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~Deceptiøn
Related Questions
Please help!
4x(5y-x)-5y(4x-y)
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= 20xy-4x²- 20xy+5y²
= -4x²+5y²
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?
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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
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The area in square centimeters is 68.8.
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Have a great day!
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
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
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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?
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ur answer would be 44.56
Help please ....zzzghg
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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]
I= $30 p= $500 r= 3%
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Answer:2 years
Step-by-step explanation:
Find f(-5) if f(n) = n3 + 3n2
A) -50
B) -7
C) 0
D) 22
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[tex]f(-5) = -125 + 3(25)[/tex]
[tex]f(-5) = -125 + 75[/tex]
[tex]= -50[/tex]
substitute the f(-5)
f(-5) = (-5)^3 + 3(-5)^2
solve
f(-5) = -125 + 75
f(-5) = -50
That is the solution
A.) -50
Hope this helps :)
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?
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[tex]1115=(9x)(5+x)[/tex]
[tex]1115=45x+9 x^{2} [/tex]
[tex]9 x^{2} +45x-1115=0[/tex]
Using the quadratic formula to solve the equation, we get that:
[tex]x=8.9[/tex] or [tex]x=-13.9[/tex]
Since distances cannot be negative, the solution is [tex]x=8.9[/tex]
We can conclude that the width of each campsite is 8.9 yards.
Answer:
i think it is 54
Step-by-step explanation:
What is the volume of a rectangular prism with side lengths14.7 m, 23.4 m, and 3.2 m?
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Volume = Length x Width x Height; substitute values.
Volume = 14.7 x 23.4 x 3.2; multiply 14.7 by 23.4 first. This allows our units to be squared (units^2).
Volume = 343.98 x 3.2; multiply these two dimensions. This determines our units to be cubed- and furthermore- our volume.
Volume = 1100.736; remember to apply your proper units.
Your answer for this problem is 1100.736 m^3.
I hope this helps!
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
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They all start the same way: Let's call the length of the rectangle b and the width a. The perimeter of the rectangle (the distance all the way around -- that is, the length of the "fence") is 2a + 2b. Since the barn is used as one of the sides (let's say b) we can subtract b ... we don't need fencing for this side. That makes the perimeter 2a + b. Since we have 300 feet of fencing we set these equal: 2a + b = 300.
We can solve for b above by subtracting 2a from both sides of the equation so we get: b = 300 - 2a.
We are asked to maximize the area. The area of a rectangle is length times width. In this case, (a)(b) and since we just found an expression for b, we can substitute this to obtain: Area = [tex](a)(300-2a)=300a-2 a^{2} [/tex]. This is a parabola when graphed and we are asked to find where it's highest point occurs because this is where the area is greatest.
METHOD 1: Using Calculus
We are looking for the highest point of the equation [tex]Area = [tex](a)(300-2a)=300a-2 a^{2}[/tex]. Let's call the function R(a) since it is in terms of a. To find the maximum we take the first derivative, set it equal to zero and solve for a. As this is a parabola (with the leading coefficient being negative) it is concave down and the point we find will be the only maximum.
First we find the derivative of the function.
[tex]R(a)=(a)(300-2a)=300a-2 a^{2} [tex]
Next set it equal to 0 and solve for a.
R^{'}(a)=300-4a 0=300-4a -300=-4a 75 = a[/tex] [/tex]
This means that the maximum value (the largest area) occurs when a = 75.
At a = 75 the area is given by
What is the largest area? Let's us substitute 75 for a in the equation of the area. This gives: [tex]Area=a(300-2a)=(75)(300-(2)(75))=(75)(150)=11250[/tex] square feet.
METHOD 2: Graphing
We know that the area is given by. Area = [tex](a)(300-2a)=300a-2 a^{2} [/tex]. To make this more familiar let's use y for the area and x for the width (a). That means we have the equation: [tex](a)(300-2a)=300a-2 a^{2} [/tex].
This is a quadratic equation (the highest exponent of x is 2) and so the equation of a parabola (like the letter U or an upside down U). Since the leading coefficient is negative (-2) we know it opens downward (called concave down -- think of a frown). We are looking for the x-coordinate of the highest point called the vertex. We can find this by remembering that the x-coordinate of the vertex is given by [tex]x= \frac{-b}{2a} [/tex] where a is the leading coefficient the coefficient of the term with the x squared (here = -2) and a is the coefficient of the linear term (the one with x...here 300). That makes the x-coordinate of the vertex [tex]x= \frac{-300}{2(-2)}= \frac{-300}{-4}=75 [/tex].
The y-coordinate of the vertex is found by substituting 75 for x in the equation for the area. [tex]y=300x-2 x^{2} y=300(75)-2(75)^{2} [/tex]
[tex]y=22500- 2(5625) y=22500- 11250 y=11250[/tex]
Since we let x be the width of the rectangle. We know that the width is 75. The area of the rectangle we called y. So the maximum area is 11250 square feet which occurs when the width of the rectangle is 75.
You could have gotten to this point by generating a list of points for the parabola and graphing it carefully on graph paper (though it might not have been exact depending on how you scale your axis).
METHOD 3: Guess and Check
The area of the rectangle is given by Area = [tex](a)(300-2a)=300a-2 a^{2} [/tex]. Here you guess values for a, plug them into the formula to get the area and keep doing this until you are comfortable you have found the largest area. Not the best method but if it's a test and you forget everything else, it might get you close to an answer or even get you the exact answer (depending on how well you guess). It might take a while so I'd do this question last if this were a test.
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?
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F+S=310
2/3 S + S = 310
(2S + 3S)/3=310
S=[(310)(3)]/5
S=186 students taking Spanish
F=2/3 of 186
F=124 students taking French
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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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).
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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.
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?
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Because the price has been reduced, this is a percent decrease.
To calculate the percentage decrease, we must use a certain formula. The formula is:
[(Old Value - New Value) / Old Value * 100]
Substitute:
[( 19,500 - 16,965) 19,500 * 100] = 13
FINAL ANSWER:
The percent decrease is 13%.
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%.
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.
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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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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
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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
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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]
∠2 and ∠3 form a linear pair. ∠3 and ∠1 are vertical angles. m∠1= 62 ∘ . What is m∠3?
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1=62
3 = 1
3 = 62
The measure of angle 3 is 62 degrees
Hope this helps =)
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?
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We compare the image to the actual painting:
4/36 = 1/9.
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?
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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.
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.
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Area of a triangle = (base * height) / 2
Area of a rectangle = length * width
I divided my graph into 3 parts. 1st part is the 2 triangles, 2nd part is the rectangle, 3rd part is the right triangle.
1st part
The 2 triangles each have a base of 4 units and a height of 3 units.
Area of a triangle = (base * height) / 2
A = (4 * 3)/2 = 12/2 = 6 square unit. per triangle.
Since there are 2 triangles, 6 sq.u * 2 = 12 sq.unit
2nd part
rectangle length = 8 units ; width = 3 units
Area of a rectangle = length * width = 8 * 3 = 24 sq. unit
3rd part
Right triangle: short leg = 2 units ; long leg = 8 units
Area of a right triangle = (long leg * short leg) / 2
Area of a right triangle = (8 * 2) / 2 = 16/2 = 8 sq. unit
Total area of the heptagon = 12 sq.u + 24 sq. u + 8 sq. u = 44 sq. unit.
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
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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.
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?
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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
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=$14.16
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
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The study hall is 4 times as many
4*16 = 64
There must be 64 students in the study hall.
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.
Answers
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
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?
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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.
Find the length of x?
Answers
.. 15/10 = x/8
.. x = 8*(15/10) = 12
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
Answers
18.20-5= 15.20
15.20÷4=3.8
The price of 1 hotdog is $3.80
Answer:
$3.8
Step-by-step explanation:
Find the correct selling price. Round to the nearest dollar.
What was the clerk's error?
Answers
b. I think the clerk thought 30% was 3 dollars, and he added 3 dollars to 27, which is 30.