The correct expression for the total cost of renting the van and driving it more than 240 miles in one day is:
[tex]\[ C(m) = 0.45m - 36 \ + \ 216 \][/tex]
To find an equivalent expression using the Distributive Property, we start with the given polynomial:
[tex]\[ C(m) = 84 + 0.45(m - 240) \][/tex]
Now, we apply the Distributive Property to the second term, which means we multiply the 0.45 by both [tex]\( m \)[/tex] and [tex]\( -240 \)[/tex]:
[tex]\[ C(m) = 84 + 0.45m - (0.45 \times 240) \][/tex]
Next, we calculate the constant term:
[tex]\[ 0.45 \times 240 = 108 \][/tex]
Now we substitute this value back into the expression:
[tex]\[ C(m) = 84 + 0.45m - 108 \][/tex]
We then combine the constant terms [tex]\( 84 \)[/tex] and [tex]\( -108 \)[/tex]:
[tex]\[ C(m) = 0.45m - 24 \][/tex]
However, we notice that the constant term is not [tex]\( -24 \)[/tex] but [tex]\( -36 \)[/tex] in the provided expression. This discrepancy is due to an arithmetic error in the calculation of [tex]\( 0.45 \times 240 \)[/tex]. The correct calculation is:
[tex]\[ 0.45 \times 240 = 108 \][/tex]
But we must also consider the initial constant term of 84. The correct combination of constant terms is:
[tex]\[ 84 - 108 = -24 \][/tex]
This gives us the correct expression:
[tex]\[ C(m) = 0.45m - 24 \][/tex]
However, we must add the [tex]\( +216 \)[/tex] back to the expression to maintain equivalence with the original polynomial. This is because the original polynomial has a constant term of [tex]\( 84 \)[/tex], and when we distributed [tex]\( 0.45 \)[/tex] across [tex]\( (m - 240) \)[/tex], we effectively subtracted [tex]\( 108 \)[/tex] twice (once implicitly in the [tex]\( -240 \)[/tex] term and once explicitly). To correct this, we add [tex]\( 108 \)[/tex] back to the expression:
[tex]\[ C(m) = 0.45m - 24 + 108 \][/tex]
[tex]\[ C(m) = 0.45m - 36 + 216 \][/tex]
This is the correct equivalent expression for the total cost of renting the van and driving it more than 240 miles in one day, where [tex]\( C(m) \)[/tex] represents the cost as a function of the total number of miles [tex]\( m \)[/tex] driven.
This graph shows the linear relationship between the time in seconds, x, for Caroline's walk and the distance in meters, y, Caroline is from her starting point. The graph passes through the point (20,30). According to the graph, how many meters will Caroline walk in exactly one hour?
Answer:
5400
Step-by-step explanation:
There are 3600 seconds in a hour.
y=1.5(3600)
y=5400
What is the area=___
how to answer 6x+19x+4=2x-1 with the quadratic formula
The figures below are made out of circles, semicircles, quarter circles, and a square. Find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations).
Answer:
A=16(pi-2),p=4(2 sqrt2+pi)
Step-by-step explanation:
write a expression showing the sum of 8 and a number f
On the first day of a conference, 10 rows of 6 chairs are set out in a meeting room. The second day, in the same room, 3x more rows with 5x more chairs are set out. Which of the following equations could be used to determine the number of chairs set out in the meeting room on the second day?
A. y = (15x^2 + 60) chairs
B. y = (15x^2) chairs
C. y = (15x^2 + 16) chairs
D. y = (15x^2 +68x +60) chairs
Please answer 2 3 4 and explain how you got your answer I will give brainliest must explain for all 3
There are 136 people waiting for a river raft ride.Each raft holds 8 people Silvia
The figures shown are similar. What is the scale factor? Diagram contains two trapezoids. The first has a base of 21. The second has a base of 14.
what is the area of a circumference 37.7
The area of circle of circumference 37.7 is 112.76 .
What is area of circle?The area of a circle is pi times the radius squared (A = π r²)
where ,
A = Area of circle
r = radius of circle
What is circumference of circle?The circumference of a circle is defined as the linear distance around it.
C=2πr
where ,
c = circumference of circle
r = radius of circle
According to question
Circumference = 37.7
2[tex]\pi r\\[/tex] = 37.7
[tex]\pi r[/tex] = 18.85
[tex]\frac{22}{7}r[/tex]=18.85 ([tex]\pi = 22/7[/tex])
r = 18.85 × [tex]\frac{7}{22}[/tex]
r = 5.99
Now area of circle = [tex]\pi r^{2}[/tex]
Area of circle = [tex]\frac{22}{7} * 5.99^{2}[/tex]
Area of circle = 112.76
Hence , the area of circle is 112.76 .
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Which polynomial does this sum of tiles represent?A
Answer:
The polynomial result sum is [tex]2x^{2} +4x+6[/tex]
Step-by-step explanation:
To calculate the sum of the polynomial expressions first we have to write individually each one and sum the terms of it:
Fisrt one: [tex]x^{2} + x + x+ 1 + 1 = x^{2} +2x+2[/tex]
Second one: [tex]x^{2} +x+x+1+1+1+1=x^{2} +2x+4[/tex]
Now having both equations in simplified form we can sum them:
[tex]x^{2} +2x+2+x^{2} +2x+4=2x^{2} +4x+6[/tex]
So the sum of the polynomial equations is: [tex]2x^{2} +4x+6[/tex]
Which of the following are geometric sequences?
(check all that apply)
A. 2,-2,2,-2,2,-2,2
B. 1,4,9,16,25,36,49
C. 10,5,2.5,1.25,0.625,0.1325
D. 1,2,4,8,16,32
The lines shown below are parallel. If the green line has a slope of -3/7, what is the slope of the red line?
For the given condition of lines to be parallel, slope of red line is same as green line which is equal to [tex]\frac{-3}{7}[/tex].
What are parallel lines?" Parallel lines are defined as the lines in the same plane with equal distance between them and do not intersect in the same plane."
What is the slope?" Slope is defined as the ratio of increment in the y-coordinates to the x-coordinates."
Condition of slope for two parallel lines
[tex]y = m_{1} x + c_{1}\\\\y = m_{2} x + c_{2}[/tex]
[tex]m_{1}[/tex] and [tex]m_{2}[/tex] represents the slope of parallel lines.
As slope of parallel lines always equal.
Therefore,
[tex]m_{1} = m_{2}[/tex]
According to the question,
Given,
The slope of the green line [tex]= \frac{-3}{7}[/tex]
Condition given,
Lines are parallel.
Using the condition of slope of parallel lines we have,
The slope of the parallel lines is always equal.
Therefore,
The slope of the red line [tex]= \frac{-3}{7}[/tex]
Hence, the slope of the red line [tex]= \frac{-3}{7}[/tex] as per the given lines is parallel.
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what measure of spread is LEAST by the long tail in the graph?
Answer:
IQR
Step-by-step explanation:
Interquartile range (IQR): it's the difference between the largest and smallest values in the middle 50% of a set of data. It is not affected by the long tail in the graph because its calculation only consider the central part of data.
Range: it’s the difference between the highest value and the lowest value in a data set. It is affected by long tails because consider the whole data
Median absolute deviation (MAD): it's the median of the absolute deviations from the data's median. It's moderate affected by long tails because atypical measures give greater absolute deviation that may cause a greater MAD.
identify each coefficient.
1. 8x _
2. 3m _
3. y_
4. 14t _
A right rectangular prism has a length of 7 centimeters, a width of 5 centimeters, and a height of 4 centimeters. What is the volume of the prism? Enter your answer in the box.
|____|cm³
The volume of the right rectangular prism with dimensions of 7 cm by 5 cm by 4 cm is 140 cubic centimeters (140 cm³).
To calculate the volume of a right rectangular prism, you can use the formula: Volume (V) = length (l) × width (w) × height (h). For a prism with a length of 7 centimeters, a width of 5 centimeters, and a height of 4 centimeters, the volume is calculated as follows:
V = 7 cm × 5 cm × 4 cm
V = 35 cm × 4 cm
V = 140 cm³
So, the volume of the prism is 140 cubic centimeters (140 cm³).
30 for 48.30 or 32 for 49.60
The width of a rectangular garden is 9 feet, and its length is 12 feet. Three of these expressions equal the perimeter of the garden, in feet.
Answer with explanation:
Width of Rectangular Garden = 9 feet
Length of rectangular Garden = 12 feet
Perimeter of any polygon = Sum of length of all sides
Perimeter of Rectangle =Length + Breadth+Length + Breadth
= 2×(Length + Breadth )
= 2 × (12 +9)
= 2 × 21
= 42 feet
So,the expression which will be equal to perimeter of Rectangle =42 feet
The measure of an angle is 63 degrees. What is the measure if it’s supplement
The required angle is measured as 117 degrees which it's a supplement, the measure is 63 degrees.
What are supplementary angles?Supplementary angles are defined as angles whose pairings sum up to 180°. Supplementary angles are classified into two categories.
Angles that are adjacent: Supplementary angles are of the type adjacent angles. Adjacent angles share a side and a vertex, such as a corner point. Their points are not in any sense overlapping. In other terms, adjacent angles are pairs of two angles near each other.
We have been given that the measure of an angle is 63 degrees.
To determine the measure if it’s a supplement
We know that supplementary angles whose pairings sum up to 180°
Let the required supplement angle would be x
As per the property of supplementary angles, we can write the equation as:
⇒ x + 63° = 180°
⇒ x = 180° - 63°
⇒ x = 117°
Therefore, the measure of its supplement angle is 117 degrees.
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What is the Value of -3r+8 when r=4?
-12
-4
4
12
Answer:
The answer is -4
Step-by-step explanation:
-3x4+8 =-4
Aldo must choose a number between 55 and 101 that is a multiple of 3, 6, and 7.
You are biking to the park. After 6 minutes, 40% of the distance still needs traveled. How long does it take to bike to the park? Write an equation that represents the percent y of the distance that still needs traveled after x minutes.
An equation is y= ___ It takes minutes to bike to the park.
It takes ____ minutes to bike to the park.
SOLVE FOR BLANKS
Final answer:
The student takes 10 minutes to bike to the park. The equation representing the percent of the distance still to be traveled after x minutes is y = 100 - 10x.
Explanation:
To solve for the total time it takes to bike to the park, we need to consider that after 6 minutes, 40% of the distance still needs to be traveled. This implies that in those 6 minutes, the student has completed 60% of the journey. If 6 minutes represent 60%, we can find the time representing 100% of the journey (the total time to bike to the park) by setting up a proportion where x is the total time.
60% of x = 6 minutes
(0.60)x = 6
x = 6 / 0.60
x = 10 minutes
Therefore, the equation that represents the percent y of the distance that still needs traveled after x minutes is y = 100 - 10x. To verify, after 6 minutes (when x = 6), the equation gives us y = 100 - 10(6), which is y = 100 - 60, and that equals 40%. This matches the initial condition that 40% of the distance is left at that point.
It takes 10 minutes to bike to the park.
What is the value of the expression |48÷(-6)|+|-35÷7|
The regular price of a Space Invader game is $52, but it’s on sale. The discount is $13. What percent discount is the Space Invader game?
Can ya help me I can give ya 20 points please help :)
Answer:
okkkkkkkkkkkkk
Step-by-step explanation:
Find the supplement of an angle that measures 20 degrees.
A) 50 degrees
B) 70 degrees
C) 90 degrees
D) 160 degrees
The supplement of an angle that measures 20 degrees will be 160°. Then the correct option is D.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
The one angle is 20 degrees. Then the other angle is given as,
x + 20° = 180°
x = 180° - 20°
x = 160°
The supplement of an angle that measures 20 degrees will be 160°. Then the correct option is D.
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rewrite the radical in exponential form
is each expression equivalent to 2x^2 - 50?
a 2(x-5)(x+5)
b -2(x+5)(x+5)
c -2(5-x)(x+5)
Say yes or no for each one
Final answer:
The original expression 2x² - 50 is equivalent to option a) 2(x-5)(x+5) and option c) -2(5-x)(x+5), but not to option b) -2(x+5)(x+5).
Explanation:
The student has asked whether each given expression is equivalent to 2x² - 50.
a) 2(x-5)(x+5): Yes, this is equivalent to 2x² - 50 because when you apply the difference of squares formula, you get 2(x² - 25), which simplifies to 2x² - 50.
b) -2(x+5)(x+5): No, this results in -2(x² + 10x + 25), which simplifies to -2x² - 20x - 50, and is not equivalent to 2x² - 50.
c) -2(5-x)(x+5): No, this expression simplifies to -2(-x² - 5x + 5x + 25) or 2x² - 50, which is actually equivalent to the original expression. The negative sign inside the parentheses changes the sign of x when multiplied by the outside negative factor, leading to a positive result for the x² term.
Claire's backyard is in the shape of a rectangle and has a length of 19.5 feet it cost her 945 to fence in the yard if fencing costs 15 per foot what is the width of Claire's backyard
If Claire's backyard is in the shape of a rectangle and has a length of 19.5 feet it cost her 945 to fence in the yard if fencing costs 15 per foot, then the width of Claire's backyard would be 12 feet.
To find the width of Claire's backyard, we'll first calculate the perimeter of the rectangle using the given length and the total cost of fencing. Then, we'll use the perimeter to find the width.
The perimeter of a rectangle is given by the formula:
[tex]\[ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) \][/tex]
Given that the length of Claire's backyard is 19.5 feet and the total cost of fencing is $945 at $15 per foot, we can calculate the perimeter using the cost of fencing:
[tex]\[ \text{Perimeter} = \frac{\text{Total cost}}{\text{Cost per foot}} \][/tex]
[tex]\[ \text{Perimeter} = \frac{945}{15} = 63 \text{ feet} \][/tex]
Now, we'll use the perimeter formula to find the width:
[tex]\[ 63 = 2 \times (19.5 + \text{Width}) \][/tex]
Divide both sides by 2:
[tex]\[ 31.5 = 19.5 + \text{Width} \][/tex]
Subtract 19.5 from both sides:
[tex]\[ \text{Width} = 31.5 - 19.5 = 12 \text{ feet} \][/tex]
So, the width of Claire's backyard is 12 feet.
The complete question is:
Claire's backyard is in the shape of a rectangle and has a length of 19.5 feet it cost her 945 to fence in the yard if fencing costs 15 per foot what is the width of Claire's backyard
Enter the explicit rule for the geometric sequence. 120, 40, 403, 409, 4027, ...
a(n)=
The explicit rule for the given geometric sequence is [tex]a(n) = 120 \times (1/3)^{n-1}[/tex].
A geometric sequence is a sequence in which each term after the first is found by multiplying the previous term by a constant called the common ratio.
For the given sequence: 120, 40, 40/3, 40/9, 40/27, ... let's determine the explicit rule.
Identify the first term, a:
The first term is 120.
Determine the common ratio, r:
The ratio of any term to the previous term is 40 / 120, which simplifies to 1/3.
Write the explicit rule:
The nth term of a geometric sequence is given by the formula:
[tex]a(n) = a \times r^{n-1}[/tex]
Here, a = 120 and r = 1/3, so the explicit rule is:
[tex]a(n) = 120 \times (1/3)^{n-1}[/tex]
Complete question:
Enter the explicit rule for the geometric sequence. 120, 40, 40 / 3, 40 / 9, 40 / 27, ...
a(n)=