Find The length of one leg of a right triangle if the length of the hypotenuse is 18 feet and the length of the other leg is 14 feet. Leave your answer as a simplified radical.

Answer:

a. 3/4

Step-by-step explanation:

6:8

=6/8

=3/4

Hope it Helps

Answer:

Yes, it is a right triangle.

Step-by-step explanation:

8²+15²=17²

64+225=289

289=289 YES, it is a right triangle

Answer:

(D) The passenger's height aloe the ground is increasing by 15.708 meters per minute 7.5 minutes after the ride begins.

Step-by-step explanation:

Here, H(t) is the height after the t minutes of time.

Given :

H'(7.5) = 15.708 meters / minute

H'(t) = [tex]$\frac{d(H(t))}{dt}$[/tex]

     = rate of change of the height

So, here, H'(t) = rate of change of height

Therefore, H'(7.5) = 15.708 meters / minute

It shows that the passenger's height is increasing at rate 15.708 meters per minute at time t = 7.5 minutes after the ride begins.

Answer:

1. S.A. = 4350 cm²

2. S.A. = 864 cm²

3. S.A. = 240 cm²

4. S.A. = 224 m²

5. S.A. = 301.6 in.²

6. S.A. = 6,082.1 cm²

7. S.A. = 923.6 in.²

Step-by-step explanation:

1. Surface area of the rectangular prism = 2(LW + LH + WH)

L = 45 cm

W = 25 cm

H = 15 cm

S.A. = 2(45*25 + 45*15 + 25*15)

S.A. = 4350 m²

2. Surface area of the cube = 6a²

a = 12 cm

S.A. = 6(12²)

S.A. = 864 cm²

3. Surface area of triangular prism = bh + (s1 + s2 + s3)*H

b = 4 cm

h = 6 cm

s1 = 4 cm

s2 = 7 cm

s3 = 7 cm

H = 12 cm

Plug in the values

S.A. = 4*6 + (4 + 7 + 7)*12

S.A. = 24 + (18)*12

S.A. = 24 + 216

S.A. = 240 cm²

4. Surface area of the square based pyramid = area of the square base + 4(area of 1 triangular face)

S.A. = (8*8) + 4[(8*10)/2]

S.A. = 64 + 4(40)

S.A. = 64 + 160

S.A. = 224 cm²

5. Surface area of the cone = πrl + πr²

r = 6 in.

l = 10 in.

S.A. = π*6*10 + π*r²

S.A. = 60π + 36π

S.A. = 301.592895

S.A. = 301.6 in.² (nearest tenth)

6. Surface area of the sphere = 4πr²

r = 22 cm

S.A. = 4*π*22²

S.A. = 1,936π

S.A. = 6,082.1 cm² (nearest tenth)

7. Surface area of the cylinder = 2πrh + 2πr²

r = 7 in.

h = 14 in.

S.A. = 2*π*7*14 + 2*π*7²

S.A. = 923.6 in.² (nearest tenth)

Answer: 60 + 13 sqrt 10

the top part adds up to 10 and the bottom part is 13

so you get a 7-3-2 sqrt 10 triangle to the left

the area of that is 3 sqrt 10

the area of the leftmost rectangle is 5 * 2sqrt 10 which is 10 sqrt 10

the area of the big vertical rectangle is 5*12 which is 60

so you add them up

60 + 13 sqrt 10

Answer:

LINE GRAPH : the profits of a company over a year

SCATTER PLOT : a person's income based on age

CIRCLE GRAPH : percent of student athletes in each sport

BAR GRAPH: the numbers and types ofdifferent species of fish at an aquarium

Step-by-step explanation:

The scatter plot are useful when trying to create a graphical relationship between two measured variables, like the camparison or relationship between age and income.

Line graph is used to monitor changes in a certain variable over time. Observing the fluctuation or variation in income over a certain period.

The circle graph represents the segmentation of a whole into groups or categories with each segment representing a proportion or percentage of the whole.

The bar graph also useful for categorization using vertical bars.

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Answer:

  (a)  (-3/4, 1/2)

Step-by-step explanation:

There are 4 grid lines between 0 and 1 in each direction, so each grid line represents 1/4 unit. Two of them is 1/2 unit; 3 of them is 3/4 unit. The x-dimension is listed first in the ordered pair.

Point S has coordinates (-3/4, 1/2).

Answer:

[tex](-5,-4)[/tex]

Step-by-step explanation:

Given

[tex]P = (5,4)[/tex]

Rotation: 180 degrees counterclockwise

Required

P'

Rotation: 180 degrees counterclockwise

The rule is:

[tex](x,y) \to (-x,-y)[/tex]

So: [tex]P = (5,4)[/tex] becomes

[tex](5,4) \to (-5,-4)[/tex]

Answer:

Y values will stay the same

Step-by-step explanation:

Reflecting over the Y axis will alter the distance left and right but not up and down. so only Y remains unchanged

Answer: 14

Step-by-step explanation:

1/16x = 7/8

x = 7/8*16/1 = 14

He can sell his candy

Give away to people.

Answer:

a-16 and a half c-12

Step-by-step explanation:

Answer:

Step-by-step explanation:

From the given information:

There are 30 collections of gems, of which 8 are worthless;

Thus, the number of the genuine diamonds = 30 - 8 = 22.

Let X = random variable;

X consider the value as 0 (for  2 worthless stone selection),

X = 1200(1 worthless stone  & 1 genuine stone)

X = 2400 (2 genuine stones selected)

However, the numbers of ways of selecting and chosen Gems can be estimated as:

[tex](^n_r) = (^{30}_2) \\ \\ \implies \dfrac{30!}{2!(30-2)!} \\ \\ \implies \dfrac{30!}{2!(28)!} \\ \\ \implies \dfrac{30*29*28!}{2!(28)!} \\ \\ \implies \dfrac{30*29}{2*1} \\ \\ \implies 435[/tex]

Thus;

[tex]Pr (X = 0) = \dfrac{(^8_2)}{435}[/tex]

[tex]Pr (X = 0) = \dfrac{\dfrac{8!}{2!(8-2)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8!}{2!(6)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8*7*6!}{2!(6)!}}{435} \\ \\ Pr (X = 0) = \dfrac{\dfrac{8*7}{2*1}}{435} \\ \\ Pr (X = 0) = 0.0644[/tex]

[tex]P(X =1200) = \dfrac{(^{8}_{1})(^{22}_{1})}{435}[/tex]

[tex]P(X =1200) = \dfrac{ \dfrac{8!}{1!(8-1)!}) ( \dfrac{22!}{1!(22-1)!}) }{435}[/tex]

[tex]P(X =1200) = \dfrac{ (8) ( 22) }{435}[/tex]

[tex]P(X =1200) =0.4046[/tex]

[tex]Pr (X = 2400) = \dfrac{(^{22}_2)}{435}[/tex]

[tex]Pr (X = 2400) = \dfrac{\dfrac{22!}{2!(22-2)!}}{435} \\ \\ Pr (X = 2400) = \dfrac{\dfrac{22!}{2!(20)!}}{435} \\ \\ Pr (X = 2400) = \dfrac{\dfrac{22*21*20!}{2!(20)!}}{435} \\ \\ Pr (X =2400) = \dfrac{\dfrac{22*21}{2*1}}{435} \\ \\ Pr (X = 2400) = 0.5310[/tex]

To find E(X):

E(X) = (0 × 0.0644) + (1200 × 0.4046)  + (2400 × 0.5310)

E(X) = 0 + 485.52 + 1274.4

E(X) = 1759.92

Answer:

I hope this helps you hehehe :)

Step-by-step explanation:

=√256

=√4×4×4×4

=√4^4

=44/2

=4^2

=16

Answer:

0.088

Step-by-step explanation:

Given two cylinders

Volume of one = 64cm^3

Volume of the other = 729cm^2

Scale factor = Volume of the small/Volume of the large

Scale factor = 64:729

Scale factor = 0.087

Answer:

80

Step-by-step explanation:

18^2 + 80^2 = 82

324 + 160 = c^2

Answer:

80 cm

Step-by-step explanation:

To solve this problem, you can use the pythagorean theorem which is a^2 + b^2 = c^2. We are given that a = 18, and c as the hypotenuse equals to 82. We can plug these numbers into the theorem:

18^2 + b^2 = 82^2

324 + b^2 = 6724

b^2 = 6400

b = 80 cm

Answer: Because the graphs of the two equations overlap each other

Step-by-step explanation:

Every point on the first line also satisfies the second equation.

This is the same as equivalent fractions

where 1/2 = 2/4 = 3/6 = 4/8

Graphing these on a number line would only show one dot.

Answer:

9

Step-by-step explanation:

Plug in 6 to x, since this is the x-value in the ordered pair.

[tex]3(6)+2y=36\\18+2y=36\\2y=18\\y=9[/tex]

Answer:

(6, 9)

Step-by-step explanation:

3x + 2y = 36

Substitute 6 into the equation to get the output.

3(6) + 2y = 36

Multiply 3 and 6.

18 + 2y = 36

Subtract 18 from both sides.

2y = 18

Divide both sides by 2.

y = 9

The ordered pair when x = 6 is

(6, 9)

Answer:

[tex]Worth = \$284258.1[/tex]

Step-by-step explanation:

Given

[tex]Dimension: 7in\ * 3in\ * 1in[/tex]

[tex]Value = \$1214/oz[/tex] ---- value of Gold

Required

The worth of 1 gold bar

First, calculate the volume (n) of the gold bar

[tex]n = 7in * 3in * 1in[/tex]

[tex]n = 21in^3[/tex]

Next, calculate the weight of the gold bar using:

[tex]w = 11.15n[/tex]

[tex]w = 11.15 * 21[/tex]

[tex]w = 234.15oz[/tex]

Multiply the value of Gold by the weight of the gold bar to get the worth of the gold bar.

[tex]Worth =Value * w[/tex]

This gives:

[tex]Worth = \$1214/oz * 234.15oz[/tex]

[tex]Worth = \$1214 * 234.15[/tex]

[tex]Worth = \$284258.1[/tex]

Answer:

Scalene

Step-by-step explanation:

Answer: Acute scalene triangle

A triangle with uneven degrees on all sides is known as a scalene triangle. Since none of the degrees are above 90, this triangle can also be described as acute.

Answer:

10

Step-by-step explanation:

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Answer:

Step-by-step explanation:

The law of sines tells you the ratio of sides is the same as the ratio of sines of their opposite angles.

This post has 2 kinds of problems.

1) 2 angles and the side between them are given.

2) 2 sides and the angle opposite the longest is given.

For the first type, you need to determine the missing angle (opposite the given side). That comes from the sum of angles of a triangle being 180°. Then you find the remaining sides using the ratio of sines.

For the second type, the angle opposite the shorter side is found using the ratio of sides to find the sine of that angle. Then the third side and third angle can be found using the ratio of sides to find the sine of the angle, and using the ratio of sines to find the missing side.

Straightforward, and tedious. For more than one, I like to use a spreadsheet to crunch the numbers.

_____

1) BC = 24.0

2) AC = 26.0

3) m∠B = 73.4°

4) m∠B = 30.0°

__

In the spreadsheet, the given values are in the first 3 columns. The 4th column is the first one calculated. As indicated above, the angle calculation for problems 1 and 2 uses the sum of angles relation. For problems 1 and 2, this is the angle opposite the given side. The "first side" is the side opposite the "first angle". c = b·sin(C)/sin(B), for example.

For problems 3 and 4, the first unknown angle is the one opposite the "short side", which is the shorter of the given sides. As it happens, this is the side that is asked for in the question. B = arcsin(c·sin(B)/sin(C))

_____

Additional comment

In a spreadsheet, angles are presumed to be in radians for all of the trig functions. We use the DEGREES( ) and RADIANS( ) functions to convert as appropriate.

Answer:

b = 7.56

C = 9.24

Step-by-step explanation:

Find the last angle of the triangle.

The sum of all the angles in a triangle is  

180 degrees.

A+

90+55=180

A=35

Then find c

The cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse.

cos(B)=adj/hyp or Cos(55) = 5.3 / c

re write as

C = 5.3 / cos55

This gives you c = 9.24

Then use the Pythagorean theorem to find the unknown side.

[tex]a^{2} +b^{2} = c^{2} \\rewrite as\\ b^{2} = c^{2} - a^{2} \\b^{2} = 9.2^{2} - 5.3^{2} \\b^{2} = 57.29\\b = 7.56[/tex]

Answer:

The answer is 181

Step-by-step explanation:

PEDMAS

1 x 1 + 9 x 20

1 x 1 = 1

1 + 9 x 20

9 x 20= 180

1+180

which equals 181

Answer:

181

Step-by-step explanation:1x1=1 9x20=180+1=181

Thats your answer my fellow brains

Answer:

x = 14 for the first one, x = 60 for the second one

Step-by-step explanation:

Step-by-step explanation:

We know the measure of a straight line is 180° . So that ,

> 5x - 10 + 120 = 180

> 5x = 60 + 10

> 5x = 70

> x = 70/5

> x = 14

Solution 2 :-

> x + 50 + 70 = 180

> x = 180 - 120

> x = 60

Answer:

B

Step-by-step explanation:

Answer:

131.5

Step-by-step explanation:

To find the area of the rectangle, we multiply the base and the height.

In this case, the base is 8 and the height is 13 I think. ( Your picture cuts it off very poorly)

8 x 13 = 104

Now, we need to find the area of the triangle. It is the same equation as the rectangle but we divide the result by 2.

11 * 5 = 55

55/2 = 27.5

27.5 + 104 = 131.5

If it's wrong, it's probably because of the picture. I can't tell what the height is of the rectangle, because it's certainly not 3.

Answer:

a) Acceleration = 2.4 m per seconds²

b) Distance traveled = 132 m

Step-by-step explanation:

a). Acceleration of an object is defined by the equation,

v = u + at

Here, v = Final speed

u = Initial speed

a = Acceleration

t = Duration Or time

From the graph attached,

Between t = 0 and t = 5 seconds,

v = 12 meter per second

u = 0

t = 5 seconds

B substituting values in the equation,

12 = 0 + a(5)

a = [tex]\frac{12}{5}[/tex]

a = 2.4 m per seconds²

b). Equation representing distance traveled by an object,

v² = u² + 2as

Here, v = Final speed

u = Initial speed

a = Acceleration

s = Distance traveled

By substituting these values in the given equation,

1). Between t = 0 to t = 5 seconds,

(12)² = 0 + 2(2.4)s

s = [tex]\frac{144}{4.8}[/tex]

s = 30 m

2). Between t = 5 to t = 12 sec

Car moved with a constant speed (Acceleration = 0)

Distance traveled = Speed × Time

                             = 12 × 7

                             = 84 m

3). Acceleration of the car between t = 12 sec to t = 15 sec

By substituting the values in the equation,

v = u - at

0 = 12 - a(3)

a = 4 meter per seconds²

Distance traveled in this duration,

v² = u² - 2as

0 = (12)² - 2(4)s

144 = 8s

s = [tex]\frac{144}{8}[/tex]

s = 18 m

Therefore, total distance covered by the car = 30 + 84 + 18

= 132 meters