Fiona is standing 26 meters from the base of an oak tree. If she measures the angle of elevation to the top of the tree to be 37 degrees, how tall is the tree? Estimate your answer to two decimal places.

Answer:

Option C. [tex]sin(\theta)=-\frac{\sqrt{33}}{7}[/tex] , [tex]tan(\theta)=-\frac{\sqrt{33}}{4}[/tex]

Step-by-step explanation:

we know that

If cosine of angle theta is positive  then angle theta belong to the I or IV quadrant

and

If co secant of angle theta is negative then angle theta belong to the III or IV quadrant

therefore

angle theta belong to the IV quadrant (common solution)

Part 1) Find [tex]sin(\theta)[/tex]

we know that

[tex]sin^{2} (\theta)+cos^{2} (\theta)=1[/tex]

we have

[tex]cos(\theta)=4/7[/tex]

substitute the value

[tex]sin^{2}(\theta)=1-(4/7)^{2}[/tex]

[tex]sin^{2}(\theta)=1-(16/49)[/tex]

 [tex]sin^{2}(\theta)=(33/49)[/tex]

[tex]sin(\theta)=-\frac{\sqrt{33}}{7}[/tex] ----> is negative because the angle belong to the IV quadrant

Part 2) Find [tex]tan(\theta)[/tex]

we know that

[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]

we have

[tex]sin(\theta)=-\frac{\sqrt{33}}{7}[/tex]

[tex]cos(\theta)=4/7[/tex]

substitute the values

[tex]tan(\theta)=\frac{-\frac{\sqrt{33}}{7}}{4/7}[/tex]

[tex]tan(\theta)=-\frac{\sqrt{33}}{4}[/tex]

Divide 7.8 by 1.18:

7.8 / 1.18 = 6.61 = 6.6 rounded to the nearest tenth.

When you divide scientific notation, subtract the exponents: 20 - 13  =7

The answer becomes 6.6 x 10^7

Division is one of the four fundamental arithmetic operations. The number of times the milk way is wider than the solar system is 6.61 × 10⁷.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that our solar system is 1.18 × 1013 meters in diameter, and the Milky Way galaxy is 7.8 × 1020 meters in diameter. Therefore, the number of times the milk way is wider than the solar system is,

Number of times = (Diameter of MIlky way)/(Diameter of Solar System)

                            = 7.8 × 10²⁰ meters/ 1.18 × 10¹³ meters

                            = 6.61 × 10⁷

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Answer:

Step-by-step explanation:

Yesterday, her rate was 8mph, her time was x hours.

Today, her rate was 13mph, her time was 13 - x hours.

So the total distance she biked on the two days is

d = 8x + 13(13 - x), or 169 - 5x

Answer:

[tex]8x+13(9-x)[/tex] or [tex]-5x+117[/tex] miles.

Step-by-step explanation:

Let x represent number of hours Carmen biked yesterday.

[tex]\text{Distance}=\text{Speed}\times \text{Time}[/tex]

We have been given that yesterday Carmen's average speed was 8

miles per hour. So distance covered in x hours would be [tex]8x[/tex].

We are also told that Carmen biked for a combined total time of 9

hours. So the number of hours biked second day would be [tex]9-x[/tex]. The distance covered in [tex]9-x[/tex] at a speed of 13  miles per hour would be [tex]13(9-x)[/tex].

Total distance covered by Carmen would be: [tex]8x+13(9-x)[/tex]

[tex]8x+117-13x[/tex]

[tex]8x-13x+117[/tex]

[tex]-5x+117[/tex]

Therefore, the total distance covered by Carmen in the two days would be [tex]-5x+117[/tex] miles.

Answer: 6 teaspoons of sugar

Step-by-step explanation: Create a proportion

4 ounces of frosting = 2 teaspoons of sugar

8 ounces of frosting = 4 teaspoons of sugar

12 ounces of frosting = 6 teaspoons of sugar

To make 12 ounces of frosting, you would need 6 teaspoons of sugar.

To find out how much sugar is needed to make 12 ounces of frosting, we can set up a proportion using the given information. The recipe calls for 2 teaspoons of sugar for 4 ounces of frosting. We can set up the proportion: 2 teaspoons / 4 ounces = x teaspoons / 12 ounces.

To solve the proportion, we can cross multiply and divide. So, (2 teaspoons)(12 ounces) = (4 ounces)(x teaspoons). This simplifies to 24 = 4x. Dividing both sides by 4, we find that x = 6 teaspoons.

Therefore, you would need 6 teaspoons of sugar to make 12 ounces of frosting.

he has 84 hockey cards total

Answer:

no solution

Step-by-step explanation:

Given

- 3 | 6n - 2 | + 5 = 8 ( subtract 5 from both sides )

- 3 | 6n - 2 | = 3 ( divide both sides by - 3 )

| 6n - 2 | = - 1

The absolute value always returns a positive value and so

| 6n - 2 | ≠ - 1

Hence there is no solution to the equation

The second one should be it

I’m not sure bc I’m going off of my head

find the radius:

r = C/2pi

r= about 7 (6.99645)

find the area:

A = pi(r)^2

A = about 153.78194 inches^2

Answer: The area of the circle in inches is A= 153.64 inches²

Step-by-step explanation:

This problem bothers on the calculations on shapes

In this Case a circle

The circumference of a circle is given by

C=2πr

Given that C =43.96 inches

We need to solve for the radius, because we also need the radius to solve for the area

43.96= 2*3.142*r

43.96=6.284r

r= 43.96/6.284

r=6.99 inches

Now back to the area of a circle which is given by

A=πr²

Substituting our value for Pi we have

A= 3.142*6.99²

A=3.142*48.89

A= 153.64 inches²

Answer:

Step-by-step explanation:

A diameter of a rhombus is an angle bisector. Therefore we have the equation:

[tex]3x-11^o=x+23^o[/tex]              add 11° to both sides

[tex]3x=x+44^o[/tex]                subtract x from both sides

[tex]2x=44^o[/tex]             divide both sides by 2

[tex]x=22^o[/tex]

h = 12.

See the attached picture:

Answer:

23 Cards were given to your brother.

Step-by-step explanation:

12 + 24 = 36

36 - 13 = 23

Answer:

you gave him 23 cards

Step-by-step explanation:

12+24=36, 36-13=23

Answer:

3rd group of possible answers is the correct set

Step-by-step explanation:

Each of the three points in the 3rd line of possible answers is a solution of the given equation, as can be verified by substitution:

If x = -2, y = -8(-2) = +16

If x = 3, y = -8(3) =  -24

If x = -4, y = -8(-4) = +32

Answer:

c

Step-by-step explanation:

Answer:

The slope is undefined

Step-by-step explanation:

x = -4 is a vertical line.  Slope is defines as the change in y divided by the change in x.  

(change in y)/(change in x)

All the points on this line have the same x value, so the change in x is zero.  This means we have

(change in y)/0, which is undefined.

Answer:

UNDEFINED

Step-by-step explanation:

Any initial value set to equal x is considered an undefined rate of change [slope], which is a vertical line.

I am joyous to assist you anytime.

Answer:

[tex]\large\boxed{x=\dfrac{27}{2}\to x=13\dfrac{1}{2}\to x=13.5}[/tex]

Step-by-step explanation:

[tex]\dfrac{2}{3}x-2=7\qquad\text{add 2 to both sides}\\\\\dfrac{2}{3}x-2+2=7+2\\\\\dfrac{2}{3}x=9\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{2}{3\!\!\!\!\diagup_1}x=3\cdot9\\\\2x=27\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{27}{2}\\\\x=\dfrac{27}{2}\to x=13\dfrac{1}{2}\to x=13.5[/tex]

Answer:

Ella's Grade: 15

Minh's Grade: 16

Step-by-step explanation:

If each grade has 20 girls in the grade, then that implies effectively that the ratios would apply via fractions, which are 3:4 and 4:5. As such, take both Fractions and increase them both to 20: 15:20 and 16:20.

The number of boys in Ella's grade is 15 and Minh's grade is 16

Given that,

The ratio of  boys to girls in Ella's grade is 3:4

And the ratio of  boys to girls in Minh's grade is 4:5

The total number of girls is 20

Computation:

Let the number of boys be [tex]x[/tex]

So in the case of  Ella's,

[tex]\frac{3}{4}=\frac{x}{20}\\x=\frac{20\times3}{4}\\x=15[/tex]

And in case of Minh's,

[tex]\frac{4}{5}=\frac{x}{20}\\x=\frac{20\times4}{5}\\x=16[/tex]

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Answer: form by math and can multiply two numbers or divide your choice

Step-by-step explanation:

Answer:

Step-by-step explanation:

r = [tex]\frac{a_n}{a_{n-1}} = \frac{896}{3584} =  \frac{1}{4}[/tex]

Using the geometric series formula for the nth term:

[tex]S_n = a \cdot \frac{1-r^n}{1-r} => S_{6} = 3584 \cdot \frac{1 - (\frac{1}{4})^{6} }{1 - \frac{1}{4} }  = 4777\frac{1}{2}[/tex]

Final answer:

The equation for the nth term of the geometric sequence is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio. The sixth term of the sequence is 14.

Explanation:

The given sequence is a geometric sequence. In a geometric sequence, each term is found by multiplying the previous term by a common ratio. To find the equation for the nth term of the geometric sequence, we need to find the common ratio. We can do this by dividing any term in the sequence by the previous term.

For example, dividing the second term 896 by the first term 3584 gives us a common ratio of 1/4.

So, the equation for the nth term of the sequence is:

an = a1 × r(n-1)

where a1 is the first term and r is the common ratio.

To find the sixth term, we can substitute n = 6 into the equation:

a6 = 3584 × (1/4)(6-1)

a6 = 3584 × (1/4)5

a6 = 14

5y+2x=10y=−25x+2246810−2−4−6−8−10246810−2−4−6−8−10Let's solve for x.5y+2x=10Step 1: Add -5y to both sides.2x+5y+−5y=10+−5y2x=−5y+10Step 2: Divide both sides by 2.2x2=−5y+102x=−52y+5Answer:x=−52y+5

Do make the intercepts twice as big, you simple divide the function by 2, but leave it =10.

The function 5y+2x=10 has intercepts (0,2) and (5,0)

Therefore by dividing by 2 we get 2.5y+x=10 which is your answer. It has intercepts (0,4) and (10,0)

Slope = (y2-y1)/(x2-x1)

Slope = (3-2)/(4-0)

Slope = 1/4

Answer:

[tex]\large\boxed{the\ slope=\dfrac{1}{4}}[/tex]

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have (0, 2) and (4, 3). Substitute:

[tex]m=\dfrac{3-2}{4-0}=\dfrac{1}{4}[/tex]

Answer:

  y = 116

Step-by-step explanation:

The central angle is double any inscribed angle that intercepts the same arc.

Inscribed angle HGF intercepts arc HF, so central angle HOF will be double the value of HGF.

  2×58° = 116° = y°

  y = 116

Answer:

It can't be simplified.

Answer:

For a unique solution, there must be as many consistent, independent equations as there are variables.

Step-by-step explanation:

Each equation lets you write an expression for one variable in terms of the others in that equation. That expression can be substituted throughout the system, reducing the number of equations and variables by one each.

After n-1 such substitutions in a system of n equations, there will be one equation left. If that is an equation in one variable, then the solution to the system can be easily found. If more than one variable remains (> n variables in n equations), then the system cannot be solved for definitive values of each of the variables.

___

If the equations are inconsistent, there is no solution. If the equations are dependent, then there is no unique solution.

To solve a system of linear equations, one generally requires the same number of equations as there are variables for a unique solution, otherwise the system may have either an infinite number of solutions or none.

To solve a system of linear equations, you generally need as many equations as there are variables. If you have two variables, you should have two linear equations to find a unique solution. For example, the equations 3x - 2y = 24 and 3x + 9y = 30 form a system that can be solved because there are two equations with two variables (x and y).

If there are more variables than equations, then you may either have infinitely many solutions or no solution, depending on the equations' consistency. If you have fewer equations than variables, as in the case of three variables with only two equations, you typically have an undetermined system where you can choose one variable as a parameter and express the others in terms of it, leading to an infinite number of solutions.

For homogeneous equations where the vector b is zero (Ax = 0), the solutions form a subspace of the vector space, and nontrivial solutions exist if the system is not of full rank.

Answer:

The correct option is D) All real numbers.

Step-by-step explanation:

Consider the provided function.

Range: Range is the set of output value produce by the function, or the range is the set of all possible y values.

Now consider the provided graph of the function.

The graph of the function is a straight line and function produces the positive and negative value of y.

By interpreting the graph it can be concluded the the range of the function is all real numbers.

Thus, the correct option is D) All real numbers.

➷ The data set is not approximately periodic

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Answer:

Step-by-step explanation:

The given data doesn't show any periodic pattern, the change is not constant, and it doesn't simulate any simple pattern because the increase is like random, the first increase is for 1.35, the second is for 0.13, the third one is for 0.65, it doesn't show any periodic behaviour.

In addition, the variables involved aren't periodic, because it's about stocks, which it changes randomly.

Therefore, the right answer is the first option.

Answer:

You cant solve this without one more number.

Step-by-step explanation:

You need the length of the blue piece because it could be smaller or larger at this point. I may be wrong but unless I am missing something, and I totally might be if this is a kind of math I've never done, then please feel free to ignore me :) and have a lovely day!

Answer:

The area of the triangle = 31.5 feet² ⇒ answer (c)

Step-by-step explanation:

∵ Area of any Δ = 1/2 (side 1)(side 2)(sin the angle between them)

∴ The area of the Δ = 1/2 (b)(c) sin(∠A)

∵ b = 11 feet

∵ c = 10 feet

∵ m∠A = 35°

∴ Area of the Δ = 1/2 (11)(10) (sin(35)) = 31.547 feet²

∴ The area of the triangle = 31.5 feet²

∴ The answer is (c)

Graph of constant function is a horizontal line

It’s a horizontal line because all of the x’s must be different

Answer:

56 in.

Step-by-step explanation:

By proportion  8/5 = L/35  where L is the length of the picture.

5L = 8*35

L = 8*35/5

L = 56 in.

The length of a similar picture frame is Option (a) 56 in.

The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. A ratio indicates how many times one number contains another. It is expressed as a:b where a and b are parameters for any given set of relation.

Given length to width ratio is 8:5.

We have to find the length of similar picture frame which has a width of 35 inches.

Let length of the picture frame be L inches.

Using ratio equation for solving, we have

   8:5 = L:35

⇒ 8/5 = L/35

∴  L = (8/5) * 35 = 56 inches.

Therefore the length of a similar picture frame is Option (a) 56 in.

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Answer:

16 pounds

Step-by-step explanation:

Total cereal she ate = 256 ounces

How many pounds she ate = ?

Given that (16 ounces = 1 pound)

Therefore, we have to divide the total ounces by 16 to calculate the cereal she ate in pounds = 256/16 = 16 pounds

Answer:

A. 16

Step-by-step explanation:

It’s a if the quotation is bigger than the dividend the answer is just a mixed number