To wash a window that is 4 meters off the ground, Rafi leans a 5-meter ladder against the side of the building. To reach the window, how far away from the building should Rafi place the base of the ladder?

Answer:

ES LA NUME  C                                        R

Step-by-step explanation:

Answer:

[tex]\displaystyle \displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}\text{ and } \sin A = \frac{2ab}{a^2 + b^2}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle \tan A = \frac{2ab}{a^2 - b^2}[/tex]

And we want to find the value of cos(A) and sin(A).

Recall that tangent is the ratio of the opposite side to the adjacent side.

Therefore, the opposite side measures 2ab, and the adjacent side measures a² - b².

Using the Pythagorean Theorem, solve for the hypotenuse:

[tex]\displaystyle \begin{aligned} c^2 &= a^2 + b^2 \\ \\ c&= \sqrt{(2ab)^2 + (a^2-b^2)} \\ \\ &= \sqrt{(4a^2b^2)+(a^4-2a^2b^2+b^4)} \\ \\ &= \sqrt{a^4 + 2a^2b^2 + b^4 } \\ \\ &= \sqrt{(a^2 +b^2)^2} \\ \\ &= a^2 + b^2\end{aligned}[/tex]

Thus, our hypotenuse is given by a² + b².

Cosine is the ratio between the adjacent side and the hypotenuse. Thus:

[tex]\displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}[/tex]

And sine is the ratio between the opposite side and the hypotenuse. Thus:

[tex]\displaystyle \sin A = \frac{2ab}{a^2 + b^2}[/tex]

In conclusion:

[tex]\displaystyle \displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}\text{ and } \sin A = \frac{2ab}{a^2 + b^2}[/tex]

Answer:

Step-by-step explanation:

[tex]sec^2A-tan^2A=1\\sec^2A=1+tan^2A=1+\frac{4a^2b^2}{(a^2-b^2)^2} =\frac{(a^2-b^2)^2+4a^2b^2}{(a^2-b^2)^2} =\frac{(a^2+b^2)^2}{(a^2-b^2)^2} \\cos^2A=\frac{(a^2-b^2)^2}{(a^2+b^2)^2} \\cos A=\frac{a^2-b^2}{a^2+b^2} \\sin A=\sqrt{1-cos^2A} =\sqrt{1-(\frac{a^2-b^2}{a^2+b^2} )^2} =\sqrt{\frac{(a^2+b^2)^2-(a^2-b^2)^2}{(a^2+b^2)^2} } =\sqrt{\frac{4a^2b^2}{(a^2+b^2)^2} }=\frac{2ab}{a^2+b^2}[/tex]

Step-by-step explanation:

(+4)+(-7)

=4-7

=-3

Hope it will help you..

Some additional context would be helpful in providing a complete answer. But the basic idea is this:

• Object ABC has a price X set on it.

• Hey, ABC is on sale! Let's say there's a 20% discount. That means 20% of the price X is subtracted from X.

• Boo, there's a 15% sales tax! This means whatever you would pay for ABC, discount included, you will ultimately have to pay an additional 15% of, or 0.15 times, that amount in tax.

Suppose you're looking to buy a T-shirt. The price tag on says it costs $25, but there's a 20% discount and a 15% sales tax.

• The discount has a value of 0.2 ($25) = $5. Subtract this from the original price, and its discounted price is $20.

• The sales tax is applied to this discounted price, and comes out to 0.15 ($20) = $3. This gets added to the discounted price, so you end up paying $23.

Answer:

(2x+3y)^2

= (2x)^2 + 2(2x)(3y) + (3y)^2

= 4x^2 + 12xy + 9y^2

Answer:

4x^2 12xy +9y^2

Step-by-step explanation:

(2x+3y)^2

(2x+3y)(2x+3y)

FOIL

4x^2 + 6xy+6xy + 9y^2

4x^2 12xy +9y^2

[tex]\\ \sf\longmapsto (-42)+15+(-63)[/tex]

[tex]\\ \sf\longmapsto -42+15+(-63)[/tex]

[tex]\\ \sf\longmapsto -27+(-63)[/tex]

[tex]\\ \sf\longmapsto -27-63[/tex]

[tex]\\ \sf\longmapsto -90[/tex]

Answer:

42 + 15 + (-63) = -90

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

B. Never

Step-by-step explanation:

When a number is irrational, it means that it cannot be written as a fraction.

I hope this helps!

pls ❤ and mark brainliest pls!

Answer:

c) when it is improper fraction

Segment addition postulate states that given points X, and Z, on a line, a point Y, can be located between X, and Z, ony if we have;

XZ = XY + YZ

The length of the segment BD is 36  cm

The reason the above value is correct is as follows:

Known:

The ratio in which the points A, B, C, and D divide the line segment = 4:3:1

The length of segment AD = 72 cm

Required:

The length of BD

Method:

Calculate the length of BC and CD and add their values to get BD

Solution:

Let the ratios be given unit proportions of the segment AD such that we have;

AB = 4 units

BC = 3 units

CD = 1 unit

By segment addition postulate, we have;

AD = AB + BC + CD

∴ AD = 4 units + 3 units + 1 unit = 8 units = 72 cm

∴ 1 unit = 72 cm/8 = 9 cm

1 unit = 9 cm

BD = BC + CD by segment addition postulate

BC = 3 units = 3 × 1 unit

∴ BC = 3 × 9 cm = 27 cm

BC = 27 cm

CD = 1 unit

∴ CD = 9 cm

∴ BD = 27 cm + 9 cm = 36 cm

The length of segment BD = 36 cm

Learn more about segment addition postulate here:

https://brainly.com/question/17015321

Answer:

Step-by-step explanation:

Number cube:

Coin:

Required probability:

Answer: Probability of rolling a number more than one: 5/6

Probability of heads: 1/2

Probability of both: 1/2 + 5/6 = 4/3

Step-by-step explanation:

Answer:

The answer would be -a

Step-by-step explanation:

In the examples,

5 + (-5) = 0

-1.33 + 1.33 = 0

THat means there will be a negative then a positive, or a positive then a negative.

INVERSE is the key word in this problem.

Answer: x = 74.3

Step-by-step explanation:

Let 22 be reference angle

so

tan 22 = p/b

tan 22 = 30/x

or, x= 30/tan22

so, x = 74.252

so, x = 74.3

Answer:

Step-by-step explanation:

Answer:

I think E

Step-by-step explanation:

You know the shortest building is 25 m.

to find the rest, use trigo so Tan(20)=opposite/adjacent.

Adjacent is 50. Do the math and add the answer with 25.

Answer:

The answer would be E. 43.2

According to TOA, The opposite side is tan(20) x adjacent side( 50m)

the answer is 18.2( to 1 dp). Add the height of the second building together with 18.2 and you will get ur answer. HOpe this helps:)

Answer:

sorry

Step-by-step explanation:

polynomial is not given

question is incomplete

Answer:

Klog earned $135.45 altogether.

Step-by-step explanation:

Hours

Monday - Friday : 5 days / 3.5 hours

Saturday : 1 day / 4 hours

3.5 · 5 + 4

= 17.5 + 4

= 21.5

Money

$6.30 per hours / 21.5 hours

6.30 · 21.5

= $135.45

Part (a)

This is the empty set

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

Explanation:

It doesn't matter what set A is composed of. Intersecting any set with the empty set Ø will always result in the empty set.

This is because we're asking the question: "What does some set A and the empty set have in common?". The answer of course being "nothing" because there's nothing in Ø. Not even the value zero is in this set.

We can write Ø as { } which is a set of curly braces with nothing inside it.

=========================================================

Part (b)

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

Explanation:

When you union the universal set with any other set, you'll get the universal set.

The rule is [tex]A \cup B = B[/tex] where I've made B the universal set to avoid confusion of the letter U and the union symbol [tex]\cup[/tex] which looks nearly identical.

Why does this rule work? Well if an item is in set [tex]\overline{A}[/tex], then it's automatically in set U (everything is in set U; it's the universe). So we're not adding anything to the universe when applying a union involving this largest set.

It's like saying

we can see that [tex]\overline{A} \cup U[/tex] will basically form the set of every item, aka the universal set.

Answer:

A) 2 cm

Step-by-step explanation:

By definition, regular polygons have equal sides and angles. Therefore, each side of the regular hexagon must be equal. Since one side is marked as 2 cm, the length of PQ must also be 2 cm.

Answer: 21

Step-by-step explanation:

Step-by-step explanation:

tbh I have no idea

doing this for points

so yeah

Answer:

2=124  124/2

4=248 248/4

5=310 310/5

8=496 496/8

Step-by-step explanation:

40 + 22 = 62

62 x 2 = 124

62 x 4 = 248

62 x 5 = 310

62 x 8 = 496

i think

Answer:

B

Step-by-step explanation:

8 yards = 3 * 8 = 24 ft^2

1 mile = 5280

3*3 = 9 square feet

9 square feet holds 9 people.

1 square foot holds 1 person

8*3 * 5280 people could stand in an area of 8 yards * 1 mile

Though it's not quite correct, the answer is B

Answer:

[tex]P(x \ge 5) = 0.60[/tex]

Step-by-step explanation:

Given

[tex]S = \{5, 2, 7, 2, 3, 4, 10, 6,4,6,3, 6, 6, 4, 8,5,7,7,1,5\}[/tex]

[tex]n(S) = 20[/tex]

Required

[tex]P(x \ge 5)[/tex]

First, we count the number of trials that are at least 5

[tex]x = \{5, 7, 10, 6,6, 6, 6, 8,5,7,7,5\}[/tex]

So, we have:

[tex]n(x \ge 5) = 12[/tex]

So, we have:

[tex]P(x \ge 5) = \frac{n(x \ge 5)}{n(S)}[/tex]

This gives

[tex]P(x \ge 5) = \frac{12}{20}[/tex]

[tex]P(x \ge 5) = 0.60[/tex]

Answer:

(0.5,3)

Hope this helps..Have a good day!!

Answer:

the first difference are all 20.

since the first differences of this relation are constant, it is a linear relation

Answer:

Linear because the account balance increases by a constant 20.

Step-by-step explanation:

→ The first difference is 20 for all values because :

20 - 0 = 20

40 - 20 = 20

60 - 40 = 20

80 - 60 = 20

100 - 80 = 20

Answer:

Option 4. All real numbers greater than or equal to 2.

I hope this will help.

Answer:

B. $28

Step-by-step explanation:

Find the sales tax by finding 4% of 711:

711(0.04)

= 28.44

This is closest to 28.

So, the correct answer is B. $28

Answer:

Step-by-step explanation:

1) The smaller sticks will range in length from almost 0 unit up to a maximum of 0.5 unit, with each length equally possible.

Therefore, the average length will be about (0 + 0.5)/2 = 0.25 unit

2)If you assume that each break in the stick is uniformly distributed along the length of the stick and is independent of the location of the other break, then the odds are 25% that you will be able to form a triangle with the 3 pieces.

We'll call the length of the stick 1, so each break can occur at a position in the interval [0,1]. Let x and y represent the two breaks. Then we can look at the area of the region in the square bounded x=0, x=1, y=0, y=1, which represents combinations of x and y, for which we can form a triangle. Since the area of the whole square is 1, the area of the region inside is our probability.

If y>x, then the lengths of the pieces are x, y-x, and 1-y.

The triangle inequality must hold for each combination of edges.

for y>x ...

x+y−x≥1−y

x+1−y≥y−x

y−x+1−y≥x

these simplify to...

for y>x ...

y≥1/2

x+1/2≥y

x≤1/2

If we cut our 1x1 square into two triangles along the line x=y,

then the region in the upper triangle which satisfies the inequalities above forms a smaller triangle which connects the midpoints of the upper triangle.

The lower triangle (x>y), is just a reflection about x=y of the upper triangle, so together, the entire region looks like a bow-tie at a 45 degree angle.

This region takes up 25% of the square, so the probability that you can form a triangle is 25%

Answer:

Equation of line is y = -8x + 21

Step-by-step explanation:

Slope, m = -8

General equation of line:

[tex]{ \boxed{ \bf{y = mx + c}}}[/tex]

At point (2, 5), y = 5 and x = 2:

[tex]{ \tt{5 = ( - 8 \times 2) + c}} \\ { \tt{c = 21}}[/tex]

Therefore:

[tex]{ \sf{y = - 8x + 21}}[/tex]

[tex]{ \underline{ \blue{ \sf{christ \:† \: alone }}}}[/tex]