Answers
The domain is the set of allowed inputs (x). The points on this graph have x coordinates that span from x = 0 to x = 35. Because x is time in minutes, we can have fractions of a minute (eg: x = 7.5 ---> 7 and a half minutes). So we won't just have integers.
Related Questions
Steven investigates the amount of damage to the head gaskets on the trucks in his fleet and finds that the damage index depends on the ambient temperature. He develops the equation y = - 2 3 x + 14 to model the relationship. If the temperature increases 1 degree, what happens to the damage index for the head gasket?
Answers
Answer:
d
Step-by-step explanation:
A painter charges an initial fee of $50 and $30 for each hour of labor. Write a linear function to determine the total cost. How much will it cost if the painter takes 4.5 hours to paint?
Answers
The slope is m = 30 because each increase of 1 hour leads to the cost bumping up by 30 dollars. In other words, slope = rise/run = (change in cost)/(change in hours) = 30/1
So we plug m = 30 and b = 50 into the y = mx+b formula to get y = 30x+50
Replace y with f(x) to get f(x) = 30x+50
The linear function for the cost is f(x) = 30x+50
Note: Some books may use other letters (instead of x and f(x)), but the idea is still the same
Once you know the cost function, you replace x with 4.5 to find the amount it will cost to have a painter work for 4.5 hours.
f(x) = 30x+50
f(4.5) = 30*4.5+50
f(4.5) = 135+50
f(4.5) = 185
It will cost 185 dollars to have the painter work for 4.5 hours
Y = -27x + 577, where x represents the number of weeks and y represents the amount of money left in her account. After how many weeks will Alma have $145 left in her account?
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y = -27x +577
145 = -27x +577
145 -577 = -27x
-432 = -27x
-432/-27 = -27x/-27
16 = x
x = 16
After 16 weeks she will have $145 dollars in her account.
The quotient of 4 and the difference of an integer and 3 is the same as two-thirds. Find the integer.
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Solution:
4/(x-3)= 2/3
12 = 2x-6
18=2x
x= 9
The circumference of a circular field is 295.16 yards what is the radius of the field use 3.14 for pi and do not round your answer
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295.16 = 6.28 x radius
295.16 / 6.28 = radius
47 = radius
The radius of circle is 47 yards.
What is Circumference of circle?The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle. It is typically expressed in units like cm or unit m.
The radius of the circle is considered when applying the formula to determine the circumference of the circle. Therefore, in order to calculate the circle's perimeter, we need to know the radius or diameter value.
Given:
Circumference of circle= 295.16 yards
Now,
circumference of circle= 2πr
295.16= 2 x 3.14 x r
295.16 = 6.28 x r
r = 295.16/ 6.28
r = 47 yards.
Hence, the radius of circle is 47 yards.
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How to solve 3d+8=2d-17
Answers
d + 8 = - 17
d = - 25
The value of d for the expression 3d + 8 = 2d - 17 is -25.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 8 is an equation.
3x = 4 is an equation.
2x = 4 is an equation.
We have,
3d + 8 = 2d - 17
3d and 2d are like terms.
So,
keep like terms on one side.
3 - 2d = -17 - 8
d = -25
Thus,
The value of d is -25.
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The formula for the perimeter of a square is p = 4s, where s is the length of a side. find the perimeter of each square.
Answers
NEED HELP BADLY PLEASEEEE WILL GIVE BRAINLY
List the next three terms in the following sequence:
1, 2, 4, 8, 16, 32,...
a. 48, 80, 128
b. 64, 96, 160
c. 64, 128, 256
d. 46, 92, 184
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Given f(x) = x − 7 and g(x) = x2 . Find g(f(4)). g(f(4)) =
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Hey!
Hope this helps...
~~~~~~~~~~~~~~~~~~~~~~
To solve this we will first find out what f(x) equals at the given point of 4, and than substitute that answer it for g(f(4))...
f(x) = x - 7
f(4) = 4 - 7 = -3
g(f(4)) = (x - 7)^2 > -3^2 = 9
So...
The answer is: g(f(4)) = 9
Answer: 9
Step-by-step explanation:
A given cube has a volume of 1728 cubic inches. Find the length of an edge, area of one side, surface area, and surface area in square feet.
Answers
v=s³
SA=6s²
area of 1 side=s²
s=length of 1 edge
so
1728=s³
cube root both sides
12=s
length of an edge is 12in
the area of one side is 12² or 144 in²
surface area is 6s² or 6(144) or 864 in²
A given cube with a volume of 1728 cubic inches:
Find the length of an edge:The edge length (s) can be found using the formula for the volume of a cube: s³ = 1728. Therefore, s = 12 inches.Find the area of one side:
Each face of the cube is a square, so area of one face = s² = 12² = 144 square inches.Find the surface area:
Total surface area = 6 * (area of one face) = 6 * 144 = 864 square inches.Find the surface area in square feet:
To convert square inches to square feet, divide by 144 (since 1 square foot = 144 square inches). Therefore, surface area in square feet = 864 / 144 = 6 square feet.
16 pound turkey cost $14.24 what is the price per pound
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$14.24 divided by 16
What value of c makes the trinomial below a perfect square x2 + 10x + c?
Answers
x² + 10x + c
calculate the discriminant Δ = b²-4ac a = 1 b = 10 c = c
Δ = 10²-4c
the trinomial below a perfect square when : Δ = 0
10² -4c = 0
4c = 10²
c= 25
x²+10x+25 = x² +2(5)x+5² = (x+5)²
Explain how the energy of a toy car is transformed as it slides down a ramp. Give evidence that the energy of the car remains the same at all points on the ramp.
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Answer:
as the car slides down the ramp it is in kinetic energy and when it is on the top of the ramp it is on potential energy we see that the energy is being transferred
What is the 100th term in the following arithmetic number pattern: 2,7,12
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one dozen eggs cost 1.98$. How much does 1 egg cost? ( round to the nearest cent )
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So, $1.98 divided by 12 = .165 There is a 5 so you would round it up to 17 cents.
The cost of one egg is $0.165.
Given that, one dozen eggs cost 1.98$.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Now, cost of 1 egg = Cost of one dozen eggs ÷ 12
= 1.98/12
=0.165
Therefore, the cost of one egg is $0.165.
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Solve the following problem for the roots by completing the square
3x^2 -12x = 9
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Divide both sides by 3
x^2 - 4x = 3
To make a square with "x^2 - 4x", you need to have a "+ 4" after it so it can be simplified as (x-2)^2. So add 4 to both sides.
x^2 - 4x + 4 = 7
(x-2)^2 = 7
x - 2 = (square root) of 7
x = 2 (+/-) (square root) of 7.
x = {-0.65, 4.65}
The solutions are -0.65 and 4.65.
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Patty is, right now, 3 times as her brother Terry. in 10 years, the sum of their age will be 36. how old are they right now? show your work.
Answers
In 10 years (year z) the sum of their age will be 36
36-20=16
(Twenty being ten years gained for each of them)
16 is now the sum of their age in year x
The following are options for the ages they could possibly be
1-15 (1*3 does not equal 15)
2-14(2*3 does not equal 14)
3-13(3*3 does not equal 13)
4-12(4*3 equals 12)!!!!
5-11(5*3 does not equal 11)
6-10(6*3 does not equal 10)
7-9 (7*3 does not equal 9)
8-8(8*3 does not equal 8)
Therefore the answer would be:
Patty is 22 and his brother is 14
Patty is 12 years old, and Terry is 4 years old. After setting up an equation based on their ages now and in 10 years, we determine that Terry is 4, and since Patty is three times as old, she is 12.
The problem presented is a typical age-related algebraic question. To solve it, we can set up equations based on the information given. Let's define Patty's current age as 3T, where T represents Terry's current age. In 10 years, Patty will be 3T + 10 and Terry will be T + 10. According to the problem, the sum of their ages in 10 years will be 36. So, we can write the following equation:
3T + 10 + T + 10 = 36
Solving this equation:
Combine like terms: 4T + 20 = 36Subtract 20 from both sides of the equation: 4T = 16Divide both sides by 4 to find Terry's age: T = 4With Terry's age being 4, Patty's current age is 3 times Terry's age, which means Patty is 3 × 4 = 12 years old. So, Patty is 12 and Terry is 4 years old right now.
Question 1 (3 points) study the Proof Given.
List the reasons for Items 2,3, & 4.
Right the number and then the answer.
Question 2 (3 points
)Study the Proof: Give the reasons for the missing reason. List the number and then state the reason.
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2. Definition of midpoint
3. Given
4. Transitive Property
Question 2
1. Given
2. Addition Property of Equality
3. Segment Postulate Property.
Express the volume v of the box as a function of the length x of the sidfe of the square cut from each corner
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It snowed 4 times during October. The snowfall amounts were 0.75 inches, 1.93 inches, 4.73 inches, and 2.33 inches. What was the total snowfall for October?
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The total snowfall for October was 9.74 inches. Adding the snowfall amounts of 0.75, 1.93, 4.73, and 2.33 inches resulted in this sum.
Let's break down the calculation step-by-step:
Identify the given snowfall amounts for October:
The snowfall amounts are 0.75 inches, 1.93 inches, 4.73 inches, and 2.33 inches.
Add up the snowfall amounts to find the total:
Total snowfall = 0.75 inches + 1.93 inches + 4.73 inches + 2.33 inches.
Perform the addition
Total snowfall = 9.74 inches.
The total snowfall for October was 9.74 inches. This result is obtained by adding all four individual snowfall amounts together.
So, the calculation in step-by-step form is as follows:
0.75 + 1.93 + 4.73 + 2.33 = 9.74 inches.
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what property is illustrated by this problem 2(3 + 4) = 2x 3 +2 x 4
Answers
The quotient of a number and five increased by four is sixteen answer
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Answer: [tex]\dfrac{x}{5}+4=16\\\\and\\\\x=60[/tex]
Step-by-step explanation:
Since we have given that
The quotient of a number and five increased by four is sixteen a
Let the number be 'x'.
The quotient of a number and five is written as
[tex]\dfrac{x}{5}[/tex]
And it is increased by 4 is written as
[tex]\dfrac{x}{5}+4[/tex]
And the equation is equal to 16.
[tex]\dfrac{x}{5}+4=16[/tex]
And the solution would be
[tex]\dfrac{x}{5}+4=16\\\\\dfrac{x}{5}=16-4=12\\\\x=12\times 5\\\\x=60[/tex]
Hence, [tex]\dfrac{x}{5}+4=16\\\\and\\\\x=60[/tex]
Explain why the following statement are equivalent 4(x+y)=4x+4y
Answers
The equation 4(x+y)=4x+4y represents the same value after solving.
What is Distributive Property?This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.
Given:
We have 4(x+y)=4x+4y.
We have the Distributive Property
a x ( b+ c )= a x b + a x c
let x= 2 and y = 5
So, 4 (x+ y) = 4 (2+ 5)= 4(7) = 28
and, 4x+ 4y= 4(2)+ 4(5) = 8+ 20 = 28
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six times the reciprocal of a number equals 2 times the reciprocal of 6. find the number.
Answers
6(1/x) = 2(1/7)
-----
6/x = 2/7
-----
2x = 42
x = 21
6/x = 1/3
6/x*1/6 = 1/3*1/6
x= 1/18
the number is 18
40 students are going on a field trip to the aquarium. Every student needs to be in a group, and all groups must have the same number of students. If there is 1 group, there will be students in the group. If there are groups, there will be 20 students in each group. If there are 4 groups, there will be students in each group.
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If there is 1 group there will be 40 students in the group. There will be 20 students in each group if there are 2 groups. If there are 4 groups, there will be 10 students in each group.
What is Division?Division is one of the four basic operations of mathematics.
On performing the operation division, a number is divided into some number of equal parts.
The number which is being divided is called the dividend, the number which divides the dividend is called divisor and the number got when division is performed is called the quotient and the remaining number which has not divided is called the remainder.
Total number of students = 40
If there is 1 group, number of students in the group = 40/1 = 40
If there are 20 students in each group, then the number of groups = 40/20 = 2.
If there are 4 groups, then number of students in each group = 40/4 = 10.
Hence there will be 40 students in the group if there is 1 group. There are 2 groups if there will be 20 students in each group. There will be 10 students in each group if there are 4 groups.
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A kennel owner needs 4 1/2 feet of wall space for each crate. How many crates can she fit along a 27 foot wall?
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Is 0 prime odd or even prime or composite?
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Answer:
0 is nor prime or composite
Step-by-step explanation:
The definition of a prime number is a positive integer that has exactly two positive divisors. Therefore, the simplest reason why 0 is not prime is that 0 is not a positive integer, and the axiom says that all whole numbers greater than 1 are either prime or composite.
Determine if f is a linear or nonlinear function and if f is a constant function.
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function is linear when are the form : y = ax +b
function is linear constant are the form : y = b
235+374= use rounding or compatible numbers to estimate the sum
Answers
round to hundreds: 200 + 400 = 600
hope this helps
With regard to mathematics, what is an accepted statement of fact that is used to prove other statements