The number of miles that the car can go on one gallon of gas is:
12 miles.
How to calculate the rate of miles per gallon?The rate of miles per gallon is given by the number of miles divided by the number of gallons, according to the equation presented as follows:
miles per gallon = miles / gallon.
In the context of this problem, the measures are found as follows:
Miles = 1/4 = distance traveled.Gallon = 1/48 = amount of fuel used to travel the given distance.Hence the rate is given as follows:
miles per gallon = (1/4) / (1/48)
For a division of fractions, we multiply the inverse of the denominator by the numerator, hence:
miles per gallon = 48 x 1/4 = 48/4 = 12 miles.
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(10, 10) А (2, 4) Find point C so that that the ratio of length Ad to the length of CB is 3:1
ANSWER
[tex](8,8.5)[/tex]EXPLANATION
When a line segment is divided by ratio m:n, the coordinates of the point of division are given as:
[tex](\frac{mx_2+nx_1}{m+n},\frac{my_2+my_1}{m+n})[/tex]where (x₁, y₁) and (x₂, y₂) are the coordinates of the ends of the line.
Therefore, we have that:
[tex]\begin{gathered} m=3;n=1 \\ (x_1,y_1)=(2,4) \\ (x_2,y_2)=(10,10) \end{gathered}[/tex]Therefore, the coordinates of point C are:
[tex]\begin{gathered} (\frac{3\cdot10+1\cdot2}{3+1},\frac{3\cdot10+1\cdot4}{3+1}) \\ (\frac{30+2}{4},\frac{30+4}{4}) \\ (\frac{32}{4},\frac{34}{4}) \\ (8,8.5) \end{gathered}[/tex]Those are the coordinates of C.
7
1
-5
35
-4 24
-3 15
-2 8
-1 3
0 0
1 -1
Match the average rates of change of f(x) to the corresponding intervals.
-7
-4
300
[-5, -1]
(-4,-1]
[-3, 1]
-2,1]
The rates of changes of the given function for the corresponding intervals are: [-5, -1] = -8, [-4, -1] = -7, [-3, -1] = -6, [-2, -1] = -5.
What is function?
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
This means that a function f will map an object x to exactly one object f(x) in the set of potential outputs if the object x is in the set of inputs (referred to as the domain) (called the codomain).
The rate of change of a function can be calculate using the formula:
[tex]R = \frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
Putting the value from the question:
given [x₁, x₂] = [-5, -1]
f(-5) = 35 , f(-1) = 3
Putting these value in formula:
[tex]R = \frac{3-35}{-1 -(-5)}[/tex]
R = -32/4
R = -8
given [x₁, x₂] = [-4, -1]
f(-4) = 24, f(-1) = 3
Putting these value in formula:
[tex]R = \frac{3-24}{-1 -(-4)}[/tex]
R = -21/3
R = -7
given [x₁, x₂] = [-3, -1]
f(-3) = 15, f(-1) = 3
Putting these value in formula:
[tex]R = \frac{3-15}{-1 -(-3)}[/tex]
R = -12/2
R = -6
given [x₁, x₂] = [-2, -1]
f(-2) = 8, f(-1) = 3
Putting these value in formula:
[tex]R = \frac{3-8}{-1 -(-2)}[/tex]
R = -5/1
R = -5
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2x-5y = 16 solve for y
[tex]\frac{2(x-8)}{5}[/tex] = y
To Solve: value of y
Given: 2x-5y=16
Solution: The solution to this problem involves the following steps:
2x-5y-16=0
2x-16=5y
[tex]\frac{2x-16}{5}[/tex] = y
[tex]\frac{2(x-8)}{5}[/tex] = y
Answer: The final answer is : [tex]\frac{2(x-8)}{5}[/tex] = y
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RS = 8y +4, ST = 5y + 7, and RT = 115.What is the value of y?
EXPLANATION:
1.The first thing we must do is use a suitable method that allows us to find the value of y for the two equations of the line
2. The correct and most appropriate method is the matching method.
The exercise is as follows:
[tex]\begin{gathered} RS\text{ }=8y+4\text{ } \\ ST=5y\text{ }+7 \\ RS=ST\text{ } \\ 8y+4=5y+7 \\ 8y-5y=7-4 \\ 3y=3 \\ y=\frac{3}{3} \\ \textcolor{#FF7968}{y=1} \\ \text{\textcolor{#FF7968}{the answer is y}}\textcolor{#FF7968}{=1}\text{\textcolor{#FF7968}{ }}\textcolor{#FF7968}{as}\text{\textcolor{#FF7968}{ a whole number or y}}\textcolor{#FF7968}{=\frac{3}{3\text{ }}}\text{\textcolor{#FF7968}{ as a }}\textcolor{#FF7968}{fractional}\text{\textcolor{#FF7968}{ number}} \end{gathered}[/tex]Reflect the figure over the line y = 1. Plot all of the points of the reflected figure. You may click a plotted point to delete it.
Answer:
Step-by-step explanation:
XYZ has coordinates X(2, 3), Y(1, 4), and Z(8, 9). A translation maps X to X′(4, 8). What are the coordinates for Z′? *
Answer:
Z'(10, 14)
Explanation:
Taking into accoun that the vertex point X(2, 3) is mapped to X'(4, 8), we can say that the translation rule is:
(a, b) ----> (a + 2, b + 5)
Because
X(2, 3) ----> (2 + 2, 3 + 5)
----> X'(4, 8)
So, using this rule, we can find the coordinates for Z' as:
Z(8, 9) ----> (8 + 2, 9 + 5)
----> Z'(10, 14)
Therefore, the answer is Z'(10, 14)
Explain how the points A(9,-) and 8(9,3) are related. Use vocabulary words
in your explanation.
Answer: The points (9,-) and (9,3) Both have the same (y) coordinate.
Step-by-step explanation:
Determine the intervals on which the function is increasing, decreasing, and constant.
A) Increasing on (- 5, - 3) and (2, 5) Decreasing on (- 3, 0) Constant on (0, 2) B) Increasing on (- 3, - 1) Decreasing on (- 5, - 2) and (2, 4) Constant on (- 1, 2) C) Increasing on (- 3, 1) ; Decreasing on (- 5, - 3) and (0, 5) ; Constant on (1, 2) D ) Increasing on (- 3, 0) Decreasing on (- 5, - 3) and (2, 5); Constant on (0, 2)
Answer:
The answer is D
Step-by-step explanation:
Check to see when the graph is increasing and decreasing from left to right.
It is decreasing from x = -5 to x = -3 or (-5,-3) These look like a points but are not. They are intervals.
Then, it increases from x = -3 to x = 0 or (-3,0)
Then, it stays constant from x = 0 to x = 2 or (0,2)
Lastly, it decreases from x - 2 to x = 5 or (2,5)
To summarize, the graph is increasing from (-3,0). Decreasing on (-5,-3) and (2,5). and constant on (0,2)
The only option that fits these conditions is D.
You and a friend have each randomly draw a card.
There are 52 cards in a deck.
There are 12 face cards in the deck, that is 3 face cards per suit.
The probability of getting at least from two draws is given to be:
[tex]P=P(X=1)+P(X=2)[/tex]Therefore, the probability is calculated using the formula:
[tex]P=\frac{^{12}C_1\times^{40}C_1}{^{52}C_2}+\frac{^{12}C_2}{^{52}C_2}[/tex]Using the combination formula, we have the solution to be:
[tex]\begin{gathered} \Rightarrow\frac{12\times40}{1326}+\frac{66}{1326}=\frac{480}{1326}+\frac{66}{1326} \\ P=\frac{546}{1326} \\ P=\frac{7}{17} \end{gathered}[/tex]The LAST OPTION is correct.
What number is five times the first number. The third number is 100 more than the first number. Of the sound of three numbers is 490, find the numbers
Answer:
The three numbers are:
4.62,
23.1, and
462.2
Step-by-step explanation:
Let X be the "first number."
B = What number is five times the first number: 5X
C = third number is 100 more than the first number: 100X
The sum of all three is 490: X + B + C = 490
----
X + B + C = 490
X + 5X + 100X = 490
106X = 490
X = 4.622
Check:
X = 4.622
B = 5X = 23.11
C = 100X = 462.2
Check:
Sum (4.622 + 23.11 + 462.2) = 490
6. Create a systems of inequalities to represent the graph below
System of inequalities
We are given the graph where two lines represent the solution of a system of inequalities.
The solution is the double-shaded region of the graph.
We need to find the equation of the blue line and the red line and then convert them to inequalities.
Let's start with the blue line. We need to find two clear points through which it passes. These are (0,6) and (2,0). Now we write the equation of the line when knowing two points (the point-point form):
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex][tex]\begin{gathered} \displaystyle y-6=\frac{0-6}{2-0}(x-0)=-3x \\ \text{Adding 6:} \\ y=-3x+6 \end{gathered}[/tex]For the red line, the points are (0,0) and (2,2):
[tex]\begin{gathered} y-0=\frac{2-0}{2-0}(x-0)=x \\ y=x \end{gathered}[/tex]Now we have the equations of the lines, we must convert the equation to inequality by inserting one of these symbols instead of the equal sign:
> ≥ < ≤
For the blue line, the equation of the line is:
y = -3x + 6
Testing the origin (0,0):
0 = 0 + 6
0 = 6
To convert this to a true inequality we must replace the = for < or ≤
Since the blue line is solid, the points on the line belong to the solution, thus the first inequality is:
y ≤ -3x + 6
Now for the red line. The equation is
y = x. Let's test the point (2,1)
1 = 2
We must use the sign ≤ to make the expression true, thus the second inequality is:
y ≤ x
Thus, the system of inequalities is:
y ≤ -3x + 6
y ≤ x
A glacier is moving at a rate of 0.3 inches every hour. The table below represents this relationship.
Glacial Movement
Distance Moved (inches)
Time
(hours)
0.3
1
0.6
2
0.9
3
x
4
What value of x completes the table?
1.2
1.5
3.6
13.3
Answer:
1.2
Step-by-step explanation:
The diameter D of a sphere is 12.4 m. Calculate the sphere's surface area A.
Use the value 3.14 for , and round your answer to the nearest tenth.
The sphere has a surface area of 482.8064 square meters
How to determine the surface area of the sphere?From the question, the given parameters are:
Diameter, D = 12.4 meters
π = 3.14
The surface area of the sphere is calculated using the following formula
S = 4π(D/2)²
Substitute the given parameters in the above formula
So, we have
S = 4 * 3.14 * (12.4/2)²
Evaluate the exponent
This is represented as
S = 4 * 3.14 * 38.44
Evaluate the product
This is represented as
S = 482.8064
Hence, the surface area of the sphere is 482.8064 square meters
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25 lbs of potatoes cost $100. How much
would 15 lbs cost?
Round the answer to two decimal digit
Julia just let a new candle and then let it burn all the way down to nothing. The candle
burned at a rate of 0.75 inches per hour and its initial length was 9 inches. Write an
equation for L, in terms of t, representing the length of the candle remaining
unburned, in inches, t hours after the candle was lit.
L=
Answer: L= 9-.75x
Step-by-step explanation: since it starts at 9 inches tall and is melting at .75 inches per hour, it's going to be the initial length, 9, minus the rate, .75, times the time/hours past, so x
Complete the table and use the results to find the indicated limit.
Given the function:
[tex]k(x)=\frac{x^3-x-6}{x-2}[/tex]when x = 1.9
[tex]k(x)=\frac{1.9^3-1.9-6}{1.9-2}=\frac{-1.041}{-0.1}=10.41[/tex]when x = 1.999
[tex]k(x)=\frac{1.999^3-1.999-6}{1.999-2}=\frac{-0.0109944}{-0.001}=10.994001[/tex]When x = 2.001
[tex]k(x)=\frac{2.001^3-2.001-6}{2.001-2}=\frac{0.011006}{0.001}=11.006[/tex]When x = 2.1
[tex]k(x)=\frac{2.1^3-2.1-6}{2.1-2}=\frac{1.161}{0.1}=11.61[/tex]so, the limit of the function k(x) = 11
The answer is option A. 11
5) Naomi painted 16.5 square feet of a mural at a rate of 2 square feet per hour. Calire painted 7.5 square
feet of the mural at a rate of 4 square feet per hour. If they continue to paint at the same rates, how many
more hours will it take until Naomi and Claire have painted equal areas of the mural?
Answer: 4.5
Step-by-step explanation:
We need to find the amount of time until Calire paints a total of 9 more square feet.
Since the difference in their rates is 2 square feet per hour, it will take 9/2 = 4.5 more hours.
The sum of three palm tree heights range from 32 to 42 feet. The height of two of the trees are 8 feet and 16 feet. If the height of the third tree is x feet, write and solve a compound inequality to show the possible heights of the third tree.
The inequality to show the possible heights of the third tree is 8 ≤ x ≤ 18.
How to calculate the value?Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤
Let the height of the third tree be x.
By the given condition, this will be:
8 + 16 + x ≥ 32 and 8 + 16 + x ≤ 42
The first relation will give x ≥ 32 - 24 = x ≥ 8
The second relation will give:
8 + 16 + x ≤ 42
24 + x ≤ 42
x ≤ 42 - 24
x ≤ 18
The inequality is 8 ≤ x ≤ 18.
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If sum of three palm tree heights range from 32 to 42 feet. The height of two of the trees are 8 feet and 16 feet. If the height of the third tree is x feet. Then compound inequality is 8 ≤ x ≤ 18.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Let height of the third tree be x.
By the given condition
The sum of three palm tree heights range from 32 to 42 feet
8 + 16 + x ≥ 32 and 8 + 16 + x ≤ 42
Solve these inequalities
8 + 16 + x ≥ 32
24+x ≥ 32
x≥ 32-24
x≥ 8
and 8 + 16 + x ≤ 42
24+ x ≤ 42
x≤ 42-24
x ≤ 18
Hence the inequality is 8 ≤ x ≤ 18.
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Graph the equation after rewriting it in slope-intercept form. 9x+3y=18
The equation of a line in the slope intercept form is expressed as
y = mx + c
The given equation is
9x + 3y = 18
We would rearrange it so that it takes the form of the slope intercept equation shown above.
We would divide both sides of the equation by 3, we have
9x/3 + 3y/3 = 18/3
3x + y = 6
Subtracting 3x from both sides of the equation, we have
3x - 3x + y = 6 - 3x
y = 6 - 3x
The slope intercept form is
y = - 3x + 6
To plot the graph, we would substitute values of x into the equation to get corresponding y values. These x and y values would be plotted on the x and y coordinates of the graph. We have
For x = - 2, y = 6 - 3(- 2) = 6 + 6 = 12
For x = - 1, y = 6 - 3(-1) = 6 + 3 = 9
For x = 0, y = 6 - 3(0) = 6 - 0 = 6
For x = 1, y = 6 - 3(1) = 6 - 3 = 3
For x = 2, y = 6 - 3(2) = 6 -6 = 0
The graph is shown below
Can someone help me out (I will give branliest)
Answer: Emma > Amelia > Brandon > Celesle > Damian
Step-by-step explanation:
We convert all the fractions to decimals (2 decimals).
Amelia 4.35 lbs
Brandon [tex]4\frac{1}{3}= \frac{12}{3} +\frac{1}{3} =\frac{13}{3}[/tex] ≈ 4.33 lbs
Celesle 4.2 lbs
Damian √15 ≈ 3.87 lbs
Emma [tex]4\frac{2}{3} =\frac{12}{3} +\frac{2}{3} =\frac{14}{3}[/tex] ≈ 4.67 lbs
4.47 lbs > 4.35 lbs > 4.33 lbs > 4.2 lbs > 3.87 lbs
Emma > Amelia > Brandon > Celesle > Damian
What is the solution to 4x-5(2x-1) <= 7(2x+3)
Mr. Stewart wants to cut a board that is 34 inches long into four pieces that are the same length. How long will each
board be after he cuts them?
08.0 inches
8.2 inches
8.4 inches
O 8.5 inches
How do you solve -m=9
Hello!
So, we are given the following to solve:
[tex]-m=9[/tex]
To solve this, simply divide both sides by -1.
[tex]\frac{-m}{-1}= \frac{9}{-1}[/tex]
Then, simplify the expression and you have your solution.
[tex]m=-9[/tex]
Hope this helps! If so, please lmk! Thanks and good luck!
Answer:
m= -9
Step-by-step explanation:
Divide both sides by -1
[tex]\frac{-m}{-1} =\frac{9}{-1}[/tex]
Simplify m = - 9
For each of the following quadrilaterals, select all the properties that must be true.
Answer:
Rhombus: All sides congruent, two pairs of parallel sides
Parallelogram: Two pairs of parallel lines
Rectangle: 4 right angles, Two pairs of parallel sides
Step-by-step explanation:
Solve the compound inequality. 2x-4 > 8 or 3x-1 < -10
-3 < x < 6
x > 6 or x < -3
x > 2 or x < -3
x < 6 or x < -3
The solution to the compound inequality is x > 6 or x < -3
How to solve compound inequality?An inequality is a mathematical expression that has <, >, ≤ and ≥.
A compound inequality is an inequality that combines two simple inequalities.
Therefore, let's solve the compound inequality as follows:
2x - 4 > 8 or 3x - 1 < - 10
2x - 4 > 8
add 4 to both sides of the inequality
2x - 4 + 4 > 8 + 4
2x > 12
divide both sides by 2
x > 12 / 2
x > 6
3x - 1 < - 10
add 1 to both sides of the inequality
3x - 1 + 1 < - 10 + 1
3x < - 9
divide both sides by 3
x < -9 / 3
x < -3
Therefore, x > 6 or x < -3
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The solution to the compound inequality will be; x > 6 or x < -3
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two functions in an problem.
A compound inequality is defined as an inequality that combines two simple inequalities.
Therefore, solve the compound inequality that will be;
2x - 4 > 8 or 3x - 1 < - 10
2x - 4 > 8
Then add 4 to both sides of the inequality so,
2x - 4 + 4 > 8 + 4
2x > 12
Now, divide both sides by 2
x > 12 / 2
x > 6
3x - 1 < - 10
Again, add 1 to both sides;
3x - 1 + 1 < - 10 + 1
3x < - 9
Then divide both sides by 3;
x < -9 / 3
x < -3
Therefore, solution to the compound inequality is; x > 6 or x < -3
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6) Bill found a pair of jeans that cost $35.00. If he had a 20%-off coupon, how much would the
jeans cost?
What is the value of the expression below when z=3?
10z^2 +7z+4
The value of the expression [tex]10z^2[/tex]+7z+4 when z = 3 is 115
The expression is
[tex]10z^2[/tex]+7z+4
The expression is defined as the statements that have a minimum of two terms containing numbers or variables , connected by an operator in between. The operator maybe addition, subtraction, division, multiplication etc..
The expression is
[tex]10z^2[/tex]+7z+4
The value of z = 3
Substitute the value of z in the given expression
= [tex]10(3)^2[/tex]+ 7×3 + 4
= 10×9 + 21 + 4
Multiply the terms first
= 90 + 21 + 4
Add them together
= 115
Hence, the value of the expression [tex]10z^2[/tex]+7z+4 when z = 3 is 115
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Hi, can you help me to solve this problem, please !!!
Remember that
The y-intercept is the value of y when the value of x=0
In this problem
we have the equation
y=7x^2+4
For x=0
substitute
y=7(0)^2+4
y=4
the y-intercept is (0,4)Describe the end behavior of the graph of the following polynomial function:
We will have the following:
From the polynomial we will have that:
*It falls to the left and rises to the right.
This can be seeing as follows:
Pls help solve all 3 questions
Thank you :)
Answer:
Q18: x = 21, y = 15
Q19: x = 16, y = 10
Q20: x = 24, y = 19
Step-by-step explanation:
Q18:
(3x - 16) + (6x + 7) = 180 (corresponding angles, sum of angles on a straight line=180°)
9x - 9 = 180
9x = 189
x = 21
11y - 32 = 6x + 7 (vertically opposite angles)
11y - 32 = 6(21) + 7
11y - 32 = 133
11y = 165
y = 15
Q19:
8x - 14 = 5x + 34 (corresponding angles, vertically opposite angles)
3x = 48
x = 16
(8x - 14) + (5y + 16) = 180 (sum of angles on a straight line=180°)
8(16)-14 + (5y + 16) = 180
114 + 5y + 16 = 180
5y + 130 = 180
5y = 50
y = 10
Q20:
47 + 3x + (2x + 13) = 180 (corresponding angles, sum of angles on a straight line=180°)
5x + 60 = 180
5x = 120
x = 24
5y - 23 = 3x (corresponding angles)
5y - 23 = 3(24)
5y - 23 = 72
5y = 95
y = 19