to prove that, you'll need to know what f and g are. For example, if f(x) = x - 3 and g(x) = x2, then f(g(x)) is not equal to g(f(x)) because

f(g(x)) = x2 - 3 and g(f(x)) = (x - 3)2. Those 2 functions are not the same because f(g(0)) = -3 ≠ 9 = g(f(0)).

Function rules by equations | Algebra functions that match 1 variable to the other in a 2-variable equation. Functions are written using function notation. Create functions that match 1 variable to the another in a 2-variable equation.

there are Some Examples of Functions

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Answer:

Step-by-step explanation:

56.3% of the student got A

15 students got A

Then,

Let the total number of students be x

56.3% of x= got A

56.3/100 × x =15

0.563x=15

Then x=15/0.563

x=26.6

The number of students can't or be 26.6 so let approximate it

Then, x=27

Therefore 27students are in the class

Answer:

27/7.

Step-by-step explanation:

(f/g)x = (7 + 4x) / 7

(f/g)(5) = (7 + 4(5)/ 7

= 27/7.

Yo sup??

f(x)=7+4x

g(x)=7

f/g(5)

=7+4*5/7

=27/7

Hope this helps

The absolute error is 2 feet and percent error is 18.18%

Step-by-step explanation:

Given,

Estimated length = 13 feet

Actual length = 11 feet

Absolute error = Estimated length - Actual length

Absolute error = 11 - 13 = -2 feet

Absolute error = 2 feet

Percent error = [tex]\frac{Absolute\ error}{Exact\ value}*100[/tex]

Percent error = [tex]\frac{2}{11}*100[/tex]

Percent error = [tex]\frac{200}{11}=18.18 \%[/tex]

The absolute error is 2 feet and percent error is 18.18%

The absolute error is 2 feet and the percent error is approximately 18.2%

The absolute error in Deon's estimate can be found by subtracting the actual value from the estimated value and taking the absolute value. So that's |13 - 11| which equals 2 feet.

The percent error can be found by dividing the absolute error by the actual value and then multiplying by 100 to convert it into a percentage. That's (2 / 11) * 100 which equals approximately 18.2%. If we round to the nearest tenth, we get 18.2%.

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Answer:

its A (4,4)

Step-by-step explanation:

The solution of the system y = x² - 6x + 12 and y = 2x - 4 is (4, 4).

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, y = x² - 6x + 12 and y = 2x - 4.

∴ The solution set of this system is,

x² - 6x + 12 = 2x - 4.

x² - 8x + 16 = 0.

x² - 4x - 4x + 16 = 0.

x(x - 4) - 4(x - 4) = 0.

(x - 4)(x - 4) = 0.

x - 4 = 0 Or x - 4 = 0.

x = 4 Or x = 4.

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To find the number that 37.5% of it equals 6, set up an equivalent fractions equation, cross-multiply, and solve for the unknown number. In this case, 37.5% of 16 is 6.

The question pertains to finding a certain number when given a percentage of that number. Here, we're asked to find the number of which '37.5% is 6'. We can solve this through simple arithmetic and the use of equivalent fractions. An important rule to remember is that 'percentage' literally means 'per 100', so 37.5% can be written as the fraction 37.5/100.

To find the unknown number (let's call it X), you can set up the equation 37.5/100 = 6/x, where 'x' is the number we're trying to find. Then you cross-multiply to solve for 'x': 37.5 * X = 6 * 100. Simplifying this, X = (6 * 100) / 37.5. Calculating that out gives X = 16. Therefore, 37.5% of 16 is 6.

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The value of the unknown number whose 37.5 percent equals 6 is 16.

Given the parameter:

37.5% of what number is 6

The problem is asking for 37.5% of some unknown number which gives 6.

We can represent the unknown number as x.

Now, the equation to find the unknown number will be:

37.5% of x = 6

Replace 37.5% with 37.5/100:

37.5/100 of x = 6

37.5/100 × x = 6

Solve for x:

0.375 × x = 6

0.375x = 6

Divide both sides by 6:

x = 6/0.375

x = 16

Therefore, the value of the number is 16.

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Answer:

B) X || Z

Step-by-step explanation:

Hope it helps you in your learning process.

Answer:

68in

Step-by-step explanation:

Divide the area by 2 because a= l x w and squares sides are all the same.

To find the approximate side length of a square game board with an area of 136in^2, you can use the formula for the area of a square and take the square root of the given area. The approximate side length is 11.66 inches.

To find the approximate side length of a square game board with an area of 136in2, we can use the formula for the area of a square, which is length * length. In this case, we need to find the square root of 136 to get the side length. The square root of 136 is approximately  11.66 inches.

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Answer:

[tex]y=\frac{1}{2} x+2.5[/tex]

Step-by-step explanation:

I graphed the equation on the graph below.

If this answer is correct, please make me Brainliest!

Final answer:

To calculate the number of calories from fat in a serving of refried beans, multiply the grams of fat by the calories per gram of fat. In this case, there are 9 calories from fat in a serving of refried beans.

Explanation:

In order to determine the number of calories from fat in a serving of refried beans, we need to know the total amount of fat per serving. The question states that there is 1 gram of fat in a serving. It also mentions that each serving is 110 calories. To calculate the number of calories from fat, we can use the formula:

Calories from fat = Fat (in grams) × Calories per gram of fat

Plugging in the values: Calories from fat = 1 gram × 9 Calories/gram of fat = 9 Calories

Therefore, there are 9 calories from fat in a serving of refried beans.

Final answer:

In a serving of refried beans that contains 1 gram of fat, there are 9 calories from fat.

Explanation:

The question asks how many calories are from fat in a serving of refried beans. To answer this, we need to know the amount of fat and the calories in the serving. The question provides that there is 1 gram of fat in the serving and that the serving is 110 calories. Therefore, 1 gram of fat in the serving would contribute 9 calories (since fat contains 9 calories per gram). So, the number of calories from fat in the serving of refried beans is 9 calories.

To calculate the number of calories from fat in a serving of refried beans, we need to use the fact that fat provides 9 calories per gram. With 1 gram of fat in a serving of refried beans, we do the following calculation:

Multiply the amount of fat in grams by the number of calories that fat provides per gram: 1g × 9 calories/g = 9 calories.

Therefore, 9 calories of the total 110 calories in a serving of refried beans come from fat.

Answer:

10/11

Step-by-step explanation:

You can find this answer by dividing the top and bottom numbers by 2.

Final answer:

Equivalent fractions of 20/22 can be found by simplifying it to 10/11 or by scaling it up, such as 40/44 or 60/66, by multiplying the numerator and denominator by the same whole number.

Explanation:

To find fractions equivalent to 20/22, you can simplify or scale the fraction up by multiplying both the numerator and the denominator by the same nonzero whole number. An equivalent fraction is one that represents the same value when both the top number (numerator) and the bottom number (denominator) are multiplied or divided by the same value.

Simplifying 20/22 means finding the greatest common divisor of 20 and 22, which is 2. So, dividing both by 2, we get 10/11. To scale up, you can multiply both the numerator and the denominator by any nonzero whole number, such as 2, to get 40/44, or 3 to get 60/66, and so on. Each of these fractions represents the same part of a whole as 20/22.

Answer:

Step-by-step explanation:

An obtuse triangle must contain an obtuse angle and two acute angles. An equilateral triangle must be 60 degrees in every corner, and thus there are 2+ acute angles. An isosceles triangle can have two angles that are 30 degrees (thus two acute), and a 120 degree angle

Addition property of equality

Division property of equality

Solution:

Given inequality is:

3x - 2 > 4

[tex]\mathrm{Add\:}2\mathrm{\:to\:both\:sides}[/tex]

Here, Addition property of equality is used

When the same amount is added to both sides of an inequality, then the inequality is still true

3x - 2 + 2 > 4 + 2

3x > 6

[tex]\mathrm{Divide\:both\:sides\:by\:}3[/tex]

Here, Division property of equality is used

When we divide both sides of an equation by the same nonzero number, the sides remain equal.

[tex]\frac{3x}{3}>\frac{6}{3}\\\\x > 2[/tex]

Thus the property used in each step of solving the inequality is found

The unit rate is 17 chairs per table.

Step-by-step explanation:

Given,

Total number of chairs at 6 tables = 102 chairs

Number of tables = 6

Unit rate in terms of tables = [tex]\frac{Total\ chairs}{Number\ of\ tables}[/tex]

Unit rate in terms of tables= [tex]\frac{102}{6}[/tex]

Unit rate in terms of tables = 17

The unit rate is 17 chairs per table.

"The correct unit rate is 17 chairs per table.

To find the unit rate, we need to divide the total number of chairs by the number of tables. The question states there are 102 chairs and 6 tables. The unit rate is the number of chairs per table, which can be calculated as follows:

Unit rate = Total number of chairs / Number of tables

Unit rate = 102 chairs / 6 tables

Now, we divide 102 by 6 to find the unit rate:

Unit rate = 102 / 6

Unit rate = 17

Therefore, the unit rate is 17 chairs per table. This means that at each table, there are 17 chairs."

Answer:

96 units^2

Step-by-step explanation:

Base: 6 × 6 = 36

Faces: 5 × 6 = 30 (×2 = 60)

Add: 36 + 60 = 96

Answer:

96 units^2

Step-by-step explanation:

The Base: 6 × 6 = 36

The Faces: 5 × 6 = 30 (×2 = 60)

Then Add: 36 + 60 = 96

Hope to help.

Answer:

Tyree’s solution is inaccurate. In step 1, he substituted incorrectly.

Step-by-step explanation:

to find the distance between two point A(-4, -2) and B(-7, -7) we use the following distance formula

[tex]d=\sqrt{(x_{2} -x_{1})^2+(y_{2}-y_{1} )^2 \\\\[/tex]

x1=-4, x2=-7

y1=-2, y2=-7

so,

[tex]d=\sqrt{(-7-(-4))^2+(-7-(-2) )^2\\}\\\\d=\sqrt{(-7+4)^2+(-7+2)^2 }\\\\d=\sqrt{(-3)^2+(-5)^2 }\\\\\\\\d=\sqrt{9+25}\\ \\d=\sqrt{34}[/tex]

Answer:

Tyree’s solution is inaccurate. In step 1, he substituted incorrectly.

Explanation:

I got it right,

Hope this Helps!

Answer: The products of corresponding x- and y- values of an inverse variation function are constant.

As x increases, y also increases.

The product of coordinate pairs are not equal: (165) (198) = 32,670 and (170) (204) = 34,680.

Step-by-step explanation:

Step-by-step explanation:

Since, x=8 and x=-5 are the roots.

Therefore, (x - 8) & (x - 5) will be factors.

Hence, required quadratic equation can be given as:

[tex](x - 8)(x - 5) =0 \\ \\ \therefore {x}^{2} + ( - 8 - 5) x+ ( - 8) \times ( - 5) = 0 \\ \\ \therefore {x}^{2} + ( - 13) x+ 40= 0 \\ \\ \huge \red{ \boxed{ \therefore {x}^{2} - 13x+ 40= 0 }} \\ is \: the \: required \: quadratic \: equation.[/tex]

Step-by-step explanation:

if you see the number the line is divided into 6 or to get from 0 to 1 or 2 to 3 it takes 6 space that means the fraction should n/6.

n= a number

2 5/6 that means that there is 2 wholes or 2 6/6

6/6= 1

it is easy to plot 2 5/6 because it is already 5/6, you plot it right on the line that is before 3 or 5 spaces after 2.

1 2/3 is the same as 1 4/6

there is 1 whole or one 6/6. now it is easy you plot it on the line that is 4 spaces away from 1.

Plotted the points on the line. Please see attached.

2 5/6 = 17/6 = 2.83

1 2/3 = 5/3 = 1.67