The required equations can be used to model the situation is x = 1/2y - 3 and y = 10(x-1)
What is equation ?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
Equations can be classified as either conditional equations or identities. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth. When two expressions are joined together by the equals sign ("="), the result is an equation.
If the smaller number is 3 less than half a larger number, this is expressed as:
x = 1/2y - 3 ⇒(1)
If the larger number is 10 times 1 less than the smaller number, this is expressed as;
y = 10(x-1) ⇒ (2)
Substitute equation 2 into 1 as shown;
x = 1/2y - 3
x = 1/2(10x-10)- 3
x = 5x - 5 - 3
-4x = -8
x = 2
The required equations can be used to model the situation is x = 1/2y - 3 and y = 10(x-1)
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Answer:
a d
Step-by-step explanation:
If you can make payments of $450 on a 5-year loan that has an APR of 6.5%,
what is the maximum loan amount you can afford?
Answer:
To determine the maximum loan amount you can afford, you need to know the amount of your monthly payment and the annual percentage rate (APR) of the loan. The APR is the interest rate of the loan, expressed as a yearly rate. It takes into account not only the interest rate, but also any fees or other charges associated with the loan.
In this case, you know that you can make monthly payments of $450 and that the APR of the loan is 6.5%. To determine the maximum loan amount you can afford, you can use the following formula:
Maximum loan amount = (Monthly payment / (APR / 100 / 12)) * (1 - (1 + (APR / 100 / 12))^-n)
where n is the number of monthly payments. In this case, you are taking out a 5-year loan, which means you will make 60 monthly payments (5 years * 12 months/year = 60 months), so n = 60. Plugging these values into the formula, we have
Maximum loan amount = ($450 / (6.5% / 100 / 12)) * (1 - (1 + (6.5% / 100 / 12))^-60)
= ($450 / 0.00542) * (1 - (1 + 0.00542)^-60)
= $83,146.54
Therefore, the maximum loan amount you can afford is $83,146.54. This is the maximum amount you can borrow, assuming that you make monthly payments of $450 and the APR of the loan is 6.5%. You should carefully consider your ability to make these monthly payments before taking out a loan of this amount.
Step-by-step explanation:
Answer: Monthly Payment: $8.80
Total Interest Paid: $78.29
Total Paid: $528.29
Step-by-step explanation:
during dry weather the water level in a river drops by 2.6 inches each day for 4 days which expressions can represent the total change in water level in inches choose all that apply
Answer:
Step-by-step explanation:..:&:&:&:
The answer to this Question related to Water Level is 10.4 inch
What is water level?
It is mark for safe amount of water in seas oceans etc and which is safe for Humans and Nature but sometimes due to heavy rains water level increase that is not good most of the times
Solution:
Here we can see water level rise per day = 2.6 inch
and rain continued for 4 days
hence after 4 days total water level reached = 2.6(4) = 10.4 inches
If rain would continued more than water level would've increased more
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During the _________________ stage, kids develop the ability to take in other people’s perspective and begin to make cause-and-effect connections between events in their surroundings.
Answer:
Concrete Operational Stage or Perceptive thinking
Easton went shopping for a new phone. Sales tax where he lives is 5.5%. The price of the phone is $26. Find the total price including tax. Round to the nearest cent.
The total price after the tax is given as $27.43.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
Given that,
The price of phone is $26.
And, the percent sales tax is 5.5%.
Now, the price of phone after tax can be calculated as,
26 + 5.5% of 26
= 26 + 5.5/100 × 26
= 27.43
Hence, the total price of the phone including tax is $27.43.
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The y-intercept of the function f(x) = :
2/3[x| + 4 is (0,4). If the
function is translated down 9 units, what will be the new y-intercept?
The new y-intercept of the function is (0. -5)
How to determine the new y-intercept?From the question, we have the following parameters that can be used in our computation:
f(x) = 2/3|x + 4}
y-intercept = (0. 4)
The function is translated by
9 units down
This is represented as
(x, y) = (x, y - 9)
Substitute the known values in the above equation, so, we have the following representation
New y-intercept = (0. 4 - 9)
Evaluate
New y-intercept = (0. -5)
Hence, the new y-intercept = (0. -5)
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Noah has $200.00 He spends $ 120.00 on a new coat . What percent of his money does Noah spend on his new coat.
Answer:
Step-by-step explanation:
120/200=.6(100)
=60
1) Give an example of a system of linear equations.
3x + 2y = 18
2x + 5y = 14 are both linear equations
The system of linear equations in two variables is an equation with two different variables. Any equation with different variables can be in this system.
The solution for this type of equation by solving and getting two different values for both x and y but the same values are used in both equations.
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The length of Benson’s desk is 6 feet. Which of the following illustrations is drawn to a scale of 1 centimeter = 3 feet?
Answer: 2 cm
Step-by-step explanation:
2 x 3 = 6
Graph a triangle ABC and perform a translation of (x + 4, y - 3) to create triangle A'B'C'.
1. Describe the transformation using words. Make sure you refer to the characteristics
and the coordinates.
2. Draw a line through points A and A' and through points B and B'. What do you
notice about the lines you drew? Do you think you would notice the same
characteristics if you drew another line through points C and C'? How do you know?
1. The translation was of 4 units right and 3 units down.
2. All the blue lines connecting the equivalent vertices will have a slope of -3/4.
What is the translation?
The translations of the triangle is given by the rule presented as follows:
(x,y) -> (x + 4, y - 3).
Hence the meaning of each of these translations is given as follows:
x -> x + 4 is a translation of four units right.y -> y - 3 is a translation of three units down.The coordinates of the original vertices are given as follows:
(0,0), (0,4), (3,0).
Then the coordinates of the translated vertices are given as follows:
(4,-3), (4,1), (7,-3).
For a linear function, the slope is given by the vertical change divided by the horizontal change.
From these translations, the changes are given as follows:
Vertical change of 3 units down, hence of -3.Horizontal change of 4 units right, hence of +4.Thus the slope of the linear function connecting the original vertices are given as follows:
m = -3/4.
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Which trigonometric ratio will not have the same value as sin A?
A.
COS A
B.
sin C
C.
tan C
D.
COS C
Answer: sin
Step-by-step explanation:
ASAP HELPPP!!
Before he started washing windows on weekends, Rob had $20. He earned $60 over each of the first three weekends that he spent washing windows. So far, Rob has not spent any of his money.
If n represents a whole number less than or equal to 3, which function shows the total amount of money Rob had after n weekends of washing windows?
A. t(n) = 20 + 60n
B. t(n) = 60 + 20n
C. t(n) = 200n
D. t(n) = 200
Answer:
A. t(n) = 20 + 60n
Step-by-step explanation:
$20 is the money Rob had before washing windows.
He earns $60 in each of the first three weekends. So he gains an additional $60 for each weekend.
n = the number of weekends
the total amount of dollars he will have is 20 + 60n
Answer:A. t(n) = 20 + 60n
Step-by-step explanation:
$20 is the money Rob had before washing windows.
He earns $60 in each of the first three weekends. So he gains an additional $60 for each weekend.
n = the number of weekends
the total amount of dollars he will have is 20 + 60n
Determine the APR.
1. Helen Olson needs an installment loan of $999.00. She must repay the loan in 24 months. The monthly
payment is $44.96.
Answer:
Based on the information you provided, it seems that Helen Olson is looking to take out a loan for $999.00 and will need to make monthly payments of $44.96 in order to repay the loan within 24 months. It is important for Helen to carefully consider the terms of the loan, including the interest rate and any fees that may be associated with the loan, to ensure that she is able to make the monthly payments and repay the loan in full within the agreed-upon time frame. It may also be helpful for Helen to create a budget and plan for how she will manage her finances to make sure she has enough money each month to make the loan payments.
A box of nails weighs 1 5/8 pounds. Mark used 3 1/3 boxes of nails to build his treehouse
How many pounds of nails did Mark use?
At one point the average price of regular unleaded gasoline was $3.65 per gallon. Assume that the standard deviation price per gallon is $0.06 per gallon and use Chebyshev's inequality to answer the following.
(a) What percentage of gasoline stations had prices within 4 standard deviations of the mean?
(b) What percentage of gasoline stations had prices within 1.5 standard deviations of the mean? What are the gasoline prices that are within 1.5 standard deviations of the mean?
(c) What is the minimum percentage of gasoline stations that had prices between $ 3.43 and $3.83 ?
Prices at 93.75% of gasoline stations were within four standard deviations of the mean. Prices at 44.44% of gas stations were within 1.5 standard deviations of the mean. The prices within 1.5 standard deviations of the mean are $3.56 to $3.74. The minimum percentage of gasoline stations with prices between $3.43 and $3.83 is 15.46%.
Chebyshev's inequality states that the proportion of data within k standard deviations of the mean is at least 1 - 1/k² for all values of k.
(a) To find the percentage of gasoline stations with prices within 4 standard deviations of the mean, we can plug k = 4 into the formula above to get 1 - 1/4² = 1 - 1/16 = 15/16 = 93.75%.
(b) To find the percentage of gasoline stations with prices within 1.5 standard deviations of the mean, we can plug k = 1.5 into the formula above to get 1 - 1/1.5² = 1 - 1/2.25 = 4/9 = 44.44%. The prices within 1.5 standard deviations of the mean are $3.65 +/- (1.5 × 0.06) = $3.65 +/- $0.09, so the prices within 1.5 standard deviations of the mean are $3.56 to $3.74.
(c) To find the minimum percentage of gasoline stations with prices between $3.43 and $3.83, we can use Chebyshev's inequality with k = ($3.83 - $3.43)/(0.06) = 4.17. Plugging this value into the formula gives us 1 - 1/k² = 1 - 1/17.3 = 15.46%, which is the minimum percentage of gasoline stations with prices between $3.43 and $3.83.
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Laws of Exponents with Integer Exponents
What is the value of {(-1/3)}⁻³ ?
19,683
1
-1
-19,683
The value of the expression ((-1/3)^3)^-3 is option (D) -19683
The given expression is
((-1/3)^3)^-3
The exponent is defined as the number of times the number is multiplied by its self. If the exponent is a^m, then the number a is multiplied m times
According to the power of the power rule is
(a^m)^n = a^(m×n)
We have to apply the power of the power rule in this question
((-1/3)^3)^-3 = (-1 / 3)^(3 × -3)
Multiply the numbers
=(-1 / 3)^-9
We know
(1/a)^-b = a^b
Then the terms will become
= -3^9
Find the power of the number
= -19683
Therefore, the result is -19683
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Which table shows a proportional relationship between x and y?
We can consider that table (A) shows a proportional relationship of 7/1.
What is the proportional relationship?Relationships between two variables that are proportional occur when their ratios are equal.
Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value.
The "constant of proportionality" is the name of this constant.
So, consider the tables as follows:
Table A:
7/1
14/2 = 7/1
28/4 = 7/1
35/5 = 7/1
Proportional relationship: 7/1
Now, we don't need to calculate further.
Therefore, we can consider that table (A) shows a proportional relationship of 7/1.
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I don't understand, someone please help me I am giving 100 points
Answer:
a=40
b=70
c=20
d=30
Step-by-step explanation:
Please help me with this I’m stuck on this and you can get 100 points while your at it.
If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the
fraction becomes 1.
What is the numerator of the fraction?
016
02
Answer:
Step-by-step explanation:
it all equals 4n+12=3d
David was asked to solve the problem below:
If a = 5x - 4 and b = 3x, what is the value of a - b?
David used the steps below to solve the problem
Step 1: a - b
Step 2: (5x-4) - 3x
Step 3: 5x-4-3x
Step 4: -2x
Determine whether David's solution is correct. If he is correct, show the work that proves he is
correct. If he made an error, explain what he should have done instead, and provide the correct
solution.
Answer:
not correctStep 4: 2x -4Step-by-step explanation:
You want to know if David's solution of -2x for (5x-4) -(3x) is correct, and what David should have done.
SolutionDavid's solution is correct up to Step 4.
At that point, it appears as though David treated -4 as if it were -4x. The constant cannot be combined with x terms. Step 4 should have been ...
Step 4: (5 -3)x -4 = 2x -4
David's incorrect solution should have been 2x -4.
What is the slope of the line that passes through the points (6, -5) and (−6,−5)?
Slope of the line having passing points (6,-5) and (-6,-5) is 0.
What do you mean by slope of the line?
A line's slope is defined as the ratio of the change in y coordinate to the change in x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
Hence, the change in y-coordinate with regard to the change in x-coordinate is given by,
m = change in y/change in x
Given passing points :
(6,-5) and (-6,-5)
Slope of the line having passing points (x,y) and (a,b) is given by [tex]\frac{b-y}{a-x}[/tex]
Slope of the line become , [tex]\frac{-5+5}{-6-6}[/tex] = [tex]\frac{0}{-12}=0[/tex]
Therefore, slope of the line having passing points (6,-5) and (-6,-5) is 0.
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Find m
(9x - 17)
(4x + 28)
The angle measurement of T is 80°.
What is an angle measurement?When two lines or rays intersect at a common point, an angle is formed. The common point is referred to as the vertex. An angle measure in geometry is the measurement of the angle formed by two rays or arms at a common vertex.Here given,
∠Q = (9x - 17)°
∠R = (4x + 28)°
Since ∠Q and ∠R are co-interior angles in parallel lines.
∠Q + ∠R = 180°
So,
(9x - 17) + (4x + 28) = 180°
= 9x - 17 + 4x + 28 = 180°
By adding x variables together,
13x + 11 = 180°
=> 13x = 180°-11
=> x = 169° ÷ 13
x = 13
By substituting x,
∠Q = 9 x 13 - 17
= 117 - 17
= 100°
∠Q + ∠T = 180° (angles on a straight line is 180°)
100 + ∠T = 180°
∠T = 180 - 100
∠T = 80°
Therefore the value of ∠T is 80°.
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- Using Eddie's time card, find his total pay for the week if his overtime rate is 2 times his regular hourly
rate of $17.25 per hour for a regular 37-hour week.
The expression that represents Eddie's pay for the week including overtimes are 34.5x + 638.25.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Assuming the no. of extra work hours to be 'x'.
He has a regular work hour of 37 which pays him $(17.25×37) = $638.25.
And his overtime rate is twice his regular rate which is $(2×17.25)
= $34.5.
Therefore, His total pay for the week including his overtime is,
= 34.5x + 638.25 and we can replace x with the given values in the chart
to find his pay for the week.
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Answer
Question for me please
Answer:
y=8/11x-2
Step-by-step explanation:
in y=mx+b, the m= the slope, and the b=the y-intercept
Type here to search
How can you find the value of y?
9y = 27
NE
O
i
B.
?
Add
Subtract
Multiply by
Divide by
A ?
on both sides.
Answer:
Step-by-step explanation:
Divide 9 on both sides and you'd get y=3
Pls help its urgent solve it
Answer:
[tex]x=-10[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{x+2}=-2 \\ \\ x+2=-8 \\ \\ x=-10[/tex]
100 points and will mark brainlest
The slope of the line in the function is 1
Slope of LineThe slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. So the change in y coordinate with respect to the change in x coordinate can be written as,
m = y₂ - y₁ / x₂ - x₁
Taking two points;
P = (5, 0)Q = (3, -2)Substituting the values into the formula;
m = -2 - 0 / 3 - 5
m = -2 / - 2
m = 1
The slope is calculated as 1
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HELP AGAIN PLEASE PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
4/6 and 1/6
Step-by-step explanation:
6 is the least common denominator found by multiplying 3 by 2
In the picture below, which lines are lines of symmetry for the figure?
A. 1 and 3
B. 2
C. only 3
D. 1, 2, and 3
Considering the given image, we can easily spot that (B) line 2 is the line of symmetry.
What are lines of symmetry?A form or item is divided into two equal and symmetrical portions by a line of symmetry.
Because it divides the figure symmetrically and the separated portions resemble mirror images of one another, we also refer to this line as the axis of symmetry or the mirror line.
Rotational symmetry, reflection symmetry, translation symmetry, and glide reflection symmetry are some examples of symmetries.
Planar symmetry, which refers to various types of symmetry on a flat surface, is illustrated by these four different types of symmetry.
So, according to the given image:
LIne 1 and 3 are not making the 2 identical halves of the figure.
Line 2 is making the exact identical half of the figure.
Therefore, considering the given image, we can easily spot that (B) line 2 is the line of symmetry.
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HELP ASAP PLEASE IVE BEEN WAITING ONE HOUR ILL GIVE BRAINLIEST
Question below