What is the equation of the line that passes through the point (8,-4) and has a slope of 1/2
Answers
Answer:
y = 1/2x - 8
Step-by-step explanation:
Assuming that they want the equation in slope intercept form we would use the following form: y = mx + b
where m = slope and b = y intercept.
We are given the slope and a point on the line. We need to find the y intercept. We can do this by plugging in what we are given and then solving for b.
y = mx + b
slope (m) = 1/2
x value of given point (x) = 8
y value of given point (y) = -4
- plug in these values -
-4 = (1/2)(8) + b
now solve for b
multiply 1/2 and 8
-4 = 4 + b
subtract 4 from both sides
-8 = b
So the y intercept (b) is -8
We now plug in the slope and y intercept into slope intercept form
y = mx + b
m = 1/2 and b = -8
y = 1/2x - 8 is the equation of the line that passes through the point (8,-4) and has a slope of 1/2
For more validation refer to the attached image.
[tex]\text{Given that,}\\\\(x_1,y_1) = (8,-4), ~~ \text{and slope, m} = \dfrac 12\\\\\text{Equation with given points,}\\\\y -y_1 = m(x-x_1)\\\\\implies y -(-4) = \dfrac 12 (x-8)\\\\\implies y+4 = \dfrac 12 x - 4\\\\\implies y= \dfrac 12x -4 -4 \\\\\implies y = \dfrac 12 x -8\\\\\implies y = \dfrac{x-16}2\\\\\implies 2y = x -16\\\\\implies x -2y = 16[/tex]
Related Questions
Which facts are true for the graph of the function below? Check all that apply.
F(x)-(3/7)^x
Answers
Answer:
Step-by-step explanation:
ALGEBRA 2 SIMPLIFY THE EXPRESSION
Answers
Step-by-step explanation:
here's the answer to your question
Consider the probability that greater than 26 out of 124 software users will call technical support. Assume the probability that a given software user will call technical support is 97%. Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
Answers
Answer:
Since [tex]n(1-p) = 3.72 < 10[/tex], the normal curve cannot be used as an approximation to the binomial probability.
100% probability that greater than 26 out of 124 software users will call technical support.
Step-by-step explanation:
Test if the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
It is needed that:
[tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex]
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Out of 124 software users
This means that [tex]n = 124[/tex]
Assume the probability that a given software user will call technical support is 97%.
This means that [tex]p = 0.97[/tex]
Conditions:
[tex]np = 124*0.97 = 120.28 \geq 10[/tex]
[tex]n(1-p) = 124*0.03 = 3.72 < 10[/tex]
Since [tex]n(1-p) = 3.72 < 10[/tex], the normal curve cannot be used as an approximation to the binomial probability.
Consider the probability that greater than 26 out of 124 software users will call technical support.
The lowest possible probability of those is 27, so, if it is 0, since it is considerably below the mean, 100% probability of being greater. We have that:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 27) = C_{124,27}.(0.97)^{27}.(0.03)^{97} = 0[/tex]
1 - 0 = 1
100% probability that greater than 26 out of 124 software users will call technical support.
Find the value of [(33.7)² - (15.3)²]^½ leaving your answer correct to 4 significant figures
Answers
Answer:
30.03
Step-by-step explanation:
[(33.7)² - (15.3)²]^½
= [1135.69 - 234.09]^½
= [901.6]^½
= 30.02665483
= 30.03 (4sf)
The recursive formula for a geometric sequence is given below.
f(1) = 5
(n) = 3 . f(n − 1), for n > 2
What is the 7th term in the sequence?
Answers
Answer:
3645
Step-by-step explanation:
f(1)=5
f(2)=3*5=15.
f(3)=45, basically it's a geometric sequence with formula an=5*(3)^(n-1). The 7th term is 5*(3)^6=3645
Need help please due in 1 hour and 30 mins
Answers
Answer:
the answer of that is number C
Michael is 4 times as old as Brandon and is also 27 years older than Brandon.
How old is Brandon?
Answers
Answer:
9
Step-by-step explanation:
b = Brandon
4b=b+27
-b -b
-------------
3b = 27
---- ----
3 3
b = 9
Brandon is 9 years old.
I am struggling and I would be so happy if any of you helped me. Can someone help me with the last two red boxes please? The rest of the question is for reference to help solve the problem. Thank you for your time!
Answers
Answer:
I think you can go with:
The margin of error is equal to half the width of the entire confidence interval.
so try .74 ± = [ .724 , .756] as the confidence interval
Step-by-step explanation:
what is the base? Look at picture.
Answers
Answer:
14
Step-by-step explanation:
The area of a parallelogram is
A = bh where b is the base and h is the height
140 = b*10
Divide each side by 10
140/10 = 10b/10
14 = b
6. (4 points) (a) The edge of a cube was measured to be 6 cm, with a maximum possible error of 0.5 cm. Use a differential to estimate the maximum possible error in computing the volume of the cube. (b) Using a calculator, find the actual error in measuring volume if the radius was really 6.5 cm instead of 6 cm, and find the actual error if the radius was actually 5.5 cm instead of 6 cm. Compare these errors to the answer you got using differentials.
Answers
Answer:
A) ± 54 cm^3 ( maximum possible error in volume )
B) i) 58.625 cm^3 ii) 49.625 cm^3
Step-by-step explanation:
A) using differential
edge of cube = 6 cm , maximum possible error = 0.5 cm
∴ side of cube ( x )= ± 0.5 cm
V = volume of cube
dv /dx = d(x)^3 / dx
∴ dv = 3x^2 dx ---- ( 1 )
input values into 1
dv = 3(6)^2 * ( ± 0.5 )
= ± 54 cm^3 ( maximum possible error in volume )
B) Using calculator
actual error in measuring volume when
i) radius = 6.5 cm instead of 6 cm
V1= ( 6.5)^3 = 274.625 , V = ( 6)^3 = 216
actual error = 274.625 - 216 = 58.625 cm^3
ii) radius = 5.5cm instead of 6cm
actual error = 49.625 cm^3
For a given function ƒ(x) = x2 – x + 1, the operation –ƒ(x) = –(x2 – x + 1) will result in a
A) reflection across the x-axis.
B) horizontal shrink.
C) reflection across the y-axis.
D) vertical shrink.
Answers
Given:
The function is:
[tex]f(x)=x^2-x+1[/tex]
To find:
The result of the operation [tex]-f(x)=-(x^2-x+1)[/tex].
Solution:
If [tex]g(x)=-f(x)[/tex], then the graph of f(x) is reflected across the x-axis to get the graph of g(x).
We have,
[tex]f(x)=x^2-x+1[/tex]
The given operation is:
[tex]-f(x)=-(x^2-x+1)[/tex]
So, it will result in a reflection across the x-axis.
Therefore, the correct option is A.
Answer:
A) reflection across the x-axis.
Step-by-step explanation: I took the test
The height of a projectile fired upward is given by the formula
s = v0t − 16t2,
where s is the height in feet,
v0
is the initial velocity, and t is the time in seconds. Find the time for a projectile to reach a height of 96 ft if it has an initial velocity of 128 ft/s. Round to the nearest hundredth of a second.
Answers
Answer:
The projectile will reach a height of 96 feet after about 0.84 seconds as well as after about 7.16 seconds.
Step-by-step explanation:
The height of a projectile fired upward is given by the formula:
[tex]\displaystyle s = v_{0} t - 16t^2[/tex]
Where s is the height in feet, v₀ is the initial velocity, and t is the time in seconds.
Given a projectile with an initial velocity of 128 ft/s, we want to determine how long it will take the projectile to reach a height of 96 feet.
In other words, given that v₀ = 128, find t such that s = 96.
Substitute:
[tex](96) = (128)t-16t^2[/tex]
This is a quadratic. First, we can divide both sides by -16:
[tex]-6 = -8t+t^2[/tex]
Isolate the equation:
[tex]t^2 - 8t + 6 = 0[/tex]
The equation isn't factorable, so we can consider using the quadratic formula:
[tex]\displaystyle t = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]
In this case, a = 1, b = -8, and c = 6. Substitute:
[tex]\displaystyle t = \frac{-(-8)\pm\sqrt{(-8)^2-4(1)(6)}}{2(1)}[/tex]
Simplify:
[tex]\displaystyle t = \frac{8\pm\sqrt{40}}{2} = \frac{8\pm 2\sqrt{10}}{2} = 4\pm \sqrt{10}[/tex]
Hence, our two solutions are:
[tex]\displaystyle t = 4+\sqrt{10} \approx 7.16\text{ or } t= 4-\sqrt{10} \approx 0.84[/tex]
So, the projectile will reach a height of 96 feet after about 0.84 seconds as well as after about 7.16 seconds.
Can someone please help
Me
Answers
Answer:
$3735
Step-by-step explanation:
2/5 = 8/20
8/20 + 7/20 = 15/20 = 3/4
3/4*4980 = 3735
Jill records the temperature outside every hour for 4 hours. She finds that the temperature dropped by the same amount each hour. After 4 hours, she finds that the temperature dropped a total of 20∘F. She writes this number sentence.
(−20)÷4=−5
What does the number sentence mean?
The total drop in temperature, −20∘F, divided by 4 hours equals −5∘F per hour. The temperature dropped 5∘F each hour.
The total number of drops, 20, divided by 4 hours equals 5 times per hour. The temperature dropped 5 times per hour.
The total number of hours, 20, divided by 4∘F equals 5 hours. The temperature dropped once every 5 hours.
The total drop in temperature, −20∘F, divided by 4∘F in the first hour, equals −5 drops. The temperature dropped 5 times.
Answers
Answer:
It is the first one, The total drop in temperature, −20∘F, divided by 4 hours equals −5∘F per hour. The temperature dropped 5∘F each hour.
Step-by-step explanation:
A package contains 12 resistors, 3 of which are defective. If 4 are selected, find the probability of getting
Answers
Answer:
Incomplete question, but I gave a primer on the hypergeometric distribution, which is used to solve this question, so just the formula has to be applied to find the desired probabilities.
Step-by-step explanation:
The resistors are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
12 resistors, which means that [tex]N = 12[/tex]
3 defective, which means that [tex]k = 3[/tex]
4 are selected, which means that [tex]n = 4[/tex]
To find an specific probability, that is, of x defectives:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = x) = h(x,12,4,3) = \frac{C_{3,x}*C_{9,4-x}}{C_{12,4}}[/tex]
A coin is tossed and a die is rolled. Find the probability of getting a head and a number greater than 1.
___.
(Type an integer or a simplified fraction.)
Answers
Answer:
5/12
Step-by-step explanation:
Heads: 1/2
Number greater than 1
A dice has 6 sides. 5 are greater than 1
The probability is 5/6
P(heads and a die greater than 1) = 1/2 * 5/6 = 5/12 or a little less than 1/2
Which behavior would best describe someone who has good communication skills with customers ? a) Following up with some customers b) Talking to customers more than listening to them c) Repeating back what the customer says d) Interrupting customers frequently
Answers
Answer:
C. repeating back what the customer says
A car which was advertised for sale for 95000, was ultimately sold for 83600. Find the percent reduction in the price?
Answers
Answer: 12%
Step-by-step explanation:
95,000-83,600=11,400
(11,400/95000)(100) = 12%
The percentage reduction in the price of the car is 12%
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here: Original price of car=95000 and Selling price=83600
Thus the reduction in price= 95000-83600
=11400
Thus percentage reduction in the price of the car is
= 11400/95000 × 100
=12%
Hence, The percentage reduction in the price of the car is 12%
Learn more about percentages here:
https://brainly.com/question/29306119
#SPJ2
the guys is wrong i checked
Answers
Step-by-step explanation:
the guys is wrong i checked
if x, y, and z are positive integers and 2^x * 3^y * 5^z = 54,000, what is the value of x + y + z
Answers
Given:
If x, y, and z are positive integers, then
[tex]2^x\times 3^y\times 5^z=54000[/tex]
To find:
The value of [tex]x+y+z[/tex].
Solution:
First we need to find the prime factors of 54000.
[tex]54000=2\times 2\times 2\times 2\times 3\times 3\times 3\times 5\times 5\times 5[/tex]
[tex]54000=2^4\times 3^3\times 5^3[/tex] ...(i)
We have,
[tex]54000=2^x\times 3^y\times 5^z[/tex] ...(ii)
On comparing (i) and (ii), we get [tex]x=4,y=3,z=3[/tex].
The sum of [tex]x,y,z[/tex] is:
[tex]x+y+z=4+3+3[/tex]
[tex]x+y+z=10[/tex]
Therefore, the value of [tex]x+y+z[/tex] is 10.
PLEASE HELP THIS IS DUE ASAP!!!!!!!!!!!!!!
Answers
the answer is 1/12
the first rolling a 4 has a 1/6 chance of happening and half of the numbers on the die are odd, so 1/6*1/2=1/12
Use the order of operations to simplify 3/4+8(2.50-0.5).
Answers
Answer:
16[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 55% salt and Solution B is 70% salt. She wants to obtain 30 ounces of a mixture that is 60% salt. How many ounces of each solution should she use?
Answers
Answer:
Let x = the number of ounces of Solution A
Let y = the number of ounces of Solution B
x + y = 180 y = 180 - x
.60x + .85y = .75(180)
.60x + .85y = 135 Multiply both sides of the equation by 100 to remove the decimal points.
60x + 85y = 13500
60x + 85(180 - x) = 13500
60x + 15300 - 85x = 13500
-25x = -1800
x = 72ounces
y = 180 - 72
y = 108 ounces
Step-by-step explanation:
Wyzant (ask an expert) solution on their website.
Find the missing side of the triangle
Answers
Answer:
x = 4[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Pytago:
x[tex]x^{2} +7^{2} = 9^{2} \\\\x = \sqrt{9^{2} - 7^{2} } x = 4\sqrt{2}[/tex]
Step-by-step explanation:
a^2 + b^2 = c^2
7^2 + b^2 = 9^2
49 + b^2 = 81
b^2 = 81 - 49
b^2 = 32
b^2 = 5.65 or sqrt rt of 32
4) The measure of the linear density at a point of a rod varies directly as the third power of the measure of the distance of the point from one end. The length of the rod is 4 ft and the linear density is 2 slugs/ft at the center, find the total mass of the given rod and the center of the mass
Answers
Answer:
a. 16 slug b. 3.2 ft
Step-by-step explanation:
a. Total mass of the rod
Since the linear density at a point of the rod,λ varies directly as the third power of the measure of the distance of the point form the end, x
So, λ ∝ x³
λ = kx³
Since the linear density λ = 2 slug/ft at then center when x = L/2 where L is the length of the rod,
k = λ/x³ = λ/(L/2)³ = 8λ/L³
substituting the values of the variables into the equation, we have
k = 8λ/L³
k = 8 × 2/4³
k = 16/64
k = 1/4
So, λ = kx³ = x³/4
The mass of a small length element of the rod dx is dm = λdx
So, to find the total mass of the rod M = ∫dm = ∫λdx we integrate from x = 0 to x = L = 4 ft
M = ∫₀⁴dm
= ∫₀⁴λdx
= ∫₀⁴(x³/4)dx
= (1/4)∫₀⁴x³dx
= (1/4)[x⁴/4]₀⁴
= (1/16)[4⁴ - 0⁴]
= (256 - 0)/16
= 256/16
= 16 slug
b. The center of mass of the rod
Let x be the distance of the small mass element dm = λdx from the end of the rod. The moment of this mass element about the end of the rod is xdm = λxdx = (x³/4)xdx = (x⁴/4)dx.
We integrate this through the length of the rod. That is from x = 0 to x = L = 4 ft
The center of mass of the rod x' = ∫₀⁴(x⁴/4)dx/M where M = mass of rod
= (1/4)∫₀⁴x⁴dx/M
= (1/4)[x⁵/5]₀⁴/M
= (1/20)[x⁵]₀⁴/M
= (1/20)[4⁵ - 0⁵]/M
= (1/20)[1024 - 0]/M
= (1/20)[1024]/M
Since M = 16, we have
x' = (1/20)[1024]/16
x' = 64/20
x' = 3.2 ft
If Damien does a job in 21 hours less time than Caitlyn, and they can do the job together in 14 hours, how
long will it take each to do the job alone?
Answers
Answer: Damien = 7.5 hours and Caitlyn = 28.5 hours
Step-by-step explanation:
Damien = X -21
Caitlyn = X
2X - 21 = 14
2X = 14 + 21
X = (14+21)/2
X = 7.5
Solve for x
-1/2x + 3 = -x + 7
Answers
Answer:
8
Step-by-step explanation:
If you add x to the left side of the equation you get positive 1/2x +3=7
you then would subtract 3 from 7 to get 4
this would leave you with 1/2x=4
if you divide 4 by 1/2 you get 8 as the answer.
e movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. How could you correctly rewrite the equation 4(10+5) = 6(12 - 2) using the distributive property
Answers
9514 1404 393
Answer:
4·10 +4·5 = 6·12 -6·2
Step-by-step explanation:
Each outside factor multiplies each inside term.
4(10 +5) = 6(12 -2)
4·10 +4·5 = 6·12 -6·2
If a tank holds 6000 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as
V=5000 (1-1/50*t)^2 0⤠t ⤠50.
1. Find the rate at which water is draining from the tank after the following amount of time. (Remember that the rate must be negative because the amount of water in the tank is decreasing.)
a. 5 min
b. 10 min
c. 20 min
d. 50 min
2. At what time is the water flowing out the fastest?
3. At what time is the water flowing out the slowest?
Answers
Answer: hello from the question the volume of tank = 6000 gallons while the value in the Torricelli's equation = 5000 hence I resolved your question using the Torricelli's law equation
answer:
1) a) -180 gallons/minute ,
b) -160 gallons/minute
c) -120 gallons/minute
d) 0
2) The water is flowing out fastest when t = 5 min
3) The water is flowing out slowest after t = 20 mins
Step-by-step explanation:
Volume of tank = 5000 gallons
Time to drain = 50 minutes
Volume of water remaining after t minutes by Torricelli's law
V = 5000 ( 1 - [tex]\frac{1}{50}t[/tex] )^2 ----- ( 1 )
1) Determine the rate at which water is draining from the tank
First step : differentiate equation 1 using the chain rule to determine the rate at which water is draining from the tank
V' = [tex]-10000[ ( 1 - \frac{1}{50}t ) (\frac{1}{50}) ][/tex]
a) After t = 5minutes
V' = - 10000[ ( 1 - 0.1 ) * ( 0.02 ) ]
= -180 gallons/minute
b) After t = 10 minutes
V' = - 10000[ ( 1 - 0.2 ) * ( 0.02 ) ]
= - 160 gallons/minute
c) After t = 20 minutes
V' = - 10000 [ ( 1 - 0.4 ) * ( 0.02 ) ]
= -120 gallons/minute
d) After t = 50 minutes
V' = - 10000 [ ( 1 - 1 ) * ( 0.02 ) ]
= 0 gallons/minute
2) The water is flowing out fastest when t = 5 min
3) The water is flowing out slowest after t = 20 mins because no water flows out after 50 minutes
please answer the question below:
Answers
Answer:
It's letter b
Step-by-step explanation:
I hope this help
