Standard for slope intercept form
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = - \frac{3}{4}x - 9[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The given equation is :
[tex]\qquad\displaystyle \tt \rightarrow \: 9x +12y = -108[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 12y = - 108- 9x[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{ -108}{12} - \frac{9x}{12} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = - \frac{3}{4}x - 9[/tex]
And this the equation of same line in its slope intercept form, where slope (m) = -3/4 and y - intercept = -9
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
100 points pls helppppp
Answer:
[tex](g \circ f)(0)=216[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=2x+6\\g(x)=x^3\end{cases}[/tex]
(g o f)(x) is a composite function.
Composite functions are when the output of one function is used as the input of another.
Therefore, the given composite function (g o f)(0) means to substitute the function f(x) when x=0 in place of the x in function g(x).
[tex]\begin{aligned}\implies (g \circ f)(0)&=g[f(0)]\\& = g(2(0)+6)\\&=g(0+6)\\&=g(6)\\&=6^3\\&=216\end{aligned}[/tex]
write an equation for the line shown on the right. answer needs to be in slope-intercept form.
Given:
A linear graph
To find:
the equation of the line
The formula for linear equation is given as:
y = mx + b
m = slope
b = y-intercept
We need to get the slope and y-intercept of the line. To get the slope, two points will be picked on the line
Using points: (-8, -1) and (0, 2)
[tex]\begin{gathered} slope\text{ = }m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ x_1=-8,y_1=-1,x_2=0,y_2\text{ = 2} \\ m\text{ = }\frac{2-(-1)}{0-(-8)}=\frac{2+1}{0+8} \\ m\text{ = 3/8} \end{gathered}[/tex]The y-intercept is the value of y when x = 0. On the graph, it is the value of y when the line crosses or touches the y-axis.
The line crosses the y axis at y = 2
b = y-intercept = 2
The equation of the line in slope-intercept form becomes:
[tex]y\text{ = }\frac{3}{8}x\text{ + 2}[/tex]Write an equation that represents your total earnings based on the price of your item and how many you sell.
The price of the item is $3, and I sell 40 items.
Answer:
y = 3(40)
Step-by-step explanation:
Let's break it down:
Total earnings = y
Price of item = 3
Amount of items sold = x (in this case 40)
Math
I need an explanation too btw
The transformation from the graph of f to the graph of g is reflection in the x-axis.
We are given the function f(x) = -4x + 8
Also it says that g(x) = -f(x)
= 4x - 8
Since f(x) is a linear function, the graph of f(x) and hence the graph of g(x), both are straight lines. But the graph of g(x) will be a transformed image of the graph of f(x).
Here, if f(x) = y, then the transformation from f(x) to g(x) can be represented as, (x, y) -------> (x, -y)
This transformation corresponds to the reflection in the x-axis. When reflected along x-axis, the x- co-ordinate does not change, but the y- co-ordinate changes its sign. This is exactly what happens when the function f(x) is transformed to g(x) = -f(x).
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Suppose that 3 j of work is needed to stretch a spring from its natural length of 24 cm to a length of 33 cm. (a) how much work is needed to stretch the spring from 29 cm to 31 cm? (round your answer to two decimal places.) (b) how far beyond its natural length will a force of 15 n keep the spring stretched? (round your answer one decimal place.)
a) 14.81 J of work is needed to stretch the spring from 29 cm to 31 cm.
b) 2 cm far beyond its natural length will a force of 15 N keep the spring in stretched position.
It is mentioned that 3 J of work is needed to stretch a spring from its natural length of 24 cm to 33 cm.
We know the work done on the spring is expressed by the following given equation:
[tex]W=\frac{1}{2} ke^{2}[/tex]
Where, W = workdone that is done on the spring
k = elastic constant
e = extension of the given material
So, Work (W) = 3 J and e = 33 cm - 24cm = 9 cm = 0.09 m
So, putting the above values we calculate the value of 'k' as below:
[tex]W=\frac{1}{2} ke^{2}[/tex]
⇒ [tex]3=\frac{1}{2} k(0.09)^{2}[/tex]
⇒ 3 x 2 = 0.0081k
⇒ k = [tex]\frac{6}{0.0081}[/tex] N/m
⇒ k = 740.74 N/m
a) Now using the same formula for work, we will determine the amount of work that is needed to stretch the spring from 29 cm to a length of 31 cm.
k = 740.74 N/m
e = 31 cm - 29 cm = 2 cm = 0.02 m
[tex]W=\frac{1}{2} ke^{2}[/tex]
⇒ W = [tex]\frac{1}{2} (740.74) (0.02)^{2}[/tex]
⇒ W = 14.81 J
The work that is done to stretch the spring from 29 cm length to 31 cm is 14.81 J.
b) From the Hooke's law we have, F = ke, where F is the force applied on the spring. Now here we have been given that a force of 15N is applied and we have to find the 'e' that is the extennsion in the natural length of the given spring.
k = 740.74 N/m
F = 15 N
F = ke
⇒ 15 N = 740.74 x e
⇒ e = [tex]\frac{15}{740.74}[/tex] m
⇒ e = 0.02 m = 2 cm
Therefore the natural length of the spring will be stretched by a length of 2 cm when a force of 15 N is applied.
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Find the output, y, when the input, z, is -7. y =
In linear equation, y = -6 is the output .
What is a linear equation example?
Ax+By=C is the usual form for two-variable linear equations.As an illustration, the conventional form of the linear equation 2x+3y=5 When an equation is given in this format, finding both intercepts is rather simple (x and y).A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.We want to find the y value on the graph when x = -7
Got to x = -7 and find the value of the blue line
y = -6
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The complete question is -
Find the output, y, when the input, x, is -7
4/6= ? x 1/6 what number makes the equation
The first step here is to write out this question as a proper algebraic expression. That means you assign a letter to the question mark and you now have;
4/6 = y * 1/6
(Note that the symbol * represents the multiplication sign)
y * 1/6 can be re-written as y/6 since it is actually y/1 * 1/6
Therefore you now have;
4/6 = y/6
Cross multiply and you now have,
4 * 6 = y * 6
24 = 6y
Divide both sides of the equation by 6 (to eliminate the 6 on the right hand side)
4 = y
Therefore the number that should be in the question mark is 4.
What is the slope of the line that passes through the points (-7, -10) and (-19,-10)? Write your answer in simplest form.
The slope of the line that passes through the points (-7, -10) and (-19,-10) is 0.
What is the slope of the line with the given coordinates?Slope is simply expressed as change in y over the change in x.
It is expresses as;
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1 ( -7, -10 )
x₁ = -7y₁ = -10Point 2 (-19,-10)
x₂ = -19y₂ = -10Plug the given x and y values into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( -10 - (-10) )/( -19 - (-7) )
Slope m = ( -10 + 10 )/( -19 + 7 )
Slope m = ( 0 )/( -12 )
Slope m = 0/-12
Slope m = 0
Therefore, the slope of the line is 0.
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100PTS PLS HELP (4 PART QUESTION)
Find the exact value of the following:
1. cos195°
2. sin195°
3. tan195°
4. Verify the identity: sin(x+y)-sin(x-y)= 2cosxsiny
Please show all work! I'd prefer if you'd do it on paper and upload it! Thank you so much!! <3
The trigonometric functions for the angle of 195º are given as follows:
1. cos(195º) = -0.9659.
2. sin(195º) = -0.2589.
3. tan(195º) = 0.2680
The identity is verified at the end of the answer.
Trigonometric functions for 195ºOne of the functions have to be given/found using a calculator, hence:
cos(195º) = -0.9659.
The sine and the cosine of the same angle are related according to the following identity:
sin²(x) + cos²(x) = 1.
Hence:
sin²(195º) + cos²(195º) = 1
sin²(195º) + (-0.9659)² = 1
sin²(195º) + 0.93296281 = 1
sin²(195º) = 1 - 0.93296281.
sin(195º) = ±sqrt(1 - 0.93296281)
sin(195º) = -0.2589. (the angle of 195º is on the third quadrant, where both the sine and the cosine are negative).
The tangent of an angle is given by the sine of the angle divided by the cosine of the angle, hence:
tan(195º) = sin(195º)/cos(195º) = -0.2589/(-0.9659) = 0.2680. (negative divided by negative is positive)
IdentityThe identities for the sine of the sum and of the subtraction are given as follows:
sin(x + y) = sin(x)cos(y) + cos(x)sin(y)sin(x - y) = sin(x)cos(y) - cos(x)sin(y)Hence the subtraction is:
sin(x + y) - sin(x - y) = (sin(x)cos(y) + cos(x)sin(y)) - (sin(x)cos(y) - cos(x)sin(y))
sin(x + y) - sin(x - y) = sin(x)cos(y) + cos(x)sin(y) - sin(x)cos(y) + cos(x)sin(y)
sin(x + y) - sin(x - y) = 2cos(x)sin(y).
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Convert the following percents to fractions and decimals. SHOW YOUR WORK
1. 89%
2. 35%
3. 64%
After conversion, the percentages in fractions and decimals are:
89/100, 0.897/20, 0.3514/25, 0.64Calculations and ParametersRecall that a percentage is over 100 and the symbol is %
Therefore, for 89%, it would be 89/100.
This is the fraction, then the decimal would be 0.89
For 35%, the fraction would be 35/100
We break it down to the lowest value possible, it would be 7/20. This is the fraction, the decimal is 0.35
For 64%, it would be 64/100
It would be broken down to the lowest value possible which would be 14/25
The decimal would be 0.64
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I’ll give brainliest!! What is the standard form of the equation for a line that passes through (1, 2) and that has a slope of -4?
PLEASE SHOW WORK OR EXPLAIN
Answer:
[tex]y=-4x+6[/tex]
Step-by-step explanation:
Point Slope Form = Y-y1=m(X-x1)
m=-4, (x1,y1) = (1,2)
y-2=-4(x-1)
y-2=-4x+4
y=-4x+6
:]
(Lol please give Brainliest if I'm correct :] )
Travis is compiling a list of cities that had a temperature colder than 6°F below zero for the month of January. Which cities from the table above would Travis include on his list? A. Chicago, St. Paul, Fargo, and Bismarck B. Chicago only C. St. Paul, Fargo, and Bismarck D. Fargo and Bismarck
Help asap please :]
Travis should include A. Chicago, St Paul, Bismarck and Fargo on his lost because these cities had temperature of 6°F below zero for the month of January.
The only countries which Travis is including on his list are those which has a temperature of 6 degrees Fahrenheit below zero in the month of January.
The correct choices are provided in the option A.
He should include Chicago, St. Paul, Fargo and Bismarck.
He should add these cities because they all had temperature of 6 degrees Fahrenheit below zero for the month of January.
These cities are very cold because of their geological location.
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a company has developed a new computer sound card, but the average lifetime is unknown. in order to estimate this average, 200 sound cards are randomly selected from a large production line and tested and the average lifetime is found to be 5 years. the 200 sound cards represent the:
The 200 sound cards represent the sample if they are randomly selected from a large production line.
A sample in statistics can be defined as a small part or subset of a population or group that intends to represent what the whole population is like. A sample may be randomly selected or may be selected non-randomly.
In this case, the whole production line of the sound card can be considered as a population. Out of this population of sound cards, 200 are randomly selected to estimate the average lifetime thus determining the characteristic of the whole population, therefore it is said to be the sample of the sound cards and the 5 years is the value of the statistic.
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The owner of a restaurant wants to move the restaurant from Braddock Avenue to a new location onKnox Avenue that has more foot traffic. The owner would also like to double the perimeter of therestaurant due to the expected increase in business but keep the overall shape exactly the same, asshown in the coordinate plane.
We want to find a series of transformations that change the polygon ABCD into the polygon A'B'C'D'.
We see that a counter-clockwise rotation must be necessary, as:
By doing a traslation of 4 units to the right, and a dilation by a scale factor of 2, we obtain the desired figure. This is, the answer is B.
Which expression is equivalent to 2(−4.1s − 3.4)?
−2.1s − 3.4
−2.1s − 6.8
−8.2s − 3.4
−8.2s − 6.8
Answer:
D. −8.2s − 6.8
Step-by-step explanation:
Hope this helps you! :))
PLS HURRY ILL GIVE BRAINLIEST!! Which number sentence is true?
Answer:
B
Step-by-step explanation:
Let's go through each, step-by-step and simplify to see if we find a true number sentence:
A)
[tex]3\frac{1}{3} < \sqrt{7}?[/tex]
[tex]3.3333 < 2.64575?[/tex] Not true
B)
[tex]4.8 < \sqrt{32}?[/tex]
[tex]4.8 < 5.65685?[/tex] True
Knowing B is true, we have found our answer and don't need to go any further.
ASAP!! Justin bought a calculator and a binder that were both 15% off the original price. The original price of the binder was $6.20. Justin spent a total of $107.27. What was the original price of the calculator?
Include all steps for branliest.
If Justin bought a calculator and a binder that were both 15% off the original price. The original price of the binder was $6.20. Justin spent a total of $107.27. Then $120 the original price of the calculator
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100.
Let,
x be the original price of the calculator
y be the original price of the binder
we know that
15%=15/100=0.15
(x+y)(1-0.15)=$107.27
(x+y)(0.85)=$107.27....(1)
y=6.20....(2)
substitute the value of y in the equation A and solve for x
(x+6.20)(0.85)=107.27
(x+6.20)=107.27/0.85
x=107.27/0.85-6.20
x=126.20-6.20
x=120
Hence the original price of calculator is $120.
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please help, i’ll give points
The linear equation represented in the table is:
y = -3x + 20
How to find the linear equation?A general linear equation of the form is:
y = a*x + b
We know that if a line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:
slope = (y₂ - y₁)/(x₂ - x₁)
Here we can use the last two points on the table:
(-2, 26) and (-4, 32)
Then the slope is:
slope = (26 - 32)/(-2 + 4) = -6/2 = -3
So this is like:
y = -3*x + b
To find the value of b we can use one of the points, i will use (-2, 26), then:
26 = -3*-2 + b
26 = 6 + b
26 - 6 = b = 20
The linear equation is y = -3x + 20
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Name two transformation sequences that can be done in any order without changing the outcome and explain how you know.
Answer:
There are two different categories of transformations: The rigid transformation, which does not change the shape or size of the preimage. The non-rigid transformation, which will change the size but not the shape of the preimage.
Step-by-step explanation:
yep sorry if you get it wrong it is
B
Calculate the cost of one pen is eight pens cost $32.
Answer:
8 pens = 32
1 pen = 32 ÷ 8
= 4
Cost of one pen is $4.
Please please someone help me on this!!! ( 30 points + brainliest )
m<A, which is 48 degree.
The values of mL and mJ are 55 and 61 degrees, respectively.
Since vertical angles are equal in magnitude and are created by intersecting two lines, they are known as the opposing angles.
what are the explanation of the problems?
1.Angles in the vertical plane coincide. They are equal in size, thus this indicates. Calculate x x = 4x - 24 by putting them on an equal footing. In the equation, deduct x from both sides.
o = 3x - 24 On both sides, add 24.
24 = 3x Divide both sides by 3
Multiply both sides by 3
8 to get x
m<A, which is 8.
4x-24
=3*8+24=24+24=48 degree
2.We can thus write,
The angles L and Z are vertical.
∠L = 2x + 9 and,
∠Z = 3x - 14.
Given that both angles are vertical,
∠L = ∠Z
2x + 9 = 3x - 14
Continuing to solve
3x - 2x = 9 + 14
x = 23
The value of L is therefore,
= 2(23)+9
= 46+9
= 55°
Angle L has a value of 55°.
2. Y and J are equal because they are both vertical angles.
∠Y = 7x + 12
∠J = 10x - 9
∠Y = ∠J
7x + 12 = 10x - 9
Continuing to solve
3x = 21
x = 7
So, the value of ∠J is, = 10(7) - 9 = 70 - 9 = 61°
The value of ∠J is 61°.
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recall the birthday paradox problem: take a random sample of size k with replacement from the set {1, 2,⋯, 365}. let pk be the probability that there is repetition in the sample (there are at least two people who share a common birthday).
the probability of at least two person have same birthday would be: 100%-99.72%= 0.28%
In this question, you are asked the probability for any of the 2 person to have the same birthday. To answer this it will be easier to calculate how much the probability for no one has same birthday. Let say the first person birthday is 1. Then the next person birthday should be other than 1, which mean 364 possible days out of 365 days.
Then the calculation for 2 people would be:
(365!/365-2!)/(365^(2)= (365!/363!)/ 365^2= 0.9972=99.72%
Then the probability of at least two person have same birthday would be: 100%-99.72%= 0.28%
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solve the system of equations algebraically y=4x + 1 6x-2y=3
The solution of the system of equation is as follows:
x = 1 / 14y = 9 /7How to solve system of equation?The system of equation can be solved algebraically using substitution method.
The system of equation can be solved when we find the value of x and y as follows:
y = 4x + 1
6x - 2y = 3
Let's substitute the equation(i) in equation(ii)
6x + 2(4x + 1) = 3
6x + 8x + 2 = 3
14x + 2 = 3
14x = 3 - 2
14x = 1
x = 1 / 14
let's find y as follows:
y = 4(1 / 14) + 1
y = 4 / 14 + 1
y = 2 / 7 + 1
y = 2 + 7 / 7
y = 9 / 7
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The stadium design currently has a 3:2 ratio of premium seats to bleacher seats (12,000 premium seats and 8,000 bleacher seats). If the team wants to keep the total of premium seats and bleacher seats at 20,000 but wants to change the ratio to 4:1, how many of each seat would the stadium have?
To keep the total seats still at 20,000 but change the ratio to 4 : 1; the number of premium and bleachers seats the stadium would have are; 16,000 and 4,000 respectively.
What number of premium and bleacher seats would the stadium have?It follows from the task content that the total number of seats which the stadium would have if the ratio is to be changed to 4:1 be determined.
Since the number of seats, 20,000 remains constant.
To divide the number 20,000 in the ratio; 4 : 1;
The number of premium seats would be; (4/5) × 20,000 = 16,000 seats.
And the number of bleacher seats would be; (1/5) × 20,000 = 4,000 seats.
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an urn contains 18 red marbles and 15 blue marbles. 12 marbles are chosen. in how many ways can 7 red marbles be chosen? a) 792 b) 95,567,472 c) 34,827 d) 31,824 e) 126 f) none of the above.
The total number of ways 7 red marbles can be chosen is 95,567,472 i.e., option b is correct.
12 marbles are chosen in which 7 are red marbles and remaining marbles, which are 5, are blue marbles.
In order to find in how many ways 7 red marbles can be chosen we will follow the steps mentioned below:
Out of 18 red marbles 7 are chosen and out of 15 blue marbles 5 are chosen. So, we can write
Total number of ways 7 red marbles can be chosen= [tex]18C_{7}[/tex] × [tex]15C_{5}[/tex]
Total number of ways 7 red marbles can be chosen= [tex](\frac{18!}{7! (18-7)!} )[/tex][tex](\frac{15!}{5! (15-5)!})[/tex]
Total number of ways 7 red marbles can be chosen= 31824 × 3003
Total number of ways 7 red marbles can be chosen= 95,567,472
Thus, we can conclude that in 95,567,472 number of ways 7 red marbles can be chosen.
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What are the slopes of these lines and how are they perpendicular
Answer:
Line A's slope is 2 and Line B's slope is 1/2.
Step-by-step explanation:
The slope of perpendicular lines is such that the slope of one line is the negative reciprocal of the slope of another line
PLEASE HELP ASAP!!!!!!!!!!! Point A is one vertex of triangle ABC. Point B is the x-intercept of 6x−4y=−12 and point C is the y-intercept. What are points B and C? Sketch the triangle in the coordinate plane.
the quotient of 98 and a number
Answer:
98 ÷ 98 = 1 OR 98 ÷ 1 = 98
Step-by-step explanation:
Division is breaking something up into equal parts. The "dividend" is the whole you start with, the "divisor" is what you use to divide up the whole, and the "quotient" is the answer like this: Dividend ÷ Divisor = Quotient. So, the quotient of 98 and a number would be represented as such: 98 ÷ 1 = 98 or 98 ÷ 98 = 1
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the file p02 45.xlsx contains the salaries of 30 business school professors at a (fictional) large state university. if you increased every professor's salary by $4,000, what would happen to the mean and median salary?
We are increasing every professor's salary by 4000, let this new salary be Yi for every professor then mean of new salary Y will be
Y = 1/n∑Yi
Y = 1/n∑(Xi + 4000)
Y = 1/n(∑Xi + ∑4000/n)
Y = X + 4000
Median Xm is the middle most value of the Professor's old salary, since new salary is
Yi = Xi + 4000
then new median salary Ym will be
Ym = Xm + 4000
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Answer:
Step-by-step explanation:The mean and Median salary would increase by $4,000.
Let sum of the salaries be n1+n2+n3+.......... +n30
Mean = sum of observation / no. of observation
Thus,
Initial mean, M1 = n1+n2+n3+.......... +n30 / 30
When $4,000 is added to every salary 4000 is added 30 times to the sum.
Thus,
New mean, M2 = n1+n2+n3+.......... +n30 +( 4000 * 30)
30
= M1 + ( 4000 * 30)
30
Thus, M2 = M1+ 4000
Therefore, The mean salary increase by $4,000.
We know Median of even number of observation = [(n/2)th term + ((n/2) + 1)th term]/2
Here n/2th term is n15 and (n/2 +1)th term is n16
Thus,
Initial Median, Median 1 = n15 + n16
2
When $4,000 is increased in each salary
New Median, Median 2 = n15 + 4000 + n16 + 4000
2
= Median 1 + 2 * 4000
2
Thus, Median 2= Median 1 + 4000
Therefore, The median salary increases by $4,000
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