What are the solutions to the system of equations?

{y=x²−4x+8
y=2x+3

Answers

Answer 1

Answer:

x = 1, y = 5

x = 5, y = 13

Step-by-step explanation:

y = x² − 4x + 8 .......(1)

y = 2x + 3 .......(2)

Substitute the value of y in equation 2 into equation 1

y = x² − 4x + 8

y = 2x + 3

x² − 4x + 8 = 2x + 3

Rearrange

x² − 4x − 2x + 8 − 3 = 0

x² − 6x + 5 = 0

Solve by factorization

Find the product you x² and 5. The result is 5x²

Find the factors of 5x² such that their sum will result in −6x. The factors are −x and −5x.

Replace −6x in the equation above with −x and −5x. This is illustrated below:

x² − x − 5x + 5 = 0

x(x − 1) − 5(x − 1) = 0

(x − 1)(x − 5) = 0

x − 1 = 0 or x − 5 = 0

x = 1 or x = 5

Substitute the value of x into equation 2 to obtain the value of y.

y = 2x + 3

x = 1

y = 2(1) + 3

y = 2 + 3

y = 5

x = 5

y = 2x + 3

y = 2(5) + 3

y = 10 + 3

y = 13

SUMMARY:

x = 1, y = 5

x = 5, y = 13


Related Questions

A student recorded the weight of potatoes she used for a science fair project. Read


the data. For each potato, draw an X above the line plot to show its weight.


B


E


1


Weight in


읍 유 2 / 4 1 2 3 4 2


A


Potato


С


3


D


F


G


H


2


4


pounds


Кеу


1 potato = x


4.


4


O


2


4.


4


What is the total weight of all the potatoes? Give your answer in simplest form.


3


What is the difference in weight between potatoes that weigh 4 pound and those that


weigh pound? Give your answer in simplest form.

Answers

what?

Step-by-step explanation:

I dont understand

Can someone help me out

Answers

Answer:

10.2

Step-by-step explanation:

195×2×3×π/360

= 13π/4

= 10.2 (rounded to the nearest tenth)

Answered by GAUTHMATH

In an input/output table, all outputs are 0, regardless of the input. What could the function equation be? Select all that apply.

y = 0 x
y = x
y = x/0
y = 0/x

Answers

Answers:

choice A)   y = 0x

choice D)  y = 0/x

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

Explanation:

Choice A is the same as y = 0 because 0x turns into 0. Multiplying 0 with any number always leads to 0.

Similarly, choice D is the same as y = 0 as well. Dividing 0 over any nonzero value leads to 0. Note the key term "nonzero" here. We cannot have 0 in the denominator. So x = 0 is not allowed for choice D.

So for any nonzero x, we have 0x and 0/x result in the same thing.

-----------

Extra info:

Choice B can be ruled out because something like x = 2 leads to y = 2.

Choice C is ruled out because we can never have 0 in the denominator.

Please hurry I will mark you brainliest

Answers

Answer:

D y=2/3 x +1

  y= -3/2 x+2

Step-by-step explanation:

Perpendicular lines have slopes that multiply to -1

The equations are written in slope intercept form

y = mx+b where m is the slope

A 1/5* 5 = 1  not perpendicular

B 2/3 * 3/2 = 1  not perpendicular

C -1/5 * -5 = 1  not perpendicular

D 2/3 * - 3/2 = -1   perpendicular

uhhhh try using caculator

Find the graph of the inequality ys-=x+ 1.

Answers

Answer:

C

Step-by-step explanation  

The y-intercept is 1, the slope is -1/3, and the shaded area is under the graph because y is LESS than -x/3 + 1.

Which graph represents a function?
1, 2, 3, or 4

Answers

Answer:

The given graph is a function.

Step-by-step explanation:

There is only one given graph, and that graph is a function. In order to determine which graph is a function, conduct the vertical line test. Can a vertical line pass through the represented data set without crossing two y-values? (i.e. A 'sideways parabola' is not a function).

find the missing length

Answers

Answer:

it is an rigjt angle triangle you shoult pythogores therom if you will know it it will be easy to you to understand this question

The distance between Detroit, Ml to Paris, France is approximately 3930 mi. Flying from Detroit to Paris take 8 hr with the jet stream. The return flight takes 8.3 hr since the plane is flying against the jet stream. a. What the plane Soren still in air, rounded to the nearest whole number, is blank mph b. What the speed of the jet stream, rounded to the nearest whole number, is blank mph

Answers

Answer:

a)   [tex]s=482moh[/tex]

b)  [tex]s'=9mph[/tex]

Step-by-step explanation:

From the question we are told that:

Distance [tex]d=3930mi[/tex]

Time of flight [tex]T=8hr[/tex]

Flight back [tex]T_b=8.3hr[/tex]

Generally the equation for Time for flight with jet steam is mathematically given by

[tex]T=\frac{d}{s+s_1}[/tex]

[tex]8=\frac{3930}{s+s'}[/tex]

[tex]s+s'=491.3 ....equ1[/tex]

Generally the equation for Time for flight against jet steam is mathematically given by

[tex]T=\frac{d}{s-s_1}[/tex]

[tex]8.3=\frac{3930}{s-s_1}[/tex]

[tex]s+s'=473.5......equ 2[/tex]

Solving equ 1 and equ 2 simultaneously

[tex]s+s'=491.3[/tex]

[tex]s+s'=473.5[/tex]

Therefore

[tex]s=482moh[/tex]

[tex]s'=9mph[/tex]

I'M BEGGING YOU PLEASEEEE
A carnival game has 4,000,000 dollars as prizes. The first ticket drawn wins $15, the second ticket drawn wins $45, the third ticked wins $135 and so on.
a) How many tickets can be drawn without giving away more than the allotted prize money?
b) how much money is left over after all the prizes are awarded?

I WILL GIVE BRAINLIEST

Answers

if possible brainlist?

Step-by-step explanation:

A i think 3

and

B 3,999,805 will be left over

PLZ HELP I'LL GIVE BRAINY!!!! AND EXPLAIN


For this exponential function,
what is the output value (y),
when the input value (x) is 1?

y = 4.3x



(1, [?])

Answers

you have to plug in the x value to discover the y

y= 4.3 x 1

y = 4.3

so, the ordered pair is (1, 4.3)

hope it helps :)

Answer is y =4.3 that’s all filjkkks

Insert the missing number.
4
6 9 14
23
40
?
138
266

Answers

Answer: The missing number is 73

Step-by-step explanation:

Given:

4, 6, 9, 14, 23, 40, ?, 138, 266

Solve:

First, we try arithmetic patterns.

6 - 4 = 2

9 - 6 = 3

14 - 9 = 5

23 - 14 = 9

40 - 23 = 17

Clearly, there aren't arithmetic patterns.

Then, try through multiplication, exponents, and combination.

Finally, the pattern is multiplied by 2 on each number, then subtract 2 starting with 4 and add 1 for each increasing number.

4×2-2=6

6×2-3=9

9×2-4=14

As it goes on, the missing number would be:

40×2-7=73

Hope this helps!! :)

Please let me know if you have any questions

If p (x) = x4 + 2x2 + 1 and q (x) = x4 – 2x2 + 1, find p (x) -q (x).

Answers

Answer:

the answer is 4x2

Step-by-step explanation:

p(X)-q(X) = x4 + 2x2 + 1 - ( x4 - 2x2 + 1 )

p(X)-q(X) = x4 + 2x2 + 1 - x4 + 2x2 - 1 )

p(X)-q(X) = 2x2 + 2x2

p(X)-q(X) = 4x2

Answer:

p(x) - q(x) = 4x²

Step-by-step explanation:

p(x) - q(x)

= [tex]x^{4}[/tex] + 2x² + 1 - ([tex]x^{4}[/tex] - 2x² + 1)  ← distribute parenthesis by - 1

= [tex]x^{4}[/tex] + 2x² + 1 - [tex]x^{4}[/tex] + 2x² - 1 ← collect like terms

= 4x²

Evaluate: 2-4 А. =100 В. -8 ОО С. -16 D. 1 16​

Answers

Answer:

D. 1/16

Step-by-step explanation:

Evaluate: 2^-4

А. =100

В. -8ОО

С. -16

D. 1/16

Given

2^-4

= 1 / 2⁴

= 1 / (2 * 2 * 2 * 2)

= 1 / 16

Therefore,

2^-4 = 1/16

D. 1/16

what is the total amount of RS.7500 at the rate of 5.5% per annum in 42 months?find it.

Answers

Answer:

Please check out the attachments below to get the answer

below are properties of a square which one is not a all sides are equal b all angles are right angles C has five interior angles d diagonals are equal​

Answers

Answer:

has five interior angles

a square is a quadrant meaning it has four interior angles

Find the derivative of f(x) = 6/x at x = -2. (2 points)

Answers

Using the definition of the derivative,

[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{f(x) - f(-2)}{x - (-2)}[/tex]

[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{\dfrac6x + 3}{x + 2}[/tex]

[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{\dfrac{6+3x}x}{x + 2}[/tex]

[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{6+3x}{x(x + 2)}[/tex]

[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{3(x+2)}{x(x + 2)}[/tex]

[tex]\displaystyle f'(-2) = \lim_{x\to-2}\frac{3}{x} = \boxed{-\dfrac32}[/tex]

CAN SOMEONE HELP PLEASE

Answers

Answer:

72

The result is rational because it can be written as the ratio of two integers and its decimal expansion can terminate or repeat.

Answered by GAUTHMATH

Find the measure of GH. PLEASE HELP ASAP!!
A. 12
B. 10
C. 11
D. 7

Answers

Answer:

10 is the correct answer.

Answer:

10

Step-by-step explanation:

\HURRY PLZ
evaluate k divided (-11) for k=33

Answers

Answer:

-3

Step-by-step explanation:

k/-11

Let k =33

33/ -11

-3

Answer:

-3

Step-by-step explanation:

33/-11 = -3

NOTE

division and multiplication = negative

addition and subtraction are a pair.

I hope this helped!

WILL GIVE BRAINLIEST. Given: SLant Prism, m

Answers

Hi! I ran into a similar problem so i will try, but sorry if i get it wrong, so basically all you do i

What is the sign of 3ay when 2 > 0 and y < 0?
Choose 1 answer
Positive
Negative
Zero

Answers

Option A - Positive Step-by-step explanation:
Given : Expression when
To find : What is the sign of the expression ?
Solution :
Expression
when
We know that,
When a negative unit is divided by a negative unit then the negative sign became positive sign as negative sign get cancel in numerator and denominator.

A textbook store sold a combined total of 240 chemistry and history textbooks in a week. The number of chemistry textbooks sold
was two times the number of history textbooks sold. How many textbooks of each type were sold?

Answers

Answer:

160 chemistry books and 80 history books

Step-by-step explanation:

C=chemistry books sold, H=history books sold

C=2H

C+H=240, 3H=240, H=80, C=160

Multi step equations!
No links, thank you<33

Answers

Answer:

22/5

Step-by-step explanation:

3m+18+2m=40

5m=40-18

5m=22

m=22/5

[tex] \bf \large \longrightarrow \: 3m \: + \: 18 \: + \: 2m \: = \: 40[/tex]

[tex] \bf \large \longrightarrow \:5m \: + \: 18 \: = \: 40[/tex]

[tex] \bf \large \longrightarrow \:5m \: = \: 40 \: - \: 18[/tex]

[tex] \bf \large \longrightarrow \:5m \: = \: 22[/tex]

[tex] \bf \large \longrightarrow \:m \: = \: \frac{22}{5} \\ [/tex]

[tex] \bf \large \longrightarrow \:m \: = \: \cancel\frac{22}{5} \: \: ^{4.4} \\ [/tex]

[tex] \bf \large \longrightarrow \:m \: = \: 4.4[/tex]

please help don’t understand question!

Answers

Answer:

[tex]{ \sf{ - 2 {a}^{5} + 4 {a}^{4} + 5 {a}^{3} + \frac{2}{3}a }}[/tex]

Answer:

D

Step-by-step explanation:

A polynomial is in standard equation when the degree of the polynomial are in descending order.

The numerator and denominator of a fraction are in the ratio of 2 to 5. If the numerator and denominator are both decreased by 2, the fraction is now equal to .



If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?

2 n = 5 d and 2 n - 4 = d - 2
2 n = 5 d and n - 2 = 2 d - 4
5 n = 2 d and n - 2 = 2 d - 4
5 n = 2 d and 2 n - 4 = d - 2

Answers

Step-by-step explanation:

according to question let 2a and 5a be the given rations

2a/ 5a given fraction

2a-2/5a-2

Given a triangle MTN, prove that
<m+<t+<n= 180° strictly
use m, T and N with other
Letters in your triangle.​

Answers

Answer:

[tex]\angle m + \angle t + \angle n = 180[/tex]

Step-by-step explanation:

Required

Show that:

[tex]\angle m + \angle t + \angle n = 180^o[/tex]

To make the proof easier, I've added a screenshot of the triangle.

We make use of alternate angles to complete the proof.

In the attached triangle, the two angles beside [tex]\angle m[/tex] are alternate to [tex]\angle t[/tex] and [tex]\angle n[/tex]

i.e.

[tex]\angle 1 = \angle t[/tex]

[tex]\angle 2 = \angle n[/tex]

Using angle on a straight line theorem, we have:

[tex]\angle 1 + \angle m + \angle 2 = 180[/tex]

Substitute values for (1) and (2)

[tex]\angle t + \angle m + \angle n = 180[/tex]

Rewrite as:

[tex]\angle m + \angle t + \angle n = 180[/tex] -- proved

Giving brainliest! View the image!

Answers

Answer:

a- 15 b- 1292^cm this is the answer

A giant pie is created in an attempt to break a world record for baking. The pie is shown below:

A circle is shown with a central angle marked 45 degrees and the diameter marked 15 feet.

What is the area of the slice of pie that was cut, rounded to the nearest hundredth?

Answers

The area of the slice of pie that was cut, rounded to the nearest hundredth is 22.08 square feet.

The slice of pie will form a sector as shown;

The area of the slice of pie will be expressed as:

[tex]A=\frac{\theta}{360}* \pi r^2[/tex]

[tex]\theta\\[/tex] is the central angle = 45 degrees

r is the radius

[tex]r=\frac{d}{2}\\r= \frac{15}{2}\\r= 7.5feet[/tex]

Substitute the given values into the formula above;

[tex]A=\frac{45}{360} * 3.14*7.5^2\\A=\frac{1}{8} * 176.625\\A=22.08ft^2[/tex]

Hence the area of the slice of pie that was cut, rounded to the nearest hundredth is 22.08 square feet.

The area of the slice of pie that was cut, rounded to the nearest hundredth is 22.08 square feet.

Learn more about an area of a sector here: https://brainly.com/question/12792310

Answer:

the guy on top is right

Step-by-step explanation:

i took the test

PLEASE SOMEONE HELP ME!!!!!!

Answers

Answer:

(B)5 is the correct answer for the question

What is the slope of the line that passes through (-4,5) and (2,-3)​

Answers

Answer:

solution,

(X1,y1)= (-4,5)

(X2,Y2)=(2,-3)

slope of the line(m)= y2-y1/x2-x1

=-3-5/2-(-4)

=-8/6

=-4/3

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