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♨[tex] \large{ \tt{ E \: X \: P \: L \: A \: N \: A \: T \: I\: O \: N}}: [/tex]

⤻ Before solving the given question , you should know the answer of these questions :

✺How do you find the hypotenuse , perpendicular and base when the angle ( [tex] \theta \: , \alpha \: ,\beta [/tex] ) is given ?

⇾ The longest side , which is the opposite side of right angle is the hypotenuse ( h ). There are two other sides , the opposite and the adjacent. The naming of these sides depends upon which angle is involved. The opposite is the side opposite the angle involved and it is called the perpendicular ( p ) . The adjacent us the side next to the angle involved ( buy not the hypotenuse ) and it is called the base ( b ).

☄ [tex] \large{ \tt{REMEMBER}} : [/tex]

In the above cases , [tex] \theta[/tex] is taken as the angle of reference.

♪ Our Q/A part ends up here! Let's start solving the question :

❈ [tex] \large{ \tt{GIVEN}} : [/tex]

✧ [tex] \large{ \tt{TO \: FIND} : }[/tex]

✎ [tex] \large{ \tt{SOLUTION}} : [/tex]

Firstly , Finding the value of perpendicular ( p ) using Pythagoras theorem :

❃ [tex] \boxed{ \sf{ {h}^{2} = {p}^{2} + {b}^{2} }}[/tex] [ Pythagoras theorem ]

[tex] \large{ ⇢ \sf{p}^{2} + {b}^{2} = {h}^{2} }[/tex]

[tex] \large{⇢ \sf{ {p}^{2} = {h}^{2} - {b}^{2} }}[/tex]

[tex] \large{ ⇢\sf{ {p}^{2} = {18}^{2} - {16}^{2} }}[/tex]

[tex] \large{⇢ \sf{ {p}^{2} = 324 - 256}}[/tex]

[tex] \large{⇢ \sf{ {p}^{2} = 68}}[/tex]

[tex] \large{⇢ \sf{p = \sqrt{68}}} [/tex]

[tex] \large{ ⇢\sf{p = \boxed{ \tt{2 \sqrt{17}}} }}[/tex]

Okey, We found out the perpendicular i.e [tex] \tt{2 \sqrt{17}} [/tex] . Now , We know :

❊ [tex] \large{ \sf{ \tan \theta} = \frac{perpendicular}{base} }[/tex]

[tex] \large {\tt{↬ \: tan \theta = \frac{2 \sqrt{17} }{16}}} [/tex]

[tex] \large{ \tt{ ↬ tan \theta = \frac{ \cancel{2} \: \sqrt{17} }{ \cancel{16} \: \: 8} }}[/tex]

[tex] \large{ \tt{ ↬ \boxed{ \tt{tan \theta = \frac{ \sqrt{17} }{8}}}}} [/tex]

⟿ [tex] \boxed{ \boxed{ \tt{OUR\: FINAL \: ANSWER : \boxed{ \underline{ \bf{ \frac{ \sqrt{17} }{8}}}}}}} [/tex]

۵ Yay! We're done!

♕ [tex] \large\tt{RULE \: OF \:SUCCESS }: [/tex]

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Answer:

√(17)/8

Step-by-step explanation:

We are given with hypotenuse and base. We can have any ratio related to it, such as secant.

secA = hypotenuse/base

secA = 18/16 = 9/8

sec²A = 81/64

Using sec²A - 1 = tan²A

=> 81/64 - 1 = tan²A

=> 17/64 = tan²A

=> √(17)/8 = tanA

______________________

Using cosine of angle A.

cosA = base/hypotenuse

cos²A = (16/18) = (8/9)² = 64/81

sin²A = 1 - cos²A = 1 - 64/81 = 17/81

Hence,

tanA = √(tan²A) = √(sin²A/cos²A) = √((17/81)/(64/81)) = √(17)/8

This looks complex, either go with the 1st or one Or directly find the value of height using Pythagoras theorem,

18² = 16² + height²

√17 = height

tanA = height/base = √17/8

Answer:

njuvcjgxyrsdfygjhkl

Step-by-step explanation:

Answer:

28.26[tex]in^{2}[/tex]

Step-by-step explanation:

Given,

Radius of the circle = 3in.

Area = ?

They have told us to use 3.14 for [tex]\pi[/tex]

Area formula = [tex]\pi r^{2}[/tex]

=> 3.14 * 3 * 3

=> 3.14 * 9

=> 28.26[tex]in^{2}[/tex]

Therefore the area of the circle is  28.26[tex]in^{2}[/tex]

Hope it helps :)

Answer:

28.26

Step-by-step explanation:

You want to plug everything in to the equation that you can. It says that pi=3.14, and the radius (aka r) is equal to 3. Therefore when plugging everything in, the equation reads (3.14)(3)^. ^ means squared, its the tiny 2 above the r. when something is squared it means you multiply it by itself 2 times. therefore 3 squared = 3 x 3= 9. After finding out 3^=9, the equation reads (3.14)(9). Now all you have to do is multiply the 2 together which results in 28.26.

Answer:

He was gone for 36 minutes

Step-by-step explanation:

Sorry if wrong

Answer:

26degrees

Step-by-step explanation:

Find the diagram attached

From the diagram, Angle ABC and angle CBD are complementary hence;

<ABC + <CBD = 90

Given

<ABC = 2x

<CBD = 38

Substitute

2x + 38 = 90

2x = 90 - 38

2x = 52

x = 52/2

x = 26degrees

Hence the value of x is 26degrees

Answer:

4%

Step-by-step explanation:

We solve this question using z score formula

z = (x-μ)/σ,

where

x is the raw score = 100 feet

μ is the population mean = 86 feet

σ is the population standard deviation = 8 feet

Hence,

x > 100 feet

z = (100 - 86)/8

z = 1.75

Probability value from Z-Table:

P(x<100) = 0.95994

P(x>100) = 1 - P(x<100) = 0.040059

Converting to Percentage

= 0.040059 × 100

= 4.0059%

Approximately = 4%

Therefore, the percentage of the pine trees in this forest are taller than 100 feet is 4%

Answer:

[tex] \displaystyle A_{ \text{triangle}} = 102 {m}^{2} [/tex]

Step-by-step explanation:

remember that,

[tex] \displaystyle A_{ \text{triangle}} = \frac{1}{2} bh[/tex]

given that,b is 17 m and h is 12m

thus substitute:

[tex] \displaystyle A_{ \text{triangle}} = \frac{1}{2} \times 17\times 12[/tex]

reduce fraction:

[tex] \displaystyle A_{ \text{triangle}} = 17\times 6[/tex]

simplify multiplication:

[tex] \displaystyle A_{ \text{triangle}} = 102 {m}^{2} [/tex]

Answer:

a) 4:3

b) 7:3

Step-by-step explanation:

No. of roses= 8

No. of daisies = 6

Total no. of flowers = 14

a) Ratio of roses to daisies = No. of roses/No. of daisies

8/6

= 4/3

= 4:3

b) Ratio of all flowers to daisies = No. of all flowers/ No. of daisies

14/6

= 7/3

= 7:3

Answer:

4

Step-by-step explanation:

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Answer:

x = 5 cm

Step-by-step explanation:

Big rectangle

Length = 30 cm

Width = 12.5 cm

Length : width = 30 cm : 12.5 cm

Small rectangle

Length = 12 cm

Width = x cm

Length : width = 12 cm : x cm

Equate the ratios

30 cm : 12.5 cm = 12 cm : x cm

30/12.5 = 12/x

Cross product

30 * x = 12.5 * 12

30x = 150

x = 150/30

x = 5 cm

Answer:

184.96

Step-by-step explanation:

V = (base × height) ÷ 3

base = pi × radius^2

2 × pi × radius = circumference

2×pi×r = 29.516

÷2 ÷2

pi×r = 14.758

÷3.14 ÷3.14

r=4.7

base= 3.14 × 4.7^2

= 69.36

V = (69.36 × 8) ÷ 3 = 184.96

Answer:

7000

Step-by-step explanation:

Thus the truck delivers 7 tons of gravel.

"A unit conversion expresses the same property as a different unit of measurement. A conversion factor is a ratio that expresses how many of one unit is equal to another unit".

For the above situation,

A truck delivers 14,000 pounds of gravel.

We know that,

1 US ton = 2000 pounds

Thus, 14000 pounds = [tex]\frac{14000}{2000}[/tex]

⇒ [tex]7 tons[/tex]

Hence we can conclude that the truck delivers 7 tons of gravel.

Learn more about unit conversions here

https://brainly.com/question/20950399

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Answer:

B: 12/25

Step-by-step explanation:

You have the correct answer marked. This is correct because the probability of grabbing a purple marble is 24/50 which if we divide by 2 to simplify is 12/25.

Answer:

A is the correct answer 450 cm

Step-by-step explanation:

area of base = 1/2 (7.5+ 5) × 6 = 37.5

volume = area × height

= 37.5 × 12

= 450cm³

Answer:

YESSSSS I AM APART OF THE KENMA CULT

Step-by-step explanation:

Answer:

the answer is 101/9, in fraction it would be 11.2222..... in whole number would be 11, as mixed number would be 11 2/9

Answer:

-14

Step-by-step explanation:

step 1:

Subtract 11 from both sides.

y+11−11<−3−11

y<−14

Answer:

y is less than -14

Step-by-step explanation:

You move all the terms to the side not containing the y. So it would be -3-11 on one side and y on the other. The sign does not change so the inequality would be y is less than -14.

Answer:

Solution given:.

area of traingle EFG=1/2b×h=1/2×7×6=21cm²

area of rectangle ABCD=l×b=(20+9)×7=203cm²

area of rectangle BHIJ=l×b=9×11=99cm²

Total area =21+203+99=323cm² is a required answer

Answer:

35

Step-by-step explanation:

find area of each rectangle then add

Answer:

We have:

The conclusion is:

Answer:

1. C. 52.51 cm3

2. C. 78.5 in3

3. A. 661.83 ft3

Step-by-step explanation:

just finished the quick check

Answer:

3 is the answer

Step-by-step explanation:

because x is also equals to -4. if u can see there is big circle that is blue, if that circle was empty that means does not equal, and the xs are bigger than -4 therfore the answer is option 3.

Answer:

Greater than or equal to -4

Step-by-step explanation:

Hope this helps

Answer:

2 and 5

Step-by-step explanation:

ez

Group of answer choices.

A. It can be expressed as a non repeating, non terminating decimal.

B. It can be a perfect square

C. It cannot be pie π

D. It is not possible to have a irrational number solution.​

Answer:

A. It can be expressed as a non repeating, non terminating decimal.

Step-by-step explanation:

An irrational number can be defined as real numbers that cannot be expressed as a simple fraction or ratio of two integers.

Additionally, it is the opposite of a rational number and as such its decimal is continuous without having any repetition or termination. For example, pie (π) = 3.14159 is an example of an irrational number.

Assuming the solution to a mathematical problem is an irrational number. The statement which is true about the solution is that it can be expressed as a non-repeating, and non-terminating decimal.

Answer:

If you still need the answer it’s c

Step-by-step explanation: The zeros of the graph are 2 and 3 , which is where the graph crosses the x axis,

The factorization is the form

(x-a) (x-b) where a and b are the zeros

(x-3) (x-2)

9514 1404 393

Answer:

  (a)  No, because it will not go through the origin

Step-by-step explanation:

The equation is that of a straight line, but its y-intercept is 2, not 0. Because the y-intercept is not zero, the line does not go through the origin, and the relationship is not proportional.

Answer:

G(x)=2x32+c

Step-by-step explanation:

Answer:

Her oldest was 9, and the other 2 were 2