1. Create an equation of a straight line in slope-intercept form.2. Find a parallel and perpendicular line to your original equation.
Answers
The slope intercept form of a line equation is:
\(y=mx+b\)Where "m" is the slope and "b" is the y-intercept.
To create one line, we just need to choose values for "m" and "b", for example, let's pick m = 2 and b = 1.
Then the line is:
\(y=2x+1\)Every parallel line will have the same slope, so to find a different line that is paralle to it, we just need to maintain the same slope (the same "m") and change "b", for example, le'ts pick b = 2 now.
A parallel line is, then:
\(y=2x+2\)The slope of a perpendicular line can be found by inverting the slope and changin its sign, that is:
\(m^{\prime}=-\frac{1}{m}\)So, the slope of a line perpendicular to the original will be:
\(m^{\prime}=-\frac{1}{2}\)The "b" value can be any value and the line will still be perpencular. Le'ts pick b = 1 again.
So, a perpendicular line is:
\(y=-\frac{1}{2}x+1\)Original:
\(y=2x+1\)Parallel:
\(y=2x+2\)Perpendicular:
\(y=-\frac{1}{2}x+1\)Related Questions
factor step by step:
x^2+1
Answers
Answer:
(x + i) (x - i)
Step-by-step explanation:
The expression x^2 + 1 is a sum of squares, which means that it cannot be factored using real numbers. However, it can be factored using complex numbers.
To factor x^2 + 1, we can use the fact that i^2 = -1, where i is the imaginary unit.
We can rewrite x^2 + 1 as:
x^2 + 1 = x^2 - (-1)
Now, we can use the difference of squares formula to factor x^2 - (-1):
x^2 - (-1) = (x + i)(x - i)
Therefore, the factored form of x^2 + 1 is:
(x + i)(x - i)
What is the prime factored form of the lowest common denominator of
2/3 + 7/10
Answers
Answer:
common denominator = 2·3·5
Step-by-step explanation:
You want the factorization of the common denominator of 2/3+7/10.
DenominatorsThe denominators of the fractions in the given sum are 3 and 10. Their prime factors are ...
3 = 3
10 = 2·5
Common denominatorThe common denominator factors will be the product of the unique factors in the above list:
common denominator = 2·3·5
__
Additional comment
Using the common denominator, the sum is ...
20/30 +21/30 = 41/30 = 1 11/30
Find the area of a sector with a central angle of 170° and a radius of 17 millimeters. Round to the nearest tenth. 1) 857.5 mm22) 100.9 mm23) 428.7 mm24) 25.2 mm2
Answers
Problem statement: we have been given a task to find the area of the sector.
We are given some parameters:
\(\begin{gathered} \text{central angle=170}^0 \\ \text{radius}=17\operatorname{mm} \\ \end{gathered}\)Method: We will apply the formula:
\(\begin{gathered} A=\frac{\theta}{360}\times\pi r^2 \\ \text{where} \\ \theta=\text{ central angle} \\ r=17\operatorname{mm} \\ A=\text{Area of the sector} \\ \pi=\frac{22}{7} \end{gathered}\)Thus, applying the formula
\(A=\frac{170}{360}\times\frac{22}{7}\times17^2\)\(A=428.7\operatorname{mm}^2\)The area of the sector is 428.7mm²
The answer is option 3
On a multiple-choice test over English vocabulary, Roy got 16 out of 20 correct. What percent of the problems did she
miss? Round your answer to the nearest tenth of a percent, if necessary.
Answers
Answer:
20%
Step-by-step explanation:
100/20 (the number of questions) = 5 (how much each question is worth)
16(the number of questions she got correct) times 5 is 80
She got 80 percent correct
That means that she missed 20 percent
Charlie will run at most 35 miles this week. So far, he has run 17 miles. What are the possible numbers of additional miles he will run?
please help can not figere out 9th grade math
by matthew
Answers
Step-by-step explanation: We may determine the range of potential further miles Charlie will run by deducting his present mileage from the maximum mileage if he has already run 17 miles and will only cover 35 miles this week.
Maximum mileage - current mileage = potential extra miles.
17 miles minus 35 miles equals 18 miles.
As a result, Charlie may run somewhere between 0 and 18 additional miles.
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Answer:
18 possible numbers
Step-by-step explanation:
If Charlie has already run 17 miles and he will run at most 35 miles this week.
We can calculate the possible numbers of additional miles he will run by subtracting the distance he has already run from the maximum distance he can run.
Maximum distance Charlie can run = 35 miles
Distance Charlie has already run = 17 miles
Possible additional miles he will run = Maximum distance - Distance already run
= 35 miles - 17 miles
= 18 miles
Therefore, there are 18 possible numbers of additional miles Charlie will run.
Complete the sentence to describe the triangle shown.
GHI is _____ and _____.
Answers
We saw that about 34% of
all students received at least one referral. Suppose we have concerns about the number of
disciplines in one particular school - it seems very high, and we've had concerns from parents at the school. In one particular year, 162 out of the 340 students at that school had a referral.
a. If we selected a random sample of 340 students, would the sample proportion that are
disciplined be approximately normally distributed? Why or why not?
b.
Use the normal distribution to find the probability of randomly selecting a sample of 340
students and finding that 162 of them or more have received a referral during that
particular year.
C. Would we think that is unusual? Explain your reasoning.
Answers
The likelihood of discovering a z-score of 4.39 or higher with a regular normal distribution table or calculator is extremely low, roughly 0.00001.
what is probability ?It is a scale among 0 and 1 that represents the probability or likelihood of an event happening. In many disciplines, including statistics, physics, economics, law, and computer science, probability theory is extensively used. Many situations, such as games of chance, weather predictions, medical diagnoses, and more, can be explained using the concept of probability. The mathematical computation of probabilities, the analysis for random variables, and the conclusion-making process are all included in the study of probability.
given
The likelihood that 162 or more kids in a randomly chosen sample of 340 pupils will have received a referral in that particular year can be calculated using the normal distribution.
Calculating the sample proportion is necessary:
The predicted value of p is equal to the 0.34 underlying proportion of referred pupils. It is possible to compute the sample proportion's standard deviation as follows:
P equals sqrt[p(1-p)/n] = sqrt[0.34(1-0.34)/340] = 0.031
Calculate the z-score to determine the likelihood of locating 162 or more kids with referrals:
\(z = (0.476 - 0.34) / 0.031 = 4.39\)
The likelihood of discovering a z-score of 4.39 or higher with a regular normal distribution table or calculator is extremely low, roughly 0.00001.
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If fixed costs are $450,000 and the unit contribution margin is $50, the sales necessary to earn an operating income of $50,000 are 10,000 units. true or false
Answers
Answer:
true
Step-by-step explanation:
PLEASE HELP!!! You want to distribute 7 candies to 4 kids. If every kid must receive at least one candy, in how many ways can you do this?
Answers
Answer:
1140 ways.
Step-by-step explanation:
The applicable formula is: (n +r - 1)C(r-1), where n is the number of identical items (the candies), and r is the possible number of recipients (the kids).
The 17 identical candies, can be distributed among the 4 children in :
=(17 + 4 - 1)C(4–1) = 20C3 ways.
= 20!/((20–3)!*3!) ways.
= 20*19*18*17!/(17!*(3*2*1)) = 20*19*18/6 ways
= 20*19*3 ways.
=1140 ways.
Please if you know the answer tell me it and the steps also thank you.
Answers
Step-by-step explanation: Well to begin, you take 15$ and multiply it by 4, since he wants to buy 4 of those tickets, which is 60$. Then, take the 10$ and multiply it by 2 since he wants 2 of those tickets, which is 20$, you then apply 10% to 60 and 20 by taking 10 percent of 60, then adding it to 60 once have that, which is 66, you take the 3% and find 3% of 66, then add the answer of that to 66, which is 67.98$, you then do the same thing to the 20$.
Sorry if this didnt help, im sure it didnt because im a very bad explainer, but i tried..
may you guys help :)
Answers
Answer:
its the last one (d)
Step-by-step explanation:
which expression is equivalent to g^2/3h
Answers
The given expression \(g^2/3h\) is equivalent to the option (c) \(8g^2/24h\)as we have multiplied 8 in both numerator and denominator.
The given expression is \(g^2/3h\).
Now, to further simplify the expression, we can multiply both numerator and denominator by 8. This gives us:
\((g^2/3h) * (8/8)\)
Simplifying further, we get:
\((8g^2)/(24h)\)
Therefore, the expression equivalent to \(g^2/3h\) is \((8g^2)/(24h)\).
Thus, the given expression \(g^2/3h\) is equivalent to the option (c) \(8g^2/24h\) as we have multiplied 8 in both numerator and denominator.
The numerator is the top part of a fraction, which represents the number of equal parts being considered. It is the value that is above the fraction bar and represents the quantity being divided into equal parts.
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The complete question is :
Which expression is equivalent to \(g^2/3h\)?
Click on the correct answer.
(A) \(g^2+5/3h+5\)
(B) \(6g^2/15h\)
(C) \(8g^2/24h\)
Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2, Use the given sample sizes and numbers of successes to find the pooled estimate overbar(p). Round your answer to the nearest thousandth.
n1 = 100 n2 = 100
x1 = 42 x2 = 45
A. 0.435
B. 0.305
C. 0.392
D. 0.479
Answers
Option c 0.932 is the correct option of the given statement.
Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2, Use the given sample sizes and numbers of successes to find the pooled estimate overbar(p)
n1 = 100 n2 = 100
x1 = 42 x2 = 45
"In mathematics, what are probabilities?On a linear scale from 0 (impossibility) to 1 (certainty), or as a percentage between 0 and 100%, the word "probability" is commonly used to refer to the likelihood that a specific event (or group of events) will take place. Statistics describes the examination of events subject to probability.
What does probability formula mean?The proportion of favorable outcomes to all possible outcomes serves as the basis for the formula used to determine an event's probability. Always between 0 and 1 are the possible outcomes. Probability = Number of Favorable Outcomes / Total Number of Outcomes is a general form of the probability formula.
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Find the length of the line joining A (3,5) and B (1,3)
Answers
Answer:
2√2 units.
Step-by-step explanation:
To find the length of the line joining points A(3, 5) and B(1, 3), we can use the distance formula. The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates of points A and B into the formula, we have:
d = sqrt((1 - 3)^2 + (3 - 5)^2)
= sqrt((-2)^2 + (-2)^2)
= sqrt(4 + 4)
= sqrt(8)
= 2sqrt(2)
Therefore, the length of the line joining points A and B is 2√2 units.
6. Error Analysis Dakota said the third term of the expansion of (2g + 3h) is 36g2h². Explain Dakota's error. Then correct the error.
Answers
The binomial expansion is solved and the error in Dakota's statement is the incorrect substitution of 36g^2h^2 for the correct expression
Given data ,
Dakota made a mistake because the third term of the expansion of (2g + 3h) should have been 36g2h2. The binomial theorem asserts that the expansion of (2g + 3h) is as follows:
( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ
Here, x = 2g and y = 3h. Since term numbers begin at 0, since we are seeking for the third term, r = 2.
So , on simplifying the equation , we get
= nC2 * (2g)⁽ⁿ⁻²⁾ * (3h)²
= (n! / (2! * (n - 2)!)) * (2g)⁽ⁿ⁻²⁾ * (3h)²
= ((n * (n - 1)) / 2) * (2g)⁽ⁿ⁻²⁾ * (3h)²
Hence , the correct expression for the third term of the expansion of (2g + 3h) is ((n * (n - 1)) / 2) * (2g)^(n - 2) * (3h)², where n is the exponent in the binomial expansion.
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Which algebraic representation of a transformation on a coordinate grid does not preserve congruence A (x,y)-(x+6,y+6 .B(x,y)-(-x,y)C(x,y)-(6x,6y)D(x,y)-(-y,x)
Answers
Answer:
It’s A
Step-by-step explanation:
3. If a 35-foot cable were run from the top of the pole and anchored to the ground at a distance from the pole, about how far away from the pole would it be anchored?
Answers
The distance from the pole at which the cable is anchored is about 25 feet from the pole .
Given that a 35-foot cable is run from the top of the pole and anchored to the ground at a distance from the pole. The problem is to determine about how far away from the pole would it be anchored.
Let AB be the pole of length 40 feet, and CD be the 35-foot long cable anchored to the ground at D and attached to the top of the pole at C. Let E be the point on the ground at which the cable is taut and is anchored. The distance ED is to be determined.
we can see that ∆CDE is a right-angled triangle with ∠CED = 90°.
Using Pythagoras Theorem, we have:CD² = CE² + DE²35² = (40 - ED)² + DE² .
Simplifying the above equation
1225 = 1600 - 80ED + ED²
1225 - 1600 + 80ED - ED² = 0ED² - 80ED + 375 = 0
Factorizing the above quadratic equation
ED² - 25ED - 15ED + 375 = 0ED(ED - 25) - 15(ED - 25)
= 0(ED - 15)(ED - 25) = 0So, ED = 15 ft or ED = 25 ft.
The negative value of ED is extraneous since it represents a point below the ground, which is not possible. Therefore, the distance from the pole at which the cable is anchored is about 25 feet from the pole.
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Let (-3, 4) be a point on the terminal side of 0. Find the exact values of sin 0, csc 0, and cot 0.
Answers
Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4 using trigonometric ratio.
Trigonometric ratio calculation.
We know that the point (-3, 4) is on the terminal side of the angle θ, and we can use the Pythagorean theorem to find the value of the hypotenuse:
r² = x² + y²
r² = (-3)² + 4²
r² = 9 + 16
r² = 25
r = 5
Now we can find the values of sin θ, csc θ, and cot θ:
sin θ = y/r = 4/5
csc θ = r/y = 5/4
cot θ = x/y = -3/4
Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4.
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which number has a 6 whose value is 10 times greater then the value of 6 in 237,629
Answers
Any number with the 6 on the fourth place value, for example:
Which number has a 6 whose value is 10 times greater?
Each place value (which are counted from the right side) adds a factor of 10 to the previous place value.
This means that the 1 in 10, is 10 times the 1 in 1.
The 1 in 100, is 10 times the 1 in 10.
Then if we want to find a number where the 6 is 10 times greater than the value of the 6 in 237,629, we only need to move the 6 one time to the left.
We will have:
236,329
(any number with the 6 on the fourth place value).
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Each day, you run on a treadmill for r minutes and lift weights for 15 minutes. Which expressions can you use to find how many minutes of exercise you do in 5 days?
Explain your reasoning. there's two answers
They are both expressions with r as the variable.
They are not equivalent expressions.
They are equivalent expressions.
Both expressions contain the terms 5, r, and 15.
Answers
Answer:
5(15+r)= however many minutes 5*r is
or (5*15)+(r*15)
Step-by-step explanation:
Three times the sum of a number and 7 is equivalent to 57.
Answers
Answer:
3(x+7)=57
Step-by-step explanation:
3 is being multiplied by "the sum of a number(or x) and 7". So, we write it as 3(x+7). That is equal to 57, so that makes the expression 3(x+7)=57.
-hope it helps
Equivalent expressions are expressions that have the same values.
The expression is \(3(x + 7) = 57\) and the number is 12
Represent the number with x.
So, the sum of a number (x) and 7 would be represented as: x + 7
Three times the sum would be represented as: 3(x + 7)
This expression is equivalent to 57.
So, we have:
\(3(x + 7) = 57\)
Divide both sides of the equation by 57
\(x + 7 = 19\)
Subtract 7 from both sides of the equation
\(x + 7 - 7 = 19 - 7\)
\(x = 12\)
Hence, the number is 12
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Write a situation involving sales at an ice cream shop that could be reasonably modeled by the equation
4.50+0.50t=6.
Answers
Answer:
4.50 is for two scoops and a normal cone. Upgrades on cone is $0.50 and any additional toppings are also $0.50
Answer:5 × t = 6
Step-by-step explanation:
Step 1: 4.50 + 0.50 = 5
Step 2: We has 5t is 5 × t
Step 3: 5 × t = 6
From the picture, two cylindrical glasses of the same capacity. Find the diameter length (X) of a small glass of water.
8
12
14
10
Answers
Answer:
12
Step-by-step explanation:
πr²h=πr²h
π(4.5)²*10=π(x/2)²4.9
The LA Lakers had a PCT of 583 in the 2020-21 season. What does this mean in practical terms?
Answers
The meaning when LA Lakers had a PCT of 58.3 in the 2020-21 season is that the percentage of winning is 58.3%.
How to illustrate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
From the information given, the LA Lakers had a PCT of 58.3 in the 2020-21 season. It should be noted that PCT simply means percentage. Therefore, it denotes 58.3 percent.
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Complete question
The LA Lakers had a PCT of 58.3 in the 2020-21 season. What does this mean in practical terms
.a) Imagine you and your friend get a new card with an 18% APR and a $10 minimum payment and use this card to purchase the same mobile phone. If the first friend pays the minimum each month, while the second friend pays $20, what will their balances be after one month?
Answers
Answer:
yes
Step-by-step explanation:
yes yes you need to do the thing yeah
Answer:
yes
Step-by-step explanation:
a) Imagine you and your friend get a new card with an 18% APR and a $10 minimum payment and use this card to purchase the same mobile phone. If the first friend pays the minimum each month, while the second friend pays $20, what will their balances be after one month?
Mina bought 8 dozen bagels and 3 pounds of cream cheese for $85.50
Answers
Answer:
whats the question?
Step-by-step explanation:
4. What angle measures larger than 90 degrees, but less than 180 degrees? A reflx B straight C obtuse D right
Answers
Answer:
C obtuse
Step-by-step explanation:
An Obtuse angle measures more than 90° but less than 180°. A Straight angle or a half turn is always 180 °. Reflex is the next largest measuring more than 180° but less than 360°.
How to learn
basic algebra
Answers
Answer:
I recommend watching videos of Indian people explaining it to you they are the best.
Answer:
Khan Academy, Brainly, and Algebra tiger have helped me
Step-by-step explanation:
The wesbites listed will provide step by step answers to problems, and as you have seen on here, you can ask personalized questions and get step by step answers to remember how to work out a problem.
I hope this helped becuase these are the main websites that helped me!
Is 3 Liters equal to 300 mL. Is 3 yards equal to 12 feet. Is 3 tons equal to 9,000 lb
Answers
Answer:
3 Liters = 3000 ml
3 Yards = 12 feet
3 tons = 6000 lb.
Hope that this helps!
Answer:
3 Liters is equal to 3,000 mL
3 Yards is equal to 9 feet
3 Tons is 6,000 lbs
Step-by-step explanation:
Hope this helped!
What’s the answer to the 4th question?
Answers
Answer:
1440 Buckets of Water
Step-by-step explanation:
1 Bucket = 2.5 Gallons of Water
1 Cubic Foot = 7.5 Gallons of Water
1 Cubic Foot = 3 Buckets
480 x 3 = 1440