what is the value of x
The value of the variable x for the similar triangles is equal to 25
How to evaluate the value of x for the similar trianglesThe triangles BDR and QDC are similar, this implies that the length DC of the smaller triangle is similar to the length DR of the larger triangle
and the length DQ of the smaller triangle is similar to the length DB of the larger triangle
so;
x/(15 + x) = 40/64
64x = 40(15 + x) {cross multiplication}
64x = 600 + 40x
64x - 40x = 600 {subtract 40x from both sides}
24x = 600
x = 600/24
x = 25
Therefore, the value of the variable x for the similar triangles is equal to 25
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Which table of values represents the linear function y=4x+1
The values represents the linear function are:
x y
0 1
1 5
2 9
3 13
4 17
What is linear function ?
A linear function is a mathematical function that can be represented by a straight line on a graph. It has the form of:
y = mx + b
where m is the slope of the line, which determines how steeply the line rises or falls, and b is the y-intercept, which is the point where the line crosses the y-axis.
According to the question:
The table of values that represents the linear function y=4x+1 is:
x y
0 1
1 5
2 9
3 13
4 17
To generate these values, we can substitute different values of x into the equation y=4x+1 and solve for y.
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Q) which table of values represents the linear function y=4x+1 ?
Can somebody find me a pencil to write please
Try going to the store and they should be surprisingly cheap.
Answer: here it is.
Step-by-step explanation:
Please helpppp it’s urgent!!! Assume you have a balance of $3000 on a credit card with an APR of 24 %, or 2 % per month. You start making monthly payments of $200, but at the same time you charge an additional $100 per month to the credit card. Assume that interest for a given month is based on the balance for the previous month. How long does it take to pay off the credit card debt? Round your numbers to the nearest cent?
It will take around 3.72 months to pay off the credit card debt.
Explain about the annual percentage rate APR?The annual rate of interest that a person must pay on a loan or receives on a bank account is known as the annual percentage rate (APR).APR is utilized for everything, including credit cards, auto loans, and mortgages.The formula for APR is:
A = P * [tex](1 + r/n)^{nt}[/tex]
In which,
A = amount after compounding.
P = balance amount
r = rate of interest.
n = number of time compounded.
Initial balance: $30,000.
Payments per month = $200.
Expenses = $100
Balance amount = 30,000 - 12 *(200 - 100)
Balance amount = $28800
So, time taken for paying off credit card debt.
30,000 = 28800 [tex](1 + 0.24/1)^{1*t}[/tex]
[tex](1.24)^{t}[/tex] = 30,000 / 28800
[tex](1.24)^{t}[/tex] = 1.04
Solve by using logarithmic function.
t = ln (1.04) / 1.24
t = 0.31 year
t = 3.72 months
Thus, it will take around 3.72 months to pay off the credit card debt.
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Parts of similar triangles
Find x
The measurement of the side EF in ΔDEF is 13 units.
What's the triangle formula?Tο determine the area οf a triangle, use the fοrmula area = 1/2 * base * height. Determine the height οf the triangle frοm a base side. Then enter the base and height measurements intο the fοrmula.
Because the twο in the figure are similar, we can set up an equatiοn and sοlve fοr the unknοwn value οf x using the prοpοrtiοnality οf cοrrespοnding sides:
As ΔDEF ≅ ΔJHI
Then EF ≅ IH
3x - 2 = x + 8
3x - x = 8 + 2
2x = 10
x = 10/5
x = 5
EF = x + 8
= 5 + 8
= 13
Thus, The measurement of the side EF in ΔDEF is 13 units.
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Jump to level 1
What are m and b in the linear equation 3 + 7x + 11 + 10x = y?
m = Ex: 50 ÷
b = Ex: 50
Answer:
The given equation is 3 + 7x + 11 + 10x = y.
Simplifying the equation, we get:
y = 17x + 14
Comparing with the standard linear equation y = mx + b, we can see that:
m = 17
b = 14
Therefore, m = 17 and b = 14.
Decomposing numbers to add make a new 10 adding.
29+14
29 + 14 = 44 by decomposing numbers to add and make a new 10.
Describe Decomposition of numbers?Decomposition of numbers involves breaking a number down into its constituent parts or smaller numbers that add up to the original number. This can be done in different ways depending on the purpose and context of the problem.
For example, one common way of decomposing a number is by place value. In this case, the number is broken down into its digits, which represent different powers of ten. For instance, the number 562 can be decomposed into 500 + 60 + 2.
Another way of decomposing numbers is by factoring. In this case, the number is expressed as a product of its factors. For example, the number 12 can be decomposed as 2 x 2 x 3.
Decomposing numbers is a useful skill in many areas of mathematics, including arithmetic, algebra, and geometry. It is often used to simplify problems, make computations easier, and facilitate further analysis.
To decompose 29 to make a new 10, we can break it into 9 and 20. Then, to decompose 14 to make a new 10, we can break it into 6 and 8.
So, we have:
29 + 14 = (9 + 20) + (6 + 8)
Now, we can regroup the numbers to make a new 10:
= (9 + 1) + (20 + 6) + 8
= 10 + 26 + 8
= 44
Therefore, 29 + 14 = 44 by decomposing numbers to add and make a new 10.
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The box plots below show data from a survey of students under 14 years old. They were asked on how many days in a month they read and draw. Based on the box plots, which is a true statement about students? pg780337 A Most students read less than 12 days a month. B Most students draw at least 12 days a month. C Most students draw more often than they read. D Most students read more often than they draw.
The Correct answer is D) Most students read more often than they draw.as the median of the "read" plot is lower than the median of the "draw" plot.
Based on the box plots, we can see that:
The median for the "read" data is around 8 days per month, and the interquartile range (IQR) is between 4 and 12 days.
The median for the "draw" data is around 12 days per month, and the IQR is between 8 and 16 days.
So, we can conclude that:
A) Most students read less than 12 days a month. This is true, since the median for the "read" data is below 12 days per month, and the box plot shows that most of the data is concentrated in the lower half of the range.
B) Most students draw at least 12 days a month. This is not true, since the median for the "draw" data is around 12 days per month, and the box plot shows that there is a considerable amount of data below that median.
C) Most students draw more often than they read. This is not true, since the median for the "read" data is lower than the median for the "draw" data.
D) Most students read more often than they draw. This is true, since the median for the "read" data is lower than the median for the "draw" data, and the box plot shows that most of the "read" data is concentrated in the lower half of the range, while most of the "draw" data is concentrated in the upper half of the range.
The box plots below show data from a survey of students under 14 years old. They were asked on how many days in a month they read and draw. Based on the box plots, which is a true statement about students? pg780337 A Most students read less than 12 days a month. B Most students draw at least 12 days a month. C Most students draw more often than they read. D Most students read more often than they draw.
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The slope of a line is undefined, and the x-intercept is -7. What is the equation of the line?
Oy=-7
Ox=-7
Oy=-7x
Answer:
"Undefined slope"
Step-by-step explanation:
The line is vertical on the graph.
Every point on the line has the same x-coordinate.
If the line crosses the x-axis where x=-7, then the
x-coordinate of every point on the line is -7, and the
equation of the line is
x = -7 .
Hodgman Honest is evaluating a new project for her firm, Basket Wonders (BW). She has determined that the after-tax cash flows for the project will be $10,000; $12,000; $15,000; $10,000; and $7,000, respectively, for each of the Years I through 5. The initial cash outlay will be $40.000. For this project, assume that it is independent of any other potential projects that Basket Wonders may undertake. The management of Basket Wonders has set a maximum PBP of 3.5 years for projects of this type. Required: Evaluate this project using payback period technique and advise the management accordingly.
Answer:
To calculate the payback period (PBP) for this project, we need to determine how long it will take for the initial cash outlay of $40,000 to be recovered from the after-tax cash flows.
Year 1 cash flow = $10,000
Year 2 cash flow = $12,000
Year 3 cash flow = $15,000
Year 4 cash flow = $10,000
Year 5 cash flow = $7,000
Total cash inflows for year 1 and year 2 = $10,000 + $12,000 = $22,000
Total cash inflows for year 3 = $15,000
Total cash inflows for year 4 = $10,000
Total cash inflows for year 5 = $7,000
Cumulative cash inflows for year 1 and year 2 = $22,000
Cumulative cash inflows for year 3 = $37,000
Cumulative cash inflows for year 4 = $47,000
Cumulative cash inflows for year 5 = $54,000
It can be seen that the cumulative cash inflows reach the initial cash outlay of $40,000 after year 2, and therefore the payback period for this project is 2 years. Since the payback period is less than the maximum PBP of 3.5 years set by management, this project can be considered acceptable.
So, Hodgman Honest should recommend that Basket Wonders should accept this project as it has a payback period of only 2 years, which is less than the maximum PBP of 3.5 years set by management.
Friend need help I ain’t doing all dat to solve
Answer:
1. is 10
2. is 4
3. is 2
?= is 2
Can someone help me, please?
I need help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation: 1. is Yes 2 is no 3. is all 4 is Y and 50 5 is yes and -1
I’m thinking of three numbers: X, Y, and Z. We have X ≤ Y ≤ Z. The median of the
three numbers is 90, the mean of the three numbers is 92, and the range of the three
numbers is 6. What are the values of X, Y, and Z? Show your work
The X, Y, and Z values are 84, 90, and 90, respectively. To answer this question, we need to understand the meaning of the words "median", "mean" and "range".
What is median?Median is the middle number of a set of numbers - it is the number in the middle when the numbers are ordered from smallest to largest.
Since the median is 90, this means that Y (the mean number) is 90. Since the average is 92, this means that the sum of the three numbers is 276 (92 x 3). The interval is 6, which means that the difference between the largest number and the smallest number is 6.
To solve for X and Z, we can use the equation X Y Z = 276. We know that Y is 90, so we can plug 90 into Y:
X 90 Z = 276
Then we can subtract 90 from both sides to find the value of X and Z:
X Z = 186
Since the range of the three numbers is 6, this means that X and Z must be 6 plus. The only two numbers that differ by six and add up to 186 are 84 and 90.
Therefore the X, Y, and Z values are 84, 90, and 90, respectively.
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luke wants to buy an ipod. determine the equivalent cash price if luke makes 18 monthly payments of $31.48 at an interest rate of 15.2% compounded monthly
Answer:
We can use the formula for the present value of an annuity:
PV = PMT x [(1 - (1 + r)^(-n)) / r]
where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the number of payments.
Substituting the given values, we have:
PV = $31.48 x [(1 - (1 + 0.152/12)^(-18)) / (0.152/12)]
PV = $31.48 x [(1 - 0.5159) / 0.0127]
PV = $1,007.97
Therefore, the equivalent cash price of the iPod is $1,007.97.
A sports medicine specialist determines that a
hot-weather training strategy is appropriate for
a 165 cm tall individual whose BSA is less
than 2.0. To the nearest hundredth, what can
the mass of the individual be for the training
strategy to be appropriate?
hom
BSA <2.0
20
1789
Finish
165 cm
^
The mass of the individual can be up to 87.27 kg for the hot-weather training strategy to be appropriate.
How do you solve for the mass of of the individual using the equation provided?Given that the training strategy is appropriate for a BSA less than 2.0, we need to find the maximum mass (M) for the individual with a height (H) of 165 cm. The equation for BSA is:
BSA = √(H x M) / 3600
We can rearrange the equation to solve for M:
M = (BSA^2 x 3600) / H
Since we want the maximum mass for a BSA less than 2.0, we can use BSA = 2.0 as the upper limit:
M = (2.0^2 x 3600) / 165
M = (4 x 3600) / 165
M = 87.27 kg
The above question is in response to the full question as seen in the image;
A sports medicine specialist determines that a hot-weather training strategy is appropriate for a 165 cm tall individual whose BSA is less
than 2.0. To the nearest hundredth, what can the mass of the individual be for the training strategy to be appropriate?
The equation for BSA is BSA = √(H x M)/3600
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Which of the following quotients are true? Select all that apply. A. 1 2 ÷ 2 = 4 B. 1 3 ÷ 4 = 4 3 C. 1 2 ÷ 6 = 1 12 D. 1 5 ÷ 2 = 10 E. 1 8 ÷ 3 = 1 24
We may conclude after answering the presented question that None of the given quotient equations are true.
What is an equation?
A formula is a statement that two expressions are equal. An equation consists of two sides separated by an algebraic equation (=).
For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9."
The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements.
[tex]x^2 + 2x - 3 = 0.[/tex] Lines are utilized in many different areas of mathematics, such as algebra, calculus, and geometry.
None of the given quotients are true.
A. 1/2 ÷ 2 = 1/4, not 4.
B. 1/3 ÷ 4 = 1/12, not 4/3.
C. 1/2 ÷ 6 = 1/12, not 1/6.
D. 1/5 ÷ 2 = 1/10, not 10.
E. 1/8 ÷ 3 = 1/24, not 1/3.
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En un canal se necesitan diariamente 36 kg de maiz para alimentar a 480 gallinas ¿Cuantos kg se necesitan ahora si se vendieron 120 gallinas?
Resolver con reglla de 3
Answer:
Step-by-step explanation: it is -2x + 430298= -9n79000.
14 yd
21 yd find the area of the triangle
Answer:
147
Step-by-step explanation:
A= h^b b=21*14= 147
I need this work sheet done in 10 minutes or less!!
Answer:
3. 216 cm^3
4a. A = 5 ft, B = 4 ft.
4b. 88 ft^3
Step-by-step explanation:
3. Separate into two rectangular prisms:
Volume of first one: 4cm*2cm*3cm = 24cm^3
Volume of second one: 4cm*12cm*4cm = 192cm^3
Add them together: 24 + 192 = 216cm^3
4a.
Length A = 8-3 = 5ft.
Width B = 8-4 = 4ft.
4b. Separate into two rectangular prisms:
Volume of first one: 2ft*3ft*4ft = 24ft^3
Volume of second one: 8ft*4ft*2ft = 64ft^3
Add them together: 24 + 64 = 88ft^3
D
L
F
DM = 8
M
K
FM = 2x
E
EM = 6
Answer: yes correct i love math
Step-by-step explanation:
Please I need help
The area of the shaded region is
The area of the shaded region under normal distribution is: 3.51
What is the area under the normal distribution?The standard normal distribution is defined as the normal distribution with a mean of 0 and a standard deviation of 1.
The z-table or the standard normal table is one that provides the area under the standard normal curve to the left of a specified value, or "z-value". The value for the area is also the probability that the variable is less than the specified z-value.
To the right of -2.25 and to the left of -0.35
From standard normal table, we have the p-values as:
Area to the left of -0.35 = 0.3632
Area to the left of -2.25 = 0.0122
Area of the shaded region = 0.3632 - 0.0122 = 0.351
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1. You purchase a car using a $12,500 loan with a 5.6% simple interest rate.
(a) Suppose you pay the loan off after 6 years. How much interest do you pay on your loan? Show your work.
(a) Suppose you pay the loan off after 3 years. How much interest do you save by paying the loan off sooner? Show your work.
The interest that is paid on the loan in 6 years will be $4,200.
The amount of interest that is saved is $2,100.
What is the interest on the loan?The simple interest is a linear function of the number of years of the loan, value of the loan and the duration of the loan. The higher either of these values are, the higher the simple interest.
Simple interest = loan x time x interest rate
Simple interest if the loan is paid off after 6 years: $12,500 x 6 x 0.056 = $4,200
Simple interest if the loan is paid off after 3 years: $12,500 x 3 x 0.056 = $2100
Interest saved = $4200 - $2100 = 2100
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John drives to work each morning, and the trip takes an average of µ = 38 minutes. The distribution of driving times is approximately normal with a standard deviation of σ = 5 minutes. For a randomly selected morning, what is the probability that John’s drive to work will take between 36 and 40 minutes?
The probability that John's drive to work will take between 36 and 40 minutes is 0.3413.
What is Probability?Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probability is used in many areas of life, such as gambling, finance, and science. It is also used to make decisions in everyday life, such as estimating the likelihood of rain or the chance of winning a bet.
Using the normal distribution, the probability of John's drive taking between 36 and 40 minutes can be calculated using the standard normal distribution table. The formula for calculating the probability is: P(x<X<y) = P(y) - P(x).
For the given problem, the lower boundary is 36 minutes and the upper boundary is 40 minutes. Using the standard normal distribution table, the probability of John's drive taking between 36 and 40 minutes can be calculated by subtracting the probability of 36 minutes from the probability of 40 minutes. This gives us a probability of 0.3413.
Therefore, the probability that John's drive to work will take between 36 and 40 minutes is 0.3413.
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The probability that John's drive to work will take between 36 and 40 minutes is 0.3829.
What is Probability?Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probability is used in many areas of life, such as gambling, finance, and science. It is also used to make decisions in everyday life, such as estimating the likelihood of rain or the chance of winning a bet.
The probability that John's drive to work will take between 36 and 40 minutes can be calculated using a normal distribution table. The mean of the distribution is µ = 38 minutes, and the standard deviation is σ = 5 minutes.
To calculate the probability, we need to convert the given range (36 minutes to 40 minutes) into standard normal scores. This is done by subtracting the mean (µ = 38 minutes) from the lower bound (36 minutes) and then dividing by the standard deviation (σ = 5 minutes). The result is a standard normal score of -0.4. The same calculation is carried out for the upper bound (40 minutes) and the result is a standard normal score of 0.4.
Using a normal distribution table, we can then determine the probability that John's drive to work will take between 36 and 40 minutes. This probability is equal to the area under the normal curve between the two standard normal scores of -0.4 and 0.4. The result is a probability of 0.3829.
Therefore, the probability that John's drive to work will take between 36 and 40 minutes is 0.3829.
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Which of the following equation will produce the graph shown below
The quadratic equation in the given graph can be written in the vertex-form as:
y = -2(x - 1)² + 4
Which of the equations produce the given graph?We can see the graph of a quadratic equation. Remember that a quadratic equation with a vertex (h, k) and a leading coefficient a can be written as:
y = a*(x - h)² + k
in the graph we can see that the vertex is (1, 4), replacing that we will get:
y = a*(x - 1)² + 4
In the graph we also can see that the curve passes through the point (0, 2), replacing thesevalues in the equation we will get:
2 = a*(0 - 1)² + 4
2 = a + 4
-2 = a
Then the quadratic is:
y = -2(x - 1)² + 4
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which is more 7,000 millimeters or 7 liters?
BEAINEST IF CORRECT
if x= 60 would they be similar or not? explain ur answer.
Answer: no they wouldn't be similar
Step-by-step explanation: if x=60 if triangle 1 then the third angle would be (180-(58+60)) =180-118=62
if we decide to calculate the third angle in triangle 2 we will have 180-(50+58) = 180-108=72
therefore not all angles in 1 are similar to angles in 2 so the triangles aren't similar
Rewrite quadratic function in standard form
Since the function is already in standard form (ax^2 + bx + c form) you don't have to change anything and simply rewrite it.
For the vertex, if you have a quadratic function in standard form -b/2a is the x value of the vertex.
-b/2a = -4/(2(2)) = -1
Since we now know the x-value of the vertex we can plug it into the function to find the corresponding y-value.
h(-1) = 2(-1)^2 + 4(-1) - 10 = -12
So, the vertex is at (-1,-12)
15 points! please help me out!
Answer: 260 ft^2
Step-by-step explanation:
Find the area of the triangle: 0.5*height*base = 0.5*10*20 = 100 ft^2
Find the area of the rectangle: 20*8 = 160 ft^2
Add them together: 160+100 = 260 ft^2
Represent the following sentence as an algebraic
expression, where "a number" is the letter x. You
do not need to simplify.
9 less than six times a number.
Algebraic expressions are useful for solving different and complex equations in mathematics, as well as for modelling real-life situations such as revenue, cost, inference, etc
The algebraic expression is: [tex]6x - 9[/tex].
What is the use of algebraic expression?To represent the sentence as an algebraic expression, we can follow these steps: Identify the variable. In this case, “a number” is x. Identify the operation. In this case, “less than” means subtraction and “times” means multiplication.
An algebraic expression is an expression that contains variables, constants and mathematical operations. Algebraic expressions are useful because they can help us solve different and complex equations.
For example, if you want to calculate the area of a rectangle with length x and width y, you can use the algebraic expression xy to represent the area.
Write the expression using the order of operations. In this case, we need to multiply six by x first, then subtract nine from the result.
Therefore, The algebraic expression is: [tex]6x - 9[/tex]
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