An equivalent expression of (5.1u + 8) + 6 is 5.1u + (8 + 6)
How to write an equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
(5.1u + 8) + 6
The associative property states that
(a + b) + c = a + (b + c)
Using the above as a guide, we have the following equation
(5.1u + 8) + 6 = 5.1u + (8 + 6)
Hence, the expression is 5.1u + (8 + 6)
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find area of isosceles triangle when the heights are both 13cm and the base is 10cm.
Create a polygon JKLMNOPQ that is a dilation of polygon ABCDEFGH with a scale factor of 3 about the origin
The dilated polygon and polygon are created. And the scale factor of the polygon STUVWXYZ to JKLMNOPQ will be 9.
What is dilation?Dilation is the methodology of expanding the dimensions of an object without impacting its appearance.
The coordinate of the polygon ABCDEFGH is given as,
(3, -3), (4, -4), (5, -3), (8, -6), (10, -4), (9, -3), (8, -4), (5, -1)
a) If the scale factor is 3, then the coordinate of the polygon JKLMNOPQ is given as,
⇒ 3 [(3, -3), (4, -4), (5, -3), (8, -6), (10, -4), (9, -3), (8, -4), (5, -1)]
⇒ (9, -9), (12, -12), (15, -9), (24, -18), (30, -12), (27, -9), (24, -12), (15, -3)
b) If the scale factor is 1/3, then the coordinate of the polygon STUVWXYZ is given as,
⇒ 1/3 x [(3, -3), (4, -4), (5, -3), (8, -6), (10, -4), (9, -3), (8, -4), (5, -1)]
⇒ (1, -1), (4/3, -4/3), (5/3, -1), (8/3, -2), (10/3, -4/3), (3, -1), (8/3, -4/3), (5/3, -1/3)
c) The polygon JKLMNOPQ and STUVWXYZ are similar. Then the scale factor is given as,
Scale factor = 9/1
Scale factor = 9
The diagram is given below.
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I need help with this review
The slope of f(x) = x² - x + 2 at x = 3 is 6.
How to calculate the slopeThe limit definition of a derivative is given by:
f'(x) = lim(h->0) [f(x+h) - f(x)] / h
To find the slope of f(x) = x² - x + 2 at x = 3, we need to evaluate this expression at x = 3.
f'(3) = lim(h->0) [f(3+h) - f(3)] / h
f'(3) = lim(h->0) [(3+h)² - (3+h) + 2 - (3² - 3 + 2)] / h
f'(3) = lim(h->0) [(9 + 6h + h² - 3 - h + 2 - 9 + 3 - 2)] / h
f'(3) = lim(h->0) (6h + h²) / h
f'(3) = lim(h->0) (h(6 + h)) / h
f'(3) = lim(h->0) (6 + h)
Now we can evaluate the limit by plugging in h = 0:
f'(3) = 6 + 0 = 6
Therefore, the slope of f(x) = x² - x + 2 at x = 3 is 6.
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EASY MATH POINTS!
Answer from the screenshot below :)
For the mapping diagram 1, we have that the domain and the range are given as follows:
The domain is: {10}.The range is: {-8, 2, 1.1}.It does not represent a function, as the input of 10 is mapped to different outputs.
For the mapping diagram 2, we have that the domain and the range are given as follows:
The domain is: {-8, 2, 1.1}.The range is: {10}.It represents a function, as each value of the input is mapped to a single output.
How to obtain the domain and the range of the diagram?The concepts for the domain and the range of the diagram are defined as follows:
Domain: all input values from which an arrow is departing.Range: all output values to which an arrow arrives.The mapping diagram will represent a function if each value of the input is mapped to a single output.
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Solve 9x^2-6x+1=2 using the square root property. Round to the nearest hundredth if necessary.
[tex]9x^2-6x+1=2 \iff (3x)^2-2(3x)+1=2\\[/tex]
[tex](3x - 1)^2 = 2[/tex]
[tex]3x-1=-\sqrt{2} \iff 3x = 1 - \sqrt{2} \implies x_{1} = \dfrac{1-\sqrt{2} }{3}\\[/tex]
[tex]3x-1=\sqrt{2} \iff 3x = 1 + \sqrt{2} \implies x_{2} = \dfrac{1+\sqrt{2} }{3}\\[/tex]
[tex](-0.14, \ 0.8)[/tex]
Levi wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three sides will be enclosed with wire fencing. If Levi has 400 feet of fencing, what dimensions would maximize the area of the pen? (a) Let w be the length of the pen perpendicular to the barn. Write an equation to model the area of the pen in terms of w
Answer:
Step-by-step explanation:
Let's call the length of the pen perpendicular to the barn "w", and the length parallel to the barn "l".
The total amount of fencing available is 400 feet. The side against the barn will be of length l, and the other two sides will each be of length w. Therefore, the total length of fencing required is:
l + 2w
This length of fencing must equal 400 feet:
l + 2w = 400
We want to maximize the area of the pen. The area of a rectangle is given by:
A = lw
We can use the equation l + 2w = 400 to solve for l:
l = 400 - 2w
Substituting this expression for l into the equation for the area, we get:
A = w(400 - 2w)
Simplifying:
A = 400w - 2w^2
So the equation to model the area of the pen in terms of w is:
A = 400w - 2w^2
Jeff claims that a number and its opposite will always have the same aboslute value. Is Jeff correct? Yes or no
Answer:
Step-by-step explanation:
yes
Yes, Jeff is correct.
The diagram shows Triangle ABC. What is the height of Triangle ABC? Show your work.
The height of Triangle ΔABC is calculated using Pythagoras theorem will be 8 units.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as,
H² = P² + B²
The height of Triangle ΔABC is given as,
17² = h² + 15²
289 = h² + 225
h² = 289 - 225
h² = 64
h = 8 units
The height of Triangle ΔABC is calculated using Pythagoras theorem will be 8 units.
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Calculate the rate of power drainage per hour if the capacity of the cell phone is 3600 mAh
calculate the rate of power drainage per hour if the capacity of the cell phone is 3600 mAh
how to find the length of a pond 85 feet across; 1 inch = 4 feet
Answer:
21.25 inches.
Step-by-step explanation:
I'm guessing that you want to find how many inches a pond is if 1 in. = 4 ft.
To do this, we have to take our feet 85.
Then, we divide by how many feet equals one inch.
85/4 = 21.25 inches.
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Step-by-step explanation:
he should have multiplied
How many minutes are there in 2 years?
Answer:1,051,200 minutes.
Step-by-step explanation:
To analyze how many minutes there are in a year will allow us to multiply that number by two to get how many minutes there are in two years.
GIVENThere are 365 days in a year.
There are 24 hours in a day.
There are 60 minutes in an hour.
SOLUTION365 days x 24 hours x 60 minutes
= 525, 600 minutes in one year
525, 600 minutes x 2 (year)
= 1, 051, 200 minutes
ANSWERThere are 1, 051, 200 minutes in 2 years.
The function, A,B and C represent the amount owed (in dollars)for a loan A,B and C respectively: the input for the functionalist t,the number of years without payment.
1. For each loan, find the average rate of change per year between:
a. the start of the loan and the end of the second year
IM
15.4: Comparing Average Rates of Change
The functions a, b, and e represent the amount owed (in dollars) for Loans A, B, and C
respectively: the input for the functions is t, the number of years without payments.
b. the end of the tenth year and the end of the twelfth year
Illustrative
Mathematics
2. How do the average rates of change for the three loans compare in each of the
two-year intervals?
a. Find (A(2)-A(0))/2, (B(2)-B(0))/2, and (C(2)-C(0))/2.
b. Find (A(12)-A(10))/2, (B(12)-B(10))/2, and (C(12)-C(10))/2. Compare the rates of change between the three loans for each interval.
a. To find the average rate of change per year between the start of the loan and the end of the second year, we need to calculate the difference in the amount owed after two years and the amount owed at the start of the loan, and then divide by two.
For loan A:
Average rate of change = (A(2) - A(0))/2
For loan B:
Average rate of change = (B(2) - B(0))/2
For loan C:
Average rate of change = (C(2) - C(0))/2
b. To find the average rate of change per year between the end of the tenth year and the end of the twelfth year, we need to calculate the difference in the amount owed at the end of the twelfth year and the amount owed at the end of the tenth year, and then divide by two.
For loan A:
Average rate of change = (A(12) - A(10))/2
For loan B:
Average rate of change = (B(12) - B(10))/2
For loan C:
Average rate of change = (C(12) - C(10))/2
2. We can compare the average rates of change for the three loans in each of the two-year intervals by comparing their values. If the average rate of change is positive, it means the amount owed is increasing, while if it is negative, it means the amount owed is decreasing. We can compare the rates to see which loan is increasing or decreasing at a faster rate in each interval.
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[tex]\sqrt{x} +\sqrt{8}=\sqrt{x+8}[/tex]
The equation [tex]\sqrt{x} +\sqrt{8}=\sqrt{x+8}[/tex] is an example of the square root property. The square root property states that for any real number a, b, and c, if and only if a + b = c. This property can be used to simplify and solve equations involving square roots.
What does square root mean?
The square root of a number is the number that, when multiplied by itself, produces the original number. For instance, the square root of 16 is 4, because 4 multiplied by itself (4 x 4) equals 16.
The equation [tex]\sqrt{x} +\sqrt{8}=\sqrt{x+8}[/tex] is true because it satisfies the square root property. To see this, note that [tex]\sqrt{x} +\sqrt{8}=\sqrt{x+8}[/tex] implies that x+8=x+8, which is true. Therefore, the equation is true.
To solve for x, we will use the square root property. We know that [tex]\sqrt{x} +\sqrt{8}=\sqrt{x+8}[/tex], so we can rewrite the equation as [tex]\sqrt{x} +\sqrt{8}-\sqrt{x+8}=0[/tex]. We can then use the square root property to simplify the equation to [tex]\sqrt{x} -\sqrt{x}=0[/tex], which implies that x=0. Therefore, the solution to the equation [tex]\sqrt{x} +\sqrt{8}=\sqrt{x+8}[/tex] is x=0.
In conclusion, the equation [tex]\sqrt{x} +\sqrt{8}-\sqrt{x+8}=0[/tex] is an example of the square root property, and the solution to the equation is x=0.
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8 ft
4 ft
8 ft
Find area
Answer:
Step-by-step explanation:
HI:
Area of rectangle: 8*8= 64
Area of triangle: 4*8=32/2= 16
64+16= 80
Answer: 80ft^2
Bob ran 4/5 of a mile his sister ran one-half of a mile how much further did Bob run than his sister
30% or 3/10
Bob is 4/5
His sister is 1/2
convert to percents so 80% and 50%
he ran 30% more of a mile (3/10)
The number of passes completed by Brett Favre, quarterback for the Green Bay
Packers, was recorded for each of the 16 regular season games in the fall of 2006
(www.espn.com).
15 31 25 22 22 19 17 28
24 5 22 24 22 20 26 21
a. Draw a stem and leaf plot to describe the data.
b. Calculate the mean and standard deviation for Brett Favre’s per game pass
completions.
c. What proportion of the measurements lie within two standard deviations of
the mean?
2
Camille made a quilt for her cousin's doll. The quilt had an 8 × 8 array of different color square patches. If each patch is 2 2/3 in long, what is the area of the whole quilt?
As a result, the total quilt's area is 512/9 square inches.
What is square used for?Square offers businesses a range of goods and services to help them complete sales deals, use marketing strategies, and control their finances, inventory, and workforce.
The quilt has an 8 x 8 array of square patches, which means it has a total of 8 x 8 = 64 square patches. Each square patch is 2 2/3 inches long.
To find the area of the whole quilt, we need to find the total area covered by all 64 square patches. We can do this by multiplying the length and width of one square patch by the total number of patches:
Area of one square patch = length x width = (2 2/3 in) x (2 2/3 in) = (8/3 in) x (8/3 in) = 64/9 sq in
Total area of all 64 square patches = (64 patches) x (64/9 sq in per patch) = 512/9 sq in
Therefore, the area of the whole quilt is 512/9 square inches.
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Find the length in each isosceles right triangle.
a. Find the leg if the hypotenuse is 102√
Leg =
b. Find the hypotenuse if the leg is 92√
Hypotenuse =
(33 points)
The answer of the given question based on the length in each isosceles right triangle is given below,
What is Isosceles right triangle?An isosceles right triangle is right triangle in which two legs have the same length, making it isosceles triangle, and one of angles is right angle, making it right triangle. an isosceles right triangle, two acute angles are congruent, each measuring 45 degrees, and hypotenuse is equal in length to legs multiplied by √2.
The isosceles right triangle is special case of 45-45-90 triangle, where angles measure 45 degrees, 45 degrees, and 90 degrees, respectively. In 45-45-90 triangle, the hypotenuse is equal in length to legs multiplied by √2.
a. If the hypotenuse is 102√, then each leg is the same length as the hypotenuse divided by √2. Therefore:
Leg = 102√/√2 = 102
b. If one leg is 92√, then the hypotenuse is the length of that leg multiplied by √2. Therefore:
Hypotenuse = 92√ * √2 = 92 * 2 = 184.
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Please help me answer the question in the file link
Answer:
x=65
Step-by-step explanation:
So how I would think the equation would be would be 108 + x = 173. So how I would solve this is subtracting 108 from both sides to get x = 65. There is most likely a different way to set this up but thats what comes to mind with me.
55 employees to employees 66
The required, there is a 20% increase from 55 employees to 66 employees.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
To calculate the percentage increase from 55 employees to 66 employees, we need to find the difference between the two numbers, divide that difference by the original number, and then multiply by 100 to convert the result to a percentage.
The difference between 66 and 55 is 11.
So, the percentage increase is:
(11/55) x 100% = 20%
Therefore, there is a 20% increase from 55 employees to 66 employees.
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The question seems to be incomplete, the complete question is shown below,
55 employees to employees 66, calculate the percentage increase?
HELP!!!!!! evaluate and fully simplify each of the following
For function f(x)= -4x²-4x-1, f(x+h)= -4x² - 8xh - 4h² - 4x - 4h - 1, (f(x+h) - f(x))/h= -8x - 4h - 4
Describe function ?The input values of a function are called the domain, and the output values are called the range. The domain can be any set of values, but each input value must have a unique corresponding output value. If there are multiple input values that produce the same output value, the function is not considered to be well-defined. Functions are used to model a wide range of phenomena in many different fields, including science, engineering, and economics. They are also used in calculus to study rates of change and slopes of curves.
To find f(x+h), we need to replace x with (x+h) in the given function:
f(x+h) = -4(x+h)² - 4(x+h) - 1
= -4(x² + 2xh + h²) - 4x - 4h - 1
= -4x² - 8xh - 4h² - 4x - 4h - 1
To find (f(x+h) - f(x))/h, we first need to find f(x):
f(x) = -4x² - 4x - 1
Then we can substitute f(x+h) and f(x) in the formula:
(f(x+h) - f(x))/h = (-4x² - 8xh - 4h² - 4x - 4h - 1 - (-4x² - 4x - 1))/h
= (-4x² - 8xh - 4h² - 4x - 4h - 1 + 4x^2 + 4x + 1)/h
= (-8xh - 4h² - 4h)/h
= -8x - 4h - 4
So, f(x+h) = -4x² - 8xh - 4h² - 4x - 4h - 1, and (f(x+h) - f(x))/h = -8x - 4h - 4.
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Sven can buy tomatoes for $2.50 a pound at Grandiose Grocers, one block from
his house.
He can get tomatoes for $2.00 a pound at EconoFoods, but he has to spend $3
on bus fare to get there and back.
The graph shows the cost of buying tomatoes from each grocery store.
How should the x-axis be labeled?
The x-axis should be labeled
How should the y-axis be labeled?
The y-axis should be labeled
What does the slope of each line represent?
The slope of each line répresents the
What does the y-intercept of each line represent?
The y-intercept of each line represents the
The x-axis should be the number of pounds of tomatoes bought.
The y-axis should be the total cost of x pounds of tomatoes.
The slope of each line represents the cost of tomatoes/pound.
The y-intercept of each line represents the bus fare.
What is an equation of the line?To determine which point would not be found on the line, we can use the slope-intercept form of the equation of a line, which is:
y = mx + b
As per the given data:
Tomatoes from Grandiose Grocers = $2.50/pound
Tomatoes from EconoFoods = $2/pound
Bus fare for EconoFoods = $3
The x-axis should be the number of pounds of tomatoes bought.
The y-axis should be the total cost of x pounds of tomatoes.
For Grandiose Grocers:
y = 2.50x
For EconoFoods:
y = 2x + 3
From comparing with the slope-intercept form of a line, y = mx + c
m(Grandiose Grocers) = 2.50 {cost of tomatoes per pound}
m(EconoFoods) = 2 {cost of tomatoes per pound}
c is the y intercept:
c(Grandiose Grocers) = 0 {bus fare is $0}
c(EconoFoods) = 3 {bus fare is $3}
Hence, The x-axis should be the number of pounds of tomatoes bought.
The y-axis should be the total cost of x pounds of tomatoes. The slope of each line represents the cost of tomatoes/pound. The y-intercept of each line represents the bus fare.
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y= X b X y C
find the y- intercept and write the slope equation to match slope intercept
The slope of the equation is -2/3 and the y-intercept is 14/3.
What is y-intercept?A y-intercept is the place where a line or curve crosses, or touches, the y-axis the vertical, often darkened line in the center of a graph.
Since, the equation is not clear, let us consider the equation, 2x+3y = 14
The slope intercept form of a line is given by =
y = mx+c, where m is the slope and the c is the y-intercept.
Converting the assumed equation into slope intercept form,
2x+3y = 14
3y = -2x+14
y = -2x/3+14/3
Here we get the slope = -2/3 and y-intercept = 14/3
Hence, the slope of the equation is -2/3 and the y-intercept is 14/3.
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Please help me anyone with this?!!!
Answer:
B
subtract 20
80,60,40.....
Step-by-step explanation:
it's the arithmetic sequence having difference of 20
Help me, please thank you
scatter plot, label each axis, and choose a
Over the last 8 snowstorms, Julian recorded the amount of
snowfall to the nearest inch and the amount of time it took him
to shovel his driveway. He recorded the data in the table.
Snowfall (in.)
2
5
8
18
10
6
12
14
Time Shoveling
1
2
2
5
3
2
4
4
Answer:
Have a good day and time and I6ykjjuu7ttggfszd to the 5tjyyv
Hello! 5/6 2/5 in simplest form
Answer:
Step-by-step explanation:
5/6 - 2/5 = 25/30 - 12/30 = 13/30
Answer:
Step-by-step explanation:
To subtract two fractions, we need a common denominator. The smallest number that 6 and 5 both divide into is 30.
Converting the fractions to have 30 as the denominator, we get:
5/6 = 25/30
2/5 = 12/30
Now we can subtract:
25/30 - 12/30 = 13/30
Therefore, 5/6 - 2/5 = 13/30 in simplest form.
Rewrite as a single logarithm: log 8 + log 3.
We can rewrite the sum of logarithms as:
log(8) + log(3) = log(24)
How to write this a single logarithm?
Remember that if we have two logarithms of the same base, then we can write:
log(a) + log(b) = log(a*b)
Here the base of the logarithms is the same, then we can use that rule, we can rewrite the given sum as:
log(8) + log(3) = log(8*3) = log(24)
That is the expression rewritten as a single logarithm.
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the parallelogram below has an area of 54 units²
The height of the parallelogram is 5.4 units.
What is area ?
In mathematics, the area is the measure of the size of a two-dimensional surface or region, usually expressed in square units, such as square inches or square meters. The area of a flat shape or planar figure is the amount of space inside its boundary, or the surface of the object, that is covered by a two-dimensional geometric shape.
One way to find the height is to draw a perpendicular line from point B to line segment AD, forming a right triangle. Let's call the length of this perpendicular line h.
Now we can see that the base of the parallelogram is 10 units (from A to D), and the height is h units (from B to the perpendicular line we drew). The area of the parallelogram is given as 54 units², so we can set up the following equation:
Area = base x height
54 = 10h
Solving for h, we get:
h = 54/10 = 5.4
Therefore, the height of the parallelogram is 5.4 units.
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