An equation is formed of two equal expressions. The equation of the perpendicular bisector is y=(1/3)x.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The equation of the line that passes through (2, 4), (3, 1), and (4,-2), are,
m = (4-1)/(2-3) = 3/-1 = -3
Since the product of the slope of two perpendicular lines is -1. The slope of the perpendicular line is,
m₁m₂ = -1
(-3) m₂ = -1
m₂ = 1/3
Since the line is the perpendicular bisector it will pass through midpoint,
1 = (1/3)(3) + C
1 = 1 + C
C = 0
Hence, the equation of the perpendicular bisector is y=(1/3)x.
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Question 9 of 10
Which pairs of angles in the figure below are vertical angles?
Check all that apply.
Answer:
B and C
Step-by-step explanation:
vertical angles are angles that are opposite of each other when two lines cross. Vertical angles are congruent = they are equally large.
the angles listed in B and C are mirrored across either an imaginary or a directly visible line. and that makes them vertical angles.
Helppp
The functions f and g are defined as follows:
#a
[tex]\\ \rm\Rrightarrow f(-4)[/tex]
[tex]\\ \rm\Rrightarrow 3(-4)+2[/tex]
[tex]\\ \rm\Rrightarrow -12+2[/tex]
[tex]\\ \rm\Rrightarrow -10[/tex]
#b
#1
[tex]\\ \rm\Rrightarrow y=\dfrac{2x-1}{3}[/tex]
Interchange x,y[tex]\\ \rm\Rrightarrow x=\dfrac{2y-1}{3}[/tex]
Find y
[tex]\\ \rm\Rrightarrow y=\dfrac{3x+1}{2}[/tex]
Inverse is
[tex]\\ \rm\Rrightarrow g^{-1}(x)=\dfrac{3x+1}{2}[/tex]
#2
[tex]\\ \rm\Rrightarrow gof(x)[/tex]
[tex]\\ \rm\Rrightarrow g(f(x))[/tex]
[tex]\\ \rm\Rrightarrow g(3x+2)[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{2(3x+2)-1}{3}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{6x+4-1}{3}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{6x+3}{3}[/tex]
If we factor out
[tex]\\ \rm\Rrightarrow \dfrac{2x+1}{1}[/tex]
[tex]\\ \rm\Rrightarrow 2x+1[/tex]
#c
[tex]\\ \rm\Rrightarrow f(x)=g(x)[/tex]
[tex]\\ \rm\Rrightarrow 3x+2=\dfrac{2x-1}{3}[/tex]
[tex]\\ \rm\Rrightarrow 3(3x+2)=2x-1[/tex]
[tex]\\ \rm\Rrightarrow 9x+6=2x-1[/tex]
[tex]\\ \rm\Rrightarrow 7x=-7[/tex]
[tex]\\ \rm\Rrightarrow x=-1[/tex]
Answer:
Given functions:
[tex]f(x)=3x+2[/tex]
[tex]g(x)=\left(\dfrac{2x-1}{3}\right)[/tex]
Part (a)
[tex]\begin{aligned}\implies f(-4) & = 3(-4)+2\\& = -12+2\\ & = -10\end{aligned}[/tex]
Part (b)(i)
[tex]\begin{aligned}g(x) & =\left(\dfrac{2x-1}{3}\right)\\\\\textsf{Swap }g(x) \textsf{ for }y : \\\implies y & = \left(\dfrac{2x-1}{3}\right)\\\\\textsf{Make } x \textsf{ the subject}: \\\implies 3y & = 2x-1\\3y+1 & = 2x\\x & = \dfrac{3y+1}{2}\\\\\textsf{Swap }x \textsf{ for }g^{-1}(x) \textsf{ and }y \textsf{ for }x:\\\implies g^{-1}(x) & = \dfrac{3x+1}{2}\end{aligned}[/tex]
Part (b)(ii)
[tex]\begin{aligned}gf(x) & = \dfrac{2[f(x)]-1}{3}\\\\& = \dfrac{2(3x+2)-1}{3}\\\\& = \dfrac{6x+4-1}{3}\\\\& = \dfrac{6x+3}{3}\\\\& = \dfrac{6x}{3}+\dfrac{3}{3}\\\\& = 2x+1\end{aligned}[/tex]
Part (c)
[tex]\begin{aligned}f(x) & = g(x)\\\\\implies 3x+2 & = \dfrac{2x-1}{3}\\\\3(3x+2) & = 2x-1\\\\9x+6 & = 2x-1\\\\7x & = -7\\\\\implies x & = -1\end{aligned}[/tex]
can someone please help me with this
Answer:
[tex]d = \sqrt{109}[/tex]
Step-by-step explanation:
Use the distance formula.
[tex]\text{The distance between two points } (x_1, y_1) \text{ and } (x_2, y_2) \text{ is given by the formula:}\\d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Your points are (-4, 11) and (6, 8).
[tex]d = \sqrt{(-4 - 6)^2 + (11 - 8)^2}\\\\d = \sqrt{(-10)^2 + (3)^2}\\\\d = \sqrt{100 + 9}\\\\d = \sqrt{109}[/tex]
Part D
What is the difference of the earnings of movies C and D for that week?
The difference of the earnings of movies C and D for that week is $10,652,270.46 .
What is the difference in earnings?Subtraction is used to determine the difference between two or more numbers.
The difference = earnings of movie D - earnings of movie C
$34.311,887.98 - 23,659,617.52 = $10,652,270.46
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Will be marked the brainliest if correct
Answer:
6 is the answer
Hope that helps.
Let me know if im wrong :)
Step-by-step explanation:
if population function x has mean M(x)=2 and M(x²)=8, find its standard deviation
The standard deviation of the population function is 2
How to determine the standard deviation?The given parameters are:
M(x) = 2
M(x²)=8
The standard deviation is calculated using:
[tex]\sigma = \sqrt{M(x^2) - (M(x))^2[/tex]
Substitute known values
[tex]\sigma = \sqrt{8 - 2^2[/tex]
Evaluate the expression
[tex]\sigma = 2[/tex]
Hence, the standard deviation of the population function is 2
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In an agricultural class, there are 17 freshmen students and 19 sophomore students. What ratio compares the number of freshmen to the number of sophomores (F:S), and what ratio compares the number of sophomores to the number of freshmen (S:F)
Answer:
Freshmen to sophomores - (17:19)
Sophomores to freshmen - (19:17)
Step-by-step explanation:
I hope this helps! Have a lovely day!! :)
Evaluate P(4, 2)
O 24
O 12
06
Where is the other endpoint located if the midpoint is at (0,-5) and one of the endpoints is (-3,-2)?
Answer:
3,-8
Step-by-step explanation:
x: from -3 to 0 is +3 add +3 more 3
y: from -2 to -5 is -3 add -3 more -8
atty had four times as many quarters as nickels. She had $12.60 in all. How many nickels and how many quarters did
he have?
Which of the following equations could be used to solve the problem?
n+5n=1,260
25n+100 n=1,260
On+ 5 n=12.60
O5 n+100 n=12.60
[tex] \frac{2}{3} n (4p + \sqrt{36} - 2 {n}^{2} [/tex])
n= -3
p=5
need urgent help
Answer:
-16.
Step-by-step explanation:
2/3 * (-3) * (4*5 + 6 - 2(-3)^2)
= -2(20 + 6 - 18)
= -2 * 8
= -16.
Can somebody help me find the surface area
To calculate the area of the complex shape:
⇒ must separate the shape into simpler shape
2 rectangles with a length 9ft and a width 6ft1 rectangle with a length of 9 ft and a width 3ft2 triangles with a base of 3 ft and a height 5.4ftLet's calculate:
2 rectangles with a length 9ft and a width 6ft[tex]Area = 9*6+9*6=54+54=108[/tex]
1 rectangle with a length of 9 ft and a width 3ft[tex]Area= 9*3=27[/tex]
2 triangles with a base of 3 ft and a height 5.4ft[tex]Area = \frac{1}{2}* 3*5.4+\frac{1}{2}* 3*5.4=8.1+8.1=16.2[/tex]
Total Area = [tex]108+27+16.2= 151.2[/tex]
Answer: 151.2 ft²
Hope that helps!
Bill is also planning to buy a condo and he needs to finance $115,000. At which mortgage lender will Bill get the better deal? How much less will Bill pay with this lender?
The better deal based on the information is mortgage A as it's cheaper.
How to calculate the better deal?From the information given, the loan amount for mortgage A will be:
= 3% × $4500
= $135
The loan amount for mortgage B will be:
= 6% × $7500
= $450
From the information, the better deal is mortgage A.
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Can you do it on paper and photos? the answer!
help me
The value of x in all case is
1. The value of x is 2
2. The value of x is 1
3.The value of x is 57
4.The value of x is 93
What is complementary and supplementary angle?If the sum of two angles is 180 degrees then they are said to be b angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.
1. As the given angle is 90 degree i.e., complementary angle.
So,
54+10x+16=90
20=10x
x=2
2. 65x-12=43x+10 (Vertically opposite angle)
22x= 22
x=1
3. 72= x+15 (Vertically opposite angle)
x= 57
4.x+244+23=360 (Complete angle)
x=93
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Question in the Picture
Step-by-step explanation:
the picture is not representing the real angle sizes. so, don't let yourself get confused by that.
the right neighbor angle of 90° at E is also 90°.
it has to be, because it is the supplementary angle to the left 90° (that means together they are 180°).
remember, all angles around a single point on one side of a line have to sum up to 180° (because the line can be seen as the diameter of a circle, with the point being the center of the circle, and so one side of the line is representing a half-circle and therefore 180°).
for the same reason angle 1 (the lower neighbor of the 90° angle at A) is also 90°.
for the same reason the lower neighbor angle of the 60° angle at E is 180 - 60 = 120°.
for the same reason the angle ABC is 180 - 40 = 140°.
for the angle BCD we need to remember :
the sum of interior angles of a polygon with n sides is
(n − 2) × 180°.
in our case ABCDE has 5 sides, so the sum of all interior angles is
(5 - 2) × 180 = 3×180 = 540°
we know 4 of the interior angles already, so
angle BCD = 540 - 90 - 90 - 120 - 140 = 100°
x is now the supplementary angle to the angle BCD.
so,
x = 180 - 100 = 80°
A school has 600 pupils. 1/5are in the upper school, 1/4 in the middle school and the remainder in the lower school. How many pupils are in the lower school?
Answer: 330 pupils
Step-by-step explanation:
the number of pupils are in the lower school
= (1- 1/5 - ¼) × 600
= (20/20 - 4/20 - 5/20)×600
= (11/20) ×600
= 330 pupils
1.
Solve the equation below.
a.
x = 1
x = -2
x = 3
x = -4
b.
C.
d.
2x + 3 = 5
Answer:
a) x = 1
Step-by-step explanation:
Given: 2x + 3 = 5
1. Subtract 3 from both sides:
2x + 3 - 3 = 5 - 3
⟹ 2x = 2
2. Divide both sides by 2:
2x ÷ 2 = 2 ÷ 2
⟹ x = 1
3. Check your work:
2(1) + 3 = 5
2 + 3 = 5
⟹ 5 = 5 ✔
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i need help with this pls
Answer:
The answer is the first bullet. (number 1)
Elijah made 14 quarts of punch for a party. How many gallons of punch did he make?
Answer:
3.5 gallons of punch
Step-by-step explanation:
There are 4 quarts in 1 gallon.
Set up equation to convert 14 quarts to gallons: 14÷4 = 3.5.
Elijah made 3.5 gallons of punch.
Lisa kicked a ball against the wall at the indicated angle. what is the measure, in degrees, of <1?
The measure of angle ∠1 will be 68 degrees.
The missing graph is given below.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
The diagram is given below.
Then the measure of angle ∠1 will be
68° + 44° + ∠1 = 180°
∠1 = 68°
The measure of angle ∠1 will be 68 degrees.
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If the coordinate of A is (0, -2) and the coordinate of B is (10, -6), the then midpoint of \overline{AB} AB is: Part A The X portion of the midpoint is __________________. Part B The Y portion of the midpoint is _________________.
Step-by-step explanation:
it is very simple :
the midpoint coordinates are created as the midpoint of the x coordinates, and the midpoint of the y coordinates.
the x coordinate of the midpoint is
(0 + 10)/2 = 10/2 = 5
the y coordinate of the midpoint is
(-2 + -6)/2 = -8/2 = -4
A six-sided die is rolled seven times. What is the probability that the die will show an even number at least six times?
Answer:
Step-by-step explanation:
Explanation
On a 6 sided die, there are three even numbers (2,4,6)
That's 1/2 the number on the die.
So getting 6 even numbers is
P(6) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 0.00781
Where did that extra 1/2 come from? Well one of the numbers thrown was an odd number, and it has to be counted.
P(7) = the same answer. 0.00781
Total 0.0156
Select the correct answer from each drop-down menu. policy is the actions taken by the to influence the real gdp and the inflation rate in the economy.
Monetary policy is the actions taken by the reserve banks to influence the real GDP and the inflation rate in the economy.
What is Monetary policy?These are actions done by the central bank of a country and involves adjusting money supply so as to achieve economic growth.
This influences the real gross domestic product and inflation rate of the country .
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Answer: Monetary and Reserve Bank
Step-by-step explanation:
;)
Simplify the expression.
(x6y-6)
————
(x8y-8)
PLEASE HELP ASAP <3
Evaluate: 23+x/8 for x = 8
O 24
O 3.875
O 20
O 18
Answer:
Your first step would be to rewrite the equation, were x =8 so it would look like this
Step-by-step explanation:
23 + 8/8 = ?
than solve. 8/ 8 = 1 and 23+1 = 24
One force of 700 pounds and one force of 490 pounds act on a body at the same point so that the resultant force is 1120 pounds. find the angle between the resultant and the smaller force, to the nearest degree.
Answer:
angle 700 < angle 1120 pounds
If LogN= 3.8609, find the value of N, to the nearest integer
[tex]~~~~~~~\log_{10} N = 3.8609\\\\\\\implies N = 10^{3.8609} ~~~~~~~~~;[\log_b c =d \implies b^d = c]\\\\\\\implies N \approx 7259[/tex]
What is the recursive formula for this geometric sequence?
6, -24, 96, -384, ...
Answer: a1=6
An = An-1 - 4
Step-by-step explanation:
N represent what number in the sequence you choose. So in the equation n-1 would be the umber in the equation subtracting 1 then subtracting the difference. The factor you are multiplying by in this sequence is -4. You find the difference by taking any number in the sequence and dividing it by the previous number in the sequence.
Simplify to create an equivalent expression. 2(-n-3)-7(5+2n)
Answer:
-16n-41
Step-by-step explanation:
Answer:
-16n - 41
Step-by-step explanation:
(2 • (-n - 3)) - 7 • (2n + 5)
-n - 3 = -1 • (n + 3)
-2 • (n + 3) - 7 • (2n + 5)
-16n - 41 = -1 • (16n + 41)
Use the leading term for your answer
-16n - 41
Describe how you would The list below shows the ages of all the presidents inaugurated in the twentieth century. Make a stem-and-leaf plot to answer the question.
42, 51, 56, 55, 51, 54, 51, 60, 62, 43, 55, 56, 61, 52, 69, 64, 46, 54
In a stem-and-leaf plot of the data, how many leaves does stem 5 have?show the number 4 and 89 on a stem-and-leaf plot.
The stem-and-leaf plots for both data set are shown in the attachment below.
Stem 5 would have 10 leaves.
How to Make a Stem-and-leaf Plot?For example, if 23, 24, 25, 28 are data points in a data distribution, 2 would be represented as a stem while 3, 4, 5, 8 would be the leaf of the stem. The data would be represented on the stem-and-leaf plot as: 2 | 3, 4, 5, 8.
Given the data, 42, 51, 56, 55, 51, 54, 51, 60, 62, 43, 55, 56, 61, 52, 69, 64, 46, 54, the stem-and-leaf plot is shown in the image attached below.
Stem 5 would have 10 leaves, as shown in the stem-and-leaf plot attached below.
The numbers 4 and 89 are represented on the second stem-and-leaf plot in the attachment below.
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