Answer:
The equation of perpendicular bisector is:
[tex]y = 2x-2[/tex]
Step-by-step explanation:
Given the points
(-4, 3)(8, -3)First, we need to find the midpoint of the points (-4, 3) and (8, -3)
[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-4,\:3\right),\:\left(x_2,\:y_2\right)=\left(8,\:-3\right)[/tex]
[tex]=\left(\frac{8-4}{2},\:\frac{-3+3}{2}\right)[/tex]
[tex]=\left(2,\:0\right)[/tex]
Thus, the midpoint of the points is: (2, 0)
Now, finding the slope between (-4, 3) and (8, -3)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-4,\:3\right),\:\left(x_2,\:y_2\right)=\left(8,\:-3\right)[/tex]
[tex]m=-\frac{1}{2}[/tex]
Therefore, the slope m = -1/2
The slope of the line perpendicular to the segment = [-1] / [-1/2] = 2
Using the point-slope form of the equation of the line, the equation of perpendicular bisector is:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line
substituting the slope 2 and the point (2, 0)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y - 0 = 2 (x-2)[/tex]
[tex]y = 2x-2[/tex]
Therefore, the equation of perpendicular bisector is:
[tex]y = 2x-2[/tex]
What is the value of this expression when g=-3.5?
8 - 12g-51
A.
20
B.
10
O
C. 6
OD.
-4
Answer:
The value of the expression 8 - I2g - 5I is -4 ⇒ D
Step-by-step explanation:
The absolute value always gives a positive value IaI = a and I-aI = a
Let us solve the question
∵ The expression is 8 - I2g - 5I
∵ The value of g is g = -3.5
→ To find the value of the expression substitute g by -3.5
∵ 8 - I2g - 5I = 8 - I2(-3.5) - 5I
∴ 8 - I2g - 5I = 8 - I-7 - 5I
∴ 8 - I2g - 5I = 8 - I-12I
→ By using the rule above
∵ I-12I = 12
∴ 8 - I2g - 5I = 8 - 12
∴ 8 - I2g - 5I = -4
∴ The value of the expression 8 - I2g - 5I is -4
ABCD is a rectangle with sides 6 cm and
8 cm. If its diagonals cross at X, the length
of AX is
Answer:
The length of AX is 5 cm
Step-by-step explanation:
Diagonal of a Rectangle
Given a rectangle of dimensions W by L (as shown in the image below), the diagonal D is the segment that joins two opposite corners of the rectangle.
The diagonals cross at the center of the rectangle in point X, thus the length of AX is half the length of the diagonal.
Note the diagonal is the hypotenuse of a right triangle with legs W and L, thus:
[tex]D^2=W^2+L^2[/tex]
[tex]D^2=6^2+8^2[/tex]
[tex]D^2=36+64=100[/tex]
[tex]D=\sqrt{100}=10[/tex]
The length of the diagonal is 10 cm, thus the required distance is AX=10/2 = 5 cm.
The length of AX is 5 cm
Amanda is choosing between two cells phones plans plan a cost 15+0.08 per minute plan B cost 35 for unlimited calling X represent the number of minutes calling the time and why represents the total cost of the calling plan which system of equations could represent The scenario
Answer:
y = 15 + 0.08x
y = $35
Step-by-step explanation:
Given :
Plan A:
Flat rate = $15
Cost per minute = 0.08
Let x = number of minutes
Total. Cost = flat fee + (per minute charge * number of minutes)
y = 15 + 0.08x
Plan B:
$35 unlimited calling
Total cost, yregardless of minutes used :
y = $35
. Water in a 10 gallon tank is draining at a rate of 2 gallons per hour. Water in a separate tank is filling at a rate of 4 gallons per hour. How long until the tanks have the same amount of water?
Answer:
Step-by-step explanation:
Water in a 10 gallon tank is draining at a rate of 2 gallons per hour.
= 10 - 2x
Water in a separate tank is filling at a rate of 4 gallons per hour.
= 10 + 4x
Equating both Equations together
10 - 2x = 10 + 4x
10 - 10 = 4x - 2x
How long until the tanks have the same amount of water?
Let the time = x
Carlos lives 5 3/8 blocks from a restaurant. The ball field is 7 1 /4 blocks away in the same direction. Carlos plans to go to the restaurant to eat, and then go to the ball field. After he eats, how much farther will he have to walk to get to the ball field?
Answer:
[tex]\dfrac{15}{8}=1\dfrac{7}{8}\ \text{blocks}[/tex]
Step-by-step explanation:
Distance to the restaurant from Carlos is [tex]5\dfrac{3}{8}=\dfrac{43}{8}\ \text{blocks}[/tex]
Distance of the ball field from Carlos' home is [tex]7\dfrac{1}{4}=\dfrac{29}{4}\ \text{blocks}[/tex]
He first goes to the restaurant so he covers a distance of [tex]\dfrac{43}{8}\ \text{blocks}[/tex].
Now the distance from the restaurant to the ball field is
[tex]\dfrac{29}{4}-\dfrac{43}{8}\\ =\dfrac{58-43}{8}\\ =\dfrac{15}{8}=1\dfrac{7}{8}\ \text{blocks}[/tex].
So, Carlos would have to walk [tex]1\dfrac{7}{8}\ \text{blocks}[/tex] farther to get to the ball field.
is 2 greater than negative 2?
Answer:
yes
Step-by-step explanation:
The net of a rectangular prism is shown below. What is the total surface area of the rectangular prism represented by this net?
Answer:
150.88 cm²
Step-by-step explanation:
A rectangular prism also known as cuboid is a three dimensional object with six rectangular faces and eight vertices. It is a prism because it has the same cross section along the length. It is called a rectangular prism because its cross section is rectangular.
The opposite faces of a rectangular prism are equal to each other.
The total surface area (TSA) of a rectangular prism is:
TSA = 2(wl + wh + lh)
where w is the width of the base, l is the length of the base and h is the height of the prism.
From the question, we can see that:
w = 5 cm, l = 7.4 cm and h = 3.1 cm. therefore:
TSA = 2(wl + wh + lh) = 2[(5 * 7.4) + (5 * 3.1) + (7.4 * 3.1)] = 2(37 + 15.5 + 22.94)
TSA = 2(75.44)
TSA = 150.88 cm²
c + d - ___ = c
i dont really get this
Answer:
c + d - d = c
Step-by-step explanation:
c = c
d - d = 0
c + 0 = c
c = c
a blank is a group of data points that are close together?
Answer:
Clustering
Step-by-step explanation:
Data groups that are grouped closely together
Isaac has a bag of n peanuts. He shares the peanuts with 5 of his friends. Each person gets at least 18 peanuts. Write an inequality to represent this situation. *
Answer:
Total number of peanuts =n
He shared with 5 people = 6 people
Each person had at least 18
n/6>=18
Step-by-step explanation:
When question like this is given , the English is very important. He shares with his friends is different from he shares among his friends. Then also, at least means greater than or equal to.
Answer:
18 ≤ n ÷ 6
Step-by-step explanation:
My text book says Isaac has a bag of n peanuts. He shares the peanuts with 5 of his friends. Each person gets at least 18 peanuts. The inequality 18 ≤ n ÷ 6 represents this situation. Graph the solution of this inequality
I NEED HELP ASAP!!!
Answer:
The first and second
Step-by-step explanation:
The first one is right 12/3=4
The second one is right 12*5=60
The third one is wrong 100-184=-84 not 84
A 13 sided figure has how many
total degrees in its interior angles?
9514 1404 393
Answer:
1980°
Step-by-step explanation:
The formula for the sum of interior angles of an n-gon is ...
angle sum = 180°(n -2)
For n=13, the angle sum is ...
angle sum = 180°(13 -2) = 180°×11
angle sum = 1980°
What is the area of a 3/4 yards and 5/6 yard rectangle?
Answer:
3/4 x 5/6 = 15/24 = 5/8 multiply the length and width.
Step-by-step explanation:
Solve the following answer
Answer:
18
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
3x + 2y + 4
x = 2
y = 4
Step 2: Evaluate
Substitute: 3(2) + 2(4) + 4Multiply: 6 + 8 + 4Add: 14 + 4Add: 18Answer:
18
Step-by-step explanation:
3x + 2y + 4 can be broken down like this:
3x = 3 • 2 = 6
2y = 2 • 4 = 8
So, 6 + 8 + 4 = 18.
Hope this helps.
please help and show work if you can
Answer:
14. x = 6, y = 8
15. x = 5, y = 7
16. x = 7, y = 10
Step-by-step explanation:
For a parallelogram, the length across the point of intersection of its diagonals are equal.
So that;
14. PT = TR
QT = TS
So that,
2x = y + 4
2x - y = 4 ...........1
x + 2 = y
x - y = -2 ............. 2
subtract equation 2 from 1,
x = 6
substitute the value of x in equation 1,
2 x 6 - y = 4
y = 12 - 4
= 8
x = 6, y = 8
15. PT = TR
QT = TS
x + 2 = y
x - y = -2 .......... 1
2x = y + 3
2x - y = 3 ......... 2
Subtract equation 1 from 2
x = 5
substitute the value of x in equation 1
5 - y = -2
5 + 2 = y
y = 7
x = 5, y = 7
16. PT = TR
QT = TS
y = x + 3
x - y = -3 ......... 1
2y = 3x -1
3x - 2y = 1 ......... 2
Multiply equation 1 by 2 to have;
2x - 2y = -6 ....... 3
subtract equation 3 from 2
x = 7
substitute the value of x in equation 1
7 - y = -3
-y = -7 -3
-y = -10
multiply through by minus
y = 10
x = 7, y = 10
The cost to enter the fair is $9. Rides cost $5 each. Write the equation to represent this problem.
Class comments
Use the discriminant to determine the number and type of solutions for the equation x^2+49=14x
(A). This equation has 1 real solution and one imaginary solution because the discriminant is negative.
(B). This equation has 2 imaginary solutions because the discriminant is negative.
(C). This equation has 2 real solutions because the discriminant is positive.
(D). This equation has 1 real solution because the discriminant is 0.
Answer:
d is the answer
Step-by-step explanation:
Select the correct answer.
In which table does y vary directly with x?
Answer:
Option C.
Step-by-step explanation:
y and x have a Direct variation if the function looks looks like y = mx (b is equal to zero). The only option that can be written like that is option C. And it can be written as
y = 26x
what is 5x + 2 - 4x +3
Solve for Angle Measures
What is the value of x in the figure?
X =
A cat adoption facility takes in an average of 4 cats per day. The facility has to keep their cat occupancy below 200. Currently, the facility has 164 cats. If none of their cats get adopted, how many more days, x, can the facility continue to take in cats? Select the inequality that includes the largest number of days this facility can continue to take in cats without exceeding its occupancy limit.
i dont understand this question
Explain how to describe the data on a histogram.
Answer:
A histogram shows bars representing numerical values by range of value. A bar chart shows categories, not numbers, with bars indicating the amount of each category. Histogram example: student's ages, with a bar showing the number of students in each year.
Step-by-step explanation:
I HOPE THIS HELPS *
Answer:
A cluster is a group of bars, meaning the frequency is higher in these intervals. A peak is a bar that is higher than the other bars around it. So a peak is where the frequency is highest. Intervals on a histogram where there are no bars means the frequency is 0. If the graph is symmetrical, then the data are evenly distributed.
Step-by-step explanation:
Sample Response on EDG.
how do you solve it tho
Answer:
solve what
Step-by-step explanation:
there's no question
Answer:
you forgot the picture lol
PLEASE SOMONE HELP ME PLEASE I NEED HELP I BEG OF YOU
Answer:
48 feet
Step-by-step explanation:
So first find the amount of fence they would need in terms of x, which would be (x - 2) + (3x - 1) + (5x + 8) + (3x - 1) + (x - 2). Then, you know these add up to 106 so you get the equation:
[tex]x-2+3x-1+5x+8+3x-1+x-2 = 106[/tex]
Now, you just have to solve.
First, combine like terms
[tex]13x + 2 = 106[/tex]
Then, subtract 2 from both sides
[tex]13x = 104[/tex]
Next, divide both sides by 13.
[tex]x = 8[/tex]
The last step is to find the length of 5x + 8 by substituting x = 8 in
[tex]5*8+8=40+8=48[/tex]
what would 5,445 time 5,554 be
Answer:
30241530
Step-by-step explanation:
Plz help u will get branliest!
Solve the system of linear equations by substitution.
3x + y = -9
y=5x+7
Answer:
The solution is x = -2, y = -3
Step-by-step explanation:
Let's start with the equation 3x + y = -9
Substitute the y for 5x+7 seen in the second equation
Now you have 3x + (5x+7) = -9
Lets solve:
Let's add the x's
Now we have 8x + 7 = -9
Substracy seven from each side
Now we have 8x = -16
Now let's divide 8 on each side
Now we have x = -2
Now lets plug in -2 to the second equation
The second equation is y = 5x+7
When we plug in -2 we get y=5(-2)+7
We multiply
We now have y = -10+7
Add
y = -3
The solution is x = -2, y = -3
Brittney attempted to order a set of numbers from least to greatest
-2.9 72/80 2.979 3 1/5 π
what does Brittney need to do to make the order correct?
She needs to convert all the numbers be be the same type ( fraction or decimal).
With the numbers she has it would be easiest to convert all the numbers to decimals.
72/80 = 0.9
3 1/5 = 3.3
Pi = 3.14
Now she can arrange the decimals in order:
-2.9, 0.9, 2.979, 3.14, 3.2
She needs to switch 3 1/5 and pi
Answer:
3 1/5 is tha one
Step-by-step explanation:
M is a multiple of 26. Which of the following cannot be true?
A. M is odd
B. M is a multiple of 3
C. M is 26
D. M is zero