Pls solve this problem!!

Given:

The figure of a right triangle.

To find:

All the six trigonometric ratios for the angle θ.

Solution:

Using the Pythagoras theorem, we get

[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]

[tex]Hypotenuse^2=(9)^2+(12)^2[/tex]

[tex]Hypotenuse^2=81+144[/tex]

[tex]Hypotenuse^2=225[/tex]

Taking square root on both sides, we get

[tex]Hypotenuse=15[/tex]

Now, the six trigonometric ratios for the angle θ are:

[tex]\sin\theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\sin\theta=\dfrac{12}{15}[/tex]

[tex]\sin\theta=\dfrac{4}{5}[/tex]

[tex]\cos\theta=\dfrac{Base}{Hypotenuse}[/tex]

[tex]\cos\theta=\dfrac{9}{15}[/tex]

[tex]\cos\theta=\dfrac{3}{5}[/tex]

[tex]\tan\theta=\dfrac{Perpendicular}{base}[/tex]

[tex]\tan\theta=\dfrac{12}{9}[/tex]

[tex]\tan\theta=\dfrac{4}{3}[/tex]

[tex]\csc\theta=\dfrac{1}{\sin \theta}[/tex]

[tex]\csc\theta=\dfrac{1}{\dfrac{4}{5}}[/tex]

[tex]\csc\theta=\dfrac{5}{4}[/tex]

[tex]\sec\theta=\dfrac{1}{\cos \theta}[/tex]

[tex]\sec\theta=\dfrac{1}{\dfrac{3}{5}}[/tex]

[tex]\sec\theta=\dfrac{5}{3}[/tex]

[tex]\cot\theta=\dfrac{1}{\tan \theta}[/tex]

[tex]\cot\theta=\dfrac{1}{\dfrac{4}{3}}[/tex]

[tex]\cot\theta=\dfrac{3}{4}[/tex]

Therefore, the six trigonometric ratios are [tex]\sin\theta=\dfrac{4}{5},\cos\theta=\dfrac{3}{5},\tan\theta=\dfrac{4}{3},\csc\theta=\dfrac{5}{4},\sec\theta=\dfrac{5}{3},\cot\theta=\dfrac{3}{4}[/tex].

Answer:

Volume of rectangular prism = 4d² unit²

Step-by-step explanation:

Given:

Length of rectangular prism = 4 unit

Width of rectangular prism = d unit

Height of rectangular prism = d unit

Find:

Volume of rectangular prism

Computation:

Volume of rectangular prism = [l][b][h]

Volume of rectangular prism = [4][d][d]

Volume of rectangular prism = 4d² unit²

Answer:

the radius is 32

Step-by-step explanation:

the radius of a circle is half the diameter

hope this helps

Answer:

45%

Step-by-step explanation:

45 out of 100 equals 45%.

Answer:

$m + $12 = $26

Or

m + 12 = 26

Step-by-step explanation:

Amount spent by Richard = $m

Amount spent by Jordan = $12

Total amount spent together = $26

An equation that describes this situation would be:

$m + $12 = $26

Or

m + 12 = 26

Answer:

Step-by-step explanation:

23+87+98=208

2.08+1=3.08

3.08-----> 308p

Answer:

36.5miles/gallon

Step-by-step explanation:

Given the equation y=36.5x which represents the number of miles, y, that Katherine can drive her car for every, x, gallons of gas. The rate of change of the function is expressed as dy/dx

On differentiating the function;

dy/dx = 36.5

Hence the rate of change of the function is 36.5miles/gallon

Answer:

inside the circle

Step-by-step explanation:

Khan Academy

Answer:

[tex]\boxed {\boxed {\sf 87 \ degrees}}[/tex]

Step-by-step explanation:

The angles in a triangle must add to 180 degrees.

We are given three angles: 2x+6, x, and 3x. Their sum must be 180, so we can create an equation.

[tex]2x+6+x+3x=180[/tex]

Combine like terms (all terms with an x) on the left side.

[tex](2x+x+3x)+6=180[/tex]

[tex]6x+6=180[/tex]

Now solve for x by isolating the variable.

6 is being added and the inverse of addition is subtraction. Subtract 6 from both sides.

[tex]6x+6-6=180-6\\6x=174\\[/tex]

x is being multiplied by 6. The inverse of multiplication is division. Divide both sides by 6.

[tex]6x/6=174/6 \\x=29[/tex]

Substitute 29 for x in the angle measures.

The largest angle is 87 degrees.

2/5 , 1/2 , 7/10 , 10/7 , 3/1

Step-by-step explanation:

hope this helped

Answer:

3 grey and 1 red

Step-by-step explanation:

5 x 3 = 15

15 + 7 = 22

The rate of change is the slope. The slope is the number in front of the x

Function 1 rate of change is -1/2

Function 2 rate of change is -3/4

The greater rate of change would be the steepest slope.

Function 2 has the greater rate of change

See the attached picture.

Answer:

The absolute value of -9 is less than 9 I'm pretty sure

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

Explanation:

We could add 9 to both sides, and then apply the square root to both sides. Don't forget about the plus minus

x^2 - 9 = 0

x^2 = 9

x = sqrt(9) or x = -sqrt(9)

x = 3 or x = -3

To check these answers, you replace x with those values we found. I'll show you how to check x = 3

x^2 - 9 = 0

(3)^2 - 9 = 0

9 - 9 = 0

0 = 0

So that confirms x = 3. The confirmation for x = -3 is nearly the same. Keep in mind that (-3)^2 = (-3)(-3) = 9. You'll be squaring the negative as well.

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

Another method you could do is to use the difference of squares rule

x^2 - 9 = 0

x^2 - 3^2 = 0

(x - 3)(x + 3) = 0

Now apply the zero product property. This effectively means you set each factor equal to zero and solve for x

x-3 = 0 or x+3 = 0

x = 3 or x = -3

We end up with the same solution set.

Yet another method you could use is the quadratic formula, but that may be overkill. It's still good practice to do.

Graphing is a visual way to find the answers. You'll graph y = x^2 - 9 and look to see where the curve crosses or touches the horizontal x axis.

x = 36

Step-by-step explanation:

The angles 4x and x are supplementary, meaning they add up to 180; therefore we have

[tex]4x + x = 180[/tex]

[tex]5x = 180[/tex]

dividing both sides by 5 gives

[tex]x = 36[/tex]

the measure of angle x is 36 and that of 4x is 4 * 36 = 144

The angle opposite to 4x also measures 144 and the one opposite to x is 36.

Answer:

x° + 4x° = 180°

5x° = 180°

x° = 180°/5

x° = 36°

Answer:

D.

tangent = opp over adj

Step-by-step explanation:

Answer:

4 of her flowers are yellow.

Step-by-step explanation:

[tex] \frac{2}{6} = \frac{4}{12} [/tex]

6 x 2 = 12 and 2 x 2 = 4

Answer:

S₁₅ = 645

Step-by-step explanation:

The sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Using the nth term formula [tex]a_{n}[/tex] = 5n + 3 , then

a₁ = 5(1) + 3 = 5 + 3 = 8

a₂ = 5(2) + 3 = 10 + 3 = 13 , then

d = a₂ - a₁ = 13 - 8 = 5

Thus

S₁₅ = [tex]\frac{15}{2}[/tex] [ (2 × 8) + (14 × 5) ]

     = 7.5( 16 + 70)

     = 7.5 × 86

     = 645

Answer:

puede cargar 205 killos pero no mas de 260 por el peso.

Step-by-step explanation:

5t. 3q 85kg

Answer: C/A+B

Step-by-step explanation:

i’m doing this course on acellus rn too

1/5

Step-by-step explanation:

I have done this sir

Lee laaa

Answer:

1/5

Step-by-step explanation:

5/25 = ?

well so

5 x 5 = 25 so that means that there is 5 parts for each 1 whole

5/25 = 1/5

Answer: 70

Step-by-step explanation:

do 21*3 which would be 90% but the actual number would be 63. but there is still 10% left and you are given and number for 30% so divide 21 by 3 which you get 7 so 63+7=70

Answer:

5x

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

In [tex]a^2+bx+c[/tex], b is the middle term.

Answer:

2.575844

Step-by-step explanation:

This is a simple change of temp problem, from 539K to -62C but to start you have to change the C to K, which is simply adding 273 to the -62 so 211K.

Now you take P1/T1 = P2/T2 so,

6.58 = x

539 = 211

now cross multiply and divide, 211 x 6.58 then divide by 539.

this will give you your answer

***BTW DONT CLICK THE LINK ON THE ANSWER BELOW OR ABOVE THAT LEADS TO SOME MALWARE***

Answer:

1,420 grams per 100 baseballs

Step-by-step explanation:

Set up an equation:

Variable x = grams per 100 baseballs

1/14.2 = 100/x

Cross multiply

1 × x = 14.2 × 100

1x = 1420

x = 1420