I need help with this question.

You can simply collect terms, subtract the constant and divide by the x-coefficient. It is generally considered easier to do those steps if you eliminate fractions first (multiply by 12).

Multiply by 12

... 4(x -1) +3(x +5) = 6

... 4x -4 +3x +15 = 6 . . . . . eliminate parentheses

... 7x +11 = 6 . . . . . . . . . . . .collect terms

... 7x = -5 . . . . . . . . . . . . . . subtract the constant 11

... x = -5/7 . . . . . . . . . . . . . divide by the x-coefficient

_ _ _ _ _ _ _

Here it is the other way.

... x(1/3 +1/4) +(-1/3 +5/4) = 1/2

... (7/12)x + 11/12 = 1/2 . . add the fractions to finish collecting terms

... x + 11/7 = 6/7 . . . . . . . multiply by 12/7

... x = -5/7 . . . . . . . . . . . subtract 11/7

At the third step here, you could subtract 11/12 before doing the multiply. You get the same answer, but you have to do the extra conversion of 1/2=6/12.

8 0

3 years ago

6. Find d. Please help

Anvisha [2.4K]

Answer:

Step-by-step explanation:

The first thing we are going to do is to fill in the other angles that we need to solve this problem. You could find ALL of them but all of them isn't necessary. So looking at the obtuse angle next to the 35 degree angle...we know that those are supplementary so 180 - 35 = the obtuse angle in the small triangle. 180 - 35 = 145. Within the smaller triangle we have now the 145 and the 10, and since, by the Triangle Angle-Sum Theorem all the angles have to add up to equal 180, then 180 - (10 + 145) = the 3rd angle, so the third angle is 180 - 155 = 25. Now let's get to the problem. If I were you, I'd draw that out like I did to keep track of these angles cuz I'm going to name them by their degree. In order to find d, we need to first find the distance between d and the right angle. We'll call that x. The reference angle is 35, the side opposite that angle is 12 and the side we are looking for, x, is adjacent to that angle. So we will use the tan ratio to find x:

$tan(35)=\frac{12}{x}$ Isolating x:

$x=\frac{12}{tan(35)}$ so

x = 17.1377 m

Now we have everything we need to find d. We will use 25 degrees as our reference angle, and the side opposite it is 12 and the side adjacent to it is

d + 17.1377, so that is the tan ratio as well:

$tan(25)=\frac{12}{d+17.1377}$ and simplifying a bit:

$d+17.1377=\frac{12}{tan(25)}$ and a bit more:

d + 17.1377 = 25.73408 so

d = 8.59, rounded

3 0

2 years ago