Answer:
The equation of the perpendicular bisector is y = [tex]\frac{-1}{2}[/tex] x - 3
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
m is the slopeb is the y-interceptThe rule of the slope is m = [tex]\frac{y2-y1}{x2-x1}[/tex] , where
(x1, y1) and (x2, y2) are two points on the lineThe rule of the mid-point is M = ([tex]\frac{x1+x2}{2},\frac{y1+y2}{2}[/tex])The product of the slopes of the perpendicular lines is -1, that means if the slope of one is m, then the slope of the other is [tex]\frac{-1}{m}[/tex] (we reciprocal m and change its sign).∵ A line passes through points (-1, 5) and (-7, -7)
∴ x1 = -1 ad y1 = 5
∴ x2 = -7 and y2 = -7
→ Use the rule of the slope above to find the slope of the line
∵ m = [tex]\frac{-7-5}{-7--1}[/tex] = [tex]\frac{-12}{-7+1}[/tex] = [tex]\frac{-12}{-6}[/tex] = 2
∴ m = 2
→ Reciprocal the value of m and change its sign to find the slope of
the line perpendicular line
∴ m⊥ = [tex]\frac{-1}{2}[/tex]
→ Substitute in the form of the equation above
∵ y = [tex]\frac{-1}{2}[/tex] x + b
∵ The ⊥ line is also the bisector of the given line, find the mid-point
of the given line because it is also lying on the ⊥ line
∵ M = ([tex]\frac{-1+-7}{2},\frac{5+-7}{2}[/tex]) = ([tex]\frac{-8}{2},\frac{-2}{2}[/tex]) = (-4, -1)
∴ M = (-4, -1)
→ Substitute the coordinates of M in the equation of the ⊥ line above
∵ x = -4 and y = -1
∴ -1 = [tex]\frac{-1}{2}[/tex] (-4) + b
∴ -1 = 2 + b
→ Subtract 2 from both sides
∴ -3 = b
→ Substitute the value of b in the equation
∴ y = [tex]\frac{-1}{2}[/tex] x + -3
∴ y = [tex]\frac{-1}{2}[/tex] x - 3
∴ The equation of the perpendicular bisector is y = [tex]\frac{-1}{2}[/tex] x - 3
Which expression is equivalent to Negative 2 and one-fourth divided by negative two-thirds?
StartFraction 9 over 4 EndFraction divided by three-halves
Negative StartFraction 9 over 4 EndFraction divided by (negative two-thirds)
Negative StartFraction 9 over 4 EndFraction divided by two-thirds
StartFraction 9 over 4 EndFraction divided by (negative three-halves)
Answer:
ITS B !!!!!!!!!!!!!
Step-by-step explanation:
The equivalent expression is -9/4 ÷ (-2/3).
Option B is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Negative 2 and one-fourth divided by negative two-thirds.
This can be written as,
-2(1/4) ÷ (-2/3)
= -9/4 ÷ (-2/3)
= -9/4 x -3/2
= 27/8 _____(A)
Now,
StartFraction 9 over 4 EndFraction divided by three-halves
This can be written as,
9/4 ÷ 3(1/2)
= 9/4 x 2/7
= 18/28 ______(1)
Negative StartFraction 9 over 4 EndFraction divided by (negative two-thirds)
This can be written as,
-9/4 ÷ (-2/3)
= -9/4 x -3/2
= 27/8 ______(2)
Negative StartFraction 9 over 4 EndFraction divided by two-thirds
This can be written as,
-9/4 ÷ 2/3
= -9/4 x 3/2
= -27/8
StartFraction 9 over 4 EndFraction divided by (negative three-halves)
This can be written as,
9/4 ÷ -3(1/2)
= 9/4 x 2/7
= 18/28
Thus,
From (A) and (2),
-9/4 ÷ (-2/3) is the equivalent expression.
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Sort each equation according to whether it has one solution, infinitely many solutions, or no solution.
5(x - 2) = 5x - 7
One Solution
Infinitely Many Solutions
No Solution
-30% - 4) =-3x + 12
4(x + 1) = 34+4
-2x - 3) = 2X-6
6(x + 5) = 6x + 11
5) Intro
Answer:
Equations with one solution: [tex]-2(x-3) = 2x-6[/tex]
Equations with no solution:
[tex]6(x+5) = 6x+11\\5(x-2) = 5x-7[/tex]
Equations with infinite many solutions: [tex]-3(x-4) = -3x+12[/tex]
Step-by-step explanation:
We will solve each equation to see if it has one solution, no solution or infinite many solutions.
An equation where the value of variable can be found has one solution.
An equation with no solution has both sides different.
An equation with infinite solution will have both sides equal after solution(number)
So,
Equation 1:
5(x-2) = 5x-7
[tex]5(x-2) = 5x-7\\5x-10 = 5x-7\\5x-5x = -7+10\\0 = 3[/tex]
As both sides are not equal, equation has no solution.
Equation 2:
[tex]-3(x-4) = -3x+12\\-3x+12 = -3x+12\\-3x+3x = -12+12\\0=0\\[/tex]
As both sides are equal the equation has infinite many solutions.
Equation 3:
[tex]-2(x-3) = 2x-6\\-2x+6 = 2x-6\\-2x-2x = -6-6\\-4x = -12\\\frac{-4x}{-4} = \frac{-12}{-4}\\x = 3[/tex]
As x=3, the equation has only one solution.
Equation 4:
[tex]6(x+5) = 6x+11\\6x+30 = 6x+11\\6x-6x+30 = 11\\30 =11[/tex]
The equation has no solution.
Hence,
Equations with one solution: [tex]-2(x-3) = 2x-6[/tex]
Equations with no solution:
[tex]6(x+5) = 6x+11\\5(x-2) = 5x-7[/tex]
Equations with infinite many solutions: [tex]-3(x-4) = -3x+12[/tex]
What is 5 Left-bracket cosine (StartFraction pi Over 4 EndFraction) + I sine (StartFraction pi Over 4 EndFraction) right-bracket raised to the 3rd power?
Answer:
C
Step-by-step explanation:
I took it on edg 2020
The Complex Alternative form to the expression (5[cos(π/4) + i sin(π/4)])^3 is given as: (Option C).
What is a complex Alternate form?A complex number of equations will take the form x + yi, where x and y are real numbers and i is an indeterminate that satisfies the rule i² = -1.
Hence, the solution to the above is given as follows:
Step 1 - Ludooph's number pi is given as:
π ≈ 3.14159265
Step 2 - Divide 3.14159265/4
= 0.78539816
Step 3
Cos (0.78539816)
= 0.70710678
It is assumed that the trigonometric angle argument is in radians.
Step 4
Divide: 3.14159265 / 4
= 0.78539816
Step 5 - find the Sin of the result of step 4
sin(0.78539816)
= 0.70710678
It is assumed that the trigonometric angle argument is in radians.
Step 6
Multiply i by the result of Step No 5
= i * 0.70710678
= 0.7071068i
Step 7 - Add the result of step no. 3 and the result of step number 6
= 0.70710678 + 0.7071068i
= 0.7071068+0.7071068i
Step 8 Multiply 5 by the result of step 7
= 5 * (0.7071068+0.7071068i)
= 5 * 0.70710678118655 + 5 * 0.70710678118655i
= 3.53553391+3.53553391i
= 3.53553391 +i(3.53553391)
= 3.5355339+3.5355339i
Step 9 - Exponentiate the results of Step 8 to the third power:
= (3.5355339+3.5355339i) ^ 3
= (5 × ei π/4)3 = 53 × ei 3 × π/4
= 125 × ei 3π/4
= -88.3883476+88.3883476i
If left in the Alternate Complex form, we have:
125[cos(3π/4) + i sin(3π/4)]
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What is a reasonable estimate for the addition equation 1.5 + 0.9 = ________ when you round each addend to the nearest whole number? (2 points)
A. 1.5
B. 2
C. 2.5
D. 3
In a sale, a shopkeeper reduced the advertised selling price of a dress by 20%. This resulted in a profit of 4% over the cost price of the dress. What percentage profit would the shopkeeper have made if the dress had then been sold at the original selling price?
HELP my dad will kill me if I don't finish this and I'm stuck on this question
Answer:
30% profit
Step-by-step explanation:
The amount by which the shopkeeper reduced the advertised selling price = 20%
The resulting profit over the cost price = 4%
Let x represent the initial advertised selling price, and let y represent the new selling price, and let c represent the cost price, we have;
x - 20% of x = y
x - x × 20/100 = y
0.8·x = y
y = c + 4% of c = 1.04·c
∴ 0.8·x = 1.04·c
x = 1.04·c/0.8 = 1.3·c
x = 1.3·c = c + 0.3·c = c + 30% of c
x = c + 30% of c
From which we have that the initial advertised selling price, x = The cost price + 30% of the cost price
Therefore, the initial advertised selling price = The cost price + 30%profit on cost price.
The shopkeeper would have made 30% profit if the dress had then been sold at the original selling price.
For a new neighborhood, 1.4 acres of land will be split into 8 lots. How many acres of land
will each lot have?
Answer:
0.175
Step-by-step explanation:
8/1.4 = 0.175 which is how many each will have
write a linear equation given the two points 3,4 and 0,5
Answer:
where is the graph
Step-by-step explanation:
did your teacher put in a graph
what is it called when a sea bird lands on a channel maker
Answer:
This question is actually a riddle. The answer to this riddle is, "Buoy meets gull."
Step-by-step explanation:
Answer:
ligand-gated channel.
Step-by-step explanation:
Describe the set of all complex numbers that are at a distance of 2 units from the origin.
Answer:
The description of the set is [tex]A = \{s\in \mathbb{C}|\|s\| = 2\}[/tex].
Step-by-step explanation:
From Complex Analysis, we remember that complex numbers are numbers whose form is:
[tex]s = a+i\, b[/tex], [tex]a,b \in \mathbb{R}[/tex] (1)
Where [tex]i = \sqrt{-1}[/tex].
In addition, the distance from the origin is defined by the following Pythagorean identity:
[tex]\|s\| = \sqrt{a^{2}+b^{2}}[/tex] (2)
The following condition must be satisfied:
[tex]\|s\| = 2[/tex]
Then, the set of all complex numbers that are at a distance of 2 units from the origin is described below:
[tex]A = \{s\in \mathbb{C}|\|s\| = 2\}[/tex] (3)
The set of all complex numbers that are at a distance of 2 units from the origin is [tex]\{z\in \mathbb{C} :\text{ }|z|=2\}[/tex]
A complex number, written in rectangular form is
[tex]z=a+ib\\a,b\in \mathbb{R}[/tex]
The distance of a complex number from the origin (the modulus of the complex number, denoted by [tex]|z|[/tex]) is given by the formula
[tex]|z|=\sqrt{a^2+b^2}[/tex]
Since we want all the complex numbers to be at the distance of 2 units from the origin, they must satisfy
[tex]|z|=2[/tex]
thus, the set we are looking for is
[tex]D=\{z\in \mathbb{C} :\text{ }|z|=2\}[/tex]
where [tex]\mathbb{C}[/tex] is the set of all complex numbers
Learn more about complex numbers here: https://brainly.com/question/12274048
what is the answer to this question. PLEASE HELP
Answer:
Im going to guess a i have no idea tho
Step-by-step explanation:
A box has 5 marbles numbered from 1 to 5. Determine the following theoretical probabilities of the totals of two marbles ( a marble is taken from the box, the number noted, put back in the box, and then a second marble taken from the box and the number noted)
a) P(a total of 4)
b) P(a total of 5)
c) P(an odd total)
Answer:
4
Step-by-step explanation:
can someone do 6,7 and 8 pls
Question 6
Given the points
(-2, 1)(-3, -3)Finding the slope between (-2, 1) and (-3, -3)
[tex]\left(x_1,\:y_1\right)=\left(-2,\:1\right),\:\left(x_2,\:y_2\right)=\left(-3,\:-3\right)[/tex]
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-3-1}{-3-\left(-2\right)}[/tex]
[tex]m=4[/tex]
Question 7
Given the points
(-4, 3)(-2, -1)Finding the slope between (-4, 3) and (-2, -1)
[tex]\left(x_1,\:y_1\right)=\left(-4,\:3\right),\:\left(x_2,\:y_2\right)=\left(-2,\:-1\right)[/tex]
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-1-3}{-2-\left(-4\right)}[/tex]
[tex]m=-2[/tex]
Question 8
Given the points
(0, -2)(0, -4)Finding the slope between (0, -2) and (0, -4)
As we know that the slope of the line given by the equation x=0 is undefined.
[tex]\mathrm{m}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-4-\left(-2\right)}{0-0}[/tex]
[tex]=\frac{-4+2}{0}[/tex]
[tex]=\frac{-2}{0}[/tex]
= ∞
Answer:
nah im good XD
Step-by-step explanation:
HELP PLEASE 20 POINTS
Solve for x for both and show how you got the answer (WILL MARK BRAINLIEST)
Answer:
1.) 9.32
2.) 4.82
Step-by-step explanation:
neat trick i learned that really helps: SOH-CAH-TOA
Sine (opposite, hypotenuse), Cosine (Adjacent, Hypotenuse), Tangent (Opposite, Adjacent)
1.)
sin(21) = x/26 <----------- multiply by 26 to get x by itself
26*sin(21) = x <----------- multiply 26 by sin(21)
9.32 = x <------ rounded answer
2.)
cos(64) = x/11 <------------ multiply by 11 to get x by itself
11*cos(64) = x <---------------- multiply 11 by cos(64)
4.82 = x <-------- rounded answer
Evaluate the diagram below.
Find the value of x and the measure of side EF.
Answer:
x=5
EF = 22in.
Step-by-step explanation:
We know EF and DE are equal, so we can solve for x.
5x-3=3x+7
5x-3x=7+3
2x=10
x=5
Now we plug that into EF.
EF = 3x+7 = 3(5)+7 = 15+7=22
Please help with numbers 6,7,8 will brainlist
Answer:
6. -3
7. 16
8. -39
Step-by-step explanation:
describe the slope of the line and then find the slope.
Answer:
-4/3
Step-by-step explanation:
The line is decreasing so the slope will be negative. The slope formula is [ y2-y1/x2-x1 ].
-1-3/1-(-2)
-4/3
Best of Luck!
Tara owns a pizza shop. She sells pizzas for $6.00 plus a $10 delivery fee.If you are having a party and you have $58 how many pizzas can you buy?
Answer:
You can buy 8 pizzas
Step-by-step explanation:
$58 - $10 = $48
$48/$6 = 8
What is the area of a circle with a diameter of 200cm? Use 3.14 for pie.
Answer:
A≈31415.93cm²
Step-by-step explanation:
what’s the slope of (1,7) and (6,10)
marco needs to buy some cat food. At the nearest store, 3 bags of cat food cost 13.50. How much would Marco spend on 5 bags of cat food
Answer:
$22.50
Step-by-step explanation:
if 3 bags of cat food = 13.50, divide 13.5 by 3 to get the cost of one bag, which is $4.50.
since hes getting 5, we can use 13.50 once and then the price of one bag (4.5) twice for the other two.
so that would be 13.5 + 4.5 + 4.5 = $22.50
hope this helped :)
Answer:
cost of three bags of cat food = 13.50
cost of 1 cat food = 13.50/3 = 4.50
cost of 5 cat food = 4.50*5 = 22.5
Step-by-step explanation:
BRAINLIST +50 POINTS
Answer:
The answer is first one.
Hope it helps uh!
3) 7.NS.1.b *
The temperature on Sunday was 87°F. On Saturday the
temperature was 4°F higher. On Friday the temperature was 7°F
lower than on Saturday. What was the temperature on Friday?
Answer:
84°
Step-by-step explanation:
Answer:
84
Step-by-step explanation: It says 4 high which meanS added by four then it says 7 lower than it means subtract by it.
please answer for me appreciate it
Please help ASAP I will give brainliest
Answer:
the answer is -3
have a nice day
Find the measure of
Answer:
46 degrees
Step-by-step explanation:
I would assume that angle is 90 degrees, as there is no way to find the measure if it isn't. You subtract 43 from 90 and get 46 so the 2nd angle is 46 degrees. Can I get brainliest?
The ticket sales for a concert started at 4:00 P.M. The table shows the linear relationship
between the number of tickets remaining and the number of hours since 4:00 P.M.
Ticket Sales
Answer: I just took the test so the answer would be y=3,000x+12,000
Step-by-step explanation: hope this help thx for the points :D
PLEASE HELP, DUE SOON!!
Answer:
x= 34 y= 99 z= 41
Step-by-step explanation: A.
Answer:
D
Step-by-step explanation:
First I solved for the triangle on the right by adding 58 and 81 then subtracting by 180 and I got 41 degrees for the missing angle. Now for the left triangle you subtract 47 from 180 and you get 133. Answer choice D is the only answer choice that has x and y equal to 133 this is why answer choice D is the correct solution.
If you liked my answer then please mark it as the brainliest it would be much appreciated. Thanks!
I needddd helppppp pleaseee
Answer:
w = 59°
Step-by-step explanation:
sides AC and BC are congruent thus Δ ABC is isosceles, then the 2 base angles are congruent, that is
∠ A = ∠ B , so
w = [tex]\frac{180-62}{2}[/tex] = [tex]\frac{118}{2}[/tex] = 59°
True or False
It is possible to have complementary angles where one is acute and one is obtuse.
Explain why or why not.
Answer:
A triangle cannot be right-angled and obtuse angled at the same time. Since a right-angled triangle has one right angle, the other two angles are acute. Therefore, an obtuse-angled triangle can never have a right angle; and vice versa. The side opposite the obtuse angle in the triangle is the longest.
Step-by-step explanation: