What is the equation of a line that is perpendicular to 2x+y=−4 and passes through the point (2, −8) ?
Answers
Answer:
y=1/2z-9= Perpendicular line
y=-2x-4= parrallel
Step-by-step explanation:
Answer:
y = \(\frac{1}{2}\) (x) - 9
Step-by-step explanation:
Set the given equation to standard form: y = -2x -4
Set the slope of the given equation's slope to the reciprocal ( -2 --> 1/2).
Thus, you will have y = 1/2x + b
Insert the given information: (2, -8)
-8 = 1/2 (2) + b
Half of 2 is 1: subtract it on both sides...
-8 = 1 + b
-1 -1
-9 = b
So, the equation will be y = 1/2(x) - 9
Related Questions
Calculate the sum of 45 and 39
Answers
Answer:
84
Step-by-step explanation:
45 + 39 = 84
Find the sum or difference.
1. -80+77 =
2. 77 + 160 =
3. -64+ (-33) =
4. 104-(-92) =
5. -105-(-122) =
6. 185-(-154) =
7. -53-(-59) =
8. -6+ (-35) =
9. 15-(-26)-(-39) =
10. -93 +191+ (-179)
Find the product or quotient.
11. 60+ 12 =
12. -194+ (-2)=
13. 88 (-2) =
14. -12 10 =
15. -10 (-11) =
16. 90+ (-6)=
17. 3 (-59) =
18. -7 (-2) =
19. 100 (0) =
20.100/0=
Answers
After answering the presented question, we may conclude that the solution of the expressions are as follows.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.
the solution of the expressions are as follows -
-3237-97196173396-4152-8172-196-176-12011084-177140undefined (division by zero is undefined)To know more about expressions visit :-
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Find the difference between the actual quotient and the estimated quotient of 54,114÷29 . (Dividend is rounded off to nearest thousand and divisor to nearest ten)
Answers
The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.
To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.
Actual quotient:
Dividing 54,114 by 29, we get:
54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)
Estimated quotient:
Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:
54,000 ÷ 30 = 1,800
Difference between actual and estimated quotient:
Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379
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Please help me will vote the person who does brainiest person or something
Answers
Answer:
quadratic
y=mx+c
Step-by-step explanation:
Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 56 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean µ = 56 tons and standard deviation Ï = 1.1 ton.
Required:
a. What is the probability that one car chosen at random will have less than 49.5 tons of coal?
b. What is the probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal?
Answers
Answer:
a) 0% probability that one car chosen at random will have less than 49.5 tons of coal
b) 0% probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
\(\mu = 56, \sigma = 1.1\)
a. What is the probability that one car chosen at random will have less than 49.5 tons of coal?
This is the pvalue of Z when X = 49.5. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{49.5 - 56}{1.1}\)
\(Z = -5.9\)
\(Z = -5.9\) has a pvalue of 0
So 0% probability that one car chosen at random will have less than 49.5 tons of coal.
b. What is the probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal?
Now we have \(n = 35\), applying the Central limit theorem \(s = \frac{1.1}{\sqrt{35}} = 0.1859\)
This is the pvalue of Z when X = 49.5. So
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{49.5 - 56}{0.1859}\)
\(Z = -35\)
\(Z = -35\) has a pvalue of 0
So 0% probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal
A truck rental company charges $25 per day plus $.32 per mile. If you paid $265, how many miles did you drive?
Answers
Answer:
750 miles
Step-by-step explanation:
Given
\(Daily\ Charge = \$25\)
\(Per\ Mile = \$0.32\)
\(Total = \$265\)
Required
Determine the number of miles
Represent the number of miles with m
So, we have:
\(Total = 25 + 0.32 * m\)
\(265 = 25 + 0.32 * m\)
\(265 = 25 + 0.32m\)
Collect Like Terms
\(0.32m = 265 - 25\)
\(0.32m = 240\)
Solve for m
\(m = 240/0.32\)
\(m = 750\)
Hence, I travelled 750 miles
in desperate need of help for this question
Answers
Answer: Do you wanna go out with me
Step-by-step explanation:
HELP PLEASE!!! A three-column table is given. Part A C D Part 25 35 50 Whole B 56 80 What is the value of B in the table?
Answers
Answer: (READ IT ALL PLS)
56.8
Convert 56.8
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5680
Step-by-step explanation:
I'm not really sure, Because I don't get the
way you explained it. But I hope it helps.
: )
The age of United States Presidents on the day of their first inauguration follows a Normal distribution with mean 56 and standard deviation 7.3. (a) (5 points) Compute the probability that a randomly selected President was less than 60 years old on the day of their first inauguration. (b) (5 points) Compute the 75th percentile for the age of United States Presidents on the day of inauguration. (c) (5 points) Compute the probability that the average age on the day of their first inauguration for a random sample of 4 United States Presidents exceeds 60 years.
Answers
Answer:
a) 0.7088 = 70.88% probability that a randomly selected President was less than 60 years old on the day of their first inauguration.
b) The 75th percentile for the age of United States Presidents on the day of inauguration is 61.
c) 0.8643 = 86.43% probability that the average age on the day of their first inauguration for a random sample of 4 United States Presidents exceeds 60 years.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The age of United States Presidents on the day of their first inauguration follows a Normal distribution with mean 56 and standard deviation 7.3.
This means that \(\mu = 56, \sigma = 7.3\)
(a) (5 points) Compute the probability that a randomly selected President was less than 60 years old on the day of their first inauguration.
This is the pvalue of Z when X = 60. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{60 - 56}{7.3}\)
\(Z = 0.55\)
\(Z = 0.55\) has a pvalue of 0.7088
0.7088 = 70.88% probability that a randomly selected President was less than 60 years old on the day of their first inauguration.
(b) (5 points) Compute the 75th percentile for the age of United States Presidents on the day of inauguration.
This is X when Z has a pvalue of 0.75. So X when Z = 0.675.
\(Z = \frac{X - \mu}{\sigma}\)
\(0.675 = \frac{X - 56}{7.3}\)
\(X - 56 = 0.675*7.3\)
\(X = 61\)
The 75th percentile for the age of United States Presidents on the day of inauguration is 61.
(c) (5 points) Compute the probability that the average age on the day of their first inauguration for a random sample of 4 United States Presidents exceeds 60 years.
Now, by the Central Limit Theorem, we have that \(n = 4, s = \frac{7.3}{\sqrt{4}} = 3.65\)
This is the pvalue of Z when X = 60. So
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{60 - 56}{3.65}\)
\(Z = 1.1\)
\(Z = 1.1\) has a pvalue of 0.8643
0.8643 = 86.43% probability that the average age on the day of their first inauguration for a random sample of 4 United States Presidents exceeds 60 years.
A class did an experiment to see if students could taste water and identify bottled water versus tap water. Each student was presented with three cups of water—one of which contained bottled water—and they were directed to identify which cup they thought contained bottled water. The class wants to test if they correctly identified the bottled water significantly better than they would have done by simply guessing.
Let p represent the proportion of these students that would correctly identify the bottled water.
Which of the following is an appropriate set of hypotheses for their significance test?
ANSWER:
H0:p=1/3
Ha:p>1/3
Answers
Answer:
A
Step-by-step explanation:
Kahn
Can u please help me with 3&4 I’m giving 20 point please help me
Answers
Answer:
Step-by-step explanation:
Find the ratio for sin(-120)
Answers
Answer:
- [square root (3) / 2]
Step-by-step explanation:
sin( -120) = sin( -120 + 360) = sin 240 = -sin ( 240-180)
-sin60= - [square root (3) / 2]
Remember Sin is negative in the 3rd quadrant and 240 falls on the 3rd quadrant.
Fill in the blanks.
(x+_)^2=x^2+14x+_
Answers
Step-by-step explanation:
(ax + b)² = a²x² + 2abx + b²
In this case, a = 1, so:
14 = 2b
b = 7
(x + 7)² = x² + 14x + 49
Diven {x) = 3x- 1 and 9(x) = 2x-3, for which value of x does g(X) = {2)?
Answers
The calculated value of x at g(x) = 2 is x = 2.5
How to determine the value of x at g(x) = 2from the question, we have the following parameters that can be used in our computation:
f(x) = 3x - 1
Also, we have
g(x) = 2x - 3
When g(x) - 2, we have
2x - 3 = 2
So, we have
2x = 5
Divide by 2
x = 2.5
Hence, the value of x at g(x) = 2 is x = 2.5
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Share £65 in the ratio 3:2
Answers
First step u do is add 3:2 (3+2) which is 5 then u divide that by 65 (65/5) which will give u 13 and 13 will be one so then u do is 13x3 to get the ratio of 3 which id 39 and then the 13x2 to get the ratio of 2 and then that’s ur answer 39:26 and u can check by adding them up to see if u get £65
And yes it does so that’s how u do it
Answer:
£39 : £26
Step-by-step explanation:
3 + 2 = 5
65 ÷ 5 = 13
13× 3 = 39
13 × 2 = 26
The diameter of a circle is 3 centimeters. What is the circumference?
Answers
Answer:
9.42
Step-by-step explanation:
please help.
definitions: 1. definition of right triangle
2. definition of isosceles TrianglesReflexive
3. HL
4. definition of perpendicular
5. CPCTC
6. reflexive
Answers
From the two column proof below, we have seen ∠BAC ≅ ∠DAC by CPCTC
How to solve two column proof problems?The two column proof to show that ∠BAC ≅ ∠DAC is as follows:
Statement 1: ΔABD is Isosceles with base BD, AC ⊥ BD
Reason 1: Given
Statement 2: AB ≅ AD
Reason 2: Definition of isosceles Triangles
Statement 3: ∠1 and ∠2 are right angles
Reason 3: Definition of perpendicular
Statement 4: AC ≅ AC
Reason 4: Reflexive Property
Statement 5: ΔABC and ΔADC are right triangles
Reason 5: Definition of right triangle
Statement 6: ΔABC ≅ ΔADC
Reason 6: HL Congruency
Statement 7: ∠BAC ≅ ∠DAC
Reason 7: CPCTC
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The yearly Avrage
4. An old furnace cost $850 per year to run. A new one costs $2,500 to buy and will save 34% annually in
energy costs to run it. In how many years will it pay for itself?
Answers
Answer:
9 years
Step-by-step explanation:
To determine the number of years it will take for the new furnace to pay for itself, we need to compare the cost of running the old furnace for that period with the cost of buying and operating the new furnace during the same time.
Let's calculate the cost of running the old furnace for one year:
Old furnace cost per year = $850
Now, let's calculate the savings in energy costs for the new furnace:
Savings in energy costs per year = 34% of $850
= 0.34 * $850
= $289
The total cost of buying and operating the new furnace for one year is:
New furnace cost per year = Cost of buying the new furnace + Savings in energy costs per year
= $2,500 + $289
= $2,789
To find the number of years it will take for the new furnace to pay for itself, we divide the cost of the new furnace by the annual savings:
Number of years to pay for itself = Cost of buying the new furnace / Annual savings
= $2,500 / $289
≈ 8.65
Since we cannot have a fraction of a year, we can round up to the nearest whole number. Therefore, it will take approximately 9 years for the new furnace to pay for itself.
Glven: 3x + y = 1.
Solve for y.
y = 3x - 1
O y=-3x - 1
O y=-3x+1
Answers
Answer:
y = -3x + 1Step-by-step explanation:
3x + y = 1
⇔ -3x + 3x + y = -3x + 1 (we added -3x to both sides of the equation)
⇔ y = -3x + 1 ( because -3x + 3x = 0)
Which of these statements are correct about two parallel lines in a coordinate plane? Select three that apply.
Answers
Answer:
Step-by-step explanation:
URGENT PLEASE
One number is 5 more than two times the other. Their sum is 11.
Answers
Answer:
the numbers are 8 and 3.
The base of the mountain is 6,500 feet above sea level and AB measures 230 feet across. Given that the measurements for QAP is 20° and QBP is 35°, how far above sea level is peak P ? Express your answer to the nearest foot.
Height above sea level:
Answers
Answer:
6610
Step-by-step explanation:
We have tan(X) = opposite/ adjacent
tan(QBP) = PQ/BQ
tan(35) = PQ/BQ ---eq(1)
tan(QAP) = PQ/AQ
tan(20) = \(\frac{PQ}{AB +BQ}\)
\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)
230*tan(20) + PQ*tan(20)*tan(35) = PQ
⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)
⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]
\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)
\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)
PQ = 110.4
≈110
Height above sea level = 6500 + PQ
6500 + 110
= 6610
4x - 5 > 3 OR -4x < -28
Answers
Answer: x=35
Step-by-step explanation:
Two fire-lookout stations are 13 miles apart, with station B directly east of station A.
Both stations spot a fire. The bearing of the fire from station A is N35°E and the
bearing of the fire from station B is N49°W. How far is the fire from station B?
Choose the correct formula given below.
Answers
The distance between the fire and station B is 10.7miles
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
The angle at A = 90- 35
= 55°
The angle at B = 90-49
= 41°
Angle at the fire = 180-(41+55)
= 180-96 = 84°
Using sine rule
sin84/13 = sin55/x
xsin84 = 13sin55
0.995x = 10.65
x = 10.65/0.995
x = 10.7 miles
Therefore the distance between the fire and station B is 10.7 miles.
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On average, adults in the US consume 2741 calories per day, with a standard deviation equal to 608. A sample of 9281 random US adults participate in a study on eating behaviors. What is the probability that their mean caloric intake differs by more than 8.3 calories per day from the population mean? Round your answer to four decimal places.
Answers
Which of the following expressions is equal to -3x2 - 12?
Answers
Answer:
C. (-3x+6)(x+2)
Step-by-step explanation:
that should help you
A child has $9.30 in a piggy bank. If the child spends 13 of the money on a snow cone and then finds $0.75 to put in the piggy bank, how much money does the child now have in the piggy bank?
Answers
The child will have $9.92 in his piggy bank.
What is basic arithmetic operations?
Basic arithmetic operations are the foundation of mathematics and include addition, subtraction, multiplication, and division. These operations are used to perform mathematical calculations and are necessary for solving a wide range of problems, from simple arithmetic problems to more complex mathematical equations.
The child has $9.30 and spends $0.13 on a snow cone, so their piggy bank balance becomes $9.30 - $0.13 = $9.17.
After finding $0.75 to put in the piggy bank, the child now has $9.17 + $0.75 = $9.92 in their piggy bank.
Hence, the child will have $9.92 in his piggy bank.
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PLEASE HELP
Feel free to write on the document. Show your work or there won't be any brainliest
Answers
a) The formula to represent the relationship is y = 0.50x + 15
b) On a coordinate plane the graph will be a straight line because it is a linear function
c) the slope is 0.50 and y intercept is 15
2.(a) The slope of the line is calculated to be 2/5
b) In one minute, Kailee will run 0.4 laps
c) In 24 minutes, she will run 9.6 laps
How to solve for slope of the lineThe slope, m of the linear function is calculated using the points on the graph (5.5, 2.2) and (11, 4.4)
m = (y₀ - y₁) / (x₀ - x₁)
m = (2.2 - 4.4) / (5.5 - 11)
m = (-2.2) / (-5.5)
m = 2/5
The equation is y = mx where m = 2/5 = 0.4
in one minute, x = 1,
y = 2/5 * 1 = 2/5 laps
in 24 minutes, x = 24
y = 2/5 * 24 = 9.6 laps
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ASAP
What is the area of this triangle?
E.(5,1) F.(4,0) D. (8,0)
Units2
Answers
Quick I need help pls
Answers
Answer:
361
Step-by-step explanation: