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4 years ago

-12 = -6(-8n + 6) + 8(-4+n) How do you solve this equation

Mathematics

1 answer:

ollegr [7]4 years ago

3 0

Answer:

n=1

Step-by-step explanation:

distribute

-6 times -8n is =48n

-6 times 6 =-36

8 times -4 = -32

8 times n =8n

rewrite equation

48n-36+-32+8n=-12

48n+8n-36-32=-12

56n-68=-12

add 68 on both sides

=56

56n=56

n= 1

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A triangle has a base of x 1/2 m and a height of x 3/4 m. If the area of te triangle is 16m to the power of 2, what are the base

Olenka [21]

Answer:

The base of triangle is $\frac{8}{\sqrt{3}} \ m$ and the height of triangle is $\frac{12}{\sqrt{3}} \ m.$

Step-by-step explanation:

Given:

A triangle has a base of x 1/2 m and a height of x 3/4 m. If the area of the triangle is 16m to the power of 2.

Now, to find the base and height of the triangle.

The base of triangle = $x\times\frac{1}{2} =\frac{x}{2} \ m.$

The height of triangle = $x\times \frac{3}{4} =\frac{3x}{4}\ m.$

The area of triangle = $16\ m^2.$

Now, we put the formula of area to solve:

$Area=\frac{1}{2} \times base\times height$

$16=\frac{1}{2} \times \frac{x}{2} \times \frac{3x}{4}$

$16=\frac{3x^2}{16}$

Multiplying both sides by 16 we get:

$256=3x^2$

Dividing both sides by 3 we get:

$\frac{256}{3} =x^2$

Using square root on both sides we get:

$\frac{16}{\sqrt{3}}=x$

$x=\frac{16}{\sqrt{3}}$

Now, by substituting the value of $x$ to get the base and height:

$Base=\frac{x}{2}\\\\Base=\frac{\frac{16}{\sqrt{3}}}{2} \\\\Base=\frac{8}{\sqrt{3}} \ m.$

So, the base of triangle = $\frac{8}{\sqrt{3}} \ m.$

$Height=x\times\frac{3}{4} \\\\Height=\frac{16}{\sqrt{3}}\times \frac{3}{4} \\\\Height=\frac{12}{\sqrt{3}} \ m.$

Thus, the height of triangle = $\frac{12}{\sqrt{3}} \ m.$

Therefore, the base of triangle is $\frac{8}{\sqrt{3}} \ m$ and the height of triangle is $\frac{12}{\sqrt{3}} \ m.$

7 0

4 years ago

List the integers that satisfy both of these inequalities 2x+9<0 x>-12 put the answers on one line

lbvjy [14]

Answer:

-11, -10, -9, -8, -7, -6 and -5

Step-by-step explanation:

Given the inequality expressions

2x+9<0 and x>-12

2x+9<0

2x< 0-9

2x < -9

x < -9/2

x < -4.5

Since x >-12

-12 < x

Combining both inequalities

-12 <x < 4.5

The integers between the intervals are -11, -10, -9, -8, -7, -6 and -5

6 0

3 years ago

Let’s think about another type of scenario. What if you were told that a bracelet requires 10 beads and 10 minutes to make while

Georgia [21]

Answer:

$425

Step-by-step explanation:

Let x represent the number of bracelets made and let y represent the number of necklace made.

Since the craftsman has 1000 beads to work with, hence:

10x + 20y ≤ 1000 (1)

Also, the craftsman has 1600 minutes, hence:

10x + 40y ≤ 1600 (2)

From ploting equations 1 and 2 on the geogebra online graphing, we can see that the solution to the problem is (40, 30).

Since the bracelet costs $5 and a necklace costs $7.50, hence the maximum revenue is:

Revenue = 5x + 7.5y = 5(40) + 7.5(30) = $425

4 0

3 years ago

Helppppppppp.......!!!!!!!

lubasha [3.4K]

7(12 + x)

84 + 7x

Hope my answer helps!

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4 years ago

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Please help me ASAP easy problem giving brainlist!!

Harman [31]

Answer:

inequalities can have zero, one, or infinite solutions

i hoped that help you

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3 years ago

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