solve this nonlinear system of equations.
y=-x^2+6x-5
y=3
step 1: use substitution to combine the equations. Rewrite so that one side is equal to zero.
step 2: factor the equation
step 3: identify the x-values of the solutions.
step 4: identify the solutions to the system.

Answers

Answer 1

Answer:

1. [tex]x^2-6x+8=0[/tex]

2. [tex](x-4)(x-2)=0[/tex]

3. [tex]x=4 \text{ and } x=2[/tex]

4. [tex]x=4 \text{ and } x=2[/tex]

Step-by-step explanation:

1. When using substitution all we do would be is substituse the y for a 3.

This leaves us with the equation:

[tex]3=-x^2+6x-5[/tex]

Rewriting it we get:
[tex]0=-x^2+6x-8[/tex]

or if we shift the 0 to the other side:

[tex]x^2-6x+8=0[/tex]

2. In order to factor the equation we can use the butterfly method:

[tex]\left[\begin{array}{ccc}1&-4\\1&-2\end{array}\right][/tex]
So it factors out to:

[tex](x-4)(x-2)=0[/tex]
You can also use the quadratic formula.

3. To find the solutions we just set each factor to 0
[tex]x-4=0\\\text{and}\\x-2=0[/tex]
So the x-values would be:
[tex]x=4 \text{ and } x=2[/tex]

4. To find the solution to the system we just plug in the values and it turns out to be the same numbers as before.


Related Questions

Convert to standard form: y=-7x/2-3

Answers

Answer:

7x + 2y = −6

Step-by-step explanation:

I need help guys I got like 1 hour left.

Answers

Answer:

Domain: x <= 4

Step-by-step explanation:

The domain is all the x's on the graph or all the x's that can be used in the equation. see image for graph. The graph exists coming from negative infinity (the left side of the graph) and then stops at the point where x is 4. So x must be less than 4 or equal to 4.

Algebraically, if x is bigger than 4, you get a negative number inside the radical (the square root symbol) and that is not allowed. Again we find that x has to be less than or equal to 4.

How many whole groups of 63 go into 504?
I will mark brainliest answer!

Answers


Answer: 8
504÷63= 8
I hope this helps! :)

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Answers

Answer:

Final answer -

[tex]Area \: of \: figure = 60 \: m {}^{2} [/tex]

hope helpful :D

Find x and y

Y 12 x 6

Answers

Answer:

Step-by-step explanation:

y= x^2-2x+2 complete the square to determine the vertex and maximum or minimum value. Determine the number of x-intercepts.

Answers

Answer:

Step-by-step explanation:

y = x^2 - 2x + 2

y = (x - 1)^2 - 1 + 2

y = (x - 1)^2 + 1

Vertex is at (1, 1) and minimum value is  1.

answeeeer plssssss..

Answers

ok well- what time do you need it to be answered by?

Let a represent a positive number and let b represent a negative number. Tell whether each statement is True or False. True False a. The difference (a - b) could be negative. True False b. The difference (b − a) cannot be positive. True False C. The sum (a + b) could be positive. True False d. The sum (b + a) must be negative. ​

Answers

a. False; if b is negative, then -b is positive, so

a - b = a + (-b)

is the sum of two positive numbers, which must be positive.

b. True; the sum of two negative numbers is again negative.

c. True; a + b will be positive as long as a > |b|. (For example, if a = 2 and b = -1, then of course 2 > |-1| = 1, and a + b = 2 + (-1) = 1 > 0.)

d. False; this would contradict the result of part (c). b + a is only negative if a ≤ |b|. (For example, if a = 1 and b = -2, then b + a = -2 + 1 = -1 < 0.)

Alice has 2290 dollars, Cindy has 987 more than Alice
What is the amount of money combined with Alice and Cindy? ​

Answers

Answer: 3,277

Step-by-step explanation: all you have to do is add 2290 and 987 toghther  

Answer:

5567 $.

Step-by-step explanation:

The amount of money Alice has = 2290 $.

Cindy = Amount of money Alice has + 987

= 2290 + 987

= 3,277.

Now,

The amount of money combined = 2290 + 3277

= 5567 $.

Kristine wants to do hardwood flooring for her room. A floor plan of the room (in feet) is shown. How much hardwood flooring does she need?

Answers

Kristine would require at least 116ft of hardwood flooring for her room.

The answer is arrived at by using simple calculations of the area of a square - a polygon.

How do we arrive at the answer above?

Note that there are missing portions on the shape of the floor. (See a more elaborate version attached).

The side labeled F = 12ft

The side labeled CDE comprises three sides: 8, 2, and 2 respectively. This is also equal to 12.

With this information, we can calculate the area of the square assuming it was full.

The area of a square is given as:

Length x Breadth or L²;

that gives us: 12 x 12 or 12² = 144ft.

Now we get the total actual area by removing the areas of the missing segments.

Section Ax and Ay is also a square. because the length and the breadth are equal.

hence the area of AxAy = 16ft.

We also have the area of the section labeled D,Dx. This section is a rectangle. The formula for the area of a rectangle is:

Length x Breadth.

Hence, we have

6 x 2 = 12ft.

Total area of missing sections are:

12 + 16 = 28ft.

The total area of the square less the missing areas is:

144 - 28 = 116ft.

Hence the total amount of Hardwood that Kristine would require in square ft is 116ft.


See the attached images and learn more about areas of polygons at:
https://brainly.com/question/10567784

a ball is dropped from a height of one meter. every time it hits the ground, it rebounds to exactly 2/3 of the previous height. what is the total distance the ball has traveled after its hits the ground for the eigth time?

Answers

Answer:69/56 that is your answer did it help


Pls help I’ll give 30 points

Answers

Answer:

C

Step-by-step explanation:

30, 32, 33, 33, 34, 37, 39, 41, 43, 47, 49, 52, 53, 57

Middle numbers: 39 + 40 = 80/2 = 40

Highest number: 57

Lowest number: 30

I hope this helps!

A six-sided number cube has sides labeled 1, 1, 2, 2, 3, and 3. What is known about the probability model for this situation? Select all correct answers.
The probability model for this situation is uniform.
The probability model for this situation is non-uniform
. The probabilities of the individual outcomes are the same.
The probabilities of the individual outcomes are not the same.

Answers

Answer:

The probabilities of the individual outcomes are the same.

The probability model for this situation is uniform.

Step-by-step explanation:

There is 2 of each number so there is an equal chance. when there is an equal chance that is uniform.

Answer:

i hope this helped :)

Step-by-step explanation:

please help and tysm!! :)) <3 ​

Answers

Answer:

39

Step-by-step explanation:

above 50 it's nearest 100.

Please mark me as a brainliest

Answer:

38.98

Step-by-step explanation:

Step 1: look at the number after the hundredths place, in this problem being 7

Step 2: Indecate wither thr number is larger than 5 or smaller than 5. If larger you would round up, if smaller you'd round down.

In this problem you would round up.

Step 3: When rounding up you go to the hundredths place and add one to that place. When rounding down, you delete all the values after the hundredths place.


Please help me with this thank you

Answers

Answer:

  -11x² +14x -11

Step-by-step explanation:

When one polynomial is subtracted from another, each of the terms of the subtrahend is subtracted from the corresponding term of the minuend.

  (-2x² +4x -10) -(9x² -10x +1)

  = (-2 -9)x² +(4 -(-10))x +(-10 -1)

  = -11x² +14x -11

your answer should be a polynomial in standard form. -t(-4t^3+8t^2)=

Answers

is there any answer choices

If the probability that the Islanders will beat the Rangers in a game is 85%, what is the probability that the Islanders will win exactly three out of five games in a series against the Rangers? Round your answer to the nearest thousandth.

.138


.037


.158


.232

Answers

The probability that the Islanders will win exactly three out of five games in a series against the Rangers is mathematically given as

P(x=3)=0.26367

What is the probability that the Islanders will win exactly three out of five games in a series against the Rangers?

Generally, the equation for the probability is mathematically given as

P(x=3)=nC3 (P)^r (q)^{n-r}

Therefore

P(x=3)=5C3 (0.75)^3 (0.25)^{5-3}

P(x=3)=10 (0.75)^3 (0.25)^{5-3}

P(x=3)=0.26367

In conclusion, The probability of the islander

P(x=3)=0.26367

Read more about probability

https://brainly.com/question/795909

An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 22 feet up. The ladder makes an angle of 77^{\circ} ∘ with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.

Answers

Now

[tex]\\ \rm\Rrightarrow sin\theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{22}{H}=sin77[/tex]

[tex]\\ \rm\Rrightarrow H=22/sin77[/tex]

[tex]\\ \rm\Rrightarrow H=22.59ft\approx 23ft[/tex]

The length of the extension ladder that is against the outside wall of the house is 22.58 feet.

What is the length of the ladder?

When the ladder lies against a house, a right triangle is formed. The length of the ladder is the hypotenuse. The distance from the base of the ladder to the house is the base. The lenfth off the house is the length.

To find the length of the ladder, Sin would be used:

Sin = opposite / hypotenuse

Sin 77 = 22 / h

h = 22 / 0.9743 = 22.58 feet

To learn more about trigonometry, please check: https://brainly.com/question/22782564

#SPJ2

What is the percent if 200 is the total and 150 is the part?

Answers

Answer:

75%

Step-by-step explanation:

75% of 200 is 150

Answer:

75% since [tex]50 + 50 + 50 = 150[/tex] which is [tex]3[/tex] quarters of [tex]200[/tex]

Please mark brainliest.

A swimming pool measures 10 feet by 8 feet by 5 feet. What is the volume of the swimming pool

Answers

Answer:

400 ft^3

Step-by-step explanation:

To find volume you simply do length x width x height

So, 10 x 8 x 5 which equals 400 ft; We make it have a power of 3 (cubed) because it is 3 dimentional object.

Hope this helps!

How many solutions does this system of equations have?
Sy=-4x + 3
2x + 8y = 10

Answers

Answer:

Step-by-step explanation:

Assuming the s is a typo the answer to this system is x=7/15 and y=17/15

giving brainiest and 85 points!

Answers

Answer:

12 560 cubic feet

Step-by-step explanation:

radius of circular cross section = 20ft/2 = 10ft

Area of circular cross section = πr²

                                                 = 3.14 x 10 x 10

                                                 = 314 square feet

Volume of cylindrical tank =  314 ft² x 40ft

                                            = 12 560 ft³

                           

I need an answer for all those please!

Answers

Ok so, number one is ……………….number two is ……………….

Find the missing angle.

Answers

Answer:

32 degrees

Step-by-step explanation:

The angle supplementary with the 122 degree angle measures 180-122=58 degrees.

So, the triangle has interior angles of f, 90, and 58 degres.

Since the angles in a triangle add to 180 degrees, f+180-90-58=32 degrees

I need help on this please its really hard its due in thirty min

Answers

Answer:

L < 5.25yd

Step-by-step explanation:

We can think of Mrs. Klein's composting area as a rectangle, and the formula for finding the area of a rectangle is Base * Height = Area (B*H=A)

Let's just say for the sake of solving the problem that they say that area of the garden had to be exaclty 6 square feet. Because the area must be 6sqft (sqyd = square yards) then we can enter 6 into our formula.

B*H=A now equals B*H=6

They also tell us that the width (which is a stand-in for height) is [tex]1\frac{1}{7}[/tex] so we can enter that in our formula as well

B*H=6 now is [tex]B*1\frac{1}{7} =6[/tex] and now we just have one unknown... the B (base)

And since [tex]B*1\frac{1}{7} =6[/tex] then [tex]6/1\frac{1}{7} =B[/tex]

Thus,

[tex]6yd / 1\frac{1}{7} = 5.25yd[/tex]

And because the question said that the area must be less then 6sqyd, then the length can be anything less then 5.25yd.

Thus,

L < 2.25

Hope that helped... Chow!

there are 56 customer in a shop 24 of them are men the rest of the customer are women find the ratio of the number of men to the number of women in the shop

Answers

Answer:

There are 32 women in the shop.

Choose the angle which is vertical to angle BFC in the following figure.
answer A angle CFD
answer B angle DFE
answer C angle AFC
answer D angle EFA

Answers

Angle DFE. Hope this helped.

I need help with this question.

Answers

Step-by-step explanation:

the volume of a cylinder is as for any regular shaped object

ground area × height

here the ground area is a circle, so we get

pi×r²×h

with r being the radius (half the diameter), and h the height.

therefore,

pi×(2.7/2)²×10 = 3.14×1.8225×10 = 57.25552611... cm³

so, the first option is correct.

please b quick

The display on a calculator reads 9.378 E - 5. Which value does this represent?

a. 937,800,000
b. 937,800
c. 0.00009378
d. 0.000009378​

Answers

Answer:  C.0.0009378

Step-by-step explanation:

9.378E-5 is basically 9.378 x 10∧-5. Move the decimal to right 5 times.

The radius of a circle is 15 in. Find its area in terms of \piπ

Answers

Answer:

Step-by-step explanation:

A = [tex]\pi[/tex]r²

A = [tex]\pi[/tex]15²

A = [tex]\pi[/tex]225

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