2x-5y=-3
5x+2y=6
Is this a perpendicular lines ?

Answers

Answer 1

Perpendiculat Line is when both slopes of equation multiplying each others and equal to -1.

[tex] \large \boxed{m_1m_2 = - 1}[/tex]

For an easier way to understand, a perpendicular line has a negative reciprocal slope. For example if we are given the equation of y = 2x then the equation that is perpendicular to y = 2x would be y = (-1/2)x.

From both equations. We can either arrange in slope-intercepy form or use the slope formula which is m = -A/B when the equation is in Ax+By+C = 0 or Ax+By = C.

[tex] \large{ \begin{cases} 2x - 5y = - 3 \\ 5x + 2y = 6 \end{cases}}[/tex]

To find if these two lines are perpendicular to each others. Use the slope formula of -A/B.

[tex] \large{ \begin{cases} m_1 = - \frac{2}{ - 5} \\ m_2 = - \frac{5}{2} \end{cases}} \\ \large{ \begin{cases} m_1 = \frac{2}{ 5} \\ m_2 = - \frac{5}{2} \end{cases}}[/tex]

Now recall that it is perpendicular when one of them is negative reciprocal of one another (-5/2 is negative reciprocal of -(-2/5) = 2/5 and 2/5 is negative reciprocal of -5/2).

Or in definition of perpendicular lines, both slopes multiply and must equal to -1.

[tex] \large{( \frac{2}{5} )( - \frac{5}{2} ) = - 1} \\ \large{ - 1 = - 1}[/tex]

Thus the equation is true which makes both lines perpendicular to each others.

Answer

Both lines are perpendicular to each others.

Let me know if you have any doubts!


Related Questions

Given the equation sqrt(x+1)+3=0, explain how to and solve this equation. Is the solution extraneous? Explain​

Answers

√(x + 1) + 3 = 0   ==>   √(x + 1) = -3

has no real solutions, since the square root cannot be a negative number. But if we were to ignore that for the moment, one might try taking the square of both sides, which gives

(√(x + 1))² = (-3)²   ==>   x + 1 = 9   ==>   x = 8

But this is not a valid solution, since

√(8 + 1) = √9 = 3 ≠ -3

While -3 is a square root of 9, we had started off with the *positive* square root of x + 1.

Need help ASAP !!!!!

Answers

Answer:

Option A is correct answer

hear is explaination

[tex]\longrightarrow{\blue{a.\:90}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] - 3xy[/tex]

Plugging in the values "[tex]x = 5[/tex]" and "[tex] y = -6[/tex]", we have

[tex] = - 3(5)( - 6)[/tex]

[tex] = - 3( - 30)[/tex]

[tex] = 90[/tex]

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Which expression is equivalent to the following complex fraction?
3
-4
x-1
2.
X-1
2-
0
2(X-2)
-4X+7
-4X+7 D.
2(X-2)
4x+7
2(x2-2)
2(x2-2)
4x+7

Answers

Answer:

[tex]\frac{-4x+7}{2(x-2)}[/tex]

Step-by-step explanation:

[tex]For x \neq 1 \\\frac{\frac{3}{x-1}-4}{2-\frac{2}{x-1}}=\frac{\frac{3}{x-1}-\frac{4x-4}{x-1}}{\frac{2x-2}{x-1}-\frac{2}{x-1}}=\frac{\frac{-4x+7}{x-1}}{\frac{2x-4}{x-1}}=\frac{-4x+7}{2(x-2)}[/tex]

The equivalent expression is 2(x - 2) / (-4x + 7).

Option A is the correct answer.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To simplify the given expression:

[3/(x - 1) - 4] / [2 - 2/(x - 1)]

We need to find a common denominator for the two fractions in the numerator and denominator of the main fraction.

The common denominator for the numerator is (x - 1) and for the denominator is 2(x - 1).

We can then rewrite the expression as:

[3 - 4(x - 1)/(x - 1)] / [2(x - 1) - 2/(x - 1)]

Simplifying the numerator by distributing the -4:

(3 - 4x + 4) / (x - 1)

(-4x + 7) / (x - 1)

Now, simplifying the denominator by finding a common denominator:

2(x - 1) - 2/(x - 1)

= (2x - 2 - 2)/(x - 1)

= 2(x - 2)/(x - 1)

Substituting back into the original expression, we get:

(-4x + 7)/(x - 1) / [2(x - 2)/(x - 1)]

Multiplying by the reciprocal of the denominator:

(-4x + 7)/(x - 1) x (x - 1)/[2(x - 2)]

(-4x + 7)/[2(x - 2)]

Therefore,

The equivalent expression is 2(x - 2) / (-4x + 7).

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ5

Solve for x.
Please helppp

Answers

Answer:

x = 23

Step-by-step explanation:

2x + 19 + 5x = 180

I say this because it is an angle that is equivalent to the one adjacent to 2x+19, which is on a straight line. That means it is equal to 180.

7x + 19 = 180

180 - 19 = 7x

161/7 = x

x = 23

Step-by-step explanation:

5x+2x+19=180

7x+19=180

7x=180-19

7x=161

x=161/7

x=23

if u want more ans

5x

5×23

115

2x+19

2×23+19

65

hope it helps

HELP FAST I NEVER SAW THIS BEFORE IN MY LIFE

I'll mark brainliest for the best answer!!

Answers

Answer:

GIRL NO WAY IM LITTERALY TAKING THAT TEST RN AND IM TRYING TO FIGURE OUT THAT SAME QUESTION LOL

Step-by-step explanation:

BUT I THINK ITS -0.5 DONT TAKE MY WORD FOR IT IM JUST ASSUMING ITS THE ANSWER BC ITS THE ONLY ONE THAT MAKES SENSE

Please solve for X and Y

Answers

Answer:

x=16

..................

What is the area of a circle that has a diameter of 16in? A: 50.24 square inches B: 803.84 square inches C: 200.96 square inches D: 25.12 square inches​

Answers

Answer:

A = 200.96 in² (Answer C)

Step-by-step explanation:

The formula for the area of a circle of radius (not diameter) is A = πr².

Here the diameter is 16 in, so the radius is half that, or 8 in.

Then the area of the circle in question is

A = π(8 in)² = 64π in²

If tis is evaluated, we get    A = 200.96 in² (Answer C)

Solve 2x + 5y = -13
3x - 4y = -8
(4,1)
(-4,1)
(4.-1)
(-4,-1)

Answers

The answer is (-4,-1). Hopes this helps :)

I need help fast!!!!!!!!!!

Answers

g(x)=2/5(10)-x it the last one

What is the surface area of a cube in which each face of the cube has an area of 7 cm^2?

Answers

Answer:

In a cube, the length and width are the same, so both sides will be 7 cm, yielding an area of 49 square centimeters. The surface area of a 7 cm cube will be 294 cm2 . Hope this helps!

How do you rewrite an equation by completing the square?
x^2+10x+21=0

Answers

Answer:

Step-by-step explanation:

x²+10x+21=0

x²+10x+(10/2)²-(10/2)²+21=0

x²+10x+25-25+21=0

(x+5)²-4=0

(x+5)²=4

(x+y)²=(x+y)(x+y)=x(x+y)+y(x+y)=x²+xy+xy+y²=x²+2xy+y²

(x+y)²=x²+2xy+y²

coefficient of x=2y

y²=[(coefficient of x)/2]²=(2y/2)²=y²

20 points I beg you help
What is the common difference for the arithmetic sequence 14, 8, 2, -4, -10…. ?

Answers

Answer : -6

The common difference of a sequence is the value that changes every time the sequence continues.

In your sequence it is seen that 6 is subtracted from each term in order to get to the next in the sequence.

Answer:

common difference = -6

Step-by-step explanation:

A rectangular prism has a length of 11cm, a height of 20cm, and a width of 10cm.
What is its volume, in cubic cm?

Answers

Answer:

la respuesta es nose

A mixture of concrete is made up of sand and cement in the ratio of 5:3.How many cubic centimeters of sand is needed to make 160 cubic centimeters of concrete mix?

Answers

Answer: [tex]100\ cm^3[/tex]

Step-by-step explanation:

Given

The ratio of mixture of sand and cement is 5:3

If the total volume of mixture is [tex]160\ cm^3[/tex]

Suppose there is 5x and 3x cubic centimeter of sand and cement respectively i.e.

[tex]\Rightarrow 5x+3x=160\\\Rightarrow 8x=160\\\Rightarrow x=20\ cm^3[/tex]

Sand [tex]5x=5\times 20=100\ cm^3[/tex]

So, there is [tex]100\ cm^3[/tex] of sand in the mixture

The amount of taxes on a chair was $3.60 the text is the tax rate was 5% find the original price of the chair??

Answers

Answer:

Original Price = $72.

Step-by-step explanation:

You first need to know that $3.60 is 5% of the original price.

Then you need to multiply by 20, because 100/5 is 20, meaning that the price multiplied is $72.

The answer is $72.

find the sum of this infinite geometric series.
HELP!!

Answers

The answer would be 128!!!
The sum of the geometric series is 128

15 points!! Are any of these right?

Answers

Answer:

it is the second one

Step-by-step explanation:

the y intercept for the first one isnt the origin

It is decreasing from negative infinity to -2.5 for the first one

(Help fast plz)Which of these tables represents a linear function

Answers

Answer:

Step-by-step explanation:

3rd one

Mallory goes to the farmers market every weekend. She buys six apples for $0.75 each and a bagful of oranges that are priced at $1.25 per orange. The total charge is $14.50. Write the equation representing this situation where n represents the number of oranges.

Answers

Answer:

Number of oranges = 8

Step-by-step explanation:

let

a = number of apples

n = number of oranges

Number of apples = 6

Cost of each apple = 0.75

Number of oranges = n

Cost of each orange = $1.25

Total cost = $14.50

Total cost = Number of apples * Cost of each apple + Number of oranges * Cost of each orange

14.50 = 6 * 0.75 + n * 1.25

14.50 = 4.5 + 1.25n

14.50 - 4.5 = 1.25n

10 = 1.25n

n = 10 / 1.25

n = 8

Number of oranges = n = 8

Therefore, there are 8 oranges in a bagful of orange

Which product results in x^2-1

Answers

the answer is d!! hope this helps

help ASAP Please show working​

Answers

Answer:

(a) -1

(b) -2

Step-by-step explanation:

(a) Replace the a's with 1 and the b's with 3 to get 1*3 = 1-3+1 = -1

(b) We already figured out that (1*3) equals -1 so we just need to find -1*2. Using same strategy as part a, replace a and b with -1 and two, respectively. -1*2 = -1-2+1= -2. Hope this helps and sorry if I made a mistake. :)

7th grade math help me pleaseeee

Answers

Answer:

The lower left one.

Step-by-step explanation:

If you expand and rearrange it, you will find out both of its constant cancel out, and leave you with 3w=3w. So w have infinite number of solutions.

Answer:

[tex]6(\frac{1}{2} w-1)=3(w-2)[/tex]

Step-by-step explanation:

[tex]6(\frac{1}{2} w-1)=3(w-2)[/tex]              (Isolate parentheses)

[tex]3w-6=3w-6[/tex]                      (Add six to both sides to isolate one variable w)

[tex]3w=3w[/tex]                                  (Divide by three to isolate variable w)

[tex]w=w[/tex]

Because we got [tex]w=w[/tex], that means that any number you put in for w will still get you the same answer, or "infinite answers." If you try, say 5, you would still get the same answer if you put in 9. It has infinite answers.

I hope this helped :)

Write an equation of a line in slope-intercept form for the
given conditions.
passes through (4,33) and (1,21)

Answers

Answer:

The desired equation is thus   y = 4x + 17

Step-by-step explanation:

The slope-intercept form of the equation of a straight line is y = mx + b.  There are two values to find:  slope m and y-intercept b.

The line passes through (4, 33).  Thus, 33 = m(4) + b.

The line also passes through (1, 21).  Thus, 21 = m(1) + b, or m = 21 - b.

Thus we have a system of linear equations to solve, and will use the substitution method:

Substitute 21 - b for m in 33 = 4m + b:

33 = 4(21 - b) + b, which, in expanded form, is 33 = 84 - 4b + b, or

                                                                             33 = 84 - 3b, of

                                                                             -51 = -3b.

Thus, b = 17.  Since m = 21 - b, when b = 17, m = 21 - 17 = 4

The desired equation is thus   y = 4x + 17

Of course there are other ways to find this equation.  You could, if you wished, find the slope of the line passing through the given points using the definition of slope, and then find the y-intercept.

If you flip a coin 50 times, what is the best prediction possible for the number of times it will land on tails?

Answers

Answer: 25

Step-by-step explanation: 50 divided by 2 is 25

The answer to this will be 25 correct

A furnace was originally priced at $907.07 but went on sale for 33% off. If Omar bought the furnace and paid 9%
sales tax, how much did he pay in total?

PLZ HELP I’LL MAKE YOU A BRAINLEST

Answers

Answer:

662.44 total paid

Step-by-step explanation:

907.07X.33(33% off)=299.33 discount

907.07-299.33=607.74 sales price

607.74+.09=54.70 sales tax

607.74+54.70=662.44 sales price including sales tax

Sthephanie has 3 3/4 bags of soli to put in her garden. Each bag of soil will cover 125.3 ft how many square feet will sthephanie be able to cover if she uses all bags of soli?

Answers

Answer:

469.875 square feet

Step-by-step explanation:

Find how many square feet she can cover by multiplying 125.3 by 3.75 (same as 3 3/4):

125.3(3.75)

= 469.875

So, she will be able to cover 469.875 square feet with soil


Which of the following is the value of g(60)?

Answers

It is number one hope it helps :D

The incorrect work of a student to solve an equation 2(y + 4) = 4y is shown below:
Step 1: 2(y + 4) = 4y
Step 2: 2y + 6 = 4y
Step 3: 2y = 6
Step 4: y = 3
Which of the following explains how to correct Step 2 and shows the correct value of y?
1. The equation should be y + 4 = 4y after division by 2; y = 5
2. The equation should be y + 4 = 4y after division by 2; y = 2
3. 2 should be distributed as 2y + 8; y = 4
4. 2 should be distributed as 2y + 8; y = 2

Answers

Answer:

3;  y=4

Step-by-step explanation:

2 should be distributed as 2y + 8; y = 4

2(y +4) = 4y

2y + 8 = 4y

8 = 2y

y = 4

Please help me! Thank you

Answers

Step-by-step explanation:

5⁰= 1

2–3 means 1/2³

1/8

=0.125

find x pls n ty!4?2!<3

Answers

Answer:

x = 8

Step-by-step explanation:

A² + B² = C²

x² + 15² = 17²

x² + 225 = 289

x² = 289 - 225

x² = 64

x = [tex]\sqrt{64}[/tex]

x = 8

Hope this helps!

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