In the equation: log (x) = -0.123, what is the value of x?
1 answer:
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Answer:
Step-by-step explanation:
Given: 8x² + 10x - 7 = 0
<u>When factoring trinomials of the form ax² + bx + c</u>:
- multiply the leading coefficient and the last term.
- find the product factors that add to give you the coefficient of the middle term.
- rewrite the polynomial with those factors replacing the middle term.
1. Split the middle term:
⇒ 8 × -7 = -56 [multiply the leading coefficient and the last term]
⇒ 14, -4 [find the product factors that add to the middle term's coefficient]
⇒ 8x² + 14x - 4x - 7 = 0 [rewrite with those factors replacing the middle term.]
2. Factor by grouping:
⇒ 8x² + 14x - 4x - 7 = 0 [factor out 2x]
⇒ 2x(4x + 7) - 4x - 7 = 0 [factor out -1 or the negative sign]
⇒ 2x(4x + 7) -1(4x + 7) = 0 [factor out 4x + 7]
⟹ (4x + 7)(2x - 1) = 0
3. Separate into 2 cases:
- 4x + 7 = 0
- 2x - 1 = 0
<u><em>Case 1:</em></u>
⇒ 4x + 7 = 0 [subtract 7 from both sides]
⇒ 4x + 7 - 7 = 0 - 7
⇒ 4x = -7 [divide both sides by 4]
⇒ 4x ÷ 4 = -7 ÷ 4
⟹ x =
<u><em>Case 2:</em></u>
⇒ 2x - 1 = 0 [subtract 1 from both sides]
⇒ 2x - 1 + 1 = 0 + 1
⇒ 2x = 1 [divide both sides by 2]
⇒ 2x ÷ 2 = 1 ÷ 2
⟹ x =
Solutions:
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Answer:
Step-by-step explanation:
Hello There!
To solve for the area of this figure we need to split the figure into 3 different parts:
A rectangle with a length of 9 ft and a width of 7 ft
a rectangle with a width of 9ft + 7ft and a length of 25 ft
a rectangle with a width of 18 ft and a length of 22 ft
To find the area of a rectangle we use the formula
where w = width and l = length
for the first one we plug in the values
A = 9 * 7
9 * 7 = 63 so the area of the smallest rectangle is 63ft²
Now lets find the area of the larger rectangle
The dimensions are l = 25 ft and w = 9 + 7 (16 ft)
Now we can plug in the values into the area formula
A = 16 * 25
16*25=400 so the area of the larger rectangle is 400 ft²
Now lets find the area of the last rectangle
The dimensions are l = 22 ft and w = 18 ft
now lets plug in the values to the formula
A = 22 * 18 =396
so the area of the last rectangle is 396 ft²
Finally we want to add all of the areas together
396 + 400 + 63 = 859
So the area of the figure is 859 ft²