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Morgarella [4.7K]
3 years ago
9

Two functions are shown in the table below: Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = x + 2 Complete the table on your ow

n paper, then select the value that is a solution to f(x) = g(x). x = 2 x = 3 x = 5 x = 6
Mathematics
1 answer:
zubka84 [21]3 years ago
3 0

Answer:

x   f(x)   g(x)

1    15    3

2    16   4

3    15    5

4    12    6

5    7     7

6    0     8

f(x) = g(x) when x = 5

Step-by-step explanation:

f(x) = -x² + 4x + 12

f(1) = -(1)² + 4(1) + 12 = 15

f(2) = -(2)² + 4(2) + 12 = 16

f(3) = -(3)² + 4(3) + 12 = 15

f(4) = -(4)² + 4(4) + 12 = 12

f(5) = -(5)² + 4(5) + 12 = 7

f(6) = -(6)² + 4(6) + 12 = 0

g(x) = x + 2

g(1) = 1 + 2 = 3

g(2) = 2 + 2 = 4

g(3) = 3 + 2 = 5

g(4) = 4 + 2 = 6

g(5) = 5 + 2 = 7

g(6) = 6 + 2 = 8

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The reaction force exerted by the floor of the elevator on the man is D.944 N

Step-by-step explanation:

When the elevator is accelerating upwards at 2 m/s² there occurs a fictitious force acting downwards to produce a downward acceleration of 2 m/s².

The formula to apply here is ;

Weight due to gravity=mg where m is mass of the man and g is acceleration due to gravity.

Due to additional downward acceleration the total acceleration downwards will be : 9.8+2 = 11.8 m/s²

The man weighs down on the elevator floor with a force of ;

F=m(a+g) where m is mass of man, a is acceleration

F=80( 9.8+2)

F=80(11.8)= 944 N

The reaction force by the floor of the elevator is thus 944 N

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3 years ago
Find the diagonal of a rectangular frame which measures 77 in. by 36 in.
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Answer:

Diagonal of a rectangular frame = 85 inch

Step-by-step explanation:

Given:

Length of rectangle = 77 inch

Width of rectangle = 36 inch

Find:

Diagonal of a rectangular frame

Computation:

Diagonal of a rectangle = √l² + b²

Diagonal of a rectangular frame = √77² + 36²

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3 years ago
Consider a Triangle ABC like the one below. Suppose that C = 98, A = 74, and b = 11 (figure is not drawn to scale.) solve the tr
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Answer:

A=73.8\°

B=8.2\°

c=76.3\ units

Step-by-step explanation:

step 1

Find the measure of side c

Applying the law of cosines

c^{2}= a^{2}+b^{2}-2(a)(b)cos(C)

substitute the given values

c^{2}= 74^{2}+11^{2}-2(74)(11)cos(98\°)

c^{2}=5,823.5738

c=76.3\ units

step 2

Find the measure of angle A

Applying the law of sine

\frac{a}{sin(A)}=\frac{c}{sin(C)}

substitute the given values

\frac{74}{sin(A)}=\frac{76.3}{sin(98\°)}

sin(A)=(74)sin(98\°)/76.3

A=arcsin((74)sin(98\°)/76.3)

A=73.8\°

step 3

Find the measure of angle B

we know that

The sum of the internal angles of a triangle must be equal to 180 degrees

so

A+B+C=180\°

substitute the given values

73.8\°+B+98\°=180\°

171.8\°+B=180\°

B=180\°-171.8\°=8.2\°

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Step-by-step explanation:

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plan 1

it is the probabilty that either A works, or (if it is not working) B works.

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plan 2

either B works, or (if it is not working) A works

0.9 + 0.1×0.6 = 0.9 + 0.06 = 0.96

both plans have the same success probability.

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