Write an equation of the line passing through point P (2,3) that is perpendicular to the time y-4=-2(x+3)
Answers
The equation of line which is perpendicular to the given line and has a given point is required.
The equation of the line is [tex]y=\dfrac{1}{2}x+2[/tex].
The given line is
[tex]y-4=-2(x+3)\\\Rightarrow y-4=-2x-6\\\Rightarrow y=-2x-2[/tex]
The slope of the given line is [tex]m_1=-2[/tex]
For a line to be perpendicular we have the condition
[tex]m_1m_2=-1\\\Rightarrow m_2=\dfrac{-1}{-2}\\\Rightarrow m_2=\dfrac{1}{2}[/tex]
The point is [tex]P(2,3)[/tex]
The equation will be
[tex]y=m_2x+c\\\Rightarrow 3=\dfrac{1}{2}\times 2+c\\\Rightarrow c=3-1=2[/tex]
[tex]y=\dfrac{1}{2}x+2[/tex]
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The equation of the line passing through point P(2,3) that is perpendicular to the line y-4=-2(x+3) is y = (1/2)x + 2.
Explanation:To find the equation of the line passing through point P(2,3) that is perpendicular to the line y-4=-2(x+3), we need to find the slope of the perpendicular line first. The given line has a slope of -2. The slope of the perpendicular line will be the negative reciprocal of -2, which is 1/2.
Now that we have the slope, we can use the point-slope form of the equation of a line. The equation is given by y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Plugging in the values, we have y - 3 = (1/2)(x - 2).
This simplifies to y - 3 = (1/2)x - 1, and further simplifies to y = (1/2)x + 2.
Related Questions
The sum of two numbers is 35 . the smaller number is 19 less than the larger number. what are the numbers?
Answers
x+x+19=35
2x=16
x=8
x+19=27
the numbers are 8 and 27.
A one celled organism measures 32 millimeters in a length in a photograph. If the photo has been enlarged by a factor of 100, what is the actual length of the organism? Show your work
Answers
Final answer:
The actual length of the organism is 0.32 millimeters, which is obtained by dividing the photograph length (32 mm) by the magnification factor (100).
Explanation:
To determine the actual length of the one-celled organism when the photograph has been enlarged by a factor of 100, we use the formula:
Actual length = Photograph length ÷ Magnification factor
Substituting the given values:
Actual length = 32 mm ÷ 100
Actual length = 0.32 mm
This calculation shows that the actual length of the organism is 0.32 millimeters, which is equivalent to 320 micrometers (320 µm). It's interesting to note that this is well within the size range for many microorganisms, which may require magnification to be seen clearly, such as with a microscope.
He length of a rectangle is six times its width. if the perimeter of the rectangle is 70 in , find its area.
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Which of the following equations represents the perpendicular bisector of WX graphed below?
Thank you! :)
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First, we find the midpoint M using the midpoint formula:
[tex]\displaystyle{ M_{WX}= (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )= (\frac{-5+5}{2}, \frac{2+(-4)}{2} )=(0, -1).[/tex]
Nex, we find the slope of the line containing M, perpendicular to WX. We know that if m and n are the slopes of 2 parallel lines, then mn=-1.
The slope of WX is [tex]\displaystyle{ m= \frac{y_2-y_1}{x_2-x_1}= \frac{2-(-4)}{-5-5}= \frac{6}{-10}= -\frac{3}{5} [/tex].
Thus, the slope n of the perpendicular line is [tex]\displaystyle{ \frac{5}{3} [/tex].
The equation of the line with slope [tex]\displaystyle{ n= \frac{5}{3} [/tex] containing the point M(0, -1) is given by:
[tex]\displaystyle{ y-(-1)=\frac{5}{3}(x-0)[/tex]
[tex]\displaystyle{ y+1= \frac{5}{3}x[/tex]
[tex]\displaystyle{ 3y+3=5x[/tex]
[tex]\displaystyle{ 5x-3y-3=0 [/tex]
Answer: 5x-3y-3=0
Suppose you divide a 52 card deck into its four suits, and draw one card from each suit. what is the probability that you draw two red face cards and the two black aces?
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clover - only 1 black ace
hearts(red) 3 face cards out of 13
spade - only 1 black ace
3/13 * 3/13 *1/13 *1/13 = 9/28561
is it possible to draw three lines in two planes such that all three lines are skew?
Answers
Answer with explanation:
→Two lines in three dimensional plane are said to be Skew if they are neither parallel nor Intersecting.
→Skew lines can be drawn in three dimensional plane only.
→Drawn two skew lines in a Plane , and then drawn another line in a plane and found that , they are skew.
⇒Yes, it is possible to draw three lines in two planes such that all three lines are skew.
Skew lines are non-coplanar lines that are not parallel, and they do not intersect.
In a 2D plane, it is not possible to draw three skew linesIn a 3D plane, it is possible to draw three skew linesThe question does not state the type of plane. So, I will answer this question in 2 ways.
(a) 2D plane
Lines in 2D planes can only be drawn in a flat direction.
This means that, when three lines are drawn in the two planes, one of the following would happen.
The three lines would intersectTwo lines would intersectSee attachment for illustration
So, 3 lines in a 2D plane cannot be skewed lines
(b) 3D plane
Lines in 3D planes can only be drawn in several directions.
The above statement imply that:
Several lines can be drawn where none of the lines would be parallel and none of the lines would intersect.
This means that, when three lines are drawn in the two planes, one of the following would happen.
The three lines would intersectTwo lines would intersectNone of the lines would intersectThe third highlight means that:
It is possible to have skew lines in a 3D plane
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A stop sign is a regular octagon formed by cutting triangles off the corners of a square. if we have a square with sides of length square root 2, what is the side length of the resulting octagon
Answers
The side length of the resulting octagon is 2√2.
Explanation:A stop sign is a regular octagon formed by cutting triangles off the corners of a square. To find the side length of the resulting octagon, we can use the Pythagorean theorem. Since the square has sides of length √2, its diagonal can be found by multiplying its side length by √2. This gives us a diagonal length of 2√2. The diagonal of each triangle cut off the corners of the square will be the side length of the resulting octagon. So, the side length of the octagon is 2√2.
Question 25 the sum of three numbers is 79 . the second number is 9 less than the first. the third number is 2 times the first. what are the numbers?
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Can you help me solve this proof please?
Answers
A can of paint is 15 centimeters high and has a ddiameter of 13.6 cm. what is the volue of the can? Round to the nearest tenth.
Answers
Answer:
V=πr2h=π·6.8^2·15≈2179.00866
2179 cm^3
Step-by-step explanation:
When constructing parallel and perpendicular lines, how are the steps similar
Answers
When constructing parallel and perpendicular lines the steps are similar because they both include creating and connecting intersecting arcs.
Nathan and Steven stacked boxes on a shelf. Nathan lifted 13 boxes and Steven lifted 15 boxes. The boxes that Nathan lifted each weighed 12 lb more than the boxes Steven lifted.
Let s represent the weight of the boxes that Steven lifted.
Which expression represents the total number of pounds Nathan lifted?
s + 12
12(s+13)
15(s+12)
13(s+12)
Answers
13 boxes that each weigh 12 more pounds than steven's boxes.
Answer:
13(s+12) is your answer
Step-by-step explanation:
F. determine if (x + 3) is a factor of (x) = 2x3 + x2 –8x + 21 by using synthetic division. if so, find the other factors.
Answers
-3| 2 1 -8 21 (these are the # without the x)
___________________
-6 15 -21
-------------------------------
2 -5 7 0
Drag the 2 down, multiple it by -3 to get -6
1+(-6) = -5. -5 * -3 =15 . 15+(-8) = 7
7*-3 = -21. -21 +21 = 0
Since last # is 0 we have a factor.
factor is 2x^2 -5x -7 (we start with a power 1 less the original.)
please help. !!!!!!!!
Answers
So
J: (-2,-2)
K: (-1, -4)
I: (-2, -5)
Those are your new points. I hope this helps love! :)
HOW many times can times 6 go into 59
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If 5(x+7)=-3, then 5x+35=-3
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1st step: Distributive Property
5x+35=-3
So, yes this is true.
Help please
Solve for r.
s=2πrh
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hope this helps u
I hope that will help you
Find the lengths of the missing sides if side a is opposite angle a, side b is opposite angle b, and side c is the hypotenuse.
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The length of each side of a square prism is ten ft
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A regular hexagon is shown.
What is the length of the apothem, rounded to the nearest inch? Recall that in a regular hexagon, the length of the radius is equal to the length of each side of the hexagon.
4 in.
5 in.
9 in.
11 in.
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In a 30-60-90 triangle, the sides are is the ratio of:
[tex]x \: \\ x \sqrt{3} \\ and \: 2x[/tex]
where x is opposite the 30° and 2x is opposite the 90°
Since the base is 10 and the hypotenuse is 10, 1/2 that is 5 (the x), and so:
[tex]x \sqrt{3} = 5 \sqrt{3} = 8.66[/tex]
So rounded up, you apothem then is closest to D) 9 in.
The length of the apothem of a regular polygon that has a radius of 10 inches would be 9 inches .
What is the apothem of a regular polygon?The apothem of a regular polygon is defined as a line segment from the center to the midpoint of one of its sides.
It is Given that the hexagon has a radius of 10 inches and the length of the radius is equal to the length of each side of the hexagon.
The apothem AB divides the side of the hexagon into two equal parts of 5 Inches.
Using Pythagoras Theorem
[tex]10^2 = 5^2 + AB^2\\AB^2 = 10^2 -5^2\\AB^2 = 100 - 25\\AB^2 = 75\\AB = \sqrt{75}[/tex]
AB = 8.66
So, rounded up, we get the apothem closest to D that is 9 in.
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Hurry When solving a system of equations, Jared found y = x 10 for one equation and substituted x 10 for y in the other equation. Nicole found x = y – 10 for the same equation and substituted y – 10 for x in the other equation. Who is correct? Explain.
Answers
Jared and Nicole both have found the correct value and will get the same solution to the system of equations.
Given information:
Jared found that [tex]y = \dfrac{x} {10}[/tex] for one equation and substituted [tex]\dfrac{x}{10}[/tex] for y in the other equation.
Nicole found [tex]x = y -10[/tex] for the one equation and substituted [tex]y -10[/tex] for x in the other equation.
So, there are two equations. Based on the question, the equation should be,
[tex]x=10y[/tex] and [tex]y-x=10[/tex].
Now, Jared and Nicole have found the value of one variable from one equation and have put it in the other equation.
This method is the substitution method which is used to find the solution of the system of equations.
Therefore, Jared and Nicole both have found the correct value and will get the same solution to the system of equations.
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Which of these ratios is NOT in simplest form? 12/5 8/5 7/10 9/15
Answers
9 / 3 = 3
15 / 3 = 5
find the difference without using a calculator 201-72.35
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Since its decimal ma!e your equation look like this:
201.00
72.35-
Its going to make 99 because its zeros but add the 1
10-5=5
Then make another 9:
And another use the 2
10-3=7
10-2=8
Which will equals:
201-72.35=128.65
(Since there's 100. Decimal)
As a student you are able to earn extra money by assisting your neighbors with odd jobs. If you charged $10.25 an hour for your assistance about how many hours would you need to work to earn $8,425
Answers
821.9
It would take about 822 hours
For an hour of assistance if a student charged $10.25 than total number hours a student need to work to earn $8,425 is 821.95 hours and this can be determine by the help of unitary method.
Given :
Charge for 1 hour assistance = $10.25
Total earning through assistance = $8425
In this problem unitary method can be use to determine the total number of hours need to work to earn $8425. In unitary method, single unit value is determine first to evaluate the necessary value by multiplying the single unit value.
For an hour of assistance if a student charged $10.25 than total number hours a student need to work to earn $8,425 can be:
[tex]= \dfrac{8425}{10.25} \times 1[/tex]
= 821.95 hours
So a student need to work a total of 821.95 hours to earn $8425.
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Solve 12g=12(2/3g-1)+11
Answers
Put each term in (2 g)/3 - 1 over the common denominator 3: (2 g)/3 - 1 = (2 g)/3 - (3)/3:12 g = 12 (2 g)/3 - (3)/3 + 11
(2 g)/3 - (3)/3 = (2 g - 3)/3:12 g = 12 (2 g - 3)/3 + 11
12/3 = (3×4)/3 = 4:12 g = 4 (2 g - 3) + 11
4 (2 g - 3) = 8 g - 12:12 g = 8 g - 12 + 11
Grouping like terms, 8 g - 12 + 11 = 8 g + (11 - 12):12 g = 8 g + (11 - 12)
11 - 12 = -1:12 g = 8 g + -1
Subtract 8 g from both sides:12 g - 8 g = (8 g - 8 g) - 1
12 g - 8 g = 4 g:4 g = (8 g - 8 g) - 1
8 g - 8 g = 0:4 g = -1
Divide both sides of 4 g = -1 by 4:(4 g)/4 = (-1)/4
4/4 = 1:Answer: g = (-1)/4
On which number line do the points represent negative 4 and 1 over 2 and +3?
Answers
What do they call the guy who invented the first blue jeans
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Answer:
Levi Strauss!
Step-by-step explanation:
By the 1860s, Levi Strauss's blue pants were daily wear for miners and farmers and cattlemen throughout the West. In 1873 he bought, for $69—the price of the patent application — an idea from a Russian immigrant tailor in Reno for making miner's pants stronger by riveting the critical seams.
Hope this helped!
Which inequality describes all the solutions to 5(3 - x) < -2x + 6?
A) x < -9
B) x > 3
C) x > 7
Answers
The inequality describes the solution to 5(3 - x) < -2x + 6 will be x > 3. The correct option is B.
What is inequality?
Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
The given expression 5(3 - x) < -2x + 6 will be solved as below:-
5(3 - x) < -2x + 6
15 - 5x < -2x + 6
-5x + 2x < -15 + 6
-3x < -9
x > 3
Therefore, the inequality describes the solution to 5(3 - x) < -2x + 6 will be x > 3. The correct option is B.
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In isosceles triangle the length of the base is twice shorter than the length of a leg. The perimeter of this triangle is 50cm. Find the lengths of all sides.
Answers
If the short side is X, the other two sides would be 2X and 2X (since the short side is twice shorter)
P = x + 2x + 2x
50 = 5X
10 = X
Short side is 10, other two sides are 2(10) or 20.
The coordinates of the vertices of quadrilateral JKLM are J(-3,2), K(4,-1), L(2,-5) and M(-5,-2).
Find the slope of each side of the quadrilateral and determine if the quadrilateral is a parallelogram.