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2 years ago

What is the area of an equilateral triangle that has a perimeter of 36 centimeters? Round to the nearest square centimeter.

Mathematics

1 answer:

Vika [28.1K]2 years ago

5 0

Answer:

(a is size of side of triangle)

the perimeter of equilateral triangle =3a

or, 36=3a

Thus, a = 13cm

area of equilateral triangle

=√3/4*(a^2 )

=√3/4*(13^2)

=73cm^2

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Slope 8 ; through (4,3)

Reptile [31]

Answer:

y=8x-29

Step-by-step explanation:

Since we know the slope (m) is 8, we can plug it in the slope-intercept formula y=mx+b, making y=8x+b.

Now we need to find the y-intercept (b). To do that, you would need to plug in the points given to you, which were (4,3).

x=4, y=3... so 3=8(4)+b

Now you can solve for the variable b to find the y-intercept.

3=8(4)+b, multiply...

3=32+b, subtract 32 on both sides...

-29=b

Therefore, the y-intercept, or b, is -29.

The equation would be y=8x-29

7 0

2 years ago

17_2_3_8=3 insert + - × or ÷ symbols to make each statement true

erastova [34]

Answer:

17-2*3-8=3

Step-by-step explanation:

We have given:

17_2_3_8=3 insert + - × or ÷ symbols to make each statement true?

Solution:

We will insert multiplication sign between 2 and 3 and then subtract all the terms

17-2*3-8=3

We will solve it according to the DMAS rule:

DMAS rule is followed when multiple arithmetic operations are there in a given problem like addition, subtraction, multiplication and division. It tells they should be performed in order of Division, Multiplication, Addition and Subtraction. Without DMAS rule all mathematical equations will come up with different answers.

Lets solve the expression and check whether the L.H.S = R.H.S

17-2*3-8=3

17-6-8=3

11-8=3

3 =3

Be sure to multiply first and then subtract

⇒You can also insert addition sign in place of multiplication. It will give the same answer

3 0

3 years ago

Read 2 more answers

What are the solutions to the equation 2(x-3)^2=54 ?

erastova [34]

Answer:

x =(6-√108)/2=3-3√ 3 = -2.196

x =(6+√108)/2=3+3√ 3 = 8.196

Step-by-step explanation:

Step 1 :

Equation at the end of step 1 :

2 • (x - 3)2 - 54 = 0

Step 2 :

2.1 Evaluate : (x-3)2 = x2-6x+9

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

2x2 - 12x - 36 = 2 • (x2 - 6x - 18)

Adding 9 has completed the left hand side into a perfect square :

x2-6x+9 =

(x-3) • (x-3) =

(x-3)2 (x-3)1 =

x-3

Now, applying the Square Root Principle to Eq. #4.3.1 we get:

x-3 = √ 27

Add 3 to both sides to obtain:

x = 3 + √ 27

Since a square root has two values, one positive and the other negative

x2 - 6x - 18 = 0

has two solutions:

x = 3 + √ 27

x = 3 - √ 27

Solve Quadratic Equation using the Quadratic Formula

4.4 Solving x2-6x-18 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

In our case, A = 1

B = -6

C = -18

Accordingly, B2 - 4AC =

36 - (-72) =

108

Applying the quadratic formula :

6 ± √ 108

x = —————

Can √ 108 be simplified ?

Yes! The prime factorization of 108 is

2•2•3•3•3

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 108 = √ 2•2•3•3•3 =2•3•√ 3 =

± 6 • √ 3

√ 3 , rounded to 4 decimal digits, is 1.7321

So now we are looking at:

x = ( 6 ± 6 • 1.732 ) / 2

Two real solutions:

x =(6+√108)/2=3+3√ 3 = 8.196

or:

x =(6-√108)/2=3-3√ 3 = -2.196

7 0

3 years ago

What is 310,763,146 in expanded form

lesya [120]

In expanded form, the number would look like this:

300,000,000 + 10,000,000 + 700,000 + 60,000 + 3,000 + 100 + 40 + 6

When you add the value of all of these digits, it'll get you the number: 310,763,146. Adding all of these values up and getting the number you originally started with is a great method of making sure you got the right answer.

6 0

3 years ago

1. Describe a situation that could be modeled by x≤50

Dimas [21]

There are many ways to answer. The x represents some number. We don't know what the number is, but we know that it must be less than or equal to 50. Put another way, the number can be anything you want as long as it doesn't go past 50. We say that 50 is the so called "ceiling" more or less.

Some examples:

* An elevator can only hold 50 people at maximum. Therefore, x can be any number smaller than 50 or 50 itself. Having 51 or over will be too much.

* You can only work 50 hours for one stretch of some 2 week period. If x is the number of hours you work, then x must be 50 or less as written by $x \le 50$ . So x could be x = 37 as it's less than 50, but x = 62 is not possible.

* For some small ride at a theme park, the seats are designed such that only people 50 inches or less can ride on them. If x is the height of a person in inches, then $x \le 50$ means something like x = 37 is possible but x = 62 is too high.

8 0

3 years ago