A perpendicular bisector is a line that passes through the midpoint of two points, and is perpendicular to the line connecting the two points.
An example of a perpendicular bisector is the line between points A(2,4) and B(4,6). The midpoint of A and B is (3,5), and the equation of the line perpendicular to A and B is y= -x+10. To verify that the equation is perpendicular to A and B, we can calculate the slope of the line connecting A and B. The slope of A and B is (6-4)/(4-2) which is equal to 2. The slope of a perpendicular line is the negative reciprocal of 2, which is -1/2. Therefore, the equation of the perpendicular line is y = -(1/2)x + 10. This equation passes through the midpoint (3,5) which verifies that it is a perpendicular bisector of A and B.
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A triangle has side lengths of (6a-3b)(6a−3b) centimeters, (5a+5c)(5a+5c) centimeters, and (8c-b)(8c−b) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Answer:
P = a(61a - 36b + 50c) + 10b² + 89c² - 16bc
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsExpand by FOIL (First Outside Inside Last)FactoringGeometry
Perimeter Formula [Triangle]: P = L₁ + L₂ + L₃
L₁ is one sideL₂ is another sideL₃ is the 3rd sideStep-by-step explanation:
Step 1: Define
L₁ = (6a - 3b)(6a - 3b)
L₂ = (5a + 5c)(5a + 5c)
L₃ = (8c - b)(8c - b)
Step 2: Find Perimeter
Substitute in variables [Perimeter - Triangle]: P = (6a - 3b)² + (5a + 5c)² + (8c - b)²Expand [FOIL]: P = (36a² - 36ab + 9b²) + (25a² + 50ac + 25c²) + (b² - 16bc + 64c²)Combine like terms (a²): P = 61a² - 36ab + 9b² + 50ac + 25c² + b² - 16bc + 64c²Combine like terms (b²): P = 61a² + 10b² - 36ab + 50ac + 25c² - 16bc + 64c²Combine like terms (c²): P = 61a² + 10b² + 89c² - 36ab + 50ac - 16bcRearrange variables: P = 61a² - 36ab + 50ac + 10b² + 89c² - 16bcFactor: P = a(61a - 36b + 50c) + 10b² + 89c² - 16bcIn 3 hours, Jim can walk 14 miles. To find the time
he would take to walk 25 miles, he wrote the proportion 3/14= 25/h.
Explain his error.
Answer:
He should have used the proportion:
3/14=h/25
h=5.36 hours
Step-by-step explanation:
He should have used the proportion:
3/14=h/25
14h=3(25)
14h=75
h=5.36
A= bh;
A = 28, h = 4
What is the slope of the line
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
When finding the slope, pick two points on the linear line.
( -1.5, -1) (0.5, 0)
-1.5 is x1
-1 is y1
0.5 is x2
0 is y2
Place these numbers in a slop formula.
m = [tex]\frac{0 - (-1)}{0.5 - (-1.5)}[/tex] = [tex]\frac{1}{2}[/tex]
(m means slope)
Slope = [tex]\frac{1}{2}[/tex]
Answer:
1/2
Step-by-step explanation:
rectangle with length 8 in. and width 6 in.
Answer:
Area of 48
Step-by-step explanation:
Answer:
Area = 48 in square
Perimeter = 28 inches
Hope that helps!
Step-by-step explanation:
math work pls help :)
Answer:
b. side angle side. hope this helps
Which rate does not belong with the other three? 8 pounds for every 2 feet 12 pounds per 3 feet 20 pounds per 4 feet 24 pounds for every 6 feet
Answer:
20 pounds per 4 feet
all the others have the same proportion, 4 pounds per foot
Step-by-step explanation:
To rent a bike, Max pays a flat rate plus an hourly rental fee. The graph shows the amount, c dollars, he pays based on the number of hours, t, he uses the bike.
a) Find the vertical intercept of the graph and explain what information it gives about the situation.
b) Find the slope of the graph and explain what information it gives about the situation.
Answer:
The vertical intercept is 5y. The slope is 1/2
Step-by-step explanation:
Please mark Brainliest
Since my last question got reported ill give branliest + 20 points for like 2 mins of your time
Answer:
the diameter of the semi-circle is 5 in
the area of the shape is 79.63 in squared
Step-by-step explanation:
NEED HELP A mine extracts 2 tons of ore in an hour. Of the total ore extracted in a day, 4 tons is purchased by the government and more than 10 tons is sold to a mineral extractor. If the mine operates for x hours in a day, what is the simplest inequality that represents the number of hours the mine must operate to meet its obligations?
A.
x > 3
B.
x > 4
C.
x > 5
D.
x > 7
Answer:
D. x > 7
Step-by-step explanation:
The mine operates x hours per day and extracts 2 tons of ore per hour.
The amount of ore extracted as a function of hours of operation is
2x
The mine must produce 4 tons plus more than 10 tons each day. The mine must produce more than 14 tons in one day. That means that 2x must be greater than 14.
2x > 14
Divide both sides by 2.
x > 7
Answer: D. x > 7
A $50 item is discounted 30%. How much is the discount?
Answer:
$15
Step-by-step explanation:
Discount = $50 x 30% = $15
Step-by-step explanation:
❁ [tex] \underline{ \underline{ \large{ \tt{ \: G \: I \: V \: E \: N}}}} : [/tex]
Marked price ( MP ) = $ 50Discount % ( Dis % ) = 30 %❁ [tex] \underline{ \underline{ \large{ \tt{ T \: O \: \: F \: I \: N \: D}}}} : [/tex]
Discount amount = ?❁ [tex] \underline{ \underline{ \large{ \tt{S \: O \: L \: U \: T \: I \: O \: N}}}} : [/tex]
[tex] \boxed{ \sf{Discount \: amount = Dis\% \: of \:MP}}[/tex]
Plug the known values :
➝ [tex] \large{ \tt{30\% \: of \: 50}}[/tex]
Convert 30% to fraction. For that divide 30 by 100 and remove the percentage symbol.
➝ [tex] \large{ \tt{ \frac{30}{100} \times 50}}[/tex]
➝ [tex] \large{ \tt{ \bold{ \$ \: 15}}}[/tex]
[tex] \large{ \underline{ \pink {\boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ \bold{ \tt{ \bold{ \$ \: 15}}}}}}}}}}}[/tex]
Hope I helped ! ♡
Have a wonderful day! ツ
# [tex] \underline{ \underbrace{\tt{ \pink{Carry \: on \: learning ! }}}}[/tex]
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
Please help!!! If you can
Answer:
Im guessing its B. Im sorry of this didnt help.
Step-by-step explanation:
[tex]y = 12000 {(1.04)}^{30}[/tex]
Merton's population = 38920.77012
//
18000 + 30(500) = 33000
Hapville's population = 33000
//
38920.77012 - 33000 = 5920.77012
5920.77012 ---> 6000
The answer is B.
Which equation represents the total cost of a repair by an electrician after x hours?
An electrician charges $90 per hour plus a $50 travelling fee.
Answer:
y = 90x + 50
Step-by-step explanation:
In this situation, let's define the variable and the constant.
The variable is what changes, so in this case the wage ($90) changes with how many hours the electrician is hired for.
The constant is the number that stays the same, in this case it would be the $50 traveling fee because it remains the same every time.
The equation should be written in this form:
y = mx + b
m = slope (variable)
b = y-intercept (constant)
Therefore, you can write the equation like this:
y = 90x + 50
Hope this helps!!
- Kay :)
It’s sad when I help people because they don’t do the same thing to so please please please... answer me once :((((((((((((((((((((((((((((((((((((((((((((((
Answer:
Where is the question????????
Friend
What's your question, my friend?
The area of a billboard sign is represented by (x+12)^2 square feet. Find the product
Tamika is ordering a taxi from an online taxi service. The taxi charges $3.50 just for the pickup and then an additional $0.75 per mile driven. How much would a taxi ride cost if Tamika is riding for 5 miles? How much would a taxi ride cost that is m miles long?
Answer:
m= 7.50
Step-by-step explanation:
0.75x5=4.00
4.00+3.50=7.50
A taxi ride cost if Tamika is riding for 5 miles will be $7.25.
What is Linear function?A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph.
Given, Tamika is ordering a taxi from an online taxi service. The taxi charges $3.50 just for the pickup and then an additional $0.75 per mile driven.
Let "m" be the miles Tamika is riding along.
Total additional charges = m *0.75
pick up charges = 3.50
So, Total charges Tamika has to pay for m miles = 0.75*m + 3.50
For m = 5 miles
Tamika has to pay for 5 miles = 0.75 * 5 + 3.50
Tamika has to pay for 5 miles = 7.25
Therefore, 7.25$ would a taxi ride cost if Tamika is riding for 5 miles.
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Which sequence is an arithmetic sequence?
-9, -6, -2, 0
5,7,9,15
3,6,12,24
-7, -3, 1, 5
Answer:
-7, -3, 1, 5 is an arithmetic sequence
What is the quotient of 3/7 and 14?
Answer:
Answer down below
Step-by-step explanation:
If its 3/7 divided by 14 it is 3/98
If its 14 divided by 3/7 it is 98/3
Hope this helps
1. Lawrence's parents pay him a base allowance of $10 per week and $3.20 per hour for extra chores he completes.
Mr. Williams pays Lawrence $7.80 per hour to fix broken washing machines at the laundromat. Which equation
models Lawrence's total weekly income?
Answer: 1. C and number 2 is A
Step-by-step explanation: Hope this helps
What is the y-intercept of the line shown?
−1
0
0.5
1
Answer:
-1
Step-by-step explanation:
It crosses the y axis at negative 1, the y axis is the vertical line
Complete or rewrite each equation using the property indicated (algebra).
Property: Associative
Equation: 5 x (3 x 4)
Rewrite 5 x (3 x 4) in associative property
Please explain.
Answer:
60
Step-by-step explanation:
Ok so,
in PEMDAS the first thing to do is parentheses so 3 times 4 = 12. now it should look like this
5x12 which equals 60
hope this helps! have a good day! please mark brainliest
PLEASE HELP how do i solve (5-3i)^2
Answer:
16-30i
Step-by-step explanation:
This is what I got :)
Answer:
16−30i
Step-by-step explanation:
Use Square of Difference: {(a-b)}^{2}={a}^{2}-2ab+{b}^{2}(a−b)
2
=a
2
−2ab+b
2
.
{5}^{2}-2\times 5\times 3\imath +{(3\imath )}^{2}
5
2
−2×5×3+(3)
2
2 Simplify {5}^{2}5
2
to 2525.
25-2\times 5\times 3\imath +{(3\imath )}^{2}
25−2×5×3+(3)
2
3 Use Multiplication Distributive Property: {(xy)}^{a}={x}^{a}{y}^{a}(xy)
a
=x
a
y
a
.
25-2\times 5\times 3\imath +{3}^{2}{\imath }^{2}
25−2×5×3+3
2
2
4 Simplify {3}^{2}3
2
to 99.
25-2\times 5\times 3\imath +9{\imath }^{2}
25−2×5×3+9
2
5 Use Square Rule: {i}^{2}=-1i
2
=−1.
25-2\times 5\times 3\imath +9\times -1
25−2×5×3+9×−1
6 Simplify 2\times 5\times 3\imath2×5×3 to 30\imath30.
25-30\imath +9\times -1
25−30+9×−1
7 Simplify 9\times -19×−1 to -9−9.
25-30\imath -9
25−30−9
8 Collect like terms.
(25-9)-30\imath
(25−9)−30
9 Simplify.
16-30\imath
16−30
(7a^2 -a + 4) – (3a^2 - 4a - 3)
Step-by-step explanation:
Answer. in the attachment
The value of 23 + 33 = ___. Numerical Answers Expected!
Answer:
75.76%
Step-by-step explanation:
An expression is given
4x + 5y + 7x
Identify the coefficient(s) and constant.
Coefficient: 4,5 and Constant: 7
Coefficient: 4,5,7 and Constant: None
Coefficient: None and Constant: 4,5,7
Coefficient: 4,7 and Constant: 5
Step-by-step explanation:
The coefficients are 4, 5 and 7
There is no constant
The second one is right
Answer:
Coefficient: 4,5,7 and Constant: None
Step-by-step explanation:
A coefficient can be defined as the number next to the variable or unknown numbers
This would be 4, 5, and 7
However, there does not seem to be a constant, which is a value that should not be the coefficient of a variable.
1. Dolores is on a bridge that is 42 feet above a lake. What is the distance from Dolores to the boat? G
Answer:
See answer below
Step-by-step explanation:
You are missing data such as the angle of the boat next to Dolores. I found an exercise similar to this, and I'm going to show it here and use the missing data to show you how to do it:
Dolores is on a bridge that is 45 feet above a lake. She sees a boat at a 30 degree angle of depression. What is Dolores' approximate horizontal distance from the boat?
According to that, I will use the angle of 30° to do this, but the distance of 42 feet.
Now, we can see this as a triangle. Dolores is on a bridge 42 feet above a lake, this 42 feet distance should be one side of the triangle (The vertical forming the 90° angle), and the boat that is on the lake, is seen with an angle of 30°. So the distance of the boat, to the spot where dolores is, under the bridge would be the horizontal side.
With this, we have the opposite side (a) and the adyacent side (b) of the triangle, and we have the angle, therefore:
tanα = a/b
Replacing we have:
tan30° = 42/b
b = 42 / tan30°
b = 72.75 feet
Hope this helps
1. Which of the following is equal to 10
A. (6-2)+3 B. (3+11) 4 C. 12-742 D. 6+5-2
2. Which of the following is NOT equal to 2?
A. 7+5-3 B. -84-941 C. 11-5-4 D. 55+2
3. If a=3, what is the value of a-5?
A.-5
B. -2
C, 2
D. 5
4. Which of the following equations is TRUE?
A (1+7)+3=20-9
C. 12-7-5+(7-6)
B. (6+9) 415-4-2
D. 4-5=3-(2+8)
5. Which of the following is equal to 22?
1. 14+15-5
il. (4)(5)+2
1. 54-24-8
iv. 16+5+10-9
A. i only B. li only C. i, ii, in only D. it, 1, iv only
6. What is the value of the algebraic expression x=3y-1? If y=-9
A.27
B. 28
C.-27
D. -28
7. If x=4, what is the value of the expression 5x+17
A 10
B. 21
C. 32
D. 55
8. Let y=10x-2, what is y when x=4?
A. X=3, y=4 B. X=-2, y=4 C. X=-3, y=2 D. X=4, y=-2
9. Which values of x and y will make the expression 4y-2x equal to -16?
A 10
B. 21
C. 32
D. 55
10. Which expression will snow the value 18 if x = 3?
A. 2x + 6 B. 12+
C. 8x4
D. 5x + 3
Step-by-step explanation:
noneexcept c-2A1+7)+3=20-9il. (4)(5)+2D. -283738D. X=4, y=-2A. 2x + 6Step-by-step explanation:
noneexcept c-2A (1+7)+3=20-9(4)(5)+2-2837389) X=4, y=-2
10) 2x + 6
I need someone to confirm it is this correct?
Answer:
Yes your answers are correct.
Step-by-step explanation:
Answer:
Yes it is. Good job!
Step-by-step explanation:
Among two supplementary angles the measure of the larger angle is 400 more than the
measure of the smaller. Find their measures.
9514 1404 393
Answer:
70° and 110°
Step-by-step explanation:
The sum of angles is 180°; their difference is 40°. So, the larger is ...
(180° +40°)/2 = 110°
The smaller is 180° -110° = 70°
The two angles are 70° and 110°.
_____
Above, we have "cut to the chase." If you let the larger be 'a' and 's' and 'd' represent the sum and difference, you have ...
a + (a-d) = s . . . . the sum of the larger and smaller angles
2a = s+d . . . . . . add d
a = (s+d)/2 . . . . the relation we used.
represent
[tex] \frac{ - 7}{5} [/tex]
on the number line
Given:
The number is [tex]-\dfrac{7}{5}[/tex].
To find:
The location of the given number of the number line.
Solution:
We have,
[tex]Number=-\dfrac{7}{5}[/tex]
It can be written as
[tex]Number=-\dfrac{5+2}{5}[/tex]
[tex]Number=-\dfrac{5}{5}-\dfrac{2}{5}[/tex]
[tex]Number=-1-\dfrac{2}{5}[/tex]
It means the number is less than -1 but more than -2. So, the number lies between -2 and -1.
The mixed fraction form of given number is
[tex]Number=-(1+\dfrac{2}{5})[/tex]
[tex]Number=-(1\dfrac{2}{5})[/tex]
[tex]Number=-1\dfrac{2}{5}[/tex]
Divide the number in 5 equal parts between two consecutive integers.
Now each unit represents [tex]\dfrac{1}{5}[/tex].
Since [tex]Number=-1-\dfrac{2}{5}[/tex], therefore, it is 2 units left from -1.
The number line is given below.