Which represents the solution(s) of the graphed system of equations, y = x2 + x -2 and y = 2x - 2?
Ty
2
1
O (-2, 0) and (0, 1)
O (0, -2) and (1,0)
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Answers

Answer 1

Answer:

(0, -2) and (1, 0)

Step-by-step explanation:

y = x² + x - 2 and y = 2x - 2    

  y = x² + x - 2  ⇔ do not change;       y = x² + x - 2

  y = 2x - 2        ⇔ multiply by -1  ;        -y = - 2x + 2  

Now add the two equations:  

     y = x² + x - 2

(+)  -y = - 2x + 2                  

      0 = x² - 2x + x  + 0      

       0 = x² - x            

        0 =  x (x - 1)    Factor out x

     0 = x;  0 = x - 1    Set each factor = to 0 and solve.

      x = 0;   x = 1    

  Substitution the value of x into both equations and solve for y

If x = 0                                                 If x = 1

y = (0)² + 0 - 2  ;   y = 2(0) - 2               y = 1² + 1 - 2  ;  y = 2(1) -2

y = 0 +0 -2      ;     y =  0 - 2                  y = 1 + 1 -2    ;  y = 2 - 2

  y = -2   ;    y = -2                                   y =  0           ;   y = 0

Solutions to the question:  (0, -2) and (1, 0)


Related Questions

neeeeeeeeeeeeeeeeeeeeeeeeeeed answer

Answers

Answer:

B

Step-by-step explanation:

3t+6=9 or -9
1. 3t+6=9

3t=9-6=3

t=3/3-=1

2. 3t+6=-9

3t=-9-6=-15

t=-15/3=-5

t=1, -5

Answer:

B {-5, 1}

Step-by-step explanation:

Separate into possible cases

3t + 6 = 9

3t + 6 = -9

Solve the equations

t = 1

3t + 6 = -9

The equation has 2 solutions

t = -5

t = 1

Please help quick, brainly crown will be given when I have the option

Answers

Answer:

56

Step-by-step explanation:

just multiply 8 by 7. to check do 56 divided by 7 which equals 8.

Answer:

P=56

Step-by-step explanation:

Multiply both sides by 7 &p/7=8x7

Simplify P=56

someone should help me please

Answers

Answer:

it is a

Step-by-step explanation:

I might not know but I guess the answer is D

The length of a rectangle is 5 yd longer than its width.
If the perimeter of the rectangle is 42yd, find its area.

Answers

Answer:

8+8+13+13= 42yd

Length: 13

Width: 8

Multiplied equals:

104yd²

4. Which of the following is a geometric sequence?
O 3,6,9, 12,...
50,25,0, -25,...
011, 15, 19, 23, ...
4,-16,64, -256,...
HELP PLSS

Answers

Answer: Choice D

Explanation:

We can verify this by noticing the ratio between adjacent terms is the same

term2/term1 = -16/4 = -4term3/term2 = 64/(-16) = -4term4/term3 = -256/64 = -4

The common ratio is -4. Each time we need a new term, multiply the previous term by -4. Example: -16*(-4) = 64.

A sculptor creates an arch in the shape of a parabola. When sketched onto a coordinate grid, the function f(x) = –2(x)(x – 8) represents the height of the arch, in inches, as a function of the distance from the left side of the arch, x. What is the height of the arch, measured 3 inches from the left side of the arch? 14 inches 15 inches 28 inches 30 inches.

Answers

The height of the arch, measured 3 inches from the left side of the arch is 30 inches.

Given

A sculptor creates an arch in the shape of a parabola.

When sketched onto a coordinate grid, the function f(x) = –2(x)(x – 8) represents the height of the arch, in inches, as a function of the distance from the left side of the arch, x.

What is a parabola?

The path of a projectile under the influence of gravity follows a curve of this shape.

Therefore,

The height of the arch, measured 3 inches from the left side of the arch is;

[tex]\rm f(x) = -2(x)(x - 8)\\\\f(3) = -2(3)(3-8)\\\\f(-3)=(-6)(-5)\\\\f(-3)=30[/tex]

Hence, the height of the arch, measured 3 inches from the left side of the arch is 30 inches.

To know more about Parabola click the link given below.

https://brainly.com/question/8495268

Answer:30 inches

Step-by-step explanation:

just took test

Given that AB is a line segment and the angle y= 133, work out the value of the angle marked T. A B​

Answers

Step-by-step explanation:

if seven times a number decreased by 4 is less than 27,then find the solution set

5z+2z^3+3z^4 in standard form

Answers

Answer:

= 3z4 - 2z2 -5z

Step-by-step explanation:

Draw a model to show 12*6 show 6 in each group how many groups are there

Answers

Answer:

there would be 12 in each group or you could do 6 groups with 12 in them

Do you understand?
A seven-foot frame
Rats along his back
When he calls your name
It all fades to black
Yeah, he sees your dreams
And feasts on your screams (hey!)
We don't talk about Bruno, no, no, no! (We don't talk about Bruno, no, no, no!)
We don't talk about Bruno (we don't talk about Bruno!)

Answers

Answer:

36/24 is greater than 9/6

Step-by-step explanation:

He told me my fish would die

The next day dead! (No, no!)

He told me I'd grow a gut!

And just like he said... (no, no!)

He said that all my hair would disappear, now look at my head (no, no! Hey!)

Your fate is sealed when your prophecy is read!

The ratios of the fraction [tex]\frac{9}{6}[/tex] and [tex]\frac{36}{24}[/tex] are compared and  [tex]\frac{9}{6}=\frac{36}{24}[/tex].

Given data:

The first fraction is represented as p.

The value of [tex]p=\frac{9}{6}[/tex].

The second fraction is represented as q.

The value of [tex]q=\frac{36}{24}[/tex]

Now, multiplying the fraction p by [tex]\frac{4}{4}[/tex] :

[tex]p=\frac{9}{6}*\frac{4}{4}[/tex]

On simplifying the equation:

[tex]p=\frac{36}{24}[/tex]

So, the value of p = q.

Hence, the ratios are similar.

To learn more about fractions, refer:

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Heeelllp I’m too stoopid 4 this

Answers

I think that you have to do 360/9 because the sum of a polygons exterior angles is 360° and if I’m correct then the answer would be 40

Can someone please help me with this thanks

Answers

Answer:

24 (units)

Step-by-step explanation:

Because Quadrilateral EFGH is being dilated by a scale factor of 3/4, this means that each side of E'F'G'H' gets multiplied by 3/4. In this case, we are going to divide by 3/4 to return to the original figure (or multiply by 4/3 since that is the reciprocal)

This means that side HE is 18/(3/4) = 18(4/3) = 72/3 = 24 units

It costs 95$ for 20 students to visit an aquarium. How much does it cost for 162 students?

Answers

Answer:

769.50

Step-by-step explanation:

First find how much is one student

95/20=4.75

Then, 162 x 4.75=769.50

if we do 95/20 we get 4.25 that would be the cost for each student and all we have to do is multiply 162 by 4.25 and u get your answer of 688.5

NEED HELP ASAP!!!!
John left some delicious food in the corner of the classroom on Tuesday. On Wednesday, there were 15 ants eating the food. On Thursday there were 19 ants eating the food. Assuming the increase in ants is arithmetic, how many ants will be eating the food on Sunday of that same week?

Answers

Answer:

31

Step-by-step explanation:

Add 4 for every day there after. 15+4=19; 19 +4=23 and so on.

Which of these numbers are greater than 3. 2 × 10-3? 2. 1 × 10-3 4. 2 × 10-4 5. 2 × 10-2 5. 2 × 10-1.

Answers

Answer:

your answer would be 4.2 x 10-4

Step-by-step explanation:

PLEASE ILL GIVE YOU BRAINLIEST!

Solve `x^{2}-36=0`


Which solution method would be most efficient?

-Factoring

-Taking the square root

-Quadratic Formula
Show your work!

Answers

Answer:

Taking the square root

Step-by-step explanation:

[tex]x^2-36=0[/tex]

[tex]x^2=36[/tex]

[tex]x=\pm6[/tex]

Alternatively, you can use a difference of squares to factor and solve:

[tex]x^2-36=0\\(x+6)(x-6)=0\\x=-6,x=6[/tex]

PLEASEE HELP ME WITH THIS……..

Answers

Answer:

KM/KL = HJ/HI

Step-by-step explanation:

Triangle JIH is similar to MLK due to Angle-Angle similarity. So, KM/KL = HJ/HI

Examine the system of linear equations. –3x y = 2 2x 4y = –20 Which number could be multiplied by the first equation to eliminate the y when the equations are added together? -4 4 2 10.

Answers

Answer:

A - -4

Step-by-step

Answer:

The answer is A Or 4

Step-by-step explanation:

EDGE 2022

Which expression is equivalent to
5x – 30?
-
A 5(x - 30)
B 5(x - 6)
© 5x(x – 6)
D x(5 – 30)

Answers

B) 5(x-6)

you factor out 5 for each term

A movie, including the previews, is 2 hours and 40 minutes long. If the previews last 20 minutes. What fraction of the total time is the actual movie?

Answers

Considering the definition of fraction, the fraction of the total time is the actual movie is [tex]\frac{7}{8}[/tex].

What is fraction

The fraction is an expression that marks a division, therefore, it can be said that a fraction represents a distribution or a portion of a unit.

In other words, a fraction is a representation of the parts of a whole, that is, it is divided into equal parts and each part is the fraction of the whole.

Fractions are composed of an upper term called the numerator and a lower term known as the denominator separated by an oblique or horizontal bar.

Fraction of the total time that is the actual movie

In this case, you know:

A movie, including the previews, is 2 hours and 40 minutes long. The previews last 20 minutes.

So, the movie is 2 hours and 20 minutes long. (2 hours and 40 minutes - 20 minutes [the previews])

Knowing that 1 hour contains 60 minutes, then:

A movie, including the previews, is 160 minutes long. The previews last 20 minutes.So, the movie is 140 minutes long.

Then, the fraction of the total time is the actual movie is:

[tex]\frac{140 minutes}{160 minutes}[/tex]

To simplify a fraction is to transform it into a simpler equivalent fraction. To simplify a fraction, we divide the numerator and denominator by the same number.

Finally, simplifying, the fraction of the total time is the actual movie is [tex]\frac{7}{8}[/tex].

Learn more about fraction:

brainly.com/question/17820556

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Write h(x) = 7 10x x2 in vertex form. Write h in standard form. H(x) = x2 10x 7 Form a perfect square trinomial by adding and subtracting StartFraction b Over 2 EndFraction squared. H(x) = (x2 10x 25) 7 – 25 Write the trinomial as a binomial squared. Write the function in vertex form, if needed. What is h(x) = 7 10x x2 written in vertex form? h(x) = (x – 25)2 – 18 h(x) = (x – 5)2 32 h(x) = (x 5)2 – 18 h(x) = (x 25)2 32.

Answers

You can use the definition for the vertex form of a quadratic equation and then can can do conversion of that quadratic equation in that form.

The correct vertex form of the given equation is given by

Option C: [tex]h(x) = (x-5)^2 - 18[/tex]

What is vertex form of  a quadratic equation?

If a quadratic equation is written in the form

[tex]y = a(x-h)^2 + k[/tex]

then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)

This point is called the vertex of the parabola that quadratic equation represents.

How to convert the given equation to vertex form?

We first take out coefficient of x squared, and then inside the bracket, we try to make perfect square like situation.

The given equation is [tex]h(x) = 7 + 10x + x^2\\[/tex]

Converting it in vertex form, we get:

[tex]h(x) = 7 + 10x + x^2\\\\\\h(x) = x^2 + 10x + 7\\h(x) = x^2 + 10x + 25 -25 + 7\\h(x) = (x+5)^2 - 18 \text{\: (Note how the form} \: a^2 + b^2 + 2ab = (a+b)^2 \:\rm got\: made)[/tex]

Thus, we have h = -5 and k = -18

The plot of the given equation is attached below.

Thus,

The correct vertex form of the given equation is given by

Option C: [tex]h(x) = (x-5)^2 - 18[/tex]

Learn more about vertex form of quadratic equations here:
https://brainly.com/question/9912128

Answer:

c

Step-by-step explanation:

Help pls. I will mark brainliest to the correct answer:)

Answers

Answer:

-2

Step-by-step explanation:

p = -2.5

r = 0.5

p + r =

-2.5 + 0.5 =

-2

Answer:

-1

Step by step explanation

Suzy bought a 20 ounce
soda for $1.50, Jacob
bought a 1 liter bottle of
soda for $2.50. Who got the
best deal per ounce?

Answers

Answer:

Suzy got the best deal per once

Step-by-step explanation:

The table lists how poverty level income cutoffs​ (in dollars) for a family of four have changed over time. Use the midpoint formula to approximate the poverty level cutoff in 1987 to the nearest dollar.

Answers

The poverty level cutoff in 1987 to the nearest dollar  was $10787.

How to find a midpoint?

The midpoint as the point that divides the line segment exactly in half having two equal segments. Therefore, the midpoint presents the same distance between the endpoints for the line segment. The midpoint formula is: [tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex].

For solving this exercise, first you need plot the points in a chart. See the image.

Your question asks to approximate the poverty level cutoff in 1987 to the nearest dollar using the midpoint formula. Note that the year 1987 is between 1980 and 1990, thus you should apply the midpoint formula from data for this year (1987).

[tex]\mathrm{Midpoint\:of\:}\left(1980,8429),\:\left(1990,13145):\quad \left(\frac{1990+1980}{2},\:\:\frac{13145+8429}{2}\right)\\\\ \\[/tex]

[tex]\mathrm{Midpoint\:of\:}\left(1980,8429)\:=\left(\frac{1990+1987}{2},\:\frac{13145+3843}{2}\right)\\ \\ =\left(\frac{3977}{2},\:\frac{21574}{2}\right)[/tex]

[tex]\mathrm{Midpoint\:of\:}\left(1980,8429)\:=\=(\frac{3977}{2},10787)[/tex]

The answer for your question will be the value that you calculated for the y-coordinate. Then, the poverty level cutoff in 1987 to the nearest dollar  was $10787.

Read more about the midpoint segment here:

https://brainly.com/question/11408596

:) There are 18 animals in the field. Some are horses and some are geese. There are 56 legs in all.
How many of each animal are in the field?

Answers

Let number of horses be x, number of geese be y
x+y=18
4x+ 2y = 56
Substituting in Equation 1 into 2,
4x + 2y - 2(x+y) = 56-2(18)
2x = 20
x = 10
when x= 10, y= 8

Please help and I will give you brainliest 5 stars and a thank you on answer and profile just please help

Answers

Answer:

#1 D. 360

#2 54

#3 D. 252

Step-by-step explanation:

1. What is the area of the wall that surrounds the garage door?

Notice that the wall can be broken into two parts, a parallelogram and a triangle. The triangle's base would be 30 - 18 (as it is stated that the parallelogram's length is 18), while the height is shared with the rectangle's width, which is 12:

Area of triangle = 1/2bh

b = 12

h = 12

Area of triangle = (12 * 12)/2 = (144)/2 = 72 ft²

Area of parallelogram = bh

b = 18

h = 12

Area of parallelogram = (18 x 12) = 216 ft²

216 + 72 = 288 ft²

Next, find the amount missing because of the garage door. It is given that the door's area can be found by multiplying the length and side (both 9ft). Subtract the gotten number from the total amount:

Area of parallelogram = bh

b = 9

h = 9

9 x 9 = 81 ft²

288 - 81 = 207 ft²

A) 207 ft²

~

First, note that there are two full rows in the bottom. This can be made into the rectangle. The rest would be solved using the triangle formula. Add the two results together at the end to get your total units.

Rectangle:

base = 9 units

height = 2 units

Area of Rectangle = base x height

                               = 9 x 2

                               = 18 units²

Triangle:

base = 9 units

height = 4 units

Area of Triangle = (base x height)/2

                           = (9 x 4)/2

                           = (36)/2

                           = 18 units²

Add the two areas together for your total units²:

18 + 18 = 36 units²

36 units²

~

The "base" of the triangle is 3 ft greater than the height of the triangle. The given height is that it is 12 ft. This means that the base is 15 ft.

Use a² + b² = c² to solve for the sides:

c = hypotenuse = 21 ft

b = base = 15 ft

c² - b² = a²

21² - 15² = a²

(441) - (225) = a²

a² = 216

√a² = √216

a = √216 = 6√6

~

I am not too sure if there is actual enough information that can be used to solve for this triangle. I understand that you will need the answers soon, so I will try to work on it and edit my answer later on. In my opinion, they would need to give at least one more measurement or information regarding which side is which to be able to obtain the answer. If i had to guess, I would guess as well the largest one, considering the 12 ft and 21 ft. Again, they will need to define "b", as well as what the "base" & "height" would be.

At Mead Middle school there are 125 6th graders. 60% of these 6th graders are in pre-athletics. How many 6th graders are NOT in pre-athletics?

Answers

The answer is 50. 40% of 125 is 50

Write an expression equivalent to
x^2+7x+6x

Answers

Answer:

x(x+13), or x^2+13x

Step-by-step explanation:

You factor one x out, or you can just add the x values.

A jewelry salesperson earns 6 3/7​% commission on all sales. Today sold ​$4570 in jewelry. What is total commission​ earned?

Answers

[tex]\stackrel{mixed}{6\frac{3}{7}}\implies \cfrac{6\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{45}{7}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\frac{45}{7}\textit{\% of 4570}}{\left( \cfrac{~~\frac{45}{7}~~}{100} \right)4570}\implies \left( \cfrac{45}{700} \right)4570~~ \approx~~293.79[/tex]

finally, divide both sides of 15=5x by 5 what is the result???

Answers

Answer:

x = 3

Step-by-step explanation:

15 = 5x

15/5 = 5x/5

3 = x

x = 3

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