Each side of the triangle is represented by an expression. Find the value of x is the triangle has a perimeter of 73.

[tex]\tt (1 - sin ^2x)\times(1+tan^2x) = 1[/tex]

L.H.S

[tex]\tt cos^2x \times sec^2x[/tex]

[tex]\tt cos^2x \times \frac{1}{cos^2x}[/tex]

[tex]\tt \cancel{ cos^2x} \times\cancel{ \frac{1}{cos^2x}}[/tex]

[tex]\tt 1[/tex]

R.H.S

Hence proved

Step-by-step explanation:

[tex]{ \tt{ \blue{(1 - { \sin}^{2}x )(1 + { \tan }^{2}x) = 1 }}}[/tex]

• Remember → 1 + tan²x = sec²x

[tex] = { \tt{ \blue{(1 - { \sin }^{2}x)( { \sec}^{2}x) }}}[/tex]

• But sec²x → 1/cos²x

[tex] = { \tt{ \blue{(1 - { \sin}^{2} x)( \frac{1}{ \cos {}^{2} x} )}} }\\ \\ = { \blue {\tt{ \frac{1 - { \sin }^{2}x }{ { \cos }^{2}x } }}}[/tex]

• Remember from the first identity of trignometry;

[ cos²x + sin²x = 1 ].

• Therefore: [ cos²x = 1 - sin²x ]

[tex] = { \blue{\rm{ \frac{1 - { \sin}^{2}x }{1 - { \sin }^{2}x } }}} \\ \\ { \rm{ \blue{= 1 \: }}}[/tex]

Hence proved.

Answer:

9.2 ft

Step-by-step explanation:

The shape is a triangle, the 11 ft is your hypotenuse

You need to use the Pythagorean Theorem!

a^2 + b^2 = c^2 (solve for a, the missing length that they ask for)

so --->

a^2 + (6^2) = 11^2

      a^2 + 36 = 121

             ~subtract 36 to the right side~

               a^2 = 85

now find the square root of 85:

               a = 9.21954

        round it to the nearest tenth:

                   a = 9.2

final answer: 9.2 ft

hope this helpsss

Step-by-step explanation:

Apply Pythagoren Theorem.

[tex] {x}^{2} + {y}^{2} = {c}^{2} [/tex]

where x and y is the legs (the sides that form a right triangle) and c is the hypotenuse.

the legs are 6 and our unknown. so let x represent the unknown

[tex] {6}^{2} + {x}^{2} = {11}^{2} [/tex]

[tex]36 + {x}^{2} = 121[/tex]

[tex] {x}^{2} = 85[/tex]

[tex]x = \sqrt{85} [/tex]

x=9.2

Answer: 7r/3

Step-by-step explanation:

5r*7/15 = 35r/15 = 7r/3

Answer:

the image was not clear....hope the values are correct

Answer is in the attached file.

Answer:

Step-by-step explanation:

The volume of the pool is given by ...

  V = LWH

Here, we have ...

  V = 2800 ft³

  H = 8 ft

  L = 3.5W

Filling in these values, we have ...

  2800 ft³ = (3.5W)(W)(8 ft)

  100 ft² = W² . . . . . . . . . . . . divide by 28 ft

  W = √(100 ft²) = 10 ft

  L = 3.5W = 35 ft

The pool is 10 ft by 35 ft.

Answer:

x is 24°

Step-by-step explanation:

angles substended by the same chord or arc....90-66= 24°.

Answer:

{- 3, - 2, 0, 2 }

Step-by-step explanation:

The range is the y- coordinates of the points

(- 4, - 3 ) , (- 1, - 2 ) , (- 2, 0 ) , (0, 2 )

The y- coordinates are - 3, - 2, 0, 2

Then the range is { - 3, - 2, 0, 2 }

Answer:

C. Public colleges are cheaper for in-state residents.

Step-by-step explanation:

Answer: 14 miles

Step-by-step explanation: 3.5d+5+2.5d+3

Answer:

yes they form a proportion

Step-by-step explanation:

11x-4<15

11x<15+4

11x<19

x<1

Answer:

mean/average is calculated by adding all of the values and dividing by the number of values

ur welcome queen besitie slay

Answer:

The answer is A and B

Step-by-step explanation:

y-y=m(x-x)

y-(-3)=m(x-(-5))

y+3=0.4(x+5)

y-y=m(x-x)

y-1=0.4(x-5)

Answer: 10

Step-by-step explanation:

I did the math, also not to be rude but stop using so many 'enter' commands

Answer:

4th option

Step-by-step explanation:

noting that i² = - 1

(8i)(5i)(- 4 - 6i)

= 40i²(- 4 - 6i)

= 40(- 1)(- 4 - 6i)

= - 40(- 4 - 6i) ← distribute parenthesis by - 40

= 160 + 240i

[tex](8i)(5i)(-4-6i)\\\\=40i^2(-4-6i)\\\\=-40(-4-6i)~~~;[i^2=-1]\\\\=160+240i[/tex]

Answer:

heterogeneous is the answer

Step-by-step explanation:

44 ÷ 33

= 1.333333333..........

Hope it's helpful.

Answer:

1. Becky, 2. No one, 3. Brian and Carol, 4. Tom, 5. Jake

Step-by-step explanation:

The order has to be Brian, Tom, Jake, Becky, and Carol.

1. Becky

2. No one

3. Brian and Carol

4. Tom

5. Jake

Answer:

The number of students would have increased by 25%.

Step-by-step explanation:

Answer:

25% more

Step-by-step explanation:

640  100

800   x

---------------

cross-multiplication = 100*800 = 80000/640 = 125

Answer:

49

Step-by-step explanation:

9*7=63

7*7=49

There are 49 questions did Jackson answer correctly.

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

Jackson answered every 7 out of 9 questions correctly on a Spanish Quiz.

Total number of questions = 63

Now,

Let number of correct questions = x

So, By the definition of ratio, we can formulate;

⇒ 7 : 9 = x : 63

Solve for x as;

⇒ 7 : 9 = x : 63

⇒ 7 / 9 = x / 63

⇒ 7 × 63 / 9 = x

⇒ x = 7 × 63 / 9

⇒ x = 7 × 7

⇒ x = 49

Thus, There are 49 questions did Jackson answer correctly.

Learn more about the ratio visit:

https://brainly.com/question/2914376

#SPJ2

Answer: not shaded i think

Step-by-step explanation:

Answer:

Not shaded, because the equation is not true when you plugged in ( 0,0)

Step-by-step explanation:

Answer:

45 percent

Step-by-step explanation:

Have an awesome day!

Answer:

2

Step-by-step explanation:

n = the smaller even integer

n +2 = the next even integer

The wording of the question translates into:

2n + (n+2) = -4

3n +2 = -4

3n = -6

n = -2

Answer:

[tex]x\approx4.5[/tex]

Step-by-step explanation:

In relation to ∠U, we are given the triangle's opposite side and adjacent side. Therefore, we should use the tangent function to determine the opposite side:

[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]

[tex]tan(34^\circ)=\frac{x}{6.7}[/tex]

[tex]6.7tan(34^\circ)=x[/tex]

[tex]x=6.7tan(34^\circ)[/tex]

[tex]x\approx4.5[/tex]

Answer:

x=68/9; y=38/3.

Step-by-step explanation:

1) according to the condition m(ABC)=m(DEF), then 6y-4=80, ⇒ y=38/3;

2) according to the condition AB=DE, then 10=3x-y. If y=38/3, then 10=3x-38/3; ⇒ x=68/9.