NEED HELP PLEASE- ANSWER BOTH TASKS, WILL MARK BRAINLIEST

Task 1 - Nonlinear Systems of Equations

Create a system of equations that includes one linear equation and one quadratic equation.
-
Part 1. Show all work in solving your system of equations algebraically.
-
Part 2. Graph your system of equations and show the solution graphically to verify your solution.
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Task 2 - Polynomial Identities

Part 1. Pick a two-digit number greater than 25. Rewrite your two-digit number as a difference of two numbers. Show how to use the identity (x − y)2 = x2 − 2xy + y2 to square your number without using a calculator.
-
Part 2. Choose two values, a and b, each between 8 and 15. Show how to use the identity a3 + b3 = (a + b)(a2 − ab + b2) to calculate the sum of the cubes of your numbers without using a calculator.
-

Answers

Answer 1

Answer:

f(x)5.79(3)^2 for task 1

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

Task 1:

Non linear systems of equations:

x + y = 1 -------------------(I)     {Linear equation}

     y =  1 - x

y = x² - 5 ---------------(II)   {Quadratic equation}

Substitute y =1 - x in equation (II)

(II) -->   1 -x = x² -5

Add 'x' to both sides

1 = x² + x - 5

0 = x² + x - 5 - 1   {Subtract 1 from both sides}

x² + x - 6 = 0

x² + 3x - 2x - 6 = 0    {Rewrite the middle term}

x( x + 3) - 2(x + 3) = 0    

(x + 3)(x - 2) = 0

x + 3 = 0       ;  x - 2 = 0

x = - 3   ; x = 2

When x =  - 3 ,   y = 1 -(-3 )

                              = 1 + 3

                             y = 4

When x = 2  ; y = 1 - 2 = -1

Solution of the equations:  (-3,4)  & ( 2,-1)

Task 2:

Part 1: x = 40   ; y = 30

(x - y)² = x² - 2xy + y²

(40 - 30)² = 40² - 2*40*30 + 30²

               = 1600 - 2400 + 900

               = 2500 - 2400

                = 100

Part 2:

a = 10 , b = 11

a³ + b³ = (a + b)(a² - ab +b²)

(10)³ + (11)³ = (10 +11)(10² -10*11 + 11² )

              = 21* (100 - 110 + 121)

              = 21 * ( 221 - 110)

              = 21 * 111

              = 2331

             


Related Questions

(I GOT AN 80% )


1.(D)
Ricardo has r minutes left on his cell-phone card. He wants to call his friend and still have 8 minutes left over to make calls later. Which expression describes the length of time he can talk to his friend?

D) r – 8





2.(D)
Lorraine rode her bike one-sixth the distance Jeremy rode his bike. If b represents the distance Jeremy rode, which expression represents the distance Lorraine rode her bike?

D) b
---
6



3.(A)
Raoul rode an elevator up the floors. He entered on the 5'thand exited on the 34'th
sloor. Which equation shows an equality between two different ways of expressing the Raoul exited ?



A) 34 = 5 + e






4.(B)
Hank went to an apple orchard and paid an entrance fee of $5 and bought a pounds of apples at $2 per pound. Hank paid a total of $19.

Which equation shows an equality between two different ways of expressing how much Hank paid in all?

B) 5 + 2a = 19





5.(A)

Chen’s house is 53 years old. This is 5 more than twice the age of Sunny’s house, h.

Which equation shows an equality between two different ways of expressing the age of Chen’s house?
A) 53 = 2h + 5





6.(A)

Mandy and four of her friends want to see a movie. If m represents the cost for one person to see a movie, which expression represents the cost for Mandy and her friends to see a movie?
A) 5m






7.(WRONG ANSWER IS D)
Natalie and Juan collect marbles. The number of marbles that Natalie has is 4 more than 3 times the number of marbles Juan has. If m represents the number of marbles Juan has, which of the following expressions represents the number of marbles Natalie has?
A) 4m + 3
B) 3m + 4
C) 3m – 4
D) DO NOT PICK ITS WRONG




8.(WRONG ANSWER IS D)
Hannah baked twice the number of cookies Sam baked. Sam baked 36 cookies. Let c represent the number of cookies Hannah baked.

Which equation shows an equality between two different ways of expressing how many cookies Sam baked?
A) 36 = c – 2
B) 36 = c + 2
C) 36 = c ÷ 2

D)DO NOT PICK ITS WRONG




9.(B)
There were c members in the chess club before 8 more people joined. Which expression describes the number of members in the chess club now?

B) c + 8



10.(C)


C) P
--- + 1.5
4





(all the correct answers are next to the numbers and it says do not pick which everyone's where wrong which was 7 and 8 i hope this helps you)

Answers

Answer:

for 7 the answer is B and for 8 the answer is C.

Step-by-step explanation:

7.

Natalie and Juan collect marbles. The number of marbles that Natalie has is 4 more than 3 times the number of marbles Juan has. If m represents the number of marbles Juan has, which of the following expressions represents the number of marbles Natalie has?

A) 4m + 3

B) 3m + 4

C) 3m – 4

if Natalie has 4 more ( adding 4 more marbles) marbles that are already 3 times Juan has ( multiplying by 3) then the answers for A and C don't make since the amount of marbles is multiplied by 3 and adds 4. Bis the correct option.

8.

Hannah baked twice the number of cookies Sam baked. Sam baked 36 cookies. Let c represent the number of cookies Hannah baked.

Which equation shows an equality between two different ways of expressing how many cookies Sam baked?

A) 36 = c – 2

B) 36 = c + 2

C) 36 = c ÷ 2

if Hannah made twice as many cookie as Sam that means the amount of cookies Hannah made are equivalent to 36 x 2= c. if we were to multiply 36 x2 we'd get how many cookies Hannah made and if we needed to find out how many Sam made we'd have to divide  Hannah's cookies by two. giving us 36 = c ÷ 2. making C the correct option.

math problem for highschool

Answers

Answer:

297 units squared

Step-by-step explanation:

You just have to break the squares down and compare them to the other sides of the squares.  For example, F is a 4 by 4 square and B is a 5 by 5 square, to find the dimensions of square E, you would just subtract 5 by 4.  By looking at the side relationships of the squares, you can easily find the dimensions of each one.

A - 9 by 9

B - 5 by 5

C - 6 by 6

D - 7 by 7

E - 1 by 1

F - 4 by 4

G - 8 by 8

H - 5 by 5

Multiply and add to get 297

Answer:

297 units squared

Step-by-step explanation:

Which represents the solution set of 5 (x + 5) less-than 85

Answers

Answer:

5x+25<85

Step-by-step explanation:

distribute the 5 and use a less than sign.

(5x + 25) < 85

You have to distribute the 5 to both values in the equation. Then put the less than sign at the end. The smaller end facing the equation as you are saying the ‘whole equation’ is LESS than the 85

Please help me with this question. Please, this is due today. Helppppp meeee

Answers

Answer:

6by6by8

Step-by-step explanation:

Answer:

6m

6m

8m

Step-by-step explanation:

calm down ...

don't let a strange problem description overwhelm you right away.

always try to work with the things you know first. and only when you run into something you really don't know, start thinking.

so, perimeter.

your know, what a perimeter is ? it is the circumference. all the side lengths added together. the answer to "how much distance would you have to go, to walk all the way around it one time".

so, what is the circumference of the square based on what we know ?

well, it has 4 equal sides, right ? otherwise it would not be a square.

so, the perimeter is 4×(x+2) = 4x + 8

that is perfectly fine.

now to the next part we know.

the perimeter of the triangle is the sum of its 3 sides (otherwise it would not be a triangle).

an isoceles triangle is a special triangle that has 2 equal sides.

so, we actually know all 3 sides (at least relatively) :

x+3

x+5

and ... another

x+3 (because of the isoceles property)

so, the perimeter is

x + 3 + x + 3 + x + 5 = 3x + 11

alright.

and now we also know that both perimeters are of equal length.

what did that mean ?

that both expressions deliver the same result.

therefore,

4x + 8 = 3x + 11

aha !

x = 3

bingo !

therefore, the side lengths of the triangle are

x+3 = 3+3 = 6 (both sides in the top)

x+5 = 3+5 = 8

and that's all there is to it.

it is really not necessary to panic don't you think ?

“Model a desert community where 60% is houses, 10% is shops, and 30% is parks.”

Answers

Answer:

house are 60 squares

shops are 10 squares

and parks are 30 squares

I think because it can be a wrong answer

any way best of luck

60, and 10 square 30 squares

A square of 81cm² is cut to make two rectangles, A and B
The ratio of area A to are B is 2:3
Work out the dimensions of A and B

Answers

Answer:

Length of A: 9

Width of A: 6

Length of B: 9

Width of B: 3

Step-by-step explanation:

If you look at the diagram, you can see that the length of rectangles A and B are the same, and are also the same as they were in the original square. We can find the length of each side by finding the square root of the area of the square to give us the length and width of the square which is 9. Now that we know that the length of both rectangles A and B, we can find the width of both rectangles by taking 9, and splitting it into 3 portions of 3. Since the ratio of area is 2:1, we could also do this with the area, but since we know the lengths are the same, we know the widths are proportional to the area. Using the ratio of 2:1, and the 3 portions of 3, you can combine 2 of these portions to get 6, and since the ratio 6:3 is proportional to 2:1, these measurements can be used as the width of each rectangle. Thus, the answer given above.

Answer:

Length of A: 9

Width of A: 6

Length of B: 9

Width of B: 3

Step-by-step explanation:

Please help me! I will give brainly!

Question,

Reasoning Explain how you can tell which product is greater without multiplying or estimating.

3.75 x 922 37.5 x 9.22


Question,

Modeling Real Life Nutritionists recommend that fifth-graders should consume about 5 ounces of protein each day. One serving of yogurt contains 0.6 ounce of protein. You eat 2.5 servings of yogurt in 1 day. Do you consume enough protein for the day by eating yogurt?

Yes or No

Explain why

Answers

The first ones answer is 3.75*922 because 922 is a 3 digit number times a one digit number instead of a 2 digit number times a one digit number.

The second one 6*2.5=1.5 ounces which is 3.5 ounces too little.

Answer:

Question 1. 3.75 x 922

Step-by-step explanation:

for question 1 if u noticed that they both have the same numbers in the same order the only difference is where the decimal point is placed. First u need to anylase both equations to do that u need to look at 922 and 9.22 not the 3.75  and 37.5 because the decimal point doesn't justify anything. So you see 922 is bigger than 9.22. So the answer is 3.75 x 922.

Item 17
Your family has decided to put a rectangular patio in your backyard similar to the shape of your backyard. Your backyard has a length of 40 feet and a width of 20 feet. The length of your new patio is 12 feet. Find the perimeter of your new patio.

Answers

Answer:

80

Step-by-step explanation:

80

64 feet because the width is 20 feet plus 12 feet length times two equals 64 feet. That would be the total line boundary or perimeter.

What is the initial value of the function represented by this graph?

1
5
6
7

Answers

Answer:

the inital value is one.

Step-by-step explanation:

So basically, the initial value is just the value of y when x is zero. In this case, its 1 this point on the graph where x=0 is also known as the y intercept. Hope that helped.

Number 1 because the arrow from 6.7 is pointing to the other side with 0.1 removing the 0 would be 1

Someone help me, I’m struggling and I would be so happy if any of you helped me

Answers

Answer:

1. 75 grams of Toasty Oats for 9 grams of protein

2. Toasty Oats

Step-by-step explanation:

By using cross multiplication we can figure out how many grams of Toasty Oats is needed for 9 grams of protein:

[tex]\frac{12}{100}* \frac{9}{x}[/tex] (x) being the grams of toasty oats.

Cross multiply: 12x = 900

solve for x: 900/12 = x

x = 75 grams of toasty oats needed for 9 grams of protein

To find which one has the better ratio of proteins to grams of cereal,

we can multiply the amount of cereal together to get the same denominator

12/100 and 5/45

12/100 * 9

5/45 * 20

to get the same denominator

108/900 and 100/900

we can see the (12/100)*9 has more protein to grams of cereal ratio than (5/45)*20.

Answer:

1. 75 grams of Toasty Oats for 9 grams of protein

2. Toasty Oats

Step-by-step explanation:

Question 2 (1 point)
Luis and Jorge are exercising. Luis does 10 push-ups at the same time as Jorge does 15 push-ups. When
Luis does 40 push-ups, how many push-ups does Jorge do?

Answers

He does 60 push ups

Answer:

Jorge does 45 push-ups

Step-by-step explanation:

Why? Beacuse everytime luis does a push up it the same thing as Jorge but just five more so 40 plus 5 is 45 thats how i got my answer.

Please help me fast! I will give brainly

This is the question,

YOU BE THE TEACHER Your friend says that because of the order of operations, the expressions are equivalent. Is your friend correct?

10-(5x2)+7 or 10-5x2+7

Yes or No

And Explain the answer

Answers

Answer:

He's correct.

Step-by-step explanation:

As long as there is no change in sign of the variables.

10-(5x2)+7 or 10-5x2+7

please help me with these 2 questions will give brainly!


1 . Which integer represents the following: –(–28)?

28
-28

2. Which integer represents the following: –(–(–65))?

-65
65

Answers

Answer:

1. 28

2. -65

Step-by-step explanation:

The rule I learned, was that if there is an even number of negative signs, the outcome is positive. If there is an odd number of negative signs, the outcome is negative.

In the first question, we have 2 negative signs. So the outcome is positive. 28 is positive.

In the second, we have 3 negative signs, so the outcome is negative. -65 is negative.

I hope this helps!

Answer:

28, -65

Step-by-step explanation:

Find the perimeter of the triangle in the picture attached.

Answers

Answer:

5 2/3 inches

Step-by-step explanation:

To find the perimeter, add up the sides

1 5/6 + 1 1/6 + 2 2/3

2 6/6 + 2 2/3

3 + 2 2/3

5 2/3 inches

Answer:

5 2/3 inches

Step-by-step explanation:

To find the perimeter, add up the sides

1 5/6 + 1 1/6 + 2 2/3

2 6/6 + 2 2/3

3 + 2 2/3

5 2/3 inches

Step-by-step explanation:

The publisher considered 10 manuscripts for publication and accepted 3. What percent were rejected?

Answers

Answer:

70%

Step-by-step explanation:

First find the number that were rejected

10-3 = 7

Then take that over the total

7/10

.7

70%

Answer: 70%

Step-by-step explanation:

10 - 3 = 7

So, there are 7 manuscripts that are rejected.

7/10 are rejected.

70/100

Therefore, 70% are rejected.

Find the coordinates of the intersection of the diagonals of parallelogram GHJK with vertices G(−4, 5), H(3, 5), J(2, −1), and K(−5, −1).

Answers

Answer:  1,2.4

i'm not sure thoo

Step-by-step explanation: :3

The coordinates of the intersections of the diagonal of parallelogram GHJK will be ( -1, 2 ).

What is parallelogram?

A parallelogram is a quadrilateral having four sides and the two opposite sides are equal and parallel to each other.

Given that:-

The coordinates the intersection of the diagonals of parallelogram GHJK with vertices G(−4, 5), H(3, 5), J(2, −1), and K(−5, −1).

The intersection point will be the midpoint between the points G and J or points K and H.

The coordinates of the points H and K are ( 3,5)  and K ( -5,-1). So the midpoint will be calculated as:-

Midpoint = [tex]\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}[/tex]

Midpoint = [tex]\dfrac{-5+3}{2},\dfrac{5-1}{2}[/tex]

Midpoint = [tex]-\dfrac{2}{2},\dfrac{4}{2}[/tex]

Midpoint = (-1,2)

Therefore the coordinates of the intersections of the diagonal of parallelogram GHJK will be ( -1, 2 ).

To know more about parallelogram follow

https://brainly.com/question/970600

#SPJ2

a single piece of sod is typically rectangular in shape and measures 46 cm wide and 1.5 m long. Assuming that you can cut the sod, how many pieces of sod would be required to cover the following lawn?

Answers

The question is incomplete

Answer:

could you add more information?

Step-by-step explanation:

I will literally give you my life if you. help me with these integer questions-

Answers

Answer:

10. 23

11. -17

12. 0

13. -4

14. -6

15. 4

Explanation:

10. 8+15= 23

11. -8-9= -17

12. 8-8= 0

13. -8+4= -4 (same as 4-8)

14. -10+4= -6 (same as 4-10)

15. 12-8= 4

hahahha and ndnd cnfnfnfnc

which o fht e following numbers is the closest to 5? 22.26. 23. 28

Answers

Answer:

the answer is 23 because the number that

5 can divide is 25 so their is no 25 then you choose the number that is the closest

The answer is 23 pls put me for brainliest pls bc I need five brainliest so I can rank up pls

PLEASE TRY TO HELP SOLVE EITHER ONE (OR BOTH). THX!
1. Take an 13 by 8 rectangular grid. Color each of the 1 by 1 cells either solid red, solid white, or solid blue. Show that there are at least two 2 by 2 squares in the grid that are colored exactly the same.
2. Every day of the 10-week summer break, Pamela ate 1 or 2 carrots. Over the course of the summer, she ate a total of 100 carrots. Show that there was an interval of days during the summer break during which Pamela ate exactly 35 carrots.

Answers

Answer:

p and q are two numbers.whrite down an expression of.

Answer:

I’m doing second one

Step-by-step explanation:

I’m confused what  the first question is asking for but for the second one is it took her 25 days to eat 35 carrots

4,000 pounds of sand is used to fill sand boxes. 1,000 pounds can fill the big sandbox, and the rest can fill 4 equal-sized smaller sandboxes. how much sand can be put in each of the smaller sandboxes?

Answers

The answer is 1500 pounds

Answer:

750 pounds each

Step-by-step explanation:

You start with 4000 pounds, and 1000 goes into the big sandbox.

Now you have 3000 pounds left.

These 3000 pounds must be divided into 4 sandboxes, which means

3000/4= Small sandbox capacity=750 pounds

how did the temperature change if at first it increased by 60 and then decreased by 80

Answers

Answer:

Step-by-step explanation:

+25-80=-55

therefore there was a -55˚ change from the og temp

Answer:

-20/dropped 20 degrees

Step-by-step explanation:

60-80 = -20 (or, it dropped 20 degrees)

Can you please help me im stuck on this I would kindly appreciate it.

Answers

Answer:

[tex]{ \tt{y = 2x - 3}}[/tex]

im pretty positive the answe is y=2x-3

What is the solution to the following system of equations: 2x + 3y = 5 AND 5x = 5y -25

Answers

Answer:

point form (-2,3)

Equation form

x=-2, y=3

Step-by-step explanation:

solve for the first variable in one of the equation, then substitute the result into the other equation.

Answer:

(-2,3)

Step-by-step explanation:

5x=5y-25

x=y-5    divide both sides by 5

use substitution.

2(y-5)+3y=5

2y-10+3y=5    distribute the parenthesis

5y-10=5    combine like terms

5y=15    add 10 to both sides

y=3    divide both sides by 5 to get y alone

5x=5(3)-25    replace y with 3, the value we found above

5x=15-25    multiply 5 and 3

5x=-10    subtract 25 from 15

x=-2    divide both sides by 5 to get x alone

after a gymnastic competition, the coaches reviewed all the gymnasts scores to identify areas for improvement. a missed landing on an aerial cartwheel deducts 2 points from the score. the coaches found that aerial cartwheels were missed 5 times across the competition. how did these missed landings affect the scores overall

Answers

Answer: The missed points will subtract 10 from the total score.

Step-by-step explanation:

A missed landing subtracts 2 points.

If they miss the landings 5 times, you know have a problem of 5x2.

5x2=10

Therefore, The points will subtract 10 from the total score.

HELP ME PLEASE

SJSJSJJSJSJSJSJ

Answers

Answer:

24.12-9.8=24.32

Step-by-step explanation:

hope this helps, sorry I'm bad at explaining, but just trust me it is this im 100% positive.

Answer: 24.32

Step-by-step explanation:

   34.12  - 09.80

hope this helps

What is the magnitude (size) of -5.8?

Answers

the magnitude size of -5.8 is 5.8
magnitude size of a number is the number itself, and if it’s negative, it becomes its absolute value (in other words, you remove the subtraction sign).

The magnitude of the negative 5.8 will be 5.8 Then the correct option is D.

What is an absolute function?

The absolute function is also known as the mode function. The value of the absolute function is always positive.

The absolute function is given as

f(x) = | x – h | + k

The magnitude of the number will always be positive.

For example - The value of time, length, mass, temperature etc will always positive.

The magnitude of the negative 5.8 will be

⇒ |-5.8|

When the value in the mode may be negative or may be positive, but when the mode is removed, then the value becomes positive.

⇒ |-5.8|

⇒ 5.8

The magnitude of the negative 5.8 will be 5.8

Then the correct option is D.

More about the absolute function link is given below.

https://brainly.com/question/10664936

#SPJ5

The equation of the line of best fit relating age (in years, x) and the median height (in cm, y) of boys is given.

y = 6.5x + 75.5y=6.5x+75.5
Predict the median height of boys age 13.



123 cm

140 cm

160 cm

82 cm

Answers

Answer:

160 cm

Step-by-step explanation:

Substitute x = 13 into the equation

y = 6.5(13) + 75.5 = 84.5 + 75.5 = 160

The median height of boys age 13 is 160 cm

Answer:160 cm

Explain: I just got a feeling

1 point

The equation of the line of best fit relating age (in years, x) and the median height (in cm, y) of boys is given.

y = 6.5x + 75.5y=6.5x+75.5
Predict the median height of boys age 13.



123 cm

140 cm

160 cm

82 cm

Answers

Answer:

140cm

Step-by-step explanation:

140 is the right answer

a woodworker makes 238 wooden bowls a month. At the rate, how many bowls will he make in 12 months?

Answers

Answer:

2856

Step-by-step explanation:

if you multiply 238 by 12

you will get the ans

Answer: 2856

Step-by-step explanation:

A woodworker makes 238 bowls in a month: this is the unit rate. To find how many bowls will be produced by the woodworker in 12 months,  multiply the unit rate by 12.

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