Which of the following equations is the perpendicular bisector of the line AB given:
A(3,1) & B(-3,6)
O y = 6/5x + 4
O y = 6/5x + 9/2
O y = 6/5x + 7/2
O y = -5/6x + 7/2
Answers
Answer:
C. y = ⁶/5x + ⁷/2
Step-by-step explanation:
First, find the slope of line AB that goes through A(3, 1) and B(-3, 6):
[tex] slope(m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 1}{-3 - 3} = \frac{5}{-6} [/tex].
Slope of line AB = -⅚.
The slope of the line that is a perpendicular bisector of line AB will be a negative reciprocal of the slope of line AB.
Thus:
Negative reciprocal of -⅚ = ⁶/5. (Reciprocal of ⅚, also the sign will change from positive to negative).
Next is to find the y-intercept, b, of the line.
To do this, you need to find the midpoint where the two lines intersect:
Therefore,
Midpoint (M) of AB, for A(3, 1) and B(-3, 6) is given as:
[tex] M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) [/tex]
Let [tex] A(3, 1) = (x_1, y_1) [/tex]
[tex] B(-3, 6) = (x_2, y_2) [/tex]
Thus:
[tex] M(\frac{3 +(-3)}{2}, \frac{1 + 6}{2}) [/tex]
[tex] M(\frac{0}{2}, \frac{7}{2}) [/tex]
[tex] M(0, \frac{7}{2}) [/tex]
Substitute x = 0, y = ⁷/2, and m = ⁶/5 into y = mx + b and find the value of b.
⁷/2 = ⁶/5(0) + b
⁷/2 = b
b = ⁷/2
The slope (m) and the y-intercept, b, of the line we are looking for are ⁶/5 and ⁷/2, respectively.
Therefore, substitute m = ⁶/5 and b = ⁷/2 into y = mx + b.
y = ⁶/5x + ⁷/2
The equation that is the perpendicular bisector of the line AB is y = ⁶/5x + ⁷/2.
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Rewrite the sum using the GCF and the distributive property:
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Answer:qsgqwgiq
Step-by-step explanation:
8ytyy
105÷35.
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Step-by-step explanation:
solution of the linear equation 3x + 4y= 10
Answers
Add -4y to both sides.
3x + 4y + −4y = 10 + −4y
3x = −4y + 10
Divide both sides by 3.
3x /3 = −4y + 10 /3
x= −4 /3 y + 10 /3
Answer: x= −4 /3 y + 10 /3
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Answer:
1 question : -12
2 question : 3/7
Step-by-step explanation:
Answer:
1. is -12 that's the answer 2. 0.42857142857
Step-by-step explanation:
2. A long jump competition was held at Barangay Mathalino. John Mark
jumped of 6 meters of the field. How far did John Mark jump
Answers
This question is incomplete
Complete Question
A long jump competition was held at Barangay Mathalino John Mark
jumped 2/3 of 6 3/5 meters of the field. How far did John Mark jump?
Answer:
4 2/5 meters
Step-by-step explanation:
We are told:
John Mark jumped 2/3 of 6 3/5 meters of the field.
The distance John jumped us calculated as:
2/3 × 6 3/5 meters
Converting 6 3/5 meters to mixed fraction
= 33/5 meters
Hence, John jumped
=2/3 × 33/5 meters
= 22/5 meters
= 4 2/5 meters
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130 is 1/10 of 13 true or false
Answers
Answer:
This is true.
Step-by-step explanation:
Finding 1/10 of a number is the same as dividing it by 10. 130 divided by 10 is 13.
What is X? 8(5x-5)=8(5x-5)
Answers
Answer:
An infinite number of solutions.
Step-by-step explanation:
When you try to solve for x, the result is 0 = 0.
This means that for any value you plug in for x, the result will always be equal to each other, therefore making the equation true.
What are the solutions of the following system?
(0, –5) and (–5, 5)
(0, –5) and (5, –15)
(0, –5) and (–4, 3)
(0, –5) and (4, –13)
Answers
Step-by-step explanation:
It would be C 0,-5 and -4,3
Answer:
C
Step-by-step explanation:
for edge
Every month, your cell phone plan costs $90 and gives you unlimited talk, unlimited text messages, and 4 GB of data. The cell phone company also charges $20 for each gigabyte over 4 GB of data. How much will you be charged if you use 10 GB of data?
Answers
Answer: You will be charged $ 210 for 10 GB of data.
Step-by-step explanation:
Given : Cost of cell phone plan = $90
Additional charge over 4GB for each GB = $20
If 10 GB data is used , then after 4 GB you need to pay for 6 additional GB (10-4=6)
Total charge = (Cost of cell phone plan)+ (Additional charge) x (Number of gigabytes over 4 GB)
i.e. Total charge = $(90+20(6))
= $ (90+120)
= $ 210
Hence, you will be charged $ 210 for 10 GB of data.
Find the Horizontal Asymptote of the exponential function, and then identify the transformations.
f(x) = -2^(2-5) + 3
Answers
Answer:jjjjjjjjjjjjjjhhhhhhheeeeeeeaaaaa
Step-by-step explanation:
Answer:
f(x)=23/8
Step-by-step explanation:
To find horizontal asymptotes: If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0). If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.
what is the distance between the following point A (-2, -1) and point B (3,2)?
Answers
Answer:
5.83
Step-by-step explanation:
An adult pass for a county fair costs $2 more than a children’s pass. When 378 adult and 214 children’s passes were sold, the total revenue was $2,348. Find the cost of an adult pass.
Answers
378A + 214C = 2384
An adults pass (A) cost two dollars ($2) more than a children’s pass (C).
378 adult passes and 224 children passes are sold. The revenue is 2384.
378(C+2) + 224C = 2384
378C + 2 x 378 + 214C = 2384
592C + 756 = 2384
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There are two equations with two unknowns.
In equation (1) A is already in terms of C so substitute equation (1) into equation (2) and solve for C.
Now that C is know, substitute C back into equation (1) to get A.
Results:
Adult’s cost: $4.75
Children cost: $2.75
brainliest??
Nathan drinks 32 ounces of water per day he read that he should drink 9 ounces per day if he starts drinking 59 ounces per day what is the present increase round to the nearst percent
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Answer:
he is dead from water overdose if he does that
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Three consecutive odd integers are such that the sum of the smallest integer and the largest integer is 86. Find the value of the 2nd number. PLZ HELP
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Answer:
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Step-by-step explanation:
Robin reads 5 pages of a book in 4 minutes. Based on this rate, what is the total number of minutes it will take Robin to read 200 pages?
Answers
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Division is one of the four fundamental arithmetic operations. The time it will take Robin to read 200 pages of the book at the same rate is 160 minutes.
What is Division?The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that it takes Robin 4 minutes to read 5 pages of a book. Therefore, the rate at which Robin reads a page of the book is,
Rate at which Robin reads = 4 minutes/5 pages = 0.8 minutes per page
Now, to know the time it will take for Robin to read the book of 200 pages at the same rate can be found by multiplying the number of pages by the rate of reading. Therefore, the rate at which Robin reads is,
Time to read 200 pages = 0.8 minutes per page × 200 pages
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Step-by-step explanation:
ω = ω₀ + αt
θ = ω₀ t + ½ αt²
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t = (ω − ω₀) / α
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αθ = ω₀ (ω − ω₀) + ½ (ω − ω₀)²
αθ = ω₀ω − ω₀² + ½ (ω² − 2ω₀ω + ω₀²)
αθ = ω₀ω − ω₀² + ½ ω² − ω₀ω + ½ ω₀²
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If B = 1 – q and C = 3q – q? – 1, find an expression that equals B - C
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Answers
Answer:
[tex]q^{2} -4q+2[/tex]
Step-by-step explanation:
1. Samantha has 45 books. She can pack 7 in each box. How many boxes can she completely fill? How many books will be left? A 6 boxes; 3 books B 6 boxes; 2 books C 7 boxes; 0 books D 7 boxes; 3 books
Answers
Answer:
6 boxes, 3 books
Step-by-step explanation:
Samantha has 45 books
She can pack 7 books in each box
The number of box she can completely fill can be calculated as follows
= 45/7
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Answer:
heres an example: Replace all x's in
g(x)
with the function f(x) to get
g(f·x)=(x+3)2
Explanation:
g(f·x)
means that you replace all x's in
g(x)
with the function
(f·x)
The easiest way to do this is rewrite
g(x)
replacing all x's with a blank set of parenthesis, like this
-g(f·x)=(x)2
Now place the function into the parenthesis.
(f·x)
g(f·x)=(x+3)2
Step-by-step explanation:
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Answers
Answer:
No solution
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask me in the comments below :)
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What is f(−4)?
Answers
Answer:
f(-4) = 4
Step-by-step explanation:
Let the equation of the function is,
f(x) = mx + b
where m = slope of the line
b = y-intercept of the line
From the graph attached,
Slope = [tex]\frac{\text{Rise}}{\text{Run}}[/tex] = [tex]\frac{-2}{4}[/tex]
Slope 'm' = [tex]-\frac{1}{2}[/tex]
y-intercept 'b' = 2
Therefore, function will be,
f(x) = [tex]-\frac{1}{2}x+2[/tex]
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f(-4) = [tex]-\frac{1}{2}(-4)+2[/tex]
= 2 + 2
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Which is true from the graph.
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Answers
Answer:
that would be 1.3
Step-by-step explanation:
(thats what my calculator says)
Trevor bought 5 packages of cake mix for $32.50.How much would 8 packages of cake mix cost?
Answers
Answer:
$52
Step-by-step explanation:
32.50/5=6.50
1 costs $6.50
8x6.50=$52
Answer:
$52 dollars because you have to find the original number which is what is 1 box equal to which is $6.50 then you multiply $6.50 by 8 and get $52
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Answer:
answer is 7950
Step-by-step explanation:
compund interest=7950
What is the base of the exponential expression?
Answers
Answer:
B
Step-by-step explanation:
The base is the number the exponent is attached to.
Which phrase describes the solution set for this function?
f(x) = 2(x - 1)2 + 4
A.
one real solution and one complex solution
B.
two complex solutions
O C.
two real solutions
D.
one real solution
Answers
Note: The function is not an equation. I will form and solve an equation to answer the question.
Answer:
C. Two real solutions
Step-by-step explanation:
We have the following function:
f(x)=2(x-1)^2+4
It does not form an equation to solve, and therefore, there are no 'solutions'. We must equate the function to something to set a condition and solve it. We'll complete the equation.
Solve for x when:
f(x)=12
Substituting the function:
2(x-1)^2+4=12
Subtracting 4:
2(x-1)^2=8
Dividing by 2:
(x-1)^2=4
Taking square root:
x-1=\pm\sqrt{4}
Solving:
x=1\pm2
We have two real solutions x=3 and x=-1
Note if we had equated to 4, then the equation would have had only one real solution, and if we had equated to 0, we would have two complex solutions.
The solution of equation f(x) = 2x² - 4x + 6 is two complex solutions. Then the correct option is B.
What is the discriminant?The discriminant of a quadratic is a number that depends on the components and allows some characteristics of the roots to be deduced without calculating them.
The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,
D = b² - 4ac
If D > 0, then the roots are real and distinct root.If D = 0, then the roots are real and equal roots.If D < 0, then the roots are imaginary roots.The equation is given below.
f(x) = 2(x - 1)² + 4
f(x) = 2x² - 4x + 2 + 4
f(x) = 2x² - 4x + 6
The discriminant is given as,
D = (-4)² - 4×2×6
D = 16 - 48
D = - 32
D < 0
The roots are complex root.
The solution of equation f(x) = 2x² - 4x + 6 is two complex solutions. Then the correct option is B.
More about the discriminant link is given below.
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