Answers
Using linear functions, we have that:
a) The rate of change for Job A is of $14, while the rate of change for Job B is of $17, and these are the hourly pay for each job.
b) The slope represent the hourly pay for each job.
c) The intercepts represent the fixed salary for each job.
d) The pay will be the same on both jobs after 25 hours, of $425, as given by the intersection point on the graph.
e) For 40 hours, the payment on Job A is of $635 and on Job B of $680, hence, due to the higher payment, Tommy should accept Job B.
What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For this problem, the two functions are given as follows:
A(h) = 75 + 14h. (slope of 14 as when x changes by 2 y changes by 28).B(h) = 17h. (slope of 17 as when x changes by 2 y changes by 34).The functions are graphed at the end of the answer.
Hence:
a) The rate of change for Job A is of $14, while the rate of change for Job B is of $17, and these are the hourly pay for each job.
b) The slope represent the hourly pay for each job.
c) The intercepts represent the fixed salary for each job.
The pay will be equal when:
A(h) = B(h)
Hence:
75 + 14h = 17h
3h = 75
h = 25.
d) The pay will be the same on both jobs after 25 hours, of $425, as given by the intersection point on the graph.
For 40 hours, the payments are given as follows:
A(40) = 75 + 14 x 40 = $635.B(40) = 17 x 40 = $680.Hence:
e) For 40 hours, the payment on Job A is of $635 and on Job B of $680, hence, due to the higher payment, Tommy should accept Job B.
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Related Questions
Give an argument that shows that every polynomial family of degree n>2 contains polynomials that cannot be generated from the basic function y=xⁿ by using stretches, compressions, reflections, and translations.
Answers
Answer: because if you have a argument you have all.
Step-by-step explanation:
5. A bird is at 20 feet above sea level. A fish is 14 feet below sea level. What is the difference? on the number line
Answers
Answer:
I think its 34 feet
Step-by-step explanation:
If you subtract 20 to get to 0 its 20, minus another 14 to get to zero is 14. Add them and you get 34 feet. Hope it helps! =)
The difference in their positions on the number line is 34 feet
How to determine the difference on the number linefrom the question, we have the following parameters that can be used in our computation:
Bird = 20 feet above sea level
Fish = 14 feet below sea level
using the above as a guide, we have the following:
Bird = 20 feet
Fish = -14 feet
So, we have
Difference = 20 feet - -14 feet
Evaluate
Difference = 34 feet
Hence, the difference on the number line is 34 feet
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HAND-WRITTEN ANSWER ONLY
The state of Tennessee is shaped like a parallelogram. Its approximate
dimensions are a base of 440 miles and a height of 120 miles. Draw
Tennessee, label the dimensions and find the approximate area.
Answers
The area of a parallelogram when the dimensions are a base of 440 miles and a height of 120 miles is 52800 miles²
How to calculate the value?It should be noted that the area of a parallelogram is calculated by multiplying the base by the height.
The dimensions are a base of 440 miles and a height of 120 miles.
The area of the parallelogram will be:
= Base × Height
= 440 × 120
= 52800 miles²
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Simplify each expression.
125¹/₃
Answers
The questions tests on indices. Write 125 in form of its prime factors. Apply the power rule (a^m)^(1/n)=a^(m/n). In prime factor form 125 = 5×5×5
125 = 5^3
(125^3)^(1/3) = 5^(3×1/3) = 5
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M bisects PQ. PM=9x + 3 and MQ= 11x -17, find x.
Answers
Applying the definition of a midpoint, the value of x is calculated as: x = 10.
What is the Midpoint of a Segment?The midpoint of a segment, for example, point M, is a point that bisects a segment into two equal parts with the same measurement.
Thus, this means that:
PM = MQ
PM = 9x + 3
MQ = 11x - 17
Substitute
9x + 3 = 11x - 17
Combine like terms
9x + 3 - 11x = 11x - 17 - 11x
-2x + 3 = -17
-2x + 3 - 3 = -17 - 3
-2x = -20
-2x/-2 = -20/-2
x = 10
Thus, applying the definition of a midpoint, the value of x is calculated as: x = 10.
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HELP PLEASE I NEED HELPPI’ll make you brainlist and it’s Algebra btw
Answers
=====================================================
Explanation:
The regression equation is in the form y = mx+b
m = slope = -0.624b = y intercept = 66.022The slope tells us how much the value of y changes each time x goes up by 1. In this case, the scores decrease by 0.624 percentage points each time x goes up by 1
You can think of it like saying
slope = rise/run = -0.624/1rise = -0.624 = y drops by 0.624run = 1 = x increases by 1This is why the answer is 0.624. We don't type the negative sign because that is part of the term "decrease".
The terms grid, linear, quadrant, zone, and spiral are typically used to describe datum points. True or false?.
Answers
It is untrue to claim that words like grid, linear, quadrant, zone, and spiral are frequently used to refer to datum points.
A location that acts as a base or reference for the measurement of other quantities is known as a datum point. It can be located at any reference point where known or guessed coordinates can be used to make calculations or measurements.
Datum references, which the maker can choose, are used when marking out an object as a reference point from which all measurements are obtained. Accuracy can be increased and maintained by measuring from a limited selection of fixed points.
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b. An 80 -kg diver stands on a 6 -m diving platform. At what height should a 40 - kg diver stand to have equal potential energy? Do you need to find the potential energy of either diver to solve this? Explain.
Answers
The 40kg driver should be able to sit on the 12m driving platform to have equal potential energy.
What is potential energy?Potential energy is the energy held by an object as a result of its position relative to other objects, internal stresses, electric charge, or other factors.The gravitational potential energy of an object, which depends on its mass and distance from the center of mass of another object, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field are all examples of common types of potential energy. The joule, denoted by the symbol J, is the unit of energy in the International System of Units (SI).The formula of the potential energy of each driver:
Driver 1: PE = gmh = 9.8 · 80 · 6Driver 2: PE = gmh = 9.8 · 40 · hReplace the value of PE for driver 1 with the driver 2 formula.
9.8 · 80 · 6 = 9.8 · 40 · hNow, solve for (h) height:
9.8 · 80 · 6/9.8 · 40 ⇒ h - 12Therefore, the 40kg driver should be able to sit on the 12m driving platform to have equal potential energy.
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At a constant of 80 kilometres per hour, it would take 35 years to travel over the entire road network of the world. Taking a year as 365 days, calculate the length of the road network of the world, giving your answer in standard form.
Answers
Answer:
115
Step-by-step explanation:
For each direct variation, find the constant of variation. Then find the value of y when x=-3 .
y=-5 when x=3/2
Answers
After direct variation y = 10 when x = -3.
What do we mean when we say "direct variation"?To give the reader a hint, direct variation equations use the same phrase.The phrase could be "directly proportional" or "directly varies."For example, the area of a square is proportional to the square of its side.The variational constant is k = 3 if y varies directly as x and y = 6 when x = 2.As a result, y = 3x is the direct variation equation.So,
The initial statement is y = kx
Then to find y when x = -3.
K constant will be y/x ⇒ -5/3/2 = -10/3That is y = kx ⇒ y = -10/3 × xWhen x = -3:
y = -10/3 × -3 ⇒ y = 10Therefore, y = 10 when x = -3.
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9. Find m
a. 52
b. 38
c. 12
d. 22
Answers
Answer:
∠ ABC = 52° , ∠ CBD = 38°
Step-by-step explanation:
the 2 angles form a right angle and sum to 90° , that is
∠ ABC + ∠ CBD = 90
4x + 4 + 5x - 22 = 90
9x - 18 = 90 ( add 18 to both sides )
9x = 108 ( divide both sides by 9 )
x = 12
then
∠ ABC = 4x + 4 = 4(12) + 4 = 48 + 4 = 52°
∠ CBD = 5x - 22 = 5(12) - 22 = 60 - 22 = 38°
#11 What is the absolute
value of -19?
Answers
HELPPPP DUE IN 1 HOUR
Answers
Answer:14.12
Step-by-step explanation:
Determine whether each conjecture is true or false. Give a counterexample for any false conjecture.
1. If AB, BC, and AC are congruent, then A, B, and C and colllinear.
2. If <1 is complementary to <2, and <1 is complementary to <3, then <2 ≅ <3.
Answers
The given conjecture "If AB, BC, and AC are congruent, then A, B, and C and colllinear" is false.
How to Interpret Conditional Statements?Notice that the given conjecture does not necessarily be always true.
To be precise; there are no reasons as to why A, B and C must be noncollinear.
1. we are given If AB, BC, and AC are congruent, then A, B, and C and colllinear.
A,B ,C are not collinear so it will be false
Therefore, the given conjecture "If AB, BC, and AC are congruent, then A, B, and C and colllinear" is false.
A Counter- example of the given statement is that A, B, C are three points that lie on the same line and so they are collinear.
2. We are given If <1 is complementary to <2, and <1 is complementary to <3, then <2 ≅ <3.
It may be true.
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How can you rewrite each function as a piecewise-defined function?
f(x) = -5x - 10|
Answers
Value of the given function as a piecewise-defined function is equal to
f(x) = -5x -10 , x ≤ -2
5x +10 , x > -2
As given in the question,
Function as a piecewise-defined function
y = |x| = x , x≥0
-x , x<0
Given function: f(x) = |-5x-10|
-5x -10≥0 ⇒ -5x ≥ 10 ⇒x ≤ -2
-5x -10 <0 ⇒ -5x < 10 ⇒ x> -2
Therefore, value of the given function as a piecewise-defined function is equal to
f(x) = -5x -10 , x ≤ -2
5x +10 , x > -2
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Simplify each number.
64²/₃
Answers
The simplified form of given number is 16
We are given the number 64 with exponent ²/₃
Now, as per the known fact, cube of 4 is equal to 64. As, 4 multiplied with 4 gives 16. Further multiplying 16 and 4 gives 64. So, rewriting the number using 4 as follows -
Number = [tex]4^{3(2/3) }[/tex]
Cancelling 3 from exponent as it is present in both numerator and denominator. Rewriting the number with remaining exponent to find the simplified form of the number-
Number = 4²
Taking square of the number to find the simplified form of the number given in question
Number = 16
Hence, the simplified form of the number is 16
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The cost of downloading a book from a certain website is $5.99. The cost of downloading a video is $7.99. Tatum's mom downloads 3 books and 5 videos.
Answers
The total required cost of downloading books and videos is $57.92
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the total cost of downloading books and videos?The given parameters are:
Cost of downloading a book = $5.99
Cost of downloading a video = $7.99
The number of books and videos downlaoded are
Books = 3
Videos = 5
So, the total cost of downloading books and videos is
Total cost = Cost of downloading a book * x + Cost of downloading a video * y
This gives
Total cost = Cost of downloading a book * Books + Cost of downloading a video * Videos.
This gives
Total cost = 5.99 * 3 + 7.99 * 5
Evaluate
Total cost = 57.92
So, the total cost of downloading books and videos is $57.92
Hence, the total required cost of downloading books and videos is $57.92
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pls help w this pretty urgent
Answers
Answer:
[tex]\textsf{a)} \quad g'(x)=2x-4[/tex]
[tex]\textsf{b)} \quad y=2x[/tex]
[tex]\textsf{c)} \quad x=5[/tex]
Step-by-step explanation:
Given function:
[tex]g(x) = x^2-4x+9[/tex]
Part (a)Differentiate the given function with respect to x:
[tex]\begin{aligned}g(x) & = x^2-4x+9\\\implies g'(x) & = 2 \cdot x^{2-1}-1 \cdot 4x^{1-1}+0\\& = 2x^{1}-4x^{0}\\& = 2x-4(1)\\& = 2x-4 \end{aligned}[/tex]
Part (b)The y-value of the function at x = 3:
[tex]\begin{aligned}\implies g(3) & = (3)^2-4(3)+9\\& = 9-12+9\\& = -3+9\\& = 6\end{aligned}[/tex]
Therefore: (3, 6).
To find the slope of the function at x = 3, substitute x = 3 into the differentiated function:
[tex]\begin{aligned}\implies g'(x) & = 2(3)-4\\& = 6-4\\& = 2\end{aligned}[/tex]
Therefore, the slope of the function at x = 3 is 2.
Substitute the found slope and point (3, 6) into the point-slope form of linear equation to find the equation of the tangent line of g(x) at x = 3:
[tex]\begin{aligned} y-y_1 & =m(x-x_1)\\\implies y-6 & = 2(x-3)\\y-6 & = 2-6\\y & = 2x-6+6\\y&=2x\end{aligned}[/tex]
Part (c)To find the value of x for which the slope of the graph is equal to 6, set the differentiated function to 6 and solve for x:
[tex]\begin{aligned}g'(x) & = 6\\\implies 2x-4 & = 6\\2x & = 6+4\\2x & = 10\\x & = \dfrac{10}{2}\\x & = 5\end{aligned}[/tex]
What is the logarithmic form of each equation?
a. 36=6²
Answers
The logarithmic form is 2log₁₀6
Logarithm is a mathematical tool used to make high value calculations simple.
It is the exponent to the power of which a number must be raised to give a certain result.
Some of the important formulas in logarithm are:
loga where a is considered as base of the logarithm and b is the argument
is given as nlogab
when base and the argument is same , log is given as 1
logabc where a is the base is given as logab+logc
loga b/c where a is the base is given as logab-logac
Now it is given to us to find the logarithmic form of 36=6^2
Let us consider the base of the logarithm to be 10
thus log₁₀36=log₁₀[tex]6^{2}[/tex]
log₁₀36=2 log 6
Hence the expression becomes 2log6
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Solve each inequality using a table.
(Hint: For more accurate results, set ΔTbl=0.001. )
3(2) x⁺¹>5
Answers
After solving the given inequality the answer is x∈(5/6, ∞).
What exactly do we mean when we talk about inequality?In mathematics, an inequality is a relationship that results from a non-equal comparison of two numbers or other mathematical expressions.It is most commonly used on a number line to compare the sizes of two numbers.So,
Given: 3(2) x¹>5
Then,
3(2) x¹>5 6x>5x∈(5/6, ∞)Therefore, after solving the given inequality the answer is x∈(5/6, ∞).
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what do this mean positive number and negative numbers mean in context to sea level
and elevation.
Answers
whats the value of n
n/80 3/30
Answers
3/30 = 8/80
N = 8
Model Real Life Some firefighters are
testing their equipment. Water from
their firetruck hose hits the wall 12 feet
higher than 7 times where the spray
from a fire extinguisher hits the wall.
How many feet high does the water
from the hose hit the wall?
Answers
The height in feet that the water from the hose hits the wall is; 7x + 12 ft
How to solve Algebra Word Problems?Let the height where the spray from a fire extinguisher hits the wall be denoted as x.
Now, we are told that Water from their firetruck hose hits the wall 12 feet
higher than 7 times where the spray from a fire extinguisher hits the wall.
Thus, the algebraic equation that expresses this statement is;
7x + 12
Thus, the height in feet that the water from the hose hits the wall is; 7x + 12 ft
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Let f(x)=4 x, g(x)=1/2 x+7 , and h(x)=-2 x+4 . Perform each function operation. f(x) . g(x)
Answers
The value of f(x) . g(x) is [tex]2x^2+28x[/tex] by using multiplication of functions.
By considering the given functions
f(x)=4 x
g(x)=1/2 x+7
f(x) . g(x)
=4 x (1/2 x+7 )
[tex]=2x^2+28x[/tex]
A y-intercept, a horizontal asymptote, a domain (the range of x values at which the function exists), and a constant growth factor, b, are the four main characteristics of exponential functions.
A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions are everywhere, and they are crucial for constructing physical relationships in the sciences.
Four broad categories can be used to classify different types of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.
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29.14 × 5.2 estimation step by step please
Answers
5.2 rounded to 5.0 or 5
So…
30 X 5 = 150
The answer is 150
Owen’s parents were planning a big birthday party for him.
(a). His parents bought 8 goodie bags. Each bag costs $3.49. How much did they spend on goodie bags?
(b). They spent $150 to rent a bounce house for 4 hours. How much is the hourly rate for the rental?
(c). How much total money did Owen’s parents spend buying the goodie bags and renting the bounce house?
Answers
answer: they spend $27.92 on goodie bags
the hourly rate is $37.5
they spend $177.92 in total
You are filling traffic cones with sand to keep them from blowing over. the cone has a radius of 7 inches and a height of 28 inches. approximately how much sand, in cubic inches, can fit inside the cone?
Answers
If you are filling traffic cones with sand to keep them from blowing over and the cone has a radius of 7 inches and a height of 28 inches, then 1436 cubic inches of sand can fit inside the cone.
The volume of the cone can be described as the measure of a 3-D space occupied by matter.
The volume of sand in cubic inches that can fit inside the traffic cone can be calculated by the formula,
v = πr²h / 3
As the radius of the cone = 7 inches
Height of the cone = 28 inches
v = π(7)²28 / 3
v = (π)(49)(28) / 3
v = (π)(1372) / 3
As π = 3.14
v = (3.14)(1372) / 3
v = 4308.08 / 3
v = 1436.02 ≈ 1436 cubic inches
Hence, 1436 cubic inches of sand is calculated to fit inside the cone.
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1. What is greenhouse effect?
Answers
The heat of the sun penetrates the atmosphere and warms the Earth's surface. The warmed rEarth Radiates and this heat back into the atmosphere.The gases the surround the atmosphere such as carbon dioxide , methane , nitrous oxide and water vapour absorb some of the radiated heat and send it back to the Earth . This trapping of heat from the Sun by excess carbon dioxide and other gases present in the atmosphere is known as the greenhouse effect. The gases involved in the phenomenon are called greenhouse gases.
Hope it helps ~(•‿•)In art class, Mr. Jacobs compared the amount of glitter left on students' plates. The following dot plot shows this data. Each dot represents 1 student. If he wants to combine the two least full plates of glitter, what fraction of a plate would they take up?
Answers
When he wants to combine the two least full plates of glitter, the fraction of a plate that they would they take up is 1/4.
How to illustrate the information?It should be noted that from the information, in the art class, Mr. Jacobs compared the amount of glitter left on students' plates and the dot plot shows this data
It should be noted that the least two plates of glitters will be:
= 1/4 + 2/4
= 3/4
Therefore, when e wants to combine the two least full plates of glitter, the fraction of a plate that they would they take up will be:
= 3/4 ÷ 3
= 3/4 × 1/3
= 1/3
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Aisha organized her books for 1/6 and her coin collection for 3/7.
What's the best estimate for the total Aisha spent organizing?
(Brainliest Question)
Answers
The best estimate for the total Aisha spent organizing is; 1/2 hour
How to estimate fractions?We are told that Aisha organized her books for 1/6 and her coin collection for 3/7.
Now, normally when we want to find the total, we just add both fractions in this manner;
1/6 + 3/7 = 25/42
Now, since we want to find the best estimate, we will just approximate each fraction individually to get;
1/6 hour is closer to 0 hours than 1/2 hour. Thus;
1/6 hr ≈ 0 hour
3/7 hour is closer to 1/2 hour than 0 hours. Thus;
3/7 hr ≈ 1/2 hour
Thus;
Best estimate for total spent = 0 + 1/2 = 1/2 hour
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