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RSB [31]
2 years ago
5

Given a table of values of a quadratic function, which of the following do you absolutely need in order to find its equation? *

Mathematics
1 answer:
nadya68 [22]2 years ago
6 0

Answer:

The general form of a quadratic function is --> y = ax2 + bx + c

Since (0, -2) exists for the function, we can plug in those values:

-2 = a(0)2 + b(0) + c

-2 = 0 + 0 + c

-2 = c

So now our function so far is --> y = ax2 + bx - 2

We have two pairs of coordinates left: (-1, -8) and (3, -8).

First, plug in the first pair and simplify as much as you can:

-8 = a(-1)2 + b(-1) - 2

-8 = a - b - 2 ( add 2 to both sides )

-6 = a - b (stop here because we can't go further)

Second, plug in the second pair and simplify as much as you can:

-8 = a(3)2 + b(3) - 2

-8 = 9a + 3b - 2 ( add 2 to both sides )

-6 = 9a + 3b (stop here because we can't go further)

Now we have these two equations left:

a - b = -6

9a + 3b = -6

Now we solve for a and b using systems of equations, using one of three ways:

substitution

elimination

graphing (not my favorite, but it is doable)

Using substitution:

a - b = -6 can be rewritten as a = b - 6

plug into the second equation and solve for b

9(b - 6) + 3b = -6 (distribute the 9)

9b - 54 + 3b = -6 (combine all of the b's)

12b - 54 = -6 (add 54 to both sides)

12b = 48 (divide by 12 on both sides to isolate b)

b = 4

plug b into one of the original two equations

a - 4 = -6 (add 4 to both sides)

a = -2

The quadratic equation for this table is y = -2x2 + 4b - 2

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Find X. Enter a number for your answer. Do not type the symbol for degree or the<br> word "degrees"
Lena [83]

Use angle sum property (the 3 angles in a triangle sum up to 180°).

2x + x + 54 = 180

3x + 54 = 180

3x = 180 - 54

3x = 126

x = 126/3

x = 42

_____

Hope it helps ⚜

6 0
2 years ago
Read 2 more answers
Orbital Toys sells two types of sets of magnetic spheres, silver and brass. The store owner, Lucy Ball, pays $8 and $16 for each
sdas [7]

Answer:

The maximum profit will be reached by buying 500 brass magnetic spheres and 1500 silver magnetic spheres.

Step-by-step explanation:

In order to solve this you need to create a system of equations, with two values that will create the answer we are looking for, the thing that we don't know here is how many of each are we buying so the number of silver magnetic spheres will be represented by "y" and the brass magnetic spheres will be represented by "x".

So we know that x+y=2000

That's our first equation, our second would be the expense, which would be

8x+16y=20,000

We now just solve for one of them

x=(2000-y)

8(2000-y)+16y=20,000

16,000-8y+16y=20,000

8y=4,000

y=500

So we know that the maximum profit will be reached by buying 500 brass magnetic spheres and 1500 silver magnetic spheres.

5 0
3 years ago
Which description best fits the distribution of the data shown in the histogram?
Sedaia [141]

Option B: Approximately bell-shaped

Explanation:

Option A: Skewed

A histogram is said to be skewed if most of the larger values falls either on the left or right side.

Clearly, the given histogram is not skewed.

Thus, Option A is not the correct answer.

Option B: Approximately bell-shaped

A graph is said to be bell shaped if a vertical line is drawn at the center which will form a mirror image of the left half of the graph with the right half.

Clearly, the given histogram is approximately bell-shaped.

Thus, Option B is the correct answer.

Option C: Uniform

A graph is said to be uniform if its data is equally spread across the range.

Clearly, the given histogram is not Uniform.

Thus, Option C is not the correct answer.

Option D: Skewed left

A graph is said to be skewed left if the smaller values fall on the left side of the graph.

Clearly, the given histogram is not skewed left.

Thus, Option D is not the correct answer.

Hence, Option B is the correct answer.

5 0
3 years ago
Read 2 more answers
Please help me it’s due tonight and I’m stuck on this question!!
solniwko [45]

Answer:

The length of the ramp is 7.3 meters.

Step-by-step explanation:

The length of a triangle's side must be less than the sum of its two other sides. It also cannot have the same value as its other combined sides.

7 + 2 > 7.3

2 + 7.3 > 7

7 + 7.3 > 2

<em>r</em> is also longer than 7 meters, so that leaves option b. as your answer.

3 0
3 years ago
Some one plz help me
Deffense [45]

Answer:

Given:

- angle: E

- opposite-leg : 3

- adjacent - leg: 4

- hypotenuse: 5

sin(E) = opposite-leg / hypotenuse = 3 / 5

Answer: 3 / 5

Step-by-step explanation:

Brainliest?

5 0
3 years ago
Read 2 more answers
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