Eric Bella Joan or Maya PLEASE HELP

Y=-x^2+2x+10 y=x+2 Substitution Please show your work Need ASAP

erik [133]

Answer:

The solutions of the system of equations are the points

$(\frac{1-\sqrt{33}} {2},\frac{5-\sqrt{33}} {2})$

$(\frac{1+\sqrt{33}} {2},\frac{5+\sqrt{33}} {2})$

Step-by-step explanation:

we have

$y=-x^{2} +2x+10$ ----> equation A

$y=x+2$ ----> equation B

Solve the system by substitution

substitute equation B in equation A

$x+2=-x^{2} +2x+10$

solve for x

$-x^{2} +2x+10-x-2=0$

$-x^{2} +x+8=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-x^{2} +x+8=0$

so

$a=-1\\b=1\\c=8$

substitute in the formula

$x=\frac{-1\pm\sqrt{1^{2}-4(-1)(8)}} {2(-1)}$

$x=\frac{-1\pm\sqrt{33}} {-2}$

$x=\frac{-1+\sqrt{33}} {-2}$ -----> $x=\frac{1-\sqrt{33}} {2}$

$x=\frac{-1-\sqrt{33}} {-2}$ -----> $x=\frac{1+\sqrt{33}} {2}$

Find the values of y

For $x=\frac{1-\sqrt{33}} {2}$

$y=x+2$

$y=\frac{1-\sqrt{33}} {2}+2$ ----> $y=\frac{5-\sqrt{33}} {2}$

For $x=\frac{1+\sqrt{33}} {2}$

$y=x+2$

$y=\frac{1+\sqrt{33}} {2}+2$ ----> $y=\frac{5+\sqrt{33}} {2}$

therefore

The solutions of the system of equations are the points

$(\frac{1-\sqrt{33}} {2},\frac{5-\sqrt{33}} {2})$

$(\frac{1+\sqrt{33}} {2},\frac{5+\sqrt{33}} {2})$

5 0

3 years ago

A scientist mixes water (containing no salt) with a solution that contains 35% salt. She wants to obtain 105 ounces of a mixture

Naya [18.7K]

Answer:

60 oz of water to add

45 oz of 35% salt solution should be used

Step-by-step explanation:

Let x = amt no. ounces in the first solution

and 105 - x = amt no. of ounces in the second solution

Ist solution contains 0% salt

2nd solution contains .35(105 - x) salt

.15(105= amt of salt in mix

So.

amt of salt in 1st solution + amt of salt in 2nd solution = amt of salt in the mix

0 + .35(105 - x) = .15(105)

Let's get rid of the fractions by multipying thru the equation by 100

35(105 - x) = 15(105)

3675 - 35x = 1575

-35x = -2100

x = 60 oz of water to add

105 - 60 = 45 oz of 35% salt solution should be used

7 0

2 years ago

9 m 11 m 16 m 4 m Find the area of this figure.

coldgirl [10]

Answer:

Can u send picture with it pls so i can figure it out?

What are the two shapes

Step-by-step explanation:

rectangle: length times width

triangle: base times height divided by 2

parallelgram: Base times height

square: side times side

*If you get it right then follow me on roblox: Supertasticgg

and sub to Flamingo

ANd almost forgot trapezoid: base 1 + base 2 times by height then divide with 2

6 0

3 years ago

Examples of spiral motion

natta225 [31]

Answer:Examples of Spiral Movement are:

Step-by-step explanation:

1)Cyclone

2)Spiral fern

8 0

3 years ago

Which of the following items are elements of a monthly checking account statement?

KiRa [710]

Answer:

D.

Step-by-step explanation:

Sana makatulong pag Mali EDI Mali

3 0

3 years ago

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