Answer:
a) $2000
b) 15000(3.20)/(24+x) = new gasoline cost (replace with variable of your choice)
c) 2000-(15000(3.20)/(24+x)) = money saved (replace with variable)
d) ~34.29 miles (34.28571 miles)
Step-by-step explanation:
a) [15000(3.20)]/24 = 2000
b) use the formula above, but the denominator is 24+x (or variable of your choice) because the amount of mpg is increased
c) take the formula from a, then subtract formula in b from it
d) take formula c, replace the variable (variable = money saved) with 600
PRECISION In November 2010 the average cost of 5 gallons of regular unleaded gasoline in the United States was $14.46. What was the average cost for 16 gallons of gasoline?
Answer:
$46.272
Step-by-step explanation:
o. Find the domain and range of each of the three restricted functions.
Type your response here:
Domain
(restricted)
Function
Range
I
f(x)=sin(x)
f(x) = cos(x)
f(x) =tan(x)
The domain and range of the functions sin x, cos x, and tan x will be (-∞, ∞) and [-1, 1], (-∞, ∞) and [-1, 1], and R - (2n + 1)π/2 and (-∞, ∞) respectively.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The three restricted functions are given below.
f(x) = sin (x)
f(x) = cos (x)
f(x) = tan (x)
Then the domain of the three restricted functions will be
The domain of sin x will be (-∞, ∞).
The domain of cos x will be (-∞, ∞).
The domain of tan x will be R - (2n + 1)π/2.
Then the range of the three restricted functions will be
The range of sin x will be [-1, 1].
The range of cos x will be [-1, 1].
The range of tan x will be (-∞, ∞).
The graph is given below.
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In the third month of a study, a sugar maple tree is 82 inches tall. In the seventh month, the tree is 92 inches tall. Assuming the tree grows at a constant rate every month, what is the rule for the height of the tree during the nth month
The linear equation that gives the height on the x-th month is:
y = 2.5*x + 74.5
Which rule gives the height of the tree for the n-th month?
This will be modeled with a linear equation of the form:
y = a*x + b
Where a is the slope and b is the y-intercept.
Remember that for a line with the points (x₁, y₁) and (x₂, y₂), the slope is given by:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we have the two points (3, 82) and (7, 92). Where the first value is the number of months and the second value is the height.
So the slope is:
[tex]a = \frac{92 - 82}{7 - 3} = 10/4 = 2.5[/tex]
Then the linear equation is:
y = 2.5*x + b
To get the value of b, we use the fact that when x = 3, we have y = 82,
82 = 2.5*3 + b
82 = 7.5 + b
82 - 7.5 = b = 74.5
Then the linear equation is:
y = 2.5*x + 74.5
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what is an arithmetic pattern
Which ordered pair is a solution to the following system of inequalities?
y < –x2 + x
y > x2 – 4
(0, –1)
(1, 1)
(2, –3)
(3, –6)
Answer: (0,-1)
Step-by-step explanation:
Let's start with the first inequality, [tex]y < -x^{2}+x[/tex]. To check which points satisfy this inequality, we can substitute the x- and y-coordinates and see if they satisfy the inequality.
A) [tex]-1 < -0^{2}+0 \longrightarrow -1 < 0 \longrightarrow \text{ True}[/tex]B) [tex]1 < -1^{2}+1 \longrightarrow 1 < 0 \longrightarrow \text{ False}[/tex]C) [tex]-3 < -2^{2}+2 \longrightarrow -3 < -2 \longrightarrow \text{ True}[/tex]D) [tex]-6 < -3^{2}+3 \longrightarrow -6 < -6 \longrightarrow \text{ False}[/tex]Once again, we can repeat this for the second inequality (but this time, we only need to check the points that satisfy the first inequality).
A) [tex]-1 > 0^{2}-4 \longrightarrow -1 > -4 \longrightarrow \text{ True}[/tex]C) [tex]-3 > 2^{2}-4 \longrightarrow -3 > 0 \longrightarrow \text{ False}[/tex]Therefore, the answer is (A) (0, -1).
Which one of the following inequalities would require you to reverse the symbol?
a) 2x > -14
b) -14 < 2x
c) -14 ≤ 2x
d) -2x ≥ -14
The graph shows the relationship between the number of months different students practiced boxing and the number of matches they won:
Part A: What is the approximate y-intercept of the line of best fit and what does it represent? (5 points)
Part B: Write the equation for the line of best fit in the slope-intercept form and use it to predict the number of matches that could be won after 13 months of practice. Show your work and include the points used to calculate the slope. (5 points)
The y-intercept is 3.75, and the equation of the line of best fit is
y = 1.5x + 3.75, and after 13 months, 23 matches could be won.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
Part A:
As we can see in the graph, the line crosses the y-axis at a certain point between 3 and 4.5.
So the y-intercept lies between 3 and 4.5
We can take the middle of these two values to get the approximate value of the y-intercept.
b = (3+4.5)/2 = 3.75
We know the line of the best fit is:
y = mx + b
y = mx + 3.75
b is the y-intercept and m is the slope of a line
Plug the point (9, 18) in the equation to get the value of m:
18 = 9m + 3.75
m = 1.5
y = 1.5x + 3.75
Plug x = 13 months in the above equation:
y = 1.5(13) + 3.75
y = 23.25 ≈ 23 number of matches that could be won
Thus, the y-intercept is 3.75, and the equation of the line of best fit is
y = 1.5x + 3.75, and after 13 months, 23 matches could be won.
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please give me the answer to this
i beleive the answer is 2610.4109589
what is the y-intercept of the graph of y = 4^x-2?
Answer: Hope this helps you.
-2
Step-by-step explanation:
y = mx+b (B is y-int)
y = 4^x-2
-2 is clearly replacing the b (y-int) meaning b, the y-int, is -2
[tex]y = {4}^{x} - 2 \\ for \: y \: intercept \: x \: s \\ is \: 0 \\ y = {4}^{0} - 2 \\ y = 1 - 2 \\ y = - 1 \\ [/tex]
Y intercept : (0,-1)
Hope it helps
please give brainliest
2. Calculate the amount of compound interest paid on $7300 at the end of 3 years for each
rate. [2 marks each]
a) 10% compounded semi-annually
b) 8% compounded monthly
The compound interest when $7300 when interest is compounded semi annually is $2482.70.
The compound interest when $7300 when interest is compounded monthly is $1972.73.
What is the compound interest?An investment earns compound interest when both the amount invested and the interest accrued increases in value at predetermined time intervals.
The formula to represent compound interest is :
FV - amount invested
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate m = number of compoundingN = number of yearsa. 7300 x [1 + (0.1/2)]^(3 x 2) = 9782.70
Compound interest = 9782.70 = 7300 = $2482.70
b. 7300 x [1 + (0.08/12)]^(12 x 3) = 9272.73
9272.73 - 7300 = $1972.73
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Naomi's car exponentially depreciates at a rate of 8% per
year. If Nina bought the car when it was 4-years old for $16,500, what was
the approximate original price of the car?
The approximate original price of the car is $23032
How to determine the original price?The given parameters are:
Rate, r = 8%
Price at 4 years old = 16,500
An exponential function is represented as:
y = a(1 - r)^x
Where a represents the initial value
This gives
y = a(1 - 8%)^x
Evaluate
y = a(0.92)^x
At 4 years old, we have:
16500 = a(0.92)^4
Divide both sides by (0.92)^4
a = 23032
Hence, the approximate original price of the car is $23032
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Write -0.65 as a fraction or mixed number in simplest form. (you may use an improper or a mixed number as your final answer.)
Answer:
-13/20
Step-by-step explanation:
-0.65 can be written as -65/100. To simplify, divide both numerator and denominator with 5. 65/5=13. 100/5=20
And you get -13/20 for your answer.
Which segments are perpendicular?
Answer: B
Step-by-step explanation:
Angles that measure 90 degrees, angles that measure 90 degrees are right angles, and perpendicular lines form right angles.
Since angle EAB is a right angle, and it is formed by segments EA and AB, B is the answer.
x divided by the sum of x and 5
Answer:
1 + 1/5xStep-by-step explanation:
x divided by the sum of x and 5
x : (x + 5) =
x × (1/1x^-1 + 1/5) =
1 + 1/5x
Find the geometric mean of 5 and 8. Write your answer in the simplest radical form.
Answer:
First, multiply 5 and 8. That equals 40. Then you take the square root of 40, which doesn't result in a whole number, so you factor 40 and removing perfect squares. In which case the answer would be 2√10
10 more than w is equal to 40 what is the expression
Answer:
w + 10 = 40
Step-by-step explanation:
10 more than w is w + 10 is equal to 40 is =40
w + 10 = 40
Please mark as brainliest.
Answer:
10 + w = 40Step-by-step explanation:
10 more than w is equal to 40 what is the expression
10 + w = 40 is the expression
w = 40 - 10
w = 30 is the solution
Which of the following shows the correct steps to find the value of 27 to the power of 1 over 3 ? (1 point)
A. 27 to the power of 1 over 3 equals 9 to the power of 3 to the power of 1 over 3 equals 9 to the power of 3 multiplied by 1 over 3 equals 9
B. 27 to the power of 1 over 3 equals 3 to the power of 9 to the power of 1 over 3 equals 3 to the power of 9 multiplied by 1 over 3 equals 3
C. 27 to the power of 1 over 3 equals 3 to the power of 4 to the power of 1 over 2 equals 3 to the power of 4 multiplied by 1 over 2 equals 9
D. 27 to the power of 1 over 3 equals 3 to the power of 3 to the power of 1 over 3 equals 3 to the power of 3 multiplied by 1 over 3 equals 3
Answer:
D
Step-by-step explanation:
it shows the correct one
Marcella is flying a kite in a competition. To win the competition, her kite string must have at least 162 feet released. The kite is 75 feet above her. The angle of the string and her hand is forming a 28 degree angle. Will she be able to win the competition? Show your work.
For question 1, will she win the competition? Type yes or no
Marcella won't be able to win the competition because the length of the rope is less than 162 feet.
How to find the sides of a right angle triangle?
The situation forms a right angle triangle.
The kite released rope is the hypotenuse side of the triangle formed.
The opposite side of the triangle is the height of the kite from the ground.
Therefore,
sin 28 = opposite / hypotenuse
sin 28 = 75 / h
h = 75 / sin 28
h = 75 / 0.46947156278
h = 159.754085116
h ≈ 160 feet
Therefore, she won't be able to win the competition because the length of the rope is less than 162 feet.
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What is the equation of a line with a slope of -1 and a y-intercept of -5?
Answer:
y = -x - 5
Step-by-step explanation:
The general structure of a line in slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept.
Since you have been given the slope and y-intercept, you can substitute these values into the equation to find the answer.
m = -1
b = -5
y = mx + b
y = (-1)x + (-5)
y = -x - 5
Answer:
y = -x -5
Step-by-step explanation:
We can use y = mx + c to find the equation of the line.
Here,
m ⇒ slope of the line
c ⇒ y - intercept
They have already given that,
m ⇒ -1
c ⇒ -5
So, now we can write the equation of the line like this.
To write the equation of the line you can replace m and c with -1 & -5 respectively.
Let us write now.
y = m x + c
y = -1x - 5
What is the area of the triangle below?
O27 square units
O 45 square units
O 54 square units
20
A triangle is a 2-D shape that has 3 sides and angles. The area of the triangle below is 27 square units
Area of a triangleA triangle is a 2-D shape that has 3 sides and angles
In order to determine the area of the shape, we will determine the area of the square circumscribing it first;
Area of the square = 10 * 9 =90 square units
Find the area of the two right triangles
Area of the right triangles = 0.5(10 * 9) + 0.5(9 * 4)
Area of the right triangles = 45 + 18
Area of the right triangles = 63 square units
Take the difference
Area of the given triangle = 90 - 63 = 27 square units
Hence the area of the triangle below is 27 square units
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Need help with this
Answer:
y = 130
Step-by-step explanation:
given that y varies directly with x and z then the equation relating them is
y = kxz ← k is the constant of variation
to find k use the condition y = 150 when x = 2.5 and z = 12 , then
150 = k × 2.5 × 12 = 30k ( divide both sides by 30 )
5 = k
y = 5xz ← equation of variation
when x = 4 and z = 6.5 , then
y = 5 × 4 × 6.5 = 20 × 6.5 = 130
MATH!!! (please answer correctly...) find the surface area of the prism
Give your answer in terms of [tex]\pi \\[/tex]
The length of the band in terms of π is given by the expression:
L = 40mm + π*10mm
How to get the length of the band?
Remember that for a circle of diameter D, the circumference is:
C = π*D.
Now, if you look at the image, you can see that the length of the band will be equal to 4 times the diameter of the pencils (one time for each side). Plus 4 times one-fourth of the circumference of each pencil (for the four corners).
because the diameter is 10mm, the length of the band will be:
L = 4*10mm + 4*(π*10mm/4)
L = 40mm + π*10mm
This is the length of the band in terms of π.
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Which expression is equivalent to StartFraction 7 Superscript 5 Over 7 squared EndFraction?
(7 times 5) (7 times 2)
(7 times 7 times 7 times 7 times 7) (7 times 7)
StartFraction 7 times 5 Over 7 times 2 EndFraction
StartFraction 7 times 7 times 7 times 7 times 7 Over 7 times 7 EndFraction
The equivalent expression of [tex]\frac{7^5}{7^2}[/tex] is [tex]\frac{7*7*7*7*7}{7*7}[/tex]
How to determine the equivalent expression?The expression is given as:
[tex]\frac{7^5}{7^2}[/tex]
Expand the numerator and the denominator
[tex]\frac{7^5}{7^2} = \frac{7*7*7*7*7}{7*7}[/tex]
The above expression is represented by option (d)
Hence, the equivalent expression of [tex]\frac{7^5}{7^2}[/tex] is [tex]\frac{7*7*7*7*7}{7*7}[/tex]
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Answer:
StartFraction 7 times 7 times 7 times 7 times 7 Over 7 times 7 EndFraction
Step-by-step explanation:
Edge
Find the LCM of 16x² and 40x5
Answer:
The LCM of 16x^2 and 40x^2 is 80x^5
:) Good Luck
Step-by-step explanation:
Jonathan’s temperature this morning was 38.2°C. After 2 hours, it was 39.5°C. All are true about Mark’s condition EXCEPT
*
1 point
a. His condition worsened.
b. His condition improved.
c. His temperature went up by 1.3 C°
d. He has high fever.
2. The temperature of freshly baked hot malungay pandesal is 68°C; while hot coffee is 85°C. What is the difference between the two temperatures?
*
1 point
a. 15°C
b. 17°C
c. 23°C
d. 2.3°C
3. At 8:00 AM, the temperature in the room was 25.6°C. By noon, it had gone up by 2.5 C°. But by 6:00 PM, it had gone down by 3.3 C°. What was the temperature in the room at 6:00 PM?
*
1 point
a. 28°C
b. 24.8°C
c. 28.4°C
d. 28.5°C
Answer:
a
b
b
:)
Step-by-step explanation:
hi brother i have got the answer hope its correct
PLEASE HELP 100 POINTS:
Cylinder A has a radius of 10 inches and a height of 5 inches. Cylinder B has a volume of 750m. What is the percentage change in volume from cylinde
A to cylinder B?
50% decrease
75% decrease
50% increase
200% increase
Answer:
The percentage change in volume from cylinder A to cylinder B is 50% volume increased by 50% option (C) is correct.
What is a cylinder?
In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.
We know the formula for the volume of the cylinder is given by:
We have r = 10 inches and h = 5 inches
V = 500π cubic inches
Percent change in volume from cylinder A to cylinder B:
= 50%
Thus, the percentage change in volume from cylinder A to cylinder B is 50% volume increased by 50% option (C) is correct.
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Step-by-step explanation:
Combine like terms 2x - 5x
Answer:
-3x
Step-by-step explanation:
its just like regular subtraction, 2-5= -3, and just add an X at the end and you get -3x.
Freda waves a small flag pennant when her favorite player hits a grand slam. approximately how much fabric in square inches is used to make up the flag on her pennant
Answer: 15 inches
Step-by-step explanation:
Answer:
In a right triangle, the hypotenuse, 2x, is equal to twice the length of the shortest leg, x, and the longer leg is equal to the product of the length of the shortest leg, x, and the square root of 3.
Hypotenuse: 10 in.
Shortest Leg:2x=10 , so x=5 in,
Longer Leg: x sq rt 3 5 sq rt 3 in
area- 1/2 bh, 1/2 5*5 sq rt 3=
25t sq rt 3=21.65 sq inches
Write the following ratio using two other notations. 7:6 Use only the numbers above (not any others).
[tex]\textbf{Notation one:}~~ \dfrac 76\\\\\textbf{Notation two:} ~ \text{7 to 6}[/tex]