What is the value of d?
A)80
B)100
C)84
D)50

Answer:

[tex]\displaystyle \displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}\text{ and } \sin A = \frac{2ab}{a^2 + b^2}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle \tan A = \frac{2ab}{a^2 - b^2}[/tex]

And we want to find the value of cos(A) and sin(A).

Recall that tangent is the ratio of the opposite side to the adjacent side.

Therefore, the opposite side measures 2ab, and the adjacent side measures a² - b².

Using the Pythagorean Theorem, solve for the hypotenuse:

[tex]\displaystyle \begin{aligned} c^2 &= a^2 + b^2 \\ \\ c&= \sqrt{(2ab)^2 + (a^2-b^2)} \\ \\ &= \sqrt{(4a^2b^2)+(a^4-2a^2b^2+b^4)} \\ \\ &= \sqrt{a^4 + 2a^2b^2 + b^4 } \\ \\ &= \sqrt{(a^2 +b^2)^2} \\ \\ &= a^2 + b^2\end{aligned}[/tex]

Thus, our hypotenuse is given by a² + b².

Cosine is the ratio between the adjacent side and the hypotenuse. Thus:

[tex]\displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}[/tex]

And sine is the ratio between the opposite side and the hypotenuse. Thus:

[tex]\displaystyle \sin A = \frac{2ab}{a^2 + b^2}[/tex]

In conclusion:

[tex]\displaystyle \displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}\text{ and } \sin A = \frac{2ab}{a^2 + b^2}[/tex]

Answer:

Step-by-step explanation:

[tex]sec^2A-tan^2A=1\\sec^2A=1+tan^2A=1+\frac{4a^2b^2}{(a^2-b^2)^2} =\frac{(a^2-b^2)^2+4a^2b^2}{(a^2-b^2)^2} =\frac{(a^2+b^2)^2}{(a^2-b^2)^2} \\cos^2A=\frac{(a^2-b^2)^2}{(a^2+b^2)^2} \\cos A=\frac{a^2-b^2}{a^2+b^2} \\sin A=\sqrt{1-cos^2A} =\sqrt{1-(\frac{a^2-b^2}{a^2+b^2} )^2} =\sqrt{\frac{(a^2+b^2)^2-(a^2-b^2)^2}{(a^2+b^2)^2} } =\sqrt{\frac{4a^2b^2}{(a^2+b^2)^2} }=\frac{2ab}{a^2+b^2}[/tex]

Answer:

x^5/y^7

Step-by-step explanation:

x^8 y^2 / x^3 y^9

We know that a^b/ a^c = a^(b-c)

Simplify the x terms

x^8 / x^3 = x^(8-3) = x^5

Simplify the y terms

y^2 / y^9 = y^(2-9) = y^-7

We know a^-b = 1/a^b

y^-7 = 1/y^7

Put the terms back together

x^5/y^7

[tex]\\ \sf\longmapsto (-42)+15+(-63)[/tex]

[tex]\\ \sf\longmapsto -42+15+(-63)[/tex]

[tex]\\ \sf\longmapsto -27+(-63)[/tex]

[tex]\\ \sf\longmapsto -27-63[/tex]

[tex]\\ \sf\longmapsto -90[/tex]

Answer:

42 + 15 + (-63) = -90

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

sorry

Step-by-step explanation:

polynomial is not given

question is incomplete

Answer:

I think E

Step-by-step explanation:

You know the shortest building is 25 m.

to find the rest, use trigo so Tan(20)=opposite/adjacent.

Adjacent is 50. Do the math and add the answer with 25.

Answer:

The answer would be E. 43.2

According to TOA, The opposite side is tan(20) x adjacent side( 50m)

the answer is 18.2( to 1 dp). Add the height of the second building together with 18.2 and you will get ur answer. HOpe this helps:)

Answer:

[tex]P(x \ge 5) = 0.60[/tex]

Step-by-step explanation:

Given

[tex]S = \{5, 2, 7, 2, 3, 4, 10, 6,4,6,3, 6, 6, 4, 8,5,7,7,1,5\}[/tex]

[tex]n(S) = 20[/tex]

Required

[tex]P(x \ge 5)[/tex]

First, we count the number of trials that are at least 5

[tex]x = \{5, 7, 10, 6,6, 6, 6, 8,5,7,7,5\}[/tex]

So, we have:

[tex]n(x \ge 5) = 12[/tex]

So, we have:

[tex]P(x \ge 5) = \frac{n(x \ge 5)}{n(S)}[/tex]

This gives

[tex]P(x \ge 5) = \frac{12}{20}[/tex]

[tex]P(x \ge 5) = 0.60[/tex]

Answer:

-4

Step-by-step explanation:

a = 3

b = -4

c = -2

2a + 3b - c

= 2(3) + 3(-4) - (-2)

= 6 + (-12) + 2

= -4

Answer:

15.81 = ?

Step-by-step explanation:

Since this is a right triangle we can use the Pythagorean theorem

a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse

9^2 + 13^2 = ?^2

81 +169 = ?^2

250 = ?^2

Taking the square root of each side

sqrt(250) =?

15.8113883= ?

To the nearest 100th

15.81 = ?

Answer:

Using Pythagorean theorem:- [tex]a^{2} +b^{2} =c^{2}[/tex]

a= 13

b= 9

c= ? ( length)

[tex]13^{2} +9^{2} =?^{2}[/tex]

[tex]13^{2} =169[/tex]

[tex]9^{2} =81[/tex]

[tex]169+81=?^{2}[/tex]

[tex]250=?^{2}[/tex]

[tex]\sqrt{250}=15.811[/tex]

[tex]?=15.81[/tex]

OAmalOHopeO

Answer:

13.9

Step-by-step explanation:

For the 41° angle, x is the opposite leg, and 16 is the adjacent leg. The trig ratio that relates the opposite leg and the adjacent leg is the tangent.

tan A = opp/adj

tan 41° = x/16

x = 16 * tan 41°

x = 13.9085...

Answer: 13.9

Answer:

B. Never

Step-by-step explanation:

When a number is irrational, it means that it cannot be written as a fraction.

I hope this helps!

pls ❤ and mark brainliest pls!

Answer:

c) when it is improper fraction

The answer is C.) (0, 5)

Explaintion is in the pictures

I believe this is the answer if it isn't I'm sorry for wasting your time by answering.

Hope this helps!

1 hour = 60 minutes

3.5 hours x 60 = 210 minutes

210 minutes / 7.5 minutes per mile = 28 miles

Answer: 28 miles

Answer:

y = 3/5×x + 1

Step-by-step explanation:

Slope intercept form y= mx + b

since slope = 3/5 => y= [tex]\frac{3}{5}[/tex]x + b

Plug point (-5,-2) to the equation -2 = [tex]\frac{3}{5}[/tex] x (-5) + b

=> b=1

Answer:

2=124  124/2

4=248 248/4

5=310 310/5

8=496 496/8

Step-by-step explanation:

40 + 22 = 62

62 x 2 = 124

62 x 4 = 248

62 x 5 = 310

62 x 8 = 496

i think

Answer:

3468 children.

Step-by-step explanation:

One apple per person.

Answer:

(2x+3y)^2

= (2x)^2 + 2(2x)(3y) + (3y)^2

= 4x^2 + 12xy + 9y^2

Answer:

4x^2 12xy +9y^2

Step-by-step explanation:

(2x+3y)^2

(2x+3y)(2x+3y)

FOIL

4x^2 + 6xy+6xy + 9y^2

4x^2 12xy +9y^2

Answer:

17 =x

Step-by-step explanation:

These are alternate interior angles and alternate interior angles are equal when the lines are parallel

9x+7 = 10x-10

Subtract 9x from each side

9x+7-9x = 10x-10-9x

7 = x-10

Add 10 to each side

7+10 =x-10+10

17 =x

Answer:

First, just  to recap, the angle that has a measure of 60 and the angle that has a measure of 2x+14 are vertical angles.

This means, that they are equal to each other.

Knowing this, the rest is pretty easy. We just set up an equation:

60 = 2x+14

And solve for x: (I'm going to speed through, but let me know if you need me to go step by step...)

2x = 46

x = 23

Let me know if this helps!

Answer:

Step-by-step explanation:

Part (a)

This is the empty set

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

Explanation:

It doesn't matter what set A is composed of. Intersecting any set with the empty set Ø will always result in the empty set.

This is because we're asking the question: "What does some set A and the empty set have in common?". The answer of course being "nothing" because there's nothing in Ø. Not even the value zero is in this set.

We can write Ø as { } which is a set of curly braces with nothing inside it.

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

Part (b)

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

Explanation:

When you union the universal set with any other set, you'll get the universal set.

The rule is [tex]A \cup B = B[/tex] where I've made B the universal set to avoid confusion of the letter U and the union symbol [tex]\cup[/tex] which looks nearly identical.

Why does this rule work? Well if an item is in set [tex]\overline{A}[/tex], then it's automatically in set U (everything is in set U; it's the universe). So we're not adding anything to the universe when applying a union involving this largest set.

It's like saying

we can see that [tex]\overline{A} \cup U[/tex] will basically form the set of every item, aka the universal set.

Answer:

C. y = -f(x) - 3

Step-by-step explanation:

The given (parent) function is f(x) = √x

The given graph shows a real curve that starts from y = -3, when x = 0 and the y-value increases in magnitude in the negative direction as the x-values increases positively from left to right, by the same amount that the parent function increases from left to right

Therefore;

The graph is real, therefore, the value of x in √x is x ≥ 0, and y ≠ f(-x) + D

Where, D, is the vertical shift

The graph starts at x = 0, y = -3, compared to the parent function, the vertical shift, D = -3

The y-value of the given curve increases in the opposite direction (negatively) as the y-value of the parent function increases in magnitude in the positive direction

Therefore, the equation of the given curve comprises of the reflection of the parent function or -f(x)

The graph shows the reflection of the parent function, across the x-axis, and we have, reflection of the parent function, f(x) which is -f(x)

Therefore, the equation that describes the graphed function is y = -f(x) - 3

Answer:

even i dont know can help

Answer:

200.96

Step-by-step explanation:

Volume of cone=(1/3)*pi*r^2*h

Volume=(1/3)*pi*16*12=64*3.14=200.96

Answer:

Step-by-step explanation:

[tex]\displaystyle \Large \boldsymbol{} x^2+10x+9=0 \\\\ x^2+\underbrace{x+9x}_{10x}+9=0 \\\\x^2+x+\underline9x+\underline9=0 \\\\x(x+1)+9(x+1)=(x+9)(x+1)[/tex]

Answer:

Option C, 93.6 mi³

Step-by-step explanation:

Volume of the triangular prism,

base area × height

= (8×3.9/2)×6

= 93.6 mi³

Answer: You would use 7 cups of milk.

Step-by-step explanation:

Half of 14 is 7.