Linear function f with f(-3) = 1 and f(13) = 5 is given by [tex]\rm f(x) = \dfrac{1}{4}x + \dfrac{7}{4}[/tex] and this can be determined by using the given data.
Given :
f(-3) = 1 and f(13) = 5.
The generalised linear function is given by:
f(x) = ax + b --- (1)
Now, it is given that (f(-3) = 1) that means at (x = -3) the above function is equal to 1.
f(-3) = a(-3) + b
1 = -3a + b
b = 1 + 3a ---- (2)
Now, it is also given that (f(13) = 5) that means at (x = 13) the function (f(x) = ax + b) is equal to 5.
f(13) = 13a + b
5 = 13a + b
Now, put the value of 'b' in the above equation.
5 = 13a + 1 + 3a
4 = 16a
[tex]\rm a = \dfrac{1}{4}[/tex]
Now, put the value of 'a' in equation (2).
[tex]b = 1 +3\times \dfrac{1}{4}[/tex]
[tex]b = \dfrac{7}{4}[/tex]
Now, put the value of a and b in equation (1).
[tex]\rm f(x) = \dfrac{1}{4}x + \dfrac{7}{4}[/tex]
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A restaurant serves a 20-ounce steak.How much does the steak weigh in pounds and ounces?
Chuck has a coin collection with 30 pennies, 24 quarters, and 36 nickels. He wants to arrange the coins into rows. Each row will have the same. How many coins can he put in each row?
Write a word problem that can be solved by finding the numbers
that have 4 as a factor.
use the graph to find the capacity in quarts of a 2.5 container gallon
Niall owes $187 to his cousin. However, he doesn't have any money right now. He hopes to earn some money by painting a house. He gets paid $34 for every 2 hours he paints. Which equation of a line models y, the amount of money he will have after paying back his cousin, in terms of x, the number of hours he spends painting?
Answer:
[tex]y=17x-187[/tex] where x>11
Step-by-step explanation:
Niall gets $34 for 2 hours.
So, he gets [tex]34/2=17[/tex] dollars per hour.
Now, he owes $187 to his cousin.
Let the number of hours he works be = x
Let the money left with him after paying his cousin be = y
So, the equation forms:
[tex]y=17x-187[/tex]
Rather we can say it is :
[tex]y=17x-187[/tex] where x>11
If we want to know how many hours are needed to pay the debt, we can consider y = 0
[tex]17x-187=0[/tex]
[tex]17x=187[/tex]
[tex]x=187/17[/tex]
So, x = 11 hours
So, Niall needs 11 hours of work to pay back his cousin and after that all his earnings is 'y'. When x>11 then 'y' will have some money left.
What is 2.345×10^-2 in standard notation
Does anyone know how to solve by substitution for 1/2x+7=y and 3y-11=-x
How many solutions does this equation have: -9x+1=-9x+1
The equation -9x+1=-9x+1 has infinitely many solutions.
Explanation:This equation, -9x+1=-9x+1, is an example of an equation with infinitely many solutions. This means that any value of x will satisfy the equation. To see this, we can simplify the equation:
-9x + 1 = -9x + 1
By subtracting -9x from both sides, we get:
1 = 1
This is a true statement, which means that any value of x is a solution to the equation. Therefore, there are infinitely many solutions to this equation.
What is n x p = 185 n is a 2 digit number and p is a 1 digit number. What are n and p?
On Wednesday, Abby and Lauren could not practice together, so they practiced separately. Abby practiced for 11/12 of an hour and Lauren practiced for 2/3 of an hour. How long did they practice on Wednesday?
Abby and Lauren practiced for a total of approximately 1.58 hours on Wednesday.
Explanation:The subject of this question is Mathematics and it concerns the addition of fractions. It is aimed at Middle School grade level.
Abby practiced for 11/12 of an hour and Lauren practiced for 2/3 of an hour, and to find out how long they both practiced, we need to add these two fractions together. Converting these fractions into like fractions (with same denominator), we have Abby's time as 33/36 (since 11/12 = 33/36) and Lauren's time as 24/36 (since 2/3 = 24/36).
Adding together Abby's practice time (33/36) and Lauren's practice time (24/36), gives 57/36 or 1 21/36 hours which is approximately 1.58 hours.
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what is one third plus one fourth equal to a mixed number
The mixed number equivalent to 7/12 is 0 and 7/12.
To add one-third and one-fourth, we need to find a common denominator. The least common multiple of 3 and 4 is 12.
Converting both fractions to have a denominator of 12:
1/3 = 4/12
1/4 = 3/12
Now, we can add the fractions:
4/12 + 3/12 = 7/12
The sum of one-third and one-fourth is 7/12. To express this as a mixed number, we need to divide the numerator (7) by the denominator (12):
7 ÷ 12 = 0 remainder 7
Therefore, the mixed number equivalent to 7/12 is 0 and 7/12.
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the mathematics club wants to divide the boys and girls into the greatest number of teams. each team will have the same number of boys and the same number of girls. there are 84 boys and 72 girls. how many boys and girls will be on each team
Answer: There will be 14 boys and 12 girls
Step-by-step explanation:
GCF or 12 and 14 is 6(6 groups)84/6=1472/6=12Hope this helps
905-425
905= __ hundreds+___tens+ones__
or__hundreds+10 tens+ __ ones
425= __ hundreds+__tens+__ ones
subtract hundreds:__ hundreds
subtract tens:__ tens
subtract ones:__ones
905-425=408
The value for the expression 905 - 425 is 407.
What is place value?The place value of a number is given as:
Example:
1234.567
1 = thousand place value
2 = hundred place value
3 = tens place value
4 = ones place value
5 = tenths place value
6 = hundredths place value
7 thousandths place value
We have,
905 - 435
905 = Nine hundred + zero tens + five ones
425 = Four hundreds + two tens + five ones
Now,
905 - 435
= 407
Thus,
The value is 407.
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It cost $3.99 for 25 fl. oz. of detergent or $6.99 for 90 fl. oz. Which is a better buy?
$6.99 for 90 fl. oz of detergent is a better buy.
Arithmetic operations is a concept that concerns the study of mathematical operations like addition, subtraction, division, and multiplication.
The determination on the type which is a better buy can be estimated by finding the cost of each detergent in the two cases.
For the first case, we are being told that It cost $3.99 for 25 fl. oz. of detergent.
From that, the price for 1 fl. oz will be:
[tex]\mathbf{x = \dfrac{3.99 \times 1 }{25}}[/tex]
x = $0.1596
For the second case, if the price for 90 fl. oz is $6.99
For 1 fl.oz, we have:
[tex]\mathbf{x = \dfrac{6.99 \times 1 }{90}}[/tex]
x = $0.0777
Therefore, we can conclude that $6.99 for 90 fl. oz of detergent is a better buy since the amount of each detergent is lesser than that of 25 fl. oz.
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What is 499 divided by 2? And show steps too
Explain how to convert 6 feet into meters.
What is the quotient of 8/11 ÷ 3/5 =?
The quotient of 8/11 ÷ 3/5 is; 40/33
The quotient of 8/11 ÷ 3/5 can be evaluated as follows;
= 8/11 ÷ 3/5
= (8/11 ) × (5/3)
By multiplying the numerator s and denominators; we have;
= 40/33
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I do not understand the question. Plz help!
Select True or False. The expression 4x − 2(5x − 1) is equivalent to the expression 2 + 6x.
Answer: The given statement is FALSE.
Step-by-step explanation: We are given to check whether the following statement is True of False :
"The expression 4x − 2(5x − 1) is equivalent to the expression 2 + 6x".
We will be using the following distributive property :
[tex]a(b+c)=ab+ac.[/tex]
We have
[tex]4x-2(5x-1)\\\\=4x-10x+2\\\\=-6x+2\\\\=2-6x\\\\\neq 2+6x.[/tex]
Therefore, expression 4x − 2(5x − 1) is NOT equivalent to the expression 2 + 6x.
Thus, the given statement is FALSE.
You put $500 in your bank account. With an interest rate of 5%, how long will it take the account to reach $600? Use the formula: I = Prt.
Final answer:
To calculate how long it will take for a bank account with an initial deposit of $500 to reach $600 at a 5% simple interest rate, you first determine the total interest required ($100), then use the formula I = Prt to solve for time. The calculation shows that it will take 4 years for the account to reach $600.
Explanation:
To determine how long it will take for an account to reach $600 with an initial deposit of $500 at a simple interest rate of 5%, we can use the simple interest formula I = Prt, where I is the interest, P is the principal amount, r is the rate, and t is the time in years.
First, we calculate the total interest needed for the account to reach $600:
Total amount desired = $600Principal (initial amount) = $500Interest needed = Total amount - PrincipalInterest needed = $600 - $500 = $100Next, we use the formula I = Prt to solve for time (t):
I = $100P = $500r = 0.05 (5% expressed as a decimal)$100 = $500 × 0.05 × t$100 = $25tt = $100 / $25t = 4 yearsTherefore, it will take 4 years for the account to reach $600.
How do you solve a Rubik's Cube?
What is the area of the picture and frame shown? Write your answer as a mixed number in simplest form.
Kenny reads 3/8 page in 2/5 minute what is kennys unit rate
Kenny's unit rate of reading is 15/16 page per minute, which is determined by dividing the number of pages he reads by the time taken and then calculating the equivalent for one minute.
Kenny reads 3/8 page in 2/5 minute. To find Kenny's unit rate, we calculate how many pages he would read in one minute.
To find the unit rate, you divide the number of pages by the number of minutes:
(3/8) page / (2/5) minute
= (3/8) \/ (2/5)
= (3/8) \/ (5/2) [Because dividing by a fraction is the same as multiplying by its reciprocal]
= (3/8) * (5/2)
= (3*5) / (8*2)
= 15/16
So, Kenny's unit rate is 15/16 page per minute.
describe how to find the 99th number in this sequence. 1,4,9,16,25
Hannah hiked 5/6 of a mile along the path. Joey hiked 2/3 of the distance that Hannah hiked. How far did Joey hike? Explain in simplest form.
four students spent $12 on school lunch at this rate find the amount 10 students would spend on the same school lunch
A family pays $45 each month for cable television. The cost increases 7%.
a. How many dollars increases?
b. What is the new monthly cost?
A line goes through the point (5,-7) and has a slope m= -3. Write the equation that represents the line (show work).
The equation that represents the line y = -3x + 8
The slope intercept equation is represented as follows:
y = mx + b
where
m = slope
b = y-intercept
Therefore,
m = -3
y = -3x + b
using (5,-7)
-7 = -3(5) + b
-7 = -15 + b
b = -7 + 15
b = 8
Therefore,
y = -3x + 8
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A bottle containing 64 fluid ounces of juice cost $3.84 what is the unit rate
Answer: $0.06
Step-by-step explanation:
Given : A bottle containing 64 fluid ounces of juice cost $3.84.
i.e. The cost of 64 fluid ounces of juice= $3.84
To find the unit rate , we apply unitary method.
The cost of one fluid ounces of juice = Cost of 64 fluid ounces divided by 64
= $3.84 ÷ 64
= $0.06
Therefore , we get
The cost of one fluid ounces of juice= $0.06
Hence, the unit rate = $0.06
11d=81-16d how do you solve