Given the table below, write a linear equation that defines the dependent variable, s, in terms of the independent variable, t.
Answers
The linear equation of the table is, t = -5/3a +19
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
y = mx + c
where
y = dependent variable
m = slope
x = independent variable
c = y - intercept
Here we have the table with the values of t and the value of a.
Now, we need to find the linear equation for this table.
In order to find the linear equation, we need the values of slope and the y intercept values.
To find the value of slope we have to take two point from the given table.
They are (6,9) and (9,4).
Now, apply the value on the slope formula, then we get,
m = (4 - 9) / (9 - 6)
m = -5/3
Now, we have to use the slope m and the point (6,9), to find the value of y intercept,
Then we get the value of c as,
9= -5/3(6)+c
9=-10+c
c=19
Therefore, the linear equation of the table is, t = -5/3a +19
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Related Questions
help me pls. i dont know how to do this
Answers
Answer:
k=f(x)-ab^x-h
h=x-ln(f(x)/a-k/a)/ln(b)
a=f(x)/b^x-h - k/b^x-h
. The ratio of cups of almonds to cups of peanuts in a mixed nuts snack is 4 to 3.
How many cups of peanuts would be needed to make 49 cups of the mixed nuts
snack?
Answers
Number of cups of peanuts needed to make 49 cups of the mixed nuts snack is 21 cups
The ratio of cups of almonds to cups of peanuts in a mixed snack = 4 : 3
Number of of cups of almonds = 4x
Number of cups of peanuts = 3x
Total number of cups of mixed nuts snack = 49 cups
Then the equation will be
4x + 3x = 49
Add the like terms
7x = 49
x = 49 / 7
x = 7
Number of cups of almonds needed = 4x
= 4×7
= 28 cups
Number of cups of peanuts needed = 3x
= 3×7
= 21 cups
Hence, number of cups of peanuts needed to make 49 cups of the mixed nuts snack is 21 cups
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In 2021, Sally Morris, a single taxpayer, pays $3,000 of interest on qualified student loans. Her AGI is $40,000. What is her qualified student loan interest deduction in 2021?
Answers
The qualified student loan interest deduction in 2021 is $37500.
What is adjusted gross income?Adjusted gross income is an individual's total gross income less specific deductions in the United States income tax system. It is used to compute taxable income, which is AGI minus personal exemption and itemized deduction allowances. AGI is more important than gross income for most individual tax purposes.
AGI is calculated by taking your gross income and subtracting certain "above the line" deductions. 401(k) contributions, health savings account contributions, and educator expenses are common examples of deductions
As per Law, a maximum of $2,500 will be allowed to be deducted from the Income. Thus the following would be the solution.
Income of Sally Morris = $40,000
Less: Qualified student loan interest $2,500
Modified Adjusted Gross Income $37,500
The deduction is $37500.
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The price of a dvd is $24. 00 plus 8% sales tax. What is the sales tax on this dvd in dollars and cents?.
Answers
Answer: $1.92
Step-by-step explanation:
This is the correct answer. Have a good day
the temperature was -20 degrees in the morning when Rae woke up. At dinner time, the temperature shows 35 degrees. What was the change in temperature from the time Rae woke up un dinner time? Draw a picture and write an equation to solve.
Answers
The change in temperature is 15°
How to find Change in temperature ?
If temperature rise then Change in temperature ,t₂ = t₁ + final temperature
If temperature dropped then Change in temperature ,t₂ = t₁ - final temperatureWe have given,
In morning, when Rae woke up the temperature is (t₁) = -20°
At dinner time, the temperature is = 35°
t₂ = t₁ + 35
t₂ = (-20) + 35
t₂ = 15°
Hence, the change in temperature is 15°
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the equation of the curve is y = x^2 + ax + b. The points (0,-5) and (5,0) lie on the curve. Find the coordinates of the turning point of the curve.
Answers
The turning point of the parabola is the point (2, - 9).
What is the turning point of a quadratic equation?
Quadratic equations represents parabolae and the vertex of the parabola represents the turning point as the slope of the curve changes its sign, from positive to negative or viceversa. The vertex can be derived by the vertex form of the equation of the parabola:
y - k = C · (x - h)²
Where:
(h, k) - Coordinates of the vertex.C - Vertex constantSince the quadratic equation has two real coefficients, we need the location of two points on Cartesian plane to find one solution. First, create the system of linear equations:
b = - 5 (1)
5 · a + b = - 25 (2)
Second, substitute b in (2) and clear a:
5 · a - 5 = - 25
5 · a = - 20
a = - 4
Third, write the quadratic equation:
y = x² - 4 · x - 5
Fourth, transform the equation into vertex form by completing the square:
y + 9 = x² - 4 · x + 4
y + 9 = (x - 2)²
Fifth, write the vertex of the parabola:
(h, k) = (2, - 9)
The point (2, - 9) represents the turning point of the parabola.
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HELP MEEEEEE PLEASEEEEE
Answers
Answer:
1000-400=600km
good luck i hope it helped, its all about reading the graph!
the number of hours spent watching television by students in the week before final exams has a normal distribution with a standard deviation of 4.5 hours. a random sample of 30 students is taken. is the probability that the sample standard deviation exceeds 3.5 hours more than 0.95?
Answers
The probability that the sample standard deviations exceeds 3.5 hours more than 0.95 is 0.23 < 0.95 ..
The numbers of hours spent on watching television by a student in a weak before is normally distributed.
We have provide the following details, standard
deviations of sample ( Number of hours in weak) (σ) = 4.5 hours
sample size (n) = 30
we shall compute the mean and variance of sample .
The E of s squared is equal to 4.5 squared. The variance of S squared is equal to twice the square of sigma divided by 1, which is 30 minus 1, which is 28.6, 28.2817. The chi-square distribution here has 29 degrees of freedom, which equals 29 squared to 4.5 squared. We want to find probabilities greater than 90 because the standard deviation of our sample is greater than 3.5 hours. The probability that S squared is greater than 3.5 is The probability that chi-square with 29 degrees of freedom is greater than
17. 54321 is very high. This is the same as zero.
This is equal to 1 minus the probability that 29 degrees of freedom chi-square is greater than 51 points 5556, which is what we want for part B. we are given one Probability will be zero.
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#Complete question
The number of hours spent watching television by students in the week before final exams has a normal distribution with a standard deviation of 4.5 hours. A random sample of 30 students was taken.a. Is the probability more than 0.95 that the sample standard deviation exceeds 3.5 hours?b. Is the probability more than 0.95 that the sample standard deviation is less than 6 hours?
1. Jorge used 2 7/8 packs of pencils in the first 1/3
of the year. At what rate is Jorge using
pencils
Answers
Answer:
Jorge is using pencils at a rate of 6 packs a year or a rate of 2 packs every four months.
Step-by-step explanation:
1/3 of a year is four months so that would be 2 packs every four months and if you multiply that by three you’d get 12 month, or one year, and 6 packs of pencils.
Given that the point (-90, -56) is on the
terminal side of an angle, 0, find the exact
value of the following:
sin(0)=
cos(0)=
tan (0) =
csc(0)=
sec(0)=
cot (0)=
Answers
The value of sinθ = - 28/53, cosθ = - 45/53, tanθ = 28/45, cosecθ = -53/28, secθ = -53/45, cotθ = 45/28.
Given that:
The point (-90, -56) is on the terminal side of an angle, θ
Using Pythagoras' theorem,
Hypotenuse^2 = Perpendicular^2 + Base^2
Hypotenuse^2 = (-56)^2 + (-90)^2
Hypotenuse^2 = 3136 + 8100
Hypotenuse^2 = 11236
Hypotenuse = 106
The value of hypotenuse = 106
The exact value of the following is:
sinθ = Perpendicular/Hypotenuse = -56/106 = - 28/53
cosθ = Base/Hypotenuse = -90/106 = - 45/53
tanθ = Perpendicular/ Base = - 56/-90 = 28/45
cosecθ = 1/sinθ = -53/28
secθ = 1/cosθ = -53/45
cotθ = 1/tanθ = 45/28
Hence, we got all the values of θ.
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At an elevation of 1221. 4 feet, lake mead will hold 28,945,000 acre-feet of water. Which number is the best estimate of this amount of water?.
Answers
The best estimate of this amount of water is [tex]3*10^{7}[/tex].
Given:
At an elevation of 1221. 4 feet, lake mead will hold 28,945,000 acre-feet of water.
So, the amount of water that is in the lake will be 28,945,000 acre-feet which is estimated to be 30000000 acre-feet of water.
Because the nearest estimate to 28945000 is 30000000.
= 30000000
= 300000*[tex]10^{2}[/tex]
= 30000*[tex]10^{3}[/tex]
= 3000*[tex]10^{4}[/tex]
= 3*[tex]10^{3} *10^{4}[/tex]
= 3*[tex]10^{7}[/tex]
Therefore The best estimate of this amount of water is [tex]3*10^{7}[/tex].
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Newton and Descartes have a $50.00 gift card to a pet store.
Newton's total is $18.95 and Descartes's total is $24.38. How much
money do they have left on their gift card?
Answers
explanation:
so first we need to see how much they spent total so
18.95 + 24.38 = 43.33
so total they spent $44.33
now we need to find out how much they have left so
50.00-44.33= 5.17
so therefore they have $5.17 left on their gift card
Rewrite the following equation in slope-intercept form.
y + 6 = 9(x − 8)
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
If u can solve both the blanks that would be great
Answers
interest = $67.50
A= $367.50
I = A - P = $67.50
Equation:
A = P(1 + rt)
Calculation:
First, converting R percent to r a decimal
r = R/100 = 2.5%/100 = 0.025 per year.
Solving our equation:
A = 300(1 + (0.025 × 9)) = 367.5
A = $367.50
The total amount accrued, principal plus interest, from simple interest on a principal of $300.00 at a rate of 2.5% per year for 9 years is $367.50.
For the given table of values for a polynomial function, where must the zeros of the function lie?.
Answers
The zero of the function lie between 2.5 and 3.0 and between 4.0 and 4.5
The given question is incomplete the complete question is
x 2.0 2.8 2.5 1.1 3.0 –0.8
f(x) 3.5 –1.2 4.0 –0.3 4.5 0.7
For the given table of values for a polynomial function, where must the zeros of the function lie?
A. between 2.0 and 2.5 and between 4.0 and 4.5
B. between 2.5 and 3.0 and between 4.0 and 4.5
C. between 2.0 and 2.5 and between 3.5 and 4.0
D. between 2.5 and 3.0 and between 3.5 and 4.0
answer : If a function is continuous and you have points on opposite sides of the x-axis, there must be a zero-crossing between those points. As evidenced by the table and graph,...
(3.0, 4.0) and (3.5, -0.2)
are points on the x-axis on opposite sides. As a result, between x=3.0 and x=3.5, there must be a zero crossing.
In the same way,...
(4.0, -0.8) and (4.5, 0.1)
are points on the x-axis on opposite sides. As a result, between x=4.0 and x=4.5, there must be a zero-crossing.
The correct answer option includes both of these possible zero crossings.
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The owner of a bookstore buys used books from customers for $1. 50 each. The owner then resells the used books for 400% of the amount he paid for them. What is the price of a used book in this bookstore?.
Answers
Answer:
$7.50
Step-by-step explanation:
Find each probability if you spin the spinner and roll the number cube.
10. P(blue, 2)
12. P(not blue, 5)
11. P(red, even)
13. P(yellow, not 4)
red
blue
yellow
red
4
6
5
Answers
11. 1/8
12. 1/8
13. 5/24
The chance of the spinner landing on blue = 1/4
The chance of the number cube landing on 2 = 1/6
1/4 * 1/6 = the probability of the spinner landing on blue and the cube landing on 2 (Remember that the probability of both happening is smaller, so it cannot be addition.)
Ans = 5/12
The chance of the spinner landing on something that isn’t blue = 3/4
The chance of the number cube landing on 5 = 1/6
3/4 * 1/6 = the total probability
Ans = 1/8
The chance of the spinner landing on red = 1/4
The chance of the number cube landing on an even number = 3/6, 1/2.
1/4 * 1/2 = the total probability
Ans = 1/8
The chance of the spinner landing on yellow = 1/4
The chance of the number cube landing on something that’s not 4 = 5/6
1/4 * 5/6 = the total probability
Ans = 5/24
I really hope this helped lol
Find the equation of the line passing through the given point and parallel to the given line.
( 7,-3) , 3y = 12x + 5
(-5, -2), y + 3x = 10
Answers
The equation of the lines passing the points and parallel to the equations ( 7,-3) , 3y = 12x + 5 (-5, -2), y + 3x = 10 is as follows:
y = 4x - 31y = -3x - 17.How to find the equation of a line?The equation of a line can be represented in different form such as standard form, general form, slope intercept form and point slope form. Therefore, let's represent the line in slope intercept form.
The equation of a line in slope intercept form is as follows:
y = mx + b
where
m = slopeb = y-interceptParallel line shave the same slope.
Hence,
( 7,-3) , 3y = 12x + 5
y = 4x + 5 / 3
slope is 4
The equation of the line is y = 4x + b. let's find the y-intercept using (7, -3).
-3 = 4(7) + b
b = -3 - 28
b = - 31
Hence, y = 4x - 31
(-5, -2), y + 3x = 10
y = -3x + 10
slope = -3
Therefore, let's find y-intercept using (-5, -2)
-2 = -3(-5) + b
-2 = 15 + b
b = -2 -15
b = - 17
Therefore, y = -3x - 17.
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What is another way to write (a6)(a²)?
a4
a8
a12
a36
Answers
I WILL GIVE 30 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS
Answers
Answer:
third and last, can't promise that's right
Graph the piecewise function.
(6 points - 2 points for each piece)
Answers
Points of interval A (-1,-3) and (-2,-6)
Points of interval B is (1,1) and (2,-1)
How to find Piecewise function?
Determine which of the following intervals (or inequalities) the input belongs to before evaluating a piecewise function at any given input. The function specification for that specific interval can then simply be updated to reflect the new input.
[tex]f(x)=\left \{ {{3x, if x\leq -1} \atop {-2x+3, if 0 < x < 4}}\atop {2, if x\geq 4}\right.[/tex]
lets take 3x as Interval A
-2x+3 as interval B
and 2 as interval C
Now lets calculate the interval A
f(x)=3x
as x≤-1
∴f(-1) = 3(-1)
=(-3)
∴ point is (-1,-3)
∴f(-2) = 3(-2)
=(-6)
∴ point is (-2,-6)
Now lets calculate the interval B
f(x)=-2x+3
as 0<x<4
∴f(1) = -2(1)+3
=-2+3
=1
∴ point is (1,1)
∴f(2) = -2(2)+3
=-4+3
= -1
∴ point is (2,-1)
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Harry took a 5-hour trip on which he averaged 40 miles per hour. What distance did he travel?
Answers
Harry traveled 200 miles on a 5 hour trip
Answer:
200 miles
Step-by-step explanation:
if its 40 miles per hour then multiply 5 with 40 and you'll end up with 200 miles
I could get these right but, Its being rude to
me so Im trying one more time to clarify.
Answers
Answer: The correct answer is the one that has 4 + 5 + 2 + 3.
(I didn't say which side it is in case you got confused but it's the one right above the speaker sign.)
Step-by-step explanation:
What is the slope, m, of the following linear equation? y=x-6
Answers
Answer:
1
Step-by-step explanation:
because the 1 is actually invisible
its called invisible math
y=mx+b
Yuson must complete a certain number of hours of community service. She does 2 hours of service each day. After 8 days, Yuson has completed half of her required community service.
Write a linear equation to represent the hours that Yuson has left to do after x days.
Answers
The linear equation to represent the hours that Yuson has left to do after x days is 16 - 2x.
How to calculate the equation?From the information, Yuson has to do Y hours of community service.
She works two hours every day, so service hours in x days = 2x
Remaining service hours after x days = y-2x
Also we have after 8 days , Yuson has completed half of her required community serivice. Therefore,
8 = y/2.
Cross multiply
y = 16
So the linear equation is 16-2x.
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Which does point A represent in this box plot?
Answers
A box plot is used to study the distribution and level of a set of a set of numbers. A box plot is made up of two lines and a box. The two lines are known as whiskers.
The end of the first whisker represents the minimum number. The minimum number is the smallest number in the dataset. The end of the second whisker represents the maximum number. The maximum number is the largest number in the dataset.
The first line to the left represents the lower (first) quartile. The second line on the box represents the median. The third line on the box represents the upper (third) quartile.
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11/12+7/12 in simplest form
Answers
Answer:
The answer to your question could be either 3/2 (improper fraction), 1.5 (decimal), or 1 1/2 (mixed fraction).
Step-by-step explanation:
11/12 + 7/12 = 18/12
18/12 = 9/6
9/6 = 3/2
Identify the solution of the inequality |9m| + 40> 4 and the graph that represents it.
Answers
Answer:
can i have more info?
Step-by-step explanation:
solve the equation by elimination method 4x-2y=8,5x+3y=6
Answers
Solving the set of equation by elimination method gives
x = 1.64
y = -0.727
How to solve the equation by elimination methodThe given data
4x - 2y = 8 (1)
5x + 3y = 6 (2)
multiplying (1) by 3/2 and adding the result to (2)
6x - 3y = 12
5x + 3y = 6
6x + 5x - 3y + 3y = 12 + 6
11x = 18
x = 18/11
x = 1.64
substitute x = 18/11 into (1)
4 * 18/11 - 2y = 8
72/11 - 2y = 8
2y = 72/11 - 8
2y = -16/11
y = -8/11
y = -0.727
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Write the equation using function notation
x - y = -4
A) f(x) = x - 4
B) f(x) = x + 4
C) f(x) = -x + 4
D) f(x) = -x - 4
Answers
Answer:
C
Step-by-step explanation: