Mathematics College

Given: C is a point on the perpendicular bisector, l, of AB.

Prove: AC = BC

Answers

Answer 1
angles are never isoceles... may be you mean the triangle?
and also, what is C, where is it located? '
Answer 2

Use the drop-down menus to complete the proof. By the unique line postulate, you can draw only one segment, BC. Using the definition of reflection, reflect BC over l. By the definition of reflection, C is the image of itself and A is the image of B. Since reflections preserve length, AC = BC.

Related Questions

Evan is wrapping a shipping box in brown paper the box in the shape of a right rectangular prism the box has a length of 2ft a width of 1 ft and a height of 4 ft how many square feet of brown paper will even need to wrap the entire box? HURRY 25 POINts

Answers

You have 6 sides
2 are 2*1 = 2*2*1 square feet.
2 are 4*1 = 2*4*1 square feet
2 are 4*2 = 2*4*2
The total is 4 + 8 + 16 = 28 square feet.

Determine (without solving the problem) the maximal interval in which the solution of the given initial value problem is guaranteed to exist: ???????? ′ + tan(????) ???? = sin(????) , ????(????) = 6.

Answers

I don’t know the answer to that so just try to solve it in google or in the calculator

How many solutions are there to the system of equations graphed below if the lines are parallel

Answers

If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

Sorry, this is a general answer. I could not view the graph below...

Answer:

Zero

C is the correct option.

Step-by-step explanation:

In the given graph, the given lines are parallel to each other and hence never intersect.

Now, we know that the intersection point (s) of two curves gives us the solution.

Here the lines are parallel to each other and hence do not intersect each other.

Thus, there would not be any intersection point.

Hence, the system of equations has no solution.

C is the correct option.

Jane is going to fence in her back yard. She has purchased 100 feet of fence she wants to fence in a rectangular area where one side will be the back of her house. She knows her house is 30 feet across the back. Which of the following is the equation that Jane can use to figure out how far back from the house she can fence in? A.30x=100 B.x+30=100 C.x+x+30=100 D.30(x+30)=100

Answers

Selection C is appropriate for a fence that extends x feet away from the house and utilizes the full 30 ft width of the house.

Luke records Jesus' visit to Jerusalem when He was twelve years old for the Feast of the

Answers

passover extra words to make 20 characters lol

     



Find the orbital period (in years) of an asteroid whose average distance from the sun is 10 au.

Answers

The orbital period (in years) of an asteroid whose average distance from the sun is 10 AU is 212314723 years.

What is Orbital period ?

Orbital period of a body is the the time taken by a body to cover one circular path around the central object under whose influence it is following circular path.

Given is a asteroid moving around the sun.

Mean distance from the Sun [x] = 10 AU = 1.496 x 10¹² m.

Assume that the time period of the asteroid is T.

The formula to calculate the orbital period around the sun is -

T²/ R³ = 4π²/GM[s]

Where -

R is the mean distance from sun.

G is the universal Gravitation constant.

M[s] is the mass of Sun.

Substituting the values, we get -

T² = (1.496 x 10¹² x 4 x 3.14 x 3.14)/(6.673 x 10⁻¹¹ x 1.98 x 10³⁰)

T² = (59 x 10¹²)/(13.2 x 10⁻¹⁹)

T² = 4.45 x 10 x 10³⁰

T² = 44.5 x 10³⁰

T = √44.5 x √10³⁰

T = 6.7 x 10¹⁵ seconds

In years, the time period will be -

T = 212314723 years (approx.)

Therefore, the orbital period (in years) of an asteroid whose average distance from the sun is 10 AU is 212314723 years.

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A football is kicked off the ground. After traveling a horizontal distance of 24m, it just passes over a tree that is 3m tall before hitting the ground 28m from where it was kicked. a) Consider the ground to be the x-axis and assume the vertex lies on the y-axis. Determine the equation of the quadratic equation that models the path of the ball. b)Determine the maximum height of the ball. c)Suppose the football is kicked from a starting point at the origin. Develop a new equation of the quadratic function of the quadratic function that represents the football.

Answers

Note: The explanation of problems b) and c) are attached as images because of the maximum limit of 5,000 characters.

Answers:

a) [tex]y = -\frac{1}{32} x^2 + \frac{49}{8}[/tex]
b) [tex] \frac{49}{8} \text{ meters} [/tex]
c) [tex]y = -\frac{1}{32} (x-14)^2 + \frac{49}{8}[/tex]

Explanations:

a) Note that the path where the ball travels when kicked off the ground is the parabola. 
Let (h,k) be the vertex of the parabola. Since the vertex is in y-axis, the x-coordinate of the vertex is 0. So, h = 0. 
The equation of the parabola with vertex (h, k) is given by
 [tex]y = a(x - h)^2 + k[/tex]   (1) Since h = 0, we can replace this to equation (1) so that 
 [tex]y = a(x - h)^2 + k\\ y = a(x - 0)^2 + k\\ y = ax^2 + k[/tex]   (2)

To solve for a and k, we need to get the coordinates of the points of parabola. In the problem, it is possible to determine the coordinates of the points where the ball is kicked off from the ground and where the ball ended hitting the ground and the point where the ball hits the tree which are points of the parabola.
Since the ground is in x-axis and the ball is kicked off from the ground and ended hitting the ground, the parabola intersects the x-axis at the points where the ball is kicked off from the ground and where the ball ended hitting the ground. 
Let

A = point where the ball is kicked off from the ground
B =  point where the ball ended hitting the ground
M be the midpoint of A and B.

Note that the x-coordinate of the vertex of the parabola is the same as the x-coordinate of M. Since the x-coordinate of the vertex of the parabola is 0, the x-coordinate of M is 0. Moreover, since the ground is in x-axis, A and B are in the x-axis and so M is in x-axis. So, the y-coordinate of M is 0 because the y-coordinate of any points of x-axis is 0. Thus, the coordinates of M are (0,0).
As mentioned earlier, the y-coordinate of any points in x-axis is 0. Since A and B both lie in x-axis, their y-coordinate is 0. Now, we let j be the x-coordinate of A and k be the x-coordinate of B so that (j, 0) are the coordinates of A and (k, 0) are the coordinates of B.

Since the ball traveled with a horizontal distance of 28 meters when it is kicked off until it hit the ground, the horizontal distance from A to B is 28. Since the coordinates of A and B are (j, 0) and (k, 0) respectively, using the distance formula the distance from A and B is given by 

[tex]d = \sqrt{(j-k)^2 + (0 - 0)^2} \\ 28 = \sqrt{(j-k)^2} \\ (j-k)^2 = 28^2 \\ \boxed{j - k = \pm 28}[/tex]

Since A is the point where the ball is kicked off and B is the point where the ball hits the ground, A is in the left of B. Since A and B are both in x-axis and j and k are the x-coordinates of A and B respectively, j < k. Thus, j - k is negative and so

j - k = -28      (3)

Because M is the midpoint of A and B, the x-coordinate of M is [tex] \frac{j+k}{2}[/tex]. Since the x-coordinate of M is 0,

[tex]\frac{j+k}{2} = 0[/tex]     (4)

Multiplying both sides of equation (4) by 2, we have

j + k = 0   (5)

Now, we add equations (3) and (5) so that 

2j = -28
j = -14

Substituting the value of j in (5), we have

j + k = 0
-14 + k = 0
k = 14

Hence the coordinates of A are (-14,0) and the coordinates of B are (14,0). Since point A is in parabola, we can substitute its coordinates of A in equation (2) with x = -14 and y = 0 so that 

[tex]y = ax^2 + k \\ 0 = a(-14)^2 + k \\ 0 = 196a + k \\ \boxed{196a + k =0} [/tex]      (6)

Note that, if we substitute the coordinate of B, we also arrive at equation (6), which is useless.

So, we need to determine the coordinates of another point of parabola, which is the point where the ball hits the tree. We call this point C. Since the tree is 3 meters high and the ground is in x-axis, the y-coordinate of point C is 3. Let c be the x-coordinate of C. Since the ball hits the tree after travelling a horizontal distance of 24 meters, the horizontal distance from A to C is 24. Moreover, the horizontal distance is the difference of x-coordinates of two points. Since C is the right of A and the x-coordinate of A is -14

c - (-14) = 24
c + 14 = 24
c = 10

Hence, the coordinates of C are (10, 3). Substituting this to equation (2), we have

[tex]y = ax^2 + k \\ 3 = a(10)^2 + k \\ 3 = 100a + k \\ \boxed{100a + k =3} [/tex]       (7)

Subtracting equation (6) to (7), we have

[tex](196a + k)-(100a + k) = 0-3 \\ 96a = -3 \\ \boxed{a = -\frac{1}{32} }[/tex]

Substituting the value of a in equation (6) we have

[tex]196a + k = 0 \\ 196(-\frac{1}{32}) + k = 0 \\ \\ -\frac{49}{8} + k =0 \\ \\ \boxed{k = \frac{49}{8} } [/tex]

Using equation (2) and the values of a and k, the equation of the parabola is given by 

[tex]\boxed{y = -\frac{1}{32} x^2 + \frac{49}{8} }[/tex]

In the number 35.3816, the underlined three is __________ the other three.

Answers

Answer:
100 times bigger 

Explanation:
The given number is:
35.3186

Let's take a look at the first 3 on the left (the one in bold).
We will find that this 3 is in the tens position (10)

Now, let's take a look at the other 3 (the one directly after the point).
We will find that this 3 is in the tenth position (0.1)

Now, when multiplying the digit in the tenth position by 100, this digit would be in the tens position.
This means that the difference between the two positions is 100

Based on this:
The 3 in the tens position is 100 times greater than the 3 in the tenth position.

Hope this helps :)

The x-values in the table for f(x) were multiplied by -1 to create the table for g(x). What is the relationship between the graphs of the two function.

Answers

The graph of f is reflected across the y-axis to create the graph of g. (C)

You are basically assigning the same y-value to the opposite x-values to make g(x). So, for the point (x, 31), on f(x), x is -2, but on g(x), x is 2. Thinking about this visually, you can imagine that this represents a reflection of f across the y-axis.

(Side note: Later in math, this symmetry will be formalized so that you can find it algebraically. It's called "even" symmetry.)

As g(x) is a function that is multiplied by - 1 with f(x) D. They are reflections of each other over x = y.

What is a graph?

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, g(x) is a function that is multiplied by - 1 with f(x).

∴ f(x) = - g(x).

So, They are reflections of each other over x = y.

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Brett is making a fruit salad. The recipe calls for 1
1
2
cups of apple,
3
4
cup of oranges, and
2
3
cup of grapes. How many cups of fruit salad will Brett’s recipe make

Answers

you will just add them all up to find your answer
I'm supposing that those would practically be known to be fractions above, as I can see they are not properly placed in order, but, that would be "ok". So, from knowing this above, the main thing that we would do in this case is to understand that we would then have to consider the question, "how many cups of fruit". Therefore, we would then stop from there, we are going to consider the amount of fruit.We would then do the following:

[tex]\boxed{ 1\frac{1}{2}+ \frac{3}{4} + \frac{2}{3} = 2 \frac{11}{12} }[/tex]

She would then have to use only (2)11/12 of fruit.


Officer Brimberry wrote 8 tickets for traffic violations last week, but only 7 tickets this week. What is the percent decrease? Give your answer to the nearest tenth of a percent.

Answers

The answer is ten percent.
about 12%. you have to subtract 8 by 7 which = 1. Then you would divide one by 8 which is the original number. This would give you .125 which is better to just put as 12%.

Jeff said his City got 11/3 inches of snow.write this fraction as a mixed number

Answers

11 is divisible by three three times with a remainder of two so the mixed number would be 3 2/3
3 2/3 would be the answer

Can you guys help me figure this out ?

Answers

we have that

1 the side opposite ∡L is NM-------------- > is true

2 the side opposite ∡N is ML-------------- > is true

3 the hypotenuse is NM------------> is false
because the hypotenuse is the side NL

4 the hypotenuse is the side NL---------- > is true

5 the side adjacent ∡L is NM-------------> is false
because the sides adjacent are ML and NL

6 the side adjacent ∡N is ML-------------> is false
because the sides adjacent are NM and NL

what is the sum of the rational expressions below? x/x-2 + 7x/x+5
a. 8x/2x+3
b. 8x/x^2+3x-10
c. 8x^2-9x/x^2+3x-10
d. 8x^2-9x/2x+3

Answers

x / x-2 + 7x / x + 5
 What you must do in this case is a sum of fractions.
 Step 1:
 Common factor x in the numerator
 Step 2:
 Make addition of fractions
 Step 3:
 Rewrite the expression.
 See attached image.
 Answer:
 c. 8x ^ 2-9x / x ^ 2 + 3x-10

Final answer:

The sum of the rational expressions is found by obtaining a common denominator, combining the numerators, and simplifying the resulting expression. The correct answer is [tex](8x^2-9x)/(x^2+3x-10).[/tex]

Explanation:

The sum of the rational expressions [tex]x/(x-2) + 7x/(x+5)[/tex] requires finding a common denominator before the sum can be calculated.

The common denominator for these two fractions is the product of the individual denominators (x-2) and (x+5), which is [tex]x^2+3x-10.[/tex]

Once we have a common denominator, we can combine the numerators and simplify the expression as follows:

Multiply the first term by (x+5)/(x+5) and the second term by (x-2)/(x-2) to create a common denominator.

Combine the numerators: [tex]x*(x+5) + 7x*(x-2)[/tex]

[tex]= x^2+5x + 7x^2-14x[/tex]

[tex]= 8x^2-9x.[/tex]

Place the combined numerator over the common denominator: [tex](8x2-9x)/(x^2+3x-10).[/tex]

Therefore, the correct sum of the given rational expressions is option c. [tex](8x2-9x)/(x^2+3x-10).[/tex]

Andrew is given a weekly allowance of $17.50 he uses $4.50 for lunch on Monday what amount at the most can he spend each day if he wants to spend the same amount each of the remaining 4 days write an inequality and solve

Answers

He can spend $3.25 or $3 1/4 because you subtract 17.50 and 4.50 which gives you 13, which you then divide by 4 and get 3.25

The inequality representing Andrew's spending limit is d <= $3.25, where d is the daily spending amount for the remainder of the week. Solving this, Andrew can spend at most $3.25 per day for the next 4 days.

Andrew received a weekly allowance of $17.50. He spent $4.50 on lunch on Monday. The question is how much at most can he spend each day for the remaining 4 days if he spends the same amount each day. To answer this, we subtract the amount spent on Monday from the total weekly allowance to find the remaining balance. Then, we divide this remaining balance by the number of days left in the week to find the daily spending limit:

Total allowance = $17.50

Spent on Monday = $4.50

Remaining balance = Total allowance - Spent on Monday
= $17.50 - $4.50
= $13.00

Days left in the week = 4

Daily spending limit = Remaining balance \/ Days left
= $13.00 / 4
= $3.25

8x-2=46 what is this

Answers

Add 2: 8x=48
Divide 8: x=6
The answer is x=6
If you need me to explain message me
Hope this helps

What are the coordinates of the vertex of the table? I X Y 0 1 -1 -2 -2 -3

Answers

(The vertex formula is derived from the completing-the-square process, just as is the Quadratic Formula. In each case, memorization is probably simpler than completing the square.) For a given quadratic y = ax2 + bx + c, the vertex (h, k) is found by computing h = –b/2a, and then evaluating y at h to find k

i DONT HAVE THE TABLE THAT MENTIONED IN PROBLEM 
We observe that the function is a parabola that grows upwards.
 For this case, we must first graph the function to observe the behavior of the same.
 We see that the vertex of the function is located at the point:
 (x, y) = (- 2, -3)
 The point is a minimum.
 Answer:
 (x, y) = (- 2, -3)
 It is a minimum.
 See attached image.

A rectangular garden originally measured 5 feet by 10 feet as shown below. A path was created around the garden by increasing each side of the original rectangle by x-feet on both sides

Answers

I FOND YOUR COMPLETE QUESTION IN ANOTHER SOURCE.
 PLEASE SEE ATTACHED IMAGE.

 The width of the rectangle in this case will be given by:
 w = x + 5 + x
 Rewriting:
 w = 2x + 5
 The length of the rectangle will be given by:
 L = x + 10 + x
 Rewriting:
 L = 2x + 10
 Answer:
 w = 2x + 5
 L = 2x + 10

Jessie sorted the coins in her bank. She made 7 stacks of 6 dimes and 8 stacks of 5 nickels. She then found 1 dime and 1 nickel. How many dimes and nickels does Jessie have in all?

Answers

Hello!

So, Jessie made 7 stacks of dimes and 8 stacks of nickels.

Each stack of dimes has 6 dimes.

Each stack of nickels has 5 nickels. Multiply:

6 × 7 = 42

8 × 5 = 40

Then she finds another dime and another nickel.

42 + 1 = 43

40 + 1 = 41

43 + 41 = 84

ANSWER:

Jessie has 43 dimes, 41 nickels, and 84 coins in all.

The value of √222 is between which two integers?

a) between 13 and 14
b) between 14 and 15
c) between 15 and 16
d) between 12 and 13

Answers

14 = √196
15 = √225

√196 < √222 < √225
    14 < √222 <  15

b) between 14 and 15

plot on a number line 8 2/5 away from 2 3/4

Answers

First, draw the number line and assign the values of the real numbers that correspond (See the figure attached).
  Now, let's represent the mixed numbers given in the problem.

 Let's start with 8 2/5: This mixed number is located between 8 and 9. The numerator 2 of the fractional part, tells us how far from 8 it will be located  and the denominator 5 indicates how many parts we must divide the space between these two numbers (8 and 9). 

 Now, to plot 2 3/4 on the number line, we have to follow the same proccedure: It is located between the numbers 2 and 3. The numerator 3 of the fractional part, tells us how far from 2 it will be located  and the denominator 4 indicates how many parts we must divide the space between 2 and 3.

what is the mad for 9,7,6,2,2,1

Answers

Answer:

9 + 7 + 6 + 2 + 2 + 1 = 27 ÷ 6 = 4.5

4.5 - 9 = 4.5

4.5 - 7 = 2.5

4.5 - 6 = 1.5

4.5 - 2 = 2.5

4.5 - 2 = 2.5

4.5 - 1 = 3.5

4.5 + 2.5 + 1.5 + 2.5 + 2.5 + 3.5 = 17 ÷ 6 = 2.83 or 2.8

so our MAD is 2.83 or 2.8!

NEED HELP ASAP:
Suppose you pay $24 for a pair of shoes that has been discounted 20%. What is the original price of the shoes? Show how you identify what you are looking for, set up an equation, arrive at your answer, and check your work. Then clearly state your answer.

Answers

The discount rate is 20% so 100% - 20% = 80% of the original price is the final price (before taxes)

x = original price before discount
y = price after discount (before taxes)

y = 80% of x
y = 0.80*x
24 = 0.80*x
24/0.80 = x
30 = x
x = 30

The original price of the shoes was $30


Which line is parallel to line r?

Answers

s is parallel to line r

The average age of instructors at a local college is 55, with a standard deviation of 6 years; the average salary is $37,000 with a standard deviation of $4100. which is more variable?

Answers

To solve for the coefficient of variation you will need this formula:
CV = (SD/X) x 100 
Where: CV = Coefficient of Variance
             X = Mean/average
             SD = Standard Deviation

To determine which one is more variable, just get the coefficient of both and compare.
                   AGE                                            SALARY
   
  CV = (6/55) x 100                             CV = (4,100/37,000) x 100
        = 10.90                                             = 11.08

Based on the results, salary is more variable because 10.90<11.08.

Cheryl falkowski has a collection of silver spoons from all over the world. she finds that she can arrange her spoons in sets of 77 with 44 left​ over, sets of 88 with 33 left​ over, or sets of 1515 with 1414 left over. if cheryl has fewer than 200​ spoons, how many are​ there?

Answers

There are a number of ways to approach this problem, including writing all the numbers that match one of the arrangements, such as for sets of 15:
.. 14, 29, 44, 59, 74, 89, 104, 119, 134, 149, 164, 179, 194 (separated by 15)
Modulo 8, these numbers are
.. 6, 5, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2
This reduces the numbers of interest to those that are 3 modulo 8:
.. 59, 179 (separated by 8*15 = 120)
Looking at these modulo 7, we have
.. 3, 4
pinpointing 179 as the number of spoons in Cheryl's collection.

_____
The attachment shows a solution via graphing calculator. We simply added the absolute values of the differences of the remainders from the desired values and looked for where that sum was zero. This method, too, pointed to 179 as the solution to the problem.

an acute triangle has sides measuring 10 cm and 16 cm. the length of the third is unknown. which is best describes the range of the possible values for the third side of the triangle?


x<12.5'x>18.9


12.5


6

Answers

Answer: 6 < x < 18.9

Justification

1) An acute angle is less than 90° and greater that 0°, i.e. 0 < angle < 90°.

2) The lower bound of the third side is when the angle approaches to zero, this is both sides 10 and 16 almost overlap.

Under this condition the lenght of the third side approaches (never gets to) 16 - 10 = 6.

From this you conclude x > 6.

3) The upper bound of the third side is when the angle approaches 90°, this is the triangle is almost a right triangle. In this case, the upper limit of x is the value of the hypotenuse of a triangle withs legs 10 and 16.

=> x^2 < 10^2 + 16^2

=> x^2 < 100 + 256

=> x^ 2 < 356

=> x < 18.86

So the range is 6 < x < 18.86

Answer:

B 12.5 < x < 18.9

Step-by-step explanation:

I would like to sell 3 gallon cans of peaches. what would the diameter of the base of the can need to be for it to be 6 inches tall and able to hold 3 gallon(s) of liquid? (note: 1 gallon = 231 cubic inches)

Answers

The volume of the cylinder is
.. V = π*(d/2)^2*h
.. 3*(231 in^3) = (π/4)*d^2*(6 in) . . . . fill in the give numbers
.. (3*231*4)/(6π) in^2 = d^2 . . . . . . . . divide by the coeffient of d^2
.. d = √147.06 in ≈ 12.13 in . . . . . . . . take the square root

The diameter of the base would need to be about 12.13 inches.

the surface area of a cone is 150 Pi square inches the radius of the base is 10in what is the slant height

Answers

The surface area of a cone consists of the area of lateral side and the area of the base. The area of lateral side is determined using (π × r × s), s represents the slant height. The area of the base is determined using the formula of the area of a circle.

area of lateral side + area of base = surface area
(π × r × s) + (π × r²) = surface area

Input the numbers
(π × r × s) + (π × r²) = surface area
(π × 10 × s) + (π × 10²) = 150π
10πs + 100π = 150π
10πs = 150π - 100π
10πs = 50π
s = 50π/10π
s = 5
The slant height is 5 inches

Messi kicks a soccer ball from a position that is 3 meters from a sideline and 4 meters from a goal line. the ball lands at a position that is somwhere ... After watching the replay, the ratio between the distance of Messi and the ball is 3/2 meters to the distance between Suarez and the ball.

Answers

The actual answer to this problem is (4.8,7.6)

Using the internal division formula the coordinates of the ball are (4.8,7.6).

Let us assume the x-axis as the goal line and the y-axis as the sideline

So, coordinates Messi≡(3,4)

Similarly, coordinates Suarez≡(6,10)

Let us suppose the ball is somewhere in between Messi and Suarez

Suppose coordinates of the ball ≡(a,b)

Since the ratio between the distance between Messi and the ball to the distance between Suarez and the ball is 3/2.

This means ball is internally dividing Messi and Suarez in 3:2

So, applying the internal division formula for a straight line.

What is the internal division formula for a straight line?

If a point (a,b) is internally dividing a line segment with coordinates of endpoints as (x₁,y₁) and (x₂,y₂) in the ratio m:n then

[tex]a= \frac{m_{1}x_2+m_2x_1 }{m+n}[/tex]

[tex]a= \frac{m_{1}y_2+m_2y_1 }{m+n}[/tex]

So, [tex]a = \frac{3*6 + 2*3}{3+2}[/tex]

[tex]a=4.8[/tex]

[tex]b= \frac{3*10+2*4}{3+2}[/tex]

[tex]b=7.6[/tex]

So, the coordinates of the ball≡(4.8,7.6)

Therefore, Using the internal division formula the coordinates of the ball are (4.8,7.6).

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