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2 years ago

Which of the following represents the quadratic function f (x) = 5(x − 2)2 − 7 in standard form?

Mathematics

1 answer:

wariber [46]2 years ago

8 0

Answer:

f(x) = 10x - 27. I can't find the answer anywhere

Step-by-step explanation:

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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

Find the rule ans the graph of the function whose graph can be obtained by performing the translation 4 units peft and 5 units d

s344n2d4d5 [400]

A. f(x)=ln(x+4)-5
If it shifts to the left side then in braces put a (+) sign and if it shifts to the right then in braces put a (-) sign. If it goes up it’s positive and if it goes down it’s negative

6 0

2 years ago

HELP NEEDED IMMEDIATELY! I'M GETTING DESPERATE!

TiliK225 [7]

Answer:

The number of different possible values are {-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7}.

Step-by-step explanation:

Given : For an integer n, the inequality $x^2 + nx + 15 < 0$ has no real solutions in x.

To find : The number of different possible values of n ?

Solution :

The given inequality is $x^2 + nx + 15 < 0$ have no solution then the discriminant must be less than zero.

i.e. $b^2-4ac$

Here, a=1, b=n and c=15

${n}^{2} - 4 \times 1 \times 15 \: < \: 0$

${n}^{2} - 60 \: < \: 0$

$n^2$

$n$

i.e. $- 7.75 \: < \: n \: < \: 7.75$

The integer values are {-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7}.

7 0

2 years ago

Two spray paint machines are used to paint different portions of a large wall. The first machine (nicknamed "Paint Pro") is used

jonny [76]

Answer: The answer is 30 sq.ft/min and 25 sq.ft/min.

Step-by-step explanation: Given that there are two spray paint machines. The first machine (nicknamed "Paint Pro") is used for two hours and the second machine (nicknamed "Goldilocks") is used for an hour and a half. When they are working at the same time, they can paint 55 square feet per minute and together they painted 5850 square feet of wall.

Let 'x' and 'y' sq.ft/min be the portion of the wall painted by Paint Pro and Goldilocks respectively.

Then, according to the question, we have

$x+y=55,\\\\120x+90y=5850~~\Rightarrow 4x+3y=195.$