Simplify (a+b)(a^2-ab+b^2)

What other information do you need to prove ΔABE is congruent to ΔEDA by SSS?

Stels [109]

To prove ΔABE is congruent to ΔEDA by SSS we need that EAC should be an equilateral triangle.

What is an equilateral triangle?

A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.

Here, we have

AEC is a triangle in which B∈ AC and D∈ EC

Such that,

∠ABE = 90°,

∠ADE = 90°,

Also, BC = CD

Now, we have to prove that :

Δ ABE is congruent to Δ EDA

Proof :

If EAC is an equilateral triangle,

By the property of an equilateral triangle,

EA = AC = EC

If AC = EC

AB + BC = ED + CD

AB + CD = ED + CD

AB = ED

Also, AE = AE ( common segment )

Now, if in two right triangles hypotenuse are equal and any corresponding legs are equal,

Then, the other legs must be equal,

That is, BE = DA,

Hence, by the SSS postulate of congruence,

Δ ABE ≅ Δ EDA

Hence, to prove ΔABE is congruent to ΔEDA by SSS we need that EAC should be an equilateral triangle.

To learn more about the equilateral triangle from the given link

brainly.com/question/15294703

#SPJ4

7 0

1 year ago

Find the equation of the line parallel to y=2x+1 that contains point (14,3)

Sophie [7]

First of all, remember what the equation of a line is:

$y=mx+b$

Where:

m=slope

b=y-intercept.

Given this information, we can start by plugging in what we know, we are given the slope which is 2 so we can fill that in, remember m=slope

$y=2x+b$

To find b, think about what your (x,y) point means:(14,3). When x of the line is 14, y of the line must be 3.

Because we were given the point (14,3)

We need to find the value of b. The 2 is already set and x and y are variables. We want the equation for the line that specifically passes through the given point (14,3).

Plug in for x the number 14 and for y the number 3:
(14,3).
y=mx+b or 3=2 × 14+b,

solving for b: b=3-(2)(14). b=-25.

Plug that in for b:
y=2x-25
Final answer:
y=2x-25

8 0

3 years ago

0.7x+6=0.3(4x+6)−2x

Gelneren [198K]

Answer: $x=-2.8$

Step-by-step explanation:

Given the following equation:

$0.7x+6=0.3(4x+6)-2x$

You can follow these steps in order to solve for "x" and find its value:

1. Apply Distributive property on the right side of the equation:

$0.7x+6=0.3(4x+6)-2x\\\\0.7x+6=1.2x+1.8-2x$

2. Subract $0.7x$ from both sides and add the like terms:

$0.7x+6-(0.7x)=1.2x+1.8-2x-(0.7x)\\\\6=-1.5x+1.8$

3. Subtract 1.8 from both sides:

$6-(1.8)=-1.5x+1.8-(1.8)\\\\4.2=-1.5x$

4. Finally, divide both side of the equation by -1.5:

$\frac{4.2}{-1.5}=\frac{-1.5x}{-1.5}\\\\x=-2.8$

8 0

3 years ago

Read 2 more answers

Find the simple interest paid to the nearest cent for each principal, interest rate, and time. $570,2%, 4 years.

WARRIOR [948]

The answer is 45.6. You multiply the beginning amount to the interest rate to understand how much interest you get. Then multiply that by the amount of years the interest is gathered. 570 * .02 = 11.4 * 4 = $45.6 interest. Add this to 570 for the original amount of 615.6.

6 0

3 years ago

you order two tacos and a salad.the salad cost $2.50.you pay 8% sales tax and leave a $3 tip. you pay a total of $13.80. how muc

labwork [276]

it is given in the question that

You order two tacos and a salad.the salad cost $2.50.you pay 8% sales tax and leave a $3 tip.

Let the price of taco be $ x .

And 8 % of 2.50 is

$=0.08*2.50 = 0.20$

So the equation is

$2x+ 2.50+0.2+3 = 13.80
\\
2x + 5.70 =13.80
\\
2x = 8.10
\\
x = $4.05$

So the price of the Taco is $4.05 .

8 0

3 years ago