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2 years ago

F(x)=-x^2 -4x -2, for this equation find the solutions, the coordinates of the vertex, and the axis of the symmetry.

Mathematics

1 answer:

Zina [86]2 years ago

4 0

Answer:

Step-by-step explanation:

hello :

Completing The Square x²-4x-2= (x²-4x+4)-4-2 = (x-2)²-6

the vertex is : (2 , -6)

now calculate the solutions : (x-2)²-6 =0

(x-2)²= 6 means : x-2 =√6 or x-2 = -√6

x = 2+√6 or x = 2-√6

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Emily is solving the equation 2(x+9)=4(x+7)+2 where did she make an error

Wittaler [7]

Hello!

2(x + 9) = 4(x + 7) + 2

Distribute the 2

2x + 18 = 4(x + 7) + 2

Distribute the 4

2x + 18 = 4x + 28 + 2

Combine like terms

2x + 18 = 4x + 30

Subtract 18 from both sides

2x = 4x + 12

Subtract 4x from both sides

-2x = 12

Divide both sides by -2

x = -6

Where she did something different than me is her mistake

Hope this helps!

6 0

3 years ago

What is 10% of 50? A. 6.75 B. 7.5 C. 10.5 D. 5.25

nirvana33 [79]

Its 5. Its none of those.

10% of 50.00 = 5.0000

5 0

3 years ago

Sara receives a 9% commission on every car she sells. The car dealership paid $20,000 for a car from an auction. The next day th

Paladinen [302]

Hey there! Your answer to this problem is 2160..

Explanantion:

Since every car Sara sells, she gets 9% of the commission, this means that at the last few step, we would have to give 9% of the total cost to Sara.

If 100% is 20,000, then 50% would be 10,000. But we have to find the cost of 20%. So what we would actually be doing is multiplying 20 with 0.01. 20x0.01 is 0.2 or 0.20.

Then you add the 4,000 to the 20,000 because it states, “the next day, they sold the car 20% more than they paid. This means that you’ll have to add it. 20,000 plus 4000 would be 24,000. So 24,000 would be the cost of the car they sold.

However they didn’t wanna know the cost of the car, they wanted to know how much Sara would get. So you would have to take 9% of the cost of the cost which would be 2,160.

Final result: $2,160

4 0

2 years ago

The expression 3x2−5x2simplifies to −2x2 is this true?

Helga [31]

Answer:

I dont think so I would look at it as how did they get the -2

5 0

3 years ago

Read 2 more answers

Find the volume and area for the objects shown and answer Question

klio [65]

Step-by-step explanation:

You must write formulas regarding the volume and surface area of the given solids.

$\bold{\#1\ Rectangular\ prism:}\\\\V=lwh\\SA=2lw+2lh+2wh=2(lw+lh+wh)\\\\\bold{\#2\ Cylinder:}\\\\V=\pi r^2h\\SA=2\pi r^2+2\pi rh=2\pir(r+h)\\\\\bold{\#3\ Sphere:}\\\\V=\dfrac{4}{3}\pi r^3\\SA=4\pi r^2$

$\bold{\#4\ Cone:}\\\\V=\dfrac{1}{3}\pi r^2h\\\\\text{we need calculate the length of a slant length}\ l\\\text{use the Pythagorean theorem:}\\\\l^2=r^2+h^2\to l=\sqrt{r^2+h^2}\\\\SA=\pi r^2+\pi rl=\pi r^2+\pi r\sqrt{r^2+h^2}=\pi r(r+\sqrt{r^2+h^2})\\\\\bold{\#5\ Rectangular\ Pyramid:}\\\\V=\dfrac{1}{3}lwh\\\\$

$\\\text{we need to calculate the height of two different side walls}\ h_1\ \text{and}\ h_2\\\text{use the Pythagorean theorem:}\\\\h_1^2=\left(\dfrac{l}{2}\right)^2+h^2\to h_1=\sqrt{\left(\dfrac{l}{2}\right)^2+h^2}=\sqrt{\dfrac{l^2}{4}+h^2}=\sqrt{\dfrac{l^2}{4}+\dfrac{4h^2}{4}}\\\\h_1=\sqrt{\dfrac{l^2+4h^2}{4}}=\dfrac{\sqrt{l^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{l^2+4h^2}}{2}$

$\\\\h_2^2=\left(\dfrac{w}{2}\right)^2+h^2\to h_2=\sqrt{\left(\dfrac{w}{2}\right)^2+h^2}=\sqrt{\dfrac{w^2}{4}+h^2}=\sqrt{\dfrac{w^2}{4}+\dfrac{4h^2}{4}}\\\\h_2=\sqrt{\dfrac{w^2+4h^2}{4}}=\dfrac{\sqrt{w^2+4h^2}}{\sqrt4}=\dfrac{\sqrt{w^2+4h^2}}{2}$

$SA=lw+2\cdot\dfrac{lh_1}{2}+2\cdot\dfrac{wh_2}{2}\\\\SA=lw+2\!\!\!\!\diagup\cdot\dfrac{l\cdot\frac{\sqrt{l^2+4h^2}}{2}}{2\!\!\!\!\diagup}+2\!\!\!\!\diagup\cdot\dfrac{w\cdot\frac{\sqrt{w^2+4h^2}}{2}}{2\!\!\!\!\diagup}\\\\SA=lw+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw}{2}+\dfrac{l\sqrt{l^2+4h^2}}{2}+\dfrac{w\sqrt{w^2+4h^2}}{2}\\\\SA=\dfrac{2lw+l\sqrt{l^2+4h^2}+w\sqrt{w^2+4h^2}}{2}$

6 0

2 years ago