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BabaBlast [244]
3 years ago
5

SOMEONE PLEASE HELP ME I NEED HELP ASAP

Mathematics
1 answer:
tigry1 [53]3 years ago
5 0

y+4=(5- -4)/(0-3) . (x-3) =>

y+4=-3(x-3)

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John has a die and a coin. The die is labeled 1 through 6 and the two sides of the coin are heads and tails. The tables below sh
Alenkasestr [34]

Answer:

n = 60

Step-by-step explanation:

Total outcomes, while tossing a coin are 2, given as:

{Heads, Tails}

The probability of getting a heads up, while tossing the coin is:

P(Heads) = Favorable Outcome/Total Outcomes

P(Heads) = 1/2 = 0.5

Now, the total outcomes, while rolling a die are 6, given as:

{1, 2, 3, 4, 5, 6}

5 of these numbers are factors of 12, which are:

{1, 2, 3, 4, 6}

Thus, the probability of getting a factor of 12, while rolling a die is:

P(Factor of 12) = Favorable Outcome/Total Outcomes

P(Factor of 12) = 5/6 = 0.83

So, the probability of getting both heads and factor of 12 will be:

P(Heads and Factor of 12) = P(Heads ∪ Factor of 12)

P(Heads and Factor of 12) = P(Heads) * P(Factor of 12) = 0.5 * 0.83

P(Heads and Factor of 12) = 0.417 = 41.7%

So, for 144 trials, the number of trials in which we get heads and factor of 12, are given by:

n = P(Heads and Factor of 12) * 144

where,

n = no. of trials John would expect to roll a number on the die that is a factor of 12 and toss a coin that lands heads-up out of next 144 trials

n = 0.417 * 144

<u>n = 60</u>

7 0
3 years ago
Find the equation of line passing through
love history [14]
I think its b I had this test before and it was b for me
5 0
3 years ago
Those are my choices pls tell me which one would fit this problem!! <br>THERES A PIC ATTACHED
denis23 [38]

Answer: Opens up, has a minimum

Step-by-step explanation:

If the x^2 term is positive the parabola opens up, if it is negative it opens down. Minimum always goes with up, maximum with down

7 0
3 years ago
Write an equation. Mark buys a new iPad for $670. He makes a downpayment of $100 and pays the rest in 12 equal payments, p. What
sweet-ann [11.9K]

Step-by-step explanation: 670-100=570.    570/12

4 0
3 years ago
Read 2 more answers
2y+3x² +5+y+2x+x²+2 what are the coefficients?
saw5 [17]

Answer: 200

The quadratic function f(x) = a(x - h)2 + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k).

Any quadratic function can be rewritten in standard form by completing the square. (See the section on solving equations algebraically to review completing the square.) The steps that we use in this section for completing the square will look a little different, because our chief goal here is not solving an equation.

Note that when a quadratic function is in standard form it is also easy to find its zeros by the square root principle.

Example 3.

Write the function f(x) = x2 - 6x + 7 in standard form. Sketch the graph of f and find its zeros and vertex.

f(x) = x2 - 6x + 7.

= (x2 - 6x )+ 7.        Group the x2 and x terms and then complete the square on these terms.

= (x2 - 6x + 9 - 9) + 7.

We need to add 9 because it is the square of one half the coefficient of x, (-6/2)2 = 9. When we were solving an equation we simply added 9 to both sides of the equation. In this setting we add and subtract 9 so that we do not change the function.

= (x2 - 6x + 9) - 9 + 7. We see that x2 - 6x + 9 is a perfect square, namely (x - 3)2.

f(x) = (x - 3)2 - 2. This is standard form.

From this result, one easily finds the vertex of the graph of f is (3, -2).

To find the zeros of f, we set f equal to 0 and solve for x.

(x - 3)2 - 2 = 0.

(x - 3)2 = 2.

(x - 3) = ± sqrt(2).

x = 3 ± sqrt(2).

To sketch the graph of f we shift the graph of y = x2 three units to the right and two units down.

If the coefficient of x2 is not 1, then we must factor this coefficient from the x2 and x terms before proceeding.

Example 4.

Write f(x) = -2x2 + 2x + 3 in standard form and find the vertex of the graph of f.

f(x) = -2x2 + 2x + 3.

= (-2x2 + 2x) + 3.

= -2(x2 - x) + 3.

= -2(x2 - x + 1/4 - 1/4) + 3.

We add and subtract 1/4, because (-1/2)2 = 1/4, and -1 is the coefficient of x.

= -2(x2 - x + 1/4) -2(-1/4) + 3.

Note that everything in the parentheses is multiplied by -2, so when we remove -1/4 from the parentheses, we must multiply it by -2.

= -2(x - 1/2)2 + 1/2 + 3.

= -2(x - 1/2)2 + 7/2.

The vertex is the point (1/2, 7/2). Since the graph opens downward (-2 < 0), the vertex is the highest point on the graph.

Exercise 2:

Write f(x) = 3x2 + 12x + 8 in standard form. Sketch the graph of f ,find its vertex, and find the zeros of f. Answer

Alternate method of finding the vertex

In some cases completing the square is not the easiest way to find the vertex of a parabola. If the graph of a quadratic function has two x-intercepts, then the line of symmetry is the vertical line through the midpoint of the x-intercepts.

The x-intercepts of the graph above are at -5 and 3. The line of symmetry goes through -1, which is the average of -5 and 3. (-5 + 3)/2 = -2/2 = -1. Once we know that the line of symmetry is x = -1, then we know the first coordinate of the vertex is -1. The second coordinate of the vertex can be found by evaluating the function at x = -1.

Example 5.

Find the vertex of the graph of f(x) = (x + 9)(x - 5).

Since the formula for f is factored, it is easy to find the zeros: -9 and 5.

The average of the zeros is (-9 + 5)/2 = -4/2 = -2. So, the line of symmetry is x = -2 and the first coordinate of the vertex is -2.

The second coordinate of the vertex is f(-2) = (-2 + 9)(-2 - 5) = 7*(-7) = -49.

Therefore, the vertex of the graph of f is (-2, -49).

8 0
2 years ago
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