The slope of the line passing through the pair of points, (-2 , -4) and (1 , 2), is 2.
The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points. The formula for solving the slope is:
m = (y2 - y1)/(x2 - x1)
where m is the slope
x1 and y1 are the coordinates of one point
x2 and y2 are the coordinates of the 2nd point
Given two points in the line, (-2 , -4) and (1 , 2), plug in the values to the formula for the slope.
m = (y2 - y1)/(x2 - x1)
m = (2 - -4)/(1 - -2)
m = 6/3
m = 2
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Describe the transformations of f(x) that produce g(x) .
f(x)=3x ; g(x) = (3x/4) - 2)
A compound function is when the output of one function is used as the input of another function. If we have a function ff and another function gg, the function fg(x)fg(x) is called "ff of gg of xx" or "fgfg of xx" and is a composition of the two functions.
The order in which functions are applied is important. Find the function of the
function. If you have two or more functions, there can be many different permutations of those functions, giving you many different composite functions.
fg(x)fg (x) can be written f[g(x)]f[g(x)] to indicate that the inner function should be applied before the outer function.
Solution:
Your problem → f(x)=3x, g(x)=((3x)/4)-2, Find f(g(x))
f(x)=3x, g(x)=3x4-2, fog(x)=?
g(x)=3x4-2, f(x)=3x
fog(x)=f(g(x))
=f((3x)/4-2)
=3(3x4-2)
=9x4-6
fog(x)=9x4-6
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A 3-gallon bottle of fabric softener costs $40.32. What is the price per pint?
Determine whether the given function is linear. f(x) = 3 + 1/3x
you can either graph this or plug in values.
[tex]f(x)=3+\frac{1}{3}x[/tex]
[tex]f(-1)=3+\frac{1}{3}(-1)\\\\f(-1)=3-\frac{1}{3}\\\\f(-1)=2\ \frac{2}{3}\\\\f(0)=3\\\\f(1)=3\ \frac{1}{3}[/tex]
[tex]\therefore[/tex] we can conclude that this function is linear.
Also here is a graph
Mr.Rogers opened a savings account with an initial deposit of $4,000 and will not make any additional deposits or withdrawals. The account earns a 2% simple interest. What is the total amount that Mr.Rogers will have in his account at the end of 3 years?
Answer:
£4240
Step-by-step explanation:
2%of 4000=80
80x3=240
4000+240=4240
what is y if 3y+20=5y-16
Answer:
y is equal to 18
Step-by-step explanation:
[tex]3y+20-20=5y-16-20\\3y=5y-36\\3y-5y=5y-36-5y\\-2y=-36\\\frac{-2(y)}{-2}=\frac{-36}{-2}\\(\frac{-a}{-b} = \frac{a}{yb}) =\frac{2y}{2}\\\frac{2(y)}{2}=y\\=\frac{36}{2}\\=18\\y = 18[/tex]
A negative sign indicates the ______ of the number?
Answer:
opposite
Step-by-step explanation:
In the expression 38+27 y , which number is a coefficient?
27 is the number that is a coefficient.
An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it.
A coefficient is a number or an alphabet that is multiplied by a variable of a single term or the terms of a polynomial. For example, in the term 7x, 7 is the coefficient. The coefficient of x in the term 3xy is 3y.
The variable is a symbol for a value we don't know yet. It is usually a letter like x or y.
In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.
In the expression 38 + 27y the coefficient of y is 27, 38 is the constant and y is the variable.
we can identify a coefficient since it is always associated with a variable.
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Rita had a 28-mile head start.
Roger had a 26-mile head start.
Roger had a 25-mile head start.
Rita had a 22-mile head start.
Rita has a head start, has she began her race 28 Mile ahead of the starting point.
How to illustrate the information?Since they moved at a constant speed, then there speed is the same through out the journey.
Speed is given by the slope:
(y2 - y1) / (x2 - x1) = (130 - 65) / (2 - 1) = 65 / 1 = 65 mph
Roger's starting position, when t = 0
t = 1 ; distance = 65 miles
t = 0 ; 65 - speed per hour = 65
At t = 0 ; 65 - 65 = 0 miles
Hence, Roger does not have a head start.
For Rita :
Speed is also constant :
Speed or rate = slope of the graph :
(y2 - y1) / (x2 - x1) = (158 - 93) / (2 - 1) = 65 / 1 = 65 mph
Rita's starting position, when t = 0
t = 1 ; distance = 93 miles
t = 0 ; 93 - speed per hour
At t = 0 ; 93 - 65 = 28 miles
Hence, Rita has a head start of 28 miles.
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a truck can be rented from Company A for $110 a day plus $0.30 per mile, Company B charges $50 a day plus $0.40 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
Answer:
600 miles
Step-by-step explanation:
Plug 110+0.30x and 50+0.40x into a graphing calculator and see where they intersect
Work out the area of a rectangle with base,
b
= 38mm and perimeter,
P
= 78mm.
Answer: 38
Step-by-step explanation: In order to find the area you need to figure out all your sides. Now thankfully it's just a rectangle or this would be a bit more complicated haha!
The first step is to understand what all the sides are. Since you know you have a perimeter of 78 and base of 38, all you need to do is add 38 +38. The reason is that that's on both long sides of a rectangle. This now leaves you with a number of 76.
Second step: Take the number 76 and subtract it your perimeter 78. This obviously leaves you with the number 2, which you'll have 1 on the shorter sides.
Therefore Area: 38 x 1 = 38
Hope it helps
Which relation is function?
There are 4 graph in the given picture. The 4th graph is the function other 1st, 2nd and 3rd graph are not a function.
Given that,
There are 4 graph in the given picture.
We have to find the graph is function or not.
We have to perform the vertical line test.
Use the vertical line test to determine whether a graph accurately represents a function. If a vertical line is moved across it and only ever touches it at one point, the graph is said to be a function. The graph is not a function if the vertical line traverses it more than once.
We have to draw the vertical lines on a graph if the vertical line touches the graph more then 1 then it is not a function if it touches 1 time then it is a function.
1st graph is not a function.
2nd graph is not a function.
3rd graph is not a function.
4th graph is a function.
Therefore, the 4th graph is the function other 1st, 2nd and 3rd graph are not a function.
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Eric has scores of 71, 80, and 83 on his history tests. the final exam counts as two tests, and a b is received if the final course average is greater than or equal to 80
Answer:
he doesnt get a b
Step-by-step explanation:
71+80+83+83=317
317/4= 79.25
79.25 !=< 80
In this problem, you will investigate the relationship between the arcs of a circle that are cut by two parallel chords.
a. Use a compass to draw a circle with parallel chords -AB and -CD . Connect points A and D by drawing segment -AD .
When two arcs are parallel to each other, the two arcs between them are congruent. If the two arcs they intersect are the same length, they are congruent.
When two chords of a circle are parallel are the arcs?Chords within a circle can be related in a variety of ways. Parallel chords cut congruent arcs in the same circle. That is, the arcs whose endpoints include one of each chord's endpoints have equal measures.
The lengths of the arcs connecting two parallel chords of a circle are equal. Similarly, if the lengths of the two arcs connecting two distinct chords are the same, the chords are parallel. If two chords have the same length, the arcs between their endpoints will have the same measure.
When two arcs are parallel to each other, the two arcs between them are congruent. If the two arcs they intersect are the same length, they are congruent.
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A. Solves each equation by extracting square root.
1.) x² = 16
2.) x² = 49
3.) x² = 128
4.) x² = 108
5.) x² = 121
6.) x²-169 = 0
7.) x²-80=0
8.) x²-63=0
9.) 5x2 – 125 = 0
10.) 3x²-132-0
can you answer this please
17.- En una caja hay 5 canicas azules 3 canicas rojas y 2 canicas verdes
¿Cuál es la probabilidad de sacar una canica roja?
Answer:
La probabilidad de sacar una canica roja seria 3/10 porque hay 10 canicas en total, 3 de ellas son rojas. Tambien se puede escribir 0.3 . Espero que esto te ayude.
Find the value of Y.
Answer:
y= 21
Step-by-step explanation:
4y-42=2y
4y=2y+42
2y=42
y=21
Use each recursive definition to write an explicit formula for the sequence. a₁ = 10, an =2 a n ₋ ₁
The explicit formula is [tex]a_n = 2^{n-1}.10[/tex]
What is a sequence ?A sequence can be taken as the set of numbers having a particular order for all the terms or we can say that arrangement of numbers in some order is known as sequence. There are many types of sequences such as recursive sequences, arithmetic sequences, special sequences, quadratic sequences, geometric sequences etc.
Some examples for sequence are :
2,4,6,8,10,12
3,9,27,81,243
What is recursive sequence ?The recursive sequence is the sequence in which any term in the sequence can be find with the help of previous term of that sequence.
In a sequence , first term always known as initial term.
and difference between two terms are known as common difference. It is denoted by d.
General form of sequence is :
[tex]a_1,a_2,a_3,----,a_n[/tex]
where , [tex]a_n[/tex] = last term in sequence.
According to question,
[tex]a_1 = 10[/tex] and [tex]a_n=2a_{n-1}[/tex]
first find the sequence ,
[tex]a_2= 2 a_{2-1} = 2 a_1 = 2(10) = 20\\\\a_3= 2 a_{3-1} = 2 a_2= 2(20) = 40\\\\a_4= 2 a_{4-1} = 2 a_3= 2(40) = 80[/tex]
Thus sequence is 10,20,40,80,...
and the explicit formula for sequence is :
[tex]a_n = 2a_{n-1}\\= > a_n = 2(2a_{n-2}) = 2^2 a_{n-2}\\= > a_n = 2^2 (2a_{n-3}) = 2^3 a_{n-3}\\ .\\.\\= > a_n = 2^{n-1} a_{n-(n-1)} \\ = > a_n = 2^{n-1} .a_1 = 2^{n-1}.10[/tex]
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PLS HELP!
Drag each tile to the correct box. NOT ALL TILES WILL BE USED!
Given a horizontal line segment AB and a point C, place the steps for copying AB to create CD in the proper order.
Set the compass width to CB.
Place the compass point at point C and draw an arc.
Draw DC.
Set the compass width to AB.
Place the compass point at point B and draw an arc.
Make a point D anywhere on the arc.
The steps for copying AB to create CD in the proper order are;
1. Set the compass width to AB.
2. Place the compass point at point C and draw an arc.
3. Make a point D anywhere on the arc.
4. Draw DC.
How to copy a Line Segment?
The steps to copy a line segment are;
Step 1: Plot a point that will be an endpoint of the new line segment
Step 2: With the compass pin at the beginning of the original line segment, open the compass width to the end of the original line segment
Step 3: With the adjusted compass width from the above step place the compass pin at the plotted point of the new line segment and draw an arc in the region the new line segment is to be located
Step 4: Select a point on the arc where the other end of the new line will be
Step 5: From the selected point from the above step, draw a line to the point plotted as the beginning of the new line segment
Step 6: The length of the line drawn above is the same as the length of the original line segment..
Looking at the given options, the steps for copying AB to create CD in the proper order are;
1. Set the compass width to AB.
2. Place the compass point at point C and draw an arc.
3. Make a point D anywhere on the arc.
4. Draw DC.
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Isabel is on a ride at an amusement park that slides the rider to the right, and then rotates counterclockwise about its own center 60° every 2 seconds. How many seconds pass before Isabel completes one full rotation?
Isabel to complete one full rotation is 12 seconds.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.P ( E ) = Number of favourable outcome Total number of outcomes. Hence, the probability is the possibility of the occurrence of a random event.In every 2 seconds the ride rotates 60º.
So, it takes 6 turns to rotate 6 × 60º or 360º.
Therefore, the time it takes
Isabel to complete one full rotation is 12 seconds.
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Please resolve it and list the steps the simplest way possible, thanks. ASAP if possible
Step-by-step explanation:
Looks like it's a piecewise defined function. Where you see a circle, means it's not inclusive so at f(1) it should be define at y=3
i need help pleaseee
Answer:
UT=27
ST=18
RV=15
US=15
Step-by-step explanation:
If the entirety of RT is 30, then you'd divide that by 2 to receive the number for both RV and VT. 30 divided by 2 is 15.
Because RVS and UVT are vertical, they are both 27. Similarly, RVU and SVT are vertical to each other, so SVT is the same as RVU which is 18.
Hope this helps.
7
2-2
3-3
Question 6(Multiple Choice Worth 1 points)
(02.05 MC)
If the parent function f(x) = |x| is transformed to g(x) = |x - 3|, what transformation occurs from f(x) to g(x)?
The graph of f(x) is shifted upward to create g(x).
The graph of f(x) is shifted downward to create g(x).
The graph of f(x) is shifted to the right to create g(x).
The graph of f(x) is shifted to the left to create g(x).
Question 7(Multiple Choice Worth 1 points)
(02.05 MC)
Set
Answer: The graph of f(x) is shifted to the right to create g(x).
Step-by-step explanation:
g(x) is the graph of f(x) shifted right 3 units.
4. Drew is going to try out for the basketball team, so he decides to shoot free throws every day at the park. On the first day, he shoots 15 free throws. On the second day, he shoots 25 free throws. On the third day, he shoots 35 free throws, Drew continues to increase the number of free throws he shoots each day by the same amount. a) If Drew continues to follow this pattern, how many free throws will Drew shoot on the 20th day? b) What is the total number of free throws Drew shot during those 20 days?
Answer:
He shot a total of 2,415 free throws. He shot 255 on the 20th day.
Step-by-step explanation:
Simplify each expression.
8. (-3)+4
8. (-3)+4
= -24 +4
= -20
What is algebric equation?In algebraic equation or polynomial equation is an equation of the frame P=0 where P could be a polynomial with coefficients in a few field, regularly the field of the rational numbers.
algebraic equation, statement of the equality of two expressions defined by applying to a set of factors the algebraic operations, namely, expansion, subtraction, increase, division, raising to a control, and extraction of a root.
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I've been trying to figure this out for a while now, can I get some help? -53<9x+1<-26
Answer:
- 9 < x < - 3
Step-by-step explanation:
- 53 < 9x + 1 < - 26 ( subtract 1 from each interval )
- 54 < 9x < - 27 ( divide each interval by 9 )
- 6 < x < - 3
f(x) = -5x − 3 and g(x) = 6x - 2. Find f g and its domain.
The domain is f[tex]o[/tex]g(x)= -30x+7
The domain is all the real numbers.
Given that f(x)=-5x-3 and g(x)=6x-2.
f[tex]o[/tex]g=f(g(x))
=f(6x-2)-3
=-5(6x-2)-3
=-30x+10-3
f[tex]o[/tex]g =-30x+7
The domain is all the real numbers.
What is domain?
Specific to the internet, the term domain can refer to how the internet is structured, and domain also refers to how an organization's network resources are organized. In general, a domain is an area of control or a sphere of knowledge.
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Question below, only answer if you know
Answer:
1. translate
2.rotate
explanation:
first, translate a to the next quadrant.
second, rotate it 180 degrees.
Answer:
Figure A translated 2 figures down and mirrored to the right.
Figure A then rotated 180 degrees.
Determine whether each set of numbers can be the measure of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer.
b. 2 √3, 4√2, 3 √5
The following set of numbers 2√3, 4√2, and 3√5, can be the measures of the sides of an obtuse triangle.
A triangle is a polygon with three sides and three vertices.
To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
let a = 2√3, b = 4√2, and c = 3√5
a + b > c 2√3 + 4√2 > 3√5 9.12 > 6.71 True
a + c > b 2√3 + 3√5 > 4√2 10.17 > 5.66 True
b + c > a 4√2 + 3√5 > 2√3 12.37 > 3.46 True
To know what type of triangle based on the length of its side:
1. Take the sum of the squares of the two smaller sides.
(2√3)^2 + (4√2)^2 = 44
2. Compare it to the square of the largest side.
(3√5)^2 = 45
44 < 45
If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.
if they are equal, it is a right triangle
if they are smaller, then it is an obtuse triangle.
Hence, 2√3, 4√2, and 3√5 can be the measure of the sides of an obtuse triangle.
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Find the value of each variable (3x+31)° (2x-6)°
Answer:
x = 31°Step-by-step explanation:
Angle (3x+31)° and angle (2x-6)° are supplementary angles
(3x + 31)° + (2x - 6)° = 180°
5x + 25° = 180°
5x = 155°
x = 31°
-----------------
check
3 * 31 + 31 + 2 * 31 - 6 = 180
180 = 180 (remember PEMDAS)
the answer is good
The endpoints of CD¯¯¯¯¯¯¯¯
C
D
¯
are C(3,−5)
C
(
3
,
−
5
)
and D(7, 9)
D
(
7
,
9
)
.
The length of segment CD is 14.6 units
How to determine the length of CD?The points are given as:
C = (3, -5) and
D = (7,9).
The distance is calculated using
d = √(x2 - x1)^2 + (y2 - y1)^2
This gives
d = √(7 - 3)^2 + (9 + 5)^2
Evaluate
d = 14.6
Hence, the length of segment CD is 14.6
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