In right triangle ABC, AC = 4 and BC = 5. A new triangle DEC is formed by connecting the midpoints of AC and BC. What is the area of triangle ABC? *
Answers
You can use the Pythagoras theorem to find the height of the triangle given and then by the height and the base of the triangle, you can find its area.
The area of the triangle ABC is 6 square units.
Right angled triangle:A right angled triangle is a triangle having one of its angle with measure of 90 degrees.
The slant side of that triangle is called Hypotenuse and it is the longest side in that triangle.
The Pythagoras theorem:If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|2[/tex]
How to find the area of given right angled triangle ABC?Refer to the diagram attached below.
Since we have right angle at angle A, and we have
|AC| = 4 units, |BC| = 5 units, let |AB| = [tex]x[/tex] units, then
[tex]|AC|^2 + |AB|^2 = |CB|^2\\4^2 + x^2 =5^2\\x ^2 = 25-16\\x = \sqrt{9} = 3 \text{\:(Positive root since x is length which is non negative quantity)}[/tex]
Area of a triangle is half of its base times height.
Since the line AC s perpendicular to AB, thus we can take base as AB and height as AC, then we have:
[tex]Area = \dfrac{1}{2} \times |AC| \times |AB| = \dfrac{1}{2} \times 4 \times 3 = 6 \: \rm unit^2[/tex]
Thus,
The area of the triangle ABC is 6 square units.
Learn more about right angled triangles here:
https://brainly.com/question/4456796
Related Questions
Round to the nearest tenth.
x=
y=
Answers
Cos 55 = y/21 —> y= 21 * cos 55=12.0
Can you mark it brainliest?
least common denominator of 1/5 and 1/10
Answers
1/5 cannot be broken down anymore.
Therefore, what is equal to or less than 1/10 that 1/5 can reach? 1/10.
1/10 is the least common denominator.
Step-by-step explanation:
dhdnjdbdjfdnjdnednrjfjfr
Find the equation of a line that contains the points (4,−1) and (−1,−4). Write the equation in slope-intercept form, using fractions when required.
Answers
Answer:
y = 3/5x - 17/5
Step-by-step explanation:
slope formula: (y₂ - y₁) / (x₂ - x₁)
First, plug in these values of the two given points.
(-4 - (-1)) / (-1 - 4)
Simplify within the parentheses.
(-4 + 1) / (-1 - 4)
(-3) / (-5)
3/5
This is your slope. Plug this into a standard slope-intercept equation: y = mx + b
To find b, we want to plug in a value that we know is on this line: in this case, I will use the second point (-1, -4). Plug in the x and y values into the x and y of the standard equation.
-4 = 3/5(-1) + b
Multiply.
-4 = -3/5 + b
Add 3/5 to both sides. -- To add it easier, convert 4 to a have a denominator of 5.
-20/5 = -3/5 + b
-20/5 + 3/5 = b
-17/5 = b
Now, plug this into your standard equation.
y = 3/5x - 17/5
Check this equation by plugging in the other point you did not use (4, -1)
-1 = 3/5(4) - 17/5
-1 = 12/5 - 17/5
-1 = -5/5
-1 = -1
Your answer is correct!
Hope this helps!
Convert the equation `5x+2y=-8`into slope-intercept form.
Answers
Bradley C.
Apr 22, 2018
5
x
−
2
y
=
8
subtract
5
x
from both sides
−
2
y
=
8
−
5
x
y=
8
−
5
x
2
y=
−
5
x
2
−
4
s
l
o
p
e
=
−
5
x
2
y-intercept:
(
0
,
−
4
)
Answer:
y= -2.5x-4
Step-by-step explanation:
we have to isolate our y
subtract 5x from 5x+2y=-8 and move it to the right side
2y= -5x-8
divide everything by 2
y=-2.5x-4
I hope this helped you :)
What happens during photosynthesis?
a) carbohydrates are released into bloodstream
b) carbon dioxide is released into air
c) an organism captures energy in sunlight and uses to make its own food
d) glucose is broken down releasing energy
Answers
It’s not A because photosynthesis happens in plants which do not have a bloodstream and it’s not B because carbon dioxide is taken out of the air and oxygen is released into the air.
Answer:
C During the process of photosynthesis, cells use carbon dioxide and energy from the Sun to make sugar molecules and oxygen. ... Then, via respiration processes, cells use oxygen and glucose to synthesize energy-rich carrier molecules, such as ATP, and carbon dioxide is produced as a waste product
Step-by-step explanation:
hope this helps have a good night :) ❤
Plz help I’m confused
Geometry 15 points
Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the three given statements.
If an elephant weighs more than 2000 pounds, then it weighs more than Jill's car.
If something weighs more than Jill's car, then it is too heavy for the bridge.
Smiley the elephant weighs 2150 pounds.
Answers
I think that’s it
$745 is deposited into an account that earns 4% simple interest for 8 years.
How much interest is earned in 1 year?
Answers
9514 1404 393
Answer:
$29.80
Step-by-step explanation:
The interest earned in 1 year is ...
I = Prt
I = $745·0.04·1 = $29.80
$29.80 interest is earned in 1 year.
What is the value of the following expression if q = 10?
24 divided by (q-2)
HELPPP
Answers
Answer:
(B) 3
Step-by-step explanation:
24/(10-2)
24/8 is 3
2x-1-(-x+3) = 6-2x SHOW STEPS....DUE TODAY
Answers
Answer:
x=2
Step-by-step explanation:
Simplify both sides of the equation.
2x−1−(−x + 3)=6−2x
(Distribute the Negative Sign)
2x−1 + −1(−x + 3)=6−2x
2x + −1 + −1(−x) + (−1)(3)=6−2x
2x + −1 + x + −3=6−2x
2x + −1 + x + −3=6 + −2x
(Combine Like Terms)
(2x + x) + (−1 + −3)=−2x+6
3x + −4=−2x + 6
3x−4=−2x + 6
Add 2x to both sides.
3x−4 + 2x=−2x + 6 + 2x
5x−4=6
Add 4 to both sides.
5x−4 + 4=6 + 4
5x=10
Divide both sides by 5.
5x/5=10/5
x=2
Which of the following is a decomposition reaction?
reactant plus reactant yields product
reaciant minus reactant yields product
reactant yields product plus product reactant yields product times product
Answers
Answer:
Reactant plus reactant yields product.
Step-by-step explanation:
A decomposition reaction starts from a single substance and produces more than one substance. One substance as a reactant and more than one substance as the products is the key characteristic of a decomposition reaction.
Hope this helps.
whats the slope help pls!
Answers
Write an equation for when k= 1/6
Answers
Answer:
2/6 - 1/6 = k
Step-by-step explanation:
x + y = 4
2x - 5y = 15
Graphing
Answers
Answer:
Step-by-step explanation:
5x + 5y = 20
2x - 5y = 15
7x = 35
x = 5
5 + y = 4
y = -1
(5, -1)
The ratio that is equivalent to 15:42?
A) 5: 12
B) 10:28
C) 36:48
D) 5:21
Answers
Answer:
it's actually none of these.
Step-by-step explanation:
if we divide 15 by 3 we also have to divide 42 by 3. We end up with 5:14. 15 isn't divisible by any number other than 1, 3, 5, and 15.
James, Priya and slobhan work in a grocery store. James makes $7.00 per hour. Priya makes 20% more than James, and slobhan makes 15% less than Priya. How much does Slobhan make per hour?
he makes $_______ per hour.
is 7.20 correct?
Answers
7. The figure shows a right rectangular prism whose base is a square...
Answers
Answer:
D
Step-by-step explanation:
Write a Linear Equation in
Point-Slope Form.
m = -5
(-3, – 7)
Answers
==================================
Work Shown:
m = -5 is the slope
(x1,y1) = (-3,-7) is the point the line goes through
Plug this into the point slope form below and simplify.
y - y1 = m(x - x1)
y - (-7) = -5(x - (-3))
y + 7 = -5(x + 3)
Side note: If we solved for y, we'd get y = -5x - 22 showing that -22 is the y intercept.
5= 3j + 2
can somebody help me?
Answers
Answer:
j=1
Step-by-step explanation:
5=3j+2
3j=3
j=1
Suppose a city with population 300,000 has been growing at a rate of 2% per year. If this rate continues, find the population of this city in 20 years
I need help solving this
Answers
6000x20=120,000
The answer is 120,000
Answer:
the answer is 445,784
Step-by-step explanation:
The population y after x years of growth with the growth rate r and the original population C can be found using the exponential growth formula, . Substitute the decimal equivalent for the percent growth rate per year for r.
I will give Brainliest To whoever answers plus 10 points
1+1
Answers
If each 2 cm on the scale drawing equals 10 feet, what are the actual dimensions of the room? (5 points) Length = 11 feet, width = 9 feet Length = 30 feet, width = 20 feet Length = 8 feet, width = 12 feet Length = 22 feet, width = 20 feet
Answers
Answer:
c and i blue
Step-by-step explanation:
Please help me with this question. Thank you :)
Answers
What is the value of -34+ (-4+ 7)(2)? 28 3 15
Answers
Answer:
3/4 * 5/7 = 15/
28
≅ 0.5357143
Answer:
-28
Step-by-step explanation:
Your welcome!
22+n=−12
pls help me im kinda confused
Answers
Answer:
-34
Step-by-step explanation:
22+n=-12
n=-12-22
n=-34
When you bring a positive constant to the other side of the equal sign it goes negative and vise versa. Then you combine like terms.
Please follow me!!!! Hope this helps!!! Have a wonderful day :)
9. Carson draws a scale drawing of a city park and a parking lot. The city 10 points park is in the shape of aright triangle with legs that are 3 inches and 4 inches. The parking lot is in a shape of a rectangle with dimensions of 1.5 inches and 2.5 inches. The scale for the drawing is 1 inch = 40 feet. What are the TWO actual areas for the shapes that are represented?
Answers
Answer:
The answer is below
Step-by-step explanation:
The scale for the drawing is 1 inch = 40 feet.
The right angled triangle has legs of 3 inches and 4 inches. Using the scale, the length of the legs is:
3 inches = 3 inch * 40 feet / inch = 120 feet and 40 inches = 4 inch * 40 feet / inch = 160 feet.
The area of a right angled triangle is half the product of the two legs. Hence:
Area of right angled triangle = 1/2 * 120 feet * 160 feet = 9600 ft²
The rectangle with dimensions of 1.5 inches and 2.5 inches. Using the scale, the length of the sides is:
1.5 inches = 1.5 inch * 40 feet / inch = 60 feet and 2.5 inches = 2.5 inch * 40 feet / inch = 90 feet.
The area of a rectangle is the product of the two sides. Hence:
Area of rectangle = 60 feet * 90 feet = 5400 ft²
help pleAsee zknsmfm
Answers
Answer:
C
Step-by-step explanation:
(x+2) * x
X^2 +2x
Miguel read 1 page on Friday, 3 pages on Saturday, 9 pages on Sunday, and 27 pages on Monday. If this pattern continues, how many pages will Miguel read on Tuesday?
Answers
Answer:
81
Step-by-step explanation:
Miguel is reading 3x the pages everyday. 1x3=3 3x3=9 9x3=27 27x3=81
HELP PLEASE .... If the geometric mean between 3 and x is 6, find the value of x.
Answers
Answer:
12
Step-by-step explanation:
1. 3/6 = 6/x
2. Cross multiply: 3x=36
3. x=12
PLEASE HELP ME WITH THIS FOR BRAINLIEST AND A COOKIE
Answers
Answer:
12
Step-by-step explanation:
Answer: the answer is 12
Step-by-step explanation: im just here for the cookie
It takes a turtle 3 ¼ hours to walk 1 ½ miles. How many hours does it take to walk one mile?
Answers
Answer: 2.17 hours
Step-by-step explanation:
Answer:
2.17 hours
Step-by-step explanation: