In triangle ΔABC, with D as a point on AB such that AD = BD = CD = 5, and AB = 6, the length of AC can be found using the Pythagorean theorem. The value of AC is √11.
Let's consider triangle ΔABC with sides AB, BC, and AC. We know that AD = BD = CD = 5, and AB = 6. Since AD = BD, triangle ΔABD is isosceles, and ∠ADB = ∠ABD. Similarly, since BD = CD, triangle ΔBCD is isosceles, and ∠BDC = ∠BCD.
Let's denote the length of AC as x. Now, in triangle ΔADC, using the Pythagorean theorem, we can write:
AC² = AD² + CD²
x² = 5² + 5²
x² = 25 + 25
x² = 50
To find the value of x, we take the square root of both sides:
x = √50
Simplifying the square root, we can write:
x = √(25 * 2)
x = √(5² * 2)
x = 5√2
Therefore, the length of AC is √11.
Learn more about triangle here:
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the length of a box is double of its height and triple of its breadth. If the volume of the box is 556.5 metre cube, find the area of the base of the box.
Answer:
123.2m^2
Step-by-step explanation:
I know I went to 3 decimal places in the paper answer but just go to 1.
*
Is V50 rational or irrational?
Answer:
irrational.
Step-by-step explanation:
what is seven less than a number squared
At the beginning of the summer, Jenna had saved $141. To earn money over the summer, she is working part time at the local community center. She will earn $24 per day of work. If x represents the number of days she works, which of the following equations represents how much money she will have, including her savings?
Answer:
y=24x+141
Step-by-step explanation:
simplify the expression:
3 (3t + 3) =
Answer:
Step-by-step explanation:
All you have to do is multiply the 3
9t + 9
Choose the slope intercept equation of the line that passes through the point (6,4) and is parallel to y= 1/3x-3
Answer:
y=1/3x+2
Step-by-step explanation:
M is the midpoint of the side rectangle. Write down the ratio of the unshaded area to shade area in the form 1:n
Answer:
1:4
Step-by-step explanation:
Have a wonderful day :) and here are free pts to make your day better <3
11 x 11 = ?
Answer:
121
Step-by-step explanation:
Hi there!
How are you?
Answer:
[tex]\boxed{121}[/tex]
Step-by-step explanation:
[tex]11 \times 11 = 121[/tex]
Have a great day/night!
help please this is urgent
Answer:
32.99
Step-by-step explanation:
It took a change of 14.18 degrees to get it from -14.18 to 0, and a change of 18.81 degrees to get it from 0 to 18.81.
14.18 + 18.81 = 32.99
Hope this helps :)
Definition of Inquality
Answer:
inequality: difference in size, degree, circumstances, etc.; lack of equality.
Step-by-step explanation:
Please Help I'd Really Appreciate It.
Answer:
PB = 25
Step-by-step explanation:
T is a point in between P & B. When P & B will be joined , a line segment PB is formed. So ,
PB= PT + TB.
Here the values of PT & TB are given . So,
PB = 15 + 10 = 25
Thang decided to borrow $6000 from his local bank to help pay for a car. His loan was for 3 years at a simple interest rate of 6%. How much interest will Thang pay? Thang will pay $ nothing interest.
Answer:60009
Step-by-step explanation:You have to Add to get your answer.I'll show you how I got 60009:
6000+3=60003
60003+6=60009
Your answer is:60009
i need help fast plz
Answer:
n= 11/12
Step-by-step explanation:
Pls help I cant do math to save my life
Answer:
9x +8 + 6x +7 = 180
15 + 15x = 180
15x = 12
X = 12/15
RQS = 9(12/15) + 8
= 7.2 + 8
= 15.2
TQS = 6 (12/15) + 7
= 4.8 + 7
= 11.8
Please answer in fraction for angle questions
Thank you and please rate me as brainliest.
Temperatures in the Gobi Desert reach −30°F in the winter and 85°F in the summer. Find the range (Difference) of the temperatures. (10 points)
PLEASE EXPLAIN IN WORDS HOW YOU GOT THE ANSWER
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Calculator
Point A is at (6, 1) and point C is at (2, - 7).
Find the coordinates of point Bon AC such that AB
= {BC.
Answer: (4, -3)
Step-by-step explanation:
The Midpoint is the point equidistant from AB and BC.
Use the Midpoint formula:
[tex]M_x=\dfrac{x_1+x_2}{2}\qquad \qquad \qquad M_y=\dfrac{y_1+y_2}{2}\\\\\\M_x=\dfrac{6+2}{2}\qquad \qquad \qquad \quad M_y=\dfrac{1-7}{2}\\\\\\M_x=\dfrac{8}{2}\qquad \qquad \qquad \qquad \quad M_y=\dfrac{-6}{2}\\\\\\M_x=4\qquad \qquad \qquad \qquad \quad M_y=-3[/tex]
(4, -3)
[tex]Write\; an\; equation\; for \;the \;following...\\1...\;(-1, 1), slope = 4\\2...\;(1, 5), slope = 3\\3...\;(-2, 2), slope = -5/6[/tex]
Answer: 1) y = 4x + 5
2) y = 3x + 2
3) y = (-5/6)x + 1/3
Step-by-step explanation:
Use the Point-Slope equation: y - y₁ = m(x - x₁) where
(x₁, y₁) is a point on the linem is the slope(x₁, y₁) = (-1, 1) m = 4
y - 1 = 4(x + 1)
y - 1 = 4x + 4
y = 4x + 5
(x₁, y₁) = (1, 5) m = 3
y - 5 = 3(x - 1)
y - 5 = 3x - 3
y = 3x + 2
(x₁, y₁) = (-2, 2) m = -5/6
y - 2 = -5/6(x + 2)
y - 2 = (-5/6)x - 5/3
y = (-5/6)x + 1/3
What is the quotient of three hundred sixty nine divided by nine
Answer:
= 41
Step-by-step explanation:
I swear I almost forgot how to divide lol
Oop--
Prahlad has a gift card with an initial balance of $180.50. He goes to the
movies each week and spends the same amount each time using the gift
card. After 8 weeks he has $60.50 remaining on the gift card.
What is the rate of change?
Write the equation of a line that passes through (-2, 0) and (3, 10).
Answer:
Step-by-step explanation:
You want to find the equation for a line that passes through the two points:
(-2,0) and (3,10).
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
First, let's find what m is, the slope of the line...
The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.
For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:
So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (-2,0), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=-2 and y1=0.
Also, let's call the second point you gave, (3,10), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=3 and y2=10.
Now, just plug the numbers into the formula for m above, like this:
m=
10 - 0
3 - -2
or...
m=
10
5
or...
m=2
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
y=2x+b
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
(-2,0). When x of the line is -2, y of the line must be 0.
(3,10). When x of the line is 3, y of the line must be 10.
Because you said the line passes through each one of these two points, right?
Now, look at our line's equation so far: y=2x+b. b is what we want, the 2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-2,0) and (3,10).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.
You can use either (x,y) point you want..the answer will be the same:
(-2,0). y=mx+b or 0=2 × -2+b, or solving for b: b=0-(2)(-2). b=4.
(3,10). y=mx+b or 10=2 × 3+b, or solving for b: b=10-(2)(3). b=4.
See! In both cases we got the same value for b. And this completes our problem.
HELPPPPPP ME PLEASEEEEEEE AND THANKKKK UUUUU
Answer:
I know one is zay I think that’s it
Step-by-step explanation:
Question 3 12 points)
(01.06)
1 1
The figure below shows the quotient of 1/2 divided by 1/6
The quotient is
(2 points
Blank 1
Answer:
3
Step-by-step explanation:
Divide
1 over 2
1
2
÷ 1 over 6
1
6
= 6 over 2
6
2
I got It right
What is the common difference between successive terms in the sequence?
0.36,0.26,0.16,-0.04,-0.14
help pls this is a missing assignment
Always. The answer is always
McKenna and Lara work for their uncle Eddie, who repairs skateboards and bicycles. Uncle Eddie is leaving for a vacation to the Amazon. He asks the girls to order 54 new wheels for the 21 skateboards and bicycles in his repair shop. How many bicycles and how many skateboards are in Uncle Eddie's shop? From the list of facts, circle those you need to solve Lara and McKenna's problem. McKenna and Lara's uncle is named Eddie. There are 21 skateboards and bicycles in the shop. Uncle Eddie went on a trip. A bicycle has two wheels, and a skateboard has four wheels. 54 new wheels are needed. How many bicycles and how many skateboards are in the shop? Show your work.
Answer:
There are 21 skateboards and bicycles in the shop.
A bicycle has two wheels, and a skateboard has four wheels
54 new wheels are needed
Number of bicycles = 15
Number of skateboards = 6
Step-by-step explanation:
Number of bicycles and skateboards = 21
Number of new wheels ordered = 54
Number of wheels in a bicycle = 2
Number of wheels in a skateboard = 4
Number of skateboards and bicycles in shop?
Let number of bicycles = b
Number of skateboards = s
b + s = 21 - - - (1)
(2*b) + (4*s) = 54
2b + 4s = 54 - - - - - - (2)
From (1)
b = 21 - s
2(21 - s) + 4s = 54
42 - 2s + 4s = 54
42 + 2s = 54
2s = 54 - 42
2s = 12
s = 6
From : b = 21 - s
b = 21 - 6
b = 15
Number of bicycles = 15
Number of skateboards = 6
The GCD of two numbers is 17 and their LCM is 140.if one of the numbers is 20,find the other number
Question is wrong, please check the question
Two more than-4 times a number is greater than or equal to 26. Then solve.
Find measure of angle 1 in the diagram
Answer:
85
Step-by-step explanation:
Translate: six less than a number is 4 use x as the variable
Answer:
The equation is 6 - x = 4, x = 2
Step-by-step explanation:
Six less than a number is 4
Six less than a number means six minus an unknown number. Is 4 mean that this equation equals 4.
6 - x = 4
Move the six over by subtracting six from both sides
-x = -2
Then divide both sides by -1 so that the x is not negative
x = 2
6 - x = 4, x = 2
Step-by-step explanation:
because you can trust me fam
A lemonade mix calls for 2 tablespoons of mix for every 3 cups of water. If the container
has 24 tablespoons of mix, then how many cups of water will be needed?
Answer:
36 cups of water
Step-by-step explanation:
Make a proportion, where x is the number of cups of water needed:
[tex]\frac{2}{3}[/tex] = [tex]\frac{24}{x}[/tex]
Cross multiply and solve for x:
2x = 72
x = 36
So, 36 cups of water will be needed
Answer:
36
Step-by-step explanation:
