From the list given, the line that is perpendicular to 3x – y = 10 is x + 3y = 27. (Option C)
What is a perpendicular line?It is to be noted that lines that intersect at a right angle (90 degrees) are considered perpendicular lines.
To justify the above results, we recall that when two lines are perpendicular then the product of their slope is -1.
The slope is given by y = mx + c where m is the slope.
Hence, the slope of the given equation 3x -y = 10 is arrived at by re-writing the expression as follows:
Y = 3x -10 where
slope m₁ = 3
given Lets attempt to derive the slope of the options given:
1) y = 3x + 5
m₂ = 3
The product of the slopes are:
= m₁ x m₂
= 3 x 3
⇒ 9 ≠ -1
Therefore, this is not a perpendicular line.
2) y = -13x + 17 our new m₂ = -13
m₁ x m₂
⇒ 3 x -13
⇒ -39 ≠ -1
Again, this is not the required line.
3) x + 3y = 27 [divide all sides by 3]
y = -1/3(x) + 9
The new m₂ = -1/3
Compute for slope:
= 3 x - (1/3)
= -3/3
= -1
Hence, x + 3y = 27 is the perpendicular line.
4) y -2 = 13(3x + 36)
y = 39x + 468 +2
y = 39x + 470
New Slope (m₂) = 39
Solving to check the slope, we have:
m₁ x m₂ = 3 x 39
⇒ 117 ≠ -1.
Thus, we have our final answer as option C.
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The required line which is perpendicular to the given line is x + 3y = 27. Option C is correct.
What is the slope perpendicular line?
The slope of the perpendicular lines is equal to the inverse and of the opposite sign.
Here,
Standard equation of the line,
y = mx + c
The property of the perpendicular line states that the product of their slopes is equal to -1.
So the slope of the given line is m = 3,
Let the slope of the perpendicular line that we have to determine, be x
According to the property,
The slope of line × slope of perpendicular line = -1
3 × x = -1
x = -1/3
So looking forward to the option, the line that has a slope of -1/3 is x + 3y = 27. because
x + 3y = 23
Transform the above equation to standard form,
y = -1/3x + 23
From the above equation, the slope of the above line is m = -1/3,
Thus, the required line which is perpendicular to the given line is x + 3y = 27. Option C is correct.
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How do you write 2.467 x 10^10 in standard form?????? helpppp
Answer: 24670000000
Step-by-step explanation:
1) First, the scientific form can help you learn that each 10 in a power will increase the number its multiplying by 10.
Since we know that when multiplying a decimal number by 10, it would move the decimal once to the right. We can apply this to the equation by moving the decimal to the right 10 times.
2) Answer
12345678910 <= This indicates the decimal moving one place
24670000000.00
Please help and provide an explanation for why the answer is f(x) = 3/2x + 7
What is the equation of the line that passes through Point (-4, 1) and has a Slope of 3/2.
Answer:
see below
Step-by-step explanation:
the point-slope equation is
y-1 = 3/2 (x+4)
Answer:
[tex]y=\frac{3}{2}x+7[/tex]
Step-by-step explanation:
To write the equation of a line, two information are needed.
Slope (also known as gradient)A pair of coordinates (or a point) on the lineThe slope can be calculated using the gradient formula as long as two pairs of coordinates are given. This question provides the slope, hence we can substitute its value into the equation right away.
In slope-intercept form, the equation of a line is given by y= mx +c, where m is the slope and c is the y-intercept. The slope gives us the steepness of the line, while the y-intercept is the y value in which the line cuts through the y-axis (vertical axis).
y= mx +c
Given that slope= [tex]\frac{3}{2}[/tex], m= [tex]\frac{3}{2}[/tex].
Substitute the value of m:
[tex]y=\frac{3}{2}x+c[/tex]
Next, find the value of c by substituting a pair of coordinates.
When x= -4, y= 1,
[tex]1=\frac{3}{2} (-4)+c[/tex]
1= -6 +c
Add 6 to both sides:
c= 1 +6
c= 7
Substituting the value of c:
[tex]\bf{y=\frac{3}{2}x +7 }[/tex]
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what is 25 + 20x factor
Answer:
5(4x+5)
Step-by-step explanation:
25+20x
=5(5+4x)
:]
What is the value of V?
V-22+v+32+v=180
V-22+v+32+v=180
V+v+v=170
3v=170
v=56.67
Please do number one please thank you
1. Which part of Emily's statement is the hypothesis?
'Then you might live in Oregon' is the hypothesis.
How is the hypothesis part found in the statement?
Emily says 'if you live in a state that borders California , then you might live in Oregon.'
Emily is not sure about the exact state that is bordering California.Emily so uses the word might because of uncertainty and gives a possibility of the state to be Oregon.There may be more than one state bordering California and Emily hypothetically mentions it might to OregonWhat is hypothesis?
Hypothesis is a speculative assumption made to uncover and evaluate the ramifications of its logical or empirical implications. It's an idea for a possible explanation of a phenomenon.A working hypothesis is a hypothesis that has been tentatively accepted and is proposed for further study in a process that starts with an informed guess or thinking.To learn more about hypothesis, refer:
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Robert cuts a string that is 4 feet long into pieces that are each foot long. a. Complete the model to show 4 ÷2/6
24 pieces make up the solution to this puzzle.
I assume the query is how many pieces does she receive.
I'll respond to it. Leave a note if it is incorrect.
6 pieces will be produced from 1 foot, each measuring 1/6 of a foot (12/6 = 2 inches).
4 feet will provide 24 pieces (4 * 6).
24 pieces make up the solution to this puzzle.
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i need help show the work
Answer:
9
Step-by-step explanation:
Use Exponent rule:
[tex]\sf \boxed{(a*b)^m = a^m*b^n}[/tex]
[tex]\sf \dfrac{4(3x)^2}{(2x)^2} = \dfrac{4 * 3^2*x^2}{2^2*x^2}\\[/tex]
[tex]\sf = \dfrac{4 * 9 *x^2}{4*x^2}\\\\= 9[/tex]
A diner serves a stack of potato slices that is 2.8 centimeters tall. The thickness of a potato is .35 centimeters. How many potato slices are in the stacks?
Given that a diner serves a stack of potato slices that is 2.8 centimeters tall. The thickness of a potato is 0.35 centimeters.
We have to determine the number of potato slices in the stacks.
The number of potato slices in the stack is given by:
[tex]\frac{2.8}{0.35}=8[/tex]Thus, the number of potato slices in the stack is 8.
Determine if the relation is a
function. Use set builder and
interval notation for the
domain and range.
Function: Yes No
Domain:
Range:
Answer:
It would be helpful if you add more info on the question
Step-by-step explanation:
Need help with this
Answer:
<XMN = 122°
Step-by-step explanation:
An angle around a point is 360°
If LMN = 145° then the rest would be 360 - 145
360 - 145 = 215
4x + 5 + 6x - 10 = 215
Simplify = 10x - 5 = 215
work out = 215 + 5 = 220 ÷ 10 = 22
x = 22
XMN = 6x - 10
6 × 22 = 132
132 - 10 = 122
XMN = 122
Please need asappp Graphs of inverse functions
24 yd
15 yd
35 yd
the volume
Answer: 9633.4 cubic meters
I only assumed the shape and length, height, width, etc. so this is my best guess. Please provide with a three dimensional shape of the object being calculated and specify which measurements are the length, height, width, depth, or circumfrence. I will answer it right away :)
Answer:
12600 yd^3
Step-by-step explanation:
The equation to finding the volume of 3 dimensional shapes only including cubes, and rectangles.
L * W * H = V
Which means Length multiplied by width, multiplied by height.
So in this instance:
35 * 24 = 840 * 15 = 12600.
Hope this answers your questions.
If so please make brainliest.
Also if it does feel free to ask me any other questions needed.
4-2(5x-1)>5x+3 how do I solve this
market researchers often report disposable income. this is your income after tax deductions. your gross income is $4,000 per month. your federal tax is 10%, state tax is 7%, city tax is 3%, and you pay 7% to social security. what is your monthly disposable income?
Answer:
The monthly disposable income will be $2,920.
Step-by-step explanation:
If Sarah needs 3 cups of flour for 2 batches of cookies, How many cups of flour would she need for 18 batches of cookies?
Answer:
24 = 18
Step-by-step explanation:
3 cups = 2 cookies
Meaning she needs 24 cups of flower for 18 cookies
What type of reasoning is used to find the next amount of train cars? Explain your answer.
Using an arithmetic sequence, it is found that the next amount of train cars is of 6.
What is an arithmetic sequence?For an arithmetic sequence, the difference between consecutive terms is constant, called common difference d.
The nth term of an arithmetic sequence is given by the following rule:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
In the context of this problem, from the image, the number of train cars can be modeled by the following sequence:
(0, 2, 4, ...)
Which is an arithmetic sequence with:
A first term of 0.A common ratio of 2.Hence the next term of the sequence is given by:
4 + 2 = 6.
As 4 is the last term and 2 is the common ratio.
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The length of each side of triangle LMN is shown below.
LM = 18 cm
MN = 29 cm
LN = 20 cm
Which list shows the angles of triangle LMN in order from least measure to greatest measure?
The angles of triangle LMN in order from least measure to the greatest measure as angle ∠ N < angle ∠ M < angle ∠ L which is determined by the triangle inequality theorem.
What are the vertical angles?When two lines intersect at a location, vertical angles are generated. They are always equal to each other.
The length of each side of the given triangle LMN is shown below.
LM = 18 cm
MN = 29 cm
LN = 20 cm
According to the triangle inequality theorem, in a triangle, the largest angle is the one opposite to the longest side of the triangle.
Therefore, in triangle LMN, we have the greatest angle as angle ∠ L
And the smallest angle is ∠ N
Arrange the angles in ascending order,
angle ∠ N < angle ∠ M < angle ∠ L
Thus, the angles of triangle LMN in order from least measure to the greatest measure as angle ∠ N < angle ∠ M < angle ∠ L.
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What is the measure of m?
HELP PLEASE!
f(x)= ³ √x+8. Find the inverse of f(x).
Answer: (D)
the answer would be D
Step-by-step explanation:
Tracy is cutting out a rectangular board to construct a bookshelf.
The board is to have a perimeter of 38 inches, and its length is to be 5 inches shorter than double the width.
Let x be the width of the board.
State the expression for the length of the board in terms of x.
Answer:
28 inch
Step-by-step explanation:
half of 38 would be 19, and take away 5 from both 19. Equally each width ( top and bottom ) 14 inch and each lenght ( Left and right ) 5 inch. so x representing width would be 14 + 14= 28 inch.
14
5 5
14
A painter
mixes 2%, pints
of yellow paint with
4 pints of red paint to make a certain shade of
orange paint. How many pints of yellow paint
should be mixed with 10 pints of red paint
to
make
this shade of orange?
In linear equation, 0.005 pints are pints of yellow paint should be mixed with 10 pints of red paint to make this shade of orange.
What is a linear equation example?
Ax+By=C is the usual form for two-variable linear equations. As an illustration, the conventional form of the linear equation 2x+3y=5 When an equation is given in this format, finding both intercepts is rather simple (x and y).A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.Given,
A painter mixes 2%, pints of yellow paint with 4 pints of red paint
So to make this shade of orange ⇒
10 red pints × (2 % yellow pints/ 4 red pints) ≈ 0.005 pints
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A local building code requires that all factories must be surrounded by a lawn. The width of the lawn must be uniform and the area of the lawn must be equal to the area of the factory. What must be the width of a lawn surrounding a rectangular that measures 120 m by 80 m?
PLEASE HELP
Answer:
20 m
Step-by-step explanation:
You want to know the uniform width of a lawn around a 120 m by 80 m building such that the area of the lawn is equal to the area of the building.
SetupLet x represent the width of the lawn. Then the dimensions of the area that includes the lawn and building will be (120 +2x) meters by (80 +2x) meters. We want that area to be equal to twice the area of the building:
(120 +2x)(80 +2x) = 2(120·80)
SolutionDividing by 4 gives a slightly simpler equation.
(60 +x)(40 +x) = 60(80)
2400 +100x +x^2 = 4800 . . . . eliminate parentheses
x^2 +100x -2400 = 0 . . . . . . subtract 4800 and put in standard form
(x +120)(x -20) = 0 . . . . . . . factor
Values of x that make the factors zero are ...
x = -120, x = 20
Only the positive solution makes any sense in this context.
The width of the lawn must be 20 m.
__
Additional comment
The total area of the plot is ...
total area = (building area) + (lawn area)
When the lawn area is equal to the building area, then we have ...
total area = (building area) + (building area)
total area = 2·(building area)
This is the relation we used in the solution above.
place the numbers in order from least to greatest…PLS HELP!
Answer:
If the numbers are arranged from the least to the greatest, then it is called ascending order. In this form, the numbers are in increasing order. The first number should be lesser than the second number. If the numbers are arranged from the greatest to the least, then it is called descending order.
Absolute Value Calculator: Heron's Calculator
Coterminal Angle Calculator: Graphing Functi...
Step-by-step explanation:
Answer:
1. -[tex]\sqrt{13}[/tex] = -3.605...
2. -18/5 = -3.6
3. -[tex]\sqrt{12.25}[/tex] = -3.5
4. -|3.4| = -3.4
5. |-3.6| = 3.6
PLS PLS HELP ASAP!!!
translate the image using the rule below
Answer:
t=(1,-3) c=(-2,-2) r=(-3,-5)
Step-by-step explanation:
add 2 to each x value and subtract 4 from each y value
what is the slope of the line ?
Answer:
Step-by-step explanation:
5/2
Answer: f(x)= 2x-3
Step-by-step explanation: The formula for slope is y=mx+b, where m is equal to the slope of the line and b is equal to the y-intercept. We can find the slope by looking at the line OR solving algebraically using the following calculations:
(y2-y1)/(x2-x1)
Pick 2 points on the line and plug in.
(x1,y1)-->(2,1) and (x2,y2)-->(3,3)
(3-1)/(3-2)=2/1=2
So, the slope of the line is 2. m=2.
To find the y-intercept, we can solve algebraically or look at the graph.
y=2x+b
Plug in a point from the graph to find b, the y-intercept.
3=2(3)+b
3=6+b
-3=b
So, the y-intercept is b.
Now, we plug our values into the slope intercept equation, y=mx+b
y=2x-3
Again, you look look at the graph and see where x=0 is to find the y intercept. To find the slope you can use rise/run and count to see that to get from one point on the graph to the next, you count up 2 (rise 2) and to the right 1 (run 1) which gives you 2/1. 2/1 is equal to 2, giving you the slope of 2.
Hope this helped :))
AGAIN PLS HELP ME I NEED IT
Answer: Yes, No, No, Yes
Step-by-step explanation:
Goal: Substitute all the ordered pairs into the equation.
1) (1,-3)
5(1) + 2(-3) = -1
5 + -6 = -1
-1 = -1
Yes
2) (2,8)
5(2) + 2(8) = -1
10 + 16 = -1
25 = -1
No
3) (-4, -6)
5(-4) + 2(-6) = -1
-20 + -12 = -1
-32 = -1
No
4) (-3, 7)
5(-3) + 2(7) = -1
-15 + 14 = -1
-1 = -1
Yes
If the assumptions for the large sample confidence interval for the population proportion are not met, what adjustments can be made?.
A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.
A 95% confidence interval gives you a 5% chance of being wrong. A 90% confidence interval gives you a 10% chance of being wrong. In comparison to a 99% confidence interval, a 95% confidence interval is smaller (for example, plus or minus 4.5 percent instead of 3.5 percent).
When constructing a confidence interval for a propotion, if the condition of proportion requires 10 individuals in each category is not met, then confidence interval should be adjusted.
The number of individuals in each category is increased by 2 and sample size increases by 4.
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Write an equation of the parabola. Justify your answer.
Check the picture below.
so from the picture we can pretty much tell two solutions or zeros and another point where it passes up above, so
[tex]\begin{cases} x=-1\implies &x+1=0\\\\ x=7\implies &x-7=0 \end{cases}\hspace{8em} \begin{array}{llll} a(x+1)(x-7)=0\\\\ a(x+1)(x-7)=y \end{array} \\\\[-0.35em] ~\dotfill\\\\ \textit{we also know that} \begin{cases} x=5\\ y=3 \end{cases}\implies a(5+1)(5-7)=3 \\\\\\ a(6)(-2)=3\implies -12a=3\implies a=\cfrac{3}{-12}\implies a=-\cfrac{1}{4} \\\\[-0.35em] ~\dotfill[/tex]
[tex]-\cfrac{1}{4}(x+1)(x-7)=y\implies -\cfrac{1}{4}\stackrel{F~O~I~L}{(x^2-6x-7)}=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} -\cfrac{x^2}{4}+\cfrac{3x}{2}+\cfrac{7}{4}=y \end{array}}~\hfill[/tex]
what is the slope of the line?
Answer:
slope = - 1
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (2, 0) ← 2 points on the line
m = [tex]\frac{0-2}{2-0}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1
Answer:
-1, equation is y=-x+2
Step-by-step explanation:
I WILL GIVE BRAINLIEST!!!
Create one symmetrical (normal) and one asymmetrical set of data, and explain why each fit the definition.
+ Knowing the type of distribution and the skewness of the data, is it possible to draw conclusions about the mean and the median?
+ Why would it be best to use particular measures of center and spread if the data is symmetrical or asymmetrical?
+ What measures would you use in each case?
The median will be used as the measure of central tendency in this case, it is wise to use the inter-quarterly range as the measure of spread.
What are symmetrical and asymmetrical data?A histogram for symmetrical data will give a symmetrical shape, and the mean, median and mode will all be the same value. Therefore, the best measure of the central tendency to use is the mean.
The standard deviation indicates; how far away the values in a given data set are from the mean, and since the mean is used as the measure of central tendency, then the standard deviation should be used as the spread.
If the data is symmetrical, then the mean is the measure of central tendency; and the standard deviation is the best spread to use.
If the data is asymmetrical, the median is the best measure of central tendency; and the inter-quarterly range is the best spread to use.
The median will be used as the measure of central tendency in this case, it is wise to use the inter-quarterly range as the measure of spread.
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