The given equation can be solved in terms of E as E = V + F - 2.
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
The given equation is V - E + F = 2.
It can be solved as,
⇒ V - E + F = 2
⇒ V + F = 2 + E
⇒ E = V + F - 2
Hence, the solution for E can be obtained as E = V + F - 2.
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Final answer:
The equation V - E + F = 2 is solved for E by simple algebraic manipulation, resulting in the solved equation E = V + F - 2.
Explanation:
To solve the equation V - E + F = 2 for E, we need to isolate E on one side of the equation. This can be done through simple algebraic manipulation as follows:
Start with the original equation: V - E + F = 2.Add E to both sides: V + F = E + 2.Now, subtract 2 from both sides to solve for E: E = V + F - 2.The solved equation for E is thus E = V + F - 2.
This equation shows the relationship between the vertices (V), edges (E), and faces (F) in a polyhedron, known as Euler's formula in the context of geometry.
A sporting goods store sells right-handed baseball gloves and left handed baseball gloves. In 1 month 12 gloves were sold for a total revenue of $561. Right-handed gloves cost $45 and left-handed gloves cost $52. How many of each type of gloves did they sell?
They sold 3 left handed gloves and 9 right handed gloves.
To solve this problem, we have to write a system of equations.
Data given;
total number of gloves = 12revenue for 12 gloves = $561right handed gloves (x) = 45left handed gloves (y) = 52Equations[tex]x + y = 12...equation (i)\\ 45x + 52y = 561 equation (ii)[/tex]
From equation (i)
[tex]x + y = 12\\ x = 12 - y...equation (iii)[/tex]
Substitute equation (iii) into equation (ii)
[tex]45x + 52y = 561\\ x = 12 - y\\ 45(12- y) + 52y = 561\\ 540 - 45y +52y = 561\\ 540 + 7y = 561\\ 7y = 21\\ y = 3[/tex]
Put y = 3 in equation (i)
[tex]x + y = 12\\ x + 3 = 12\\ x = 9[/tex]
From the calculations above, they sold 9 right handed gloves and 3 left handed gloves
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Light travels 3 x 10^5 kilometers in one second. How far does it travel in 6.7 seconds? Write your answer in scientific notation.
The distance covered by the traveling light in 6.7 seconds is 2.01 × 10⁶ kilometers.
What is the distance covered by the light in 6.7 seconds?The speed formula is expressed as:
Speed = Distance / Time
Given the parameter:
Distance covered by the light = 3 × 10⁵ kilometers
Elapsed time = 1 second
Speed =?
The speed of the light is:
Speed = Distance / Time
Speed = 3 × 10⁵ kilometers / 1 second
Speed = 3 × 10⁵ kilometers per second
Now, we find the distance covered by the light in 6.7 seconds.
Speed = Distance / Time
Distance = Speed × Time
Distance = 3 × 10⁵ kilometers per second × 6.7 seconds
Distance = 2.01 × 10⁶ kilometers.
Therefore, the distance traveled is 2.01 × 10⁶ kilometers.
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The price of a car has been reduced from $19,500 to $16,965. What is the percentage change of the price of the car?
Final answer:
The percentage change in the price of the car is a reduction of approximately 13%, calculated by taking the difference between the original and reduced prices, and then dividing by the original price and multiplying by 100.
Explanation:
To calculate the percentage change in the price of the car, you first find the difference in price and then divide it by the original price. Initially, the car was priced at $19,500 and then reduced to $16,965.
To find the difference, subtract the new price from the old price.
$19,500 - $16,965 = $2,535
Now, divide the difference by the original price and multiply by 100 to get the percentage.
($2,535 ÷ $19,500) × 100 = 13% (approximately)
The percentage change in the price of the car is a reduction of approximately 13%.
A campground consists of 9 square campsites arranged in a line along a beach. The distance from the edge of a campsite to the water at the end of the beach is 5 yd. The area of the campground, including the beach, is 1115 sq yd. What is the width of one campsite?
Answer:
i think it is 54
Step-by-step explanation:
A model car has a windshield with dimensions 1/18 the size of a real car windshield. The rectangular windshield of the real car has an area of about 2318 sq in, with a width of 61 in. What are the side lengths of the model car's windshield? Round to the nearest hundredth?
Width of the model car's windshield is around 3.39 inches and the length is approximately 17.45 inches.
The area of the real car windshield is 2318 sq in, with a width of 61 in. The scale of the model car's windshield is 1/18 of the real car windshield.
To find the dimensions of the model car's windshield, first, calculate the area of the model windshield by dividing the real area by the square of the scale factor. Then, find the width and length of the model windshield by using the square root of the calculated area.
In this case, the width of the model car's windshield is around 3.39 inches and the length is approximately 17.45 inches.
Answer:
2.11 inches
Step-by-step explanation:
You want the side length of the windshield of a 1/18 scale model of a car with a 2318 in² windshield that has a width of 61 inches.
LengthThe side length of the actual windshield is found from ...
A = LW
L = A/W = (2318 in²)/(61 in) = 38 in
The length of the model windshield is 1/18 of this:
(38 in) × 1/18 = 2 1/9 in ≈ 2.11 in
The side lengths of the model car's windshield are 2.11 inches.
A farmer has 300 ft of fencing with which to enclose a rectangular pen next to a barn. The barn itself will be used as one of the sides of the enclosed area.
What is the maximum area that can be enclosed by the fencing?
_______ft^2
leon used plant fertilizer on 4/7 of his potted flowers if he has 28 potted floewers on how many did he use plant fertilizer?
Bens mom wants to buy carpet for the family room the measures 12 feet by 11 feet she can purchase the carpet on sale for $6 how much will bens mom spend to carpet the family room
Find the length of x?
William saw painting in a museum, and later found a picture of the same painting in a book. The actual painting measures 36“ x 54“. The picture of the paining measured 4“ x 6“. What is the scale factor for the dilation?
What is the area of this figure? Enter your answer in the box. units² An irregular-shaped heptagon is graphed on a coordinate plane. The horizontal x-axis ranges from negative 6 to 6 in increments of 1. The vertical y-axis ranges from negative 6 to 6 in increments of 1. The vertices of the heptagon are located at begin ordered pair negative 3 comma 5 end ordered pair, begin ordered pair negative 1 comma 2 end ordered pair, begin ordered pair 1 comma 5 end ordered pair, begin ordered pair 3 comma 2 end ordered pair, begin ordered pair 3 comma negative 1 end ordered pair, begin ordered pair negative 5 comma negative 3 end ordered pair, and begin ordered pair negative 5 comma 2 end ordered pair.
The number of students in the period 7 study hall at jins school is 4 times the number of students in Jin’s home room how many students are in the study hall if there are 16 students in Jin’s home room
Heather was asked to graph 2x + 4y = 12 by using slope and y-intercept. Her graph is shown. Which choice supports the graph that she has drawn. A) The slope is positive 1 2 and the y-intercept is (0,3). B) The slope is negative 1 2 and the y-intercept is (0, 3). C) The slope is positive 1 2 and the y-intercept is (0, -3). D) The slope is negative 1 2 and the y-intercept is (0, -3).
Answer:
B) The slope is negative 1/2 and the y-intercept is (0, 3).
Step-by-step explanation:
First we rewrite the equation so we can easily find the slope and y-intercept. We do this by isolating the y-term:
2x+4y = 12
We want to subtract 2x from each side:
2x+4y-2x = 12-2x
4y = 12-2x
4y = -2x+12
Now we divide both sides by 4 (everything on both sides gets divided!):
4y/4 = -2x/4 + 12/4
y = -2/4x + 3
y = -1/2x + 3
The slope is -1/2 and the y-intercept is 3 (the point (0, 3)).
Her graph shows the y-intercept at (0, 3); this part is correct.
The graph also shows we go down one and over two between points; this is a slope of -1/2, which is correct.
Four brothers each bought two hot dogs and a bag of chips at the football concession stand if the bag of chips was 1.25 and the total was 18.20 what was the price of one hot dog
Answer:
$3.8
Step-by-step explanation:
I= $30 p= $500 r= 3%
Answer:2 years
Step-by-step explanation:
you are going to purchase a corvette for $60,00 the interest rate is 4% and you will be paying off the loan in 5 years. What will be your monthly payment?
the bill for a stay in a hotel was $173 and the tax was an additional $15 what percent of the bill was the tax
Find f(-5) if f(n) = n3 + 3n2
A) -50
B) -7
C) 0
D) 22
Help please ....zzzghg
Answer: [tex]f=168[/tex]
Step-by-step explanation:
In the picture, there is a multiplication problem of [tex]f=56\times3[/tex]
We can use distributive property in it so that the multiplication problem become easier.
Distributive property:-[tex](b+c)a=ba+ca[/tex]
In the product, the larger number is 56
Write [tex]56=50+6[/tex]
Now, [tex]f=56\times3\\\Rightarrow\ f=(50+6)3\\\Rightarrow\ f=(50)3+(6)3\\\Rightarrow\ f=150+18\\\Rightarrow\ f=168[/tex]
the distance between two cities on a map is measured to be 4 inches. the actual distance between the cities is 448 miles. what is the scale of the map?
ur answer would be 44.56
Fair Race UNIT NAME: FUNCTIONS
Directions: Follow the instructions below to design a fair race for the new video game Animal Tracks. 1. Choose two animals with different speeds. You can choose from the chart that starts at the bottom of this page or do research to choose your own. 2. Design a fair race in which the two animals have an equal chance of winning if they race at their top speed. Here are a few tips for your design: a. The race is fair if the two animals could finish the race in the same amount of time. b. You can give the slower animal a shorter distance to race. c. Since this is a video game, the race does not need to be realistic—it can be any length, and the animals can run at a constant speed. 3. Write a system of two linear equations showing the distance each animal can travel to model the fair race. Be sure to define all variables. 4. Graph the system to prove that the two animals have an equal chance of winning the race. Explain how the graph proves the race is fair. Your equations, graph, and explanation for your race design will be submitted as your portfolio assessment.
Animal Speed (mph) cheetah 70 lion 50 coyote 43 rabbit 35 kangaroo 30 squirrel 12 chicken 9 antelope 61 elk 45 ostrich 40 giraffe 32
Animal Speed (mph) elephant 25 pig 11 mouse 8
I need help wiith 3. Write a system of two linear equations showing the distance each animal can travel to model the fair race. Be sure to define all variables. I choose The mouse and squirrel ....can i get help on the equuations? Can someone explain it to me?
The linear equation for squirrel y = 12x.
The linear equation for mouse y = 8x
The distance covered by the squirrel is 36km at time 3hours.
The distance covered by the squirrel is 24km at time 3hours.
What is linear equation?A linear equation is an "algebraic equation is of the form y=mx + b where 'm' is the slope of the line and 'b' is the y - intercept".
According to the question,
Animal Mouse Squirrel
Speed(mph) 8 12
"x" the time goes along with x-axis and "y" is the distance covered by the animal.
The mouse time and distance would plot the graph (1,8)(2,16)(3,24)....
The squirrel time and distance would plot the graph (1,12)(2,24)(3,36)....
Let us consider the track is straight line and shorter distance is 50 meters.
Formula for straight line equation y = mx + b where 'b' is the base value, 'x' is the time and 'y' is the distance.
The linear equation for squirrel y = 12x+b and the squirrel starts at 0 meters per hour. so the equation becomes y = 12x.
The linear equation for mouse y = 8x + b and the mouse starts at 0 meters. so the equation becomes y = 8x.
Distance covered by the mouse and the squirrel at time x = 3 we can find the distance covered by mouse and the squirrel.
y =12x
y = 12(3)
y = 36.
The distance covered by the squirrel is 36km at time 3hours.
For mouse, at time x = 3 hours.
y = 8(3)
y=24.
The distance covered by the squirrel is 24km at time 3hours.
Hence, The linear equation for squirrel y = 12x.
The linear equation for mouse y = 8x
The distance covered by the squirrel is 36km at time 3hours.
The distance covered by the squirrel is 24km at time 3hours.
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A rectangular prism has a length of 20 in., a width of 2 in., and a height of 3 1/4 in.
The prism is filled with cubes that have edge lengths of 1/4 in.
How many cubes are needed to fill the rectangular prism?
Enter your answer in the box.
To fill the rectangular prism,
cubes are needed.
Step-by-step explanation:
1650
car un cube de 1/4dcoespond à 1/4 x 1/4 x 1/4 pour un volume de 1/64
In the sophomore class at Dixon high school the number of students taking French is 2/3 of the number taking Spanish. How many students are studying each language if the total number of students in French and Spanish is 310?
To find the number of students studying each language, assign variables, write equations based on the given information, and solve the system of equations.
Explanation:To solve this problem, let's assign variables. Let x represent the number of students taking Spanish, and y represent the number of students taking French.
According to the given information, the number of students taking French is 2/3 of the number taking Spanish. So, we can write this as an equation:
y = (2/3)x
The total number of students taking French and Spanish is 310. So, we can write another equation:
x + y = 310
Now, we can solve these two equations to find the values of x and y. Substituting the value of y from the first equation into the second equation, we get:
x + (2/3)x = 310
(5/3)x = 310
x = (3/5) * 310
x = 186
Substituting x = 186 back into the first equation, we find:
y = (2/3) * 186
y = 124
Therefore, there are 186 students taking Spanish and 124 students taking French.
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Yesterday, Jed's bank account balance was $26.34. Today, he made a withdrawal from his account. The current balance is $12.18. How much did he withdraw from his account?
$15.84
$26.34
$14.16
$16.84
A bamboo shoot is 20 inches tall at the zero and gross 24 inches each day which functions show below can be used to determine height F(n) of the bamboo after n days
It is given bamboo shoot is 20 inches tall when time is 0. It grows at the rate of 24 inches each day .
The y intercept b=20 and m= slope = 24.
Any equation can be written in the form y=mx+b where m is slope and b is y intercept.
The equation to determine height for n number of days can be written as
f(n)=24n+20
It can also be written as 24+the growth 1 day back or
F(n)=F(n-1)+24 where f(0)=20.
Among the given options equations 1 and 111 hold true
Option D is the right answer.
∠2 and ∠3 form a linear pair. ∠3 and ∠1 are vertical angles. m∠1= 62 ∘ . What is m∠3?
What is the volume of a rectangular prism with side lengths14.7 m, 23.4 m, and 3.2 m?
what is the area in square centimeters of the trapezoid below the height is 6.4 and the base is 12.9 and 8.6
Answer:
The area of given trapezoid is 68.8 cm²
Step-by-step explanation:
Given: A trapezoid with height 6.4 cm and parallel base is 12.9 cm and 8.6 cm.
We have to find the area of area of this trapezoid.
Area of trapezoid = [tex]\frac{1}{2}\times \text{sum of parallel sides}\times height[/tex]
Given : Height = 6.4 cm
and parallel base is 12.9 cm and 8.6 cm.
Substitute, we have,
Area of trapezoid = [tex]\frac{1}{2}\times (12.9+8.6)\times 6.4[/tex]
Simplify, we have,
Area of trapezoid = [tex]\frac{1}{2}\times 21.5\times 6.4[/tex]
Area of trapezoid = 68.8 cm²
Thus, The area of given trapezoid is 68.8 cm²
At silver Gym, membership is $45 per month, and personal training sessions are $25 each. At fit factor, membership is $75 per month, and personal training sessions are $15 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
Final answer:
By setting up and solving an equation based on the monthly membership and per-session training costs at both Silver Gym and Fit Factor, it's determined that Sarah would need to buy 3 personal training sessions for the total cost at the two gyms to be equal.
Explanation:
To find how many personal training sessions Sarah would have to buy to make the total cost at Silver Gym and Fit Factor equal, we'll set up an equation. Let x be the number of personal training sessions.
At Silver Gym, the total cost is $45 (membership) + $25x (personal training sessions).
At Fit Factor, the total cost is $75 (membership) + $15x (personal training sessions).
Setting these two expressions equal to each other gives us the equation:
45 + 25x = 75 + 15x.
To solve for x, first subtract 15x from both sides, giving: 10x = 30. Then divide both sides by 10 to isolate x, resulting in x = 3.
Therefore, Sarah would have to buy 3 personal training sessions in one month for the total costs at both gyms to be equal.
Answer:
3 sessions
Step-by-step explanation:
You want to know the number of personal training sessions Sarah would have to buy to make the total costs the same at Silver Gym and Fit Factor. Silver Gym costs $45 per month and $25 per session, while Fit Factor costs $75 per month and $15 per session.
DifferencesSilver Gym costs $25 -15 = $10 more per personal training session, but $75 -45 = $30 less for the monthly fee. This means it takes $30/$10 = 3 sessions for the difference in fees to be made up by the difference in session costs.
Sarah would have to buy 3 sessions for the total cost to be the same.
EquationsIf you need to see this using equations, we can write the cost equations as ...
S = 45 +25x . . . . . . . . cost for x sessions at Silver Gym
F = 75 +15x . . . . . . . . . cost for x sessions at Fit Factor
Setting these equal, we have ...
S = F
45 +25x = 75 +15x
25x -15x = 75 -45 . . . . . . . subtract 45+15x from both sides
10x = 30
x = 30/10 = 3 . . . . sessions for equal cost
Sarah would have to buy 3 sessions for the total cost to be the same.
__
Additional comment
These "break even" problems usually have a higher fixed cost associated with a lower per use cost, and vice versa. The costs are the same when the number of uses, multiplied by the difference in use cost, comes to the same amount as the difference in fixed costs. Here, the $10 difference in session cost, times 3 sessions, is equal to the $30 difference in monthly membership fee.
The net of a square pyramid is shown below:
What is the surface area of the solid?
10 square inches
16 square inches
24 square inches
28 square inches
Answer: 28 square inches
Step-by-step explanation:
We know that the area of a triangle is given by :-
[tex]\text{A}=\dfrac{1}{2}*b*h[/tex], where b is base and h is the height of the triangle.
From the given picture, it cam be seen that alll the traingles area of same measure, the base of the triangle = 2 inches
The height of the triangle = 6 inches
Now, the area of a triangle is given by :-
[tex]\text{A}_1=\dfrac{1}{2}*6*2=6\ in^2[/tex]
Area of the square in the center =[tex](side)^2=(2)^2=4\ in^2[/tex]
Now, the total surface area of the pyramid is given by :-
[tex]\text{S.A.}=4+4(6)=28\ in^2[/tex]