a moving company charges $250 to rent a truck and $0.40 for each mile driven. Mr. Lee paid a total of $314. Which equation can be used to find m, the number of miles he drove the moving truck?
To find the number of miles Mr. Lee drove the moving truck, we can set up an equation using the given information and solve for 'm'. The equation is $250 + $0.40x = $314, where 'x' represents the number of miles driven. Simplifying the equation, we find that Mr. Lee drove a total of 160 miles in the moving truck.
Explanation:To find the number of miles Mr. Lee drove the moving truck, we can set up an equation using the given information. The moving company charges $250 to rent the truck and $0.40 for each mile driven. Let's let 'm' represent the number of miles he drove. The total cost Mr. Lee paid, including the rental fee and the cost per mile, is $314. So, the equation can be written as:
$250 + $0.40x = $314
To solve for 'm', we can subtract $250 from both sides of the equation:
$0.40x = $314 - $250
$0.40x = $64
Finally, we can divide both sides of the equation by $0.40 to find the value of 'm':
x = $64 / $0.40
x = 160
Therefore, Mr. Lee drove a total of 160 miles in the moving truck.
Which line on the graph below has an undefined slope?
Answer:
R
Step-by-step explanation:
A vertical line has slope that is "undefined". Line R is the vertical line on your graph.
_____
The slope of a vertical line is "undefined" because of the way slope is defined. Slope is the vertical change divided by the horizontal change. When the line is vertical, there is no horizontal change, so the computation of slope involves division by zero. The result of division by zero is "undefined."
Answer:
C. R
Good Luck!
Gomez runs a small pottery firm. he hires one helper at $15,000 per year, pays annual rent of $6,500 for his shop, and spends $23,000 per year on materials. he has $40,000 of his own funds invested in equipment (pottery wheels, kilns, and so forth) that could earn him $6,000 per year if alternatively invested. he has been offered $20,500 per year to work as a potter for a competitor. he estimates his entrepreneurial talents are worth $5,000 per year (input cost for organizing resources). total annual revenue from pottery sales is $82,000. calculate the accounting profit and the economic profit for gomez's pottery firm.
The accounting profit for Gomez's pottery firm is $37,500, calculated by subtracting explicit costs from total revenue. The economic profit is $6,000, figured out by subtracting both explicit costs and implicit costs from total revenue.
Explanation:To calculate the accounting profit for Gomez's pottery firm, we subtract all explicit costs (money spent) from the total revenue. In this case, we subtract the salary of the helper ($15,000), the rent of the shop ($6,500), and the amount spent on materials ($23,000) from the total annual revenue from pottery sales ($82,000). Therefore, the accounting profit is $82,000 - $15,000 - $6,500 - $23,000 = $37,500.
On the other hand, to obtain the economic profit, we need to also subtract implicit costs, which are the opportunity costs of using the resources in one way rather than the next best alternative way. Gomez could have made $6,000 by investing his own $40,000 elsewhere, and he could have earned $20,500 by working for a competitor, so these are both implicit costs. Additionally, he estimates his entrepreneurial talents to be worth $5,000. Therefore, "the economic profit is $37,500 (accounting profit) - $6,000 (returns from alternative investment) - $20,500 (salary from competitor) - $5,000 (value of his entrepreneurial talents) = $6,000".
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There were 36,000 people at a ballgame in los angeles. the day's receipts from $12 reserved seats and $6 general-admission seats were $258,000 how many of each type of seat were sold?
what is 62.19 x 32.5
What are the values of a, b, and c in the quadratic equation 0 =1/2 x2 – 3x – 2?
A. a =1/2 , b = 3, c = 2
B. a =1/2 , b = –3, c = –2
C. a =1/2 , b = 3, c = –2
D. a = 1/2, b = –3, c = 2
Answer:
B.
Step-by-step explanation:
The equation is [tex]\frac{1}{2} x^{2} -3x -2[/tex]. a is the coefficient of [tex]x^{2}[/tex], b is the coefficient of x and c is the independent term. So, for the equation we have a = 1/2, b= -3 and c = -2.
What is 0.63¯¯¯¯ expressed as a fraction in simplest form? Enter your answer in the box.
To express 0.63¯¯¯¯ as a fraction, first set it up as x = 0.6363¯¯¯¯, then follow a process of subtraction, multiplication, and division to simplify it to 4063/9900.
Explanation:To express 0.63¯¯¯¯ as a fraction in simplest form, we can set it up as x = 0.6363¯¯¯¯.
Subtract the repeating part from the original number: x = 0.6363¯¯¯¯ - 0.6 = 0.03¯¯¯¯Multiply x by 100 to shift the decimal two places to the right: 100x = 63.6363¯¯¯¯ - 60 = 3.6363¯¯¯¯Subtract the first equation from the second equation: 100x - x = 3.6363¯¯¯¯ - 0.03¯¯¯¯Combining these steps, we get:
99x = 3.606363¯¯¯¯¯¯¯¯ x = 3.606363¯¯¯¯ / 99 = 4063/9900 as the fraction in simplest form.
A rectangle is 2 4/5 meters wide and 3 1/2 m long what is its area
The area of the rectangle whose dimensions are 2 ⁴/₅ meters wide and 3 ¹/₂ m long will be 49/5 square meters.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be
Area of the rectangle = L×W square units
A rectangle is 2 ⁴/₅ meters wide and 3 ¹/₂ m long. Then the area of the rectangle will be
A = (2 ⁴/₅)(3 ¹/₂)
A = (14/5) (7/2)
A = 49/5 square meters
The area of the rectangle whose dimensions are 2 ⁴/₅ meters wide and 3 ¹/₂ m long will be 49/5 square meters.
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A group of friends are going to a cottage for the weekend. The scale used is 1 : 250,000. The distance measures 8.5cm on the map. What is the actual distance
Which graph represents the solution set of the system of inequalities?
What algebraic property is demonstrated in the equation below? 5+3(2x-7)= 5+6x-21
The distributive property is demonstrated in the equation.
Explanation:The algebraic property demonstrated in the equation is the distributive property. The distributive property states that when a number is multiplied by the sum or difference of two other numbers, you can distribute the multiplication to each term inside the parentheses.
In the given equation, 3(2x - 7) means multiplying 3 by both terms inside the parentheses. This results in 6x - 21. Therefore, the equation can be simplified to 5 + 6x - 21.
Write an equation of the line passing through (-5,5) and having slope -6. Guve the answer in slope-intercept form.
If f(x)=8x and g(x)=2x+1, find(f•g)(x).
A) 16x+1
B) 10x+1
C) 16x+8
D) 16x^2+8x
What are the values of a and b
the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are 8 and [tex]\( 2\sqrt{7} \)[/tex], respectively.
The image depicts a right-angled triangle with a hypotenuse of length 10 and one leg of length 6, with the other leg labeled as [tex]\( a \)[/tex]. There is also a smaller right-angled triangle within it, sharing the leg of length 6 with the larger triangle, with the hypotenuse of the smaller triangle labeled as 8 and the other leg labeled as [tex]\( b \).[/tex]
To find the lengths of [tex]\( a \)[/tex] and [tex]\( b \)[/tex], we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse [tex](\( c \))[/tex] is equal to the sum of the squares of the lengths of the other two sides [tex](\( a \)[/tex] and [tex]\( b \)[/tex]): [tex]\( c^2 = a^2 + b^2 \).[/tex]
For the larger triangle:
[tex]\[ 10^2 = 6^2 + a^2 \][/tex]
For the smaller triangle:
[tex]\[ 8^2 = 6^2 + b^2 \][/tex]
We will solve these two equations to find [tex]\( a \)[/tex] and [tex]\( b \)[/tex]. Let's start with the calculations for [tex]\( a \)[/tex] and [tex]\( b \)[/tex] using the Pythagorean theorem.
Using the Pythagorean theorem for each triangle, we find:
For the larger triangle:
[tex]\[ a^2 = 10^2 - 6^2 \][/tex]
[tex]\[ a^2 = 100 - 36 \][/tex]
[tex]\[ a^2 = 64 \][/tex]
[tex]\[ a = 8 \][/tex]
For the smaller triangle:
[tex]\[ b^2 = 8^2 - 6^2 \][/tex]
[tex]\[ b^2 = 64 - 36 \][/tex]
[tex]\[ b^2 = 28 \][/tex]
[tex]\[ b = \sqrt{28} \][/tex]
[tex]\[ b = 2\sqrt{7} \][/tex]
So, the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are 8 and [tex]\( 2\sqrt{7} \)[/tex], respectively.
Andrew has 10 more goldfish than todd.together they have 50 goldfish.how many goldfish each boy have?
Answer:
Andrew has 30 goldfish and Todd has 10 goldfish
Step-by-step explanation:
Lets call A the number of goldfish Andrew has and T the number of goldfish Todd has.
Andrew has 10 more goldfish than Todd:
A = T + 10
Together they have 50 goldfish:
A + T = 50
Lets replace A = (T + 10) in the las equation:
T + 10 + T = 50
Lets solve T in this equation:
2T + 10 -10 = 50 -10
2T /2 = 40 /2
T = 20
Todd has 20 goldfish
Now lets calculate A = T + 10 = 20 + 10 = 30
Andrew has 30 goldfish
a pile of newspapers in the recycling bin was 12 1/4 inches high. each week the height of the pile increases by 4 5/8 inches. what is the height of the pile after 4 weeks
Doomtown is 300 miles due west of Sagebrush and Joshua is due west of Doomtown. At 9 a.m. Mr. Archer leaves Sagebrush for Joshua. At 1 p.m. Mr. Sassoon leaves Doomtown for Joshua. If Mr. Archer travels at an average speed 20 mph faster than Mr. Sassoon and they each reach Joshua at 4 p.m., how fast is each traveling?
Answer:Archer's speed is 60 mph.
Sassoon's speed is 40 mph.
Step-by-step explanation:
Let the distance that Sassoon travels is d miles.
Let his average speed be x mph.
The time of travel is from 1 p.m. to 4 p.m., which is 3 hours.
Therefore
3x = d (1)
The distance that Archer travels is (d + 300) miles.
The time of travel is from 9 a.m. to 4 p.m., which is 7 hours.
The average traveling speed is (x + 20) mph, therefore
7(x + 20) = d + 300
That is,
7x + 140 = d + 300
7x = d + 160 (2)
Subtract (1) from (2).
7x - 3x = d + 160 - d
4x = 160
x = 40 mph (Sassoon's average speed)
x+20 = 60 mph (Archer's average speed)
From (1), obtain d = 120 mi
Answer:
Archer's speed is 60 mph.
Sassoon's speed is 40 mph.
Which graph represents the equation y=1/3x−4 ?
bottom picture is my answers
The graph of the equation y = 1/3x - 4 is a straight line that contains the points (3, -3) and (0, 04)
The bottom left is the correct answer.
We have,
To graph this equation, we can start by finding the y-intercept, which is the point where the line crosses the y-axis.
In this equation,
The y-intercept is -4, so we plot the point (0, -4).
Next, we can find another point on the line by choosing a value for x and calculating the corresponding y-value.
Let's choose x = 3.
Plugging this value into the equation, we get:
y = (1/3)(3) - 4
y = 1 - 4
y = -3
So point (3, -3) lies on the line.
Now we can plot these two points (0, -4) and (3, -3) and draw a straight line passing through them.
Since the coefficient of x is positive (1/3), the line will have a positive slope, meaning it rises as we move from left to right.
Thus,
The graph of the equation y = 1/3x - 4 would look like a straight line that slants upward as you move from left to right, crossing the y-axis at -4.
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Allison practices her violin for at least 12 hours per week. She practices for three fourths of an hour each session. If Allison has already practiced 3 hours this week, how many more sessions remain for her to meet or exceed her weekly practice goal?
A group of college students built a self-guided rover and tested it on a plane surface. They programmed the vehicle to move along the path A–B–C–D–A represented on the coordinate plane. What distance will the rover cover if it completes one circuit? 36 meters 40 meters 54 meters 60 meters 68 meters
Answer:
The answer is B. 40 meters on plato
A car can travel 30 mi on a gallon of gas and has20 gallon gas tanks let g be the number of gallons the car has in its tank the function d=30 g gives the distance d in miles that the car travels on g gallons
On Anne's bicycle, the ratio of pedal turns to rear- wheel turns in second gear is 4 to 7. If her rear wheel turns 875 times per mile, how many times does she turn the pedal in one mile? HINT: Set up and solve as a proportion to find x.
Stu hiked a trail at an average rate of 3 miles per hour. He ran back on the same trail at an average rate of 5 miles per hour. He traveled for a total of 3 hours. Which equation can be used to find the time it took Stu to hike the trail? 3t = 5 3t = 5(3 – t) 3 + t = 5 + (3 – t) 3t + 5(3 – t) = 3
Answer:
B
Step-by-step explanation:
Evaluate the line integral ∫cx4zds, where c is the line segment from (0,6,5) to (8,4,1).
To evaluate the line integral, we need to parameterize the line segment and calculate the differential arc length. After simplifying the integrand, we can evaluate the line integral by integrating the simplified expression.
Explanation:To evaluate the line integral ∫cx^4zds, where c is the line segment from (0,6,5) to (8,4,1), we need to parameterize the line segment c. Let's parameterize it with t, where t varies from 0 to 1. The parameterization of c is given by:
x(t) = 8t, y(t) = 6 - 2t, z(t) = 5 - 4t.
Next, we need to calculate ds, which is the differential arc length along the line. The differential arc length ds is given by:
ds = √(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 dt.
Substituting the parameterized values of x(t), y(t), and z(t) into the above equation, we get:
ds = √[(8)^2 + (-2)^2 + (-4)^2] dt = √84 dt.
Now, we can rewrite the line integral as:
∫cx^4zds = ∫(8t)^4(5 - 4t)√84 dt.
Next, we simplify the integrand:
(8t)^4(5 - 4t) = 4096t^4(5 - 4t).
Finally, we evaluate the line integral by integrating the simplified integrand over the interval [0, 1]:
∫(8t)^4(5 - 4t)√84 dt = √84 ∫4096t^4(5 - 4t) dt.
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Tiesha enjoys reading in her spare time. She reads 4 pages every 1/10 of an hour. The proportional relationship between the number of pages (p) and the number of hours (h) is represented by the equation ______. Write the equation in standard form with a constant of proportionality greater than 1.
The equation in standard form with a constant of proportionality greater than 1 is p=40h.
Given that, Tiesha enjoys reading in her spare time. She reads 4 pages every 1/10 of an hour.
What is the proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value time the other. That constant is known as the "constant of proportionality".
Now, p∝h
⇒p=kh-----(i)
So, 4∝1/10
⇒4=k/10
⇒k=40-----(ii)
Substitute equation (ii) in equation (i).
That is, p=40h
Therefore, the equation in standard form with a constant of proportionality greater than 1 is p=40h.
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A gas tank has a leak. Each hour it loses 3 gallons of gas. Write the equation that represents how much gas, g , the tank loses over h hours.
A boy walks for x hours at 33 mph and bicycles for (5−x) hours at 93 mph. If the total distance traveled is d miles, express d in terms of x.
Answer:
d = 465 - 60x
Step-by-step explanation:
1. Find the distances of walking and bicycling. We can express the walking distance as 33x, because x is the time and 33 is the amount of miles, and we can express the bicycling distance as 93(5-x), because 93 is the speed and 5-x is the amount of hours.
2. Construct an equation. We can say that the total distance is d = 33x + 93(5-x), the sum of both of the distances.
3. Simplify. If you simplify, you would get d = 465 - 60x
(This guy is going Super Saiyan)
Answer: d = 465 - 60x
How many feet of fencing is needed to fence in a 130 ft by 225 ft area?
20,880 times 2/5 worked out
The multiplication [tex]20880 \times \dfrac{2}{5}[/tex] is [tex]\boxed{8352}.[/tex]
Further explanation:
Always use the PEDMAS rule to solve the grouping of multiplication, addition, subtraction and division.
Here, P is parenthesis, E is exponents, M is multiplication, D is division, A is addition and S is subtraction.
Given:
The expression is [tex]20880 \times \dfrac{2}{5}.[/tex]
Explanation:
The given expression is [tex]20880 \times \dfrac{2}{5}.[/tex]
Consider the expression [tex]20880 \times \dfrac{2}{5}[/tex] as A.
[tex]A = 20880 \times \dfrac{2}{5}[/tex]
Solve the above expression to obtain the simplest form.
[tex]\begin{aligned}A&= 20880 \times \frac{2}{5}\\&= \frac{{41760}}{5}\\&= 8352\\\end{aligned}[/tex]
Another way of solving the expression can be expressed as follows,
First divide 2 by 5.
[tex]\begin{aligned}b&= \frac{2}{5}\\&= 0.4\\\end{aligned}[/tex]
Now multiply 20880 to 0.4.
[tex]\begin{aligned}A&= 20880 \times 0.4\\&= 8352\\\end{aligned}[/tex]
The multiplication [tex]20880[/tex] times [tex]\dfrac{2}{5} \:{\text{is}\: \boxed{8352}.[/tex]
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Number system
Keywords: factor, factorization, 20880, 2/5, times, greatest common factor, groups, multiplication, product, identities, common factor, expression, terms, grouping.
Find three consecutive even integers such that the sum of twice the smallest number and three times the largest is 42.
To find the consecutive even integers, we created an equation and solved for x, which represents the smallest integer. Upon solving, we found that the smallest integer is 6, and hence, the three consecutive even integers are 6, 8, and 10.
To find three consecutive even integers such that the sum of twice the smallest number and three times the largest is 42, we can form an equation based on the description. Let the smallest even integer be x. Since we are looking for consecutive even integers, the next two will be x+2 and x+4.
According to the problem, twice the smallest plus three times the largest equals 42:
2x + 3(x+4) = 42
Solving the equation:
Distribute the 3 into the parentheses: 2x + 3x + 12 = 42
Combine like terms: 5x + 12 = 42
Subtract 12 from both sides: 5x = 30
Divide both sides by 5: x = 6
Therefore, the smallest even integer is 6, and the other two are 8 and 10, which are the consecutive even integers that satisfy the given condition.