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navik [9.2K]
1 year ago
13

Which equations are true? Select all that apply. A. 30 × 100 = 3 , 000 B. 30 × 10 3 = 30 , 000 C. 30 × 1 , 000 = 3 , 000 D. 30 ×

10 4 = 3 , 000 , 000 E. 30 × 10 , 000 = 30 , 000
Mathematics
1 answer:
Katarina [22]1 year ago
3 0

30 × 100 = 3,000, 30 × 10³ = 30,000 and 30 × 1000 = 30000. Therefore, options A, B, C and D are the correct answers.

<h3>What is an equation?</h3>

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

A) 30 × 100 = 3,000

Here, LHS = RHS

B) 30 × 10³ = 30,000

Here, LHS = RHS

C) 30 × 1000 = 30000

Here, LHS = RHS

D) 30 \times 10^4 = 3000

30 × 10000 = 300,000

Here, LHS ≠ RHS

E) 30 × 10000 = 30,000

= 300,000

Here, LHS ≠ RHS

Therefore, options A, B, C and D are the correct answers.

To learn more about an equation visit:

brainly.com/question/14686792.

#SPJ1

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(HELP ASAP) Use numerals instead of words.
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Answers:

  • -1 in the first box
  • 19/2 or 9.5 in the second box
  • -12 in the third box

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

Work Shown:

We'll use the template y = ax^2 + bx + c

  • If (x,y) = (2,3) is on the parabola, then y = ax^2+bx+c turns into 3 = a(2)^2 + b(2) + c. That simplifies to 4a+2b+c = 3
  • If (x,y) = (6,9) is on the parabola, then y = ax^2+bx+c turns into 9 = a(6)^2 + b(6) + c. That simplifies to 36a+6b+c = 9
  • If (x,y) = (8,0) is on the parabola, then y = ax^2+bx+c turns into 0 = a(8)^2 + b(8) + c. That simplifies to 64a+8b+c = 0

The system of equations is

\begin{cases}4a+2b+c = 3\\36a+6b+c = 9\\64a+8b+c = 0\end{cases}

We have 3 equations and 3 unknowns.

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

Let's solve the first equation for c

4a+2b+c = 3

2b+c = 3-4a

c = 3-4a-2b

c = -4a-2b+3

Plug that into the second equation and simplify

36a+6b+c = 9

36a+6b+(-4a-2b+3) = 9

32a+4b+3 = 9

32a+4b = 9-3

32a+4b = 6

2(16a+2b) = 6

16a+2b = 6/2

16a+2b = 3 .... we'll use this later

Plug that value of c into the third equation as well

64a+8b+c = 0

64a+8b+(-4a-2b+3) = 0

60a+6b+3 = 0

3(20a+2b+1) = 0

20a+2b+1 = 0

20a+2b = -1

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

We have a new system of equations. This time it deals with 2 variables instead of 3. We can think of this as a reduced equivalent system.

\begin{cases}16a+2b = 3\\20a+2b = -1\end{cases}

Note how subtracting the terms straight down has the b terms canceling (since 2b-2b = 0b = 0)

The 'a' terms subtract to 16a-20a = -4a

The terms on the right hand side subtract to 3-(-1) = 3+1 = 4

We end up with the equation -4a = 4 which solves to a = -1

Use this value of 'a' to find b

16a+2b = 3

16(-1)+2b = 3

-16+2b = 3

2b = 3+16

2b = 19

b = 19/2

b = 9.5

Now use the values of a and b to find c

4a+2b+c = 3

4(-1)+2(9.5)+c = 3

-4+19+c = 3

15+c = 3

c = 3-15

c = -12

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

Summary:

The values of a,b,c we found were

  • a = -1
  • b = 19/2 = 9.5
  • c = -12

So the function is

f(x) = -x^2 + (19/2)x - 12

which is equivalent to

f(x) = -x^2 + 9.5x - 12

To check this answer, plug in x = 2, x = 6, x = 8 one at a time. You should get y = 3, y = 9 and y = 0 in that order.

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