What is the equation of the line that is perpendicular to the line and passes through the point (6, 2)?
Answers
So, when you find something perpendicular, you are finding the opposite reciprocal.
The slope is 1/2 because:
y=mx+b <== it is in this form; m is equal to slope.
Flip the 2 and 1 and make it negative.
2/1= -2
We already know "C" and "D" aren't the options. Now, we can just plug in the points given to see if it works. Plug in the set of points (6,2)
y=-2x+14
2=-2(6)+14
2=-12+14
2=2 <== this works. This is our answer. Let's just make sure by checking the other one.
y=-2x-2
2=-2(6)-2
2=-12-2
2=-14 <== that is not true.
The first option is correct.
I hope this helps!
~kaikers
Step [tex]1[/tex]
Find the slope of the line perpendicular to the given line
we have
the equation of the given line is
[tex]y=\frac{1}{2}x+7[/tex]
we know that
if two lines are perpendicular
then
the product of their slopes is equal to minus one
so
[tex]m1*m2=-1[/tex]
in this problem the slope m1 of the given line is
[tex]m1=\frac{1}{2}[/tex]
so
[tex]m2=-\frac{1}{m1}[/tex]
[tex]m2=-2[/tex]
Step [tex]2[/tex]
Find the equation of the line with slope m2 and passes through the point [tex](6, 2)[/tex]
we know that
the equation of the line is
[tex]y-y1=m*(x-x1)\\ y-2=-2*(x-6)\\y=-2x+12+2\\ y=-2x+14[/tex]
therefore
the answer is the option A
the equation of the line is [tex]y=-2x+14[/tex]
see the attached figure to better understand the problem
Related Questions
Tabitha is trying to find the equation of a line perpendicular to y = 1 over 2 x − 5 in slope-intercept form that passes through the point (2, −7). Which of the following equations will she use?
Answers
Answer:
[tex]y=-2x-3[/tex]
Step-by-step explanation:
we know that
If two lines are perpendicular
then
the product of their slopes is equal to minus one
so
[tex]m1*m2=-1[/tex]
Step 1
Find the slope of the given line
we have
[tex]y=\frac{1}{2}x-5[/tex]
the slope of the given line is equal to
[tex]m1=\frac{1}{2}[/tex]
Step 2
Find the slope of the line perpendicular to the given line
[tex]\frac{1}{2}*m2=-1[/tex]
[tex]m2=-2[/tex]
Step 3
Find the equation of the line into slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=-2[/tex]
[tex]point(2,-7)[/tex]
substitute and solve for b
[tex]-7=-2*(2)+b[/tex]
[tex]-7=-4+b[/tex]
[tex]b=-7+4=-3[/tex]
The equation of the line is equal to
[tex]y=-2x-3[/tex]
Can someone help me please?
Answers
now, notice Thales theorem on the semi-circle, therefore, IF those two segments in the semi-circle, namely TQ and TS, are indeed perpendicular, that means the angle at the vertex T is a right-angle, and by Thales theorem, QS must be the diameter.
Solve y=x^2 + 7 for x
Answers
y = x^2 + 7
y - 7 = x^2
sqrt(y - 7) = x
Answer:
x = sqrt(y - 7)
Hope this helps!
Final Answer:
The solutions to the equation [tex]\( y = x^2 + 7 \)[/tex] for x are: [tex]\[ x = +\sqrt{y - 7} \quad \text{and} \quad x = -\sqrt{y - 7} \][/tex]
Explanation:
To solve the equation [tex]\( y = x^2 + 7 \)[/tex] for x, you want to isolate x on one side of the equation. Here are the steps to do so:
1. **Subtract 7 from both sides**:
To isolate the [tex]\( x^2 \)[/tex] term, we first remove the constant term on the right side by subtracting 7 from both sides of the equation.
[tex]\( y - 7 = x^2 + 7 - 7 \)[/tex]
This simplifies to:
[tex]\( y - 7 = x^2 \)[/tex]
2. **Take the square root of both sides**:
To solve for x, you need to get rid of the square on the x term. This is done by taking the square root of both sides. Remember that when you take the square root of both sides of an equation, you must consider both the positive and negative square roots.
[tex]\( \sqrt{y - 7} = \pm\sqrt{x^2} \)[/tex]
Simplifying the right side (since the square root and square operations are inverses of each other), we get:
[tex]\( \sqrt{y - 7} = \pm x \)[/tex]
3. **Solve for x**:
We now have two solutions for x, a positive and a negative one, because squaring a positive or a negative number both give a positive result. Therefore, we write:
[tex]\( x_1 = +\sqrt{y - 7} \\\\ \( x_2 = -\sqrt{y - 7} \)[/tex]
So, the solutions to the equation [tex]\( y = x^2 + 7 \)[/tex] for x are:
[tex]\[ x = +\sqrt{y - 7} \quad \text{and} \quad x = -\sqrt{y - 7} \][/tex]
Remember that you can only take the square root of a non-negative number in real numbers. So if y - 7 is negative, the solutions for x would be complex numbers.
write fifty-seven and one hundred forty-two thousandths in standard form.
Answers
Fifty-seven and one hundred forty-two thousandths in standard form is 57.142, which is the conventionally written numeric form without placeholder zeroes.
The number fifty-seven and one hundred forty-two thousandths in standard form is written as 57.142. The standard form of writing numbers is also known as conventional notation, which means writing out the number as it is normally seen and used. To convert a number into standard form, you place the decimal point after the last non-zero digit and write out the number without any placeholder zeroes.
The math test scores of Mrs. Hunter's class are shown below.48, 56, 68, 72, 72, 78, 78, 80, 82, 84, 88, 88, 88, 90, 94, 98, 100 What is the range of the scores?
Answers
Highest = 100
lowest = 48
range = 100 - 48 = 52
36 years old. His son is 8 years old. In how many years will Bruce be three times as old as his son?
Answers
---
Equation:
36+x = 3(8+x)
36+x = 24+3x
2x = 12
x = 6 years
A rectangle is 25 inches long and 13 inches wide. What is the area of the rectangle?
Answers
Therefore,
25 x 13 = 325
The answer is 325 inches squared.
Hope this helps! Good luck! :D
Answer:
GUYS HE MEANT 2/5 AND 1/3
Step-by-step explanation:
THE REAL ANSWER IS 2/15
Area of rectangle is given by:
where
A is the area of rectangle
l is the length of the rectangle
w is the width of the rectangle
As per the statement:
a rectangle is 2/5 inches long and 1/3 in wide
⇒
and inches
then using area formula we have;
Simplify:
inches square.
Therefore, the area of rectangle is square inches.
A survey determined that 7/18 of the seventh grade students at Mills Middle School preferred round chocolate candies to hard candy. When Jennifer duplicated the survey, 1/9 of the students changed their preference from chocolate candy to hard candy.
What fraction of the students in the second survey preferred round chocolate candy?
A. 8/27
B. 7/162
C. 5/ 18
D. 1/2
Answers
Answer:
The correct answer is C) 5/18
Step-by-step explanation:
In order to find this answer, you need to take the fraction that answered it on the first try and subtract the number that changed their mind.
7/18 - 1/9
In order to complete this operation, you need to give them common denominators.
7/18 - 2/18 = 5/18
Match the reasons with the statements in the proof.
Given: a | | b, m 2 = m 3
Prove: m 1 = m 3
1. a||b, m∠2 = m∠3
Given
2. m∠1 = m∠2
Substitution
3. m∠1 = m∠3
If lines are ||, corresponding angles are equal.
Answers
Prove: m 1 = m 3
1. a || b, m∠2 = m∠3
Given
2. m∠1 = m∠2
If lines are ||, corresponding angles are equal.
3. m∠1 = m∠3
Substitution
The correct matching of the statement and reasons in the proof given goes thus:
a | | b - - - - - - - - - - GIVEN m∠1 = m∠2 - - - - corresponding angles are equalm∠1 = m∠2 - - - - - SubstitutionThe first reason stated when starting a proof is 'GIVEN' as it has been stated in the question a | | b and m 1 = m 3
From the diagram, the traversal cuts the two parallel lines, creating a corresponding angle at m∠1 and m∠2
Since, we've been told that m1 = m3 in the initial statement, we assign the value of the angle m∠1 to m∠3 (substitution)
Hence, the proof.
Learn more :https://brainly.com/question/6076023
the law of cosines is used to find the value of m. m2 = 272 + 182 ??? 2(27)(18)cos(28??) m2 = 729 + 324 ??? (972)cos(28??) m2 = 1053 ??? (972)cos(28??) To the nearest whole number, the value of m is .
Answers
the law of cosines establishes:
c² = a² + b² - 2 ab cos C
in this problem
a=27
b=18
C=28°
c=m
m² = 27² + 18² - 2*(27)*(18)* cos(28°)
m² = 729 + 324 - 972* cos(28°)
m² = 1053 - 972* 0.8829
m² = 194.82-------------> m=13.96-----------> 14
the answer is m=14 units
What's the explicit formula HELP
Answers
6(6+1)(2(6)+1) / 6
(6*7*13) / 6
546 / 6 = 91
Answer is C
please help with another math question
Answers
2y=4x+20 Eq 1
4y=6x+24 Eq 2
Divide both sides of equation 1 by 2.
y=2x+10
Substitute value of y in equation 2.
4(2x+10)=6x+24
8x+40=6x+24
2x+40=24
2x=-16
x=-8
Put value of x in y=2x+10
y=2(-8) + 10
y=-16+10
y=-6
Answer : (-8,-6)
Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Check all that apply.
y = –x – 2
2x + 5y = −10
2x − 5y = −10
y + 4 = –(x – 5)
y – 4 = (x + 5)
Answers
Writing [tex]5x-2y=-6[/tex] in slope-intercept form:
[tex]5x-2y=-6\\5x+6=2y\\\frac{5x+6}{2}=y\\y=\frac{5}{2}x +3[/tex]
The slope of the line is the number before "x", which is [tex]\frac{5}{2}[/tex].
The slope of the perpendicular to this line is the negative reciprocal of this.
So the slope of perpendicular is [tex]-\frac{2}{5}[/tex].
To find the equation of the perpendicular line, we need a point. It is given as [tex](5,-4)[/tex] where [tex]x_{1}=5[/tex] and [tex]y_{1}=-4[/tex].
Now we use the point-slope form of a line to figure out the equation:
[tex]y-y_{1}=m(x-x_{1})[/tex]
Plugging in the values of [tex]x_{1}[/tex] and [tex]y_{1}[/tex] and [tex]m=-\frac{2}{5}[/tex], gives us:
[tex]y-(-4)=-\frac{2}{5}(x-5)\\y+4=-\frac{2}{5}x+2\\y+\frac{2}{5}x=2-4\\y+\frac{2}{5}x=-2[/tex]
Multiplying everything by 5 [to get rid of the denominator] and re-arranging gives us:
[tex]y+\frac{2}{5}x=-2\\5y+2x=-10\\2x+5y=-10[/tex].
THIS IS THE SECOND OPTION.
ANSWER: [tex]2x+5y=-10[/tex]
what set of transformations could be applied to rectangle ABCD to create A’B’C’D’?
A)Reflected over the x-axis and rotated 180 degrees
B)Reflected over the y-axis and rotated 180 degrees
C)Reflected over the x-axis and rotated 90 degrees counterclockwise
D)Reflected over the y-axis and rotated 90 degrees counterclockwise
Answers
Rectangle ABCD has vertices A(-4,2), B(-4,1), C(-1,1) and D(-1,2).
1. Apply the reflection over the x-axis that has a rule
(x,y)→(x,-y).
Then
A(-4,2)→A''(-4,-2);B(-4,1)→B''(-4,-1);C(-1,1)→C''(-1,-1);D(-1,2)→D''(-1,-2).2. The second transformation is rotation by 90° counterclockwise about the origin. This transformation has a rule
(x,y)→(-y,x).
Then
A''(-4,-2)→A'(2,-4);B''(-4,-1)→B'(1,-4);C''(-1,-1)→C'(1,-1);D''(-1,-2)→D'(2,-1).As you can see these points are exactly those frome the diagram.
Answer: 1st transformation is reflection over the x-axis and second transformation is rotation by 90° counterclockwise about the origin.
A news reporter wants to estimate the percentage of registered voters who will vote for a particular candidate in an upcoming election.
Which statement describes a method that will help him accurately estimate this percentage?
He could ask his readers to respond to a survey that asks which candidate the reader will vote for and then calculate the percentage of people who say that they will vote for the particular candidate.
He could ask employees at the newspaper which candidate each will vote for, and then calculate the percentage who will vote for the particular candidate.
He could contact every resident in the town, ask whether the resident will vote for the particular candidate, and then calculate the percentage of residents who say they will vote for the particular candidate.
He could take a random sample of registered voters, and then calculate the percentage of the sample who will vote for the particular candidate.
Answers
He could take a random sample of registered voters, and then calculate the percentage of the sample who will vote for the particular candidate.
To best determine the number of participants, he can even use Slovin's formula to get better results.
Answer: The answer is d
Step-by-step explanation: I took this test
Your turn: Use the triangle given. What is the value of sin Θ?
Answers
The definition of the sine is
Sin(x) = Opposite / hypotenuse.
Sin(x) = 10/26 = 5/13 The fraction reduces.
The answer is B
Done.
In 1985, there was 285 cell phones subscribers in the small town of centerville.After 1985, the number of subscribers increased by 75% per year. How many cell phones subscribers were in centerville in 1994 ?
Answers
We have then:
y = 285 * (1.75) ^ x
Then, we see how many years there are in the requested period
x = 1994-1985 = 9
We evaluate the function for x = 9
y = 285 * (1.75) ^ 9
y = 43871.98637
Round nearest whole number
y = 43872
Answer:
there were 43872 cell phones subscribers in centerville in 1994
https://s3.amazonaws.com/algebranation/testyourself_uploads/MAFS9/9.029.png
Answers
Answer:
x = 14
x = negative 2
x = 2
x = negative 14
Step-by-step explanation:
Mister Stein is pushin 2.25 lb of meat that cost $2.80 per pound how much change should Mr Stein receive if he gives the cashier 20.00$
Answers
Answer:
13.7 and dang dude is really pushin big P
Step-by-step explanation:
Car = V-8 sedan
Years driven = first and second
Miles driven = 15,000 miles the first year and 12,000 the second
In dollars and cents, the total projected gas and oil cost for two years would be $
Answers
Years driven = first and second
Miles driven = 15,000 miles the first year and 12,000 the second
In dollars and cents, the total projected gas and oil cost for two years would be $
(15,000*.028)=420.00
(336.00*.028)=336.00
420.00+336.00=756.00
Answer:
In dollars and cents, the total projected cost of gas and oil for two years would be $ 756.00
Step-by-step explanation:
Hello! Let's solve this!
First we will calculate per year how much is spent.
First year:
15000 * 0.028 = 420.00
Second year:
12000 * 0.028 = 336.00
The total cost in the two years is the sum of both:
420.00 + 336.00 = 756.00
In dollars and cents, the total projected cost of gas and oil for two years would be $ 756.00
Is this tangent to the circle?
Answers
Yes since (2*6.4)²+9.6²=256=16²
Angle A=90°
[tex] hyp^{2}= adj^{2}+opposite^{2}[/tex]
hypotenuse in here is the 16 unit length side, the adjacent is AB and the opposite is the diameter with length of 6.4 unit length.
if [tex] 16^{2} = 6.4^{2}+9.6^{2}[/tex] then m(A)= 90 degrees and it will be a tangent.
[tex]16^{2}=256[/tex]
[tex]6.4^{2} + 9.6^{2}=40.96+92.16=133.12 [/tex]
so the theorem is not applicable in this situation so the [tex]m(A) \neq 90 degrees[/tex]
therefore AB is not a tangent
help me please. Find the values of x and y that make these triangles congruent by the HL Theorum.
A. x=2, y=1
B. x=3, y=2
C. x=1, y=2
D. x=2, y=3
Answers
well it means that 3y = x + 3, and that y + 1 = x, when does that happen anyway? let's see,
[tex]\bf \begin{cases} 3y=x+3\\ y+1=\boxed{x} \end{cases}\implies 3y=\boxed{y+1}+3\implies 3y=y+4 \\\\\\ 2y=4\implies y=\cfrac{4}{2}\implies y=2\\\\ -------------------------------\\\\ \textit{and since we know that }y+1 =x\implies (2)+1=x\implies 3=x[/tex]
What is the vertex of the parabola?
A. (-1,0)
B. (0,-3)
C. (1,-4)
D. (3,0)
Answers
Option C is correct, the vertex of the parabola is (1, -4).
What is Conic section?Any curve produced by the intersection of a plane and a right circular cone is called as Conic section.
A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
The vertex is either the highest point or the lowest point on the parabola depending on whether the parabola opens upward or downward.
In this case, since the parabola opens upward, we can see that
the vertex is the lowest point on the parabola which is (1,-4).
Hence, Option C is correct, the vertex of the parabola is (1, -4).
To learn more on Conic section click:
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a lab is growing bacteria in a culture dish. the amount of bacteria in the dish doubles every 3 hours. initially, there are 500 bacteria in the dish. how many are in the dish after 9 hours
a. 4,500 bacteria
b. 4,000 bacteria
c. 1,500 bacteria
d. 13,500 bacteria
Answers
I hope it is correct
Answer:
1,500 bacteria so answer C
Step-by-step explanation:
The product of three whole numbers is 120 how many different possibilities are there for the three whole numbers
Answers
2 * 2 * 2 * 3 * 5
I think there are nine different possibilities
1) 8 * 3 * 5
2) 4 * 2 * 15
3) 4 * 6 * 5
4) 4 * 10 * 3
5) 2 * 2 * 30
6) 2 * 3 * 20
7) 2 * 5 * 12
8) 2 * 6 * 10
9) 2 * 15 * 4
Solution:
It is given that,
Product of three Whole numbers = 120
Factorizing 120 into Prime Factors
120 = 2 ×2 ×2×3×5
Number of Possibilities
=Arrangement of 5 things which are numbers(2,2,2,3,5) when 3 of them are equal
= [tex]\frac{5!}{3!}=\frac{5 \times 4 \times 3!}{3!}=5 \times 4 =20[/tex]
What are the domain and range of the function f(x)=1/4(x^3+6x^2+5x-4)
Answers
Answer:
Domain and Range of f(x) is all real numbers i.e [tex](-\infty, \infty)[/tex]
Option 4 is correct.
Step-by-step explanation:
Given the function
[tex]f(x)=\frac{1}{4}(x^3+6x^2+5x-4) [/tex]
we have to find domain and range of the above function.
The domain of a function is the complete set of possible values of the independent variable i.e of x. The denominator function can't be equals to 0 when taking the values of x.
[tex]f(x)=\frac{1}{4}(x^3+6x^2+5x-4) [/tex]
Here the function defines at each and every value of x therefore
Domain of f(x) is all real numbers i.e [tex](-\infty, \infty)[/tex]
The range of a function is the complete set of all resulting values of the dependent variable i.e of y, after substituting the values of the domain.
Range of f(x) is all real numbers i.e [tex](-\infty, \infty)[/tex]
Option 4 is correct.
Answer:
d all infinities
Step-by-step explanation:
A garden has four sides that are all the same length. Each side measures x+4 units. The garden's perimeter is 112 units. What is the value of x? Enter your answer in the box.
Answers
the garden's perimeter is 112 =[(x+4)+(x+4)+(x+4)+(x+4)]
112=4*[x+4]------------ > 112/4=x+4
x=(112/4)-4=28-4=24 units
the answer is x=24 units
Answer: x=24 :)
Step-by-step explanation:
The Art Store sells three types of art pencil sets. The profit is $8.45 on watercolor pencil sets, $6.19 on pastel pencil sets and $4.62 on charcoal pencil sets. There are two branches of the Art Store. The number of sales of pencil sets for each store are shown in the table below.
Set Type
Sales for Westside Branch
Sales for Downtown Branch
watercolor
132
74
pastel
56
48
charcoal
119
126
Which store had the most profit and what was the total profit of that store?
Answers
watercolor
132*(8.45)=1115.4
pastel
56*(6.19)=346.64
charcoal
119*(4.62)=549.78
Total profit= 1115.4 + 346.64 + 549.78 = 2011.82
Sales for Downtown Branch
watercolor
74*(8.45)= 625.3
pastel
48*(6.19)= 297.12
charcoal
126*(4.62)= 582.12
Total profit= 625.3 + 297.12 + 582.12 = 1504.54
Answer:
Westside Branch had the most profit and the total profit of that store was
2011.82$
Answer:
c
Step-by-step explanation:
The length of a rectangle is 4 cm longer than the width. if the perimeter of the rectangle is 20 centimeters, what is the area of the rectangle?
Answers
length=x+4
width=x
2(x)+2(x+4)=20
use the distributive property
2x+2x+8=20
combine like terms
4x+8=20
subtract 8 from both sides
4x=12
divide both sides by 4 to isolate x
x=3
Length=x+4=3+4= 7
Width= 3
The manager of a convenience store wishes to determine how many cartons of eggs are damaged in shipment and delivery. For ten shipments of 1000 cartons of eggs, she examines every 50th carton to see how many cartons contain cracked eggs.
Identify the population and the sample
a.
population: 1,000,000 cartons of eggs
sample: every 50th carton in each shipment
c.
population: 10 shipments of 1000 cartons of eggs
sample: every 50th carton in each shipment
b.
population: 1,000,000 cartons of eggs
sample: the 50th carton of eggs
d.
population: 10 shipments of 1000 cartons of eggs
sample: the 50th carton of eggs
Answers
Answer:
Option c. Population: 10 shipments of 1000 cartons of eggs
sample: every 50th carton in each shipment.
Step-by-step explanation:
First we find out population :
For ten shipments of 1000 cartons of eggs. In other words in each 10 shipments there are 1000 cartons of eggs.
Therefore, 1000 × 10 = 10,000 cartons of eggs.
Population : 10,000 cartons of eggs
Now it is given that she examines every 50th carton to see how many cartons contain cracked eggs.
Hence, Sample would be every 50th carton in each shipment.
In option a and b given cartons of eggs are 1,000,000, so they would be eliminated and in option d it is given that sample is only 50th carton of eggs
Therefore, option c would be correct.