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!
find the sum of this infinite geometric series.
HELP!!
Which product results in x^2-1
Solve for x.
Please helppp
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
Given the equation sqrt(x+1)+3=0, explain how to and solve this equation. Is the solution extraneous? Explain
√(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.
Write an equation of a line in slope-intercept form for the
given conditions.
passes through (4,33) and (1,21)
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.
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?
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
HELP FAST I NEVER SAW THIS BEFORE IN MY LIFE
I'll mark brainliest for the best answer!!
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
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
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
Which of the following is the value of g(60)?
help ASAP Please show working
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. :)
15 points!! Are any of these right?
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
Please solve for X and Y
Answer:
x=16
..................
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
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
7th grade math help me pleaseeee
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 :)
(Help fast plz)Which of these tables represents a linear function
Answer:
Step-by-step explanation:
3rd one
Solve 2x + 5y = -13
3x - 4y = -8
(4,1)
(-4,1)
(4.-1)
(-4,-1)
The answer is (-4,-1). Hopes this helps :)
20 points I beg you help
What is the common difference for the arithmetic sequence 14, 8, 2, -4, -10…. ?
Answer:
common difference = -6
Step-by-step explanation:
If you flip a coin 50 times, what is the best prediction possible for the number of times it will land on tails?
Answer: 25
Step-by-step explanation: 50 divided by 2 is 25
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?
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
Please help me! Thank you
Step-by-step explanation:
5⁰= 1
2–3 means 1/2³
1/8
=0.125
Need help ASAP !!!!!
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]
A rectangular prism has a length of 11cm, a height of 20cm, and a width of 10cm.
What is its volume, in cubic cm?
Answer:
la respuesta es nose
find x pls n ty!4?2!<3
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!
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.
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
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??
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.
What is the surface area of a cube in which each face of the cube has an area of 7 cm^2?
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!
I need help fast!!!!!!!!!!
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
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)
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
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
How do you rewrite an equation by completing the square?
x^2+10x+21=0
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
