Which student below wrote an addition statement with the greatest sum,
and what is the sum?

Answer: y = 2 and x = 2

Step-by-step explanation:

[tex]9x^2+4(y-2)^2=36\\x^2=2y[/tex]

First, get the entire thing in terms of y, because you cant solve for two variables at the same time. They gave us the fact that x^2 = 2y

[tex]9(2y)+4(y-2)^2=36\\18y+4(y^2-4y+4)=36\\18y+4y^2-16y+16=36\\4y^2+2y-20=0[/tex]

What two numbers multiply to equal -80 but add to equal 2? That is +10 and -8.

[tex]4y^2+2y-20=0\\(4y^2-8y)+(10y-20)=0\\4y(y-2)+10(y-2=0)\\(4y+10)(y-2)=0\\y=-5/2\\y=2[/tex]

Now solve for x by plugging in y to the easier equation

[tex]x^2=2(-5/2)\\x\neq \sqrt{-5}[/tex]

If I didn't make a mistake, this should be the only answer. In the case of y = -5/2, you would get an imaginary x-value. Therefore y cannot equal -5/2

[tex]x^2=2(2)\\x=2[/tex]

The solution of the expression are,

x = 2.28 , y = 2.62

Or, x = 3.9i , y = - 7.62

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equations are,

9x² + 4 (y - 2)² = 36  .. (i)

x² = 2y  .. (ii)

Substitute the value of x² from (ii) in (i);

9x² + 4 (y - 2)² = 36

9 × 2y + 4 (y - 2)² = 36

18y + 4 (y - 2)² = 36

9y + 2 (y - 2)² = 18

9y + 2 (y² + 4 - 2y) = 18

9y + 2y² + 8 - 4y = 18

2y² + 5y + 8 - 18 = 0

2y² + 5y - 10 = 0

y = - 5 ± √5² - 4×2×- 10 / 2×2

y = - 5 ± √ 25 + 80 / 2

y = - 5 ± √ 105 / 2

y = - 5 ± 10.24 / 2

y = - 5 + 10.24 / 2

y = 5.24/2

y = 2.62

y = - 5 - 10.24 / 2

y = - 15.24 / 2

y = - 7.62

From (ii);

x² = 2y

x² = 2 × 2.62

x² = 5.24

x = 2.28

x² = 2y

x² = 2 × - 7.62

x² = - 15.24

x = 3.9i

Thus, The solution of the expression are,

x = 2.28 , y = 2.62

Or, x = 3.9i , y = - 7.62

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Answer:

63

Step-by-step explanation:

Answer:

AE - 3, EB - 2, EC - 5

Step-by-step explanation:

Use the Pythagorean theorem and you'll find that these are the answers.

I'll answer problem 19

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

Part (a)

The tickmarks on segments DE and DC indicate they are the same length. We're also told that |DC| = |DE| = 5.

So DE is also 5 cm long. Triangle DAE is a right triangle with the 90 degree angle at angle A. Let x be the length of segment AE.

We'll use the pythagorean theorem to find x

a^2 + b^2 = c^2

(AE)^2 + (AD)^2 = (DE)^2

x^2 + 4^2 = 5^2

x^2 + 16 = 25

x^2 = 25-16

x^2 = 9

x = sqrt(9)

x = 3

Segment AE is 3 cm long

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

Part (b)

For any rectangle, the opposite sides are parallel and the same length. This means AB = DC = 5 cm.

We found earlier that AE = 3 cm, so,

AE+EB = AB

3+EB = 5

EB = 5-3

EB = 2

Segment EB is 2 cm long

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

Part (c)

We know that AD = BC = 4 cm, because the opposite sides are the same length.

Earlier in part (b), we found that segment EB was 2 cm long.

Triangle EBC is a right triangle with legs EB = 2 and BC = 4. Let's apply the pythagorean theorem to find EC. Let y = EC.

a^2 + b^2 = c^2

(EB)^2 + (BC)^2 = (EC)^2

2^2 + 4^2 = y^2

4 + 16 = y^2

20 = y^2

y^2 = 20

y = sqrt(20)

y = sqrt(4*5)

y = sqrt(4)*sqrt(5)

y = 2*sqrt(5)

y = 4.4721359

As an exact value, EC is sqrt(20) or 2*sqrt(5) cm long.

As an approximate value, EC is roughly 4.4721359 cm long.

I would ask your teacher if you should use the exact or approximate value.

Answer:

Step-by-step explanation:

Use the formula,

distance = √[(x1-x2)^2 + (y1-y2)^2]

Answer:

y= -x+9

❤hope its helpful

THANK YOU.

Answer:

Step-by-step explanation:

x=2

Answer:

v = 1

Step-by-step explanation:

volume of a cube = side cubed

1 cubed = 1

Answer:

answer is 1 cubic unit

hope this helps

First Answer:

x = 12

First Step-by-step explanation:

12 + x = -3(4 - x)

12 + x = -12 + 3x

- x - x

—————————

12 = -12 + 2x

+ 12 + 12

—————————

24 = 2x

24/2 = 2x/2

12 = x

Second Answer:

No solution

Second Step-by-step explanation:

2(x - 1/2) = 8 + 2x

2x - 1 = 8 + 2x

+1 +1

—————————

2x = 9 + 2x

- 2x - 2x

—————————

0 = 9

^^ No solution

Answer:

8/12, 6/19 and 9/10!

Step-by-step explanation:

All of them cannot be simplified.

but the rest can like  

4/26 can be simplified by 2

and 10.22 can be simplified by 2

Answer:

x² + 9x + 14 can be factored as (x+2)(x+7)

Step-by-step explanation:

The general form is ax² + bx + c. If a=1, then you can start looking for two numbers that multiplied give c and added give b.

14 = 2*7

and

9 = 2+7

hence the easy factorization

(x+2)(x+7)

Keep in mind that it only works if a=1.

Answer:

( + 2 ) (x+7 )

Step-by-step explanation:

Use the sum-product pattern   2 + 9 + 1 4 2 + 7 + 2 + 1 4 2

Common factor from the two pairs   2 + 7 + 2 + 1 4 ( + 7 ) + 2 ( + 7 ) 3

Rewrite in factored form   ( + 7 ) + 2 ( + 7 ) ( + 2 ) ( + 7 )

Answer:

A

Step-by-step explanation:

A) 3/4 ÷ 5 1/5.

Answer:

[tex] \frac{15}{104} [/tex]

B) 3/7 ÷ 2 1/2.

Answer:

[tex] \frac{6}{35} [/tex]

C) 5/8 ÷ 6 5/6.

Answer:

[tex] \frac{15}{164} [/tex]

D) 8 3/10 ÷ 5/8.

Answer:

[tex]13 \frac{7}{25} [/tex]

Answer:

[tex]m^{4}n^{5}[/tex]

Step-by-step explanation: ( I'm a student, I'm not really good at explaining maths )

When dividing variables with exponents, you subtract the exponents that has the same variables, like this:

[tex]m^{16-12}n^{10-5}[/tex]

Simplifying this becomes:

[tex]m^{4}n^{5}[/tex]

Answer:

0     7

1     7.20

2    7.40

3    7.60

Step-by-step explanation:

Answer: 108°

Step-by-step explanation:

Answer:

Remember that the total amount of degrees in a pentagon is: 540, and there are 5 sides, so divide 5 by 540:

540/5 = 108

108 is your answer.

Answer:

Base = 3√5

Step-by-step explanation:

Given:

Hypotenuse = 9

Perpendicular = 6

Find:

Base(x)

Computation:

Using Pythagorean theorem

Base = √Hypotenuse² - Perpendicular²

Base = √9² - 6²

Base = √81 - 36

Base = √45

Base = 3√5

Answer:

(x-114.5), (x-14.05)

Step-by-step explanation:

Answer attached

Answer:

$0.33

Step-by-step explanation:

5.11-3.79=1.32 1.32/4

Hope this helps :)

Answer:

each postcard cost .33 or 33 cent

Step-by-step explanation:

5.11(total cost)-3.79(greeting card)= 1.32

1.32(cost of all postcards)/4= .33

Answer:

I think your problem didn't copy correctly because you didn't provide a function. if you could provide it to me I would be glad to help and give you the answer.

I also do exams and quizzes if your interested

Answer:

y = -2x - 4

Step-by-step explanation:

We transform the line equation of L:

2x + y = 3 --(-2x)--> f(x) = y = -2x + 3

We now know that L intersects the y-axis at 3 and it has a slope of -2.

In order to construct a parallel line M, it needs to have an identical slope to L.

All we need to do now is to move one step from the given point (1,-6) towards 0 with the predetermined slope of -2, resulting in the point (0,-4).

Since we know slope and intersection with the y-axis (0,-4), we can construct the line equation:

f(x) = y = -2x - 4 for line M.

Answer:

4x+4y

Step-by-step explanation:

You can write an equivalent expression by simply simplifying the expression. In order to simplify this expression, distribute the numbers.

You'll get:

(2*2x)+(2*2y) = 4x + 4y

4x + 4y is an equivalent expression.

Answer:

Step-by-step explanation:

Ok

Answer:

what

Step-by-step explanation:

:(

Answer:

B. s = 32t

Step-by-step explanation:

The equation would be in the form of s = mt.

Where, m = rate of change

Find rate of change using any two values given in the table, say (1, 32) and (2, 64)

Rate of change (m) = ∆s/∆m = (64 - 32)/(2 - 1) = 32/1 = 32

✔️To write the equation, substite m = 32 into s = mt

s = 32t

Answer:

13:6 D

Step-by-step explanation:

A ratio is just a comparison between two numbers. its asking for pizza students first so you enter that number first then it asks for the number of mac and cheese so you input that number.

The ratio of students who ate pizza to students who ate mac and cheese is 13:6.

From the given table we need to find the ratio of students who ate pizza to students who ate mac and cheese.

In mathematics, a ratio indicates how many times one number contains another.

Now, pizza: mac and cheese=13:6

Therefore, the ratio of students who ate pizza to students who ate mac and cheese is 13:6.

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Answer:

I have no idea. Is this a real question? If it, I'll answer it to the best of my ability. :)

Step-by-step explanation:

Answer:

Linear polynomial.

Step-by-step explanation:

A linear polynomial is written with a degree 1. An example of a linear polynomials includes 3x + 5. This is what 5b - 1 is.

Hope it helps!