Answers
9514 1404 393
Answer:
[tex]f(x)=\left\{\begin{array}{cl}-x^2+11x-28&\text{for $4<x<7$}\\x^2-11x+28&\text{otherwise}\end{array}\right.[/tex]
Step-by-step explanation:
The absolute value function negates its contents when those contents are negative. Here, the quadratic factors as ...
x^2 -11x +28 = (x -4)(x -7)
so will be negative when the factors have different signs. That will be the case for 4 < x < 7.
The piecewise function can be written in 3 parts, one part for x ≤ 4, another part for 4 < x < 7, and the remaining part for 7 ≤ x. The function expressions for x ≤ 4 and 7 ≤ x are identical.
In the answer above, we chose to write it with the part where the quadratic is negated being defined on the appropriate interval, and using "otherwise" for the rest of the function. It is a little unconventional to do it this way, but it is more compact and completely defines the function.
Related Questions
Which value for k makes the equation 42 ÷ k = 14 true? Select all that apply. A. 588 B. 62 C. 1452 D. 3 E. 23
Answers
3 is the value of k in the Linear equation .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
equation 42 ÷ k = 14
42/k = 14
42 = 14 * k
k = 42/14
k = 3
Learn more about Linear equation
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Imagine that you have the opportunity to purchase a large piece of land for $100,000, after taking out a loan. You have decided to take out a loan for $135,000 in order to cover the cost of the land purchase and building your park. You have hired a financial adviser to help you explore different loan options and decide which one is best for you. Below you will see the different loan options. You will need to calculate the total cost of each loan with interest. Once you have do this you and your group members will need to decide which of the loan options is best for you and why.
Option #1 – charges 5% simple interest per year; this is a short-term loan for only 5-years.
Option #2 – charges 7% simple interest per year; this is a short-term loan for only 3-years.
Option #3 – charges 3.2% simple interest per year; there is no time limit on this loan (as a group determine how long you think it will take you to make enough money to be able to pay back the loan with interest)
Option #4 - charges 10% simple interest per year; only lasts 10 months
Option #5 - charges 12% simple interest per year; only lasts 6 months
Written Response
You will be meeting with your financial adviser in two days. Write out which loan option your group is choosing to use and why. You really want to impress her with how much thought you have put into this decision so be as detailed as possible.
Answers
what is this
Step-by-step explanation:
Option #1 – charges 5% simple interest per year; this is a short-term loan for only 5-years.
Option #2 – charges 7% simple interest per year; this is a short-term loan for only 3-years.
Option #3 – charges 3.2% simple interest per year; there is no time limit on this loan (as a group determine how long you think it will take you to make enough money to be able to pay back the loan with interest)
Option #4 - charges 10% simple interest per year; only lasts 10 months
Option what is this
Answer:
Its option one
Step-by-step explanation:
Because 135,000/5=27000 then x5=135,000
What is the simplified form of (-3xy)(5xy-1)?
Answers
Answer:
-15x²y²+3xy
Step-by-step explanation:
((−3x)(y))(5xy−1)
=((−3x)(y))(5xy+−1)
=((−3x)(y))(5xy)+((−3x)(y))(−1)
=−15x²y²+3xy
Two students are reading a novel. Ashley reads 2 pages per day. Carly reads 1 page per day, but she starts early and is already on page 5. When will the two students read on the
same page?
Ashley:p=2d
Carly:p=d+5
Answers
Sara had $108 to spend on 8 books. After buying them she had $12 left. Let b represent the cost of each book. Which equation represents this situation?
Answers
Answer:
12
Step-by-step explanation:
you take 108-12=96
then you take 96/8=12
9. When Diego's phone is fully charged, it will last 18 hours. How much time 1 point
is left on his phone when the battery has 15% charge remaining? *
Answers
Answer:
2.7 hours
Step-by-step explanation:
Assuming that each percentage is worth the same amount of time. Then we can use the Rule of three since this is a ratio problem and we are given three values and a variable which is the amount of time that the battery lasts at 15%. This variable is represented by the letter x. To solve this we simply multiply the diagonal values and divide by the last remaining value which gives us the value of the variable like so...
100% <====> 18 hours
15% <====> x hours
(15 * 18) / 100 = 2.7 hours
Finally, we can see that 15% charge on the phone will last 2.7 hours
A singles tennis court measures (8x – 2) ft long and (3x – 3) ft wide.Which expression represents the area of the court?
Answers
Answer:
The expression that represents the area of the court is: [tex]24x^2 - 30x + 6[/tex]
Step-by-step explanation:
Area of a rectangle:
A rectangle has length l and width w. The area of a rectangle is:
[tex]A = lw[/tex]
A singles tennis court measures (8x – 2) ft long and (3x – 3) ft wide.
This means that [tex]l = 8x - 2, w = 3x - 3[/tex]
Which expression represents the area of the court?
The tennis court is rectangular, so
[tex]A = lw = (8x - 2)(3x - 3) = 24x^2 - 24x - 6x + 6 = 24x^2 - 30x + 6[/tex]
The expression that represents the area of the court is: [tex]24x^2 - 30x + 6[/tex]
What is the inverse of the function f(x) = 2x+1
Answers
Answer:
The answer is b. h(x) = one-halfx – one-half
Step-by-step explanation:
Answer:
hey everyone its b!!!
Step-by-step explanation:
Solve 22x − 2 = 15. Round your answer to the nearest hundredth.
Answers
Answer:
0.77
Step-by-step explanation:
Original equation: 22x-2=15
Add 2 to both sides: 22x=17
Divide by 22 on both sides: x=17/22, or 0.77
Let me know if this helps!
Roger has two golden retrievers, Sadie and Buddy. buddy weighs 14 pounds more than Sadie. If their total weight is 136 pounds, how much does Sadie weigh
Answers
Answer:
Sadie weighs 61 pounds.
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
Sadie's weight is x.
Buddy's weight is y.
Buddy weighs 14 pounds more than Sadie.
This means that [tex]y = x + 14[/tex]
Their total weight is 136 pounds.
This means that
[tex]x + y = 136[/tex]
Since [tex]y = x + 14[/tex]
[tex]x + x + 14 = 136[/tex]
[tex]2x = 122[/tex]
[tex]x = \frac{122}{2}[/tex]
[tex]x = 61[/tex]
Sadie weighs 61 pounds.
In the triangle below, angle B measures 60° and BC is 18. What is the length of AC?
Right triangle A B C is shown. Side B C is the hypotenuse.
9 StartRoot 3 EndRoot
StartFraction 9 Over StartRoot 3 EndRoot EndFraction
9
StartFraction StartRoot 3 EndRoot Over 9 EndFraction
Answers
Answer:
The Answer is D StartFraction StartRoot 3 EndRoot Over 9 EndFraction
Step-by-step explanation:
Answer:
the answer is D
Step-by-step explanation:
Trust me edge 2022
Find a linear equation whose graph is the straight line with the given property.
Through (0.5, -2.25) and (1, -5.25)
Answers
Answer:
Step-by-step explanation:
-5.25+2.25 - 3
1-0.5 = 0.5
=-6 =m
y=-6x
Brandon is 5 years older than his brother Hermie. There combined age is 23. How old is Brandon?
Find Brandon's age using the following equation:
2 + (x + 5) = 23
A
9
14
15
Answers
Answer:
9
Step-by-step explanation:
9 +5 = 14
14 +9 = 23
I need help, it’s geometry:
Answers
Answer: The area is 5x + 20
Step-by-step explanation:
Add all the numbers up.
7 + 4x - 8 = 3
13 + (x + 8) = (x + 21)
Therefore, your answer is 5x + 20
Let me know if you have any questions!
What is 0.63 divided by 0.18
Answers
Answer:
The answer is 3.5. I have included a screenshot that shows the work and how to get 3.5. I hope this helps!
And by the way yes, I do know this is a kinda old question, but I would like points and I have the answer.
:D
- Your friendly (a little bit late) responder!
When you divide 0.63 by 0.18, you get the result of 3.5.
To find the result of dividing 0.63 by 0.18, perform the division as follows:
0.63 ÷ 0.18 = 3.5
When you divide 0.63 by 0.18, the result is 3.5. This means that there are 3.5 sets of 0.18 in 0.63. To verify this, you can multiply 0.18 by 3.5:
0.18 × 3.5 = 0.63
So, 0.63 divided by 0.18 equals 3.5.
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Use synthetic division to solve (x3 + 1) = (x - 1). What is the quotient?
o x2+x+1+12
O x2 - X+1
O x2+x+1+421
x - x² + x
Answers
Answer:
x² + x + 1 and remainder 2Step-by-step explanation:
Given
(x³ + 1) ÷ (x - 1)Without using a synthetic division, we can use easier method to find the quotient.
We know the formula:
x³ - 1 = (x - 1)(x² + x + 1)Rewrite the given as:
x³ + 1 = x³ - 1 + 2 = (x - 1)(x² + x + 1) + 2This expression, when divided by (x - 1) leave the quotient (x² + x + 1) and a remainder of 2
The quotient of the equation is A = x³ + x + 1 + ( 2/x + 1 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
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 data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the first equation be p = x³ + 1
Let the second equation be q = x - 1
A = p / q
On simplifying , we get
A = x³ + 1 / ( x - 1 )
On dividing , we get the quotient as
A = x² + ( x² + 1 ) / ( x - 1 )
A = x³ + x + 1 + ( 2/x + 1 )
Hence , the quotient is A = x³ + x + 1 + ( 2/x + 1 )
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Kimberly worked for 2 weeks. The shaded parts of the model represent the fraction of each week she worked from home.
Which expression can be used to determine the number of weeks Kimberly worked from home over these 2 weeks?
Answers
Answer
she worked 1 week and 1 day
Step-by-step explanation
The FitnessGram PACER Test is a multistage aerobic capacity test that progressively gets more difficult as it continues.
Answer:
Step-by-step explanation:
f(n)=n^2-4;find (-1)
Answers
Answer:
-5
Step-by-step explanation:
f(-1) = -1^2 - 4
f(-1) = -1 - 4
f(-1) = -5
Find the vertex and focus of the parabola.
x^2 + 4x - 8y + 12 = 0
Answers
The Vertex is (-2,1)
And the focus is (-2,3)
Which relationships describe angles 1 and 2 ?
select each correct answer
-complementary angles
-vertical angles
-supplementary angles
-adjacent angles
Answers
Kelly has 7 days to read 60 pages of a book for school. She plans to read 8 pages a night for 6 nights.What percent of the assigned pages will she have left to read on the last night?
Answers
Answer:
20 percent left
Step-by-step explanation:
Answer:
20%
Step-by-step explanation:
Need help don’t know what to do I’m confused
Answers
Simplify (3^5)^2/3^-2
Answers
Answer:
the answer would be 531441
Step-by-step explanation:
Answer:
531441
Step-by-step explanation:
10. Put the numbers into least to greatest order: -33/5, 3 1/3, 3.3, -3.5
Answers
Answer:
Answer:
Order from Least to Greatest
-33/5 < -3.5 < 3.3 < 3 1/3
Step-by-step explanation:
Elena says I find 25.44 and then move the decimal point
Answers
Answer: help a homegirl out
Step-by-step explanation: let me get these points please
Please help, I will give brainliest, I am struggling badly.
Answers
Answer:
3rd option is the amswer
Tell whether each function is linear or non-linear.
Function A line1 Function B
x 0 1 2 3
y 0 1 8 27
y = –x + 5
Function A is non-linear and Function B is non-linear.
Function A is linear and Function B is non-linear.
Function A is linear and Function B is linear.
Function A is non-linear and Function B is linear.
Answers
Answer:
Function A is non-linear and Function B is linear.
Step-by-step explanation:
Linear function:
Has the following format:
y = mx + b
In which m is the slope and b is the y-intercept.
In a linear function, when x changes by 1, y will always changes by the same amount.
Function A:
When x changes by 1, y can change by various amounts. So function A is non-linear.
Function B:
y = -x + 5
In the format of a linear function, so linear
please answer i know the picture is a little blurry but please i will give you brainliest!!
Answers
Answer: the 1st one.
Step-by-step explanation: becuase today I was helping out a freind with this. So it the first one
Is the following set a function?
{(-3, -27), (-2, -18), (1, -9), (0, 0), (1,9), (2, 18), (3, 27)}
A) Yes
B) No
Answers
Answer:
yes i think
Step-by-step explanation:
Three out of nineteen students will ride in a car instead of a van. How many ways can those three students be
chosen? Use the following formula.
n!
r
C(n, r) = r!(n-1)!
