While shopping at his local home improvement store, Chen noticed that the directions for an extension ladder state, “This ladder is most stable when used at a 60° angle with the ground.” He wants to buy a ladder to paint a two-story house. How long does his ladder need to be in order to reach the top of the house if the house is 27 feet tall?

[tex]8^{-\tfrac 23}\\\\\\=\left(8^{\tfrac 13 }\ \right)^{-2}\\\\\\=\left[\left(2^3\right)^{\tfrac 13} \right]^{-2}\\\\\\=\left(2^{\tfrac 33} \right)^{-2}\\\\\\=2^{-2}\\\\=\dfrac 1{2^2}\\\\\\=\dfrac 14[/tex]

[tex] {8}^{ - \frac{2}{3} } \\ = {2}^{3 \times - \frac{2}{3} } \\ = {2}^{ - 2} \\ = \frac{1}{2^{ 2}} \\ = \frac{1}{4} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

It should be [tex]3\sqrt{2} i[/tex]

Step-by-step explanation:

Answer:

4.242.....

Step-by-step explanation:

Hope this helped!

Answer:

12 months is one year so the expression is:

Step-by-step explanation:

2year = 2(X)

so you know one year 12 months you can put 12 on the x value

2 years = 2(12)

2 years = 24 months

Answer:

KOF

Step-by-step explanation:

Khan Academy

Trust me

Answer:

KOF

Step-by-step explanation:

Khan academy

Answer:

1/10

Step-by-step explanation:

630/6300 = 0.1

0.1*100 = 10

10% a.k.a 1/10

Hope this helped!

Answer:180%

Step-by-step explanation:

72/40 = 1.8

(1.8)(100)= 180

Answer:

Answer: 180%

Step-by-step explanation:

Answer:

$36,000

Step-by-step explanation:

8% of $450,000 = $36,000

Answer:

  y = 5x +2

Step-by-step explanation:

The point (0, 2) tells us the y-intercept is 2.

If we translate the table down 2 units by subtracting 2 from every y-value, it becomes ...

  6, 30

  -2, -10

  0, 0

  10, 50

We notice these values are all related by a factor of 5 (they are proportional). That means the equation will be a straight line with slope 5 and y-intercept 2.

  y = 5x +2

There are 23 sharks and 7 octopi in the aquarium

If the total number of animals in the tank is 30, therefore;

If the total number of legs in the tank is 171 with starfish having 5 legs and Octopus having 8 legs, the required expression will be:

From equation 1, x = 30 - y ................... 3

Substitute equation 3 into 2 to have:

5(30-y) + 8y = 171

150 - 5y + 8y = 171

3y = 171 - 150

3y = 21

y = 7

Recall that x = 30 - y

x = 30 - 7

x = 23

Hence there are 23 sharks and 7 octopi in the aquarium

Learn more on simultaneous equation here: https://brainly.com/question/148035

Answer:

(-7x + 4)(-7x - 4)

Step-by-step explanation:

When you multiply two binomials together and you want the result to be the difference of squares, the two binomials must have the same terms and ONE of the terms must have the opposite sign.

Ex: (a+b)(a-b)

OR (x+2)(x-2)

OR (m-3)(m+3)

OR (2x+1)(2x-1)

OR (-5n+7)(-5n-7)

These multiplications

(–7x + 4)(–7x + 4) and

(-7x + 4)(4 - 7x) yield a perfect square trinomial.. Both factors are identical, so they are not the answer.

(–7x + 4)(7x – 4) is also not the answer because one factor is the opposite of the other factor. That is, both terms in one factor are the opposite sign from the other. We need just ONE term to have the opposite sign.

Difference of squares:

(a+b)(a-b)=

a^2 - b^2

Answer:  Child is $1 and Adult is $3, per person.

Step-by-step explanation:

We have two unknowns, so we need at least two equations.  Let C and A stand for the price of a ticket for a child and an adult, respectively.

The income for Monday and Tuesday can be calculated:

Monday:   16C + 42A = $142

Tuesday:  24C + 26A = $102

Rearrange the second equation to isolate one of the variables.  I'll pick C:

24C + 26A = $102

C  = ($102 - 26A)/24

Now use this expression for C in the first equation

16C + 42A = $142

16(($102 - 26A)/24) + 42A = $142

16(($102 - 26A)/24) + 42A = $142

(1632 - 416A)/24 + 42A = $142

(68 - 17.3333A + 42A = $142

24.6667A = 74

A = 3  [The price of an adult pool admission is $3]

Use this value in either equation to find the price of a child's admission:

24C + 26A = $102

24C + 26*($3) = $102

24C = 102 - 78

C = $1   [The price of a child's admission to the pool is $1]

Check to see if these prices satisfy both equations:

Monday:   16C + 42A = $142

Tuesday:  24C + 26A = $102

---

Monday:   16*(1) + 42*(3)  = $142   ?   YES

Tuesday:  24*(1) + 26*(3) = $102   ?    YES

Child is $1 and Adult is $3, per person.

Answer:

x=-2  and y=5

x=-1 and y=4

Step-by-step explanation:

hope tha work

We evaluate an algebraic expression by the determination of an unknown variable.

Evaluation is a systematic method used in solving most algebraic expressions in mathematics.

Let assume that we have a given algebraic expression where y is expressed in terms of x and;

y = 2x + 5    where (x = 4)

y = 2(4) + 5

y = 8 + 5

y = 13

Learn more about how to evaluate algebraic expressions here:

https://brainly.com/question/4344214

Answer:

76, 76 104

Step-by-step explanation:

Angle 3 is vertical so it is congruent to Angle 2.

Angle 6 is corresponding, so it is congruent to Angle 2.

Angle 8 is linear to Angle 6, so they add to 180

Answer:

see explanation

Step-by-step explanation:

(a)

∠ 2 and ∠ 3 are vertically opposite angles and are congruent , then

∠ 3 = 76°

(b)

∠ 3 and ∠ 6 are corresponding angles and are congruent , then

∠ 6 = 76°

(c)

∠ 2 and ∠ 8 are same- side exterior angles and sum to 180° , that is

∠ 8 + 76° = 180° ( subtract 76° from both sides )

∠ 8 = 104°

Answer:

$11.55

Step-by-step explanation:

If we convert the percentage to 1.05 and multiply it by 11, it's 11.55.

The radius of the table top, rounded to 1 dp is 5.6 cm

From the question,

We are to determine the radius of the table top

First, we will determine the volume of the cylindrical wooden table

From the given information

Density = 0.42 g/cm³

Mass = 0.25 kg = 250 g

Using the formula

[tex]Volume = \frac{Mass}{Density}[/tex]

∴ [tex]Volume = \frac{250}{0.42}[/tex]

Volume = 595.238 cm³

Now, for the radius of the table top

Using the formula for volume of a cylinder

[tex]V = \pi r^{2}h[/tex]

Where V is the volume

r is the radius

and h is the height or depth

From the given information

h = 6cm

Putting the parameters into the formula

[tex]595.238 = \pi r^{2} \times 6[/tex]

∴ [tex]r^{2} = \frac{595.238}{6\pi }[/tex]

[tex]r^{2} =31.57835667[/tex]

[tex]r =\sqrt{31.57835667}[/tex]

r = 5.6 cm

Hence, the radius of the table top, rounded to 1 dp is 5.6 cm

Learn more here: https://brainly.com/question/11178104

Answer:

I believe the answer is 47. Forgive me if I'm wrong

Answer:

$20,073.38

Step-by-step explanation: Step 1: Find the percentage. The formula for annual compound interest is A = P(1 + r)^t, where A = amount (total amount), P = principal (initial amount), r = rate (percentage), and t = time (in years). Our rate is 6%, which is 0.06 in decimal form. Add it to 1. 1 + 0.06 is 1.06.

Step 2: Raise 1.06 to the 5th power. Because we are finding the amount in 5 years, we do that step. 1.06^5 is 1.3382255776.

Step 3: Do not delete the decimal from the calculator. Multiply it by 15,000 to find the total amount. When you do, you get 20,073.383664 or 20,073.38 when rounded to the nearest hundredth.

Answer:

9

Step-by-step explanation:

[tex]54 \div 6 = 9[/tex]

Answer:

Step-by-step explanation:

"The quotient of a number and -1.5 is 21."

Let X be the "number."

X/-1.5 = 21

X = -1.5*(21)

X = - 31.5

Answer:

i am pretty sure its C

Step-by-step explanation:

Answer:

Not

Step-by-step explanation:

6/8 In Simplest Form 3/4

21/36 In Simplest Form 7/12 May Be The Answer Will Be Not Equivalent

Hope To Help!!!

Answer:

22 +22 - 8=0

=

-2 +6

=

2

-2 +4+32

2.

=

= = =

I = -4; = 2

x = -13

TI

-2 = 36

2

-2 +(2) – 4(1)(-8)

2 (1)

2

= r = -1 -3: x = -1 +3 = sin   \theta  

Step-by-step explanation:

Answer:

(1.5,-1)

Step-by-step explanation:

Answer:

(1.5), (-1)

Step-by-step explanation:

Step-by-step explanation:

3x+2

3 x 5=15

15 + 2 = 17

so your answer is 17

pemdas

Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Answer:

m = 10

Step-by-step explanation:

The triangles are similar. The scale factor is 15/9.

We multiply 6 by the scale factor and get m:

m = 6 * 15/9 = 10

Then we see that m (10) is also the lenght of a side in the smaller triangle, so we multiply 10 by 15/9 and find a.

a = 16,6 (circa)

Answer:

8.8

Step-by-step explanation:

First turn 28 kilograms into pounds by multiplying 2.2 by 28. You end up with 61.6 pounds lost in one week. Next you take 61.6 divided by 7 to know how many pounds were lost in each day. You should end up with about 8.8 pounds.

Hope This Helps:)

Answer: 8.8

Step-by-step explanation:

The statement that best describes a flaw in the students' proof is;

Option D; Angle DBC and angle BDA form a pair of corresponding angles, not a pair of alternate interior angles, which are congruent.

From the given image, we can see that;

AB ≅ DC

Let us analyze each given option;

A) ∠DBC and ∠BDA are in the same triangle ΔBDC. Now, they can't be a pair of vertical angles because vertical angles are a pair of opposite angles formed when two lines intersect but this is not the case here.

They are also not alternate interior angles because alternate angles are formed when a transverse line intersects two coplanar lines and again that is not the case here.

B) In ΔABD and ΔBDC, we see that;

AB = DC. Also, by theorem of alternate interior angles, we can tell that;

∠ABD = ∠BDC

Similarly, ∠BDA = ∠DBC from alternate interior angles.

Thus, there is one corresponding side and two non-included angles which means the triangles are congruent by AAS Congruency postulate.

C) As seen in B above, this statement is correct because the triangles are congruent by AAS postulate.

D) Corresponding angles lie on the same side of the transversal.  In this case, ∠BDA and ∠DBC lie on opposite sides and are even congruent by alternate interior angles.

Read more about congruency at; https://brainly.com/question/7727792

Answer:

B. y = -4x

Step-by-step explanation:

input x in the possible answers

y = -4x

-4(2) = 8

-4(1) = -4

-4(-3) = 12

-4(-5) = 20

Answer:

answer ????

Step-by-step explanation: