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1 year ago

Using GEMS : groupings, exponents,

Mathematics

1 answer:

nikdorinn [45]1 year ago

7 0

Answer:

Step-by-step explanation:

1) Simplify 5 - 4 to 1.

2² + 1 × 3

2) Simplify 2² to 4.

4 + 1 × 3

3) Simplify 1 × 3 to 3.

4 + 3

4) Simplify.

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1+-w2+9w and I need help cuz I’m on 76 and I’m sooo close help

Gnesinka [82]

$\huge \boxed{\mathfrak{Question} \downarrow}$

Simplify :- 1 + - w² + 9w.

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$\large \sf1 + - w ^ { 2 } + 9 w$

Quadratic polynomial can be factored using the transformation $\sf \: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$ , where $\sf x_{1} and x_{2}$ are the solutions of the quadratic equation $\sf \: ax^{2}+bx+c=0$ .

$\large \sf-w^{2}+9w+1=0$

All equations of the form $\sf\:ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\sf\frac{-b±\sqrt{b^{2}-4ac}}{2a}$ . The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$\large \sf \: w=\frac{-9±\sqrt{9^{2}-4\left(-1\right)}}{2\left(-1\right)} \\$

Square 9.

$\large \sf \: w=\frac{-9±\sqrt{81-4\left(-1\right)}}{2\left(-1\right)} \\$

Multiply -4 times -1.

$\large \sf \: w=\frac{-9±\sqrt{81+4}}{2\left(-1\right)} \\$

Add 81 to 4.

$\large \sf \: w=\frac{-9±\sqrt{85}}{2\left(-1\right)} \\$

Multiply 2 times -1.

$\large \sf \: w=\frac{-9±\sqrt{85}}{-2} \\$

Now solve the equation $\sf\:w=\frac{-9±\sqrt{85}}{-2}$ when ± is plus. Add -9 to $\sf\sqrt{85}$ .

$\large \sf \: w=\frac{\sqrt{85}-9}{-2} \\$

Divide -9+ $\sf\sqrt{85}$ by -2.

$\large \boxed{ \sf \: w=\frac{9-\sqrt{85}}{2}} \\$

Now solve the equation $\sf\:w=\frac{-9±\sqrt{85}}{-2}$ when ± is minus. Subtract $\sf\sqrt{85}$ from -9.

$\large \sf \: w=\frac{-\sqrt{85}-9}{-2} \\$

Divide $\sf-9-\sqrt{85}$ by -2.

$\large \boxed{ \sf \: w=\frac{\sqrt{85}+9}{2}} \\$

Factor the original expression using $\sf\:ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$ . Substitute $\sf\frac{9-\sqrt{85}}{2}$ for $\sf\:x_{1}$ and $\sf\frac{9+\sqrt{85}}{2}$ for $\sf\:x_{2}$ .

$\large \boxed{ \boxed {\mathfrak{-w^{2}+9w+1=-\left(w-\frac{9-\sqrt{85}}{2}\right)\left(w-\frac{\sqrt{85}+9}{2}\right) }}}$

Well, in the picture you inserted it says that it's 8th grade mathematics. So, I'm not sure if you have learned simplification with the help of biquadratic formula. So, if you want the answer simplified only according to like terms then your answer will be ⇨

$\large \sf \: 1 + - w {}^{2} + 9w \\ =\large \boxed{\bf \: 1 - {w}^{2} + 9w}$

This cannot be further simplified as there are no more like terms (you can use the biquadratic formula if you've learned it.)

4 0

2 years ago

Complete the equation…<br><br> Picture is included <br><br> Please answer!! No links please!!!

sp2606 [1]

You should subtract the powers when they are divided and add them when they are multiplied this rule is so important for now you just have to subtract them and you will get the answer
Hope it helps :)

8 0

1 year ago

Solve the inequality.<br> 8-2x < -x + 9

mezya [45]

Answer:

x > -1

Step-by-step explanation:

$8-2x < -x+9\\8-2x-8 < -x+9-8\\-2x < -x+1\\-2x+x < -x+1+x\\-x < 1\\\left(-x\right)\left(-1\right) > 1\cdot \left(-1\right)\\x > -1$

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1 year ago

0.25 milliliters of paint to 12.3 milliliters of water.How many milliliters does the mixture contain?

lord [1]

Answer:

12,55ml

Step-by-step explanation:

12,3+0,25=12,55

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2 years ago

Brandon bought a book that originally sold for $18 on sale for 30% off. He paid a sales tax of 8%.

inysia [295]

Answer:

$13.61

Step-by-step explanation:

$18 * 70% = $12.60

$12.60 * 1.08 = $13.61

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2 years ago