The angle of elevation of the top of a tree is 60°. If the point of observation is 4m from the foot of the tree. How far is the point from the top of the tree?

Answer:

[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]

Step-by-step explanation:

The slope of a line that is perpendicular to another will have an opposite-reciprocal slope. So, if the slope was -2, then the perpendicular slope would be [tex]\frac{1}{2}[/tex] .

[tex]y=-5x+11[/tex]

This is written in slope-intercept form:

[tex]y=mx+b[/tex]

m is the slope and b is the y-intercept. Find the opposite-reciprocal of the slope, -5:

[tex]y=\frac{1}{5} x+b[/tex]

Now we need to find the y-intercept. For this, substitute the given points for its appropriate value:

[tex](3_{x},3_{y})\\\\3=\frac{1}{5}(3)+b[/tex]

Solve for b:

Simplify multiplication:

[tex]\frac{1}{5}*\frac{3}{1}=\frac{3}{5}[/tex]

Insert:

[tex]3=\frac{3}{5}+b[/tex]

Subtract b from both sides:

[tex]3-b=\frac{3}{5}+b-b\\\\3-b=\frac{3}{5}[/tex]

Subtract 3 from both sides:

[tex]3-3-b=\frac{3}{5}-3\\\\-b=\frac{3}{5}-3[/tex]

Simplify subtraction:

[tex]\frac{3}{5}-3\\\\\frac{3}{5}-\frac{3}{1}\\\\\frac{3}{5}-\frac{15}{5}=-\frac{12}{5}[/tex]

Insert:

[tex]-b=-\frac{12}{5}[/tex]

Multiply both sides by - 1 to simplify b (it can be seen as -1b):

[tex]-b*(-1)=-\frac{12}{5}*(-1)\\\\b=\frac{12}{5}[/tex]

Insert:

[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]

:Done

Answer:

A graph that goes through (4, 0), (8, -3), (0, 3), and (-4, 6)

Step-by-step explanation:

Hello!

To find what this looks like it is easier to put it into slope-intercept form which is y = mx + b

To get our equation to look like that we have to get y by itself

3x + 4y = 12

Subtract 3x from both sides

4y = -3x + 12

Divide both sides by 4

[tex]y =- \frac{3}{4}x + 3[/tex]

We now know the y-intercept is (0, 3)

Now we follow the slope to give us more points

More points are (4, 0), (8, -3), and (-4, 6)

The answer would be a graph that goes through those points.

Hope this helps!

Answer:

B. ∠ABC

Step-by-step explanation:

When naming an angle using three points, the points should be given in order, with the vertex of the angle in the middle. B is the only option that has the letters in the right order.

∠CBA would also be a valid name for the angle, but that's not one of the options.

The diagram below shows what the problem is describing.

Rays BA and BC will form an angle named B. <ABC.

Therefore, the letter of the vertex will be in the middle of the three letters used in naming the angle.

The name of the angle formed by BA and BC is B. <ABC.

Learn more about naming of angles here:

https://brainly.com/question/19350659

1) multicropping

2)soilconservation

3)High carbon farming

4) clay particle

Hope it helps

Answer:

c. 40°

Step-by-step explanation:

The information given has been illustrated in the figure drawn in the attachment below.

m<BAD = 50° (angle bisector theorem)

m<ADB = 90° (perpendicular bisector)

m<ABD = 180 - (m<BAD + m<ADB) (sum of angles in a triangle)

m<ABD = 180° - (90° + 50°)

= 180° - 140°

= 40°

B = 40°

Answer:

27%

Step-by-step explanation:

27/100

Percent means out of 100

27%

Answer:

27 percent

Step-by-step explanation:

:)

Answer:

To form the converse of the conditional statement, interchange the hypothesis and the conclusion. The converse of "If it rains, then they cancel school" is "If they cancel school, then it rains." To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.

Answer:

y = 3 and x = - 5

Step-by-step explanation:

(a)

[tex]\frac{5-7y}{2+4y}[/tex] = [tex]\frac{-8}{7}[/tex] ( cross- multiply )

- 8(2 + 4y) = 7(5 - 7y) ← distribute parenthesis on both sides

- 16 - 32y = 35 - 49y ( add 49y to both sides )

- 16 + 17y = 35 ( add 16 to both sides )

17y = 51 ( divide both sides by 17 )

y = 3

-----------------------------------------------

(b)

x + 7 - [tex]\frac{8x}{3}[/tex] = [tex]\frac{17}{6}[/tex] - [tex]\frac{5x}{2}[/tex]

Multiply through by 6 to clear the fractions

6x + 42 - 16x = 17 - 15x

42 - 10x = 17 - 15x ( add 15x to both sides )

42 + 5x = 17 ( subtract 42 from both sides )

5x = - 25 ( divide both sides by 5 )

x = - 5

221 is rational since 221 = 221/1

So is 331 because 331 = 331/1

The product of any two rational numbers is also rational

--------------------------

Proof:

Let x = p/q and y = r/s be two rational numbers. The q and s values are nonzero.

Their product is

x*y = (p/q)*(r/s)

x*y = (p*q)/(r*s)

which is a ratio of two integers pq and rs, so (p*q)/(r*s) is rational

Answer:

A, D, E

Step-by-step explanation:

I hope this is correct

Answer:

a d e

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Using the identity

cos2Θ = 1 - 2sin²Θ, then

1 - 2sin²([tex]\frac{\pi }{4}[/tex] - [tex]\frac{0}{2}[/tex] )

= cos [2([tex]\frac{\pi }{4}[/tex] - [tex]\frac{0}{2}[/tex] )]

= sos([tex]\frac{\pi }{2}[/tex] - Θ )

= cos[tex]\frac{\pi }{2}[/tex]cosΘ + sin

= 0 × cosΘ + 1 × sinΘ

= 0 + sinΘ

= sinΘ = right side

Answer:  see proof below

Step-by-step explanation:

Use the Difference Identity: sin (A + B) = sin A cos B - cos A sin B

Use the following Half-Angle Identities:  

[tex]\sin\bigg(\dfrac{A}{2}\bigg)=\sqrt{\dfrac{1-\cos A}{2}}\\\\\cos\bigg(\dfrac{A}{2}\bigg)=\sqrt{\dfrac{1+\cos A}{2}}[/tex]

Use the Pythagorean Identity: cos²A + sin²A = 1   -->   sin²A = 1 - cos²A

Use the Unit Circle to evaluate: [tex]\cos\dfrac{\pi}{4}=\sin\dfrac{\pi}{4}=\dfrac{1}{\sqrt2}[/tex]

Proof LHS → RHS

[tex]\text{Given:}\qquad \qquad \qquad 1-2\sin^2\bigg(\dfrac{\pi}{4}-\dfrac{\theta}{2}\bigg)\\\\\text{Difference Identity:}\quad 1-2\bigg(\sin\dfrac{\pi}{4}\cdot \cos \dfrac{\theta}{2}-\cos \dfrac{\pi}{4}\cdot \sin\dfrac{\theta}{2}\bigg)^2\\\\\text{Unit Circle:}\qquad \qquad 1-2\bigg(\dfrac{1}{\sqrt2}\cos \dfrac{\theta}{2}-\dfrac{1}{\sqrt2}\sin \dfrac{\theta}{2}\bigg)^2\\\\\\\text{Half-Angle Identity:}\quad 1-2\bigg(\dfrac{\sqrt{1+\cos A}}{2}-\dfrac{\sqrt{1-\cos A}}{2}\bigg)^2[/tex]

[tex]\text{Expand Binomial:}\quad 1-2\bigg(\dfrac{1+\cos A}{4}-\dfrac{2\sqrt{1-\cos^2 A}}{4}+\dfrac{1-\cos A}{4}\bigg)\\\\\text{Simplify:}\qquad \qquad \quad 1-2\bigg(\dfrac{2-2\sqrt{1-\cos^2 A}}{4}\bigg)\\\\\text{Pythagorean Identity:}\quad 1-\dfrac{1}{2}\bigg(2-2\sqrt{\sin^2 A}\bigg)\\\\\text{Simplify:}\qquad \qquad \qquad 1-\dfrac{1}{2}(2-2\sin A)\\\\\text{Distribute:}\qquad \qquad \qquad 1-(1-\sin A)\\\\.\qquad \qquad \qquad \qquad \quad =1-1+\sin A\\\\\text{Simplify:}\qquad \qquad \qquad \sin A[/tex]

RHS = LHS:   sin A = sin A  [tex]\checkmark[/tex]

Answer:

20%

Step-by-step explanation:

Step 1: Find the decrease in consumption

10kg - 8kg = 2kg

So the family decrease their consumption of sugar by 2kg

Step 2: We have to find what percent did the family reduce their sugar consumption

We can divide how much they reduced by with the original amount

2kg/10kg = 1/5 kg or 20%

Therefore the family reduced the consumption of sugar by 20$

Answer:

7(x times y)

Step-by-step explanation:

Product means multiply, so it wants you to multiply two numbers and multiply THAT by 7.  So we will use two variables, in this case, I will use x and y.  X times y.  7 Times that.

Answer:

7xy

Step-by-step explanation:

Let's go by parts

The product of two numbers, since we don't know what are they we can called them x and y so the product means the multiplication

[tex]x*y=xy[/tex]

next xy has to be multiplied by 7

[tex]7*xy=7xy[/tex]

so 7xy is our answer

Answer:

x<= -4

filled in circle at -4

Answer:

0.16

Step-by-step explanation:

Given;

40% males.

If two students are selected at random, probability (P) that they are both males is given as follows;

P = P(1) x P(2)

Where;

P(1) = Probability that the first one is a male

P(2) = Probability that the second one is also a male

Remember that there are 40% males.

This means that 40 out of 100 students selected is going to be a male.

Therefore, for the first selection, any of the 40 students could be selected. The probability P(1), that the first one is male is therefore;

40 / 100 = 0.4

Also,

Assuming there is replacement, for the second selection, any of the 40 students could be selected. The probability P(2), that the second one is also male is therefore;

40 / 100 = 0.4

Now, from;

P = P(1) x P(2)

P = 0.4 x 0.4

P = 0.16

The probability that they are both males is therefore 0.16

Answer:

2000-1200+111

2000-1311

689 ans.

Step-by-step explanation:

by bodmas ( bracket,of,divide, multiplication, addition, substract )

so, first we'll multiply

3x400=1200

so,

2000-1200+111

second , we'll add

1200+111 = 1311

so,

2000-1311

third , at last we'll subtract

2000-1311 = 689

so,

Ans. 689

hope the ans. is correct :)

Answer:

k = h/9.

Step-by-step explanation:

√(h/k) = 3

Squaring both sides:

h/k = 9

9k = h

k = h/9.

Answer:

k=h/9

Step-by-step explanation:

sqrt(h/k)=3

1. square both sides

h/k=3^2

2. make k the subject

k=h/9

Answer:

Rate of return = 16%

Step-by-step explanation:

The computation of the rate of the return is shown below:

Data provided in the question

Current value of the investment = $20,880 = C

Originally cost = $18,000 = O

N = Net earnings = C - O

= $20,880 - $18,000

= $2,880

Based on the above information, the rate of return is

[tex]= \frac{N}{O} \\\\ = \frac{\$2,880}{\$18,000}[/tex]

= 16%

Hence, the rate of return is 16%

Answer:

105 ways

Step-by-step explanation:

Because the order of selection does not matter, we know that we will be using a combination instead of a permutation.

₁₅C₂ = 15! / (2! * 13!)

= 15 * 14 * ... * 2 * 1 / 2 * 1 * 13 * 12 * ... * 2 * 1

= 15 * 14 / 2 * 1 (The 13! cancels out)

= 105

Answer:

105 ways, because the order of selection does not matter, we know that we will be using a combination instead of a permutation.

Answer:

see explanation

Step-by-step explanation:

Using the double angle identity for cosine

cos2x = 2cos²x - 1

Given

cos( [tex]\frac{0}{2}[/tex] ) = [tex]\frac{1}{2}[/tex]( p + [tex]\frac{1}{p}[/tex] ) , then

cosΘ = 2[ [tex]\frac{1}{2}[/tex](p + [tex]\frac{1}{p}[/tex] ) ]² - 1

         = 2 [ [tex]\frac{1}{4}[/tex](p² + 2 + [tex]\frac{1}{p^{2} }[/tex] ) ] - 1  ← distribute by 2

         = [tex]\frac{1}{2}[/tex](p² + 2 + [tex]\frac{1}{p^{2} }[/tex] ) - 1 ← distribute by [tex]\frac{1}{2}[/tex]

         = [tex]\frac{1}{2}[/tex] p² + 1 + [tex]\frac{1}{2p^2}[/tex] - 1

        = [tex]\frac{1}{2}[/tex] p² + [tex]\frac{1}{2p^2}[/tex] ← factor out [tex]\frac{1}{2}[/tex] from each term

        = [tex]\frac{1}{2}[/tex] ( p² + [tex]\frac{1}{p^{2} }[/tex] ) ← as required

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]cos(\theta)=2cos^2(\dfrac{\theta}{2})-1\\\\=2\left(\dfrac{p+\dfrac{1}{p}}{2}\right)^2-1\\\\=\dfrac{p^2+\dfrac{1}{p^2}+2}{2}-1\\\\=\dfrac{1}{2}(p^2+\dfrac{1}{p^2})+1-1\\\\=\dfrac{1}{2}(p^2+\dfrac{1}{p^2})[/tex]

Thank you

Answer:

7 1/5

Step-by-step explanation:

You said that she poured 1 1/5 pouches in each cup. There are 5 cups, so multiply 1 1/5 by 5.

(e.g)

1 1/5+1 1/5= 3 because 1+1=2 & 1/2+1/2=1 so you add them and get 3

Do that twice and you get 6

then you have 1 one more cup left so add 1+6=7 then add the half 7+1 1/2=7 1/2

Your Welcome

Answer:

1.) The slope of an equation expressed in the form of y= mx+b is m.

Answer:

[tex]\huge \boxed{{y=2x+5}}[/tex]

Step-by-step explanation:

y = mx + b (slope-intercept form of a line)

m is slope

b is y-intercept

The y-intercept of the line is (0, 5) or 5.

y = mx + 5

The slope of the line can be found through rise over run.

(1, 7) and (2, 9) are two points on the line.

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

m = (9 - 7)/(2 - 1)

m = 2/1 = 2

The slope of the line is 2.

y = 2x + 5

Answer: Hi! The equation for this line would be c), y = 2x + 5.

Step-by-step explanation:

Slope - intercept form: y = mx + b, where m is the slope and b is the y - intercept.

First, we should determine the y - intercept. We can observe using the graph that the line intercepts the y - axis at point (0, 5), so we take the y - coordinate (5) and insert it into our equation.

y = mx + 5

This automatically rules out options d) and b).

Next, we find the slope. The formula for finding the slope is (y2 - y1) ÷ (x2 - x1).

We need to choose two coordinates before we can calculate the slope.

Let's use (1, 7) and (0,5).

We will not insert the values into or slope formula:

(7 - 5) ÷ (1 - 0)

When we solve this, the quotient is 2.

This is our slope, and we can insert the value into our slope equation - -

y = 2x + 5

This rules out option a). So, your answer is option c), y = 2x + 5.

Hope this helps!

la primera sale 1/3

la segunda 1/4

la tercera tambien 1/4

en la cuarta se puede hacer un grafico o un planteo de ecuacionas de igual manera te va a salir 1/5

y en la quinta tambien se puede hacer un grafico o un planteo de ecuacionas de igual manera te va a salir 1/8

Answer:

9

Step-by-step explanation:

21 x 3/7

= 9 ( goldfish )

Answer:

9 goldfishes

Step-by-step explanation:

Total fish = 21

Number of goldfish = 3/7 of 21

                                [tex]= \frac{3}{7}*21\\\\= 3 * 3\\\\= 9[/tex]

Answer:

x² - 3x - 18 = 0

Step-by-step explanation:

x/3 - 6/x = 1

x²/3 - 6 = x

x² - 18 = 3x

x² - 3x - 18 = 0

Answer:

24:12 = 24/12

24/12 = 2/1 or 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

The distance between two points can be found using the formula

[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

A(5,-8) and B(2,9)

The distance between them is

[tex] |AB| = \sqrt{ ({5 - 2})^{2} + ({ - 8 - 9})^{2} } \\ = \sqrt{ {3}^{2} + ({ - 17})^{2} } \\ = \sqrt{9 + 289} \\ = \sqrt{298} [/tex]

| AB | = 17.26267

We have the final answer as

17. 26 units to the nearest hundredth

Hope this helps you