In slope-intercept form ?

Answer:

x = 5.7           y = 9.4

m∠H = 31°

Step-by-step explanation:

cos of an angle = adjacent side/hypotenuse

and sine of an angle = opposite side/hypotenuse

cos 59 = x/11          and sin 59 = y/11

11 cos 59 = x                  11 sin 59 = y

x = 5.7                             y = 9.4

m∠H = 90 - 59 = 31°

You need  to memorize the definitions of all the trig functions and then these types of problems will be easy for you.

[tex]x=5.7[/tex], [tex]y=9.4[/tex]  and ∠[tex]H[/tex][tex]=31[/tex]° is the solution of the triangle.

What is trigonometric ratio?

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle.

The basic trigonometric ratios formulas are given below :

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

sec θ = Hypotenuse/Base

cosec θ = Hypotenuse/Perpendicular

cot θ = Base/Perpendicular

The sum of angles of a triangle equals the straight angle (180 degrees, π radians, two right angles, or a half-turn)

According to question,

In Δ FGH ,

∠G = 59°

Hypotenuse of triangle = 11

Base of triangle according to the ∠G = x

Perpendicular of triangle according to the ∠G = y

Now,

Cosθ =  [tex]\frac{Base}{Hypotenuse}[/tex]

[tex]Cos[/tex] 59° =  [tex]\frac{x}{11}[/tex]

   [tex]x[/tex] [tex]=11[/tex]× [tex]0.515[/tex]     (  Cos59° = [tex]0.515[/tex] )

     x [tex]=5.7[/tex]

Sinθ = [tex]\frac{Perpendicular}{Hypotenuse}[/tex]

[tex]Sin[/tex] [tex]59[/tex]° [tex]=\frac{y}{11}[/tex]

      [tex]y=11[/tex] * 0.857

       y [tex]=9.4[/tex]

According to the sum of angle of triangle

∠F + ∠G +∠H = 180°

90° + 59° + ∠H = 180°

∠H = 180° - 90 -59

∠H = 31°

Hence,[tex]x=5.7[/tex], [tex]y=9.4[/tex]  and ∠[tex]H[/tex][tex]=31[/tex]° is the solution of the triangle.

Learn more about trigonometric ratio and sum of angle of triangle here:

https://brainly.com/question/8711345

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Answer: no answer c

Step-by-step explanation:

Answer:

56.7°

Step-by-step explanation:

We solve this above question using the Trigonometric function of Sine

sin x = Opposite side/Hypotenuse

Opposite = 66mm

Hypotenuse = 79 mm

sin x = 66/79

x =arc sin(66/79)

x = arcsin(0.8354430379746836)

x = 56.661998553°

Approximately = 56.7°

Answer:

In this triangle, what is the value of x?

Enter your answer, rounded to the nearest tenth, in the box.

x = 56.7

Step-by-step explanation:

Answer:

51°

Step-by-step explanation:

so lets all know that the sum of a trapezoid is 360°

so lets find x

360-83-115-111=51

so your answer is 51°

Hope this helped :)

Answer:

x < -9 or x > 10.

Step-by-step explanation:

x + 10 > 20

x  > 10.

x + 12 < 3

x < -9.

Answer:

1 1/3 - 5/6 = 1/2

Step-by-step explanation:

First we will need to make a common denominator on both sides, so since we have the second side divided in six, we can do the same to the first side as shown;

1/3 = 2/6

now this will help us a lot, now all we have to do is take what we can out of the fraction (2/6) out of the first side so it is equal to 0, NOTE this is not a professional way to do it but it helps me a lot;

5/6 - 2/6 = 3/6

this makes it easy all of a sudden, cause now its in a simpler form, we can tell this because we know that 3/6 is equal to 1/2, so now all we have to do is take 1/2 from our 1 that we are left over with, and VWOLA;

1 - 1/2 = 1/2

GRAND TOTAL;

1 1/3 - 5/6 = 1/2

(note: the space between the 1 and the 1/3 indicates that they are two separate numbers, so you dont have to put the 'and' there)

Answer:

2nd one down

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

GCF is the largest factor that all terms have in common.

Answer:

20

Step-by-step explanation:

Answer: The greatest number of flowers that could be in a bouquet = 2

Step-by-step explanation:

Given: Sandy has 10 roses, 2 daisies, and 8 tulips.

Each bouquet has the same number of flowers and the same type of flower.

The greatest number of flowers that could be in a bouquet = GCD (10,2,8)

Since 10=2 x 5, 8 = 2 x 2 x 2

GCD (10,2,8) =2

Then, The greatest number of flowers that could be in a bouquet = 2

Answer:

y=3/5x-2

Step-by-step explanation:

Sum of all angles of a triangle = 180°

Let the third angle be x.

So, 18.6° + 113.4° + x = 180°

=> 132° + x = 180°

=> x = 180° - 132°

=> x = 48°

So, the third angle is 48°.

Step-by-step explanation:

Answer:

Step-by-step explanation:

wanna use P E M D A S, you will take 36-5 and it will be 31. so now the equation is 3(31)=2*6 times 3 and 31 + 93 then it will be 93=2*6, now it will be 93=12  and if i done it correctly youll get a decimal

Answer:

-5 1/2,      -5.2,  -5,    -5/2,    5.5

Step-by-step explanation:

Answer:

[tex]\frac{-1}{7}[/tex] or 0.14

Step-by-step explanation:

To find slope you can use the formula

mx=[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

or

[tex]\frac{rise}{run}[/tex]

Rise over run:

Rise over run is the easiest of the two so we'll be using that one first for this question, but both should give you the same answer

To find rise over run, select the points and see how many points up or down you must got to make it the same level as the other point

In this case, the point (-3,1) would have a run of -1 because you have to move down one

To find run, now that you have rise start from that point and count how far you have to go to get to the next point. You should be going in a straight line.

The run would be 7.

Now you make it a fraction/division problem

[tex]\frac{rise}{run} =\frac{-1}{7}[/tex]

-0.14285714285714285714285714285714 <- decimal value

-0.14

Depending on what it means by reduce, your answer will either be -1/7 or the decimal. Use the reduced decimal value if it's asking for a decimal

I've included a picture in case my explanation was not satisfactory or you need a visual.

Slope form:

Identify the two points

First one will be (-3,1)

Second one would be (4,0)

Now label them

-3 will be x1

1 is y1

4 is x2

0 is y2

You will be using [tex]\frac{y2-y1}{x2-x1}[/tex]

Put the values into the equation

[tex]\frac{0-1}{4--3} =\frac{0-1}{4+3} =\frac{-1}{7}[/tex]

You get the same thing as the previous way.

Same answer

Visuals also included

I hope this helps and don't be afraid to reach out with further questions!

Answer:

Explicit

Step-by-step explanation:

Given

[tex]Term: a_{50[/tex]

Required

Explicit or Recursive; which is easier

The explicit form is easier.

Take for instance, the explicit form of the sequence is:

[tex]a_n = 2n + 1[/tex]

And the recursive form is:

[tex]a_n = a_{n-1} + 2[/tex]

To find [tex]a_{50}[/tex] in [tex]a_n = 2n + 1[/tex]

You simply substitute 50 for n and then solve for [tex]a_n[/tex]

Which gives:

[tex]a_{50} = 2*50 + 1 = 101[/tex]

The case is different in: [tex]a_n = a_{n-1} + 2[/tex]

First, you substitute 50 for n

[tex]a_{50} = a_{50-1} + 2[/tex]

[tex]a_{50} = a_{49} + 2[/tex]

Next, you need to calculate a49.

This action continues until you get to a1

Then you evaluate the corresponding expressions from a1 to a49 before you get a50.

Hence, the explicit form is easier.

Answer:

1/-2

Step-by-step explanation:

To find the slope:

rise/run

From point to point

So....

From (-1,0)

you go up 2(2)

then left 4(-4)

to get to (-5,2)

so 2/-4 reduced is 1/-2

Answer:

Thanks for the points- but im a duma$s

Step-by-step explanation:

PLLSSS OMGG IM CRYINGG THE LITTLE HATT

Answer:

The answer is C. (-5, 14)

Answer:

All Real Numbers

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

According to the graph and function y = 2eˣ, we see that our x-values span from negative infinity to positive infinity. We also see that we can plug in any number x into our function:

(-∞, ∞)

or

All Real Numbers

Answer: D) all real numbers

Step-by-step explanation:

Answer:

x = -4

y = -1

Step-by-step explanation:

-2x - 9 = -5x - 21

3x - 9 = -21

3x = -12

x = -4

y = -2(-4) - 9

y = 8 - 9

y = -1

Answer:

x=−4 and y=−1

Step-by-step explanation:

I will solve your system by substitution.

y=−2x−9;y=−5x−21

Step: Solve y=−2x−9for y:

Step: Substitute−2x−9foryiny=−5x−21:

y=−5x−21

−2x−9=−5x−21

−2x−9+5x=−5x−21+5x(Add 5x to both sides)

3x−9=−21

3x−9+9=−21+9(Add 9 to both sides)

3x=−12

(Divide both sides by 3)

x=−4

Step: Substitute−4forxiny=−2x−9:

y=−2x−9

y=(−2)(−4)−9

y=−1(Simplify both sides of the equation)

Answer:

x=−4 and y=−1

Answer:

2.4 or 2[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

Let's set this up:

We have 3/1[tex]\frac{1}{4}[/tex]

That's also 3/1.25

For division, we don't divide if there is a fraction, so we move the decimal place over to the right for both the numbers

300/125

Then you long divide as normal:

And it's really hard to show how to long divide on a computer so I'm just going to go ahead and assume you know how to.

But the answer to that would be 2.4 or 2[tex]\frac{2}{5}[/tex]

Thank you, let me know if you have any questions.

Answer:

(A): As year increases the number of pikas reduces.

(B): As year increases the number of pikas increases as opposed to when the rate reduces.

Step-by-step explanation:

See comment for complete question

Given

[tex]a = 144[/tex] --- Initial Population

[tex]r = 8\%[/tex] --- rate

(A) WHEN THE RATE DECREASES

First, we need to write out the function when the population decreases.

This is given as:

[tex]f(x) = a(1-r)^x[/tex]

Substitute values for a and r

[tex]f(x) = 144(1-8\%)^x[/tex]

Convert % to decimal

[tex]f(x) = 144(1-0.08)^x[/tex]

[tex]f(x) = 144(0.92)^x[/tex]

Next, we calculate the average rate of change for both intervals using:

[tex]Rate = \frac{f(b) - f(a)}{b-a}[/tex]

For 1 to 5:

[tex]Rate = \frac{f(5) - f(1)}{5-1}[/tex]

[tex]Rate = \frac{f(5) - f(1)}{4}[/tex]

Calculate f(5) and f(1)

[tex]f(x) = 144(0.92)^x[/tex]

[tex]f(1) = 144*0.92^1 =144*0.92=132.48[/tex]

[tex]f(5) = 144*0.92^5 =144*0.66=95.04[/tex]

[tex]Rate = \frac{95.04 - 132.48 }{4}[/tex]

[tex]Rate = \frac{-37.44}{4}[/tex]

[tex]Rate = -9.36[/tex]

For 6 to 10:

[tex]Rate = \frac{f(10) - f(6)}{10-6}[/tex]

[tex]Rate = \frac{f(10) - f(6)}{4}[/tex]

Calculate f(6) and f(10)

[tex]f(x) = 144(0.92)^x[/tex]

[tex]f(6) = 144*0.92^6 =144*0.61=87.84[/tex]

[tex]f(10) = 144*0.92^{10} =144*0.43=61.92[/tex]

[tex]Rate = \frac{61.92-87.84}{4}[/tex]

[tex]Rate = \frac{-25.92}{4}[/tex]

[tex]Rate = -6.48[/tex]

So, we have:

[tex]Rate = -9.36[/tex] for year 1 to 5

This means that the number of pikas reduces by 9.36 yearly

[tex]Rate = -6.48[/tex] for year 6 to 10

This means that the number of pikas reduces by 6.48 yearly

So, we can say that, as year increases the number of pikas reduces.

(B) WHEN THE RATE INCREASES

First, we need to write out the function when the population decreases.

This is given as:

[tex]f(x) = a(1-r)^x[/tex]

Substitute values for a and r

[tex]f(x) = 144(1+8\%)^x[/tex]

Convert % to decimal

[tex]f(x) = 144(1+0.08)^x[/tex]

[tex]f(x) = 144(1.08)^x[/tex]

Next, we calculate the average rate of change for both intervals using:

[tex]Rate = \frac{f(b) - f(a)}{b-a}[/tex]

For 1 to 5:

[tex]Rate = \frac{f(5) - f(1)}{5-1}[/tex]

[tex]Rate = \frac{f(5) - f(1)}{4}[/tex]

Calculate f(5) and f(1)

[tex]f(x) = 144(1.08)^x[/tex]

[tex]f(1) = 144(1.08)^1 = 144*1.08= 155.52[/tex]

[tex]f(5) = 144(1.08)^5 = 144*1.47= 211.68[/tex]

[tex]Rate = \frac{211.68 - 155.52}{4}[/tex]

[tex]Rate = \frac{56.16}{4}[/tex]

[tex]Rate = 14.04[/tex]

For 6 to 10:

[tex]Rate = \frac{f(10) - f(6)}{10-6}[/tex]

[tex]Rate = \frac{f(10) - f(6)}{4}[/tex]

Calculate f(6) and f(10)

[tex]f(x) = 144(1.08)^x[/tex]

[tex]f(6) = 144(1.08)^6 = 228.52[/tex]

[tex]f(10) = 144(1.08)^{10} = 310.89[/tex]

[tex]Rate = \frac{310.89-228.52}{4}[/tex]

[tex]Rate = \frac{82.37}{4}[/tex]

[tex]Rate = 20.59[/tex]

So, we have:

[tex]Rate = 14.04[/tex] for year 1 to 5

This means that the number of pikas increases by 14.04 yearly

[tex]Rate = 20.59[/tex] for year 6 to 10

This means that the number of pikas increases by 20.59 yearly

So, we can say that, as year increases the number of pikas increases as opposed to when the rate reduces.