a. To find the speed at which the car achieves maximum fuel economy, we need to find the vertex of the function. The vertex of a quadratic function is given by the formula: (-b/2a, f(-b/2a)). In this case, a = -0.008 and b = 1.4. Substituting these values, we get:
Vertex = (-b/2a, f(-b/2a))
= (-1.4/(2*(-0.008)), f(1.4/(2*(-0.008))))
= (87.5, 6.125)
Therefore, the car should travel at a speed of 87.5 miles per hour to achieve maximum fuel economy.
b. To find the maximum fuel economy, we need to find the value of the function at the vertex. Substituting x = 87.5 in the function, we get:
f(87.5) = -0.008(87.5)^2 + 1.4(87.5) = 6.125
Therefore, the maximum fuel economy of the car is 6.125 miles per gallon.
c. To find the fuel economy of the car if it travels at 60 miles per hour, we need to evaluate the function at x = 60. Substituting x = 60 in the function, we get:
f(60) = -0.008(60)^2 + 1.4(60) = 7.6
Therefore, the fuel economy of the car if it travels at 60 miles per hour is 7.6 miles per gallon.
d. The point (40, 43.2) lies on the graph of the function. This means that when the car travels at a speed of 40 miles per hour, its fuel economy is 43.2 miles per gallon. However, this point does not provide any information about the maximum fuel economy or the speed at which it is achieved.
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
The correct options are: [tex]x^{2}[/tex] - 4 = 0 and 4[tex]x^{2}[/tex] = 16
What is Linear equation ?
A linear equation is an algebraic equation in which each term is either a constant or a product of a constant and a variable raised to the first power, also called a linear term.
A linear equation can be written in the form of:
y = mx + b
where y is the dependent variable, x is the independent variable, m is the slope or gradient of the line, and b is the y-intercept (the point where the line crosses the y-axis).
The equations that are true for x = -2 and x = 2 are:
[tex]x^{2}[/tex] - 4 = 0, which is true for x = -2 but not for x = 2
4[tex]x^{2}[/tex] = 16, which is true for x = 2 but not for x = -2
Therefore, the correct options are: [tex]x^{2}[/tex] - 4 = 0 and 4[tex]x^{2}[/tex] = 16
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Please Help
20 Points
Show you're work please..
Answer:
(a) 512 ft² , (b) 720 ft²
Step-by-step explanation:
the area of a rectangle is calculated as
area = length × width
(a)
area of pool = 32 × 16 = 512 ft²
(b)
the area of the deck is calculated as
area of outer rectangle - area of pool
area of outer rectangle = 44 × 28 = 1232 ft²
area of deck = 1232 - 512 = 720 ft²
Draw a dialation with center at the Irgun of the triangle with the vertices (2,0) ,(4-4), (6,2) scale factor of k =1.5
The sides of the dilated triangle are parallel to the sides of the original triangle, but their lengths are multiplied by the scale factor k.
What is triangle?A triangle is a closed two-dimensional figure with three straight sides and three angles. It is one of the basic shapes in geometry and is used in many different areas of mathematics, science, and everyday life. A triangle is defined by its three vertices (or corners), which are the points where the sides of the triangle intersect. The three sides of the triangle are the line segments connecting the vertices. The three angles of the triangle are the angles formed by the intersection of two sides.
Here,
To dilate a triangle with a center at the origin, we need to multiply the coordinates of each vertex by the scale factor k. However, in this case, the center of dilation is not at the origin, but at the point Irgun. To perform the dilation, we can follow these steps:
Plot the original triangle with vertices (2,0), (4,-4), and (6,2).
Draw a line segment from the center of dilation Irgun to each vertex of the triangle.
Measure the distance from Irgun to each vertex, and multiply it by the scale factor k = 1.5 to find the new distance.
Use the new distances to construct the dilated triangle by drawing line segments from Irgun to points that are 1.5 times farther away from Irgun than the corresponding vertices of the original triangle.
The resulting dilation of the triangle with center at Irgun and scale factor k = 1.5 is shown below:
In this image, the original triangle is shown in black, and the dilated triangle is shown in blue. The center of dilation Irgun is marked with a red dot. Note that the new vertices of the dilated triangle are (0.5,0), (3,-6), and (7.5,3), which are 1.5 times farther away from Irgun than the corresponding vertices of the original triangle.
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A loan of $12,000 with interest at 14% compounded annually is to be amortized by equal payments at the end of each year for six years. What will the balance outstanding be after second year?
thier sum is -7 thier diffrence is 14
HELP
Using algebraic expressions, x = 7/2 and y = -21/2.
An algebraic expression might be made up of a single word or a group of words.
An algebraic expression can be any number, variable, or set of operations, whereas an equation is two different algebraic expressions connected together with an equal sign.
x = 7/2 and y = -21/2
Let x and y be those numbers.
In response to your query
x + y = -7
x - y =14
both equations added
2x = 7
or x = 7/2
the equivalent x value in either equation
y = -21/2
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Complete question -
What are the two numbers if their sum is −7 and their difference is 14?
I need help with this please
Answer:
First statement is true.
Second statement is false--there are some 3d shapes that unit cubes cannot be used to find the volume of. Examples are cylinders and cones.
conaider a regular 96-sided polygon exlain how to found your anser in orlder to get full credit
To make a regular polygon with 96 sides we can take a circle as a starting point and divide it into 96 equal sides.
How to create a regular polygon with 96 sides?To create a regular polygon with 96 sides, we must take into account that all its sides must be equal, so we can take a circumference as a starting point. In this case, the circumference has 360°, so we must divide this into 96 parts and the result would be the distance between the edges of the polygon.
360° / 96 = 3.75In this case, we must make a circle with a protractor and mark every 3.75°, when we have completed this procedure in the entire circumference we will have a regular polygon with 96 sides.
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The ratio of men to women at the picnic is 4:5,if there are 819 people, how many men are there in the picnic
Answer:
819/5 is the correct answer that I think
Helppp ! , Use substitution to solve each system of equation and must show checks !!!
Four identical cubes are joined to make a new shape.
What is the new shape’s surface area?
The surface area of the shape which was formed when four identical cubes were joined, is 882 yd ².
How to find the surface area ?The surface area of a cube can be found by the formula :
= Number of faces x Length of a side ²
When four identical cubes were joined, this leads to the creation of 18 faces which means that the surface area of the cube would then be :
= 18 x 7 x 7
= 18 x 49
= 882 yd ²
In conclusion, the area is 882 yd ².
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Solve g−17≥17 . Graph the solution.
The inequality expression g - 17 ≥ 17 when solved has a solution of g ≥ 34
How to solve the given inequalityGiven the inequality expression
g - 17 ≥ 17
To solve the inequality g - 17 ≥ 17, we need to isolate the variable g on one side of the inequality.
We can do this by adding 17 to both sides of the inequality:
g - 17 + 17 ≥ 17 + 17
Simplifying, we get:
g ≥ 34
So the solution to the inequality is all values of g that are greater than or equal to 34.
We can graph this solution on a number line by placing a closed circle at 34 and shading to the right, to indicate that any value greater than or equal to 34 satisfies the inequality.
The graph looks like this the attached figure
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2074 Set B Q.No. 17 The compound interest on a certain sum at a certain rate is Rs. 204 in 2 years and simple interest at the same rate is Rs. 300 in 3 years. Find the sum and the rate of interest.
Answer:
Answer equals 2500 according to the question
An economy consists of coal, electric, and steel industries. For each $1.00 of output, the coal industry needs $0.01 worth of coal, $0.10 worth of electricity, $0.10 and worth of steel; the electric industry needs $0.03 worth of coal, $0.03 worth of electricity, and $0.04 worth of steel; and the steel industry needs $0.20 worth of coal and $0.01 worth of steel. The sales demand is estimated to be $4 billion for coal, $3 billion for electricity, and $3 billion for steel. Suppose that the demand for electricity triples and the demand for coal doubles, whereas the demand for steel increases by only 50%. At what levels should the various industries produce in order to satisfy the new demand?
The steel industry should use 1.7 billion dollars worth of coal and 0.035 billion dollars worth of steel.
What is amount?Amount is a term used to refer to the total of a certain quantity or sum. It is often used to describe the value of something, such as a financial transaction, or the size of a collection of objects. Amounts are usually expressed in units of measurement such as dollars, kilograms, or liters. Amounts can also be expressed as a percentage or fraction.
The coal industry should produce 8 billion dollars worth of output, the electric industry should produce 9 billion dollars worth of output, and the steel industry should produce 3.5 billion dollars worth of output. The coal industry should use 0.08 billion dollars worth of coal, 0.8 billion dollars worth of electricity, and 0.8 billion dollars worth of steel. The electric industry should use 0.06 billion dollars worth of coal, 0.9 billion dollars worth of electricity, and 1.2 billion dollars worth of steel. The steel industry should use 1.7 billion dollars worth of coal and 0.035 billion dollars worth of steel.
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Find exact values for the following:
Answer:
-sqrt(2)
-sqrt(2)
1
1
Step-by-step explanation:
A cylinder has a volume of 1 and one third in3 and a radius of one third in. What is the height of a cylinder? Approximate using pi equals 22 over 7.
42 over 6 inches
42 over 9 inches
42 over 11 inches
42 over 22 inches
The height of the cylinder is approximately 42/11 inches. The answer is option C.
What is the formula for the volume of the cylinder?
The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.
We are given that the volume of the cylinder is 1 and one-third in^3 and the radius is one-third in. Substituting these values into the formula, we get:
1 and one-third = 4/3
V = π(1/3)²h = 4/3
Simplifying the equation, we get:
h = (4/3) / (π(1/3)²) = (4/3) / (π/9) = (4/3) * (9/π) = 12/π
Approximating π as 22/7, we get:
h ≈ (12/π) ≈ (12/(22/7)) = 42/11 inches
Therefore, the height of the cylinder is approximately 42/11 inches. The answer is option C.
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what is a bisection
Answer:
this is the intersecting of lines
Answer:
gogel chrome. will answer faster than this app
Factorise 3-6x I don’t know how to do it
Answer:
Step-by-step explanation:
-3(2x-1)
complete the table based on the pattern you see
The figures to complete the table, based on the pattern, would be 6. 20, 7.00.
How to complete the table ?To complete the table, you need to find the common difference between the values in B which is :
= 4. 6 - 3. 8 = 5. 4 - 4. 6
= 0. 80 = 0. 80
The next two values would therefore be :
= 5. 4 + 0. 80 = 6. 20 + 0. 80
= 6. 20 = 7. 00
The complete table then is :
A - 5, 6, 7, 8, 9
B- 3.8, 4.6, 5.4, 6. 20, 7. 00
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The full question is:
Complete the table based on the pattern you see:
A- 5, 6, 7, 8, 9
B- 3.8, 4.6, 5.4, ____, ____,
Philip and Laura want to build a pool in their backyard. The length and width of the pool can be represented by the equation f(x)=(x-3)(5x+2) feet. What is the area of Philip and Laura’s pool? You must show your work and include your units.
Answer:
5x^2 - 19x + 15
Step-by-step explanation:
We must multiply the pool's length and width to determine its area. We can factor the equation f(x)=(x-3)(5x+2) to determine the length and width:
f(x) = (x-3)(5x+2)
f(x) = 5x^2 - 13x - 6
One of the parameters is the pool's length (x-3), while the other is its breadth (5x+2). We multiply these two elements to determine the area:
Area is length times width (x-3)
(5x+2)
By extending this statement using FOIL (First, Outer, Inner, Last), we may make it simpler:
Area is equal to 5x^2 - 13x - 6x + 15
Area: 5x^2 - 19x + 15
The pool at Philip and Laura's home is therefore 5x^2 - 19x + 15 square feet in size. We are unable to establish the precise square footage of the pool because we were not given a specific figure for x.
if you borrow $2,500 when you open up account the loan was for 2 years and the amount of the loan interest was $155 what were you charge when you open up the account for the loan
Answer:
the charge for opening up the account was $155.
Step-by-step explanation:
To find the charge for opening up the account, we need to subtract the interest from the total amount borrowed.
The total amount repaid at the end of the loan period is the sum of the amount borrowed and the interest charged. In this case, the total amount repaid is:
$2,500 + $155 = $2,655
The interest charged on the loan is the difference between the total amount repaid and the amount borrowed. Therefore, the amount charged for opening up the account is:
$2,655 - $2,500 = $155
So the charge for opening up the account was $155.
A local bank has determined that the daily balances of the checking accounts of its customers are normally distributed with an average of $280 and a standard deviation of $20.
a. What percentage of its customers has daily balances of more than $275?
b. What percentage of its customers has daily balances less than $243?
c. What percentage of its customers' balances is between $241 and $301.60?
Answer:
Step-by-step explanation:
Need a z-score with all of these, which essentially makes the table needed a standard normal table with mean 0 and sd 1
z=(x-mean)/sd
a. (275-280)/20=-0.25
want the probability of z <-0.25, and that is 0.4013 or 40.13%
b.(243-280)/20=-1.85, and probability of z < -1.85 is 0.0322 or 3.22%
c. this is z of -39/20 or -1.95 and z of 21.60/20 or 1.08. This has a probability of 0.8343 or 83.43%
Use 2nd VARS 2 for normal cdf and put in the numbers, with at least -6 or +6 for minus or plus infinity. 1E99 is fine but isn't really necessary.
When $0.58 tax was added to the price of a book, the total bill came to $7.05. What was the price of the book?
Step 1 of 2: Describe the above situation as a linear equation, using "x" or "y" as variable names to describe the unknown quantity
Answer:
Let's use "x" to represent the price of the book before tax.
After the tax is added, the total price becomes:
x + 0.58
We know that the total bill came to $7.05, so we can set up an equation:
x + 0.58 = 7.05
This equation represents the situation described.
Step-by-step explanation:
Answer:
I believe the answer would be $6.47
Step-by-step explanation:
new grill costs $550 discount = 15% off what is the final bill?
Suppose the demand and supply of tea are modeled by the two following functions:
Q = 34P + 53
Q = -25P + 177
What is the equilibrium price of tea? Round your answer to two places after the decimal point (0.01).
Answering the question, we may state that So the equilibrium price of equation tea is $2.10 per unit.
What is equation?A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two sentences that are written on opposite sides of a letter. Frequently, the logo and the particular software are identical. like in 2x - 4 = 2, for example.
To find the equilibrium price of tea, we need to set the quantity demanded equal to the quantity supplied:
[tex]34P + 53 = -25P + 177\\59P + 53 = 177\\59P = 124\\P = 2.10[/tex]
So the equilibrium price of tea is $2.10 per unit.
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In how many ways can the letters A, B, C, D, E, F, G, H be arranged?
Answer:
40,320
Step-by-step explanation:
There are 8 letters in total:
So, in the first place we can put all 8 letters
In the 2nd place we can put 7 (all except the letter in the first place and so on...)
Let's multiply the options (the order is important):
8! or 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40,320 (8 places for letters in total)
a) Copy and complete the table below for the graph of y = 2x.
21=33 9 1 2
1-4-2 A
b) The lines y = x and y = 2x are shown on the axis below.
Write down one similarity and one difference between these lines.
f y-20 У=2
5-
4-
3-
1-
654-32-18 1 23 45 6*
1-2
--3・
-4・
-5
-6-
Roberto bought a $340,000 house, paying 20% down, and financing the rest at 5% interest for 30 years. Her
monthly payments are $1460.15. How much will he really pay for her $340,000 house?
Roberto will pay a total of $
for the house.
Answer:
Therefore, Roberto will pay a total of $593,654 for his $340,000 house, including $253,654 in interest over the 30-year period.
Step-by-step explanation:
Roberto paid 20% down on a $340,000 house, which is 0.20 x $340,000 = $68,000.
So, the amount he financed is $340,000 - $68,000 = $272,000.
Roberto financed the $272,000 at 5% interest for 30 years, making monthly payments of $1460.15.
To find the total amount he will pay for the house, we need to calculate the total amount he will pay over the 30-year period.
First, we can calculate the total number of payments he will make over the 30 years by multiplying the number of years by the number of payments per year:
30 years x 12 months/year = 360 payments
The total amount Roberto will pay is the sum of all the monthly payments he makes over the 30 years:
Total amount = 360 x $1460.15 = $525,654
However, this includes both the principal amount of $272,000 and the interest he will pay over the 30 years. To find out how much he will pay in interest, we can subtract the principal from the total amount:
Total interest = $525,654 - $272,000 = $253,654
Therefore, Roberto will pay a total of $593,654 for his $340,000 house, including $253,654 in interest over the 30-year period.
if n square- 1 over m is equal to 4
Express n in terms of m
find n when m is 12
Answer:
n=√(4m+1) , 7
Step-by-step explanation:
According to statement
( n²-1 )÷m=4
∴n²-1=4m
⇒n²=4m+1
⇒n=√(4m+1)… … … … 1
If m=12
put the value of m in 1 equation
n=√(4×12+1)
=√49=7
If sin 0 = -2/3which of the following are possible?
Is sin (θ) = - 2/ 3, the options that are possible include:
A) sec(θ) = -3/2 and tan(θ) = 2/√5C) cos(θ) = -(√5)/3 and tan(θ) = 2/√5How to find the possible expressions?Since sec(θ) is negative, cos(θ) is also negative (sec(θ) = 1/cos(θ)). This means θ is in the second or third quadrant, but since sin(θ) is negative, θ must be in the third quadrant. Now let's check if the given tan(θ) value is correct:
tan(θ) = sin(θ)/cos(θ)
Since we already know that cos(θ) is negative, we have cos(θ) = -(√5)/3.
Now calculate tan(θ):
tan(θ) = (-2/3) / (-(√5)/3) = 2/√5
The given values in option A are correct.
cos(θ) = -(√5)/3 and tan(θ) = 2/√5
These are the same as in option A. So, this option is also possible.
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Find the area of this composite shape. 10 cm, 5 cm, 8 cm, and 4 cm.