The value of x will be 6, while the value of y will be 3 in the given pair of the ordered equation.
As we have,
The pair of equations as:
2x + 8y = 36 -----------------(i)
5x − 4y = 18 -----------------(ii)
From above,
We can see that in the first equation the coefficient of x is 2 while in the second one, the coefficient of x is 5.
So, for solving the given sets of equation we need to first equalise the co-efficient of x in both the equations.
So, to make the coefficient equal we will multiply the first equation by 5 and the second equation by 2.
Thus we will get the set of equations as:
10x+40y=180--------(iii)
10x-8y=36------------(iv)
From (iii) and (iv), Now subtracting the (iv) from (iii),
We will get it as:
48y = 144
y = (144/48) = 3
Now for getting the value of x, we will put the value of y in the first equation.
Thus, we will get it as:
2x+24=36
=>2x=12
=>x = (12/2)=6
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How much water must be added to 7 gallons of a 8% insecticide solution to reduce the concentration to 7%?
1 gallon of water must be added to 7 gallons of an 8% insecticide solution to reduce the concentration to 7%.
Let x = amount of water required
7 gallons + x gallons = (x + 7) gallons of mixture
For x gallons of water, we have 0 gallons of insecticide
For 7 gallons of 8% insecticide solution, we have 0.08(7)=0.56 gallons of insecticide
According to the question, we get the equation as follows
0.07(x + 7) = 0.56
7(x + 7) = 56
x + 7 = 8
x = 1 gallon
Therefore, the amount of water that needs to be added to 7 gallons of an 8% insecticide solution to reduce the concentration to 7% is 1 gallon.
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Maria, a teacher at Learn4Life created a histogram for the vacations she's taken in the last ten years. She hasn't added the 7-day vacation yet she took this summer. Using your pencil, draw and add the 7-day vacation Maria took this summer to the histogram on the right.
The bar representing her 7-day vacation will have a class width of 16 - 22 and a height of 1.
What is a histogram?The frequency distribution of a collection of data reveals how frequently each unique value appears.
The most typical graph for displaying frequency distributions is a histogram. Although it closely resembles a bar chart, there are significant variances.
In the given histogram class width(horizontal width) represents the number of days and frequency(vertical height) represents the number of vacations taken.
Therefore, The 7-day vacation yet she took this summer will be represented by a bar having a class width 16 - 22 and a height of 1.
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help please Consider the functions:
Answer the equations about these functions in the table below.
Select f(x), g(x), both options, or neither.
The x-intercept of (-2, 0) has both functions. The behavior of the function g(x) for x ⇒ -∞ then g(x) → ∞. The y-intercept of the function f(x) is (0, 6). And both functions have real roots.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The functions are given below.
f(x) = x³ - 2x² - 5x + 6
g(x) = - x³ + 4x
The factor of the function f(x) is given as,
f(x) = 0
x³ - 2x² - 5x + 6 = 0
(x + 2)(x - 1)(x - 3) = 0
x = -2, 1, 3
The factor of the function g(x) is given as,
g(x) = 0
- x³ + 4x = 0
x = 0, 2, -2
The y-intercept of the function f(x) is given as,
f(0) = (0)³ - 2(0)² - 5(0) + 6
f(0) = 6
The y-intercept of the function g(x) is given as,
g(0) = - (0)³ + 4(0)
g(0) = 0
The graph of the function is given below.
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What is a perfect square
A perfect square is a number obtaining by squaring a whole number
What is a perfect square?A perfect square can be defined as a number that is being expressed as the product of an integer by itself.
It is also seen as the second exponent of an integer.
In determining the perfect of a number, when you multiply an integer which could be a “whole” number, positive, zero or negative) by itself, the product of the multiplication is termed a square number, or a perfect square.
Perfect square is also described as a number made by squaring a whole number.
Some perfect squares in mathematics are;
Number 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 139, 144, etc
Hence, a perfect square is described as a number that is the product of an integer with itself.
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Paul wants to create a rectangular pig pen using 20 feet of fencing or less. To help determine the possible areas of the pig pen, Paul created a quadratic inequality. A(w) represents the possible total areas in feet2 of the pig pen with respect to width, w, in feet. The graph of the quadratic inequality is shown below:
Which of the following statements could be true about Paul's pig pen?
Select ALL that apply
Paul's pigs will have the maximum possible area if the pen has a width between 3 and 4 feet.
Paul's pig pen has a width of 3 feet and an area of 2 feet2.
With a pen width of 7 feet, Paul could still place 4 pigs in the pen and get them each an average space of approximately 5 feet2.
Paul's pig pen has a width of 2 feet and an area of 16 feet2.
Paul's pig pen h as a width of 16 feet and an area of 8 feet2.
Paul's pig pen has a width of 2 feet and an area of 16 square feet is the true statement.
What is Area of Rectangle?The area of Rectangle is length times of width.
This is a simple calculus problem but it can be solved without calculus, as follows:
let L=length of the pen and W = width
2(L + W) = 20
L + W = 10
L = 10 - W
Let A = area of the pen
A = Length × Width = 10W - W²
Sketch this parabola which has a positive maximum which occurs at W = 10/2
This means the area is maximum when w = 2, in other words the maximum area occurs when the rectangle is a square.
Hence, Paul's pig pen has a width of 2 feet and an area of 16 square feet.
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-1
5
X
f(x)
slope:
y-intercept:
0
4
of f ==
off=
1
3
2
2
of g =
of g =
3
1
The slope and the intercept of the function f(x) = -x + 5 are given as follows:
Slope: -1.Intercept: 5.How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the rate of change of the function.b is the intercept, representing the value of y at which the graph of the function crosses the y-axis.The function for this problem is defined as follows:
f(x) = -x + 5.
Comparing to the standard definition of a linear function, we have that:
The slope is of -1.The intercept is of 5.Missing InformationThe problem asks for the slope and the intercept of the function f(x) = -x + 5.
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400x(9x10 to the power of 15)
Answer: 3.6e+18
Step-by-step explanation: (400 x 9 = 3,600) 10 to the power of 15= 1,000,000,000,000,000 or quadrillion. 9x1,000,000,000,000,000=9e+15x400=3.6e+18
Roberto and Maeko open a pet store and start with 5 hamsters for sale. Hamster populations usually triple every cycle. One cycle is equal to 4 months. Write an equation in function notation to represent the change in the number of hamsters as a function of the cycle number, c. Explain how you determined your equation.
The number of hamsters as a function of the cycle number, c, can be represented by the equation:
f(c) = 5 * 3^c
This equation was determined by the fact that the population triples every cycle and the starting number of hamsters is 5. The function notation is f(c) which represents the number of hamsters as a function of the cycle number. The base of the equation is 3, which represents the rate at which the population triples. The exponent is c, which represents the cycle number. The coefficient is 5, which represents the starting number of hamsters.
the ages of 32 recruits in the police academy are normally distributed with a mean of 27 and a standard deviation of 2.
label the normal curve
Mean is 27 and SD is 2 then the normal curve with highest range would be at domain 27.
What is mean?The mean is the average of a set of numbers. It is calculated by adding all the numbers in the set together, and then dividing by the number of values in the set. It is calculated by adding up all the numbers in the set, dividing by how many values there are in the set, and then multiplying by that number. The average of a group of numbers is called the mean.
Mean is 27 and SD is 2
a) P(23<x<27)= P((23-27)/2<z<(27-27)/2)=P(-2<z<0)=P(z<0)-P(z<-2) or P(z<0)-(1-P(z<2))
From normal distribution table we get 0.5-(1-0.9772)=0.4772
b) P(x>31)=P(z>(31-27)/2)=P(z>2) or 1-P(z<2)=1-0.9772=0.0228
c) P(x<29)= P(z<(29-27)/2)=P(z<1)=0.8413
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Jackie obtains a 30-year 4/2 ARM at 5% with a 4/7 cap structure in the amount of $313,500. What is the monthly payment during the initial period? (3 points)
$1,832. 69
$1,496. 70
$1,682. 94
$870. 83
The monthly payment during the initial period is about $1,682.94
The type of loan Jackie obtains is an Adjustable Rate Mortgage, ARM, loan, which is a 4/2 ARM
The introductory interest rate of 5% is fixed for the first 4 years, and will be adjusted every 2 years after the first four years.
Let us assume that m represents the initial monthly payment.
[tex]M=\frac{P.(\frac{r}{12} ).(1+\frac{r}{12} )^n}{(1+\frac{r}{12} )^n - 1}[/tex]
where, M is the monthly payment during the initial period
P is the amount on loan
r is the interest rate = 5% = 0.05
n is period = 30 × 12 = 360
Here, P = $313,500
r = 5%
r = 0.05
n = 30 × 12
n = 360
Substituting these values in the above formula we get,
[tex]M=\frac{313500\times (\frac{0.05}{12} ).(1+\frac{0.05}{12} )^{360}}{(1+\frac{0.05}{12} )^{360} - 1}[/tex]
M ≈ 1,682.94
Therefore, the monthly payment is about $1,682.94
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6y + 14 math help people
The number of terms in the algebraic expression 6y + 14 is 2 terms
How to determine the number of terms in the algebraic expressionsFrom the question, we have the following parameters that can be used in our computation:
6y + 14
Consider an expression given as
ax + b
The number of terms in the expression is 2 and the terms are ax and b
Using the above as a guide, we have the following:
6y + 14 has 2 terms
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Complete question
Identify the number of terms and then the resend themselves for each algebraic expression
6y + 14
Here are two sets of numbers, A and B.
Set A
Set B
281
268
392
512
413
225
290
422
у
mean of Set A: mean of Set B = 7:12
Work out the value of y.
After solving the value of y is 541.
The value of set A is 281, 268, 225, 290. So
The mean of set A = (281 + 268 + 225 + 290)/4
The mean of set A = 1064/4
The mean of set A = 266
The value of set B = 392, 512, 413, 422, у
The mean of set B = (392 + 512 + 413 + 422 + у)/5
The mean of set B = (1739 + y)/5
The ratio of Mean of Set A : Mean of Set B = 7 : 12
So, 7x = 266
Divide by 7 on both side, we get
x = 266/7
x = 38
Now, 12x = 12 × 38 = 456
The mean of set B = 456
(1739 + y)/5 = 456
Multiply by 5 on both side, we get
1739 + y = 2280
Subtract 1739 on both side, we get
y = 541
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The complete question is:
Here are two sets of numbers, A and B.
Set A Set B
281 268 392 512 413
225 290 422 у
Mean of Set A : Mean of Set B = 7 : 12.
Work out the value of y.
what equation is graphed in the figure
The equation that is graphed is (c) y = x² + 2 if x < 1 and y = -x + 2 if x ≥ 1
How to determine the graphed functionFrom the question, we have the following parameters that can be used in our computation:
The graph (see attachment)
On the graph, we can see that the first curve is a quadratic function,
Also, it has an open circle at x = 1
So, we have:
x² + 2 if x < 1
Next, we have a linear equation with a closed circle at x = 1
So we have:
y = -x + 2 for x ≥ 1
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1.20 housing proposal across dorms. on a large college campus first-year students and sophomores live in dorms located on the eastern part of the campus and juniors and seniors live in dorms located on the western part of the campus. suppose you want to collect student opinions on a new housing structure the college administration is proposing and you want to make sure your survey equally represents opinions from students from all years. (a) what type of study is this? (b) suggest a sampling strategy for carrying out this study.
(a) The study is observational type.
(b) Stratified sampling can be used for carrying out this study.
(a) In the given problem, We want to hear students' opinions about the new housing structure and ensure that the survey reflects all students' views equally. The critical thing to note here is that you need to collect opinions. Not the reason behind the opinion. So researchers don't care how the data goes up. So this is an observational study.
(b) In the case of sampling strategy we can use stratified sampling. Stratified sampling refers to a type of sampling technique. In stratified sampling, researchers divide the population into separate groups called strata. A probability sample (often a simple random sample) is then drawn from each group. The same number of samples can be used each year.
Therefore, To make sure the survey equally represents opinions from students from all years (a) the study is the observational type and (b) Stratified sampling can be used for carrying out this study.
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4. The gas tank of a hybrid car fills up with 16 gallons of gas. The car can drive for an average of
85 miles per gallon. The equation d = 85g represents the distance (d, in miles) that can be
driven with g gallons of gas left in the tank. What is a reasonable range for this problem
situation?
If the vehicle has 10 gallons of fuel left, it has driven 600 miles.
What is the equation?The term "equation" refers to mathematical statements with at least two terms that contain variables or integers that are equal.
The amount of gas in the tank should be x gallons, and the distance travelled by car should be d miles.
Due to the car's 16-gallon fuel tank
So, 16 - x would be the remaining fuel in the tank.
It gets 85 miles per gallon of gas when travelling on a highway.
⇒ d = (16-x)85
if the tank still holds 10 gallons of fuel
In the equation above, if x = 10, we get
⇒ d = (16-10)85.
⇒ d = (20)85.
⇒ d = 600.
If the vehicle has 10 gallons of fuel left, it has driven 600 miles.
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Aria has two pet snakes, Mian and Udon. The combined length of the two snakes is
34
3434 inches, and Udon is
12
1212 inches shorter than Mian. Which of the following systems of equations could be used to find
m
mm, the length of Mian in inches, and
u
uu, the length of Udon in inches?
The length of Mian in inches is 23 and the length of Udon in inches is 11
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, Aria has two pet snakes, Mian and Udon. The combined length of the two snakes is 34 in and Udon is 12 inches shorter than Mian.
Let Mian be represented by M and that of Udon by U,
Therefore, according to question, establishing the equation,
M + U = 34
M - U = 12
Adding both the equations,
2M = 46
M = 23
U = 11
Hence, the length of Mian in inches is 23 and the length of Udon in inches is 11
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Prove whether the quadrilateral is a parallelogram using the slope formula:
K(2, 7), L(6, 12), M(13, 13), N(9, 8)
Parallelograms are quadrilaterals with two sets of parallel sides
Slope Formula: y2-y1/x2-x1
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
KL: 12-7/6-2 = 5/4
LM; 13-12/13-6 = 1/7
MN: 8-13/9-13 = 5/4
KN: 7-8/9-2 = 1/7
We can identify this as a parallelogram since it has congruent angles and sides, which are found on a parallelogram.
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Kathy and Jake are purchasing a house and are financing $465,000. The mortgage is a 20-year
5/1 ARM at 3. 5% with a 2/7 cap structure. What will the remaining balance be after the first 5 years?
As per the given mortgage, the remaining balance be after the first 5 years is $678125
Here Kathy and Jake are purchasing a house and are financing $465,000. The mortgage is a 20-years 5/1 ARM at 3. 5% with a 2/7 cap structure.
As we know that the formula for the calculation is written as
=> (Mortgage X Rate)/ 12 months
And then we have to subtract the Monthly PI payment from monthly interest on payment.
When we apply the value on it, then we get,
($465,000 x 3.5)/12
= $135625
Then the amount after 5 years is calculated as,
⇒ $135625 x 5
= $678125
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Which long division problem can be used to prove the formula for factoring the difference of two perfect cubes?
a-3) a² + ab +3²
a + b) a ² - ab +6²
o a+ba? +la+b+Dab? - 53
a-ba? +da+b+Dab? - b
The long division problem can be used to prove the formula for factoring the difference of two perfect cubes (a-b)(a²+ab+b²).
The difference of two perfect cubes: a³-b³ = (a-b)(a²+ab+b²)
let the two perfect cubes be a³ and b³. Factoring the difference between these two perfect cubes we have: a³ - b³
First, we need to factorize (a-b)³:
(a-b)³ = (a-b) (a-b)²
(a-b)³ = (a-b)(a²-2ab+b²)
(a-b)³ = a³-2a²b+ab²-a²b+2ab²-b³
(a-b)³ = a³-b³-2a²b-a²b+ab²+2ab²
(a-b)³ = a³-b³ - 3a²b+3ab²
(a-b)³ = (a³-b³) -3ab(a-b)
Then we will make a³-b³ the subject of the formula from the result equation;
a³-b³ = (a-b)³+ 3ab(a-b)
a³-b³ = a-b{(a-b)²+3ab}
a³-b³ = a-b{a²+b²-2ab+3ab}
a³-b³ = (a-b)(a²+b²+ab)
a³-b³ = (a-b)(a²+ab+b²)
The long division problem that can be used is (a-b)(a²+ab+b²).
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If f(x)=3x, g(x)=x+4, and h(x)=x2-1, find the value of f[g(0)]
Answer:
f(g(0)) = 12
Step-by-step explanation:
to find f(g(0)) , evaluate g(0), then substitute the value obtained into f(x)
g(0) = 0 + 4 = 4 , then
f(4) = 3(4) = 12
11 1/8 less than the product of 8 and the number z
The statement in algebraic terms is given by 8z-89/8
What is an Algebraic Expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
Given here: The statement " 11¹/₈less than the product of 8 and the number z"
The translation of the statement in the form of an algebraic expression is given by
8z - 11¹/₈
8z-89/8
Hence, The statement in algebraic terms is given by 8z-89/8
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true or false: let be a random sample from with sample variance, and a random sample from with sample variance . assume that and are independent of one another. then
This statement is False.
The formula provided in the statement is used to calculate the variance of the sample mean difference between two independent samples, but it is not necessarily true that the sample variances, and , are independent of one another.
The sample variances are calculated based on the data from their respective samples, and thus their relationship will depend on the specific data and the underlying population distributions.
For example, let's consider two samples of size n = 25, one from a normal population with mean 100 and variance 10, and another one from a normal population with mean 110 and variance 20. The sample variances for each sample are:
S1² = 9.6 and S2² = 20.8
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how does the graph of f(x)=2^x+2 compare to the graph of g(x)=2^x +2
Answer: The graph of f(x) = 2^x and g(x) = 2^x +2 are the same.
Explanation: The functions f(x) = 2^x and g(x) = 2^x + 2 are identical. The only difference between them is the constant term in the second function. This constant term does not change the shape, direction or the relative position of the graph of the function, it only shifts the graph along the y-axis. Because both functions have the same base, the graphs will have the same shape, direction and relative position, regardless of the constant term.
Need one last IXL question! Tysm to whoever helps
Answer:
w = 11 , x = 25
Step-by-step explanation:
for Δ ABC ≅ Δ TUV, then corresponding sides must be congruent, that is
AB = TU and BC = UV ( using these to create 2 equations )
- 9x + 20w + 89 = 4w + x + 15 ( subtract 4w + x + 15 from both sides )
- 10x + 16w + 74 = 0 → (1)
and
x + w + 41 = - 18w + 11x ( subtract - 18w + 11x from both sides )
- 10x + 19w + 41 = 0 → (2)
multiplying (2) by - 1 and adding to (1) will eliminate x
10x - 19w - 41 = 0 → (3)
add (1) and (3) term by term to eliminate x
0 - 3w + 33 = 0 ( subtract 33 from both sides )
- 3w = - 33 ( divide both sides by - 3 )
w = 11
substitute w = 11 into either of the 2 equations and solve for x
substituting into (1)
- 10x + 16(11) + 74 = 0
- 10x + 176 + 74 = 0
- 10x + 250 = 0 ( subtract 250 from both sides )
- 10x = - 250 ( divide both sides by - 10 )
x = 25
thus the values x = 25 and w = 11 will make the triangles congruent
What is the range of this function?
[220, 265]
(220, 265)
(150,275)
[150, 275]
The range of the function is (d) [150, 275]
How to determine the range of the function?The graph that completes the question is added as an attachment
From the graph, we have the following properties:
x values = monthsy values = profitThe range is simply the amount of values between the y axis
In this case represented by the graph, we have:
Minimum y value = 150
Maximum y values = 275
Sinfe both values are inclusive, the range would be [150, 275]
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Tommy is buying a home, its purchase price is $200,000. She has to put
down 5%, with an APR of 6.4%. What will her monthly payment be.
The required monthly payment for 6.4% of interest is $16846.6.
What is interest?Interest is the cost of borrowing money or the fee you charge to lend it. Most frequently, interest is shown as an annual percentage of the loan amount. The interest rate for the loan is denoted by this proportion.
According to question:We have,
Purchasing price = $200,000
Down payment = 5% of $200,000
= $10000
Remaining Amount = $190000
Interest of one year = 6.4%
Amount of interest = 6.4% of $190000
Amount of interest = $12160
Total amount = f $190000 + $12160
Total amount = $202160
Monthly payment = $16846.6
Thus, required monthly payment is $16846.6.
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I need help asap for this
The answer of [tex]\sqrt[4]{125a^{4} }[/tex] is 3.34a. The solution has been obtained by using the concept of exponents.
What is an exponent?
The exponent of a number shows that how many times a particular number has been multiplied by itself. For instance, the number 2^4 means that we are multiplying the number 2 itself by four times. It is enlarged to 2*2*2*2. An exponent is also known as a number's power. One may use a whole number, fraction, negative number, or decimal.
We are given [tex]\sqrt[4]{125a^{4} }[/tex]
This can be also written as (125a^4)^1/4
Splitting the power, we get
⇒[tex]a^{4^{1/4} } 125^{1/4}[/tex]
⇒a 125^0.25
⇒a 3.34
⇒3.34a
Hence, the answer of [tex]\sqrt[4]{125a^{4} }[/tex] is 3.34a.
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Since there are multiple questions so, the question answered above is
[tex]\sqrt[4]{125a^{4} }[/tex]
Help Me, Now! Lacey pays $15 for each hour of golf lesson and $10 for equipment rental. If the lesson is more than 3 hours long she only pays $5 for equiptment rental. Is the total cost of Lacey's lesson a function of the number of hours scheduled? Is This a function? (Write Yes Or No)
The total cost of Lacey's lesson a function of the number of hours scheduled is [tex]f(x)=\left \{ {{(10 + 5)x, x\leq 3} \atop {10x, x > 3}} \right.[/tex] and this one refers the function.
In math the term called function is known as a correspondence from one value x of the first set A to another value y of the second set B and it relates inputs to outputs.
Here we have know that Lacey pays $15 for each hour of golf lesson and $10 for equipment rental.
And here we have also know that If the lesson is more than 3 hours long she only pays $5 for equipment rental.
Let us consider that x be the amount time she has been taking lessons.
Then the function can be written as,
[tex]f(x)=\left \{ {{(10 + 5)x, x\leq 3} \atop {10x, x > 3}} \right.[/tex]
While we looking into it we have identified that the given situation will create the function.
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I need help please ans thank you
The length of all a triangle's sides added together yields the perimeter of a triangle.
What's perimeter formula?The length of all a triangle's sides added together yields the perimeter of a triangle.
The result of the lengths of the sides is the perimeter of any polygon. In the case of a triangle: Perimeter = Sum of the three sides.
perimeter=(length + width)2.
JKL - Delta RST^ prime , RS = 14 ST = 12 , TR = 10 , and LJ = 14 2. ADEF, if triangle DEF sim triangle ABC , AB = 27 BC = 16 CA = 25 , and FD = 15 3
RST perimeter=(length + width)2.
14+ 12+10+14 = 50
triangle ABC
27 + 16 + 25 =68
triangle PQR sim triangle LMN , LM = 16 , MN = 14 , NL = 27 ,
16+14 + 27 = 57
if triangle KTM sim triangle FGH . . FG = 30 GH = 38 , HF = 38
30 + 38 + 38 =106
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