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Gnoma [55]
3 years ago
13

Help please with this question?

Mathematics
1 answer:
xxMikexx [17]3 years ago
7 0
G(x+1)= \sqrt{(x+1)^2+4} \\ G(x+1)= \sqrt{x^2+2x+1+4} \\  G(x+1)= \sqrt{x^2+2x+5}
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Detmermine the best method to solve the following equation, then solve the equation. (3x-5)^2=-125
liq [111]

For the given equation;

(3x-5)^2=-125

We shall begin by expanding the parenthesis on the left side, after which we would combine all terms on and move all of them to the left side, which shall yield a quadratic equation. Then we shall solve.

Let us begin by expanding the parenthesis;

\begin{gathered} (3x-5)^2\Rightarrow(3x-5)(3x-5) \\ (3x-5)(3x-5)=9x^2-15x-15x+25 \\ (3x-5)^2=9x^2-30x+25 \end{gathered}

Now that we have expanded the left side of the equation, we would have;

\begin{gathered} 9x^2-30x+25=-125 \\ \text{Add 125 to both sides and we'll have;} \\ 9x^2-30x+25+125=-125+125 \\ 9x^2-30x+150=0 \end{gathered}

We shall now solve the resulting quadratic equation using the quadratic formula as follows;

\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{Where;} \\ a=9,b=-30,c=150 \\ x=\frac{-(-30)\pm\sqrt[]{(-30)^2-4(9)(150)}}{2(9)} \\ x=\frac{30\pm\sqrt[]{900-5400}}{18} \\ x=\frac{30\pm\sqrt[]{-4500}}{18} \\ x=\frac{30\pm\sqrt[]{-900\times5}}{18} \\ x=\frac{30\pm\sqrt[]{-900}\times\sqrt[]{5}}{18} \\ x=\frac{30\pm30i\sqrt[]{5}}{18} \\ \text{Therefore;} \\ x=\frac{30+30i\sqrt[]{5}}{18},x=\frac{30-30i\sqrt[]{5}}{18} \\ \text{Divide all through by 6, and we'll have;} \\ x=\frac{5+5i\sqrt[]{5}}{3},x=\frac{5-5i\sqrt[]{5}}{3} \end{gathered}

ANSWER:

x=\frac{5+5i\sqrt[]{5}}{3},x=\frac{5-5i\sqrt[]{5}}{3}

3 0
1 year ago
Victoria went shopping for ingredients to make a stew.The table shows the weight and cost of each of the ingredients that she bo
djverab [1.8K]

Answer:

a) the beef cost the most

b) $125.8

Step-by-step explanation:

A) 1.2 potatoes

1.8 carrots

2.39 beef

.5 peppers


B) 15.30-.5=14.80 x 8.5=<u>125.8</u>




7 0
3 years ago
Help me find the slope of this imagine. it a quizizz question and i cant figure it out
lidiya [134]

Answer:

slope = \frac{5}{2}

Step-by-step explanation:

Select any 2 ordered pairs from the given table, the use the slope formula to calculate the slope m

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 5) and (x₂, y₂ ) = (4, 10) ← 2 ordered pairs from table

m = \frac{10-5}{4-2} = \frac{5}{2}

5 0
3 years ago
Ten feet below sea level is farther below sea level than 2 and a half feet below sea level
bulgar [2K]

Answer:

correct

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
I need the answers to these.
MrMuchimi
The first one 6 second 8 but it’s funny
5 0
3 years ago
Read 2 more answers
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