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satela [25.4K]
2 years ago
9

Louisa states that the solution to the equation One-fourth x minus 3 = StartFraction 3 Over 8 EndFraction x + 4 is x = 56. She v

erifies her solution using the steps below.
Equation: One-fourth x minus 3 = StartFraction 3 Over 8 EndFraction x + 4
Step 1: One-fourth (56) minus 3 = StartFraction 3 Over 8 EndFraction (56) + 4
Step 2: 14 minus 3 = 21 + 4
Step 3: 11 = 25

Which statement most accurately describes Louisa’s error?
Louisa made an error when determining the original solution of x = 56.
Louisa made an error when substituting the solution in for x.
Louisa made an error when multiplying 56 by One-fourth and by StartFraction 3 Over 8 EndFraction.
Louisa made an error when adding or subtracting.
Mathematics
2 answers:
k0ka [10]2 years ago
8 0

Answer:

Its A

Step-by-step explanation: I took the test

padilas [110]2 years ago
8 0

Answer:

A

Step-by-step explanation:

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Divide the figure into known figures like rectangle and semi-circle
Calculate the area of the whole figure by adding the area of the separate figures
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3 years ago
Solve 3(2x-4)>2(x+4)
DerKrebs [107]

Answer:

x > 5

Step-by-step explanation:

3 ( 2x - 4 ) > 2 ( x + 4 )

6x - 12 > 2x + 8

4x > 20

x > 5

6 0
3 years ago
Y=-3x^2-6x+24
Lera25 [3.4K]
The x-intercept is the point at which the function intersects the x-axis.
For any point on the x-axis, y = 0. Thus we can plug in 0 for y and solve for x.

y=-3x^2-6x+24 \\ 0=-3x^2-6x+24

Let's split the middle on this quadratic.
To do this we need to find two numbers that add to equal -6 and multiply to equal -72. (-3 times 24)
Consider ways to multiply to get 72.
72 = 36 ×2...that's not going to work.
72 = 24 × 3
72 = 18 × 4
72 = 12 × 6...and 12 minus 6 is 6!
Let's add our signs; our numbers are -12 and 6.
Now, split the middle and factor.

0=-3x^2-12x+6x+24\\0=-3x(x+4)+6(x+4)\\0=(-3x+6)(x+4)

Now you should know that anything multiplied by zero is zero.
So any value that makes one of those factors equal zero is an x-intercept.
Solve each of these equations.

-3x+6 = 0
-3x = -6
x = 2

x+4 = 0
x = -4

Oh, and since all parabolas (graphs of quadratics) are symmetrical, our axis of symmetry will be the average between the two, which is x=-1.

Now for our y-intercepts. For any points on the y-axis, x=0, so if we plug in 0 for x and solve for y we'll get our y-intercept.

y = -3×0² - 6×0 + 24
y = 0 - 0 + 24
y = 24

What about our vertex? Well, we know it's going to line up with the axis of symmetry, so let's just plug in -1 for x.

y = -3×-1² - 6×-1 + 24
y = -3×1 -6×-1 + 24
y = -3 + 6 + 24
y = 27

Thus the vertex is (-1, 27)

The y value is not going to exceed 27, as this is a decreasing quadratic, (we already know y=24 is a possibilty) and this equation goes downwards infinitely, so our range is (-∞, 27)

As for x, well, it's sort of the input for our equation, meaning it can be whatever we want it to be. Thus the domain is (-∞, ∞)




3 0
3 years ago
Write a recursive formula for
algol13

9514 1404 393

Answer:

  • a[1] = 3
  • a[n] = a[n-1] -7

Step-by-step explanation:

A recursive formula consists of two parts:

  • initialization (rule for the first term(s))
  • rule for the next term

When we look at the differences between terms in the sequence 3, -4, -11, ..., we find that they are constant at -7. That is each term can be found from the previous one by subtracting 7. This is our recursive rule. The first term is obviously 3, so the recursive formula is ...

  a[1] = 3

  a[n] = a[n-1] -7

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3 years ago
Diana has just begun the process of filing her federal income tax return, and she plans to deduct medical and dental expenses. w
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Answer:

1040 tehyimngtumh

Step-by-step explanation:

Apex

5 0
3 years ago
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