Examine the table, which represents a linear function. Input (C) output (y) 8 -40 -49 -58 What is the rate of change of the function? Enter your answer as a number, like this: 42(from MATH workbook 8A)
Answers
Answer:
-3
Explanation:
To calculate the rate of change of the function, we pick two pairs of points.
(8, -40) and (17,-67)
We use the formula below:
[tex]\begin{gathered} \text{Rate of change}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{-67-(-40)}{17-8} \\ =\frac{-67+40}{17-8} \\ =\frac{-27}{9} \\ =-3 \end{gathered}[/tex]The rate of change of the function is -3.
Related Questions
the mayor of a town believes that under 46% of the residents favor construction of an adjoining bridge. is there sufficient evidence at the 0.05 level to support the mayor's claim? after information is gathered from 190 voters and a hypothesis test is completed, the mayor fails to reject the null hypothesis at the 0.05 level. what is the conclusion regarding the mayor's claim?
Answers
Since the null hypothesis was not rejected, there is not enough evidence to conclude that under 46% of the residents favor construction of an adjoining bridge.
What is the relation between the decision and the conclusion?There are two decisions possible regarding the null hypothesis, as follows;
Reject the null hypothesis.Do not reject the null hypothesis.The hypothesis are given as follows:
Null hypothesis: proportion is not under 46%.Alternative hypothesis: proportion is under 46%.The null hypothesis was not rejected, meaning that the conclusion regarding the mayor's claim is that there is not enough evidence from the sample of 190 voters to conclude that the percentage is below 46%.
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I need help with my exam practice homework . Question 3 please
Answers
we have that
The double angles formula is equal to
[tex]\cos (2\theta)=\cos ^2(\theta)-\sin ^2(\theta)[/tex]and remember that
[tex]\begin{gathered} \sin ^2(\theta)+\cos ^2(\theta)=1 \\ \cos ^2(\theta)=1-\sin ^2(\theta) \end{gathered}[/tex]therefore
substitute in the original expression
[tex]\begin{gathered} \cos (2\theta)=1-\sin ^2(\theta)-\sin ^2(\theta) \\ \cos (2\theta)=1-2\sin ^2(\theta) \end{gathered}[/tex]therefore
The third option is incorrectPls help i need this answered quickly
Tess builds a sandbox in the shape of a regular hexagon in which all the sides are 40 inches long. She then takes a photo of the sandbox and prints the photo. In the photo, the sides of the hexagon are each 4 inches long. Identify the scale factor that was used to create the printed photo of the sandbox. Express your answer as a decimal.
Answers
A scale factor of 0.1 was used to create the printed photo of the sandbox
How to find the scale factor used for the printed photo of the sandbox?A scale factor is the size by which a shape is enlarged or reduced. It is used in increasing or reducing the size of a 2D shape, such as circle, triangle, square, rectangle, hexagon, etc.
Given that: Tess builds a sandbox in the shape of a regular hexagon in which all the sides are 40 inches long, and in the photo, the sides of the hexagon are each 4 inches long
The scale factor will be:
4/40 = 1/10 = 0.1
This means the sandbox has been reduced by 10 times the original size
Therefore, the scale factor that was used to create the printed photo of the sandbox is 0.1
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How do I find the area of a trapezoid 6ft by 9ft
Answers
Given the following question:
Where the trapezoid is...
6ft by 9ft
Find the area:
[tex]A=(a+b)\times h\div2[/tex]What is an equation of the line that passes through the points (-5, -7) and
(-5, 6)?
Answers
I believe it would be x = -5.
Hope this helps!
I need help on a problem
Answers
in this problem we have that
Triangle JTN is an isosceels triangle, because the triangle has two equal sides and two equal interior angles
segment TE is the altitude of triangle JTN, its a perpendicular bisector segment JN
that means
JE=NE
we have
JT=NT
mso
triangle TJE and triangle TNE are congruent by SAS
triangles TJE and trTNE are acute triangles
Question 2(Multiple Choice Worth 2 points)
(Irrational Numbers MC)
Approximate -16+√40 to the nearest tenth.
Answers
The value of an irrational number [tex]-16 + \sqrt{40}[/tex] Is approximate, the nearest tenth is -9.675.
What are irrational numbers?Irrational numbers include all real numbers that cannot be stated as the ratio of two integers, or p/q, where p and q are both integers.
Given expression:
[tex]-16 + \sqrt{40}[/tex]
Factorize the square part as
[tex]-16 + \sqrt{10\times2^2 }[/tex]
Simplify the above expression as
[tex]-16 + 2\times \sqrt{10}[/tex]
We know that [tex]\sqrt{10} = 3.132[/tex]
Hence, -16 + 2 × 3.132
= -9.675
Therefore, the value of an irrational number [tex]-16 + \sqrt{40}[/tex] is approximately the nearest tenth is -9.675.
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help in mathematics pls i am troubled
Answers
Answer:
It's very blurry, try sending one section at a time.
Step-by-step explanation:
Question 1(Multiple Choice Worth 2 points)
(Converting Between Systems MC)
I need help pleaseeee
For a craft project you need 182 inches of ribbon, but it is only sold by the meter. Determine the amount of ribbon, in meters, you need to buy for the project. (1 inch = 2.54 centimeters and 1 centimeter = 0.01 meter)
462
47
12
5
Answers
The amount of ribbon needed to buy for the project in meters is (d) 5.
According to question,
1 centimeter = 0.01 meter
2.54 centimeter = 0.01*2.54
= 0.0254 meters
1 inches = 2.54 centimeters
= 0.0254 meters
Amount of ribbon needed for project = 182 inches
= 182 * 0.0254 meters
= 4.62 meters
≅ 5 meters
Hence, 5 meters of ribbon is needed for the project.
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Answer the question below.
Answers
The formula that can be used to find the nth term of the sequence is aₙ = 4n + 1
How to find the formula of an arithmetic sequence?The sequence follows an arithmetic patterns. Therefore, the formula for arithmetic progression can be used to find the nth term as follows:
aₙ = a + (n - 1)d
where
n = number of termsd = common differencea = first termTherefore, using the sequence 5, 9, 13, 17, 21
a = 5
d = 9 - 5 = 4
Hence,
aₙ = 5 + (n - 1)4
aₙ = 5 + 4n -4
aₙ = 5 - 4 + 4n
Therefore,
aₙ = 4n + 1
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What is the solution to this equation?
−15(x+134)=−212
Responses
x=2114
x equals 21 and 1 over 4
x=1414
x equals 14 and 1 over 4
x=1034
x equals 10 and 3 over 4
x=334
Answers
Answer: 10 3\4
Step-by-step explanation:
I did the quiz
It is possible for 2 lines to
intersect in such a way
that 3 of the angles
formed have measures 20,
70, and 20.?
Sometimes true,
Never true,
Always true.
Answers
Answer:
sometimes true
Step-by-step explanation:
Given, two straight lines intersect each other in such a way that one of the angles formed measure 90°.
We know that, lines which intersect to form a right angle are known as perpendicular lines
In the above figure , AB is perpendicular to CD
Considering ∠AOC=90°
Now,
∠AOC+∠AOD=180° [Linear pair]
90°+∠AOD=180°
∠AOD=90°
Similarly,
∠AOC+∠BOC=180° and ∠BOD+∠AOD=180° [Both making linear pair]
So, we get ∠BOC=90° and ∠BOD=90°
Hence, ∠AOC=∠AOD=∠BOC=∠BOD=90°
A cyclist travels north along a road at a constant speed of 18 miles per hour. At 1:00 P.M., a runner is 46 miles away, running south along the same road at a constant speed. They pass each other at 3:00 P.M.. What is the speed of the runner?
Answers
By forming and solving equations, we know that the speed of the runner is 4 miles per hour.
What are equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions. An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. As in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others. The three primary forms of linear equations are point-slope, standard, and slope-intercept.So, we need to form an equation to get the speed of the runner:
2 × (18 + x) = 44'x' is the speed of the runner. Now, solve for x as follows:
2 × (18 + x) = 4418 + x = 44/218+x = 22x = 22 - 18x = 4 miles per bourTherefore, by forming and solving equations, we know that the speed of the runner is 4 miles per hour.
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what is 178 x 82 ???????????????????????
Answers
Answer: It is 14,596.
Choose the line parallel to the following equation through the given point
Answers
Answer:
y = 2x + 1
Step-by-step explanation:
→ Find the gradient of this line
2
→ Write in standard format
y = 2x + c
→ Substitute in ( 0 , 1 )
1 = 0 + c ⇒ c = 1
PLEASE ANSWER QUICKLY I WILL GIVE BRAINLIEST!
Which of the following are measures of variation? Select two options.
median
standard deviation
mode
mean
range
Answers
Write the first five terms of the geometric sequence with a1 = 16 and common ratio r= 3/2
Answers
From the problem, we need to find the first five terms of the geometric sequence.
The first term, a1 = 16 and the common ratio, r = 3/2
Note that the succeeding term is the previous term multiplied by the common ratio.
This will be :
[tex]\begin{gathered} a_2=a_1r=16(\frac{3}{2})=24 \\ a_3=a_2r=24(\frac{3}{2})=36_{} \\ a_4=a_3r=36(\frac{3}{2})=54 \\ a_5=a_4r=54(\frac{3}{2})=81 \end{gathered}[/tex]The geometric series is :
an = {16, 24, 36, 54, 81, ...}
The answer is B. an = {16, 24, 36, 54, ...}
Identify the roots of:y = x² - 12x + 32
Answers
Okay, here we have this:
Considering the provided function, we are going to calculate the requested roots, so we obtain the following:
[tex]\begin{gathered} x^2-12x+32=0 \\ x_{1,2}=\frac{-(-12)\pm\sqrt{(-12^2)-4(1)(32)}}{2(1)} \\ x_{1,2}=\frac{12\pm\sqrt{144-128}}{2} \\ x_{1,2}=\frac{12\pm\sqrt{16}}{2} \\ x_{1,2}=\frac{12\pm4}{2} \\ x_{1,2}=6\pm2 \\ x_1=6+2,x_2=6-2 \\ x_1=8,x_2=4 \end{gathered}[/tex]Finally we obtain that the roots of the function are x=8 and x=4.
If given f(x) = –4x – 2 and g(x) = 2x ^2 + 4x-5, what is (f · g)(x)?
Answers
The addition of the given two functions f(x) = –4x – 2 and g(x) = 2x ^2 + 4x-5 will be (f · g)(x) = 2x²-9
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
Given f(x)= -4x-2
g(x)=2x²+4x-5
For (f-g)(x) = -4x-2+2x²+4x-5
=2x²-9
(f-g)(x) = 2x²-9
Hence, The addition of the given two functions will be (f · g)(x) = 2x²-9
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A city has 14,200 people. In a random sample
Answers
Answer:
43/80 * 14,200
Step-by-step explanation:
Since 80 random people were sampled its will become our denominator and out of 80 people there were 43 people and that 43 will become our numerator the next step is to mulitply 14,200 (im really bad at explaining stuff hope it helps!)
Answer:
43/80 * 14,200
Step-by-step explanation:
It was right when I answered it.
Kim and steve went to dinner. kim has a coupon for a 25% discount of all meals not including tax and tip. if the original price of the meal was $75, how much money will they save?
Answers
The amount Kim and Steve will save is $18.75.
Define discountDiscount refers to a price decrease on items or services that merchants are willing to sell to customers at a marked-up price. Usually, this portion of the rebate is provided to boost sales or get rid of unsold inventory. The list price, also known as the marked price, is the cost of a product as stated by the manufacturer or the seller, and it does not include any discounts. After any reductions or discounts to the list price, the selling price is the actual price at which an item is sold. Discounts are frequently referred to as "off" or "reductions," among other names. It should be noted that the discounted price is always based on the marked price (also known as the list price or original price) of the product.
Given, the discount they have is of 25%.
Original price of the meal is $75.
Now find the discount on the original price.
Discount = Discount (%) * Original Price
= [tex]\frac{25}{100} *75[/tex]
= 0.25*75
= $18.75
Therefore, they saved an amount of $18.75.
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Twenty-five of 75 fifth-grade students went to a bake sale after school. Which fraction shows, in simplest form, the part of the class that did NOT go to the bake sale?
Answers
Answer:1/3
Step-by-step explanation:
25/75
25/25=1
75/25=3
Answer is 25/75=1/3
A customer at a shipping store is planning to send a package and is considering two options. The customer can send a package for $3, plus an additional $2 per pound. The cost, y, can be represented by the equation y = 3 + 2x, where x represents the amount of pounds of the package. Another option is that the customer can pay a one-time fee of $17 to send the box, represented by the equation y = 17.
Based on the graph of the system of equations, when will the cost of the two shipping options be the same?
A package that weighs 10 pounds will cost $17 for both options.
A package that weighs 7 pounds will cost $17 for both options.
A package that weighs 17 pounds will cost $31 for both options.
A package that weighs 17pounds will cost $37 for both options.
Answers
The correct option is :
A package that weighs 7 pounds will cost $17 for both options.
What is an equation ?The declaration that shows that the provided variables exist is a mathematical equation. When describing the scenario in this circumstance, two or more factors are taken into account.
The equation can be used to symbolize the price, y: Y is equal to 3 plus 2 times the weight of the package, x.
Another choice is for the buyer to pay a one-time price of $17, which is represented by the equation y = 17, in order to send the package.
We'll compare the equation as a whole.
In this case,
3 + 2x = 17
Compile similar terms
2x = 17 - 3
2x = 14
x = 14 divided by 2x = 7
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Ellen mix is 1/3 cup of orange juice with 5/6 cups of lemonade to make fruit punch. Then she adds 1 2/3 cups of soda. Use the properties of addition to find how many cups of fruit punch she makes show your work
Answers
ANSWER:
2 5/6 cups
STEP-BY-STEP EXPLANATION:
To find the total cups, we must add the number of cups in each case, like this:
[tex]\frac{1}{3}+\frac{5}{6}+1\frac{2}{3}[/tex]For ease, we'll convert each fraction so that they all have the same denominator:
[tex]\begin{gathered} \frac{1}{3}=\frac{2}{6} \\ \frac{5}{6} \\ 1\frac{2}{3}=\frac{5}{3}=\frac{10}{6} \\ \text{therefore:} \\ \frac{2}{6}+\frac{5}{6}+\frac{10}{6}=\frac{2+5+10}{6}=\frac{17}{6} \\ \frac{17}{6}=2\frac{5}{6} \end{gathered}[/tex]That is to say that in total there are 2 5/6 cups of fruit punch
A towns population is 53,350 about 100 people move out of the town each month 200 people on average move into town. A nearby town has a population of 56,375.It has no one moving in and an average of 175 people moving away every month in about how many months will be population of the town be EQUAL?
Answers
11
this is just words because it doesn't let me submit this with just the answer
is this relation a function? Justify your answer
Answers
Answer:A
Step-by-step explanation:
Maggie and Amelia filled up 40 water balloons shaped like spheres. Each water balloon had a radius of 6.5 cm.
Answers
The total volume of the 40 sphere shaped water balloons is 46032.38 cubic cm.
Radius of 1 sphere = 6.5 cm
We know that the volume of the sphere is given by 4/3 π r³
We will take the radius as 6.5 cm and π as 22/7
Now we will find the volume : 4/3 ×22/7×6.5³ = 1150.81 cubic cm.
Volume of 40 such spheres = 40 × 1150.81 = 46032.38 cubic cm.
The radius of all the spheres are 46032.38 cubic cm.
A sphere is a geometrical entity with three dimensions that resembles a two-dimensional circle. A sphere is a group of points in three dimensions that are all situated at the same r-distance from one another.
The supplied point is the sphere's center, while the letter r stands for the sphere's radius which is half the diameter. The earliest known allusions to spheres are found in the works of two ancient Greek mathematicians.
Therefore total volume of the 40 sphere shaped water balloons is 46032.38 cubic cm .
Disclaimer: The complete question is : Maggie and Amelia filled up 40 water balloons shaped like spheres. Each water balloon had a radius of 6.5 cm.Find the total volume of water required.
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Math stuff please help
Answers
I need helping answering 15. I need to create a table and graph the function.
Answers
ANSWER and EXPLANATION
We want to order the functions from widest to narrowest:
[tex]\begin{gathered} y=3x^2 \\ y=2x^2 \\ y=4x^2 \end{gathered}[/tex]To do this, we have to plot the graphs of the functions by using a table of values.
Let us find the values of the functions for values of x = -2, 0, 2
For the first function:
[tex]\begin{gathered} y=3x^2 \\ \Rightarrow x=-2: \\ y=3(-2)^2=3*4 \\ y=12 \\ \Rightarrow x=0: \\ y=3(0)^2=3*0 \\ y=0 \\ \Rightarrow x=2: \\ y=3(2)^2=3*4 \\ y=12 \end{gathered}[/tex]Hence, its table is:
For the second function:
[tex]\begin{gathered} y=2x^2 \\ \Rightarrow x=-2: \\ y=2(-2)^2=2*4 \\ y=8 \\ \Rightarrow x=0: \\ y=2(0)^2=2*0 \\ y=0 \\ \Rightarrow x=2: \\ y=2(2)^2=2*4 \\ y=8 \end{gathered}[/tex]Hence, its table is:
For the third function:
[tex]\begin{gathered} y=4x^2 \\ \Rightarrow x=-2: \\ y=4\left(-2\right)^2=4*4 \\ y=16 \\ \Rightarrow x=0: \\ y=4(0)^2=4*0 \\ y=0 \\ \Rightarrow x=2: \\ y=4(2)^2=4*4 \\ y=16 \end{gathered}[/tex]Hence, its table is:
Now, let us plot the graphs of the functions:
Therefore, from the graph, we see that the order of the functions from widest to narrowest is:
[tex]y=2x^2;y=3x^2;y=4x^2[/tex]The library is installing new
Shelves. If the carpenter has
4/5 yard of wood to make
into 2 shelves of equal length,
how long will each shelf be?
Menth
Answers
The library is getting new shelves built. 40% will each shelf be if the carpenter has 4/5 yards of wood to create 2 shelves that are the same length.
Given that,
The library is getting new shelves built.
We have to find how long will each shelf be if the carpenter has 4/5 yards of wood to create 2 shelves that are the same length.
We know that,
We have to divide
4÷2÷5
2÷5
0.4
In percentage we write as 40%.
Therefore, The library is getting new shelves built. 40% will each shelf be if the carpenter has 4/5 yards of wood to create 2 shelves that are the same length.
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