The correct option regarding the slope and the intercept of the linear functions is given as follows:
The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
What is the definition of a linear function?The definition of a linear function is presented as follows:
y = mx + b.
In which the coefficients of the function are given as follows:
m is the slope of the function, which is the rate of change of the output variable y relative to the input variable x.b is the y-intercept of the function, which is the value of y when the function crosses the y-axis, that is, when x = 0.The points that compose function f(x) are given as follows:
(0,1) and (4,3).
Hence:
The slope is of 0.5, as when x increases by 4, y increases by 2.The intercept is of 1, as when x = 0, y = 1.The points that compose function g(x) are given as follows:
(0,1) and (4,-1).
Hence the coefficients are as follows:
The slope is of -0.5, as when x increases by 4, y decreases by 2.The intercept is of 1, as when x = 0, y = 1.Hence the correct option is:
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2 in the coordinate plane, line p has slope 1 3 and y-intercept (0, 2). Line r is the result of dilating line p by a factor of 3 centered at the origin. What are the slope and y-intercept of line r?.
The slope of the line r is 3 and the y intercept is (0,15) .
We know that coordinates of the point (x,y) after dilation by factor k centered at (a,b) is (k(x-a) + a , k(y-b) + b) .
In the question ,
it is given that
the slope of the line p [tex]=[/tex] 3
and the intercept of the line p = (0,2)
So , the equation of the line p is y = 3x + 2 .
So , the coordinates of the point (0,2) after dilation by factor 3 centered at (0,0) is (3(0 - 0) + 0 , 3(5 - 0) + 0)
= (0 , 15)
Point (0,0) does not lie on the line, so the line r after dilation is parallel to the line p,
the slope of line r = 3 , the y intercept is 15 .
Therefore , The slope of the line r is 3 and the y intercept is (0,15) .
The given question is incomplete , the complete question is
In the coordinate plane, line p has slope 3 and y-intercept (0, 2). Line r is the result of dilating line p by a factor of 3 centered at the origin. What are the slope and y-intercept of line r ?
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3.7x²+x2 combine like terms
Answer:
4.7x²
Step-by-step explanation:
3.7x² + x² = 3.7x² + 1x² = 4.7x²
Which expression can be used to determine the slope of the linear function represented in the table?
0 5
4 9
9-5
4-0
4-0
9-5
5-0
9-4
9-4
5-0
The first expression (9 - 5) / (4 - 0) is used to determine the slope of the linear function represented in the table.
What is slope of the line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. where "m" represents a line's slope. So, the slope of a line is tanθ.
From the given table the points are, (0, 5) and (4, 9).
Since, for points [tex](x_1, y_1), (x_2, y_2)[/tex] the slope can be defined as,
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Here,
[tex](x_1, y_1)=(0, 5)\\(x_2, y_2)=(4, 9)[/tex]
So, the slope is
[tex]m = \frac{9-5}{4-0}[/tex]
This is the first expression.
Therefore, the first expression (9 - 5) / (4 - 0) is used to determine the slope of the linear function represented in the table.
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An Olympic ized pool, which hold 660,000 gallon of water, i only 63% full. The pool Maintenance company add more water, filling the pill to 90% full. How many gallon of water did they add?
In linear equation, the amount of water added by the pool maintenance to make the pool 90% full is 178,200 gallons.
What are examples of linear equations?
An equation with only one variable is referred to as a linear equation in one variable.It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value.A linear equation in one variable would be 9x + 78 = 18, for instance.The amount of water an Olympic-sized pool can hold is, 660,000 gallons.
The pool is 63% full at the moment.
The of water in the pool now is
63% of 660,000 = 415,800 gallons
If the pool is 90% full then the amount of water in the pool is
90% of 660,000 = 594,000 gallons
The amount of water added by the pool maintenance is:
Amount of water added = 90% of 660,000 - 63% of 660,000
= 594000 - 415800
= 178200
Thus, the amount of water added by the pool maintenance to make the pool 90% full is 178,200 gallons.
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Let the graph of g be a vertical stretch by a factor of 2 and a
reflection in the x-axis, followed by a translation 3 units down of
the graph of f(x) = x². Write a rule for function g and identify the
vertex.
Vertex is slang for a corner or a place where two lines converge.The four corners of a square, for instance, are each referred to as a vertex.
Write a rule for function g and identify the vertex ?
The graph of g is a vertical stretch by a factor of 2 followed by a translation of 3 units down of the graph of f(x) = (x-1)²then the function g(x) = 2(x+4)²
f(x) =x²-2x+1 The graph of g be a vertical stretch by a factor of 3 and a reflection in the y-axis, followed by a translation 2 units left of the graph of .f(x) =x²-2x+1
Rewrite the given function f(x).
f(x) = (x-1)²
Now, the graph is stretched vertically by a factor of 2.
= 2(-x-1)²
reflect the graph about the y-axis.
2(x+1)²
move to the left by 3 units.
= 2(x+3+1)²
=2(x+4)²
The function g(x) =2(x+4)²
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a 130 foot tall building has a shadow that is 4 feet long. what is the angle of elevation of the sun? round to 2 decimal places.
The angle of elevation of the sun is 18°.
According to the question,
We have the following information:
A 130 foot tall building has a shadow that is 400 feet long (this is the correct question).
Now, let's take the angle of elevation of the sun to be x°.
Now, the height of the building will become perpendicular and the shadow will serve as the base for the angle of elevation.
We will use the trigonometric function tan.
Tan x = Perpendicular/base
Tan x = 130/400
Tan x = 0.325
Now, the value of x is 18°.
Hence, the angle of elevation of the sun is 18°.
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Two larger cubes are made out of unit cubes. Cube A is 2 by 2 by 2. Cube B is 4 by 4 by 4. The side length of Cube B is twice that of Cube A
Is the surface area of cube B also twice that of CUbe A?
No, the statement the surface area of Cube B is also twice that of Cube A, is False.
Cube A is of 2 by 2 by 2
So the length of each side of Cube A is 2 units
So the surface area of Cube A = 6*2*2 = 24 square units
Cube B is of 4 by 4 by 4
So each side length of Cube B is 4 units
So the surface area of Cube B = 6*4*4 = 96 square units
So Surface area of Cube B is = 96/24 = 4 times of surface area of Cube A.
So the given statement is not true.
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Two lines L1 and L2 have equations 3y = 6x + 5 and y- 2x = 1 respectively. Show that two lines are parallel.
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
line 1
3y = 6x + 5 ( divide through by 3 )
y = 2x + [tex]\frac{5}{3}[/tex] ← in slope- intercept form
with slope m = 2
line 2
y - 2x = 1 ( add 2x to both sides )
y = 2x + 1 ← in slope- intercept form
with slope m = 2
• Parallel lines have equal slopes
then line 1 and line 2 are parallel
Which number produces an irrational number when multiplied by 1/2?
OA. -√49
OB. E
C. 0.555555...
O D.
2/3
Answer:
e
Step-by-step explanation:
e is already irrational so if multiplied by 1/2 it will stay irrational
the regression equation is used to estimate a value of the dependent variable y based on a selected value of the independent variable x. true false
Answer:ummm it could be oh yea so true
Step-by-step explanation:
What does Pascal's triangle represent?.
In algebra, a triangle-shaped grouping of integers known as Pascal's triangle provides the coefficients for the expansion of every binomial formula, such as (x + y)ⁿ.
Explain the term Pascal's triangle?Although it is much older, it bears the name of the French scholar Blaise Pascal from the 17th century. In the eleventh century, the Chinese mathematician Jia Xian created a triangular form for the coefficients.
For instance, the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21), which was first discovered by the mediaeval Italian mathematician Leonardo Pisano ("Fibonacci") in his Liber abaci (1202; "Book of the Abacus"), is produced by drawing parallel "shallow diagonals" and adding the numbers on each line together. Another intriguing characteristic of the triangle is that it will form a fractal understood as the Sierpiski gasket, named for Polish mathematician Wacaw Sierpiski, who lived in the 20th century, if all the positions comprising odd numbers are shaded in black and every positions enclosing even numbers are shaded in white.To know more about the Pascal's triangle, here
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What is the midpoint of PQ
david drives from his home to the airport to catch a flight. he drives miles in the first hour, but realizes that he will be hour late if he continues at this speed. he increases his speed by miles per hour for the rest of the way to the airport and arrives minutes early. how many miles is the airport from his home?
The distance between David's home and the airport is 210 miles.
Distance traveled after 1 hourlet the distance traveled after first 1 hour = y
distance/speed = time
after 1 hour his speed = (35 + 15) = 50 mph
total time after 1 hour and 30 mins = 1.5 hr
y/50 + 1.5 = y/35
multiply through by 350
7y + 525 = 10y
3y = 525
y = 525/3
y = 175 miles
In the first 1 hour, at 35 mph, distance covered = 35 miles
Distance from his home to airport = 175 miles + 35 miles = 210 miles
Thus, the distance between David's home and the airport is 210 miles.
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The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $20.70 for 23 pounds of laundry and $34.20 for 38 pounds of laundry.
In words, describe the graph of the proportional relationship.
A line from (0, 0) going through (20.70, 23) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)
A line from (0, 0) going through (23, 20.70) where the x-axis is labeled Cost (in dollars) and the y-axis is labeled Weight (in pounds)
A line from (0, 0) going through (38, 34.20) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)
A line from (0, 0) going through (38, 34.20) where the x-axis is labeled Cost (in dollars) and the y-axis is labeled Weight (in pounds)
The graph of the proportional relationship is (c) A line from (0, 0) going through (38, 34.20) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)
How to determine the graph of the line?From the question, we have
It costs $20.70 for 23 pounds of laundry and $34.20 for 38 pounds of laundry
This means that
(x, y) = (20.70, 23) and (34.20, 38)
Where
x = Weight and y = Cost
From the question, we understand that
The graph is a proportional graph
This means that the line passes through the origin
So, we have
(x, y) = (0, 0), (20.70, 23) and (34.20, 38)
Remove one of the points
(x, y) = (0, 0) and (34.20, 38)
Hence, the graph of the proportional relationship is (c)
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Answer:
The graph of the proportional relationship is (c) A line from (0, 0) going through (38, 34.20) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)
Step-by-step explanation:
I took the exam and got it right
How can you write the prime factorization and find the greatet common factor and the leat common multiple of two number?
The term prime factorization refers to any number represented as the product of its prime factors.
For instance, the prime factors that make up the number 60 are listed as follows:
60=2×3×2×2×5
The idea behind prime factorization is to divide the provided whole numbers into their prime factors in order to find the largest common factor and least common multiple of each number.
Procedures for using prime factorization to find the greatest common factor (G.C.F.)
The given numbers should be written as their prime factors.
To find the G.C.F., multiply each of the given numbers by the product of the discovered common factors.
For instance, using the formula below, one may get the largest or greatest common factor between the values 50 and 20.
50 = 2 x 5 x 5
20 = 2 x 2 x 5
The highest common factor is found by multiplying the common prime factors of 50 and 20.
G.C.F = 2 x 5
The greatest common factor of the supplied numbers can then be computed using prime factorization.
Following these steps will help you use prime factorization to find the LCM:
In the form of their prime factors, write the given numbers.
Take the product of the numbers' rare prime factors and discovered common prime factors.
For instance, using prime factorization, the least common multiple of the numbers 50 and 20 can be calculated as follows:
Separately write the prime factors of 50 and 20.
50 = 2 x 5 x 5
20 = 2 x 2 x 5
Multiply the resulting common prime factors (2 and 5) with the remaining uncommon prime factors (2 and 5) to find the least common divisor.
L.C.M = 2 x 2 x 5 x 5
In this way, we can take advantage of prime factorization to compute the least common multiple of a given number.
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(s3-6s)+4t2 when s=5 and 3=t
Answer:
9
Step-by-step explanation:
(5)3-6(5)+4(3)2
(15-30)+4(3)2
-15+ 24
=9
Write an equation in point-slope form of the line that passes through the given point and with the given slope m. (-7,1); m=6
Answer:
y - 1 = 6(x+7)
Step-by-step explanation:
point slope form is y-y₁=m(x-x₁)
given m = 6 and the point is (-7,1)
plug in your values
remember that an ordered pair is (x,y)
y-y₁=m(x-x₁) ----> y-1 = 6(x+7)...............just plug in values
How do you find the table of values on a graph?.
The table of values on the given graph is for the polynomial y = -x+4.
The example we are using is a polynomial in one variable. It is to be represented graphically. The graph for it is given below.
From this graph, we can clearly see the coordinates of all points we have taken. In order to make the table of values, we need to find the x and y intercepts.
We see that the first point from the left is aligned to the -2 on the x-axis and to the 6 on the y-axis. Similarly, we can identify the following values from the given graph.
x = -2 and y = 6
x = -1 and y = 5
x = 0 and y = 4
x = 1 and y = 3
x = 2 and y = 2
This is the table of values that we found out through the graph.
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Kevin is choosing between two cell phone plans. Plan A has a flat monthly charge of $32 for an unlimited number of minutes. Plan B has a monthly charge of $24 plus an additional charge of $0.05 per minute. For what number of minutes of monthly usage do both plans cost the same amount?
If Plan B has a monthly charge of $24 plus an additional charge of $0.05 per minute. The number of minutes of monthly usage that both plans cost the same amount is 160 minutes.
How to find the number of minutes?Let x represent the number of minutes of monthly usage
Hence,
Formulate an equation
0.05x + 24 = 32
Combine like terms
0.05x = 32 -24
0.05x = 8
Divide both side by 0.05x
x = 8/0.05
x = 160 minutes
Therefore 160 is the number of minutes.
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Michael has 12 cups of orange juice in a jar. he pours the juice into glasses that each hold 3/4 cup. How many glasses can he fill
Answer:
Step-by-step explanation:
. = 12\0.75
. = 16
Answer:
16
Step-by-step explanation:
12÷[tex]\frac{3}{4}[/tex] = [tex]\frac{12}{1}[/tex] x [tex]\frac{4}{3}[/tex] = [tex]\frac{48}{3}[/tex] = 16
The depth at which dolphins dive, y, in feet, as related to the duration of the dive, t, in seconds, is represented by the linear model ŷ = 0.25 5.78t. if the dive duration is 3 seconds, what is the predicted depth of the dive? 0.48 feet −17.59 feet 17.59 feet −0.48 feet
According to the given linear equation depth of the dive is 17.59 feet.
What is linear equation?
A linear equation is also known as a one degree equation. The linear equation's highest power is 1. Linear equations are equations with variables on both sides that are multiplied by a constant.
Here the given linear equation is ,
=> y = 0.25+5.78t
Here t is time in seconds which is t=3 seconds.
Put t=3 sec into linear equation then,
=>y=0.25+5.78*3
=>y= 0.25+17.34
=>y=17.59.
Hence depth of the dive is 17.59 feet.
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If $10,000 is borrowed with an interest of 5. 0% compounded annually, what is the total amount of money needed to pay it back in 5 years? round your answer to the nearest cent and do not include the dollar sign. Do not round at any other point in the solving process; only round your answer.
The amount of money that is needed to pay after 5 years is 12762.9 .
In the question ,
it is given that ,
the amount borrowed(P) = $10000
the rate at which the amount is borrowed (r) = 5% = 0.05
the time for which the amount is borrowed (t) = 5 years
the number of times the interest is charge (n) = 1 .
The final amount for the compound interest is calculated using the formula .
Amount = [tex]P\times(1+\frac{r}{n})^{nt}[/tex]
Substituting the value of P , r , n and t , in the formula ,
we get
Amount = 10000 (1 + 0.05)⁵
= 10000*(1.05)⁵
= (10000)*(1.2762815625)
= 12,762.815625
≈ 12762.9
Therefore , The amount of money that is needed to pay after 5 years is 12762.9 .
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Solve b² +5b + 4 = 0 using completing the squares method
Answer:
b² +5b + 4 = 0
b² + 5b -41= 5.702
3
Step-by-step explanation:
1.1 Factoring b2+5b-4
The first term is, b2 its coefficient is 1 .
The middle term is, +5b its coefficient is 5 .
The last term, "the constant", is -4
Step-1 : Multiply the coefficient of the first term by the constant 1 • -4 = -4
Step-2 : Find two factors of -4 whose sum equals the coefficient of the middle term, which is 5 .
-4 + 1 = -3 -2 + 2 = 0 -1 + 4 = 3
I need this to be converted to a linear equation:
(-1, 3); slope = -3
After converting into a linear equation, we have the equation y = -3x
What is a linear equation?
A linear equation is one in which the variable's maximum power is consistently 1. A one-degree equation is another name for it. This indicates that there are no variables in a linear equation with exponents greater than 1. A linear equation's graph almost always takes the shape of a straight line.
Solution Explained:
From the question, we have
x = -1
y = 3
slope (m) = -3
Substituting these values in the equation,
y = mx + c
3 = (-3) x -1 + c
After simplyfing the equation, we get
c = 0
We again substitute the value of m and c in the equation,
y = mx + c
y = -3x + 0
y = -3x
Hence, the linear equation is y = -3x.
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2. Taylor is about to go car shopping, and she has $5000 saved that she can use for a down
payment while still having extra cash in her emergency fund. She expects the exact model
car she's looking for to cost $35,000. If her top priority is having the lowest monthly
payments possible, which advice should she follow?wou tonte
a. Put in $0 for your down payment, and choose a loan with a short term length
b. Put in $2500 for your down payment, and choose a loan with a short term length
c. Put in $3500 for your down payment, and choose a loan with a long term length
d. Put in $5000 for your down payment, and choose a loan with a long term length
The best option for Taylor is d. Put in $5000 for your down payment, and choose a loan with a long term length
What is a loan?A loan is the lending of money by one or more individuals, organizations, or other entities to other individuals, organizations, or other entities in finance. The recipient (i.e., the borrower) incurs a debt and is typically required to pay interest on that debt until it is repaid, in addition to repaying the principal amount borrowed.
The document evidencing the debt (for example, a promissory note) will typically specify the principal amount borrowed, the interest rate charged by the lender, and the date of repayment.
In this case, choosing a long term repayment plan will make it easier to pay back.
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Math Learning task no.2
Ming Meding prepared 12 banna muffins
and 18 squid ball's find the ratio of the number of banna muffins to the number of squid balls. Write it in throw forms.
pls pa helg need ko na sagutan ^_^
Answer:
12:18
Step-by-step explanation:
Yan te ok na ata yan
Answer:
12:18
Step-by-step explanation:
You have 12 banana muffins, and 18 squid ball's.
Put it in ratio form. so it's B:S in name form, so the final answer will be 12:18.
If you put it in this form S:B, then the answer will be 18:12.
Goodluck!
Find the perimeter of the triangle if the area of the triangle is 168 ft2
Answer:
The perimeter of the triangle is 64 feetStep-by-step explanation:
Area of triangle equation:
A = bh/2Find the value of h, using given values:
168 = 14h/2168 = 7hh = 1687h = 24Use Pythagorean and find the missing side s of the triangle:
s² = 24² + (14/2)²s² = 576 + 49s² = 625s = √625s = 25Find the perimeter of this isosceles triangle:
P = 25*2 + 14P = 50 + 14P = 64The perimeter of the triangle is 70 ft.
What is a triangle?A triangle is a polygon with 3 sides.
Given that, the area of the triangle is 168 square feet.
The formula for the area of a triangle with base b and height h is:
A = (1/2)×bh
Substitute A = 168 and b = 14 into the equation:
168= (1/2)×(14)h
168/14 = (1/2)h
12 = (1/2)h
12×2 = h
24 = h
Hence, the height of the triangle is 24 ft.
Let the length of the slant side of the triangle be s.
Use the Pythagorean theorem to find the value of s:
s² = b² + h²
Substitute b= 14 and h = 24 into the equation:
s² = 14² + 24²
s² = 196 + 576
s² = 772
s = √772
s ≈ 28
The length of both slant sides of the triangle is the same, therefore, the perimeter of the triangle is given by:
P = 14 + 28 +28
P = 70
Hence, the perimeter of the triangle is 70 ft.
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debra runs each lap in 6 minutes. she will run less than 8 laps today. what are the possible numbers of minutes she will run today?
If Debra runs each lap in 6 minutes and she will run less than 8 laps today. Then the possible number of minutes that she will run todays is less than 48 minutes
Time taken for each lap = 6 minutes
Number of laps that she run today = less than 8 laps
The possible number of minutes that she will run today ≤ Time taken for each lap × Number of laps that she run today
Here we have to use the inequality
The inequality is defined as the relation ship between two variables that is not equal. The inequality operations are less than, greater than, less than or equal to, greater than or equal to etc..
The possible number of minutes that she will run today ≤ 6 × 8
≤ 48 minutes
Hence, if Debra runs each lap in 6 minutes and she will run less than 8 laps today. Then the possible number of minutes that she will run todays is less than 48 minutes
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the question above please
Fill in the missing numbers
1/2 of 50 =
1/3 of 36 =
Answer:
25 and 12
Step-by-step explanation:
1/2 of 50 = can be rewritten as (1/2)*(50) = (50/2) = 25
1/3 of 36 = can be rewritten as (1/3)*(36) = (36/3) = 12
Answer:
1/2 of 50 could also be re-written as 1
___ × 50
2
So to solve this we need to multiply 1 by 50
like this 50×1
which is equal to 50 i.e 50 × 1 = 50
the next step is to then divide by 2
i.e 50
___ = 25
2
this is so because there are simply 2 25s in 50
So i guess you should be able to do the second one
Jaane
