Answer:
I think it is 12
Step-by-step explanation:
What is the slope of a line parallel to the line whose equation is 3x + 2y = 8
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]3x+2y=8\implies 2y=-3x+8\implies y=\cfrac{-3x+8}{2} \\\\\\ y=\cfrac{-3x}{2}+\cfrac{8}{2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{2}}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
dillon (2019, unit 2, chapter 14) recommends that the amount of time college students spend studying each week should be about the amount of time spent in class.
Using a proportional relationship, it is found that:
Dillon recommends that the amount of time college students spend studying each week should be about the amount twice the time spent in class.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality represented by k, according to the rule presented as follows:
y = kx
For this problem, the variables are presented as follows:
Variable x: number of units in class.Variable y: number of hours studied.From the table, the constant is calculated as follows:
k = 24/12 = 18/9 = 12/6 = 2.
Meaning that the amount of study should be twice the time spent in class.
Missing InformationThe table relating the variables is given at the end of the answer.
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The odometer in a car measures the number of miles driven by the car since it was made. During the trip, the odometer in Anita‘s car is modeled by the function Y=9500+55X where X represents the number of hours driven during the trip and y represents the odometer reading in miles. What is the meaning of the rate change in this function?
The given function is y=9500+55x, where x is in hours driven and y is in miles.
Therefore, the slope of the function is
[tex]\frac{miles}{number\text{ of hours driven}}[/tex]The answer is the number of miles driven each hour during the trip, the first option.1Given f(x) = 3x and g(x) = x - 2Which value is in the domain of fºg?Click on the correct answer.-225-8
Let's begin by listing out the information given to us:
[tex]\begin{gathered} f\mleft(x\mright)=3x \\ g\mleft(x\mright)=x-2 \end{gathered}[/tex]We will caculate fºg thus:
[tex]\begin{gathered} fºg=f(g(x))=3(x-2)=\text{3x}-6 \\ fºg=3x-6=0\Rightarrow3x=6\Rightarrow\frac{3x}{3}=\frac{6}{3}\Rightarrow x=2 \\ x=2 \end{gathered}[/tex]Hence, option B is correct
A concert hall is having a special. If a group of five pays $6.75 each for tickets, each person can get a snack for $4.25. Use the expression 5(6.75+4.25) to find the total cost for 5 friends?
Answer: The total cost is $55
The total cost of 5 friends is $55.
What is multiplication?
Multiplication is a basic arithmetic function in which occurs when we add a number a particular number of times.
We are given that if group of five pays $6.75 each they get the snack for $4.25.
To find the total cost we first find the cost of one
The cost of one can be given as [tex]6.75+4.25=11[/tex]
To find the cost of 5 we multiply this amount by 5
We get,
[tex]5[/tex]·[tex]11=55[/tex]
Hence the total cost is $55.
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Help! Homework: 3x-(1/3x +1)=
Answer:
39/98=90 so its 90
Step-by-step explanation:
you have to add the angles and to make sure to look at each corners of the angles for the answer
A basketball player made 74 out of 100 attempted free throws. What percent of free throws was made
Answer:
74%
Step-by-step explanation:
74 divided by 100 is 0.74, and 0.74 =
74%
If $20,000 is deposited in an account that pays 6% interest compounded annually, how much interest is earned at the end of 20 years? A $24.000 B $64.142.71 C $44.142.71 D $56.142.71
Given data:
The given principal is P=$20,000.
The given rate of interest is r=6%.
The given time is t=20 years.
The expression for the interest is,
[tex]I=P(1+\frac{r}{100})^t-P[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} I=20,000(1+\frac{6}{100})^{20}-20,000 \\ =20,000(1.06)^{20}-20,000 \\ =44,142.71 \end{gathered}[/tex]Thus, the interest earned after 20 years is $44,142.71, so (C) option is correct.
Classwork
Twelve students were given an arithmetic test, and the
times (in minutes) to complete it were
10, 9, 12, 11, 8,15, 9, 7, 8, 6, 12, and 10.
Find:
a) The range
b) Variance and
c) Standard deviation
by using all the values of the data set.
By using all the values of the data set ,
(a) The range for the given set is 9 .
(b) The variance is 6.2045 .
(c) Standard Deviation is 2.49083 .
In the question,
it is given that 12 students gave an arithmetic test , the time (in min) is given as
10, 9, 12, 11, 8,15, 9, 7, 8, 6, 12, 10 .
Arranging the data set in ascending order , we get
6,7,8,8,9,9,10,10,11,12,12,15
Part(a)
the range is calculated by using the formula
Range = highest value - lowest value
Range = 15-6 = 9
Part(b)
calculating , the mean
mean = (6+7+8+8+9+9+10+10+11+12+12+15)/12
= 117/12
= 9.75
Variance can be calculated using the formula
Variance = [tex]\frac{\sum(\(x_i-\bar{x})^{2} }{n-1}[/tex],
where [tex]x_i[/tex] represents the different terms , and
[tex]\bar{x}[/tex] represents the mean .
Substituting the values from the data given , we get
Variance = [(6-9.75)²+(7-9.75)²+(8-9.75)²+(8-9.75)²+(9-9.75)²+(9-9.75)²+(10-9.75)²+(10-9.75)²+(11-9.75)²+(12-9.75)²+(12-9.75)²+(15.9.75)²] / (12-1)
On further simplifying , we get
= 68.25/11
= 6.2045
Part(c)
Standard Deviation = √Variance
Substituting the value of variance from above
we get ,
standard deviation = √6.2045 = 2.49083
Therefore , By using all the values of the data set ,
(a) the range is 9.
(b) Variance is 6.2045
(c) Standard Deviation is 2.49083
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what is the square root of 80.
please help 100 points urgent algebra 2
write without using rational exponents
(m^3n^5)^1/4
write out the steps and the answer and please do it right
The expression (m³n⁵)¹/⁴ can be wriiten as ⁴√m³ . ⁴√n⁵.
To solve the expression (m³n⁵)¹/⁴ without using rational exponents
(m)ᵃ/ᵇ = ᵇ√mᵃ
The given algebric expression is (m³n⁵)¹/⁴
As per the Power distribution Formula :
(mᵃnᵃ)ᵇ = mᵃᵇ nᵃᵇ
(m³n⁵)¹/⁴ = m³ ˣ ¹/⁴ x n⁵ ˣ ¹/⁴
We know that
fraction formula : a¹/ⁿ = ⁿ√a
(m)ᵃ/ᵇ = ᵇ√mᵃ
(m³n⁵)¹/⁴ = m³ ˣ ¹/⁴ x n⁵ ˣ ¹/⁴
⁴√m³ x ⁴√n⁵
⁴√m³ . ⁴√n⁵
The expression (m³n⁵)¹/⁴ can be wriiten as ⁴√m³ . ⁴√n⁵.
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s
. Suppose a person who jumps on Earth returns to the ground in
0.4 second. On Phobos, the same jumper will take 6.4 minutes
to return to the ground. How many times longer would it be on
Phobos than on Earth for the jumper to return to the ground?
Explain.
Answer: 16 times longer
Step-by-step explanation: 6.4 divided by 0.4 is equal to 16.
find the value of sin² R
If the hypotenuse of PQR triangle is 5 and perpendicular is [tex]\sqrt{2}[/tex],then value of sin²R is 2/25.
Given that the hypotenuse is 5 and perpendicular is [tex]\sqrt{2}[/tex].
We are required to find the value of sin²R.
Trigonometric ratios are basically the ratios of the sides of the right angled triangle.
Sin is the ratio of perpendicular and hypotenuse of the right angled triangle. We can easily find the value of sin²R with the help of ratio of perpendicular and hypotenuse.
sin R=PQ/PR
sin R=[tex]\sqrt{2}[/tex]/5
Squaring both sides,
sin² R=[tex](\sqrt{2} )^{2}[/tex]/[tex](5)^{2}[/tex]
sin²R=2/25
Hence if the hypotenuse is 5 and perpendicular is [tex]\sqrt{2}[/tex],then value of sin²R is 2/25.
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Write -3.5 as the ratio of two integers
-3.5 number can be written as the ratio -7:2.
We have,
To write -3.5 as the ratio of two integers, we can multiply both the numerator and denominator by 10 to get rid of the decimal point.
This gives us:
-3.5 = -35/10
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 5.
This gives us:
-3.5 = -7/2
Therefore,
-3.5 number can be written as the ratio -7:2.
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An anemometer recorded yesterday's wind speeds. The strongest wind gust was 43 miles per hour. The second strongest wind gust was 39 miles per hour. How much stronger was the first gust than the second? Show your work in the space below. Don't forget to label the units on your answer.
In order to find how much stronger was the first gust than the second, we just need to subtract their values.
So we have that:
[tex]43-39=4[/tex]So the strongest wind gust was 4 miles per hour stronger than the second strongest wind gust.
Plllllllllllllllllllllllllllllllllllllllls ANSWER my. My brother need help
Suppose corn chips cost 33.5 cents per ounce. if a bag costs $4.35, how many ounces are in the bag of chips? Round your answer to the nearest hundredth, if necessary.
Answer:
13
Step-by-step explanation:
the scatter plot shows the results of a survey in which 10 people were asked how many e-mail accounts and how many credit cards they have. how many credit cards does the person with 3 e-mail accounts have?
In the scatter plot, the person with 3 e-mail accounts have 1 credit card.
Define scatter plot.Typically, the relationship between variables is observed and visually displayed using a scatter plot, a type of chart. Dots are used to indicate the variable values. Scatter plots employ Cartesian coordinates to show the values of the variables in a data set because the placement of the dots on the vertical and horizontal axes will reveal the value of each individual data point. Other names for scatter plots are scattergram, scatter graphs, and scatter charts.
The association between two numerical variables measured for the same individuals is displayed in a scatterplot. The values of one variable are plotted on the horizontal axis, and the values of the other variable are plotted on the vertical axis. On the graph, each individual in the data is represented by a point.
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Which functions have a maximum and are transformed to the left and down of the parent function, f(x)=x2? Check a
that apply.
O p(x)=14(x + 7)²+1
O g(x) = -5(x+10)²-1
D s(x) = −(x−1)2 +0.5
O g(x)=2x² +10x-35
Ot(x)=-2x² - 4x-3
The results for the given function are as follows:
1. p(x) = 14(x + 7)² + 1, The direction is upward by 1 unit.
2. q(x) = –5(x + 10)² – 1, The direction is downward by 1 unit.
3. s(x) = –(x – 1)² + 0.5, The direction is upward by 0.5 unit.
4. g(x) = 2x² + 10x – 35 = (x+5/2)² - 23.75, The direction is downward by 23.75 unit.
5. t(x) = –2x² – 4x – 3 = -(x + 1)² - 0.5, The direction is downward by 0.5 unit.
What is the function?
In mathematics, the function is an expression or rule, or law which defines the relationship between dependent and independent variable. Functions are ubiquitous and are essential for designing physical relationships.
According to the question, the given function expression as well as transformation results are as follows:
p(x) = 14(x + 7)² + 1, The direction is upward by 1 unit.
q(x) = –5(x + 10)² – 1, The direction is downward by 1 unit.
s(x) = –(x – 1)² + 0.5, The direction is upward by 0.5 unit.
g(x) = 2x² + 10x – 35 = (x+5/2)² - 23.75, The direction is downward by 23.75 unit.
t(x) = –2x² – 4x – 3 = -(x + 1)² - 0.5, The direction is downward by 0.5 unit.
By using property of the function which states that if a constant value is added to the function it will go upward, similarly, If we subtract a constant then it will go downward.
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1. Tank A will have a length in feet represented by 25x+12 and a width in feet represented by 7x + 18.
Write and simplify an expression that could be used to determine the amount of rubber stripping, in
feet, needed to place around the top edge of this rectangular settling tank.
2. For Tank B, Seymour Industries wants the width of the tank to be 8x+11 feet. If the area covered by
the top can be represented in square feet by 360x + 495, write and simplify an expression that can be
used to represent the length of the tank. Write and simplify an expression that could be used to
determine the amount of rubber stripping, in feet, needed to place around the top edge of this
rectangular settling tank.
3. Write and simplify an expression that could be used to determine the total amount of rubber stripping,
in feet, needed for both rectangular settling tanks.
4. Write and simplify an expression that could be used to determine how much more rubber stripping is
needed for Tank A than Tank B.
Due today. Need help! 4 questions in total
A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
Explain about the rectangular?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). The rectangle's longer side is its length, while its shorter side is its breadth.
A laptop has four sides, with the opposite sides being parallel to one another and having equal lengths. As a result, a laptop stands out as a common example of a rectangle-shaped device in everyday life. The keyboard and a monitor's screen are both rectangular objects in a similar way.
Note that the following are the measurements for a rectangle's perimeter:
(Length Plus Width) = 2
= 2(25x + 12) + 2(7x + 18)
= 50x + 24 + 14x + 46
= 64x + 70
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Select the correct answer from each drop-down menu.
The sum of the squares of two consecutive positive even numbers is 340. Find the numbers.
The consecutive even numbers are
and
The consecutive even numbers are 12 and 14.
How to calculate the numbers?Even numbers can be divided into two equal groups or pairs and are exactly divisible by two. For instance, 2, 4, 6, 8, and so on. These numbers can be divided into equal groups. Consecutive numbers are numbers that follow each other in descending order from smallest to greatest. Consecutive even numbers are even integers that are separated by a factor of two.
Let the consecutive even numbers be x and x+2.
The sum of the numbers is 340. This will be illustrated as:
x² + (x + 2)² = 340
x² + (x + 2)(x + 2) = 340
x² + x² + 4x + 4 = 340
Collect like terms
2x² + 4x + 4 - 340 = 0.
2x² + 4x - 336 = 0
Divide through by 2
x² + 2x - 168 = 0
x² - 14x + 12x -168 = 0
x(x - 14) + 12(x - 14) = 0.
(x + 12)(x - 14) = 0
This shows that the numbers are 12 and 14
Check: 12² + 14² = 144 + 196 = 340.
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Which is the graph of y = -f(x) + 3?
The graph of y = -f(x) + 3 is a graph that has a negative slope and is attached.
What is graph of equation of a straight line?A graph is a representation of data using the coordinate system. There are different types of graph each defining the required data.
The graph of equation of a straight line is one of the types of graphs. The graph of the form y = mx + c represents the equation of a straight line. The terms are defined as follows
m =slope of the linec = y interceptThe slope is a function of x and from the question it is negative.
The graph is plotted and attached
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A graph with the point 6,-5 with a slope of -2/3
The graph of the line y=-2/3x-1 can be given as follows,
What is a equation of ?
The general equation of straight line is y=mx+c where m is the slope and c is the y-intercept.
every point on the line satisfies its equation.
We are given a point (6,-5) and slope -2/3.
we first need to find the equation of the line
y=mx+c
[tex]y=\frac{-2}{3}x+c[/tex]
The point (6,-5) satisfies the equation.
[tex]-5=\frac{-2}{3}(6)+c[/tex]
[tex]-5=-4+c\\c=-1[/tex]
Substituting the value of c in the equation
we get,
[tex]y=\frac{-2}{3}x-1[/tex]
Now we plot the graph of the equation,
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hose a can fill a certain vat in 3 hours. after 2 hours of pumping, hose a is turned off. hose b is then turned on and completes filling the vat in 3 more hours. how long would it take hose b to fill the vat alone?
Time taken by hose B to fill the vat alone = 9 hours
Let 'x' be the capacity of the vat filled in an hour.
Hose A can fill the vat in 3 hours. i.e., 3x quantity is filled in the vat.
After 2 hours of pumping, 2x/3x = 2/3 of the vat is filled.
The remaining to be filled is x/3x = 1/3 capacity of the vat.
It takes 3 hours for hose B to fill the remaining 1/3 capacity of the vat alone.
Let t be the time taken by hose B to fill the whole vat .i.e., 3/3 = 1 capacity of the vat.
In ratio form, 3 : t = 1/3 : 1.
Thus Time taken by hose B to fill the vat alone = 3 ÷ 1/3
= 3 x 3
= 9 hours
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work this out please :)
Step-by-step explanation:
0 what number is the dividend in the division problem below? 54 divided by 6 equals 9 A. 9 B.6 C. 54 submit
The dividend in the division problem is 54
How to determine the dividend?The mathematical statement is given as
54 divided by 6 equals 9
The above statement is a quotient expression or quotient statement
A quotient statement is represented as
Dividend divided by Divisor equals Quotient
By comparing the quotient statement with the given mathematical statement, we have the following
Dividend = 54Divisor = 9Quotient= 9This implies that the dividend is 54
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A pedestrian sees a cat stuck in the tree that is 40.4 feet tall and calls 911. A fire truck arrives and sends a fireman up in a rescue lift to save the cat. If the rescue lift is ascending at a 45 degree angle of elevation, how far must the rescue bucket reach to save the cat?
Using Pythagoras's theorem we can calculate that the bucket must reach57.134 feet .
We know from the Pythagoras theorem of aright angled triangle , the sum of squares of the two legs of a right triangle is equal to the square of the hypotenuse of the same triangle.
From the question we can ascertain that the height at which the cat is stuck is 40.4 feet.
Now it is given that the rescue ladder came in at 45 ° . So the length of the legs are equal.
Therefore length of ladder which is the hypotenuse = √(2×40.4²)
Length = 57.134... feet
length ≈ 57.13 feet
Therefore the bucket must reach 57.13 feet which is the height at which the cat is stuck on the tree of length 40.4 feet.
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a. Evaluate f(5) given that f(x) =
f(5) =
b. Evaluate g(x + 3) given that g(x) = 3x² - 6x + 9.
g(x + 3) =
c. Evaluate h(2x) given that h(y) =
x² + (17-4x)
9x
h(2x)=
Preview
y³ - 5
7y
Preview
Preview
a) If function be [tex]$f(x)=\frac{x^2+(17-4 x)}{9 x}$[/tex] then the value of f(5) = 22/45.
b) If function be g(x) = 3 x² - 6x + 9 then the value of g(x + 3) = 3x² + 12x + 18.
c) If the function be [tex]$h(y)=\frac{y^3-5}{7 y}$[/tex] then the value of [tex]$h(2x) =\frac{8 x^3-5}{14 x}$$[/tex].
How to simplify the functions?a) Let the function be [tex]$f(x)=\frac{x^2+(17-4 x)}{9 x}$[/tex]
substitute the value of x = 5, then
[tex]$f(5) = \frac{5^2+(17-4 \cdot 5)}{9 \cdot 5}$$[/tex]
simplifying the above equation, we get
[tex]$=\frac{22}{45}$$[/tex]
Therefore, the correct answer is 22/45.
b) Let the function be g(x) = 3 x² - 6x + 9
substitute the value of g(x) = g(x + 3), then we get
To estimate the value of g(x + 3) = 3(x + 3)² - 6(x + 3) + 9
= 3x² + 18x + 27 - 6(x + 3) + 9
simplifying the above equation, we get
=3x² + 18x + 27 - 6x - 18 + 9
Group like terms, we get
= 3x² + 18x - 6x + 27 - 18 + 9
=3x² + 12x + 27 - 18 + 9
= 3x² + 12x + 18
Therefore, the value of g(x + 3) = 3x² + 12x + 18.
b) Let the function be [tex]$h(y)=\frac{y^3-5}{7 y}$[/tex]
substitute the value of y = 2x, then we get
[tex]$h(2x)=\frac{(2x)^3-5}{7 (2x)}$[/tex]
simplifying the above equation, we get
[tex]$=\frac{8 x^3-5}{7 \cdot 2 x}$$[/tex]
[tex]$=\frac{8 x^3-5}{14 x}$$[/tex]
Therefore, the value of [tex]$h(2x) =\frac{8 x^3-5}{14 x}$$[/tex].
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Trevon invests $1650.00 into an account that earns 2% annual interest rate compounded continuously. Assuming no other withdrawals or
deposits, how much will be in the account in 8 years? (Numeric answer only, do not type a $ sign. Round to the nearest cent).
Answer:
1914
Step-by-step explanation:
interest for one year = 33
interest of 8 years = 264
1650+264 will be in the account in 8 years.
Arrange in column then perform the indicated operations. 75 - 26.5731 =
The subtraction is shown below:
The answer is:
75 - 26.5731 = 48.4269
