find the value of y showing your steps or explain your thinking.

Answer:

\(\cos G=\dfrac{2}{3}\)

\(\csc E=\dfrac{3}{2}\)

\(\cot G=\dfrac{2}{\sqrt{5}}\)

Step-by-step explanation:

If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).

Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.

\(\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}\)

Therefore:

\(\hrulefill\)

To find cos G, use the cosine trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the hypotenuse is EG.

Therefore:

\(\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}\)

\(\hrulefill\)

To find csc E, use the cosecant trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle E, the hypotenuse is EG and the opposite side is FG.

Therefore:

\(\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}\)

\(\hrulefill\)

To find cot G, use the cotangent trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the opposite side is EF.

Therefore:

\(\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}\)

whatever how much the money is for one day on the object just multiply the money by the days it's rented out and add together the snowboard total and the boots total

Answer:

358

Step-by-step explanation:

Explanation:

-5x to the 2nd powe is: (-5x)² = (-5)²x² = 25x²

y to the 4th power is: y⁴

3xy to the 3rd power is: (3xy)³ = 3³ x³ y³ = 27 x³ y³

The product of all these expressions is:

We have to group like factors:

And solve

Answer:

The answer is 675 x⁵ y⁷

Step-by-step explanation:

f(x)=3x−2  so when the variable x is replace with an actual value ( − 1 ) we get  f(−1)=3(−1)−2

=−3−2

=−5

The output value of (g/f)(x) is 9x/(7x + 28).

The domain of g/f is (-∞, -4) U (-4, ∞)..

In this exercise, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations in simplified form as follows;

(g/f)(x) = (9/(x + 4)) ÷ 7/x

By rearranging the mathematical expression using the multiplication operation, we have the following:

(g/f)(x) = (9/(x + 4)) × x/7

(g/f)(x) = 9x/(7x + 28)

For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;

7x + 28 ≠ 0

7x ≠ -28

x ≠ -4

Domain = (-∞, -4) U (-4, ∞).

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Answer:

ur answer is right it is 9

Step-by-step explanation:

NOTE: divide the number 36 with 4 and u will get 9

GOOD JOB

Please mark as brainliest

Have a great day, be safe and healthy

Thank u  

XD

Kyle drove x hours

Sally drove x  + 7 hours

Added together they both drove 2x + 7 hours

2x +7 = 35 hours

Subtract 7 from both sides:

2x = 28

Divide both sides by 2:

x = 14

Kyle drove 14 hours

Sally drove 21 hours

Kyle drove for 14 hours and Sally drove for 21 hours

Let number of hours Kyle drove = x

Let number of hours Sally drove = x+7

Therefore,

x + (x + 7) = 35

2x + 7 = 35

Collect like terms

2x = 35 - 7

2x = 28

x = 28/2

x = 14

Also, x + 7 = 24 + 7 = 21

Therefore, Kyle drove for 14 hours and Sally drove for 21 hours.

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Convert to polar coordinates with

\(x = r \cos(\theta)\)

\(y = r \sin(\theta)\)

so that \(x^2 + y^2 = r^2\), and the Jacobian determinant for this change of variables is

\(dx\,dy = r \, dr \, d\theta\)

D is the disk centered at the origin with radius 2; in polar coordinates, this is the set

\(D = \left\{(r, \theta) \mid 0\le\theta\le2\pi \text{ and } 0 \le r \le 2\right\}\)

Then the integral is

\(\displaystyle \iint_D (x + y + 10) \, dx \, dy = \int_0^{2\pi} \int_0^2 (r \cos(\theta) + r \sin(\theta) + 10) r \, dr \, d\theta\)

\(\displaystyle = \int_0^{2\pi} \int_0^2 (r^2 \cos(\theta) + r^2 \sin(\theta) + 10r) \, dr \, d\theta\)

\(\displaystyle = \int_0^{2\pi} \left(\frac83 (\cos(\theta) + \sin(\theta)) + 20\right) \, d\theta\)

\(\displaystyle = 20 \int_0^{2\pi} d\theta = \boxed{40\pi}\)

(since cos and sin are 2π-periodic)

Answer:

If Jack adopted half of the spaniel puppies, and there are 4 spaniel puppies, that means that he adopted 2 puppies.

If Carmen adopted half of the beagle puppies, and there are 6 beagle puppies, then Carmen adopted 3 puppies. This means that Carmen adopted more puppies than Jack.

Step-by-step explanation:

1/2 of 4 = 2

1/2 of 6 = 3

Carmen adopted more puppies that is 3 and Jack adopted 2 puppies.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given that, a shelter had 4 spaniel puppies and 6 beagle puppies.

Jack adopted 1/2 of the spaniel puppies.

That is, 1/2 ×4 =2

Carmen adopted 1/2 of the beagle puppies.

That is, 1/2 ×6 =3

Therefore, Carmen adopted more puppies that is 3 and Jack adopted 2 puppies.

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Answer:

Step-by-step explanation:

Given the function f(x) = tan (x)

From trigonometry identity, tan (x) = sin(x)/cos(x)

f(x) = sin(x)/cos(x)

Using the quotient rule to find the derivative of the function, we will have;

f'(x) = cos (x)cos (x) - sin (x)[-sin (x)]/ cos²x

f'(x) = cos²x - sin²x/ cos²x

Divide through by cos²x

f'(x) = cos²x/cos²x + sin²x/cos²x / cos²x/cos²x

f'(x) = 1 + sin²x/cos²x / 1

f'(x) = 1 + (sin²x/cos²x)

f'(x) = 1 + tan²x

From trig identity,  1 + tan²x = sec²x

Hence, f'(x) = sec²x

Hence the expression  f'(x)  in terms of the secant function is sec²x

f'(x) = 1/cos²x

For the function to be defined, it means that cos²x ≠ 0

cos²x ≠ 0

cos x ≠ 0

x ≠ cos⁻¹0

x ≠ 90⁰

Hence the value of x must not be equal to 90 for the function to be defined. x can be defined at when x = 0 since cos 0 = 1, the equation will  becomes f'(0) = 1/cos²0 = 1/1 = 1.

Hence the function is defined at 0≤x<90

The function limit of f(x) as x approaches 2 is 67 and the limit of f²(x) as x approaches 2 is 4489.

The function f(x) can be rewritten as:

f(x) = (5x³ + 3x² - x)/(x+2)

Using direct substitution, we see that f(2) is undefined, as the denominator of the function becomes 0.

To evaluate the limit, we can use L'Hopital's rule:

\(\lim_{x \to 2\\) f(x) = lim x→2 (5x³ + 3x² - x)/(x+2)

= \(\lim_{x \to 2\\) (15x² + 6x - 1)/(1)

= (15(2)² + 6(2) - 1)/(1)

= 67

To find the limit of f²(x) as x approaches 2, we can simply square the limit:

f(x) = \(\lim_{x \to 2\}\)f²(x)

= \(\lim_{x \to 2\) f²(x)  

= 67²

= 4489

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Answer:

Step-by-step explanation:

n+n

Answer:

n+n

Step-by-step explanation:

I think thats right

Answer:

16

Step-by-step explanation:

Since the perimeter of the rectangle is 80, we can set up the perimeter formula:

80=2L+2W=2(3x+3)+2(2x+2)=6x+6+4x+4=10x+10

10x=70

x=7

AB=2x+2=2(7)+2=14+2=16

Answer:

AB= 16

Step-by-step explanation:

2x+2+3x+3=40

Add like terms: 2x+3x= 5x and 2+3=5

New equation: 5x+5=40

Solve: 40-5= 35

Now we know that x is equal to 7.

2(7)+2= 16

Side DC equals 16.

Side AB has the same length as side DC since it's a rectangle.

Side AB equals 16.

Let's check: 16+16=32 (side DC and side AB)

24 must be the length of the other sides.

So, when you add all the sides together...

16+16+24+24= 80

You get 80, the perimeter!

I hope this helped!

i.2

ii.4

Step-by-step explanation:

to estimate a slope simply means to differentiate,

from the equation:f(x)=x^2+1

dx/dy=2x+0=2x

where x=1

it becomes:2(1)=2

where x=2

it becomes:2(2)=4

Answer:

0 - 1 - 2 + 3 - 4 + 5 - 6 +7 - 8 + 9 = 3

Step-by-step explanation:

Step-by-step explanation:

8(15-4)

----------

4square - 5

= 8(15-4)

=120 - 32

= 88

4square - 5

=4×4 = 16

16 - 5

= 11

therefore,

88/11

= 8

Answer:

C. a=45b + 25

Step-by-step explanation:

Answer:

It would be C

Step-by-step explanation:

a = 45b + 25

Reason:

It says the plumber charges 45 dollars per hour and that b is the number of hours worked. so we multiply 45 dollars by the variable b(number of hours worked), then we add the service charge, since the service charge is only added once, we do not multiply it by a variable.

Therefore we get:

a = 45b + 25

Answer:

5 feet

Step-by-step explanation:

\(f(t) = 3 cos \bigg( \frac{\pi}{6} t\bigg) + 5 \\ \\ plug \: t = 9 \\ \\ \implies \: f(9) = 3 cos \bigg( \frac{\pi}{6} \times 9 \bigg) + 5 \\ \\\implies \: f(9) = 3 cos \bigg( \frac{3\pi}{2}\bigg) + 5 \\ \\\implies \: f(9) = 3 cos \bigg( \pi + \frac{\pi}{2}\bigg) + 5 \\ \\\implies \: f(9) = - 3 cos \bigg( \frac{\pi}{2}\bigg) + 5 \\ [ \because \: cos ({\pi}+\theta) = -\cos \theta]\\\\\implies \: f(9) = - 3 (0) + 5 \\ ( \because \: cos \frac{\pi}{2} = 0) \\ \\ \implies \: f(9) = 0 + 5 \\ \\ \implies \: \huge{ \orange{f(9) = 5 }}\)

The hospital can get 4.15 milligrams from these three companies.

A linear equation is one in which the highest power of any variable is not more than 1. A linear equation in 2 variables can be solved by substitution method, if we have two simultaneous equations.

Here, we know that

Company A's supply of medicine = 1.7 mg

also, company A's supply = 2( B's supply - C's supply)

⇒ 1.7 = 2( B - C)

⇒ 1.7 = 2B - 2C .... (1)

Moreover, we are given that

A's supply = C's supply + 0.9

⇒ 1.7 = C + 0.9

⇒ 1.7 - 0.9 = C

⇒ 0.8 = C

Now, substituting the value of C in (1), we get,

1.7 = 2B - 2(0.8)

1.7 = 2B - 1.6

1.7 + 1.6 = 2B

⇒ B = 3.3/2

B = 1.65

Thus, the total supply from all three companies is (1.7 + 1.65 + 0.8) = 4.15 mg

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We know that 22.7% of this amount is used for cooking,the family uses 300.001 gallons of water every day.

What is gallons?

Gallon is a unit of measurement used to quantify liquid volume in both the US customary and British imperial systems of measurement.

Let's start by using algebra to solve the problem.

Let x be the total amount of water the family uses every day. We know that 22.7% of this amount is used for cooking, which means:

0.227x = 68.1

To solve for x, we can divide both sides of the equation by 0.227:

x = 68.1 ÷ 0.227

x = 300.001 (rounded to three decimal places)

Therefore, the family uses 300.001 gallons of water every day.

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Answer:

The correct answer is:

$12.00 and up to $15.00 (D)

Step-by-step explanation:

Let us arrange the data properly in a tabular format.

Hourly Earnings($)         6 - 9          9 - 12     12 - 15

Frequency                          16              42          10

The frequency of a distribution is the number of times that distribution occurs in a particular group of data or intervals.

From the frequency table above the following observations can be made:

Highest frequency = 42 (hourly earnings of $9 - $12)

smallest frequency = 10 ( hourly earnings of $12 - $15)

This means that among a total of 68 workers (16 + 42 + 10), the people earning $12 - $15 form the smallest group (only 10 people), while 42 workers earn $9 - $12, forming the largest majority

The three true statements are as follows:

In the list, there are several true statements and some of them include the facts that all triangles are polygons, they are closed figures and they have three straight sides.

A polygon is a shape with two or more sides. Triangles ahve three sides, so we can easily address them as polygons. Also, all triangles are closed figures and they also have three straight sides.

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\(\huge\bold{ANSWER:}\)

\(\huge\bold{1,400} ~and~\huge\bold{361,000}\)

\(\huge\bold{SOLUTION:}\)

\(\huge\mathrm{100*14}\)

Multiply:

\(\huge\mathrm{1,400}\) (Answer)

\(\huge\mathrm{361*1,000}\)

Multiply:

\(\huge\mathrm{361,000}\)

_______________________________________

Additional Note:

\(\bigstar\) If we multiply by 100, we add 2 zeros.

Example: \(\bold{\underline{14*100=1,400}}\)

\(\bigstar\) If we multiply by 1,000, we add 3 zeros.

Example: \(\bold{\underline{361*1,000=361,000}}\)

______________________________________

Hope you find it helpful.

Feel free to ask if you have any doubts.

\(\bold{-MistySparkles^**^*}\)

Answer:

The answer is 32

Step-by-step explanation:

The formula for finding the area of a trapezoid is:

         ((base 1 + base 2)/ 2 )* h

Now all you have to do is substitute the numbers in.

Note: bases will always be the ones like 12 and 4 in this case. We have just named then 1 and 2.

Answer:

32 square units

Step-by-step explanation:

\(\displaystyle A=\frac{1}{2}(b_1+b_2)h=\frac{1}{2}(12+4)(4)=\frac{1}{2}(16)(4)=\frac{1}{2}(64)=32\)

Note that \(b_1\) and \(b_2\) are the lengths of each base of the trapezoid, so it doesn't matter which is which.