the angle of elevation of the top of a tree from a point 27m away on the same horizontal ground as the foot on the tree is 30 degrees .find the height of the tree.

Answer:

A

Step-by-step explanation:

Here in this question, we want to select which of the options particularly represents what was given in the question.

Mathematically 10^4 means that we are raising 10 into a continued exponential raising up to 4 times.

So 10^4 is pronounced as the first option in the question.

10 raised to power 10 , raised to power 10 etc

Answer:

second option

Step-by-step explanation:

Answer:

to find the slope of a linear function, there is only one formula

this formula requires two points, which are stated in tables and graphs alike

these points do not need to be one after the other as it is slope and slope predicts what the next point graphed will be.

Formula for Slope:

this should help. take any two points and substitute for each; y values in the correct spots and x values in their correct spots

make sure to put the values of second point where it is labelled y2 and x2 And make sure to substitute first point values in those labelled y1 and x1

It is important to remember that if this becomes a fraction, SIMPLIFY

We can write the slope of the function as -

{m} = (9 - 5)/(4 - 0).

A function is a relation between a dependent and independent variable. We can write the examples of function as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is a table for the function as -

{x}   0   4

{y}   5   9

We can write the slope of the function as -

{m} = (9 - 5)/(4 - 0)

Therefore, we can write the slope of the function as -

{m} = (9 - 5)/(4 - 0).

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Answer:

  B. 18.6

Step-by-step explanation:

The 'rule of 69' says the value will be doubled in 69/i years, where i is the annual interest rate in percent (compounded continuously). The interest rate is given as 3.7%, so the prediction is

  n = 69/3.7 = 10.649

  n ≈ 10.6

Answer:

[tex]AB = 10 units[/tex]

Step-by-step explanation:

The line of segment AB can be calculated using distance formula, [tex] d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} [/tex] , to calculate the distance between point A(6, 2) and point B(0, 10).

A(6, 2) can be (x1, y1),

B(0, 10) can be (x2, y2)

[tex] d = \sqrt{(0 - 6)^2 + (10 - 2)^2} [/tex]

[tex] d = \sqrt{(-6)^2 + (8)^2} [/tex]

[tex] d = \sqrt{36 + 64} [/tex]

[tex] d = \sqrt{100} [/tex]

[tex] d = 10 [/tex]

Answer:

Transformed   [tex]\,\,f(x)= -3\,(x-1)^2[/tex]

Step-by-step explanation:

The process of shifting the graph of the function 1 unite to the right can be obtained by subtracting 1 to the x-coordinate in the expression of the function:

[tex]f(x)=x^2\\new\,f(x) =(x-1)^2[/tex]

The process of stretching vertically the function, would be accomplished by multiplying now the full function by "3":

[tex]new \,\,f(x)= 3\,(x-1)^2[/tex]

the reflection over the x-axis is obtained by multiplying the full function by the constant "-1":

[tex]new \,\,f(x)= -3\,(x-1)^2[/tex]

Answer:

the width is 17.5 feet and the length is 82.5 feet.

Step-by-step explanation:

The house has a rectangular shape and we know that the length is 5 feet less than 5 times the width.

We will call the width x, thus, the length would be represented as 5x-5 (5 less than 5 times the width).

Since Darrin is going to hang garland around the perimeter of the house, we know that the perimeter is 2 times the length plus two times the width and this equals 200.

Let's write this in algebraic form

[tex]width = x\\length= 5x-5\\Perimeter= 2width +2length=200\\200=2(x)+2(5x-5)\\200=2x+10x-10\\200=12x-10\\200+10=12x\\210=12x\\210/12=x\\x=17.5[/tex]

Therefore, the width is 17.5 feet.

Now, the length is 5x-5, thus substituting the 17.5 in this equation we have:

[tex]5x-5=5(17.5)-5=87.5-5=82.5[/tex] feet

Therefore, the width is 17.5 feet and the length is 82.5 feet.

Answer:

0.5346

Step-by-step explanation:

Find the z-scores.

z = (x − μ) / σ

z₁ = (89 − 100) / 15

z₁ = -0.73

z₂ = (111 − 100) / 15

z₂ = 0.73

Find the probability.

P(-0.73 < Z < 0.73)

= P(Z < 0.73) − P(Z < -0.73)

= 0.7673 − 0.2327

= 0.5346

Answer:

2:5

Step-by-step explanation:

The structure of a ratio is x:y.

So all you have to do is place the former as the first digit and the latter as the second and separate them by a colon.

Answer:

64.08

Step-by-step explanation:

3^16.90+1*20.50-7.12

Answer:

6n or 6 x n

Step-by-step explanation:

Answer:

-2/3

Step-by-step explanation:

We have two points ( 0,3) and ( 3,1)

We can use the slope formula

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

  = (1-3) /(3-0)

   = -2/3

Answer:

-2/3

Step-by-step explanation:

Two points are given on the graph:

(0, 3) and (3, 1)

Use slope formula.

m = rise/run

m = (y₂ - y₁)/(x₂ - x₁)

x₁ = 0

y₁ = 3

x₂ = 3

y₂ = 1

m = (1 - 3)/(3 - 0)

m = -2/3

The slope of the line is -2/3.

Answer:

Step-by-step explanation:

When events are independent, the probability of some sequence of them is the product of the probabilities of the individual events in that sequence.

The probability of a child having spina bifida is 16% = 0.16, so the probability that the child will not have the condition is 1 - 0.16 = 0.84. The probability that 0 of 2 children will have spina bifida is ...

  p(0 for 2) = p(0 for 1)×p(0 for 1) = 0.84×0.84 = 0.7056

__

There are two ways that 1 of 2 children can have spina bifida: either the first one does, or the second one does. These are mutually exclusive conditions, so their probabilities add:

  p(1 for 2) = p(1 for 1)×p(0 for 1) +p(0 for 1)×p(1 for 1) = 0.16×0.84 +0.84×0.16

  p(1 for 2) = 0.2688

__

There is one way both children can have spina bifida:

  p(2 for 2) = p(1 for 1)×p(1 for 1) = 0.16×0.16 = 0.0256

__

In summary, our probability distribution is ...

  p(X=0) = 0.7056

  p(X=1) = 0.2688

  p(X=2) = 0.0256

Answer: The lines are parallel.

The slopes are equal.

The y-intercepts are different.

The system has no solution.

Step-by-step explanation:

For  a pair of equations: [tex]a_1x+b_1y=c_1\\\\a_2x+b_2y=c_2[/tex]

They coincide if [tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}[/tex]

They are parallel if [tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}[/tex]

They intersect if [tex]\dfrac{a_1}{a_2}\neq\dfrac{b_1}{b_2}[/tex]

Given equations: [tex]8 x + 10 y = 30\\ 12 x + 15 y = 60[/tex]

Here,

[tex]\dfrac{a_1}{a_2}=\dfrac{8}{12}=\dfrac{2}{3}\\\\ \dfrac{b_1}{b_2}=\dfrac{10}{15}=\dfrac{2}{3}\\\\ \dfrac{c_1}{c_2}=\dfrac{30}{60}=\dfrac{1}{2}[/tex]

⇒[tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}[/tex]  

Hence, The lines are parallel.

It has no solution. [parallel lines have no solution]

Write 8 x + 10 y = 30 in the form of y= mx+c, where m is slope and c is the y-intercept.

[tex]y=-\dfrac{8}{10}x+\dfrac{30}{10}\Rightarrow\ y=-0.8x+3[/tex]

i.e. slope of 8 x + 10 y = 30 is -0.8 and y-intercept =3

Write  12 x + 15 y = 60 in the form of y= mx+c, where m is slope

[tex]y=-\dfrac{12}{15}x+\dfrac{60}{15}\Rightarrow\ y=-0.8x+4[/tex]

i.e. slope of  12 x + 15 y = 60 is -0.8 and y-intercept =4

i.e. The slopes are equal but y-intercepts are different.

Answer: The lines are parallel.

The slopes are equal.

The y-intercepts are different.

The system has no solution.

Step-by-step explanation:

For  a pair of equations:  

They coincide if  

They are parallel if  

They intersect if  

Given equations:  

Here,

⇒  

Hence, The lines are parallel.

It has no solution. [parallel lines have no solution]

Write 8 x + 10 y = 30 in the form of y= mx+c, where m is slope and c is the y-intercept.

i.e. slope of 8 x + 10 y = 30 is -0.8 and y-intercept =3

Write  12 x + 15 y = 60 in the form of y= mx+c, where m is slope

i.e. slope of  12 x + 15 y = 60 is -0.8 and y-intercept =4

i.e. The slopes are equal but y-intercepts are different.

Answer:

k+2 or k=2

Step-by-step explanation:

combine -5 and 7 to get your answer

Answer:

K+2

Step-by-step explanation:

K - 5 + 7 ....add -5 and 7

K+2

Answer:

The length of segment A'E' is 5 units

Explanation:

From the included graph the coordinates of the points A and E, in the pentagon ABCDE with reference to point A are;

A- (0, 0)

E- (0, 2)

The length of the segment AE = √((2-0)² + (0 - 0)²) = √2² = 2

When a pentagon ABCDE is dilated to pentagon A'B'C'D'E' with a scale factor of 5/2, we have;

Length of segment A'E' = 5/2 × Length of segment AE

Therefore;

Length of segment A'E' = 5/2 ×2 = 5 units.

The length of segment A'E' is 5 units.

This question is based on distance formula.The length of segment A'E' is 5 units.

Given:

Pentagon A’B′C′D′E’, is the image of pentagon ABCDE under a dilation with a scale factor of 5/2.

From the given  graph, the coordinates of the points A and E, in the pentagon ABCDE with reference to point A are;

A- (0, 0)

E- (0, 2)

The length of the segment AE = [tex]\sqrt{(2-0)^{2} +(0-0)^{2} }=\sqrt{2^{2} } =2[/tex]

When a pentagon ABCDE is dilated to pentagon A'B'C'D'E' with a scale factor of 5/2, we have;

Length of segment A'E' = 5/2 × Length of segment AE

Therefore;

Length of segment A'E' = 5/2 ×2 = 5 units.

Therefore, the  length of segment A'E' is 5 units.

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Answer: rotate 180 degrees and reflection across the line y=2

Step-by-step explan

Answer:

Step-by-step explanation:

Answer:

Our system of equations is:

We are looking for x

Let's express y using x

Replace x in the second equation with the result

4x²+20x+3=0 is a quadratic equation

Let Δ be our discriminant

Δ= 20²-4*4*(-3)

Δ=448 > 0 so we have two solutions for x

let x and x' be the solutions

so the solutions are:

-5.15 and 0.15

Answer:

B. 1296 in.^2

Step-by-step explanation:

The rectangles are similar, and sides ST and YZ are corresponding sides.

The linear scale factor is k = YZ/ST = 24/8 = 3

The area scale factor is k^2 = 3^2 = 9

A = 144 sq in. * k^2 = 144 sq in. * 9 = 1296 sq in.

Answer: B. 1296 in.^2

Answer:

4)1,296in^2

5)510.4ft

Step-by-step explanation:

4)

24/8=3 This is the dilation

144/8=18 This is the side length for QRST

18*3=54 The side length for WXYZ

24*54=1296 The area of WXYZ

5)

319*8/5 Your fence with a scale factor of 8/5

319*1.6 Changing 8/5 into fraction form

319*1.6=510.4 The length of the friend's fence.

Hope this helps. I could not see the end of the last question so I am sorry if it is not written properly.

Have a good day!

Answer:

For numerator

2sin(2∅)=2(2sin∅cos∅)

For Denominator

(1+cos(2∅))(1+tan²∅)

=(1+cos(2∅))(sec²∅)

=(1+cos²∅-sin²∅)(sec²∅)

Recall. 1-sin²∅=cos²∅

=2cos²∅(sec²∅)

=2.

Answer is...

2(2sin∅cos∅)/2

=2sin∅cos∅ or sin(2∅)

Answer:

[tex]\huge\boxed{(2x)^\frac{1}{2}\times(2x^3)^\frac{3}{2}=4x^5}[/tex]

Step-by-step explanation:

[tex](2x)^\frac{1}{2}\times(2x^3)^\frac{3}{2}\qquad\text{use}\ (ab)^n=a^nb^m\\\\=2^\frac{1}{2}x^\frac{1}{2}\times2^\frac{3}{2}(x^3)^\frac{3}{2}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^\frac{1}{2}x^\frac{1}{2}\times2^\frac{2}{3}x^{(3)(\frac{3}{2})}=2^\frac{1}{2}x^\frac{1}{2}\times2^\frac{2}{3}x^\frac{9}{2}\\\\\text{use the commutative and associative property}\\\\=\left(2^\frac{1}{2}\times2^\frac{3}{2}\right)\left(x^\frac{1}{2}\times x^\frac{9}{2}\right)\qquad\text{use}\ a^n\times a^m=a^{n+m}[/tex]

[tex]=2^{\frac{1}{2}+\frac{3}{2}}x^{\frac{1}{2}+\frac{9}{2}}=2^\frac{1+3}{2}x^{\frac{1+9}{2}}=2^\frac{4}{2}x^\frac{10}{2}=2^2x^5=4x^5[/tex]

Answer:

[tex] 4x^5 [/tex]

Step-by-step explanation:

[tex] (2x)^\frac{1}{2} \times (2x^3)^\frac{3}{2} = [/tex]

[tex]= (2x)^\frac{1}{2} \times (2x \times x^2)^\frac{3}{2}[/tex]

[tex]= [(2x)^\frac{1}{2} \times (2x)^\frac{3}{2}] \times (x^2)^\frac{3}{2}[/tex]

[tex]= (2x)^{\frac{1}{2} + \frac{3}{2}} \times x^{{2} \times \frac{3}{2}}[/tex]

[tex]= (2x)^{\frac{4}{2}} \times x^{\frac{6}{2}}[/tex]

[tex] = 2^2x^2 \times x^3 [/tex]

[tex] = 4x^5 [/tex]

Answer:

The percentage by which the booster club fell short is 33% as shown on the chart

Step-by-step explanation:

To represent the given data pictorially, a pie chart is suitable

The circumference of the pie chart will represent the amount to be raised by the booster club and a sector of the circle which is two-thirds of the circumference represents the amount raised

Given that the amount raised = 2/3×Goal = $15,000, we have;

We represent the amount raised as a sector of the circle as follows;

Sector angle = 2/3×360° = 240°

Total sector of goal amount = Entire circle = 360°

Amount club fell short = 360° - 240° = 120°

The goal amount = 3/2 × $15,000

Percentage by which the club fell short = 120/360×100 = 1/3×100 = 33.33%

Answer:

Check below

Step-by-step explanation:

Hi, let's check

1.[tex](7x+20) + 12 \:and\: 7x +(24+12)\\[/tex]

In this case we have the Associate Property, since we can associate two, or even three terms without modify the final result.

2.[tex]21x+28y \:=\: 7(3x + 4y)[/tex]

Distributive Property, note that that the right side is the left side rewritten as a product, with the GCF outside the brackets.

3. Commutative Property

[tex]7y + 6x \:and\: 6x + 7y[/tex]

The order of these sum does not compromise the result.

4. [tex]x+4y-Sy \:and\: x-5y[/tex]

Combining like terms, similar terms are operated together.

Answer:

b

Step-by-step explanation:

you need to round 2.51 to 3 because it was the correct answer

Answer:

(-2,-4)

Step-by-step explanation:

The vertex of a parabola is it's lowest (or highest, but lowest in this context) point. Your lowest point is (-2,-4), so that is your answer.

Answer:

[tex]x=37\,\sqrt{2}[/tex]

Step-by-step explanation:

Notice you are dealing with a right angle triangle, since one of the angles measure [tex]90^o[/tex]. Now, what you are asked to find is the hypotenuse of that triangle, given an angle of [tex]45^o[/tex] and the opposite side: 37 units. Then, we can use for example the sine function which relates opposite, and hypotenuse:

[tex]sin(45^o)=\frac{opposite}{hyp} \\hyp=\frac{opposite}{sin(45^o)} \\hyp=\frac{37}{\sqrt{2}/2}\\hyp=37\,\sqrt{2}[/tex]

Answer:

1) 24Z^2 - 177.

2) 16d^2 - 32d.

6) 30x - 24.

7) 6q - 4.

Step-by-step explanation:

1) 3(8Z^2 - 52 - 7)

= 3(8Z^2 - 59)

= 24Z^2 - 177

2) 8d(2d - 4)

= (8d * 2d) - (8d * 4)

= 16d^2 - 32d

6) 6(5x - 4)

= (6 * 5x) - (6 * 4)

= 30x - 24

7) Already simplified. 6q - 4.

Hope this helps!

Answer:

2x^2 - x + 1

Step-by-step explanation:

This is polynomial long division:

Divide x + 3 into 2x^3 + 5X^2 - 2x + 3:

  Divide 2x^3 by x = 2x^2

  Multiple 2x^2 by (x + 3) =  2x^3 + 6x^2

  Subtract that from 2x^3 + 5X^2 - 2x + 3 = -x^2 -2x + 3

  Divide -x^2 by x = -x

  Multiple -x by (x + 3) = -x^2 - 3x

  Subtract that from -x^2 - 2x + 3 =  x + 3

  Divide x by x = 1

  Multiple 1 by (x + 3) = x + 3

  Subtract from x + 3 = 0

Answer:

1.475

Step-by-step explanation:

Answer:

Step-by-step explanation:

The median is 4, which is the middle number. If there is no middle number, get the average of the two numbers closest to the median.

The mean is 4, which is the average of all the numbers. you add all of them up and divide by how many integers there are in the list.

The mode is 6, which is the integer that is shown the most.

Answer:

mean=4

median=4

mode=6

Step-by-step explanation:

Mean: add 0+2+2+4+4+6+6+6+6=36

36/ (the amount of numbers) 9= 4

Median: cross out the numbers left to right until you get to the middle which is 4.

Mode: 6 occurred four times, which is the most out of any of the other numbers in this sequence, so the answer is 6.