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alukav5142 [94]
3 years ago
11

2. Use the following picture for this question:

Mathematics
1 answer:
Art [367]3 years ago
4 0

Answer:

a.  24\sqrt{3}  and 41.6

b.  52.1

Step-by-step explanation:

a.

Considering the left side triangle the blue dotted side is the side "opposite" to the angle given and the side 24 is the side that is "adjacent" to the angle given. The trigonometric ratio tan relates opposite to adjacent. Also, let the blue dotted side be y.

<u>Note:</u> the exact value of tan 60 is \sqrt{3}

Thus, we can write Tan(60)=\frac{y}{24}\\y=24*Tan(60)\\y=24*\sqrt{3} \\y=24\sqrt{3}

Approximate value (rounded to nearest tenth):  24\sqrt{3} =41.6

b.

Considering the triangle to the right, the side "opposite" to the angle given (53 degrees) is 41.6 (just found in part (a)) and the side "hypotenuse" (side opposite to 90 degree angle) is x. The trigonometric ratio sine relates opposite and hypotenuse.

Thus we can write and solve:

Sin(53)=\frac{41.6}{x}\\x=\frac{41.6}{Sin(53)}=52.1

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What is the equation in point-slope form of the line that passes through the point (−1, −3) and has a slope of 4?
Nimfa-mama [501]

The equation of line in point-slope form of the line that passes through the point (−1, −3) and has a slope of 4 is:

y+3=4(x+1)

Step-by-step explanation:

Given

m=4

and

Point = (x1,y1) = (-1,-3)

The general form of point-slope equation of line is:

y-y_1=m(x-x_1)\\Putting the values of m, x_1 and y_1\\y-(-3)=4(x-(-1))\\y+3=4(x+1)

Hence,

The equation of line in point-slope form of the line that passes through the point (−1, −3) and has a slope of 4 is:

y+3=4(x+1)

Keywords: Point-slope form, Slope

Learn more about equation of line at:

  • brainly.com/question/4361464
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5 0
3 years ago
A jet flies at a rate of 1.3x10 to the 6 feet per hour. Written in scientific notation, which is the best estimate of how many f
Semenov [28]
This is scientific notation

6 0
3 years ago
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In a garden club, 90% i ladie. The number of ladie i 12 more than 3 time the number of gentlemen. How many ladie and how many ge
wariber [46]

In the garden club there are 18 ladies and 2 gentlemen.

Given, In a garden club, 90% is ladies.

The number of ladies is 12 more than 3 times the number of gentlemen.

Let the total members be, x

the number of ladies be, l and the number of gentlemen be, g

according to the question,

l = 90x/100

l = 9x/10

also, l = 12 + 3g

g = (l - 12)/3

as, l + g = x

9x/10 + (9x/10 - 12)/3 = x

9x/10 + 9x/30 - 4 = x

36x/30 - 4 = x

6x/30 = 4

x = 20

so, ladies be, l = 9x/10 = 18

and gentlemen be, g = 20 - 18 = 2

Hence, in the garden club there are 18 ladies and 2 gentlemen.

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4 0
11 months ago
There are 12 red marbles and 8 green marbles in a bag. What is the probability of selecting a red
madam [21]

Answer:

The probability of selecting a red  marble, not replacing it, and then selecting a green marble from the bag is 24/95

Step-by-step explanation:

Number of red marbles = 12

Number of green marbles = 8

Total number of marbles = 12+8 = 20

Probability of selecting red marble =\frac{12}{20}

Since it is the case of no replacement

Remaining marbles = 20-1 = 19

Number of red marbles = 12-1=11

Number of green marbles = 8

Probability of selecting green marble =\frac{8}{19}

So, the probability of selecting a red  marble, not replacing it, and then selecting a green marble from the bag =\frac{12}{20} \times \frac{8}{19}=\frac{24}{95}

Hence the probability of selecting a red  marble, not replacing it, and then selecting a green marble from the bag is 24/95

3 0
3 years ago
Honestly help I’m slow
SashulF [63]

Answer:

46 degrees

Step-by-step explanation:

x equals 23 so just multiply by 2

4 0
2 years ago
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