Solve the system of equations. Y = 2x-2 y = x^2-x-6

Answers

Answer 1

Answer: (-1, -4) and (4, 6)

Step-by-step explanation:

Answer 2

The pair of solution to the equations y = 2x - 2  and y = x² - x - 6

are (4, 6) and (-1, -4).

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have two equations:

y = 2x - 2

y = x² - x - 6

Equate both equations:

2x - 2 = x² - x - 6

x² - 3x - 4 = 0

Solving using the quadratic formula:

[tex]\rm x_{1,\:2}=\dfrac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \left(-4\right)}}{2\cdot \:1}[/tex]

x = 4, -1

y = 6, -4

Thus, the pair of solution to the equations y = 2x - 2  and y = x² - x - 6

are (4, 6) and (-1, -4).

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Related Questions

What is the equivalent decimal?

Drag the answer into the box to match the fraction.

6/11 >>>>>>>>>


__
0.12
__
0.27

0.54
__
0.54

























Answers

Answer:

.54 repeating

(.54 with a bar over the 54)

Step-by-step explanation:

6/11 means  6÷11. That is .545454545454 ...

You would write this as .54 with a bar over the 54.

Clayton surveyed a random sample of 90 registered voters in his hometown. He asked them if they were in favor of building a new park. The results are shown below:
In favor-63
Not in favor-27
Based on these results, about how many people out of the 15,500 registered voters would be expected to vote in favor of a new park?
PLEASE HELP!

Answers

10850 would be I'm favor of building the park and 4650 would not

In which of the following quadrilaterals are consecutive angles always congruent? Check all that apply.

square
parallelogram
rectangle
rhombus

Answers

Square and rectangle

The quadrilaterals that have consecutive angles equal to each other are Square and a Rectangle, the correct option is A and C.

What is a Quadrilateral?

Quadrilateral is a polygon with four sides.

The quadrilaterals with consecutive angles always congruent are:

Square : The square has all angles of equal measure of 90 degrees.

Rectangle: A rectangle also has all angles equal to 90 degree.

To know more about Quadrilateral

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What are the roots of x2 + 10x + 29 = 0?

A. 5 ± 2i

B. -5 ± 2i

C. 10 + 4i

D. -10 + 4i

Answers

Answer:

B

Step-by-step explanation:

okay so x^2+10x+29=0

subtract 29 from both sides giving you:

x^2+10=-29

next, used (b/2)^2 to create a trinomial square, which will be 5 so you will have:

x^2-10x+(-5)^2=-29+(-5)^2

Then, simplify the equation:

x^2-10x+25=-4

Next, factor into (x-5)^2 which is:

(x-5)^2= -4

Finally, solve for X:

x=5 +/- 2i

x2+10×+29=0

answer is A 5+2i

which is the best estimate of the solution to this system of equations?​

Answers

Answer:

Option 3. (23, 14)

Step-by-step explanation:

In this figure, solution of the system of equations is the point of intersection of the equations representing two lines.

Or common points lying on both the lines will be the solutions of the system of equations.

In the given graph approximate value of x - coordinates = 23

and approximate value of y - coordinates = 14

Therefore, solution of the system is (23, 14).

3rd option (23, 14) is the answer.

Answer:

Option 3. (23, 14)

Step-by-step explanation:

Solve for X
Your answer must be simplified.

-7x > 10

Answers

Answer:

There are many solution for this problem

The solutions are -2, -3, -4..... And even fractions like -11/7, -12/7, etc.

Hope this helps!

For this case we indicate the solution of the following e-inequality:

[tex]-7x> 10[/tex]

We divide between "-7" on both sides of the inequality, keeping in mind that when doing this operation the sign will change, since we operate with a negative sign.

So:

[tex]\frac {-7x} {- 7}> \frac {10} {- 7}\\x <- \frac {10} {7}[/tex]

Thus, the domain of the variable "x" is given by all the numbers smaller than -[tex]-\frac {10} {7}[/tex]

ANswer:

[tex]x <- \frac {10} {7}[/tex]

Miguel is multiplying 58 by 12. Use the drop-down menu to complete the statement.

Answers

58×13=696!!!!!!!!!!!!!!!!!!!!

Answer:

[tex]58\times 12=696[/tex]

Step-by-step explanation:

We have to multiply 58 and 12.

This could be done by distributive property of multiplication over addition which is:

[tex]a\times b\\=a\times (c+d)\\=(a\times c) + (a\times d)[/tex]

Evaluation of [tex]58\times 12[/tex]

[tex]58\times 12\\=58\times (10 + 2)\\=(58\times 10) + (58\times 2)\\=580 + 116\\=696[/tex]

Distributive property makes us easy to calculate complicated product by dividing the number into smaller parts.

If a/b=3/4 and a/c=5 what is b/c?

I WILL MARK BRAINLIEST

Answers

Answer:

it would be 4/5 because c= 5 and b=4

Answer:

b/c = 20/3

Step-by-step explanation:

a/b =3/4

a/c = 5

a/c =5

Divide both sides by a/b

a/c ÷a/b = 5÷a/b

Replace the a/b on the right by 3/4 since they are equal

a/c ÷a/b = 5÷3/4

We will use copy dot flip

a/c * b/a  = 5 * 4/3

b/c = 20/3

Plz Ace's or any sort of professional answer this!

Answers

Look at the dots for each week and see how much money was in the account.

Week 1 was 10, week 2 was 30, this means he saved 20

Week 5 was at 50, week 6 was at 80, this means he saved 30, which was the most.

The answer is 5 & 6.

HELP! Gareth is playing a racing game. To get star rating 1, Gareth needs to win four races. Thereafter, for every three races he wins, his star rating increases by one. Determine which graph represents this situation.

Answers

Answer:

The third option C.

Step-by-step explanation:

Answer:

The graph C is the right answer.

Step-by-step explanation:

Gareth is playing a racing game. To get star rating 1, Gareth needs to win four races. Thereafter, for every three races he wins, his star rating increases by one.

So, the graph that represents this - The C graph.

We can see that the graph travels 3 places right and then 1 up. The blue solid dot represents the final count. The light dotted is the initial travel period of the graph.

After the graph moves 1 point up, it again travels 3 points right and this continues at each step.

So, C is the right graph.

Which fraction has the greatest value 1/3 2/10 1/6 or 2/7

Answers

1/3 has the greatest value

1/3 has the greatest value. Hope this helps!

Please help guys, thanks so much

Answers

I'm back again....xD

1) C'(-3, -3)

2) A - Location - Yes

B - Orientation - No

C - Size - No

3) Don't kill me, but I actually don't know this one...sorry

4) X'

5) A - Angle measures - No

B - Perimeter - No

C - Orientation - Yes

6) Rotated 90° counter-clockwise; (x, y) → (-y, x)

7) Y'(-2, -3)

8) A (x, y) → (-x, y)

9) A - Same Shape - Yes

B - Same Area - No

C - Same Perimeter - No

D - Similar - Yes

10) X'(-1.6, 0.5)

11) A - Translation - Yes

B - Rotation - Yes

C - Dilation - No

D - Reflection - Yes

Can anybody help me please

Answers

Answer: x  /  y

              0  /  4

              4  /  0

            -10  /  6

Step-by-step explanation:

Answer:

x          y

0          4

20       0

-10       6

Step-by-step explanation:

x + 5y = 20

5y = -x + 20

 y = -1/5 x + 4

so

when x = 0,

y = -1/5 (0) + 4

y = 4

when y = 0 then

0 = -1/5 x + 4

-4 = -1/5 x

x = (-4) (-5)

x = 20

when y = 6 then

6 = -1/5 x + 4

2 = -1/5 x

x = 2 * (-5)

x = -10

HELP ASAP!! GIVING BRAINLIEST!

What are the steps for constructing an inscribed circle in angle ABC using only a compass and a straightedge?

Answers

Answer:

Step-by-step explanation:

use the compass and find the midpoints of each side of the triangle. the use the ruler and find the radius and connect it to the vertex ISO - trigonometric diameter. Mark the angles as 90 deg corresponding to the rays formed by the radii. simple :)

Answer: PLATO ANSWER

Step-by-step explanation:

Step 1: Place the compass needle on vertex A, adjust the width of the compass to a medium setting, and draw one arc on line segment AB and one on line segment AC.

Step 2: Place the compass needle on the point where the arc intersects line segment AB and draw an arc inside the triangle. Without changing the compass setting, place the compass needle on the point where the arc intersects line segment AC; draw another arc intersecting the arc already inside the triangle. Label the point of intersection P.

Step 3: Draw line segment AP. This is the angle bisector of angle A.

Step 4: Place the compass needle on vertex C, adjust its width to a medium setting, and draw arcs intersecting line segment BC and line segment AC.

Step 5: Place the compass needle on the point where the arc intersects line segment BC, and draw an arc inside the triangle. Without changing its setting, place the compass on the point where the arc intersects line segment AC; draw another arc intersecting the arc already inside the triangle. Label the point of intersection Q.

Step 6: Draw line segment CQ. This is the angle bisector of angle C.

Step 7: Label the intersection of the angle bisectors M. This is the center of the inscribed circle.

Step 8: Place the compass needle on M, and draw two arcs on line segment BC.

Step 9: Place the compass needle on one of the points where an arc intersects line segment BC, and draw an arc outside the triangle; repeat from the point where the other arc intersects line segment BC to create two intersecting arcs outside the triangle. Draw a line from M passing through the point of intersection outside the triangle. This is a perpendicular line from M to line segment BC. Mark the point where the line intersects line segment BC, and label it N.

Step 10: Place the compass needle on M, set its width to N, and draw a circle. This is the inscribed circle of triangle ABC.

Rhonda has 3 different color shorts, red, blue, and green ---- and a pair of blue jeans and a pair of white jeans. She randomly chooses a t shirt and a pair of jeans. What are all the possible outcomes? What is the probability that she will pair the red t shirt with the white jeans?

Answers

Answer:

there are 6 possible outcomes with a 1/6 chance of a red shirt with white jeans

Step-by-step explanation:

I'm listing them in shirt the jeans and the letter corresponds to the color of them

r w

r b

b w

b b

g w

g b

--------------------------------------------------------------------------------------------------------------

since there are two colors of jeans that is a .5 ( or 1/2) chance of grabbing it and three different shirts which is a .33 (or 1/3)

1/3 x 1/2 = 1/6

hope this helps for the third time lol

What is the explicit rule for the sequence in simplified form?
−1,−4,−7,−10,−13…

Question 12 options:

an=4−5n

an=−4−3n

an=2−3n

an=−6−5n

Answers

Answer:

an = 2 - 3n ⇒ The third answer

Step-by-step explanation:

∵ a1 = -1

∵ a2 = -4

∵ a3 = -7

∵ a2 - a1 = -4 - -1 = -3

∵ a3 - a2 = -7 - -4 = -3

∴ It is an arithmetic sequence with

  1st term = -1 and constant difference = -3

∵ The rule of any arithmetic is: an = a + (n - 1)d

∵ a = -1 and d = -3

∴ an = -1 + (n - 1)(-3)

∴ an = -1 - 3n + 3

an = 2 - 3n ⇒ The third answer

Determine which postulate or there and can be used to prove that triangle SEA is congruent to triangle PEN

Answers

Answer:

The answer is ASA!

Step-by-step explanation:

Answer:

asa

Step-by-step explanation:

Which is the largest value of the 5 numbers below
13.05 13.5 13.06 13.45 13.07

Answers

Answer:it is 13.45

Step-by-step explanation:

Final answer:

The largest value among the provided numbers is 13.5. In decimal numbers, the higher the value after the decimal point, the larger the fraction of a whole number it represents. Therefore, 13.5, with '.5' after the decimal point, represents the largest value.

Explanation:

In order to find the largest value among the given numbers, it will be useful to first understand how decimal numbers work. Decimal numbers are a method of writing fractions in a way that is easier to work with. In a decimal number, the number after the decimal point represents a fraction of a whole number. The larger this number, the larger the fraction of the whole number it represents.

In your list, you have five numbers: 13.05, 13.5, 13.06, 13.45, and 13.07. If we compare just the numbers after the decimal point, we'll see that '.5' is the largest. Therefore, 13.5 is the largest number among your list.

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(2a^2 + a + 3) ÷ (a - 1)

Answers

Answer:

2a + 3 Remainder 6

Step-by-step explanation:

Find the attachment bellow for a step by step explanation.

Answer:

2a + 3

Step-by-step explanation:

We are given the following two terms and we are to divide them:

[tex] \frac { 2 a ^ 2 + a + 3 } { a - 1 } [/tex]

We will start by divide the highest order term in the dividend  [tex]2a^2[/tex] by the highest order term in divisor  [tex]a[/tex]:

[tex]\frac{2a^2 + a + 3}{a-1}=2a[/tex]

Then we multiply the new quotient term by the divisor where [tex]-2a^2+2a[/tex] is subtracted by [tex]2a^2+a[/tex].

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend to get:

[tex]2a+3[/tex] as the quotient and [tex]6[/tex] as the remainder.

x is 110% of 10, y% of 50 is 3.5

Answers

For the expression "X is 110% of 10," X is equal to 11.

For the expression "y% of 50 is 3.5," the value of y is 7.

From the information given, we can solve for both x and y:

1. Finding x:

"X is 110% of 10" means that x is equal to 110% multiplied by 10.

110% can be written as a decimal by dividing by 100: 110/100 = 1.1

Therefore, x = 1.1 * 10 = 11.

2. Finding y:

"y% of 50 is 3.5" means that y% multiplied by 50 is equal to 3.5.

To solve for y%, we can rearrange the equation: y% = 3.5 / 50.

To express y as a percentage, we can multiply by 100: y = (3.5 / 50) * 100 = 7.

Complete question:

Calculate the percentage: X is 110% of 10, y% of 50 is 3.5

Final answer:

We calculated x by determining that it's 110% of 10, which results in x being 11. Then, we solved for y by understanding that y% of 50 equals 3.5, leading to the conclusion that y is 7.

Explanation:

To solve for x, we consider that it is 110% of 10. To convert a percentage into a decimal, we divide by 100, so 110% becomes 1.10. Therefore, x = 1.10 × 10. After multiplying, we get x = 11.

For the second part, we have y% of 50 is 3.5. The equation can be represented as (y/100) × 50 = 3.5. To find y, we divide both sides by 50 and then multiply by 100 to get y = (3.5 × 100) / 50. Solving for y, we find y = 7.

find the positive root of x^2 + 6x -27 = 0

Answers

Answer:

This is true.

Step-by-step explanation:

+ ^2 + 6x -27

Sid needs 0.7 meters of canvas material to make a carry all bag for his wheelchair. If the canvas is $5.32 per meter how much will Sid spend ?

Answers

0.7 x 5.32= 3.759

To Make it simpler = $3.75

3 dollars and 75 cents.

I hope I’m right ^^

Sid spend $3.724 on his bag material.

What is multiplication?

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

According to the question

Sid needs 0.7 meters of canvas material to make a carry all bag for his wheelchair.

If the canvas is $5.32 per meter how much will Sid spend.

Based on the given conditions , formulate

= [tex]0.7 \times 5.32[/tex]

= $3.724

Sid spend $3.724 on his bag material.

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A square with sides of 15 cm is enlarged in a ratio 3:4. What is the area of the resulting square?​

Answers

Final answer:

When a square with 15 cm sides is enlarged by a ratio of 3:4, the resulting square has a side length of 20 cm, and consequently, an area of 400 cm².

Explanation:

If a square with sides of 15 cm is enlarged in a ratio of 3:4, we first need to determine the new length for the sides of the resulting square. To do this, we take the original side length (15 cm) and multiply it by the scale ratio.

The scale ratio is 3:4 which means for every 3 units of the original, the new square will have 4 units. Therefore, we calculate the new side length as follows:

Original side length = 15 cmScale factor = 3:4New side length = (15 cm) × (4/3) = 20 cm

Now, to find the area of the resulting square, we square the new side length:

Area = side × side = 20 cm × 20 cm = 400 cm²

So, the area of the resulting square is 400 cm².

25 POINTS FORA SPEEEDY ANSWER

A large concrete water pipe is being laid underground. The pipe has a diameter of 24 inches and is laid in 40 foot sections. How many cubic feet of water does each section hold? Express your answer in terms of pi. Show all calculations.


Answer correcty please!!

Answers

okay so I'm going to be honest I'm not fully sure if my answer is correct but I think that you must add it up and they answer that you will get is 64 because remember 4 + 2 equals 6 and 4 + 0 equal 4

Answer:

[tex]40\pi\text{ cubic feet}[/tex]

Step-by-step explanation:

Given,

The diameter of the pipe = 24 inches,

⇒ The diameter of the section = 24 inches

And, it is laid in 40 foot section,

So, the height of each section = 40 feet,

Since, the shape of a pipe is cylindrical,

The volume of a cylinder is,

[tex]V=\pi (r)^2 h[/tex]

Where, r is the radius,

h is its height,

Here, r = [tex]\frac{24}{2}[/tex] = 12 inches = 1 feet,

Also, h = 40 foot,

Thus, the quantity of water hold by the section = Volume of the section

[tex]=\pi (1)^2(40)[/tex]

[tex]=40\pi \text{ cubic feet}[/tex]

{System: I am having a bit of trouble calculating this. Will you help me out? Thank you!}

Answers

Answer:

1 3/15

Step-by-step explanation:

Take 18 divided by 15, make it a fraction which is 18/15 then divide (how many 15's go into 18?) since 1 15 goes into 18 you put a 1 in the whole number place, and the remainder is 3/15.

Answer:

D

Step-by-step explanation:

B is not correct.

Convention says that the number after the divide sign must be in the denominator. In plain English, that means you must have 18 on the top and 15 on the bottom like this

18

===

15

Since that is not one of your answers you have to break it down

18 can be divided by 15 once.  That means that  A is not right either.

So all you have left is C and D

There's 3 left over when you divide 18 by 15.

Only one answer is possible

1 3/15 which is D

6) Find the surface area of the square pyramid.
8 cm
5 cm

Answers

Answer:

the formula for surface area of a triangle is s=1/2ph=b

Step-by-step explanation:

p = perimeter of pyramid

h = height of each triangular face

BIG B = Area of base of pyramid

Solve!

i hope this helped im only in the 8th grade, so i am just learning this

6(7−3y)+6(y+1) please help

Answers

Answer: 4=y

Step-by-step explanation:

6(7 -3y)+6(y+1)

42-18y+6y+6

48-12y

48/12=4

12y/12=y

4=y

The student's algebraic expression simplifies to 48 - 12y.

The question involves simplifying an algebraic expression. Let's solve it step by step:

Distribute the 6 to each term inside the first parentheses: 6(7) / (- 6(3y)).

Do the same for the second parentheses: 6(y) + 6(1).

Combine like terms by adding or subtracting the coefficients.

Let's simplify the expression now:

6(7) - 6(3y) + 6(y) + 6(1).

42 - 18y + 6y + 6.

Combine the terms with y: -18y + 6y = -12y.

The final simplified expression is 42 - 12y + 6.

Combine the constant terms: 42 + 6 = 48.

The final answer is 48 - 12y.

3/4(x-12)=12
3/4y - 12=12
What is x? What is Y?

Answers

Answer:

x = 28y = 32

Step-by-step explanation:

3/4(x-12)=12

3/4x - 3/4(12) = 12

3/4x - 9 = 12

3/4x = 12 + 9

3/4x = 21

1/4x = 7

x = 28

3/4y - 12=12

3/4y = 12 + 12

3/4y = 24

1/4y = 8

y = 32

A credit card company charges a customer $18 interest on a $90 purchase. What is the interest rate?

Answers

Final answer:

The interest rate charged by the credit card company for a $90 purchase with an $18 interest charge is calculated to be 20%.

Explanation:

To calculate the interest rate charged by the credit card company on a $90 purchase with an $18 interest charge, we need to use the formula for interest rate:

Interest Rate = (Interest / Principal) × 100

Applying the given values:

Interest Rate = ($18 / $90) × 100

Interest Rate = 0.2 × 100

Interest Rate = 20%

The interest rate the credit card company charged on the purchase is 20%.

The if James problem please help

Answers

Answer:

The answer to this is 34 minutes and 50 seconds.

Step-by-step explanation:

First, I multiplied 23 x 2 = 46 because I wanted to see how much minutes it could be in 20 minutes.

Then, I got the answer by getting the median.

23 - 46

the median of that is 34.5. Therefore, the expected time for 15 laps is 34 minutes and 50 seconds.

Hope this Helped!!!!

~Shane

Answer:

34.5 Is the answer or 34 minutes and 5 seconds.

Step-by-step explanation:

1) Set a Proportion Minutes on top over laps

23/10 = x/15

2) cross Multiply

10 times x = 10x

23 times 15 = 345

3) Solve for X (x is the amount of minutes for 15 laps)

345 = 10x

Divide 10 on both sides

345/10= 34.5

Hopes this Helps you !

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