Answer: 3x² - 27y² = (3x²) - (27)(y²) = 3(x² - 9y²) = 3(x - 3y)(x + 3y), and 2014² - 2013² = (2014 + 2013)(2014 - 2013) = (3127)(1) = 3127
Im not 100% sure of this answer cause I'm not that good at stuff like this but I still think this is right fr fr
100 Points! Algebra question. Photo attached. Graph the function. Thank you!
The graph of the function is attached and the amplitude and the period are 5 and 2π
How to determine the amplitude and period of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 5cos(θ)
A sinusoidal function is represented as
f(x) = Acos(B(x + C)) + D
Where
Amplitude = APeriod = 2π/BSo, we have
A = 5
Period = 2π/1
Evaluate
A = 5
Period = 2π
Hence, the amplitude is 5 and the period is 2π
The graph of the function is attached
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8 +[13-(2+1] =
20
18
-3
Answer: false
Step-by-step explanation:
help with geometry please‼️‼️
estimate the original volume of the pyramid in fig 15.28 given that it's frustum has a 4 m by 4 m squared top which is 12 m vertically above the square base which is 20 m by 20 m (assume that the original problem was raised to a point . Neglect the volume of the entrance of the right of the photograph)
Answer:
Step-by-step explanation:
To estimate the original volume of the pyramid, we can use the formula for the volume of a frustum of a pyramid:
V = (1/3)h(a^2 + ab + b^2)
Where V is the volume, h is the height of the frustum, a is the side length of the top square, and b is the side length of the bottom square.
In this case, the top square has a side length of 4 m, and the bottom square has a side length of 20 m. The height of the frustum is 12 m.
Plugging these values into the formula, we get:
V = (1/3) * 12 * (4^2 + 4*20 + 20^2)
Simplifying the equation:
V = (1/3) * 12 * (16 + 80 + 400)
V = (1/3) * 12 * 496
V = 12 * 496/3
V = 1984
Therefore, the estimated original volume of the pyramid is 1984 cubic meters.
D
(x+2)(x+6)=0
In the problem shown, to conclude that x+2=0 orx+6=0, one must use the:
O zero product property
O division property
O transitive property
O multiplication property
H
OI
Answer:
zero product property
Step-by-step explanation:
To conclude that x+2=0 or x+6=0 from the equation (x+2)(x+6)=0, one must use the zero product property.
The zero product property states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero. In this case, if (x+2)(x+6)=0, it means that the product of (x+2) and (x+6) is zero. Therefore, we can conclude that either (x+2) = 0 or (x+6) = 0, based on the zero product property.
Which model represents the expression 87 - 42?
The model that represents the expression 87 - 42 is (d)
Identifying the model that represents the expression 87 - 42?From the question, we have the following parameters that can be used in our computation:
87 - 42
Using their place values, we have
87 = 8 tens 7 units
42 = 4 tens 2 units
This means that
87 - 42 = 8 tens 7 units - 4 tens 2 units
Subtract the tens
87 - 42 = 4 tens 7 units - 2 units
Subtract the units
87 - 42 = 4 tens 5 units
The model that represents the expression 87 - 42 is 4 tens 5 units
This is represented by model (d) bottom right
Hence, the model that represents the expression 87 - 42 is (d)
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What is the equation of the line that passes through (4, 3) and (-4, -1)?
Choices:
2x+1
y=2x+7
y=x/2 +1
y= -x/2 +7
The equation of the line that passes through (4, 3) and (-4, -1) is y = -x/2 + 5. So, correct option is A.
To find the equation of the line that passes through two given points, we use the slope-intercept form of a linear equation, which is:
y = mx + b
where m is the slope of the line and b is the y-intercept.
First, we need to find the slope of the line using the two given points. The formula for finding slope between two points is:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
Substituting the given points into the formula, we get:
m = (-1 - 3) / (-4 - 4) = -4/8 = -1/2
Now we know the slope, we can use one of the given points (4, 3) and substitute the slope into the slope-intercept form of the equation and solve for b.
y = mx + b
3 = (-1/2)(4) + b
3 = -2 + b
b = 5
Therefore, the equation of the line that passes through (4, 3) and (-4, -1) is:
y = -x/2 + 5
So, correct option is A.
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Complete question is:
What is the equation of the line that passes through (4, 3) and (-4, -1)?
Choices:
y = -x/2 + 5
y=2x+7
y=x/2 +1
y= -x/2 +7
Gauri Spends 0.75 of her salary every month if she earns rs 12000 per month in how many months will she save rupees 39000
Answer:
13 months--------------------
If Gauri spends 0.75 of her salary every month, that means she saves 0.25 of her salary:
0.25 * 12000 = 3000Divide the total 39000 by her monthly savings:
39000 / 3000 = 13So it will take Gauri 13 months to save rupees 39000.
Find the area of the green shaded sector of the circle. Show all of your work. Write your answer in terms of pi.
The area of the sector with an angle of 285 degrees and a radius of 6 units is 28.5π square units.
To find the area of a sector, we can use the formula:
Area of Sector = (Central Angle / 360 degrees) × π × (Radius²)
Given that the central angle is 285 degrees and the radius is 6, we can substitute these values into the formula:
Area of Sector = (285 degrees / 360 degrees) × π × (6²)
Area of Sector = (19/24) × π × 36
Area of Sector = (19/24) × 36π
Area of Sector = (19 × 36π) / 24
Area of Sector = 684π / 24
Area of Sector = 28.5π
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Cameron surveyed her friends about the number of apps they use. The responses were 15, 16, 18, 9, 18, 4, 19, 20, 17, and 36 apps. Use the range and interquartile range to describe how the data vary.
The middle half of the data values vary by:
Interquartile = [tex]Q_3-Q_1[/tex] => 19.25 - 13.5 = 5.25
The given data is :
15, 16, 18, 9, 18, 4, 19, 20, 17, and 36 apps.
We have to find:
Use the range and interquartile range to describe how the data vary.
We have to arrange the data from smallest to largest.
4, 9, 15, 16, 17, 18, 18, 19, 20, 36
Range of the data is : Highest no. - lowest no.
Range of the data is: 36 - 4 = 32
The location of the [tex]Q_1[/tex] = (n + 1) × 0.25 (where n is the total no. in the data)
The location of the [tex]Q_1[/tex] = (10 + 1) × 0.25 = 11 × 0.25 = 2.75
∴[tex]Q_1[/tex] = 15 × 0.75 + 9 × 0.25 = 13.5
The location of the [tex]Q_3[/tex] = (n + 1) × 0.75
The location of the [tex]Q_3[/tex] = 11 × 0.75 = 8.75
∴[tex]Q_3[/tex] = 19 × 0.75 + 20 × 0.25 = 19.25
Hence, The middle half of the data values vary by:
Interquartile = [tex]Q_3-Q_1[/tex] => 19.25 - 13.5 = 5.25
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Gabe learns more than just
math in Mrs. Zemla's class. Today he
learned that buying a car is a bad
investment because a car's value decreases
each year. So when Gabe was looking to
buy a 2024 Porsche Boxster for $54792,
he also reasearched the projected resale
value of the vehicle. He found that the
vehicle is expeced depreciate 19% each
year after the car is purchased. What is
the expected vaule of the car 7 years after
it was purchased?
The expected value of the car 7 years after it was purchased is $47,029.12.
To solve this problem, we need to calculate the expected value of the car after 7 years. To do this, we need to use the formula for calculating the value of a depreciating asset:
Value after n years = Initial Value - (Initial Value × (Depreciation Rate/100)×n)
In this case, the initial value of the car is $54792, the depreciation rate is 19%, and n = 7. Thus, the expected value of the car 7 years after it was purchased is:
Value after 7 years = 54792 - (54792 × (19/100)×7)
Value after 7 years = 54792 - (54792 × 0.19×7)
Value after 7 years = 54792 - 7762.88
Value after 7 years = $47,029.12
Therefore, the expected value of the car 7 years after it was purchased is $47,029.12.
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You deposit $5000 in an account earning 6% interest compounded monthly. How much will you have in the
account in 15 years?
Answer:
$12270.46----------------------
Use the compound interest formula:
[tex]A = P(1 + r/n)^{nt}[/tex]Where:
A = final amount;P = initial deposit = $5000;r = annual interest rate = 6%;n = number of times the interest is compounded per year = 12;t = time period in years = 15.Plugging in the values, we get:
A = 5000(1 + 0.06/12)¹²*¹⁵ A = 12270.46Sarah wants to buy a new laptop. Store A is currently selling the laptop for $1,640 with an additional 20% off. Store B is selling the laptop for $1,500 with an additional 10% off. Which store offers a better deal?
Answer:
Store A
Step-by-step explanation:
If an item is 20% off, then you pay 80% of the price.
If an item is 10% off, then you pay 90% of the price.
Store A
80% of $1640 = 0.8 × $1640 = $1312
Store B
90% of $1500 = 0.9 × $1500 = $1350
Answer: Store A
Answer:
Store A
Step-by-step explanation:
Store A offers a 20% discount which is equivalent to 0.20 x $1,640 = $328.
The laptop is therefore sold for $1,640 - $328 = $1,312 at Store A.
Store B offers a 10% discount which is equivalent to 0.10 x $1,500 = $150.
The laptop is therefore sold for $1,500 - $150 = $1,350 at Store B.
Therefore, Store A offers a better deal at $1,312 compared to Store B at $1,350.
A rectangular prism with a square base has a height of 17.2 cm and a volume of 24.768 cm² What is the side length of its base?
If rectangular prism with a square base has a height of 17.2 cm and a volume of 24.768 cm², the side length of the square base is 1.2 cm.
Let's denote the side length of the square base as x cm. Then, the volume of the rectangular prism can be expressed as V = x² * 17.2 cm³, and its surface area can be expressed as S = 2x² + 4x * 17.2 cm².
We are given that the volume of the rectangular prism is 24.768 cm³, so we can write the equation:
x² * 17.2 cm³ = 24.768 cm³
Simplifying this equation, we get:
x² = 24.768 cm³ / 17.2 cm² = 1.44 cm²
Taking the square root of both sides, we get:
x = 1.2 cm
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geometry need help please
100 Points! Geometry question. Identify the similar triangles. Then find each measure. Photo attached. Please show as much work as possible. Thank you!
The similar triangles for this problem are given as follows:
RST and VUT.
Then the measure VT is given as follows:
VT = 5.4 units.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.Hence the similar triangles for this problem are given as follows:
RST and VUT.
The proportional relationship for the side lengths is given as follows:
6/14 = (x + 2)/(4x - 1).
Applying cross multiplication, the value of x is obtained as follows:
14(x + 2) = 6(4x - 1)
14x + 28 = 24x - 6
10x = 3.4
x = 3.4.
Then the length VT is given as follows:
VT = 3.4 + 2
VT = 5.4 units.
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What is the value of x in the given triangle, in inches?
The numerical value of side length x in the right triangle is 8.
What is the numerical value of x?The figures in the image are two similar right triagles.
Since the two right triangles are similar, we equate the ratio of the sides of the two triangles.
x/6 = (x + 4)/9
Cross multiply and solve for x:
6( x + 4 ) = x × 9
Apply distributive property:
6 × x + 6 × 4 = x × 9
Simplifying, we get:
6x + 24 = 9x
Subtract 6x from both sides:
6x - 6x + 24 = 9x - 6x
24 = 9x - 6x
24 = 3x
3x = 24
Divide both sides by 3:
x = 24/3
x = 8
Therefore, the value of 8.
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Given m ∥ n, find the value of x.
given that m is parallel to n,
the angle opposite (2x + 16)° is also (2x + 16)° as vertically opposite angles are equal.
using the corresponding angle rule we know that:
2x + 16 = 96
2x = 80
so x = 40
The slope of a line of best fit is undefined when _____.
select all that apply
(1) the x values of the data set are constant
(2) the y values of the data set do not change when the x values change
(3) the slope of the line of best fit is vertical
(4) the slope is of the line of best fit is horizontal.
(5) the x values of the data set increase at an unspecified rate as the y values decrease
The slope of a line of best fit is undefined when the slope is of the line of best fit is horizontal. This is because a horizontal line has a slope of zero
The slope of a line of best fit is undefined when the slope is of the line of best fit is horizontal. A line of best fit is a straight line that is used to represent the data on a scatter plot. It is the line that best fits the data points in a scatter plot.
The slope of a line of best fit is the rate of change of the y-coordinate relative to the x-coordinate.. In other words, there is no rate of change of the y-coordinate relative to the x-coordinate when the line is horizontal.
The x values of the data set increase at an unspecified rate as the y values decrease. This means that the line of best fit has a negative slope. A negative slope means that the y-coordinate decreases as the x-coordinate increases.
In other words, there is a rate of change of the y-coordinate relative to the x-coordinate. The slope of the line of best fit is the value of this rate of change.
The slope of a line of best fit is used to determine the direction and strength of the relationship between two variables.
A positive slope means that the variables are directly proportional, while a negative slope means that they are inversely proportional. The slope of a line of best fit can be calculated using the formula y2 - y1 / x2 - x1.
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Which of these values for P and a will cause the function f(x)= Pa to be an
exponential growth function?
○ A. P= 1/2;a=1
OB. P = 2; a = 1
OC. P = 2; a = 3
O D. P = 1/2; a= 1/3
The values of P and a such that [tex]f(x) = Pa^x[/tex] is an exponential growth function are given as follows:
C. P = 2; a = 3.
How to define an exponential function?An exponential function has the definition presented according to the equation as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The conditions for an exponential growth function are given as follows:
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100 tickets are sold for $1 each there is $25 prizes and a $10 prize what is the expected value for a person that buys a ticket round to the nearest cent
The expected value for a person buying a ticket is $0.35 rounded to the nearest cent.
What is the expected value for the person who buys the ticket?The expected value is calculated considering the probabilities of winning each prize and the corresponding values of each prize.
Assuming:
P($25) as the probability of winning the $25 prize
P($10) as the probability of winning the $10 prize
There are 100 tickets sold, therefore, the probabilities can be found as follows:
P($25) = 1/100 (since there is only 1 $25 prize)
P($10) = 1/100 (since there is only 1 $10 prize)
The expected value (E), will then be:
E = P($25) * $25 + P($10) * $10
E = (1/100) * $25 + (1/100) * $10
E = $0.25 + $0.10
E = $0.35
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Lines y and z are parallel.
Parallel lines are cut by transversals s and t. The angles formed by lines s, t, and y, clockwise from top left, are blank, blank, (10 x + 5) degrees, blank, (4 x minus 7) degrees, blank; formed by s and z are 65 degrees, 1, blank, blank; formed by z and t are 2, blank, blank, blank.
What is the measure of angle 2?
6 degrees
11 degrees
28 degrees
37 degrees
The measure of Angle 2 is 17 degrees.
The measure of angle 2, the relationships between the given angles formed by the parallel lines and transversals.
1. The angles formed by lines s, t, and y, clockwise from top left, are:
- Blank
- Blank
- (10x + 5) degrees
- Blank
- (4x - 7) degrees
- Blank
2. The angles formed by s and z are:
- 65 degrees
- 1
- Blank
- Blank
3. The angles formed by z and t are:
- 2
- Blank
- Blank
- Blank
From the given information, we can deduce the following:
- Angle 1 is congruent to the angle formed by z and t (corresponding angles).
- Angle (10x + 5) degrees is congruent to angle 65 degrees (alternate interior angles).
- Angle (4x - 7) degrees is congruent to angle 2 (alternate interior angles).
Therefore, we can set up the following equations:
65 = 10x + 5 (Equation 1)
2 = 4x - 7 (Equation 2)
Solving Equation 1:
65 - 5 = 10x
60 = 10x
x = 6
Substituting x = 6 into Equation 2:
2 = 4(6) - 7
2 = 24 - 7
2 = 17
Hence, the measure of angle 2 is 17 degrees.
Therefore, the correct answer is:Angle 2 = 17 degrees.
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There were 104 females and 78 males present at the high school pep rally. Find the ratio of males to the total number of people present. Express as a simplified ratio.
Answer:
The ratio is 3:7
Step-by-step explanation:
You add 104+78
The un-simplified ratio is 78:182
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Find the inverse of the function.
f-¹(x) =
+
f(x) =
1
x - 2
X # 2
, X = 0
Answer:
The given function is:
f(x) = 1/(x - 2), x ≠ 2
0, x = 2
To find the inverse of the function, we need to solve for x in terms of f(x).
Let y = f(x)
Case 1: When y = 0
If y = 0, then x = 2 as per the definition of the function.
Case 2: When y ≠ 0
y = 1/(x - 2)
1/y = x - 2
x = 1/y + 2
So, the inverse function is:
f-¹(x) = 2, x = 0
1/(x - 2), x ≠ 0 and x ≠ 2
Step-by-step explanation:
2/5 of Jim's savings is equal to 4/9 of Max's savings. Jim has $30 more than Max. 5 How much money does Max have?
As Jim has $30 more than Max, as per this, Max has $270.
Let's assume Max's savings as 'x' dollars.
We have:
2/5 of Jim's savings is equal to 4/9 of Max's savings.
(2/5) * Jim's savings = (4/9) * Max's savings
We also know that Jim has $30 more than Max.
Jim's savings = Max's savings + $30
So,
(2/5) * Jim's savings = (4/9) * Max's savings
(2/5) * (Max's savings + $30) = (4/9) * Max's savings
To solve for Max's savings, we can solve this equation:
(2/5) * (x + $30) = (4/9) * x
So, for x:
(2/5) * (x + $30) = (4/9) * x
Multiplying both sides by 45 (the least common denominator of 5 and 9) to eliminate the fractions:
18(x + $30) = 20x
18x + 540 = 20x
540 = 20x - 18x
540 = 2x
x = 270
Therefore, Max has $270.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
6/MN = 8/9
8MN = 54
MN = 6 3/4
The correct answer is B.
Find the
approximate height difference between the birdhouse
and the tree house. Is it greater than or less than the
approximate difference in height between the swing
set and the tree house? Round each mixed number to
the nearest whole number.
HELP???
The approximate height difference between the birdhouse and the tree house is 3 ft.
It is less than the approximate difference in height between the swing set and the tree house.
How to find the approximate height difference between the birdhouse and the tree house?A fraction represents the parts of a whole or collection of objects e.g. 3/4 shows that out of 4 equal parts, we are referring to 3 parts.
We have:
height of birdhouse = 14[tex]\frac{9}{16}[/tex] ft
height of tree house = 11[tex]\frac{13}{16}[/tex] ft
Thus, the approximate height difference between the birdhouse and the tree house will be:
14[tex]\frac{9}{16}[/tex] ft - 11[tex]\frac{13}{16}[/tex] = 2[tex]\frac{3}{4}[/tex] ft
= 2.75 ft
= 3 ft
To determine if it is greater than or less than the approximate difference in height between the swing set and the tree house, we have to find the approximate difference in height between the swing set and the tree house. That is:
height of swing set = 8[tex]\frac{1}{4}[/tex] ft
height of tree house = 11[tex]\frac{13}{16}[/tex] ft
difference = 11[tex]\frac{13}{16}[/tex] - 8[tex]\frac{1}{4}[/tex]
= 3[tex]\frac{1}{2}[/tex]
= 3.5
= 4 ft
Therefore, it is less than the approximate difference in height between the swing set and the tree house
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elle can buy 2 quarts of milk for 3$ or 1 gallon of milk for 3$ which is the better deal
Answer:
Elle should buy 1 gallon of milk for $3.
Step-by-step explanation:
In one gallon of milk, there are four quarts. So we can multiply the number of gallons by four to convert it to quarts.
(1 gallon)x(4 quarts) = 4 quarts in one gallon
4 quarts is greater than 2 quarts so 1 gallon for $3 is a better deal than 2 quarts for $3.
Simplify (3xy³ + 8x²y - 3xy) + (7xy³ - 9x²y + 6xy).
O4xy³ - x²y - 3xy
O4xy³ - x²y + 3xy
O 10xy³ + x²y - 3xy
O 10xy³x²y + 3xy
Answer: 10xy³ - x²y + 3xy
Step-by-step explanation:
To simplify the expression (3xy³ + 8x²y - 3xy) + (7xy³ - 9x²y + 6xy), we can combine like terms.
Adding the corresponding terms together, we have:
3xy³ + 7xy³ = 10xy³
8x²y - 9x²y = -x²y
-3xy + 6xy = 3xy
Combining these terms, the simplified expression becomes:
10xy³ - x²y + 3xy
Therefore, the correct option is:
O 10xy³ - x²y + 3xy
