What are the solutions to the system of equations?

{y=2x²−6x+3
{y=x−2

Answers

Answer 1

Answer:

x = 1, y = −1

x = 5/2, y = 1/2

Step-by-step explanation:

From the question given above, the following data were obtained:

y = 2x² − 6x + 3 ........ (1)

y = x − 2 ...... (2)

We can obtain the solutions to the equation as follow:

y = 2x² − 6x + 3 ........ (1)

y = x − 2 ...... (2)

Substitute the value of y in equation 2 into equation 1

y = 2x² − 6x + 3

y = x − 2

2x² − 6x + 3 = x − 2

Rearrange

2x² − 6x − x + 3 + 2 = 0

2x² − 7x + 5 = 0

Solve by factorization

Obtain the product of 2x² and 5. The result is 10x².

Find two factors of 10x² such that their sum will result to −7x.

The factors are −2x and −5x.

Replace −7x in the equation above with −2x and −5x as shown below:

2x² − 2x − 5x + 5 = 0

2x(x − 1) − 5(x − 1) = 0

(x − 1)(2x − 5) = 0

x − 1 = 0 or 2x − 5 = 0

x = 1 or 2x = 5

x = 1 or x = 5/2

Substitute the value of x into equation 2 to obtain y

y = x − 2

x = 1

y = 1 − 2

y = −1

x = 5/2

y = x − 2

y = 5/2 − 2

y = (5 − 4)/2

y = 1/2

SUMMARY:

x = 1, y = −1

x = 5/2, y = 1/2


Related Questions

1+1×2+3+5×8÷3+2/3×8+1+1+4=?

Answers

Answer:

92/3

Step-by-step explanation:

PEMDAS

(Parentheses Exponents Multiplication Division Addition Subtraction)

No Parentheses

No Exponents

Multiplication:

1+ 2 +3+ 40 ÷3+ 16/3 +1+1+4

Division:

1+2+3+ 40/3 +16/3+1+1+4

Addition:

12 + 56/3 = 92/3

No Subtraction

**Assuming "/" indicates a fraction and "÷" indicates division (2/3 × 8 is different than 2 ÷ 3 × 8)

a grocer mixes 20.25 kg of green tea with 35.10 kg of ordinary tea and repacks all tea in 45 packets of equal weight. how much does each packet weigh?

Answers

Answer:

1.23 kg

Step-by-step explanation:

(20.25 kg + 35.10 kg) : 45 = 1.23 kg

toán 9 nha mọi người

Answers

Answer:

Thamkhao

Step-by-step explanation:

What is the sum of the interior angles of the octagon below?
Select one:
a. 360°
b.720°
C. 1,080
d. 800

Answers

Answer:

Option C, 1,080

Step-by-step explanation:

sum of the interior angles of the octagon,

(8-2)×180

= 6×180

= 1080

Answered by GAUTHMATH

Find the area of the shaded region.

A. 160 in²
B. 160.5 in²
C. 96 in²
D. 192 in²

Answers

Answer:

C. 96 in²

Step-by-step explanation:

24x8=192

1/2 x24x8= 96

192-96=96

18) Both x and y coordinates of a point in quadrant 1 are negative.

Answers

Answer:

false

Step-by-step explanation:

the first quadrant of a coordinate plane is the upper right corner

this means that both x and y coordinates of a point would have to be positive

therefore it's false

hope this helps!

Multiply the polynomial by distribution. Show your work and explain the steps you used to solve.
- 8x(x^2 – 8x + 3)

Answers

Answer:

-8x^3 + 64x^2 - 24x

Step-by-step explanation:

To distribute, we must multiple -8x to each term:

-8x(x^2) - 8x(-8x) - 8x(3)

-8x^3 + 64x^2 - 24x

Step-by-step explanation:

[tex] - 8x( {x}^{2} - 8x + 3) \\ = ( - 8x \times {x}^{2}) - ( - 8x \times 8x) + ( - 8x \times 3) \\ = - 8 {x}^{3} + 64 {x}^{2} - 24x[/tex]

distribute -8x to each term in the perenthesis i.e. multiply each term by -8x

whats the correct ordered pair for, x+y=12 and -x=-y-10

Answers

i'm doing this as a system, ok?

x + y = 12

- x = - y - 10

x + y = 12

-x + y = -10

2y = 2

y = 1

x + 1 = 12

x = 11

so, the ordered pair is (11, 1) -> remember that the x always comes first

hope it helps :)

Answer:yes yes culo Rotox (b

Step-by-step explanation: pro gard1bas x12x14x20¿142

For the quadratic, y = -2(x - 1)(x + 4), the x-intercepts are

Answers

Answer:

I think (-2, 13) or (-2, 12)

rearrange the formula to make x the subject : 5( a - 2x) = 9(x + 1)

Answers

Answer:

x = [tex]\frac{5a-9}{19}[/tex]

Step-by-step explanation:

Given

5(a - 2x) = 9(x + 1) ← distribute parenthesis on both sides

5a - 10x = 9x + 9 ( add 10x to both sides )

5a = 19x + 9 ( subtract 9 from both sides )

5a - 9 = 19x ( divide both sides by 19 )

[tex]\frac{5a-9}{19}[/tex] = x

The diagram shows the floor of a room. The carpet used to
cover the floor costs $5.25 per square foot. How much will
it cost to carpet the entire floor?

Answers

Answer:

3rd option, $672

Step-by-step explanation:

The area is,

(4×12)+(8×10)

= 128

per square foot it costs $5.25, so the total cost will be,

128×$5.25

= $672

Answered by GAUTHMATH

HELPPP PLEASE!!!

Salvador reads 12 books from the library each month for n months in a row. Write an expression to show how many books Salvador read in all. Then, find the number of books Salvador read if he read for 7 months.

Answers

Answers:

The expression is 12n

He reads 84 books in 7 months

==================================================

Explanation:

For 1 month, he has read 12*1 = 12 books

For 2 months, he has read 12*2 = 24 books

For 3 months, he has read 12*3 = 36 books

and so on

If we let n represent the number of months, then 12*n or 12n represents the number of books read after n months. The variable n is some placeholder for a positive whole number.

If we replaced n with say n = 7, then 12*n = 12*7 = 84 books are read in 7 months.

Salvador reads 12 books each months so for n months he reads 12n books. In 7 months, n=7, so he reads 12*7 which is 84 books

what is the approximate shadow in feet of the tree in the figure below.​

Answers

Answer:

224 ft

Step-by-step explanation:

The tree makes a 90° angle with the ground, so we have a right triangle.

For the 32° angle, the height of the tree is the opposite leg. The length of the shadow on the ground is the adjacent leg.

The trig ratio that relates the opposite leg to the adjacent leg is the tangent.

Let the length of the shadow of the tree on the ground be x.

tan A = opp/adj

tan 32° = 140 ft/x

x = 140 ft/tan 32°

x = 224 ft

Answer: 224 ft

In a right triangle, two sides are 12 and 13. Find the measure of the third side. Consider all cases

Answers

Answer:

Case 1

12 and 13 are legs, then find the hypotenuse.

c = [tex]\sqrt{12^2+13^2} = \sqrt{313}[/tex] ≈ 17.69

Case 2

13 is hypotenuse, 12 is a leg, find the missing leg.

b = [tex]\sqrt{13^2-12^2} = \sqrt{25} = 5[/tex]

Answer:

Solution given:

Case 1:

if base=12

hypotenuse=13

perpendicular=??

By using Pythagoras law

hypotenuse²=perpendicular²+base²

13²=perpendicular ²+12²

perpendicular ²=13²-12²

perpendicular=[tex]\sqrt{13²-12²}=\sqrt{25}=5[/tex]units

Case:2:

Case 1:

if base=12

hypotenuse=13

perpendicular=??

By using Pythagoras law

hypotenuse²=perpendicular²+base²

13²=perpendicular ²+12²

perpendicular ²=13²-12²

perpendicular=[tex]\sqrt{13²-12²}=\sqrt{25}=\bold{\large{5}}[/tex]units

Case:2:

if base=12

hypotenuse=??

perpendicular=13

By using Pythagoras law

hypotenuse²=perpendicular²+base²

hypotenuse²=13 ²+12²

hypotenuse² ²=13²+12²

hypotenuse²=[tex]\sqrt{13²+12²}=\sqrt{313}=\bold{\large{17.7}}[/tex]units

Express it in slope
Enter the corre
000
Clear all
-8
8
In slope-intercept form

Answers

In this question, we are given two points, (0,0) and (-8,8), and we want to find the equation of the line in slope-intercept formula.

Slope-intercept formula:

The equation of a line, in slope-intercept formula, is given by:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept(value of y when x = 0)[/tex]

Point (0,0):

This means that when [tex]x = 0, y = 0[/tex], and thus, the y-intercept is [tex]b = 0[/tex], and the equation of the line is:

[tex]y = mx[/tex]

Slope:

When we have two points, the slope is given by the change in y divided by the change in x.

In this question, the two points are (0,0) and (-8,8).

Change in x: -8 - 0 = -8

Change in y: 8 - 0 = 8

Slope:

[tex]m = \frac{-8}{8} = -1[/tex]

Thus, the equation of the line, in slope-intercept formula, is:

[tex]y = -x[/tex]

For another example of an equation of a line in slope-intercept formula, you can check https://brainly.com/question/21010520

The equation of the line that passes through [tex](x_{1}, y_{1}) = (0, 0)[/tex] and [tex](x_{2}, y_{2}) = (-8, 8)[/tex] is [tex]y = -x[/tex].

According to the statement, we know the location of two Points: [tex](x_{1}, y_{1}) = (0, 0)[/tex] and [tex](x_{2}, y_{2}) = (-8, 8)[/tex], and must derive the Equation of the Line from this information, whose procedure is described below:

1) Determine the Slope of the line by the Slope Equation for Secant Lines.

2) Use ([tex]x_{1}, y_{1}[/tex]) in the Equation of the Line and solve for the Intercept.

3) Write the resulting Equation of the Line.

Step 1:

The slope of a secant line ([tex]m[/tex]) is calculated from the following formula:

[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] (1)

If we know that [tex](x_{1}, y_{1}) = (0, 0)[/tex] and [tex](x_{2}, y_{2}) = (-8, 8)[/tex], then the slope of the line is:

[tex]m = \frac{8-0}{-8-0}[/tex]

[tex]m = -1[/tex]

Step 2:

The equation of the line is Slope-Intercept Form is now represented:

[tex]y = m\cdot x + b[/tex] (2)

Where:

[tex]x[/tex] - Independent variable.

[tex]y[/tex] - Dependent variable.

[tex]b[/tex] - Intercept.

If we know that [tex](x_{1}, y_{1}) = (0, 0)[/tex] and [tex]m = -1[/tex], then the intercept of the equation of the line is:

[tex]0 = -1\cdot (0) + b[/tex]

[tex]b = 0[/tex]

Step 3:

And the equation of the line that passes through [tex](x_{1}, y_{1}) = (0, 0)[/tex] and [tex](x_{2}, y_{2}) = (-8, 8)[/tex] is [tex]y = -x[/tex].

Related question: https://brainly.com/question/18894159

Which linear inequality is represented by the graph?

Answers

Answer:

Wow

Step-by-step explanation:

I love the question pls i also want to know the answer to it

HELP ME !! find the value of x​

Answers

Answer:

ERROR

Step-by-step explanation:

find the value or x.
-
a. 5
b. 11
c. 25
d. 31

Answers

11 because it is bigger than EB and smaller then DF

A box contains 28 balls of which 7 are red, 7 are blue, 14 are green.
If a ball is drawn at random, find the probability that it is neither blue nor red.

Answers

Answer:

1 /4

Step-by-step explanation:

Given that :

Number of red = 7

Number of Blue = 7

Number of green = 14

Total number of balls = 28

Probability of picking a ball that is neither red nor green.

Probability = required outcome / Total possible outcomes

P(neither red nor green) = P(picking a blue ball) = 7 / 28 = 1/4

find the 80th term following arithmetic sequence 8,14,20,26

Answers

Answer:

The 80th term is 482

Step-by-step explanation:

8,14,20,26

This is an arithmetic sequence

Find the common difference by taking the second term and subtracting the first term

14-8 = 6

We are adding 6 each time

The formula for an arithmetic sequence is

an =a1+d(n-1)  where a1 is the first term, d is the common difference and n is the term we are looking for

a80 = 8+6(80-1)

       = 8 + 6*79

     = 8+474

    = 482

The 80th term is 482

Answer: 482

Step-by-step explanation:

[tex]\displaystyle\ \Large \boldsymbol{Rule:} \\\\\boxed{ \huge \boxed{a_n=a_1+(n-1)d }} } \ \ \\\\\\ 8 \underbrace{}_6 14 \underbrace{}_620\underbrace{}_626 ......a_{80}=? \\\\\\a_1=8 \ \ ; \ \ d=6 \\\\\\ a_{80}=8+(80-1)\cdot 6=480+8-6=482 \\\\\\\\ Answer: \boxed{\boldsymbol{ a_{80}=482}}[/tex]

please help, I'm so confused how to-do this

Answers

Answer:

Step-by-step explanation:

use the quadratic formula : [tex]x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a}[/tex], where ax^2+bx+c=0

[tex]y = \frac{ -(-20) \pm \sqrt{(-20)^2 - 4(1)(50)}}{2(1)}[/tex]

[tex]y = \frac{ 20 \pm \sqrt{400 - 200}}{2}[/tex]

[tex]y = \frac{ 20 \pm \sqrt{200}}{2}[/tex]

y = 17.07106~ or 2.928932~

A 60 foot monument casts a 25-foot shadow How long is the shadow of a 4.5 tall person?
A) 1.875 feet (it’s this one)
B) 5.555 feet
C) 2456 feet
D) 13334 feet

Answers

Answer:

A

Step-by-step explanation:

Using similarities we have

(Actual size)/(Shadow length)=60/25=4.5/x

x=4.5*25/60=1.875

Answer:

A) 1.875 feet

Step-by-step explanation:

Which of the following is true about the sequence graphed below? (and Why)

Options:

• The sequence is arithmetic because the terms have a common difference.
• The sequence is arithmetic because the terms do not have a common difference.
• The sequence is not arithmetic because the terms have a common difference.
• The sequence is not arithmetic because the terms do not have a common difference.

Answers

Answer:

Step-by-step explanation:

a₂ = 9

a₃ = a₂-1.5

a₄ = a₃-1.5

a₅ = a₄-1.5

etc.

The terms have a common difference of -1.5, so the sequence is arithmetic.

Answer:

Step-by-step explanation:

The common difference is a y-thing. It looks like the difference in the y-values of each of these points is -1.5. That means that this is an arithmetic sequence because the common difference is consistently -1.5. In fact, the whole equation can be determined to be

[tex]a_n=-1.5n+12[/tex]

Help !

1. You have a 14 pencils. Two pencils are red, 5 pencils are orange, 3 pencils are
green and 4 pencils are brown

a. If a pencil is picked at random, what is the probability that the pencil
will be orange?
b. If a pencil is picked at random, what is the probability that the pencil
will be green?

c. If a pencil is picked at random, what is the probability that the pencil will be red?

d. If a pencil is picked at random, what is the probability that the pencil
will be brown?

e. If a pencil is picked at random, what is the probability that the pencil
will be brown or red?

Answers

Answer:

a. p(orange) = 5/14

b. p(green) = 3/14

c. p(red) = 1/7  

d. p(brown) = 2/7  

e. p(brown or red) = 3/7

Step-by-step explanation:

1. You have a 14 pencils. Two pencils are red, 5 pencils are orange, 3 pencils are green and 4 pencils are brown.

p(color) = (number of pencils of that color)/(total number of pencils)

p(color) = (number of pencils of that color)/14

a. If a pencil is picked at random, what is the probability that the pencil

will be orange?

p(orange) = 5/14

b. If a pencil is picked at random, what is the probability that the pencil

will be green?

p(green) = 3/14

c. If a pencil is picked at random, what is the probability that the pencil will be red?

p(red) = 2/14 = 1/7

d. If a pencil is picked at random, what is the probability that the pencil

will be brown?

p(brown) = 4/14 = 2/7

e. If a pencil is picked at random, what is the probability that the pencil

will be brown or red?

brown: 4

red: 2

brown or red: 4 + 2

p(brown or red) = 6/14 = 3/7

How to do this question

Answers

Answer:

Step-by-step explanation:

Answered by G a u t h m a t h

Please mark it as brainliest & thank it if it helped you

PLEASE HELP!!!!!!!!

Answers

Answer:  3

Step-by-step explanation:                                                                                                          

[tex]\displaystyle\ \Large \boldsymbol{} We \ have \ a \ square\ function \\\\ f(x)=ax^2+bx+c \\\\And \ we \ know \\\\ \left[\left \[ {{f(0)=a\cdot 0+b\cdot0+c=0} \atop {f(-4)=a(-4)^2+-4b+c=-24}} \right.=>[/tex]                                                [tex]\displaystyle\ \Large \boldsymbol{} \left[ \ {{c=0} \atop {16a-4b=-24}} \right. =>\boxed{4a-b=-6} \\\\\\ and \ x_0 =-\frac{b}{2a}=1 =>\boxed{ b=-2a} \\\\\\ \left \{ {{4a-b=-6} \atop {b=-2a}} \right. =>4a+2a=-6=> a=-1 \ ; \ b=2 \\\\\\then \ b-a=2-(-1)=\boxed{3}[/tex]                                                                                    

a marathon runner can jog one mile in 7.5 minutes. how many miles can the runner complete in 3.5 hours

Answers

1 hour = 60 minutes

3.5 hours x 60 = 210 minutes

210 minutes / 7.5 minutes per mile = 28 miles

Answer: 28 miles

Express (root 19 - root 7)(root 19 + root 7) in simplest form.

Answers

Answer

root 354

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

(√19 -√7)(√19 +√7)

( a +b)( a -b) = a²-b²

(√19)² -(√7)² = 19 -7 = 12

A bag contains eight tiles labeled A, B, C, D, E, F, G, and H. One tile will be randomly picked.
What is the probability of picking a vowel?
Write your answer as a fraction.

Answers

Answer:

1/4

Step-by-step explanation:

Count all of the vowels (this will be your numerator):

A and E

2

Count all of the letters (this will be your denominator):

A, B, C, D, E, F, G, and H

8

Write this as a fraction:

2/8

Simplify:

2/8 = 1/4

Which function shows a fabric with a price of $1.25 per square yard?

A table showing Price of Fleece with five columns and two rows. The first row, Square Yards, has the entries, 1, 2, 3, 4. The second row, Price, has the entries, $1.25, $2.00, $2.75, $3.50.
A table showing Price of Fleece with five columns and two rows. The first row, Square Yards, has the entries, 1, 2, 3, 4. The second row, Price, has the entries, $0.25, $1.25, $2.25, $3.25.
A coordinate plane showing Price of Fleece. The x-axis shows Number of Square Yards and the y-axis shows Price in dollars. A line starts at (0, 0) and passes through (5, 4) and ends (10, 8).
A coordinate plane showing Price of Fleece. The x-axis shows Number of Square Yards and the y-axis shows Price in dollars. A line starts at (0, 0) and passes through (4, 5) and ends (8, 10).

Answers

Answer:

D

Step-by-step explanation:

Took the test

Brainliest pls

Answer:

D

Step-by-step explanation:

E 2020

Other Questions
What are the key features of this organ?Name the organ. dleleleleldldldldlldldldldlddl A reaction vessel is charged with phosphorus pentachloride, which partially decomposes to phosphorus trichloride and molecular chlorine according to the following reaction: PCl5(g) PCl3(g)+Cl2(g) When the system comes to equilibrium at 250.0C, the equilibrium partial pressures are: PPCl5 = 0.688 atm and PPCl3 = PCl2 = 0.870 atm.Required:What is the value ofKpat this temperature? Cual es el mensaje de la cancin this is america g A catch block that expects an integer argument will catch Group of answer choices all exceptions all integer exceptions any exception value that can be coerced into an integer C list two items you can do to keep a DWI off your record! Help please guys thanks what danger did farmers face in the 1880s? Which element is necessary to make proteins for plant growth? FAst How much wrapping is needed to cover a cubed gift box that is 9 inches high? (Include the bow which takes 115 sq. inches.) A canoeist paddled down a river a distance of 2 miles in 45 minutes. Paddling up-stream on his return, it took him 90 minutes. Find the rate of the canoe in still water. Find the missing side of triangle Retrograde metamorphism a. happens under conditions of increasing temperature and pressure. b. may happen as regression brings rock closer to the Earth's surface. c. requires very high pressures but needs only low temperatures to occur. d. requires the addition of hydrothermal fluids to replace water driven off during prograde metamorphism. Can you provide a solution or a formula? can she get some help I need help I don't understand this. Need help asap, thanks :) In some organizations, trust is facilitated through root authorities outside the organization, and many organizations choose to delegate authority for trust within their own AD environment. Discuss some the challenges of managing trust within an organization, and the alternatives. Read these sentences from the excerpt:What he most dreaded, that I most desired. What he most loved,that I most hated. That which to him was a great evil, to becarefully shunned, was to me a great good, to be diligentlysought, and the argument which he so warmly urged, against mylearning to read, only served to inspire me with a desire anddetermination to learn.Which statement best explains how parallel structure advancesthe author's purpose?It emphasizes the author's belief that reading andwriting are important skills and keys to freedom.It highlights the need for slaves and slaveholders tocome together in order to end slavery.It shows that the author disagrees with the slaveownersIt provides a counter argument to the author's pointsand purpose find the slope of the tangent line of the curve r = cos (3theta) at theta = pi / 3