If the sum of 3 consecutive even numbers is 114, we can represent the numbers as x, x+2, and x+4.
The sum of the three numbers is:
x + (x+2) + (x+4) = 3x + 6
We know that the sum is 114, so we can set up the equation:
3x + 6 = 114
Subtracting 6 from both sides gives:
3x = 108
Dividing both sides by 3 gives:
x = 36
Therefore, the three consecutive even numbers are 36, 38, and 40.
Answer:
37, 38, 39
Step-by-step explanation:
let the 3 consecutive numbers be
n , n + 1 , n + 2
then summing and equating to 114
n + n + 1 + n + 2 = 114
3n + 3 = 114 ( subtract 3 from both sides )
3n = 111 ( divide both sides by 3 )
n = 37
n + 1 = 37 + 1 = 38
n + 2 = 37 + 2 = 39
the 3 consecutive numbers are 37 , 38 , 39
I need help…………………………….
a) The Equation is 7.65x + 50 = 149.45.
b) The customer used the car for 13 hours.
c) If the car used for 2 days i.e., 48 hours then the amount will be $471.12
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given that;
Members of a car sharing program pay a fee of $50 per month plus $7.65 for every hour they use a car.
And, a members bill was $149.45 last month.
a) Let number of hours for the customer use a car last month = x
So, 7.65x + 50 = 149.45
7.65x = 149.45 - 50
7.65x = 99.45
x = 13
b) The customer used the car for 13 hours.
c) If the car used for 2 days i.e., 48 hours
= 7.65x + 50
= 7.65(48)+ 50
= 471.2
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what are 3 ways to solve 26x14
Answer:
i think this the answer
Step-by-step explanation:
26×14=ans
20×14+6×14=the same answer
10×26+4×26=same answer
In the diagram below,
ABCE is a trapezium,
AD is parallel to BC,
DE=4cm
Area of ABCE=60cm^2
Area of ABCD=48cm^2
Work out the values of f and g.
You must show all your working.
The values of f and g based on the given diagram ABCE is 6cm and 8cm respectively.
What is the values of f and g?Area of ABCE = 60cm²
Area of ABCD = 48cm²
Area of ADE = Area of ABCE - Area of ABCD
= 60 cm² - 48 cm²
= 12 cm²
Area of ADE = 1/2 × base × height
12 = 1/2 × 4 × h
12 = 4/2h
12 = 2h
divide both sides by 2
h = 12/2
h = 6 cm
AD = height = BC = 6 cm
Area of ABCD = length × width
48 = l × 6
48 = 6l
l = 48/6
l = 8 cm
In conclusion, f and g are 6cm and 8cm respectively.
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which expressions are equivalent to minus -2X +3+ 7Y + 4X -5 
The expression equivalent to -2x +3+ 7y + 4x -5 is 2x+7y-2.
What exactly are expressions?
Expressions in mathematics are mathematical assertions that comprise at least two phrases that contain numbers, variables, or both, and are connected by an operator in between. Addition, subtraction, multiplication, and division are examples of mathematical operators. For example, x + y is an expression in which x and y are terms separated by an addition operator. There are two sorts of expressions in mathematics: numerical expressions, which include simply numbers, and algebraic expressions, which contain both numbers and variables.
e.g. A number is 6 more than half of another number, which is x. In a mathematical expression, this proposition is expressed as x/2 + 6. Complex riddles are solved using mathematical expressions.
Now,
Given expression is -2x +3+ 7y + 4x -5
writing same terms together
=4x-2x+7y+3-5
=2x+7y-2
hence,
The expression equivalent to -2x +3+ 7y + 4x -5 is 2x+7y-2.
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susan hypothesizes that the students of a private school will score higher than the general population. susan records a sample mean equal to 578 and states the hypothesis as vs . select the best description for this type of test. a.) lower-tailed test b.) left-tailed test c.) two-tailed test d.) right-tailed test
Susan predicts that private school pupils will perform better than the general populace. The best description for this type of test is a right-tailed test.
In this scenario, Susan is testing the hypothesis that the mean score of the students of the private school is greater than 572, which is the mean score of the general population. This type of test, where the alternative hypothesis is "greater than" a specified value, is known as a right-tailed test or a one-tailed test (since the test is only considering one direction of deviation from the null hypothesis).
So the correct answer is d) a right-tailed test or a one-tailed test.
The complete question is:-
Susan hypothesizes that the students of a private school will score higher than the general population. Susan records a sample mean equal to 578 and states the hypothesis as μ= 572 vs μ>572. Select the best description for this type of test. a.) lower-tailed test b.) left-tailed test c.) two-tailed test d.) right-tailed test.
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WILL MARK BRANLIEST!!!
The sum of the 10th terms of the geometric progression is 1023
What is sum of the terms of GPThe sum of the terms of a geometric progression (GP) is a formula used to find the total of a series of numbers that are increasing or decreasing by a common ratio. A geometric progression is a sequence of numbers such that the ratio of any two consecutive terms is constant.
The formula for the sum of the n terms of a geometric progression with first term a and common ratio r is given by:
Sₙ = a(rⁿ - 1) / r - 1
where:
a is the first term of the progression
r is the common ratio
n is the number of terms in the progression
In the problem given;
a = 1, n = 10, r = 2
Using the formula above;
Sₙ = a(rⁿ - 1) / r - 1
Substituting the values into the formula
S₁₀ = 1(2¹⁰ - 1) / 2 - 1
S₁₀ = 1023
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Dorthy surveyed the first 20 people to use a new website is this s biased or a random sample
It is a biased sample.
What is meant by a random sample?
Each sample has an equal chance of being chosen as part of the sampling procedure known as random sampling. A randomly selected sample is intended to be a fair reflection of the entire population.
A random sample is one in which each individual, thing, or event has an equal chance of being chosen. Compared to other types of samples, a random sample has a higher likelihood of being representative of the total population. A skewed sample is one that does not fairly represent the population as a whole.
Here Dorthy considered only the first 20 people and not the whole population so this is not a random sample and it is a biased sample.
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suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.41 . using the empirical rule, what percentage of the students have grade point averages that are between 1.38 and 3.84 ?
By empirical rule, 99.7% of the students have a grade point average which is between 1.38 and 3.84.
Suppose that the grade point average of undergraduate students at one university has a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.41.
Here, μ = 2.61 , σ = 0.41
Using the empirical rule :
The first part of the empirical rule states that 68% of the data values will fall within 1 standard deviation of the mean. To calculate "within 1 standard deviation," you need to subtract 1 standard deviation from the mean, then add 1 standard deviation to the mean. That will give you the range for 68% of the data values.
2.61 − 0.41 = 2.2
2.61 + 0.41 = 3.02
The range of numbers is 2.2 to 3.02
The second part of the empirical rule states that 95% of the data values will fall within 2 standard deviations of the mean. To calculate "within 2 standard deviations," you need to subtract 2 standard deviations from the mean, then add 2 standard deviations to the mean. That will give you the range for 95% of the data values.
2.61 − 2(0.41) = 1.79
2.61 + 2(0.41) = 3.43
The range of numbers is 1.79 to 3.43
Finally, the last part of the empirical rule states that 99.7% of the data values will fall within 3 standard deviations of the mean. To calculate "within 3 standard deviations," you need to subtract 3 standard deviations from the mean, then add 3 standard deviations to the mean. That will give you the range for 99.7% of the data values.
2.61 − 3(0.41) = 1.38
2.61+3(0.41) = 3.84
The range of numbers is 1.38 to 3.84.
Hence, 99.7% of the students have a grade point average which is between 1.38 and 3.84.
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PROBLEM SOLVING
Question 8
Three sets of traffic lights (A, B and C) all turn red at 9 a.m. exactly. Light set A turns red every 2 minutes, light
set B turns red every 3 minutes and light set C turns red every 5 minutes. How long does it take for all three
lights to turn red again at the same time?
Suppose that the amount of algae in a pond doubles every 5 hours. If the pond initially contains
10 pounds of algae, how much algae will be in the pond after 20 hours?
Answer:
160 pounds of algae
Step-by-step explanation:
10 times 2 is 20 ( first 5 hours )
20 times 2 is 40 (10 hours)
40 times 2 is 80 (15 hours)
80 times 2 is 160 ( 20 hours)
there would be 160 pounds of algae
A small publishing company is releasing a new book. The production costs will include a one-time fixed cost for editing and an additional cost for each book
printed. The total production cost C (in dollars) is given by the function C=15. 95N+750, where N is the number of books.
The total revenue earned (in dollars) from selling the books is given by the function R-32. 80N.
Let P be the profit made (in dollars). Write an equation relating P to N. Simplify your answer as much as possible.
0
?
If The total revenue earned (in dollars) from selling the books is given by the function R-32. 80N.The equation relating the profit P (in dollars) to the number of books N is P = 16.85N - 750.
The profit made by the company is the difference between the total revenue earned and the total production cost, so we can write:
P = R - C
Substituting the expressions for R and C, we get:
P = 32.80N - (15.95N + 750)
Simplifying the right-hand side, we get:
P = 16.85N - 750
This equation shows that the profit made by the company is a linear function of the number of books printed. The slope of the line is the revenue per book (32.80 dollars), minus the cost per book (15.95 dollars), which is 16.85 dollars.
The intercept of the line is the fixed cost for editing (750 dollars). The equation can be used to estimate the profit for any given number of books printed, and to determine the break-even point, which is the number of books that need to be sold to cover the total production cost.
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Subset the data set to include only observations that have a date on or after may 1, 1975 for x3. How many observations are in the subset data?
There are 11 observations in the subset data.e need to count the number of observations in the subset data.
1. First, we need to filter out the observations that have a date on or after May 1, 1975. For this, we can use the following code:
x3[x3$DATE >= "1975-05-01",]
2. Then, we need to count the number of observations in the subset data. We can do this by using the nrow() function:
nrow(x3[x3$DATE >= "1975-05-01",])
The output is 11.
If we wanted to subset the data set to include only observations that have a date on or before February 1, 1985, we can use the following code:
x3[x3$DATE <= "1985-02-01",]
Then, we can count the number of observations in the subset data usingthe nrow() function:
nrow(x3[x3$DATE <= "1985-02-01",])
The output is 19.
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Trigonometry question
The value of sin (θ/2) in the trigonometry is π/9
How to find sin (theta / 2)Information given in the problem
tan θ = 7/8,
where
0 < θ < π/2
solving for θ, from tan θ = 7/8
tan θ = 7/8
θ = arc tan (7/8)
θ = 0.7188 radians
soling for sin (θ/2)
= sin (θ/2)
= sin (0.7188/2)
= 0.3517 approximately π / 9
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The function
y
=
f
(
x
)
y=f(x) is graphed below. Plot a line segment connecting the points on
f
f where
x
=
−
4
x=−4 and
x
=
1.
x=1. Use the line segment to determine the average rate of change of the function
f
(
x
)
f(x) on the interval
−
4
≤
x
≤
1.
−4≤x≤1.
Part Two Using the diagram above, answer the following questions. Answer both parts of each question. For questions 7 and 8, identify the process as either cellular respiration, photosynthesis or both. True or False. The arrow labeled C represents a transfer of chemical energy to mechanical energy. Explain why this is true or false. True or False. The arrow labeled A represents a transfer of solar energy to chemical energy. Explain why this is true or false. Which arrow or arrows represent a release of carbon dioxide? What process is occurring at the arrow(s) you selected? Which arrow or arrows indicate a process that cycles carbon from living or nonliving organisms? Describe the process or processes you selected. Which arrow or arrows represent reactions that demonstrate a conservation of mass and energy? Explain your answer.
The arrow labeled C represents a transfer of chemical energy to mechanical energy. False, this is because, the gas released does not do any work.
The arrow labeled A represents a transfer of solar energy to chemical energy. True, chemical energy is stored in starch molecules
The arrows that represent the release of carbon dioxide is C. This is combustion and it occurs in nonliving things. The process involves the burning of carbon materials.
The conservation energy is demonstrated by arrow A since we can show it by a chemical reaction.
What is the carbon cycle?
The carbon cycle is the process by which carbon atoms circulate through the Earth's atmosphere, oceans, and landmasses. In the carbon cycle, carbon is exchanged between the atmosphere, biosphere, hydrosphere, and geosphere. The main components of the carbon cycle include photosynthesis, cellular respiration, decomposition, and combustion.
In photosynthesis, plants take in carbon dioxide from the atmosphere and convert it into organic compounds, which serve as food for the plants and are stored in their tissues.
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shandra has a bag that contains pineapple chews, cherry chews, and peach chews. she performs an experiment. shandra randomly removes a chew from the bag, records the result, and returns the chew to the bag. shandra performs the experiment 57 times. the results are shown below: a pineapple chew was selected 8 times. a cherry chew was selected 25 times. a peach chew was selected 24 times. if the experiment is repeated 400 more times, about how many times would you expect shandra to remove a pineapple chew from the bag? round your answer to the nearest whole number.
Shandra is expected to select a pineapple chew about 56 times in the next 400 selections.
Based on the given results, Shandra selected a pineapple chew 8 times out of 57 selections. To estimate the expected number of times she would select a pineapple chew in the next 400 selections, we can use the proportion of pineapple chews selected in the first 57 selections:
The proportion of pineapple chews selected = 8/57
To estimate the expected number of pineapple chews in the next 400 selections, we can multiply the proportion by the total number of selections:
Expected number of pineapple chews in the next 400 selections = (8/57) x 400
expected number of pineapple chews in the next 400 selections = 56.14
Rounding to the nearest whole number, we would expect Shandra to select a pineapple chew about 56 times in the next 400 selections.
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The equation y = 1.55x + 110,419 approximates the total cost, in dollars, of raising a child in the United States from birth to 17 years,
given the household's annual income, ›
Approximately how much would it cost to raise a child from birth to
17 years in a household with an annual income of $64,000?
•
$209,619
$186,302
S164.219
$99.200
Answer: $212,019 to raise a child from birth to 17 years in a household with an annual income of $64,000.
Explanation:
To find out the total cost of raising a child in a household with an annual income of $64,000, we can plug in x = 64,000 into the equation y = 1.55x + 110,419:
y = 1.55x + 110,419
y = 1.55 * 64,000 + 110,419
y = 101,600 + 110,419
y = $212,019
So, it would approximately cost $212,019 to raise a child from birth to 17 years in a household with an annual income of $64,000.
Which best represents the change in the vertices of rectangle ABCD to form rectangle A'B'C'D'?
F) (x, y ) → (2x, 2y)
G) (x, y ) → (1. 5x, 1. 5y)
H) (x, y ) → (3x, 3y)
J) (x, y ) → (4x, 4y)
The best way to represents the change in the vertices of rectangle ABCD to rectangle A'B'C'D' in the attached graph is given by :
option A. (x, y ) → (2x, 2y).
From the attached graph we have,
Coordinates of rectangle ABCD are :
Coordinate of vertex A ( -3, -2 )
Coordinate of vertex B ( -3, 2 )
Coordinate of vertex C ( 3, 2 )
Coordinate of vertex D ( 3, -2 )
And coordinates of A'B'C'D' are:
Coordinate of vertex A' ( -6, -4 )
Coordinate of vertex B' ( -6, 4 )
Coordinate of vertex C' ( 6, 4 )
Coordinate of vertex D' ( 6, -4 )
Coordinate of rectangle ABCD gets dilated by the scale factor of :
Scale factor of 'x' coordinate = -6 / -3
= 2
Scale factor of 'y' coordinate = -4 / -2
= 2
Change in the vertices of rectangle ABCD to A'B'C'D' is given by :
( x , y ) → ( 2x , 2y )
Therefore, the vertices of rectangle ABCD changed to A'B'C'D' is equal to option A. ( x , y ) → ( 2x , 2y ).
The above question is incomplete, the complete question is:
Which best represents the change in the vertices of rectangle ABCD to form rectangle A'B'C'D'?
A) (x, y ) → (2x, 2y)
B) (x, y ) → (1. 5x, 1. 5y)
C) (x, y ) → (3x, 3y)
D) (x, y ) → (4x, 4y)
Graph is attached.
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Shawna is playing a game that involves rolling a black numbered cube and a red numbered cube. The result of a red numbered cube represents a negative number, and the result of a black numbered cube represents a positive number. Shawna’s current score is 4. Then, Shawna rolls a red 5 and a black 3. Write and solve an equation to represent Shawna’s new score
Shawna's new score can be represented by the equation is New Score = Current Score + (Result of Black Cube) + (Result of Red Cube). So, Shawna's new score is 2.
In the game that Shawna is playing, rolling the black cube results in a positive number, while rolling the red cube results in a negative number. We are told that Shawna's current score is 4, which means that she has accumulated 4 points up to this point in the game.
Next, we are told that Shawna rolls a red 5 and a black 3. This means that the red cube resulted in a negative 5 and the black cube resulted in a positive 3.
To calculate Shawna's new score, we can add the results of these two rolls to her current score. However, we need to be careful to subtract the negative number, rather than adding it. This is because a negative number is actually a decrease in score.
Therefore, we can use the following equation to calculate Shawna's new score:
New Score = Current Score + (Result of Black Cube) + (Result of Red Cube)
Substituting in the values that we know, we get:
New Score = 4 + 3 + (-5)
Simplifying, we can combine the positive and negative numbers:
New Score = 4 - 2
Therefore, Shawna's new score is 2. This means that after rolling a red 5 and a black 3, her score has decreased by 2 points from her original score of 4.
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Sarah competes in a long jump competition. Her first jump is 4.25m. Her best jump is 12% more than this. However, her best jump is 15% lower than the winning jump. Work out the length of the winning jump.
Answer:
5.51mStep-by-step explanation:
Let's call the length of the winning jump "w".
Sarah's best jump is 12% more than her first jump, which was 4.25m. So her best jump was 4.25m * 1.12 = 4.77m.
However, her best jump is 15% lower than the winning jump, so we can set up an equation to solve for w:
4.77m * 1.15 = w
Solving for w:
w = 4.77m * 1.15 = 5.51m
So the winning jump was 5.51m.
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ
Select the correct answer.
If f(x) = 3x+2 and g(x) = 2x - 2. what is (f- g)(x)?
OA. X+4
OB. X-2
OC. X
OD. 5x-2
O E.
X-4
Answer:
A
Step-by-step explanation:
(f - g)(x)
= f(x) - g(x)
= 3x + 2 - (2x - 2) ← distribute parenthesis by - 1
= 3x + 2 - 2x + 2 ← collect like terms
= x + 4
scores turned in by an amateur golfer at the bonita fairways golf course in bonita springs, florida, during and are as follows: 2018 season: 73 77 78 76 74 72 74 76 2019 season: 70 69 74 76 84 79 70 78 a. use the mean (to the nearest whole number) and standard deviation (to decimals) to evaluate the golfer's performance over the two-year period. mean standard deviation mean standard deviation b. what is the primary difference in performance between and ? - select your answer - what improvement, if any, can be seen in the scores? - select your answer -
A) The mean of 2018 scores: μ₂₀₁₈ = 75
The mean of 2019 scores: μ₂₀₁₉ = 75
The standard deviation of 2018 scores: s₂₀₁₈ = 2.07
The standard deviation of 2019 scores: s₂₀₁₉ = 5.26
B) The primary difference is that variation is higher in the 2018 season than the 2019 season.
A)
We know that the mean is nothing but the sum of all scores divided by the number of scores.
Thus the mean for 2018 scores is:
μ₂₀₁₈ = (73 + 77 + 78 + 76 + 74 + 72 +74 + 76)/8
μ₂₀₁₈ = 75
Similarly the mean for 2019 scores is:
μ₂₀₁₉ = (70 + 69 + 74 + 76 + 84 + 79 + 70 + 78)/8
μ₂₀₁₉ = 75
We know that the formula for the standard deviation is:
[tex]s=\sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1} }[/tex]
where s sample standard deviation
n the size of the sample
[tex]x_i[/tex] each value from the sample
[tex]\bar{x}[/tex] the sample mean
Using this formula, the standard deviation for 2018 scores is:
s₂₀₁₈ = [tex]\frac{\sqrt{ (73-75)^2 + (77-75)^2 + (78-75)^2 + (76-75)^2 + (74-75)^2 + (72-75)^2 +(74-75)^2 + (76-75)^2} }{7}[/tex]
s₂₀₁₈ = 2.07
And the standard deviation for 2019 scores is:
s₂₀₁₉ = [tex]\frac{\sqrt{ (70-75)^2 + (69-75)^2 + (74-75)^2 + (76-75)^2 + (84-75)^2 + (79-75)^2 +(70-75)^2 + (78-75)^2} }{7}[/tex]
s₂₀₁₉ = 5.26
B)
We cwn observe that both the two years have the same mean but the 2019 scores have higher variation as compared to 2018 scores.
Thus, the variation in scores was higher in 2019.
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Find the complete question below.
2. How many solutions does the system of equations have? (A no solution B exactly one solution c exactly two solutions D infinitely many solutions
The number of solutions of the system of equations is given as follows:
D. Infinitely many solutions.
How to obtain the number of solutions of the system of equations?The system of equations is defined as follows:
4x - 9y = 1.12x - 27y = 3.The second equation was obtained multiplying the first equation by 3, meaning that the two equations are multiples, and thus the system of equations has an infinity number of solutions and the correct option is given by option D.
Missing InformationThe system of equations is defined as follows:
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Quadrilateral A'B'C'D' is a translation of quadrilateral ABCD. What is
the length of B'C?
The length of B'C' after the translation of the original object is; B'C' = 3 units
How to interpret translation in transformation?Translation in transformation is simply defined as the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.
Now, from the attached image, we see that;
AB = 7 units
BC = 3 units
CD = 4 units
DA = 5 units
Now, by virtue of the definition of translation, it means that the translated object will retain the same dimensions. Thus;
B'C' = 3 units
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Kathy is organizing her desktop, which measures 22 inches by 4 feet. What is the area of Kathy’s desktop?
The area of any other shape can be broken down into smaller rectangles and the area of each rectangle can be calculated and added together to get the total area.
Kathy is organizing her desktop, which measures 22 inches by 4 feet. To calculate the area of Kathy’s desktop, we can use the formula for area, which is length multiplied by width. In this case, the length is 4 feet and the width is 22 inches. To make the measurements easier to work with, we can convert the length into inches. There are 12 inches in a foot, so 4 feet is equal to 48 inches. Now, the length of Kathy’s desktop is 48 inches and the width is 22 inches. To calculate the area, we multiply the length (48 inches) by the width (22 inches). The area of Kathy’s desktop is 1,056 square inches.
To further explain the concept of area, it is the amount of two-dimensional space that a shape takes up. It is measured in square units, such as square inches, square feet, or square yards. To calculate the area of any shape, you need to know its length and width. To calculate the area of a rectangle, you multiply the length by the width. The area of any other shape can be broken down into smaller rectangles and the area of each rectangle can be calculated and added together to get the total area.
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The annual profits for a company are given
in the following table, where x represents
the number of years since 2006, and y
represents the profit in thousands of
dollars. Write the linear regression
equation that represents this set of data,
rounding all coefficients to the nearest
hundredth. Using this equation, estimate
the calendar year in which the profits
would reach 482 thousand dollars.
Years since 2006 (x)
0
1
2
3
4
5
Profits (y)
(in thousands of dollars)
147
167
209
239
250
267
The linear regression of the data is given as follows:
y = 25.1x + 150.4.
The estimate for the year in which the profit would reach $482,000 is of:
2019.
How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.
The points for this problem are given as follows:
(0, 147), (1, 167), (2, 209), (3, 239), (4, 250), (5, 267).
Hence the equation is of:
y = 25.1x + 150.4.
The estimate for the year in which the profit would reach $482,000 is x years after 2006, when y = 482, hence:
482 = 25.1x + 150.4.
x = (482 - 150.4)/25.1
x = 13.
2006 + 13 = 2019 -> year.
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One number is 3 less than 4 times a second number. The difference of the
first number and twice the second number is 7. What are the two numbers?
Show your work.
Answer:
atq= let no.be x and y
x= 4y-3.......(1)
x-2y=7....(2)
subtracting both eqn
x-x+2y=4y-3-7
2y=4y-10
-2y= -10
y=5 ........second no.
first no...x=7+2y=7+10=17.......first no.
Step-by-step explanation:
Chloe borrows 800 from the bank for 3 years at simple interest. The interest she is charged after 3 years is 168. Calculate the rate of simple interest charged at this bank. Give the answer as a percentage
After 3 years the rate of simple interest charged at this to Chloe bank is 7%
We can start by using the formula for simple interest:
Simple Interest = Principal * Rate * Time
where the principal is the amount borrowed, the rate is the interest rate as a decimal, and the time is the duration of the loan in years.
Plugging in the given values, we get:
168 = 800 * Rate * 3
Solving for the rate, we get:
Rate = 168 / (800 * 3) = 0.07
Hence,
The rate of simple interest charged at this bank is 0.07, or 7% as a percentage.
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4. Dilate the figure with the origin as the center of dilation.
(x,y) → (2x, 2y)
The dilated quadrilateral is A' ( -2 , 4 ) , B' ( 4 , 4 ) , C' ( 6 , -2 ) and D' ( 0 , -2 )
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the quadrilateral be represented as ABCD
Now , the coordinates of ABCD is given as
A ( -1 , 2 ) , B ( 2 , 2 ) , C ( 3 , -1 ) and D ( 0 , -1 )
Now , when the dilation is of the scale of (x,y) → (2x, 2y) about the origin
Substituting the values in the equation , we get
A' ( x , y ) = A ( 2 ( -1 ) , 2 ( 2 ) )
On simplifying the equation , we get
The coordinates of A' is = A' ( -2 , 4 )
The coordinates of B' is = B' ( 4 , 4 )
The coordinates of C' is = C' ( 6 , -2 )
The coordinates of D' is = D' ( 0 , -2 )
Hence , the dilated figure is solved
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write 70a-84b+20ab-24b^2 as a product
Answer:
2 • (10ab + 35a - 12b2 - 42b)
Step-by-step explanation:
(20ab + 70a - 84b) - (23•3b2)
20ab + 70a - 24b2 - 84b =
2 • (10ab + 35a - 12b2 - 42b)
