The rate of change of y with respect to x for this linear function is 1/5 or 0.2
What is a linear function?A linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate. This ultimately implies that, a linear function is typically used for uniquely mapping an input variable to an output variable.
How to calculate the average rate of change?Mathematically, the average rate of change (slope) of a linear function can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Average rate of change = (3 - 2)/(10 - 5) = (4 - 3)(15 - 10)
Average rate of change = 1/5 or 0.2
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Joshua is driving to the store
a soda company had sales of $35,109 million in 2010 and $45,984 million in 2014. use the midpoint formula to estimate the sales in 2012. assume that the sales followed a linear pattern.
The sales in 2012 is estimated to be $40546.5 million if we use the midpoint formula assuming that the sales followed a linear pattern.
Midpoint is a term used in geometry and can be described as the center or middle point of a line segment. It enables you to take two endpoints, and then by using these endpoints you can find the point that is midway between them in the line segment.
Considering,
[tex]P_{1} = (x_{1},y_{1})[/tex]
[tex]P_{2} = (x_{2},y_{2})[/tex]
Here;
[tex]x_{1}[/tex] = 2010
[tex]x_{2}[/tex] = 2014
[tex]y_{1}[/tex] = $35,109 million
[tex]y_{2}[/tex] = $45,984 million
The formula for the midpoint is given as;
[tex]P_{m}[/tex] = {( [tex]x_{1} + x_{2}/2[/tex] ), ( [tex]y_{1} + y_{2} / 2[/tex] )}
[tex]P_{m}[/tex] = {(2010 + 2014 / 2), (35109 million + 45984 million / 2)}
[tex]P_{m}[/tex] = {(4024 / 2), (81,093 million / 2)}
[tex]P_{m}[/tex] = {2012 , 40546.5 million}
Therefore, the sales in 2012 are calculated to be $40546.5 million by using the midpoint formula.
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Do the values in this table represent a proportional relationship?
X
y
2
O I don't know.
1
O Yes, and the constant of proportionality is 1/2.
O Yes, and the constant of proportionality is 2.
O No.
4
Creative Section - B
7. a) The average of daily income of a plumber from Sunday to Friday is Rs 1,300
in the last week. If he earned Rs 2,000 on Saturday, find
income of the week.
could i get a hand here please
Answer:
4 inches
Step-by-step explanation:
the cube has a volume (V) calculated as
V = s³ ( s is the side length )
given V = 64 , then
s³ = 64 ( take the cube root of both sides )
s = [tex]\sqrt[3]{64}[/tex] = 4
side length is then 4 inches
I need help please on this it is very hard for me
Answer:
Below in bold.
Step-by-step explanation:
3/20
We divide 3 by 20:-
3 / 20 = 0 so we divide 30 by 20 and proceed as below:
20)3.00 ( 0.15
20
100
100
......
The answer is 0.15 which is terminating.
5/11
If we divide as above we get 0.45454545....
The 45 keeps repeating
2/15
Dividing gives 0.133.........
Repeating
7/8 = 0.875
terminating.
9/16
= 0.5625
terminating.
Answer:
3/20 = 0.15 (Terminating)
5/11 = 0.45454 (Repeating)
2/15 = 0.13333 (Repeating)
7/8 = 0.875 (Terminating)
9/16 = 0.5625 (Terminating)
Explanation:
The definition of Terminate means to bring to an end. This would also apply to the decimals. To find whether a fraction is terminating or not, is to simply divide and you will get a decimal, unless it is mixed fraction. Terminating will bring an end, Ex: 1/2 ( 1 ÷ 2 ) which would equal = 0.5 This is an example of a terminating decimal. A repeating decimal is a decimal that never ends of its repetition, Ex: 0.13333333 (Continuous).
I hope this helps my grammar might bit a bad sorry.
Hope you get an A ^^
Have a great day
a) Work out (8 × 10³) × (2 x 10¹)
Give your answer in standard form.
Answer:
8000 times 2x times 1
Step-by-step explanation:
(8 times 10^3) (2xtimes 10^1)
8 times 10^3=8000
= 8000 times 2x times 1
= 160000x
A rock climber throws a first aid kit to another climber who is higher up the mountain. The initial velocity of the kit is 12 m/s at an angle of 71 above the horizontal. At the instant when the kit is caught, it is traveling horizontally, so its vertical speed is zero. How far apart are the two climbers (horizontally)?
A rock climber throws a first aid kit to the another climber who is higher up the mountain, the initial velocity of the kit is 12 m/s at an angle of 71 above the horizontal, at the instant when the kit is caught, it is traveling horizontally, so its vertical speed is zero, height difference between climbers is 0.85 m.
What is velocity?Velocity is the direction at which an object is moving and serves as a measure of the rate at which its position is changing as seen from a specific point of view and as measured by specific unit of time (for example, 60 km/h northbound). In kinematics, area of classical mechanics that deals with the motion of bodies, velocity is a fundamental idea.
Vertical motion of the first aid kit:
The Initial vertical velocity, u = 5.70 sin 45.7 = 4.08 m/s
Acceleration, g = -9.81 m/s²
When climber who is higher up the mountain catches the kit it's vertical speed is zero.
Final vertical velocity, v = 0 m/s
We have the equation of motion, v² = u² + 2as
Substituting
0² = 4.08² + 2 x -9.81 x s
s = 0.85 m
So kit travels 0.85 m vertically.
Height difference between the climbers = 0.85 m.
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14. Matthew bought 2 movie tickets for $11, and Rosa
bought 7 movie tickets for $38.50. What is the
constant of proportionality?
When two amounts are proportionate, they fluctuate at the same rate, maintaining the constancy of their relationship.
Here x be the proportionality constant its value 5.5.
What is meant by proportionality constant ?The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.When two amounts are proportionate, they fluctuate at the same rate, maintaining the constancy of their relationship.In mathematics, we use the constant of proportionality to compute the rate of change and identify whether we are working with direct variation or inverse variation.Matthew bought 2 movie tickets for $11,
Rosa bought 7 movie tickets for $38.50.
let the value of per ticket is x
2x = 11 and 7x = 38.5
7x- 2x = 38.5 -11
x = 5.5
here x be the proportionality constant its value 5.5.
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Find the values of x,y, and z.
guys please help me. I missed a class and can't find the video to help me solve this
Answer:
x = 7.2 , y = 57 , z = 10.8
Step-by-step explanation:
the sum of the 3 angles in the outer triangle = 180° , that is
y + 88 + 35 = 180
y + 123 = 180 ( subtract 123 from both sides )
y = 57
------------
the outer and inner triangles are similar ( AA postulate ) then the ratios of corresponding sides are in proportion, that is
[tex]\frac{x}{12}[/tex] = [tex]\frac{9}{9+6}[/tex] = [tex]\frac{9}{15}[/tex] ( cross- multiply )
15x = 108 ( divide both sides by 15 )
x = 7.2
and
[tex]\frac{z}{18}[/tex] = [tex]\frac{9}{15}[/tex] ( cross- multiply )
15z = 162 ( divide both sides by 15 )
z = 10.8
12x=12x+3 solve for x step by step!!
answer:
I hope the solution is helpful.
[tex]2(40 - 5y)=10y+5(1 - y)[/tex]
Answer:
y = 5
Step-by-step explanation:
2(40 - 5y) : 80 - 10y
10y + 5(1 + y) : 5y + 5
80 - 10y = 5y +5
-10y = 5y -75
-10y - 5y = 5y - 75 - 5y
-15y/-15 = -75/-15
-15y/-15 : y
-75/-15 : 5
Hence, The answer should be 5
Jasmine drives every morning to her office that is 12 miles from her home.
Suppose Jasmine drives from home to the office in 20 minutes. Use this information and part (b) to write an equation
I will Mark Brainlist Please Help!!! its a algebra 2 Question image is attached below thanks so much !!
Using the law of indices, [tex]1024^{\frac{2}{5} } = 16[/tex]
How to solve exponent using law of indices?The expression can be solved using the law of indices as follows:
[tex]1024^{\frac{2}{5} }[/tex]
using law of indices, involving bracket.
Brackets with indices are where we have a term inside a bracket with an index (or power) outside of the bracket.
To do this we can raise everything inside the bracket to the power.
[tex](a^{b} )^{x} = a^{bx}[/tex]
Therefore,
1024 = 2¹⁰
Hence,
[tex]2^{\frac{2}{5} (10)} = 2^{\frac{20}{5} } = 2^{4} = 16[/tex]
Therefore,
[tex]1024^{\frac{2}{5} } = 16[/tex]
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Which expression has a value of 74?
Responses
(75−5)×(1+4)
open parenthesis 75 minus 5 close parenthesis times open parenthesis 1 plus 4 close parenthesis
75−5×(1+4)
75 minus 5 times open parenthesis 1 plus 4 close parenthesis
(75−5)×1+4
open parenthesis 75 minus 5 close parenthesis times 1 plus 4
75−(5×1+4)
The expression that will give a value of 74 is C. (75 - 5) × 1 + 4.
What is an expression?It should be noted that an expression is used to how the relationship between the variables that are expressed in the data or information given.
In this case, we want to find the expression that will give a value of 74. This will be :
= (75 - 5) × 1 + 4
= 70 × 1 + 4
= 70 + 4
= 74
The correct option is C.
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Answer: yes then no
Step-by-step explanation:
Laura Russo lost her earnings statement from Siler's Lawn
and Garden. She recalls paying $43.00 in federal income taxes and
knows she deposited $306.36 in her checking account. Each week she
had deductions for Social Security and Medicare taxes; $22.35 for
medical insurance; 1.5% state tax; 1.5% local tax; and $25.00 for the
credit union. What is her gross weekly pay?
Employee's gross pay is their salary before any payroll deductions such as taxes, benefits, and other expenses are made.
Her goss weekly pay is $409.13.
How to find her gross weekly pay?
Before taxes, benefits, and other payroll deductions are deducted, an employee's gross pay is what they are paid.
Net pay, often known as take-home pay, is the sum that is left over after all deductions have been taken into consideration.
Federal income tax:
306.36+ 43 = 349.36
Medical insurance:
349.36 + 22.35 = 371.71
Credit union:
371.71 + 25 = 396.71
State tax:
396.71 increased by 1.5% is 396.71 * (1.015) = 402.66
Local tax:
402.66 increased by 1.5% is 402.66 * (1.015)= 409.13
Her goss weekly pay is $409.13.
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i need help on this, thanks
Answer: m<1 = 151 m<2 = 29 m<3 = 151
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:\angle1 = 151° [/tex]
[tex]\qquad \tt \rightarrow \: \angle2 = 29 \degree[/tex]
[tex]\qquad \tt \rightarrow \: \angle3 = 151 \degree[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
We can use angle pairs of intersecting lines to find the remaining angles :
[tex]\qquad \tt \rightarrow \: \angle4 + \angle1 = 180 \degree[/tex]
[ linear pair ]
[tex]\qquad \tt \rightarrow \: 29 \degree + \angle1 = 180 \degree[/tex]
[tex]\qquad \tt \rightarrow \: \angle1 = (180 - 29) \degree[/tex]
[tex]\qquad \tt \rightarrow \: \angle1 = 151\degree[/tex]
next,
[tex]\qquad \tt \rightarrow \: \angle2 = \angle4[/tex]
[ by vertical opposite angles ]
[tex]\qquad \tt \rightarrow \: \angle2 = 29 \degree[/tex]
and,
[tex]\qquad \tt \rightarrow \: \angle3 = \angle1[/tex]
[ by vertical opposite angles ]
[tex]\qquad \tt \rightarrow \: \angle3 = 151 \degree[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Find the difference and quotient of 8 and 4
FINDING THE DIFFERENCE WE SUBRACT
[tex]8 - 4 \\ = 4[/tex]
FINDING THE QUOTIENT WE DIVIDE
[tex]8 \div 4 \\ = 2[/tex]
HOPE THIS HELPS
Please answer the question in the photo for a Brainliest
I need help and I appreciate anyone who helps
Two angles form a linear pair. One angle is 5
more than four times the size of the other angle.
Find the measure of the largest angle.
Answer:
The measure of the largest angle is 145°
Step-by-step explanation:
Since the angles form a linear pair taking two angles that add to 180 and solving for x will give you the answer. the sentence "One angle is 5 more than four times the size of the other angle." your equation should look like this:
5 + 4x. the other angle uses the variable x. So the equation 5 + 4x + x = 180 should result in x = 35. That saying, the smaller angle is 35 and to find the larger angle either plug in x or subtract 180-35. both shoukd result in 145° which is the larger angle.
Convert 62 miles/hour to feet/second (5280ft-1 mile)
In mathematics, an operation is a function that transforms 0-n operands or parameters into a known output value. The number of operands affects how complicated the operation is. 90.95 feet per second equates to 62 miles per hour.
What is mathematical operation?An operation in mathematics is the function that converts 0–n parameters or operands into definite output value. The complexity of operation depends on how many operands there are.
The operations that are the most frequently studied are binary operations (i.e., operations of the arity 2), which include addition and multiplication, and the unary operations (i.e., operations of the arity 1), which include additive inverse and the multiplicative inverse. A zero-arity operation, also known as nullary operation, is a constant. An illustration of ternary operation, also known as an operation of arity 3, is the mixed product.
Usually, it is considered that arity is constrained. Even so, the infinitary operations are occasionally considered, in which case "normal" finite dimensionality operations are referred to as finiteary operations.
A partial operation is described as being similar to operation but using a partial function in place of a function.
1miles/hour= 1.467feet/second
62 miles/ hours= 62*1.467feet/second
= 90.95 feet/second
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a special deck of cards has 10 cards. four are green, three are blue, and three are red. when a card is picked, the color of it is recorded. an experiment consists of first picking a card and then tossing a coin.a. how many elements are there in the sample space?
The number of elements that are there in the sample space is 6.
What is sample space?It should be noted that sample space simply means the collection or the set of possible outcomes that are in the random experiment.
From the information, in the special deck of cards has 10 cards. four are green, three are blue, and three are red.
Therefore, the sample space will be:
S = GH, GT, BH, BT, RH, RT
It should be noted that H and T represents the head and tail.
Therefore, there are 6 elements.
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what is the answer for 8x - 4
Answer:
Step-by-step explanation:
100 points please answer!!!!!!!!!
help
Answer:
16
Step-by-step explanation:
gof(-6) means g(f(-6))
f(-6)=-(-6)-2
=6-2=4
g(4)=4^2=16
An arcade in Boulder, Colorado uses 3 different colored tokens for their game machines. For $20 you can purchase any of the following mixtures of tokens: 14 gold, 20 silver, and 24 bronze; OR, 20 gold, 15 silver, and 19 bronze; OR, 30 gold, 5 silver, and 13 bronze. What is the monetary value of each token?
The monetary value of gold, silver and bronze is $0.5, $0.35 and $0.25 respectively.
What is defined as the elimination method?The elimination method involves removing a single variables by combining the two equations. This method eliminates one variable, enabling you to solve for the other. Since there are two variables in a two-equation system, eliminating one simplifies the purpose is to solve for the other.The given conditions in the question are-
Let the monetary value of gold be 'a'.
Let the monetary value of silver be 'b'.
Let the monetary value of bronze be 'c'.
The total monetary value is $20.
The equation will be;
14 gold, 20 silver, and 24 bronze
14a + 20b + 24c = 20 .......eq1
20 gold, 15 silver, and 19 bronze
20a + 15b + 19c = 20 .......eq 2
30 gold, 5 silver, and 13 bronze.
30a + 5b + 13c = 20 .....eq 3.
Solving equation 1,2 and 3 by elimination method.
a = 1/2
b = 7/20 and
c = 1/4
Thus, the monetary value of gold, silver and bronze is $0.5, $0.35 and $0.25 respectively.
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4. Find the value of x.
6x + 14
8x + 12
The answer is x = 1, assuming that the space is meant to be an equal sign.
the population of a village increased from 234 to 275 during one year.Find the percentage increase
Answer:
275-234 = 41
41/275 times 100
4100/275
=14.90909
=15%
Step-by-step explanation:
Multiply (3-i) (7+2i)
Answer:
23-i
Step-by-step explanation:
Multiply using the FOIL method and after that combine the real and imaginary parts of the expression.
find x : 5( x + 4 ) - 3^2 = 2^4
Answer:x=1
Step-by-step explanation:
you would have to distribute the 5 into the (x+4)
then it would be
5x+20-3^2=2^4
then do the exponents
5x+20-9+16
then add 9 by both sides
5x+20=25
then subtract 20 on both sides
5x=5
then divide 5 on both sides
x=1
then check your work by putting 1 for x and you get 2^4=16
Answer:
x = 1Step-by-step explanation:
find x :
5( x + 4 ) - 3^2 = 2^4
5x + 20 - 9 = 16
5x = 16 - 20 + 9
5x = 5
x = 5 : 5
x = 1
----------------
check
5(1 + 4) - 3^2 = 2 ^4
25 - 9 = 16
16 = 16
the answer is good
3. On a flash drive, 800 megabytes out of 1000 megabytes are used. Write the
amount occupied as a percent.
Answer:
80%
Step-by-step explanation:
you're occupying 800 out of 1000
the way to write this mathematically is to write: 800/1000,
which equals 0.8
then to make this a percentage you x100
and your answer is 80%