The graph below represents the number of miles, y, that Jacob can drive his car for
every gallons of gas. Find the rate of change.
Answers
The average rate of change of the given graph is 31.3
How to determine the average rate of changeThe graph of the function is represented as the given parameter
From the graph, we have the following points
(x, y) = (10, 313) and (20, 626)
The average rate of change is the slope of the function and the average rate of change is calculated as
Average rate = [f(b) - f(a)]/[b - a]
Where
(a, f(a)) = (10, 313) and (b, f(b)) = (20, 626)
Substitute the known values in the above equation
So, we have
Average rate = [626 - 313]/[20 - 10]
Evaluate
Average rate = 31.3
Hence, the average rate is 31.3
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Related Questions
A single piecewise-defined function f(x) has been
graphed for you on the display to the left.
At how many values c on the interval x€[−6, 4) is it
true that the limx→cf(x) = 1?
Answers
Answer: 1
Step-by-step explanation:
[tex]\lim_{x \to -6} f(x) \neq -1[/tex] because the left and right hand limits are not the same.
[tex]\lim_{x \to -1} f(x) \neq -1[/tex] because the left and right hand limits are not the same.
However, somewhere between 1 and 2, the limit does equal -1 because the left and right hand limits are the same.
Zahra and some friends are going to the movies. At the theater, they sell a bag of
popcorn for $3.50 and a drink for $5. How much would it cost if they bought 8 bags
of popcorn and 5 drinks? How much would it cost if they bought p bags of popcorn
and d drinks?
Total cost, 8 bags of popcorn and 5 drinks:
Total cost, p bags of popcorn and d drinks:
Answers
After performing some mathematical operations, we know that the total cost of 8 popcorn bags and 5 drinks is $53.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The rules that specify the order in which we should solve an expression involving multiple operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).So, the total cost:
1 bag of popcorn costs $3.50.1 drink costs $5.Cost of a total of 8 bags of popcorn and 5 drinks:
(8 × 3.50) + (5 × 5)28 + 25$53Therefore, after performing some mathematical operations, we know that the total cost of 8 popcorn bags and 5 drinks is $53.
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The correct question is given below:
Zahra and some friends are going to the movies. At the theater, they sell a bag of popcorn for $3.50 and a drink for $5. How much would it cost if they bought 8 bags of popcorn and 5 drinks?
fine the value of x. please help
Answers
Answer:
141 degrees
Step-by-step explanation:
The total angle interior of a triangle is 180 degrees. And the 2 angles opposite of x equal it so x=103+38
The carpenter cuts 1-
1
inches off a piece of wood every 2 minutes. How many inches
2
will be cut in 25 min?
Answers
What is the lowest common multiple of 19 & 9
Answers
Solution:
LCM of 9 and 19 is the smallest number among all common multiples of 9 and 19.
The first few multiples of 9 and 19 are (9, 18, 27, 36, 45, 54, . . . ) and (19, 38, 57, 76, 95, . . . ) respectively.
There are 3 commonly used methods to find LCM of 9 and 19 - by listing multiples, by division method, and by prime factorization.
To calculate the LCM of 9 and 19 by the division method, we will divide the numbers(9, 19) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 19.
In this case, we get:
Then, the LCM would be:
[tex]3\text{ x 3 x 19 = }171[/tex]so that, the correct answer is:
[tex]171[/tex]Whileat the fruit stand, ramon bought 3 punds of apples that cost $0.89 per pound and 4 cantaloupes that each cost $1.09. about how much money did he spend, not including tax?
Answers
The total money spent on fruits is $7.03
While at the fruit stand, Ramon bought the following fruits,
3 pounds of apples that cost $0.89 per pound
4 cantaloupes that each cost $1.09
So, the total amount he spent on the materials he bought without including taxes is,
Total money spent = 3 x ( 0.89 ) + 4 x ( 1.09 )
= 2.67 + 4.36
= 7.03
The total money spent on fruits is $7.03
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I need help with number 16 can I please get help?
Answers
We will break apart the figure into triangles, rectangles, squares etc. We will then find area of each individual figure and sum it.
We can break apart the figure as shown below:
7. Solve by using extracting square roots 4a²-25= 0
pa answer po rn
w solution po
Answers
[tex]4a^{2} -25=0\\(2a-5)(2a+5)=0\\2a-5=0 \\or 2a+5=0\\\\a=\frac{5}{2} \\\\or\\\\a=-\frac{5}{2}[/tex]
IF YOU CHECK CAREFULLY YOU WILL FIND THAT THIS EQAUTION IS MADE OF DIFFERENCE OF SQUARES.
GOODLUCK!!
in 1982, the us mint changed the composition of pennies from all copper to zinc with copper coating. pennies made prior to 1982 weigh 3.1 grams. pennies made since 1982 weight 2.5 grams. if you have a bag of 1267 pennies, and the bag weighs 3541.9 grams, how many pennies from each time period are there in the bag?
Answers
Prior to 1982, pennies weighed 3.1 grams. Coins produced after 1982 weigh 2.5 grams. 647 coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.
Given that,
The 1982 change in pennies composition from all copper to zinc with copper coating was made by the US Mint. Prior to 1982, pennies weighed 3.1 grams. Coins produced after 1982 weigh 2.5 grams.
We have to find how many coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.
An issue of quantity and amount. In this context, the term "amount" refers to weight. The variables should be identified with letters that will make them easy to distinguish: Z for largely zinc and C for all copper. Create weight and quantity equations:
C + Z = 1287
3.1 C + 2.5 Z = 3601.5
By multiplying all three components of the first equation by -2.5 and placing them under the second equation, drawing a line, and then subtracting, you can eliminate the Z using this method.
3.1 C + 2.5 Z = 3601.5
-2.5 C - 2.5 Z = -3217.5
--------------------------------
0.6 C = 384
Divide both sides by .6.
C = 640
Subtract 640 from 1287.
Z = 647
Therefore, 647 coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.
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RS =9y + 2, ST = 2y + 3, and RT = 60
Answers
Answer:
y=5
Step-by-step explanation:
RS + ST = RT
9y+2 + 2y+3 = 60
11y + 5 = 60
11y = 55
Y = 5
Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that can be evaluated without a calculatorlog5 (15x + 20y)
Answers
The given expression is
[tex]\log _5(15x+20y)[/tex]Factor out the greatest common factor between 15x and 20y.
[tex]\log _5(5(3x+4y))[/tex]Then, use the product property to expand the logarithm.
[tex]\log _55+\log _5(3x+4y)[/tex]At last, simplify the first logarithm because its base is equal to its argument.
[tex]1+\log _5(3x+4y)[/tex]Therefore, the simplest form of the logarithm is
[tex]1+\log _5(3x+4y)[/tex]17. What are the roots of the equation s² - 7 = 74?
18. One of the roots of x² - 8x = 0 is 8. What is the other root?
paanswer po ngaun
w solution if meron po sana
Answers
Answer:
17. s = 9
18. x = 8x^(½)
Step-by-step explanation:
s² - 7 = 74?
s² = 74 + 7
s² = 81
√(s²) = √(81)
s = 9
x² - 8x = 0
x² = 0 + 8x
x² = 8x
√(x²) = √(8x)
x = 8x^(½)
OR by factoring
x²−8x=0
x(x−8)=0
x=0 or x−8=0
x=0 or x=8
There are 60 members in the school glee club. The glee club needs to raise at least $5,000 for a trip toa national competition. The school agreed to contribute $1,000 toward the trip. Which of theinequalities below shows the amount of money that each glee club member needs to raise to help payfor the trip.a) 60x + 1,000 > 5,000b) 60x + 5,000 > 1,000c) 1,000x + 60 < 5,000
Answers
Let x be the amount raised by each club member. Since there are 60 members, the amount raised by them would be
[tex]60x[/tex]Now, we know the school contributed $1,000. Now, the amount raised is:
[tex]60x+1000[/tex]Since this amount has to be at least $5,000, we have that the inequality that shows the amount of money that each glee club member needs to raise to help pay for the trip is:
[tex]60x+1000>5000[/tex]Answer: Option A
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answers
Answer:
c = 23
Step-by-step explanation:
To start, the interior of ∠L is needed to complete the equation. Since the total value of an interior and exterior angle is equal to 180°, we can confirm that 180° - 83° = 97°. Now, we can plug in the numbers.
(2c + 51)° = 97°
Next, you want to subtract 51 from both sides.
(2c + 51) - 51 = 97 - 51
2c = 46
Lastly, you isolate c by dividing 46 by 2.
c = 46 ÷ 2
c = 23
Andrew earns 30% on all sales plus a retainer of £125 per week.
If he earns £893 in one week, find the value of his sales for that week.
Answers
If Andrew earns 30% on all sales plus a retainer of $125 per week and If he earns $893 in one week, then the value of the his sales for that week is $2560.
The total amount he earned = $893
The amount of retainer he earned = $125
The percentage he earned = 30%
30% of the sales = The total amount he earned - The amount of retainer he earned
Substitute the values in the equation
= 893-125
= $768
Consider the total sales as x
Then,
x × (30/100) = 768
0.3x = 768
x = 768/0.3
x = $2560
Hence, if Andrew earns 30% on all sales plus a retainer of $125 per week and If he earns $893 in one week, then the value of the his sales for that week is $2560.
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if a baker has 7/3 cups of chocolate, the baker can make a maximum of .... cakes.
Answers
She calls for 4/5 cup of chocolate
She had 7/3 cups of chocolate.
[tex]\begin{gathered} \text{The bake can make a ma}\xi mum\text{ of = }\frac{7}{3}\text{ }\frac{.}{.}\text{ }\frac{4}{5} \\ \text{ = }\frac{7}{3}\text{ x }\frac{5}{4} \\ \text{ = }\frac{35}{12} \\ \text{ = 2}\frac{11}{12} \\ \end{gathered}[/tex]Maximum number of cakes a baker can make = 2
PLS HELP ON THIS 50-(-20)
Answers
15 points to help me out.
Answers
Answer:
can't answer the first two questions as figure is not mentioned in picture
3. -3
4. 6
5. 3/4
6. -3
7. 5
8. 3
Step-by-step explanation:
passes through (1,4) and perpendicular to y=2x-7
Answers
The equation of the line is found as y = -x/2 + 9/2.
What is meant by the equation of the line?This is an x and y equation for whom solution set is just a line in the (x,y) plane. The "slope-intercept" form is the most commonly used in algebra. y = mx + b. In effect, x is used as a parameter, and y is written as just a function of x: y = f(x) = mx+b.For the given question;
The equation of the perpendicular line is given as;
y = 2x - 7
Compare the equation with the standard form of slope intercept.
y = mx + c
m = slope and c is the y intercept.
m1 = 2
Now, the line is perpendicular, thus the relation between both slopes is;
m1 × m2 = -1
m2 = -1/2
The passing coordinates of the line is (1. 4).
Find the equation using formula.
y - y1 = m2(x - x1)
y - 4 = (-1/2) (x - 1)
Simplifying,
y = -x/2 + 9/2
Thus, the equation of the line is found as y = -x/2 + 9/2.
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[tex]x + 49 \ \textgreater \ 28[/tex]I need it now please
Answers
To solve an inequation for x you have to follow the same procedure you follow when solving equations, with exception that when you multiply/divide by a negative number the direction of the inequality gets inverted.
So to solve the given inequelity for x, you have to pass "+49" to the other side of the expression. To do so, subtract it from both sides of the expression:
[tex]\begin{gathered} x+49-49>28-49 \\ x>-21 \end{gathered}[/tex]The result of the inequality is x > -21
Suppose each street in the map shown represents a line. Provide an example of
each angle relationship.
Vertical angles
Supplementary
angles
Linear pair
Adjacent angles
Vertical angles
Congruent angles
10
15
16
11
12
17
18
Willow Drive
4
8
13 14 Franklin Drive
19 20
21
23
Sixth Ave
Main Street
22 Fifth Ave
24
Answers
Vertical angles are : 1 and 6
supplementary angles : 1 and 2
linear pair : angle 4 and 8
adjacent angles: 21 and 22
What is a supplementary angle?A supplementary angle is an angle that, when added to another angle, results in a total angle measure of 180 degrees. In other words, if two angles are supplementary, the sum of their angle measures will be equal to 180 degrees.
For example, if angle A measures 100 degrees, its supplementary angle B would measure 80 degrees, since 100 + 80 = 180. Conversely, if angle B measures 120 degrees, its supplementary angle A would measure 60 degrees, since 120 + 60 = 180.
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The population of the United States increased from 249 million in 1990 to 308 million in
2010.
The absolute change in the population was
The relative change in the population was
of a percent)
million.
% (round to the nearest tenth
Answers
The absolute change in the population was 59 million. The relative change in the population was 23.69%
The absolute population change is the magnitude of the increase or decrease in population for a defined period.
What is absolute change ?Absolute change describes the straightforward difference between the indicator over two time periods. The indicator's value in the earlier period is used to calculate the relative change, which expresses the absolute change as a percentage.
Small numbers can make relative changes appear more significant than they actually are. This is true because a minor change in the number's absolute value can generate a significant change in the percentage.
Big numbers may make relative changes appear less significant. This is so that any change in the number that represents a substantial relative change may be seen.
The relative change can be minor even when the absolute change is significant if it is a change on a larger number.
Absolute change = Final value – Initial value
= 308m- 249m = 59m
The absolute change in the population was 59 million
Relative change Formula = (Final value – Initial value) / Initial value * 100%
= 308m- 249m/ 249*100 = 23.69%
The relative change in the population was 23.69%
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I need some explanation on how to do piece wise functions? Where do I even start with this equation, can you explain this step by step? Including breaking down the graphing of absolute functions?
Answers
A piecewise function is basically a function that behaves differently at different domain intervals.
The given piecewise function is
[tex]\begin{cases}2x\quad \quad \quad \quad \quad \quad x\le3 \\ \frac{1}{3}x^2-2x+9\quad x>3\end{cases}[/tex]As you can see, the function has a different expression for the interval x is less than or equal to 3 and a different expression for the interval x is greater than 3.
The easiest way to determine which graph corresponds to the given piecewise function is to evaluate the piecewise function at different values of x and graph it.
Evaluate the piecewise function for the interval x is less than or equal to 3.
[tex]\begin{gathered} 2x \\ x=1\rightarrow2(1)=2 \\ x=2\rightarrow2(2)=4 \\ x=3\rightarrow2(3)=6 \end{gathered}[/tex]Evaluate the piecewise function for the interval x is greater than 3.
[tex]\begin{gathered} \frac{1}{3}x^2-2x+9 \\ x=4\rightarrow\frac{1}{3}(4)^2-2(4)+9=6.33 \\ x=6\rightarrow\frac{1}{3}(6)^2-2(6)+9=9 \\ x=8\rightarrow\frac{1}{3}(8)^2-2(8)+9=14.33 \end{gathered}[/tex]Now, let us graph these points
As you can see from the graph, it matches with the graph of the 2nd option.
Therefore, the correct graph of the given piecewise function is the 2nd graph.
convert improper fractions to mixed number 7/5
Answers
The mixed fraction of the given improper fraction is [tex]1\frac{2}{5}[/tex].
According to the question,
We have the following improper fraction:
7/5
Now, to convert this into mixed fraction we will divide the numerator by the denominator and add the quotient before the fraction and the remainder will form the numerator and the denominator will remain same as that of this improper fraction.
(More to know: there are three kinds of fraction: proper fraction (in proper fraction, we have denominator larger than numerator), improper fraction and mixed fraction.
So, we will divide 7 by 5:
[tex]1\frac{2}{5}[/tex]
Hence, the mixed fraction of 7/5 is [tex]1\frac{2}{5}[/tex].
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Write the equation of the line passing through (-3,1) that is perpendicular to 3x-8y=16
Answers
two lines are perpendicular when their slope is inverted and have the opposite sign
the general form of the equation line is-3,1
[tex]y=mx+b[/tex]where m is the slope
rewrite
[tex]\begin{gathered} 3x-8y=16 \\ 3x-16=8y \\ y=\frac{3x-16}{8} \\ y=\frac{3}{8}x-2 \end{gathered}[/tex]so, the slope 3/8
the slope of the other line is
[tex]\frac{3}{8}\longrightarrow-\frac{8}{3}[/tex]to write the new equation of the line we use the slope and replace the point (-3,1)
[tex]\begin{gathered} (1)=(-\frac{8}{3})(-3)+b \\ 1=8+b \\ b=-7 \end{gathered}[/tex]now, replace b and the slope to create the line
[tex]y=-\frac{8}{3}x-7[/tex]this is a super hard one
Answers
Notice that in the given sequence the difference between the first two terms is 7 so the solution must be in terms of multiples of 7 plus a constant. The only two options that have this characteristic are first and last ones, for the sum to consider the first term the sum must start for r=0.
Answer: last option.
Tyee has $720 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. He buys a new bicycle for $401.83. He buys 4 bicycle reflectors for $12.85 each and a pair of bike gloves for $23.83. He plans to spend some or all of the money he has left to buy new biking outfits for $40.49 each. Use the drop-down menu below to write an inequality representing oo, the number of outfits he can buy while staying within his budget.
Answers
The inequality that represents the number of outfits he can buy while staying within his budget is M ≤ 6.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
We have,
Total amount to spend = $720
Cost of bicycle = $401.83
Cost of bicycle reflector = $12.85 ( 4 reflector bought )
Cost of bike cloves = $23.83
Cost of biking outfits = $40.49
The number of possible biking outfits:
401.83 + 4 x 12.85 + 23.83 + M40.49 ≤ 720
401.83 + 51.4 + 23.83 + M40.49 ≤ 720
477.06 + M40.49 ≤ 720
M40.49 ≤ 720 - 477.06
M40.49 ≤ 242.94
M ≤ 242.94 / 40.49
M ≤ 6
M = Number of possible outfits
Thus,
The inequality that represents the number of outfits he can buy while staying within his budget is M ≤ 6.
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4x > 28 solve the inequality for x and simplify your answer as much as possible
Answers
Answer:
x > 7
Step-by-step explanation:
x = 28 ÷ 4
x > 7
that's it
Hey there!
4x > 28
DIVIDE 4 to BOTH SIDES
4x/4 > 28/4
SIMPLIFY it
x > 28/4
x > 7
It is an open circle started at 7 & it’s going to the left of the number line
Therefore, your answer should be:
x > 7
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Select the conjecture with the rephrased statement of proof to show the diagonals of a parallelogram bisect each other.
BRO HELP ITS DUE TMRW WILL GIVE BRAINLIEST AND POINTS
Answers
Considering the given figure, the conjecture with the rephrased statement of proof to show the diagonals of a parallelogram bisect each other is: In parallelogram EFGH show EK is congruent to KG and F.K is congruent to KH
How to determine the correct rephrase of the proof about parallelogram diagonalsThe diagonals refer to the lines running between the two opposite ends of the parallelogram
Bisecting means sharing into two equal parts
congruent means a copy that is equal in dimension hence can be used in place of the other image
The diagonals of a parallelogram bisect each other means that the diagonals cut each other to form two equal parts such that each part is congruent to each other.
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1. Write the distance from the Sun to Mercury in scientific notation. Include units with your answer.
NEED HELP ASAP WILL GIVE BRAINLIST TO BEST AWNSER
Answers
Answer:
3.456 × 10^11
Step-by-step explanation:
= 3.456 × 10^11
scientific notation
= 3.456e11
scientific e notation
= 345.6 × 10^9
engineering notation
billion; prefix giga- (G)
= 3.456 × 10^11
standard form
11
Order of Magnitude
for scientific and standard forms
= 345600000000
(real number)
= three hundred forty-five billion six hundred million
word form
I hope this helps!! :D
