6. $80 is divided between Ethan and Michael such
that one quarter of Ethan's share is equal to one
sixth of Michael's share. How much does each of
them receive?

Answer:

Approximately [tex]101\; \rm ft[/tex] (assuming that the height of the base of the hill is the same as that of the observer.)

Step-by-step explanation:

Refer to the diagram attached.

Angles:

Let the length of segment [tex]\rm BR[/tex] (vertical distance between the base of the tree and the base of the hill) be [tex]x\; \rm ft[/tex].

The question is asking for the length of segment [tex]\rm AB[/tex]. Notice that the length of this segment is [tex]\mathrm{AB} = (x + 20)\; \rm ft[/tex].

The length of segment [tex]\rm OB[/tex] could be represented in two ways:

For example, in right triangle [tex]\rm \triangle OBR[/tex], the length of the side opposite to [tex]\angle \rm B\hat{O}R = 51^\circ[/tex] is segment [tex]\rm BR[/tex]. The length of that segment is [tex]x\; \rm ft[/tex].

[tex]\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}[/tex].

Rearrange to find an expression for the length of [tex]\rm OB[/tex] (in [tex]\rm ft[/tex]) in terms of [tex]x[/tex]:

[tex]\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}[/tex].

Similarly, in right triangle [tex]\rm \triangle OBA[/tex]:

[tex]\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}[/tex].

Equate the right-hand side of these two equations:

[tex]0.810\, x \approx 0.649\, (x + 20)[/tex].

Solve for [tex]x[/tex]:

[tex]x \approx 81\; \rm ft[/tex].

Hence, the height of the top of this tree relative to the base of the hill would be [tex](x + 20)\; {\rm ft}\approx 101\; \rm ft[/tex].

Answer: There are 20 years in a score. The year he is talking about is 1776

Step-by-step explanation:

Answer:

9425912.111

Step-by-step explanation:

Answer:

9425912.111

Step-by-step explanation:

Answer:

52 , 165 , 173 is Pythagorean triple.

Step-by-step explanation:

Pythagorean triple;

a² + b² = c²

Computation:

88² + 105² ≠ 139²

39² + 80² ≠ 119²

38² + 198² ≠ 202²

52² + 165² = 173²

So,

52 , 165 , 173 is Pythagorean triple.

Answer:

1) intersection of both lines is the solution: (-3, 1)

2) y = -1/6x + 1 will produce a perpendicular line and intersect at only one point  (slopes of 6 and -1/6 are opposite and reciprocal, thereby producing perpendicular lines)

3) 'b' can be any value except 1

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

16 x 100 = 1600

1600 / 40 = 40.0

Answer:

A. 40.0

Step-by-step explanation:

9514 1404 393

Answer:

  24

Step-by-step explanation:

The product of lengths from the point where the secants meet to the near and far circle intersection points is the same for both secants.

  RQ·RC = RS·RT

  8(27) = (3x)(8x)

  9 = x^2 . . . . . . . . . divide by 24

  3 = x

Then the length of interest is ...

  TR = 8x = 8·3

  TR = 24

Answer:

a) 9 inches

is correct answer for you

Answer:

C, 25

Step-by-step explanation:

3 x 5 = 15

5 x 5 = 25

Answer:

the answer is the third option (C)

Answer:

mLNM=63

Step-by-step explanation:

triangle JKL is isocelese so mKJL and KLJ are the same

180-72=108

108/2=54

so both mKLJ and mMLN are equal

and since triangle LMN is an isoceles then mLNM and mLMN are equal to each other

so 180-54=126

126/2=63

mLNM=63

holdig several tools because he do someting or she :

I think is a person

Step-by-step explanation:

Answer:

[tex]\boxed {\boxed {\sf 74}}[/tex]

Step-by-step explanation:

The nth term of an arithmetic sequence can be found using the following formula.

[tex]a_n=a_1+(n-1)d[/tex]

Where n is the term, a₁ is the first term, and d is the common difference.

We want to find the 21st term, we know the first term is -6, and the common difference is 4.

[tex]n= 21\\a_1= -6 \\d=4[/tex]

Substitute the values into the formula.

[tex]a_{21}=-6+(21-1)4[/tex]

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Solve inside the parentheses.

[tex]a_{21}=-6+(20)4[/tex]

Multiply 20 and 4.

[tex]a_{21}= -6+80 \\[/tex]

Add -6 and 80.

[tex]a_{21}=74[/tex]

The 21st term of the sequence is 74

Answer:

Here we will use the formula

[tex] \tt \: a_n \: = a_1 +( n - 1)\: \times d[/tex]

[tex] \tt\: a_{21} = −6+(21−1)4[/tex]

By using PEMDAS

[tex] \tt \: a_{21} = - 6 + (20)4[/tex]

[tex] \tt \: a_{21} \: = - 6 + 80 = 74[/tex]

[tex] \huge \tt \bigodot \: \: 74[/tex]

Answer:

y=2/5x + 2

Step-by-step explanation:

find slope by using formula between these two points: (0,2) and (-5,0); then put into slope-intercept form (y=mx+b)

Answer:

A

Step-by-step explanation:

Answer:

c is the correct answer

Step-by-step explanation:

Answer:

Correct Answer is B

Step-by-step explanation:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (−3,−10)

Focus: (−3,−[tex]\frac{39}{4}[/tex])

Axis of Symmetry: x = −3

Directrix: y = −[tex]\frac{41}{4}[/tex]

x               y

-5             -6

-4             -9

-3            -10

-2             -9

-1              -6

Answers:

1.) -x - 5

2.) 11x^2 + 5x

3.) 13x + 2y +3y^2

4.) -12x - 2

5.) -24

Sorry, it won’t somehow let me attach a picture of my work on paper :(

But hopefully this helps! :)

Answer:

2) Seems like 11x² +9x , 6) seems like 42

Step-by-step explanation:

Group the ones with the same variables :

3x²t8x²-2x+7x

Then add or subtract the ones with same variables from the left :

3x²+8x²=11x²

2x+7x = 9x

therefore; 11x²-9x

Answer:

translation

W(-10, 0)

X(-10, -8)

Y(-18, -4)

Z(-14, 8)

dilation

W(-8, 16)

X(-8, 0)

Y(-24, 8)

Z(-16, 32)

Step-by-step explanation:

In translation, all you are doing is taking each point and subtracting 6 from the x, and subtracting 8 from the y. The point of W is (-4, 8). Thus you do (-4 - 6 , 8-8) and you get the new point (-10,0). Repeat this for all the others.

In dilation you are multiply both x and y by 2. For point W you do (-4*2, 8*2) to get the new point (-8, 16). You repeat this for the remaining points.

please give thanks by clicking the heart button :)

Answer:

20 :3

Step-by-step explanation:

Answer:

lol currently I'm at 14, good job! I hope you have a good day, stay safe, and Happy holidays!

Step-by-step explanation:

Answer:

r=ln3/10

Step-by-step explanation:

The daily rate is given by 3 to the power x divided by 10.

We have given that a sample of bacteria is growing at a continuously compounding rate.

The sample triples in 10 days.

The daily rate of the bacteria growth is. exponential growth is in the form

y = abˣ

where y, x are variables.

a is the initial value

Sample triples, in 10 days. therefore the value of b=3.

Therefore we get,

[tex]y=3a^{\frac{x}{10}[/tex]

[tex]y=a3^{\frac{x}{10}[/tex]

Therefore the daily rate is given by [tex]3^{\frac{x}{10}[/tex].

To learn more about the daily rates visit:

https://brainly.com/question/25793394

Answer:

4(x + 15)

Step-by-step explanation:

1/2x - 1/2x = 0

You're then left with 4x + 60

Factor out the 4 and you get 4(x + 15)

Answer: ITS C.

Step-by-step explanation: It’s not B I took the test and put C and got it right

Answer:

150 in

Step-by-step explanation:

Answer:

120/2 = x/5....120 miles to 2 hrs = x miles to 5 hrs

cross multiply

(2)(x) = (120)(5)

2x = 600

x = 600/2

x = 300....the motorcyclist would travel 300 miles in 5 hrs

or u could do it this way..

120/2 = 60 miles per hr

60 * 5 = 300 miles

Step-by-step explanation:

Answer:

0.75 - 0.8

Step-by-step explanation:

4.5/6 = 0.75

The closest number to round 0.75 to is 0.8

We are given the expression:

4.5 / 6

Simplifying the given expression:

We can rewrite 4.5 as 4/10:

[tex]\frac{45}{10}*\frac{1}{6}[/tex]

Since 45 and 6 have a common factor: 3

[tex]\frac{3*15}{10}*\frac{1}{3*2}[/tex]

The 3 in the numerator and the denominator will cancel out:

[tex]\frac{15}{10}* \frac{1}{2}[/tex]

We know that 15/2 is 7.5

[tex]\frac{7.5}{10}[/tex]

0.75

Hence, the quotient of the expression: 4.5/6 is 0.75

Answer:

no because its supposed to be 24j-36

Step-by-step explanation:

so basically im trying to say is that they did the problem wrong.

Answer:

6x^2+40x

Step-by-step explanation:

2x(3x+20)

6x^2 +40x

That's your answer. you won't be able to find x

Answer:

-25 + 75 = 50

Step-by-step explanation:

Since we don't know the value of the bar, we will call it x.

-25 + x = 50

Add 25 to both sides to find the value of x.

x = 75

You can also double check this answer by doing simple math.

-25 + 75 = 50

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The calculation can be done by any method that adds 6% of the original salary to the original salary. That's equivalent to multiplying the original salary by 1.06 or 106%. The attachment shows some possibilities.

Answer:

_+_+_+_+_+_+_+_+_+_+_+_+_+_+_+_+_

Step-by-step explanation:

Answer:

3)   (4, 2)

Step-by-step explanation:

The point of intersection of the lines is the solution. That point is (4, 2).

Answer: 3)   (4, 2)

Answer:

the answer is the third one (4, 2)

Step-by-step explanation:

the solution to a system of equations is always where they intersect. in this case, the two lines intersect at (4, 2), which means that the solution is (4, 2).

hope this helped!! :D

Answer:

Explained below.

Step-by-step explanation:

The scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida are,

Season 1: {75, 79, 80, 78, 76, 74, 76, 78}

Season 2: {72, 71, 76, 78, 86, 81, 72, 80}

(a)

Compute the mean and standard deviation of the golfer's scores as follows:

Season 1:

[tex]\bar x_{1}=\frac{1}{n_{1}}\sum x_{1}\\\\=\frac{1}{8}\times 616\\\\=77[/tex]

[tex]s_{1}=\sqrt{\frac{1}{n-1}\sum(x_{1}-\bar x_{1})^{2}}\\\\=\sqrt{\frac{1}{8-1}\times 30}\\\\=2.0702\\\\\approx 2.07[/tex]

Season 2:

[tex]\bar x_{2}=\frac{1}{n_{2}}\sum x_{2}\\\\=\frac{1}{8}\times 616\\\\=77[/tex]

[tex]s_{2}=\sqrt{\frac{1}{n_{2}-1}\sum(x_{2}-\bar x_{2})^{2}}\\\\=\sqrt{\frac{1}{8-1}\times 194}\\\\=5.26444\\\\\approx 5.26[/tex]

(b)

The primary difference in performance between the two seasons is:

[tex]\text{Diff} = \bar x_{2}-\bar x_{1}\\\\=5.26-2.07\\\\=3.19[/tex]