[50 POINT QUESTION]
FInd the area of the trapezoids.

[tex]\sf{Given : 3tanx + 7 = \dfrac{2}{(1 - sinx)(1 + sinx)}}[/tex]

We know that : (a - b)(a + b) = a² - b²

[tex]\implies \sf{3tanx + 7 = \dfrac{2}{1 - sin^2x}}[/tex]

We know that : 1 - sin²x = cos²x

[tex]\implies \sf{3tanx + 7 = \dfrac{2}{cos^2x}}[/tex]

[tex]\sf{\bigstar \ \ We \ know \ that : \boxed{\sf{\dfrac{1}{cos^2x} = sec^2x}}}[/tex]

[tex]\implies \sf{3tanx + 7 = 2sec^2x}[/tex]

We know that : sec²x = 1 + tan²x

[tex]\implies \sf{3tanx + 7 =2(1 + tan^2x)}[/tex]

[tex]\implies \sf{2 + 2tan^2x - 3 tanx - 7 = 0}[/tex]

[tex]\implies \sf{2tan^2x - 3 tanx - 5 = 0}[/tex]

[tex]\implies \sf{2tan^2x - 5tanx + 2tanx - 5 = 0}[/tex]

[tex]\implies \sf{2tanx(tanx + 1) - 5(tanx + 1) = 0}[/tex]

[tex]\implies \sf{(tanx + 1)(2tanx - 5) = 0}[/tex]

[tex]\implies \sf{tanx = -1 \ (or) \ tanx = \dfrac{5}{2} }[/tex]

Given:

In triangle ABC, [tex]m\angle A=66^\circ, AB=5\text{ mi}[/tex].

To find:

The angle of depression from point A to point C.

Solution:

According to angle sum property, the sum of all interior angles of a triangle is 180 degrees.

In triangle ABC,

[tex]m\angle A+m\angle B+m\angle C=180^\circ[/tex]

[tex]66^\circ+90^\circ+m\angle C=180^\circ[/tex]

[tex]156^\circ+m\angle C=180^\circ[/tex]

[tex]m\angle C=180^\circ-156^\circ[/tex]

[tex]m\angle C=24^\circ[/tex]

We know that if a transversal line intersect the two parallel lines, then alternate interior angles are equal. So, the angle of depression from point A to point C is equal to the measure of angle C in triangle ABC.

Therefore, the angle of depression is 24 degrees.

7

___________________

Step-by-step explanation:

answer is in the above photo

there are 29 boys total

Answer:

0.3

Step-by-step explanation:

Go left to right for each digit, which one is greater. They all have a decimal so for right now we can’t eliminate any. Next digit we two 2s a 0 and a 3. Whch number is greater? The three! So the greatest number is 0.3.

Answer:

Step-by-step explanation:

Which rational function models the time, y, in hours, that it takes the train to travel between the two cities at an average speed of x miles per hour?  

✔ y = 160/x

What does the number 160 represent in the rational function that models the situation?

✔distance, in miles, between the cities

amount of fuel, in gallons, used by the train

time, in minutes, needed to travel between the cities  

Answer: NOTE Pictures Are not in order! Make sure you check page number.

Step-by-step explanation:

On page 6 the answers are ”C” and ”5lbs”

On page 7 the answers are “C”, “$ 418”, “ The cat”, and then “ $960”.

On page 8 the answers are : < Just copy paste this below.>

“Based on the calculation, they should purchase the second television as the cost is cheaper.

Based on the information given in the question, the cost of the first television will be:

= $330 + ($14 × 8)

= $330 + $102

= $442

The cost of the second television will be:

= $369 + ($9 × 8)

= $369 + $72

= $441

Therefore, the second television is cheaper.”

                   ^    

<Just copy paste this. >           [Then check. “A,B,C,”.]

On page 9 the answer is “ D “.

pregunta:x2+40=100

resultado:x=30

Step-by-step explanation:

the anwer is x=30......

Answer:

Complex roots

Step-by-step explanation:

Given

[tex]8v^2 + 8 = -11v[/tex]

Required

The type of solution

Rewrite as:

[tex]8v^2 +11v+ 8 = 0[/tex]

To determine the type of solution, we simply calculate the discriminant (D)

[tex]D = b^2 - 4ac[/tex]

Where

[tex]a = 8;\ \ \ b =11\ \ \ c = 8[/tex]

So, we have:

[tex]D = 11^2 - 4 * 8 * 8[/tex]

[tex]D = 121 - 256[/tex]

[tex]D = -135[/tex]

The above value implies that:

[tex]D<0[/tex]

When [tex]D<0[/tex], the solution of the equation is: complex roots

Answer:

(9-6.6)÷2=x

Step-by-step explanation:

Do it in reverse from 9 all the way to x.

Answer:

(9-6.6)÷2=x

Step-by-step explanation: since you had 9 as the answer, start there. Then subtract 6.6. You then divide that number by 2 to get x

Answer:

The upper bound of the interval is below 0.5, which means that it can be claimed that a majority of people are not in favor of legalized abortion

Step-by-step explanation:

Confidence interval:

Sample proportion plus/minus margin of error.

In this question:

Sample proportion of 0.45, margin of error of 0.04. So

0.45 - 0.04 = 0.41

0.45 + 0.04 = 0.49

The confidence interval is of (0.41,0.49). The upper bound of the interval is below 0.5, which means that it can be claimed that a majority of people are not in favor of legalized abortion

Answer:

[tex]base = \sqrt{ {4}^{2} + {3}^{2} } \\ = \sqrt{25} = 5 \\ x = \sqrt{ {6}^{2} - {5}^{2} } \\ x = \sqrt{11} \\ x = 3.3[/tex]

Step-by-step explanation:

may it be

9.6

may it help u

Answer:

B. [tex]g(x) = x^{3} - 5[/tex]

Step-by-step explanation:

The graph of f(x) is the graph of g(x) translated 5 units downwards.

Answer:

Volume for cube: L x W x H

L= Length, W= width, H=height

Answer:

604,800

Step-by-step explanation:

10*9*8*7*6*5*4

Answer:

4equal to plus 5 eul is to be 9

Answer:

Yes, it is:

Step-by-step explanation:

Given

[tex]f(x) =2xy[/tex]

Required

Determine if it is a direct variation

A direct variation is represented as:

[tex]f(x)\ \alpha\ x[/tex]

Express as equation

[tex]f(x) = kx[/tex]

Compare [tex]f(x) = kx[/tex] to [tex]f(x) =2xy[/tex]

[tex]k = 2y[/tex]

Hence, it is a direct variation

Answer:

d

Step-by-step explanation:

Answer:

we got 10 digits to choose from for the first digit, 9 for the second and so on

[tex]10 \times 9 \times 8 \times 7 \times 6 \times 5[/tex]

scenarios that got no repeated digits.

the total number of possible PINs with 6 digits is

[tex]10 \times 10 \times 10 \times 10 \times 10 \times 10[/tex]

or just 10⁶

so the fraction we are looking for is the number of valid states decided by all possible states.

[tex] \frac{10 \times 9 \times 8 \times 7 \times 6 \times 5}{ {10}^{6} } [/tex]

=0.1512

rounded to the nearest thousandth it's

0.151

(actually, I didn't expect the probability to be around 15 percent)

hope it helps. asked question whenever you like

kind regards

Alex

Answer:

m4+m5=180

answer is second option

Answer:

170 books

Step-by-step explanation:

Each book equals 10 books. So 17x10 equals your answer! (170)

Good luck to you!

Answers:

x = 6

Each angle is 45 degrees

The diagram is shown below

=========================================================

Explanation:

Vertical angles are always congruent

Set the two expressions equal to each other and solve for x.

5x+15 = 3x+27

5x-3x = 27-15

2x = 12

x = 12/2

x = 6

As a way to check the answer, replace x with 6 in each expression. We should get the same thing on both sides

5x+15 = 3x+27

5*6+15 = 3*6+27

30+15 = 18+27

45 = 45

Each angle is 45 degrees, so the answer is confirmed.

---------

The diagram is shown below. There are infinitely many ways to draw out the diagram. In the version I drew, the angles aren't vertically aligned but instead they are opposite one another in this X configuration. So the vertical angles could be vertically aligned, but they don't have to be.

In short: draw an X shape and mark any two opposite angles to form the vertical angles.

Answer: -12

Step-by-step explanation:

3(-2)^3 - 2(-2)^2 - 9(-2) + 2 = N

3(-8) - 2(4) - 9(-2) + 2 = N

-24 - 8 + 18 + 2 = N

-12 = N

9514 1404 393

Answer:

  a) 2π radians

  b) 10π inches

  c) 5/4π inches per minute

Step-by-step explanation:

The formulas are fairly straightforward. Use the given values in each.

a) θ = ωt

  θ = (π/4 radians/min)(8 min) = 2π radians

__

b) s = rθ

  s = (5 in)(2π radians) = 10π in

__

c) v = s/t

  v = (10π in)/(8 min) = 5/4π in/min

Answer:

333..%

Step-by-step explanation:

[tex] \large \boxed{ \boxed{ \mathrm{21.5 \: \: cm {}^{2}} }}[/tex]

By Observing the Above figure, we can conclude that the area of shaded region is equal to the Area of Square minus the sum areas of two equal semicircles (since their diameters are equal)

let's solve for area of square :

[tex]\longrightarrow \: \mathrm{side {}^{2} }[/tex]

[tex]\longrightarrow10 {}^{2} [/tex]

[tex]\longrightarrow \mathrm{100 \: cm {}^{2} }[/tex]

Now,

Radius of the both semicircles measure :

[tex]\longrightarrow \dfrac{10}{2} [/tex]

[tex]\longrightarrow5 \: cm[/tex]

now, let's solve for their area

[tex] \longmapsto 2 \times \dfrac{\pi {r}^{2} }{2} [/tex]

(Since, there are two semicircles)

[tex]\longrightarrow3.14 \times 5 \times 5[/tex]

[tex]\longrightarrow78.5 \: cm {}^{2} [/tex]

Area of Shaded region = Area of Square - Area of Semicircles, that is

[tex]\longrightarrow100 - 78.5[/tex]

[tex]\longrightarrow \mathrm{21.5 \: cm {}^{2} }[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{hope \: it \: helps \: you \: }}{\orange{.....}}}}}[/tex]

Answer:

3x+5 =x+2

3x-x=2-5

2x= –3

x=-3/2

4y+7=y+3

4y–y =3-7

3y=–4

y= —4/3

Answer:

The answer e i think

Step-by-step explanation: