The equation of the line that goes through the point (3,-3) and has a slope of -5/3 is y=(-5x+6)/3.
What is a slope?In mathematics, line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent a slope; reason for this is unclear, although it is first used in English by O'Brien in 1844, who wrote the equation for a straight line as "y = mx + b," and by Todhunter in 1888, who wrote it as "y = mx + c."
The ratio of "vertical change" to "horizontal change" between (any) two unique points on a line is used to compute slope. The ratio can also be written as quotient ("rise over run"), which produces same number for every two distinct points on the same line. A declining line has negative "rise." The line might be useful, as determined by road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.
The slope's absolute value serves as a gauge for line's steepness, incline, or grade. A steeper line is indicated by slope with a higher absolute value. A line can be drawn with one of four directions: upward, downward, horizontal, or vertical.
if we let y = mx + b, where m is the slope and b is the intercept, and y - y1 = m (x - x1), then:
3(y + 3) = - 5 (X - (-3))
3y + 9 = - 5 X + 15
3y = -5 X + 6
y=(-5x+6)/3
Check:
When x = 3, y should equal - 3, so:
Y = (- 5 (3) + 6)/3 = -3
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round to the underlined digit:
Answer:
c because if the number next to the underlined is above 5 u round up under 4 u round down
Step-by-step explanation:
Answer: c. 76
Step-by-step explanation: 0.758 to the hundredth place is 0.76 because numbers5 and above round up.
n(x) = -1-x+4
n(-2) =
n(0)=
n(5)=
Step-by-step:
n(x) = -1 - x + 4
n(-2) = -1 - (-2) + 4
= -1 + 2 + 4
= 5
___________________________
n(0)= -1 - 0 + 4
= 3
___________________________
n(5)= -1 - 5 + 4
= -2
The equation y = 0.43x + 50 models the cost y of renting a car if the car is driven x
miles.
According to the model, what is the best estimate of the cost for renting a car if you
plan to drive 489 miles? Please round your answer to the nearest dollar.
By solving the given equation (y = 0.43x + 5) we know that the cost of renting the car is $215 when we plan to drive 489 miles.
What do we mean by equations?A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15. Different types of equations exist, including linear, quadratic, cubic, and others. Let's read this article to learn more about math equations.So, y = 0.43x + 5 where 'x' is car driven and 'y' is the cost of renting.
Now, solve for y when the value of x is 489.
y = 0.43x + 5y = 0.43(489) + 5y = 210.27 + 5y = $215.27Rounding off: y = $215
Therefore, by solving the given equation we know that the cost of renting the car is $215 when we plan to drive 489 miles.
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PLEASE HELP!: I'm so confused about what equations to write for the problem. All I need is the equations and I can solve it alone! I'll give brainly!
You invest $8,000 in 3 investment accounts. The accounts are: paper, metal, and glass. Paper returns 2% income, metal returns 4% income, and glass returns 5% income. The amount invested in the glass account was double the amount invested in the metal account. The yield was a total of $280 at the end of one year. How much was invested in each account?
Using simple interest, the amounts invested into each account are given as follows:
Paper returns: $3,500.Metal returns: $1,500.Glass returns: $3,000.Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
A(t) = P(1 + rt)
In which:
P is the initial amount.r is the interest rate, as a decimal.The amount of interest after t years is given by:
I(t) = Prt
You invest $8,000 in 3 investment accounts, hence:
[tex]P_1 + P_2 + P_3 = 8000[/tex]
From the rates of the account, we have that:
[tex]I_1 = 0.02P_1[/tex][tex]I_2 = 0.04P_2[/tex][tex]I_3 = 0.05P_3[/tex]The amount invested in the glass account was double the amount invested in the metal account, hence:
[tex]P_3 = 2P_2[/tex]
The yield was a total of $280 at the end of one year, hence:
[tex]I_1 + I_2 + I_3 = 280[/tex]
[tex]0.02P_1 + 0.04P_2 + 0.05P_3 = 280[/tex]
From the first and the third equations, we have that:
[tex]P_1 + P_2 + P_3 = 8000[/tex]
[tex]P_1 + 3P_2 = 8000[/tex]
[tex]P_1 = 8000 - 3P_2[/tex]
Hence the amount of the metal investment can be found as follows:
[tex]0.02P_1 + 0.04P_2 + 0.05P_3 = 280[/tex]
[tex]0.02(8000 - 3P_2) + 0.04P_2 + 0.05(2P_2) = 280[/tex]
[tex]0.08P_2 = 120[/tex]
[tex]P_2 = \frac{120}{0.08}[/tex]
[tex]P_2 = 1500[/tex]
Hence the other investments are given as follows:
Paper: 8000 - 3 x 1500 = $3,500.Glass: 2 x 1500 = $3,000.More can be learned about simple interest at https://brainly.com/question/20690803
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Karen is driving her moterhome. It uses 3 gallons of gas for every 24 milesComplete the table below showing the number of gallons used and the distance traveled.
( The table is 3,24 6, ? 7,? ? , 72 and 10, ?)
Answer: 6, 48 and 7, 56 and 9, 72 and 10,80
Step-by-step explanation:
Find the value of x if T is the midpoint of segment XY. Segment XT = 3x-14, Segment XY = 8x-56
The value of x if T is the midpoint segment XY is 14.
How to find the mid point of a segment?The midpoint is the middle point of a line segment.
It is equidistant from both endpoints.
The midpoint is halfway between the two end points.
Therefore, the end point of the segment is XY.
The midpoint is T.
Hence,
XY = XT + YT
XT = 3x - 14 = YT
XY = 8x - 56
Let's find the value x.
Therefore,
8x - 56 = 3x - 14 + 3x - 14
8x - 56 = 6x - 28
8x - 6x = -28 + 56
2x = 28
divide both sides by 2
x = 28 / 2
x = 14
Therefore, the value of x is 14
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Suppose f(x)=4[[x-1]].
Find: f(1.7),f(-3.4), and f(9.8).
Answer:
I believe it should be
f(1.7) = 2.8
f(-3.4) = -17.6
f(9.8) = 35.
Step-by-step explanation:
Simply plug-in the different numbers for x.
Determine the intercepts of the line.
Answer:
x- intercept: ( -10,0)
y- intercept: (0, -45)
Step-by-step explanation:
An x intercept can be determined from the graph above by recognizing where the given line crosses the x-axis. The same is true for the y intercept and the y-axis.
On this graph, we see that the line crosses the x axis at the point ( -10,0), making this our x intercept.
We also see that the line crosses the y axis at the point (0, -45), making this our y intercept.
HOPE THIS HELPS!!
You cut a 90-foot rope into 6 pieces of equal length. What is the length of
each piece?
Answer:
Length = 15
Step-by-step explanation:
The problem can be solved by dividing the total length of the rope (90-feet) by the total pieces you want from the rope (6 pieces). This information can be used to make this equation
90 feet / 6 pieces
Which equals
90 feet / 6 pieces = 15 feet/piece (15 feet per peice)
Hope this helps :)
Find the area of the pool. Write as a polynomial.
Pool
6x
3x-5
please help meeee!!! :c
Function A
f(x) = x − 9
Function B
graph of line going through ordered pairs negative 1, negative 3 and 2, 3
Which equation best compares the slopes of the two functions?
Slope of Function B = 2 x Slope of Function A
Slope of Function A = Slope of Function B
Slope of Function A = 2 x Slope of Function B
Slope of Function B = − Slope of Function A
The equation best compares the slopes of two functions is,
Slope of function B = 2 × Slope of function A
Given,
The function A, f(x) = x - 9
We have to find slope of Function B
The function is in the form of y = mx + b
Here, m is the slope.
y = x - 9
m is 1 and b is -9
Now, lets consider the graph of line passing through points (-1, -3) and (2, 3)
That is,
(x₁, y₁) = (-1, -3)
(x₂, y₂) = (2, 3)
Now we can find the slope of the line:
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - (-3)) / (2- (-1))
m = (3 + 3) / (2 + 1)
m = 6/3
m = 2
That is, the slope of function B is 2
Here,
Slope of function A is 1.
That is, slope of function B is twice the slope of function A.
Therefore, the equation best compares the slopes of two functions is,
Slope of function B = 2 × Slope of function A
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Divide
-36
-8
Enter your answer as a mixed number, in simplified form, in the box.
the answer is this
4 4/8.
7. If Antonio makes x dollars per regular hours, and his boss tells him that he is
going to get paid over time at double time, write an equation to find his hourly
rate if he makes $1578.5 working 55 hours this week.
The equation for the hourly rate is 55x = 1578.5
For double hourly rate for overtime, it is 55 x 2x= 1578.5
Given
Antonia makes X dollars for regular hours
And 2x dollars for over time
Since he works 55 hours this week he works 8 hours a day
Hence the equation is as follows
55x = 1578.5
x= $28.7
In case of double payment during overtime
He gets double amount as following equation
55 x 2x
55 x 2(28.7) = $3157
Hence the equation to find his hourly rate is 55x = 157.85
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i need help with this i just need the answer.
We have to find the length of FH.
We know that G is on the line, and we know the length FG and GH, so we can represent this as:
We then, we can apply the rule that states that the length of a segment is equal to the length of the segments that are part of it:
[tex]FH=FG+GH=10+5=15[/tex]Answer: FH = 15
18x-51=9(4x+5)-6(3x-10)
[tex]18-51=36x+45-18x-60\\18x-51=36x-18x+45-60\\18x-51=18x-15\\18x-18x=-15+51[/tex]
∴ 18x-18x≠-15+51
THERE IS NO SOLUTION FOR THIS EQUATION
Someone please help me!!! ( I'll mark brainliest )
Answer: 5/3
Step-by-step explanation:
The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.
We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.
Describe the graph of y = -|x + 4| - 5.
please answer correctly this will help me pass my exam
The graph of the absolute value function is an inverted "V" such that the vertex is at (-4, -5) and opens downwards.
How to calculate the modular function?We call a modular function the function f(x) = |x|, in which its domain is given by the real numbers and its range is the positive real numbers. This is because, for every negative value on the y-axis, the modular function will make |-y| = -(-y) = y
Therefore, to plot the graph of a modular function, it is enough to adopt some values for x and apply them to the function f(x) = | x |, in order to obtain their respective values in y.
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geometry!!!!! help please!!
Answer:
CD and BG
EF and AH
Step-by-step explanation:
Skew lines are a lines that are on different planes.
BC and CD are on the same plane, and EF and FG are on the same plane.
This leaves CD and BG, and EF and AH, which are on different planes, and thus skew lines.
find the number of sides of a regular polygonwhose exterior angle measure 18°
Answer:
20
Step-by-step explanation:
The sum of the exterior angles of a polygon add to 360. 360 divided by 18 is 20.
1. 5- (-8) =
2. -3 1/2 - 4 1/2 =
3. -7 - 4 =
4. -0.5 - 3.5 =
Answer:
1. 5- (-8) = 13
2. -3 1/2 - 4 1/2 = -7 1/2
3. -7 - 4 = -11
4. -0.5 - 3.5 = -4
Step-by-step explanation:
1. 5- (-8) =
5 + 8
13
2. -3 1/2 - 4 1/2 =
-7 1/2
3. -7 - 4 =
-11
4. -0.5 - 3.5 =
-4
How do you do these?
Solve for s.
6/s = 2
Answer:
s=3
Step-by-step explanation:
So you have the equation: [tex]\frac{6}{s}=2[/tex]
If we multiply both sides by this "s" value we should maintain equality, and it conveniently cancels out our division by "s" on the left side giving us the following equation: [tex]6=2s[/tex]
The only "operation" on the value "s" is the coefficient of 2, which is multiplying the value of "s" by 2.
To undo this multiplication of 2, we simply divide by 2, since 2/2 = 1, and now we have a coefficient of 1 for the "s", which is the same as isolating "s"
But we want to divide both sides by 2 to maintain equality, so let's write out our expression
[tex]\frac{6}{2}=\frac{2s}{2}\implies3=\frac{2}{2}*s\implies 3=s[/tex]
We can double check this by plugging in this value for "s" in the original equation: [tex]s=3, \ \frac{6}{s}=2\implies \frac{6}{3}=2\implies 3=3[/tex] which is indeed true, so we have our solution!
i need help with this, thanks
Answer: 11
Step-by-step explanation:
8x + 7 = 9x - 4
7 = x - 4
11 = x
help asap please and thank u
Answer:
y = 5, 3
x = 155, 171
(y = 5, x = 155)
(y = 3, x = 171)
Step-by-step explanation:
(8y - 15) = (y²)
-8y + 15 -8y + 15
--------------------------------
y² - 8y + 15 = 0
(y - 5) (y - 3) = 0
--------------
y = 5, 3
----------------------------------------------------------------------------------------------------------
y² + x = 180
(5)² + x = 180
25 + x = 180
-25 -25
--------------------
x = 155
(3)² + x = 180
9 + x = 180
-9 -9
------------------
x = 171
----------------------------------------------------------------------------------------------------------
I really hope this helps!
Bob makes some fruit punch that contains apple and mango juice in a 1:5 ratio. If he uses 15 pints of the mango juice how many pints of apple juice will he need
he needs 3 pints of mango
Answer:3
Step-by-step explanation:
If the ratio is 1:5 that means that the number of pints of apple juice is multiplied by 5 to get the nimber of pints of mango juice
the ratio of 26,000 bytes to 48,000 bytes can be written in fractional form as
Answer:
26000:48000
26000/48000
26/48(cancel the zeros)
13/24
fractional form=13/24
If f(x) = 4x6 + x² + 4, then what is the remainder when f(x) is divided by x -1?
Answer:
9
Step-by-step explanation:
[tex]p(x)=4x^6+x^2+4 \\ \\ p(1)=4+1+4=9[/tex]
Please answer the question in the photo
Answer:
u= 30
Step-by-step explanation:
the sum of all angles on a triangle is 180* so u add the others (120+30)
that brings it to 150 then 180-150=30*
Mrs. argueta needed to fill up her gas tank. gas cost $3.66 per gallon and she needed 9 1 2 gallons. how much did it cost mrs. argueta to fill up her tank?
Answer:
$3337.92
Step-by-step explanation:
$3.66 x 912 = $3337.92
There are 135 people in a sport centre.
77 people use the gym.
62 people use the swimming pool.
65 people use the track.
27 people use the gym and the pool.
23 people use the pool and the track.
31 people use the gym and the track.
4 people use all three facilities.
A person is selected at random.
What is the probability that this person doesn't use any facility?
We can conclude that the probability of the randomly selected person does not use any facility is 0.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes.Statistics is the study of events that follow a probability distribution. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.So, the probability that the selected person does not uses any facility:
According to the given data, we can easily say that all the people use some or the other facility.So, there are 0 people present who do not use the facility.Then, the probability that the selected person does not use any facility will be 0.Therefore, we can conclude that the probability of the randomly selected person does not use any facility is 0.
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for a sequence of events in which the first event can occur n 1 ways, the second event can occur n 2 ways, the third event can occur n 3 ways, and so on, the events together can occur a total of n 1 times n 2 times n 3 times ... ways. this is called .
The most appropriate choice for Independent event and multiplicative counting rule will be given by
This is known as multiplicative counting rule.
What is Independent event and multiplicative counting rule?
Event that is not dependent on any other event is called independent event.
Let A and B be two independent events.
P(A∩B) = P(A) [tex]\times[/tex] P(B)
If two independent events occur m ways and n ways respectively then both the event together will happen in mn ways.
Here,
Let first event occur [tex]n_1[/tex] ways, second event occur [tex]n_2[/tex] ways, third event occurs [tex]n_3[/tex] ways and so on
Also assuming that the events are independent
The event together can happen [tex]n_1 \times n_2 \times n_3\times...[/tex] ways
This is known as multiplicative counting rule.
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