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guajiro [1.7K]
4 years ago
14

Help on #51 please !!

Mathematics
1 answer:
Aleks04 [339]4 years ago
4 0

Answer:

53. ±6

51. 2

Step-by-step explanation:

According to the Order of Operations [GEMS\BOMDAS\PEMDAS etc.], in this case, evaluate everything in grouping symbols first, then evaluate the exponents to avoid confusion:

\sqrt{(32 + {2}^{3} - 4)} = \sqrt{32 + 8 - 4} = \sqrt{36} = ±6 \\  \\ (17 - 11 + {4}^{2}) \div 11 = (17 - 11 + 16) \div 11 = \\  \\ 22 \div 11 = 2

I am joyous to assist you anytime.

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What does x equal? 2x-8=2x+6+x
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2x-8=2x+6+x    first put all the like terms together
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In answering a question on a multiple-choice test, a student either knows the correct answer or guesses it. Let 0.7 be the proba
Dahasolnce [82]

Answer:

The probability is 0.9211

Step-by-step explanation:

Let's call K the event that the student know the answer, G the event that the student guess the answer and C the event that the answer is correct.

So, the probability P(K/C) that a student knows the answer to a question, given that she answered it correctly is:

P(K/C)=P(K∩C)/P(C)

Where P(C) = P(K∩C) + P(G∩C)

Then, the probability P(K∩C) that the student know the answer and it is correct is:

P(K∩C) = 0.7

On the other hand, the probability P(G∩C) that the student guess the answer and it is correct is:

P(G∩C) = 0.3*0.2 = 0.06

Because, 0.3 is the probability that the student guess the answer and 0.2 is the probability that the answer is correct given that the student guess the answer.

Therefore, The probability P(C) that the answer is correct is:

P(C) = 0.7 + 0.06 = 0.76

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P(K/C) = 0.7/0.76 = 0.9211

7 0
3 years ago
Write the equation for the line that passes through the points (4, 5) and<br> (6,9). *
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Answer:

y = 2x + 1

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Find the vertex of the graph of the function.
lapo4ka [179]

Answer: The correct options are  (1) (5,10), (2) (3,-3), (3) x = -1, (4) y=(x+2)^2+3, (5) 21s and (6) 0, -1, and 5.

Explanation:

Te standard form of the parabola is,

f(x)=a(x-h)^2+k        .....(1)

Where,  (h,k) is the vertex of the parabola.

(1)

The given equation is,

f(x)=(x-5)^2+10

Comparing this equation with equation (1),we get,

h=5 and k=10

Therefore, the vertex of the graph is (5,10) and the fourth option is correct.

(2)

The given equation is,

f(x)=3x^2-18x+24

f(x)=3(x^2-6x)+24

To make perfect square add (\frac{b}{2a})^2, i.e., 9. Since there is factor 3 outside the parentheses, so subtract three times of 9.

f(x)=3(x^2-6x+9)+24-3\times 9

f(x)=3(x-3)^2-3

Comparing this equation with equation (1),we get,

h=3 and k=-3

Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.

(3)

The given equation is

f(x)=4x^2+8x+7

f(x)=4(x^2+2x)+7

To make perfect square add (\frac{b}{2a})^2, i.e., 1. Since there is factor 4 outside the parentheses, so subtract three times of 1.

f(x)=4(x^2+2x+1)+7-4

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Comparing this equation with equation (1),we get,

h=-1 and k=3

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(4)

The given equation is,

y=x^2+4x+7

To make perfect square add (\frac{b}{2a})^2, i.e., 2^2.

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h=-16t^2+672t

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h=-16(t^2-42t)

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x=\frac{b}{2a}

x=\frac{42}{2}

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Therefore,  after 21 seconds the projectile reach its maximum height and the correct option is first.

(6)

The given equation is,

f(x)=3x^3-12x^2-15x

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Use factoring method to find the factors of the equation.

f(x)=3x(x^2-5x+x-5)

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Equate each factor equal to 0.

x=0,-1,5

Therefore, the zeros of the given equation is 0, -1, 5 and the correct option is 2.

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3 years ago
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