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2 years ago

Find the altitude of an equilateral triangle whose perimeter is 18

Mathematics

1 answer:

Rainbow [258]2 years ago

5 0

Answer:

3√3 units

Step-by-step explanation:

We are asked to find the altitude of the equilateral triangle whose perimeter is 18 . Firstly let us find the side of the∆.

$\rm \implies a + a + a = 18 \\\\\rm\implies 3a = 18 \\\\\rm\implies a = 6$

Now we know that in a equilateral triangle , the altitude of the triangle with side length a is ,

$\rm\implies Altitude =\dfrac{\sqrt3}{2} a$

Plug in the value of a that is 6 , we will get ,

$\rm\implies Altitude =\dfrac{\sqrt 3}{2} a \\\\\rm\implies Altitude =\dfrac{ \sqrt3}{2}\times 6 \\\\\rm\implies Altitude = \sqrt3 \times 3 \\\\\rm\implies\boxed{ \bf Altitude = 3\sqrt3 \ units }$

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Question 1,2, and 3 how do i factor those? Can you show the work and explain how?

DiKsa [7]

1: $3n^{2}+9n+6$

notice that each part is divisible by 3

$3n^{2}$ ÷ 3 = $n^{2}$

9n ÷ 3 = 3n

6 ÷ 3 = 2

so it becomes $3(n^{2} +3n+2)$

3n can be rewritten as 2n+n

-you want to rewrite it into two numbers that multiply to the number that's alone (in this case 2)

which would get you

$3(n^{2} +2n+n+2)$

Now that it's rewritten, you can factor out n + 2 from the equation.

the answer is

3(n+2)(n+1)

And you can check that by multiplying (n+2)(n+1) which is $n^{2} +2n+n+2$ and then each of those by 3, which is $3n^{2} +6n+3n+6$ or $3n^{2}+9n+6$ , our origional equation

2: $28+x^{2} -11x$

So I rewrote this as $x^{2} -11x+28$ (it's the same thing, just reordered using the commutative property)

now -11x can be rewritten as -4x-7x

(remember, the two numbers should multiply to equal 28, which is our constant.)

$x^{2} -4x-7x+28$

now we can factor out x from the first expression and -7 from the second

$x(x-4)-7(x-4)$

and lastly you factor out x-4,

which would give you

(x-4)(x-7)

Make sure to check your work and make sure it multiplies to $x^{2} -11x+28$

3: $9x^{2} -12x+4$

The first thing I notice when looking at this problem is that both 9 and 4 are perfect squares. Not only that, but they are the squares of 2 and 3, which are products of -12

So if you rewrite 9 as $3^{2}$ and 4 as $2^{2}$ , the equation becomes

$3^{2} x^{2} -12x+2^{2}$

now that $3^{2} x^{2}$ is ugly so it can be turned into $(3x)^{2}$

and -12x can be rewritten as $-2*3x*2$

so our equation now looks like $(3x)^2-2*3x*2+2^{2}$

There's a rule that says $a^{2} -2ab+b^{2} = (a-b)^{2}$

In our case, a=3x and b=2

so the final answer is

$(3x-2)^2$

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2 years ago

Find the volume of the triangular prism, given the area of the base is 14 cm2 and the height of the prism is 15 cm.

laiz [17]

Answer:

210 cm³

Step-by-step explanation:

RULE :

the volume of the triangular prism = the area of the base × the height

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3 years ago

Help urgent, which functions are bounded below but not above? Choose all answers that apply.

evablogger [386]

Answer:

c, e, f, and i

Step-by-step explanation:

a. is bounded above at y = 1 and below at y = 0

b. is unbounded both above and below

c. is bounded below at y = 0 and unbounded above

d. is unbounded both above and below

e. is bounded below at y = 0 and unbounded above

f. is bounded below at y = 0 and unbounded above

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3 years ago

giving brainlest if explained and showed work please help! i just need it explained so i can understand it!

lawyer [7]

Answer:

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3 years ago

Jenny opened a package of screws quickly and many of them spilled on the floor. She needs to organize the fasteners according to

hichkok12 [17]

We have to compare diameters and arrange them in order smallest to greatest

We can see units for option A and B are in square inches so they represents area. So first we will find diameter from area using formula

$A = \pi r^{2}$

so for choice (A) area is given as $4.375 \times 10^{7}$ . So plug this in A place in formula and then solve for radius r

$4.375 \times 10^{7} = \pi r^{2}$

$\frac{4.375 \times 10^{7}}{\pi} = \frac{\pi r^{2}}{\pi}$

$1.393 \times 10^{7} } = r^{2}$

$\sqrt{1.393 \times 10^{7}} = \sqrt{r^{2}}$

3731.76 = r

So screw A will have
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so again plug in formula

$A = \pi r^{2}$

$14.28 = \pi r^{2}$

$\frac{14.28}{\pi} = \frac{\pi r^{2}}{\pi}$

$4.5477 = r^{2}$

$\sqrt{4.5477} = \sqrt{r^{2}}$

2.13201 = r

So screw E will have
$diameter = 2 \times r = 2 \times 2.13201 = 4.26402$ inches

So diameters of all screws are as follows:

Screw A: 7463.52 inches
Screw B: 1.5 inches
Screw C: $1\frac{7}{8} = \frac{1\times 8+7}{8} = \frac{15}{8} = 1.875$ inches
Screw D: 0.25 inches
Screw E: 4.26402 inches

Comparing all numbers 7463.52, 1.5, 1.875, 0.25, 4.26402 we can see that smallest number is 0.25, then comes 1.5, then 1.875 and then 4.26402 and then 7463.52

So order from least to greatest will be screw D (0.25), B(1.5), C(1.875), E (4.26402), A (7463.52).

So thats the order D,B,C,E,A and the final answer

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3 years ago

Read 2 more answers