Determine whether the lines 2x + 5y =7 and 5x +2y =2 are
perpendicular
true or false
Answers
To find whether the lines 2x + 5y =7 and 5x +2y =2 are perpendicular or not, first find the slope of the lines. Then check whether the slopes are negative reciprocal to each other. If yes, then they are perpendicular and if no, then they are not perpendicular.
The slope of a line is given by the formula y = mx + b where m is the slope. Rearranging the given equations in this form:2x + 5y = 7 Simplifying,2x + 5y - 2x = 7 - 2x multiplying by -1 and reversing the signs,5y = -2x + 7Dividing by 5 on both sides, y = (-2/5)x + 7/5Slope, m1 = -2/5
Similarly, for the second equation,5x + 2y = 2 Simplifying,5x + 2y - 5x = 2 - 5x multiplying by -1 and reversing the signs,2y = -5x + 2 Dividing by 2 on both sides, y = (-5/2)x + 1Slope, m2 = -5/2 Now, check if the slopes are negative reciprocals. If yes, then they are perpendicular m1 * m2 = (-2/5) * (-5/2) = 1So, m1 * m2 = 1 which is true and thus the given lines are perpendicular to each other. Hence, the statement "the lines 2x + 5y =7 and 5x +2y =2 are perpendicular" is true.
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Related Questions
Which equation is a linear function?
Answers
Answer:
its not showing up
Step-by-step explanation:
(-x-y+2z = −21
(5x-3y - 2z=-23
If the equations above are true, which of the following is a value of X-Y?
A:5
B:16
C:-11
D:0
E:21
Answers
Answer: E
Step-by-step explanation:
Simplify:
3√5. √5
3√10
15
75
5√3
Answers
The simplified form of the expression is 15.
To simplify the expression 3√5 × √5, we have to first combine the radicals using the property of multiplication of square roots:
The property of multiplication of square roots:
√a × √b = √(a × b).
Thus, We have:
3√5 × √5
Applying the property of multiplication of square roots to our expression:
= 3√(5 × 5)
Multiply the numbers under the radical:
= 3√25.
Determine the value of the radical:
= 3(5)
Multiply the numbers:
=15
To simplify this expression, we combined the radicals, multiplied the numbers inside the radical, determined the value of the radical, and then performed the resulting multiplication.
Therefore, The simplified form for the expression is 15.
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3√5 × √5 is equal to 15. b.
To simplify the expression 3√5 × √5, we can combine the square roots of 5:
3√5 × √5 = 3 × √(5 × 5)
= 3 × √25
Since the square root of 25 is 5, we have:
3 × 5 = 15
The simplified form of the expression 3√5 × √5 is 15.
The expression 3√5 × √5 can be simplified as 15.
To understand why, let's break down the steps:
The square root of 5 is represented as √5.
Multiplying √5 by itself results in (√5)² = 5.
√5 × √5 simplifies to 5.
Multiplying 3 by 5 gives us 15 as the final result.
It's important to note that simplifying the expression involves evaluating the square roots and multiplying the resulting numbers.
By simplifying, we arrive at a single value is 15 in this case.
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Round 7.09 to the nearest tenth
Answers
Answer:
7.1
Step-by-step explanation:
To round 7.09 to the nearest tenth, you must use the hundredths' place value of 7.09, which is 9 and equal or more than 5. Therefore, the tenths value of 7.09 increases by 1 to 7.1.
HELP PLZZZZZZZZZZZZZZZZZZZZ
Answers
Step-by-step explanation:
it 90 the sec one
Question 1A ten digit telephone number is of theform (XYZ) - ABC -DEFG. In one particularstate, there are 4 possible area codes(202, 341, 602, and 581). The digit 'A' isrestricted to a number 2 through 8. Thedigits B and C can be any number butthey cannot repeat. The digits D,E,F, andG have no restriction. How many sevendigit phone numbers are possible withthese restrictions?Your answer:
Answers
If a 10-digit phone number has the following format: (XYZ)-ABC-DEFG. With these limitations, there are 25,200,000 phone numbers that can have seven digits.
Possible methods
XYZ=4 C'4 could be an area code.
A numbers 2 through 8 equal C'7
C'10 + B = C'9
D,E,F, and G are the same as C'10 C'10 C'10
Hence,
Alternatives: C'4 C'7 C'10 C'9 C'10 C'10 C'10
Possible methods: 4 7 10 9 10 10 10 10
Numbers of possible ways: 25,200,000
In light of this, if a ten-digit phone number has the format (XYZ)-ABC-DEFG. These limitations make the following seven-digit phone numbers possible: 25.2 million phone numbers
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an employee makes $18.00 per hour. given that there are 52 weeks in a year and assuming a 40-hour work week, calculate the employee's yearly salary.
Answers
The employee's yearly salary is calculated as $37,440 using the arithmetic operations.
The employee earns $18 per hour and works 40 hours per week. To calculate the weekly salary, we multiply the hourly wage by the number of hours worked:
Weekly salary = Hourly wage × Hours worked per week
Weekly salary = $18/hour × 40 hours/week = $720
Next, to calculate the yearly salary, we use the multiplication operation the weekly salary by the number of weeks in a year:
Yearly salary = Weekly salary × Weeks in a year
Yearly salary = $720/week × 52 weeks/year = $37,440
Therefore, the employee's yearly salary is $37,440. This calculation assumes a 40-hour work week and 52 weeks in a year. It's important to note that this calculation does not account for overtime pay or any other additional benefits or deductions that may affect the employee's total annual income.
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Help appreciated. View attachment.
Answers
Answer: the last one is gonna be the most likley to be correct
Step-by-step explanation:
Please help I’ll give brainliest
Answers
Answer:
1000 cubic metre
Step-by-step explanation:
hopes it help
Answer:
solution,
length=10 cm
volume=?
now,
volume of cube=l×l×l
=10×10×10
therefore,the answer is 1000 cubic centimeter
a sphere of radius r carries a total charge q distributed over its surface. A small area dA of the sphere is cut off. Find the electric field at the centre due to the remaining sphere.
Answers
Answer:
Step-by-step explanation:
Use the property of equality to solve this equation 4.5x=18
Answers
Answer:
x = 4
Step-by-step explanation:
Given
4.5x = 18 ( divide both sides by 4.5 )
x = 4
Answer:
x=4
Step-by-step explanation:
to isolate x, we need to divide both sides by 4.5, and 18/4.5 is equal to 4, so x=4.
lan buys a two-quart bottle of juice for $6.40. What is the unit rate of the cost of the
juice per fluid ounce?
1 gallon 4 quarts
1 quart 2 pints
1 pint
1 cup = 8 fluid ounces
2 cups
Before you try that problem, answer the question below.
How
many fluid ounces of juice did Ian buy?
Answers
2 x 32 = 64
$6.40 divided by 64 ounces
.10 per ounce
In a run chart, the variable being measured is typically placed on what axis?
(A) X axis
(B) Y axis
(C) Either axis
(D) Neither axis;
Answers
HURRY!! (52 POINTS!!)
The ages of people visiting a senior center one afternoon are recorded in the line plot.
A line plot titled Ages At Senior Center. The horizontal line is numbered in units of 5 from 60 to 115. There is one dot above 80 and 110. There are two dots above 70 and 85. There are three dots above 75.
Does the data contain an outlier? If so, explain its meaning in this situation.
A. No, there is no outlier. This means that the people were all the same age.
B. No, there is no outlier. This means that the people are all around the mean age.
C. Yes, there is an outlier at 110. This means that one person's age was 110, which is 25 years older than the next closest age.
D. Yes, there is an outlier of 110. This means that the average person at the center is 110 years old.
Answers
Answer:
C. Yes, there is an outlier at 110. This means that one person's age was 110, which is 25 years older than the next closest age.
Step-by-step explanation:
An outlier is a data point that sticks out like a sore thumb. It's so different from the rest of the data that it makes you wonder if it's a mistake or a miracle. One way to spot an outlier is to use the 1.5IQR rule, where IQR stands for interquartile range. The interquartile range is the gap between the third quartile (Q3) and the first quartile (Q1) of the data. The 1.5IQR rule says that any data point that is more than 1.5*IQR above Q3 or below Q1 is an outlier.
In this case, the first quartile (Q1) is 75, the third quartile (Q3) is 85, and the interquartile range (IQR) is 10. So, any data point that is more than 1.5*10 = 15 above 85 or below 75 is an outlier. The only data point that does this is 110, which is 25 above 85. That means 110 is an outlier.
What does this outlier mean in this situation? It means that one person who came to the senior center that afternoon was way older than the rest of the folks. The average age of the visitors was not changed by this outlier, since it was just one out of 12 data points. But, the outlier does mess up the range and the standard deviation of the data, making them bigger than they would be without the outlier.
Answer:The answer is C
Step-by-step explanation:I did the test.
The ODE dy/dx=3y^2 will have a slope field with same slopes arranged in vertical lines because the equation is autonomous.
a. true b. false
Answers
The same slopes arranged in vertical lines because it is an autonomous equation that only depends on the value of y, and not on the independent variable x.
a. True
The given ODE, dy/dx = 3y^2, is an autonomous equation because it does not depend explicitly on the independent variable x. The slope of the solution curve at any point (x, y) only depends on the value of y at that point. This means that the slope field of this equation will have the same slopes arranged in vertical lines.
To see why this is the case, let's consider a point (x, y) in the xy-plane. The slope of the solution curve passing through this point is given by dy/dx = 3y^2. This means that the slope of the solution curve depends only on the value of y at that point, and not on x. Therefore, if we plot the slope of the solution curve at every point in the xy-plane, we will get a slope field with vertical lines of constant slope.
In summary, the given ODE dy/dx = 3y^2 will have a slope field with the same slopes arranged in vertical lines because it is an autonomous equation that only depends on the value of y, and not on the independent variable x.
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Keith has $500 in a savings account at the beginning of the summer. He withdraws $25 each week for food, clothes, and movie tickets. He wants to have an account balance of at least $200 in the account at the end of the summer.
Answers
Answer:
You can put this solution on YOUR website!
the inequality is 500 - 25x >= 200
this insures that he will have at least 200 at the end of the summer.
subtract 200 from both sides of that inequality and add 25x to both sides of that inequality to get 500 - 200 >= 25x
simplify to get 300 >= 25x
divide both sides of that equation by 25 to get 300 / 25 >= x
simplify to get 12 >= x
12 >= x means x <= 12.
when x is smaller than or equal to 12, he will be guaranteed to have at least 200 in the account at the end of the summer.
when x = 12, what is left in the account is 500 - 25 * 12 = 200.
when x = 11, what is left in the account is 500 - 25 * 11 = 225.
when x = 13, what is left in the account is 500 - 25 * 13 = 175.
the maximum number of weeks he can withdraw money from his account is 12.
Step-by-step explanation:
What does the digit 3 mean in the number 356,498?
3 hundred thousands
B
3 thousands
3 ten thousands
3 hundreds
Answers
Answer:
The answer is: Hundred Thousands
You decide to save up for a big trip and deposit 1491 in a special vacation account today. If your account earns 5.07% annually, how much will you have available to spend in 6 years? Round to two decimal places (Ex. $0,000.00)
Answers
You will have approximately $1929.29 available to spend in 6 years.
To calculate the future value of your deposit after 6 years, we can use the formula for compound interest:
Future Value = Present Value * (1 + Interest Rate)^Time
Plugging in the values:
Present Value (PV) = $1491
Interest Rate = 5.07% = 0.0507
Time = 6 years
Future Value = $1491 * (1 + 0.0507)^6
Calculating the expression:
Future Value = $1491 * (1.0507)^6
Future Value ≈ $1929.29
Therefore, you will have approximately $1929.29 available to spend in 6 years.
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What is 2/3 divided by 1/6
O 2
O 3
O4
O 6
Answers
help me with this question please
Answers
Answer:
N+1
Step-by-step explanation:
It begins with = 2
then n+1=3
then n+2=4 and so on it is n+1
Consider a cube with a side length of s.
d. Write your conjecture as an algebraic equation.
Answers
The conjecture regarding a cube with a side length of s is that the volume of the cube can be represented algebraically as V = s³, where V denotes the volume of the cube.
A cube is a three-dimensional shape with six equal square faces. Each face of the cube has a side length of s.
To express the volume of the cube algebraically, we need to consider the relationship between the side length and the volume.
The volume of a cube is calculated by multiplying the length of one side by itself twice (s * s * s), which simplifies to s³.
Therefore, the algebraic equation representing the conjecture for the volume of a cube with a side length of s is V = s³, where V represents the volume of the cube.
This conjecture aligns with the general formula for calculating the volume of a cube and can be used to determine the volume of a cube given the length of its side.
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Someone please give me the simplified answer !
Answers
Answer:
11m-3v
Step-by-step explanation:
Answer:
11m-v3 i think
Step-by-step explanation:
The following problem was given to 60 students and doctors at the famous Hevardi Medical School (HMS): Assume there exists a test to detect a disease, say D, whose prevalence is 0.001, that is, the probability, P[D], that a person picked at random is suffering from D. is 0.001. The test has a false positive rate of 0.005 and a correct detection rate of 1.
Answers
The correct detection rate is the probability that if you have D, the test will say that you have D. Given that you test positive for D, the probability that you actually have it is 16.67%.
The probability that you actually have the disease (D) given that you tested positive is 0.1667 (16.67%). This can be calculated by multiplying the prevalence of the disease (P[D] = 0.001) by the correct detection rate of the test (1) and dividing it by the sum of the prevalence of the disease and the false positive rate of the test (0.001 + 0.005 = 0.006):
P[D | positive] = (P[D] × correct detection rate) / (P[D] + false positive rate)
P[D | positive] = (0.001 × 1) / (0.001 + 0.005)
P[D | positive] = 0.1667
P[D | positive] = 16.67%
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The complete question is:
The following problem was given to 60 students and doctors at the famous Hevardi Medical School (HMS): Assume there exists a test to detect a disease, say D, whose prevalence is 0.001, that is, the probability, P[D], that a person picked at random is suffering from D. is 0.001. The test has a false positive rate of 0.005 and a correct detection rate of 1. The correct detection rate is the probability that if you have D, the test will say that you have D. Given that you test positive for D, what is the probability that you actually have it?
Select all the fractions that are equal to 4.9 Group of answer choices LaTeX: \frac{490}{10}490 10 LaTeX: \frac{49}{10}49 10 LaTeX: \frac{490}{100}490 100 LaTeX: \frac{49}{100}49 100 LaTeX: \frac{490}{1000}490 1000 LaTeX: \frac{49}{1000}
Answers
Answer:
thats a lot hold up
Step-by-step explanation:
Solve for y: -3y-6x= -18 *
Answers
Answer:
\(y=-2+6x\)
Step-by-step explanation:
\(-3y-6x= -18\)
\((-3y-6x)= -18+6x\)
\(-3y-6x+6x=6x -18\)
\(y=-2+6x\)
Solve 4t(t - 5) - 2t(3t + 2) + 108 = 3t(2t - 5) -t (8t - 3) .
Answers
Answer:
the answer is t=9
Step-by-step explanation:
hoped I helped:)
Answer:
t = 9
Step-by-step explanation:
the nth term of a sequence is n²+20
work out the first 3 terms of the sequence
Answers
The first 3 terms of the sequence are 21, 24 and 29
Working out the first 3 terms of the sequenceFrom the question, we have the following parameters that can be used in our computation:
n² + 20
This means that
f(n) = n² + 20
The first 3 terms of the sequence is when n = 1, 2 and 3
So, we have
f(1) = 1² + 20 = 21
f(2) = 2² + 20 = 24
f(3) = 3² + 20 = 29
Hence, the first 3 terms of the sequence are 21, 24 and 29
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List 3 possible numerical solutions
When I go to Target, I always spend MORE THAN $25.
can someone help me with this?
Answers
Answer:
t > 25
Step-by-step explanation:
Could you guys help me with this question?
Answers
Answer:
whats your question
Step-by-step explanation:
Answer:
Yesss what question??!...
A trinomial with a leading coefficient of 3 33 and a constant term of − 5 is called:_________
Answers
According to the question a trinomial with a leading coefficient of 3 and a constant term of -5 would be 3x² + x - 5.
A trinomial is a polynomial with three terms is in the form of Ax²+Bx+C, where, A is the leading coefficient of veriable X², B is the middle coefficient of x and C is the constant of polynomial.
A trinomial with a leading coefficient of 3 and a constant term of -5.
Here, a=3,c=-5 and consider b=1,
Therefore, a trinomial with a leading coefficient of 3 and a constant term of -5 would be 3x² + x - 5.
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