Simplify (3^-2)^4
O A. 1 /3^2
O B. 3^2
O c. 3^8
OD.1/3^8

Both methods of solving for lengths of a right triangle are effective. That being said, the Pythagorean theorem is well-known and only requires a student to know one equation (as well as where the legs/hypotenuse should be plugged in). The six trigonometric ratios are also helpful, and over time are something that students begin to recognize when looking at right triangles.

I believe that the Pythagorean theorem is more effective because of its simplicity and wide application. The six trigonometric ratios will not apply to every right triangle, and require more memorization.

Hope this helps!

Answer:

1.56 rounded 1.6

Step-by-step explanation:

MAD (Mean Absolute Value):

step 1: Find the mean of the data

formula: sum of the data set / total number of terms

sum of the data set: 4 + 9 + 4 + 5 + 3 = 24

total number of terms: there is 5 numbers in the data set

mean = 24 / 5

mean = 4.8

step 2: Find the distance between each data and mean.

3, 4, 4, 5, 9

Distance between 3 and 4.8 is 1.8                 (4.8 - 3 = 1.8)

Distance between 4 and 4.8 is  0.8               (4.8 - 4 = 0.8)

Distance between 4 and 4.8 is  0.8               (4.8 - 4 = 0.8)

Distance between 5 and 4.8 is -0.2               (4.8 - 5 = -0.2)

Distance between 9 and 4.8 is -4.2               (4.8 - 9 = -4.2)

step 3: take the absolute value of any negative numbers

|-0.2| and |-4.2| is 0.2 and 4.2

step 4: add all the distances

1.8 + 0.8 + 0.8 + 0.2 + 4.2 = 7.8

step 5: divided it by the number of data

7.8 / 5 = 1.56

Let me know if you have any questions !

The area of the rectangle ACEG is the amount of space on it, and the area of square HJFG is 9 square units

The area of a rectangle is:

Area = Length * Width

The area of a square is:

Area = Length * Length

From the question, the given parameters are:

AB =AH = x ;

BC=5;

HG=3

This means that the area of square HJFG is:

Area = HG * HG

Area = 3 * 3

Area = 9

Note that the other areas cannot be calculated because the question is incomplete

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we know the angle is between 90° and 180°, 90° < θ < 180°, that means the angle is in the II Quadrant, where the sine is positive and the cosine is negative, with that info, let's find check a few things

[tex]sin(\theta )=\cfrac{\stackrel{opposite}{3}}{\underset{hypotenuse}{5}}\qquad \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{5^2 - 3^2}=a\implies \pm\sqrt{16}=a\implies \pm 4 = a\implies \stackrel{II~Quadrant}{-4=a} \\\\[-0.35em] ~\dotfill[/tex]

[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{-4}}{\underset{hypotenuse}{5}} \\\\\\ tan\left(\cfrac{\theta}{2}\right)\implies \cfrac{sin(\theta)}{1+cos(\theta)}\implies \cfrac{ ~~ \frac{3}{5} ~~ }{1-\frac{4}{5}}\implies \cfrac{ ~~ \frac{3}{5} ~~ }{\frac{1}{5}}\implies \cfrac{3}{5}\cdot \cfrac{5}{1}\implies 3[/tex]

Answer:

3. 2x+12+3x-7=360

5x+5=360

5x=360-5

x=355/5

x=71

for exterior

2x+12=360

2x=360-12

x=348/2

x=174

Step-by-step explanation:

hope this will help you

Answer: $25.90

Step-by-step explanation:

We will have x as the youngest son's share, (the youngests son's share is the basis)

(x + 4.30) as the eldest son's share, (the eldest received 4.30 more than the youngest)

(x - 7.80) as the second son's share, (the second received 7.80 less than the youngest)

and 64.90 as their share altogether.

To find the youngest son's share:

(x) + (x + 4.30) + (x - 7.80) = 64.90

x + x + 4.30 + x - 7.80 = 64.90

x + x + x = 64.90 - 4.30 + 7.80 (group all of the like terms together. variables with variables, numbers with numbers. 4.30 became negative since it was moved to the other side, the same happened with 7.80 since it was a negative, it became a positive when it moved to another side)

Solve...

x + x + x = 64.90 - 4.30 + 7.80

3x = 68.40 (divide both sides by 3)

[tex]\frac{3x}{3} = \frac{68.40}{3}[/tex]  

x = 22.80

(The youngest son's share is $22.80)

To get the eldest son's share:

x + 4.30 (substitute x since it has already been solved)

22.80 + 4.30 = 27.10

The eldest son's share is $27.10

Answer:

F(x) = 3x × 2

F(5) = 3(5) × 2

F(5) = ( 3 × 5 ) × 2

F(5) = 15 × 2

F(5) = 30

F(x) = 3x x 2

F(5)= 3(5) × 2

F(5) = 15 × 2

F(5) = 30

Answer:

A. -1 ≤ x ≤ 3

Step-by-step explanation:

According to the graph, our x-values span from -1 to 3. Since both are closed dot, they are inclusive in the domain:

[-1, 3] or -1 ≤ x ≤ 3

Answer:

44 grams carbohydrates = 176 calories

36 gram of fat = 324 calories

37 gram of protien = 148 calories

44 grams of Carbohydrates = 176 calories

36 grams of Fat = 324 calories

37 grams of Protein = 148 calories

To calculate the number of calories from each macronutrient (carbohydrates, fat, and protein), you need to know the caloric content per gram for each nutrient.

The caloric content per gram is as follows:

- Carbohydrates: 1 gram = 4 calories

- Fat: 1 gram = 9 calories

- Protein: 1 gram = 4 calories

Now, let's calculate the number of calories for each macronutrient in the Wendy's Big Bacon Classic:

1. Carbohydrates:

Calories from Carbohydrates = 44 grams × 4 calories/gram

Calories from Carbohydrates = 176 calories

2. Fat:

Calories from Fat = 36 grams × 9 calories/gram

Calories from Fat = 324 calories

3. Protein:

Calories from Protein = 37 grams × 4 calories/gram

Calories from Protein = 148 calories

In total, the burger would have 176 + 324 + 148 = 648 calories.

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Answer:

[tex]\frac{1}{2}[/tex] , 2 , 4

Step-by-step explanation:

x = - 3 ≠ 2 , then

g(- 3) = [tex]\frac{1}{2}[/tex] × (- 3)² - 4 = [tex]\frac{1}{2}[/tex] × 9 - 4 = [tex]\frac{9}{2}[/tex] - 4 = [tex]\frac{1}{2}[/tex]

x = 2 then g(2) = 2

x = 4 ≠ 2 , then

g(4) = [tex]\frac{1}{2}[/tex] × 4² - 4 = [tex]\frac{1}{2}[/tex] × 16 - 4 = 8 - 4 = 4

Answer:

[tex]P = 8\pi[/tex]

Step-by-step explanation:

To solve this problem, we must calculate the circumference of one circle and multiply it by two because there are 2 circles (4 halves), that make up the perimeter.

We know the diameter is 4m, thus, the circumference of one circle (two halves) is:

[tex]C_1 = \pi d\\C_1 = \pi 4[/tex]

To get the total perimeter (circumference) multiply the result by 2:

[tex]C = C \times 2\\C = 4\pi \times 2\\C = 8\pi[/tex]

Answer:

both sides are the same

Step-by-step explanation:

Answer:

no solutions

Step-by-step explanation:

3(1-2x) > 3 -6x, distribute multiplication by 3 over the subtraction

3 - 6x > 3 - 6x, because the left side is the same as the right side

this statement is never true, therefore this inequality has no solutions.

The area of the triangle will be 4.2 square meters.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The height is 2.4 meters and the base is 3.5 meters.

Then the area of the triangle will be

Area = 1/2 x b x h

Then we have

Area = 1/2 x 3.5 x 2.4

Area = 4.2 square meters

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✔ formula: A =  1/2 bh

✔ 3.5

✔ 2.4

✔ multiplying

✔ 4.2

Step-by-step explanation:

Took quiz

Answer:

Option D

Step-by-step explanation:

Option D is not proper scientific notation, as the exponent is not on the 10

Answer:

Q1 = -4, Q2 = 6

Step-by-step explanation:

In this box-and-whisker plot, the first vertical line is the first quartile (-4), the second vertical line is the median (4), and the vertical line is the third quartile (6). The box contains the middle 50% of the data set.

Answer:

The winter evening settles down

With smell of steaks in passageways.

Six o'clock.

The burnt-out ends of smoky days.

And now a gusty shower wraps

The grimy scraps

Of withered leaves about your feet

And newspapers from vacant lots;

The showers beat

On broken blinds and chimney-pots,

And at the corner of the street

A lonely cab-horse steams and stamps.

And then the lighting of the lamps.

Alfred Tennyson - Summer Night

Alfred Tennyson was another poet who made great use of visual imagery. See if you can get a clear picture of the summer night he describes in this poem "Summer Night:"

Now sleeps the crimson petal, now the white;

Nor waves the cypress in the palace walk;

Nor winks the gold fin in the porphyry font:

The firefly wakens: waken thou with me.

Now droops the milk-white peacock like a ghost,

And like a ghost she glimmers on to me.

Now lies the Earth all Danaë to the stars,

And all thy heart lies open unto me.

Now slides the silent meteor on, and leaves

A shining furrow, as thy thoughts in me.

Now folds the lily all her sweetness up,

And slips into the bosom of the lake.

So fold thyself, my dearest, thou, and slip

Into my bosom and be lost in me.

William Wordsworth - I Wandered Lonely as a Cloud

Next is an excerpt from "I Wandered Lonely as a Cloud" by William Wordsworth. The first and last stanzas show a progression of the poet's emotions using visual imagery.

I wandered lonely as a cloud

That floats on high o'er vales and hills,

When all at once I saw a crowd,

A host, of golden daffodils;

Beside the lake, beneath the trees,

Fluttering and dancing in the breeze.

For oft, when on my couch I lie

In vacant or in pensive mood,

They flash upon that inward eye

Which is the bliss of solitude;

And then my heart with pleasure fills,

And dances with the daffodils.

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Theodore Rothke - My Papa’s Waltz

This famous poem by Theodore Rothke is an excellent example of olfactory and tactile imagery with plenty of visual imagery thrown in for good measure. The effect is powerful.

The whiskey on your breath

Could make a small boy dizzy;

But I hung on like death:

Such waltzing was not easy.

We romped until the pans

Slid from the kitchen shelf;

My mother’s countenance

Could not unfrown itself.

The hand that held my wrist

Was battered on one knuckle;

At every step you missed

My right ear scraped a buckle.

You beat time on my head

With a palm caked hard by dirt,

Then waltzed me off to bed

Still clinging to your shirt.

William Carlos Williams - This Is Just to Say

"This Is Just to Say" is an amazing example of gustatory imagery or imagery involving taste. There’s more going on beneath the surface of this poem, but the vivid description of taste draws the reader in.

I have eaten

the plums

that were in

the icebox

and which

you were probably

saving

for breakfast

Forgive me

they were delicious

so sweet

and so cold

Step-by-step explanation:

Answer:

red marbel

[tex] = \frac{3}{13} [/tex]

green marbel

[tex] = \frac{9}{26} [/tex]

Step-by-step explanation:

for the red marbel you first add all the number of balls given and the total is 26 then you take the number of red marbels dividing the total number of all the balls and if you are able to cancel out you can and there you get your answer same applies to the green marbel

The probability that the Geometry textbook will be first from the left and the Chemistry textbook will be second from the left is 1/30

The distribution of the books is:

Spanish, English, Chemistry, Geometry, History, and Psychology

The probability of choosing a Geometry book is:

P(G) = 1/6

Now, there are 5 books left.

The probability of choosing a Chemistry book is:

P(C) = 1/5

The required probability is:

P = 1/6 * 1/5

Evaluate

P = 1/30

Hence, the probability is 1/30

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Answer:

3.14159265359 or simplify it to 3.14...

Step-by-step explanation:

ask me if you don't understand

Answer:

NO

Step-by-step explanation:

Because the sum of the minor sides equals the measure of the major side, it must be less.

2 + 4 = 6

Hope this helps

Answer:

37.61 years

Step-by-step explanation:

I am assuming this is compound interest

35 multiplied by 1.04 to the power of 36.86 does not generate enough money.

35 multiplied by 1.04 to the power of 37.61 does.

Answer:

37.61 yrs  

Step-by-step explanation:

FV = future value = 150 000

PV = present value = 35 000

i = decimal interest = .04

annual interest periods = n

 formula    FV = PV ( 1 + i)^n      plug in the values and solve for 'n'

                 150 000 = 35000 ( 1 + .04)^n

                   150000/35000 = (1 + .04)^n      take log of both sides

                       .632 =  n log1.04

                             n = years = 37.105 years

Answer:

Step-by-step explanation:

1) Combine like terms.

⇒ (3x + 2x) ( x - 5 )

⇒ (5x) ( x - 5 )

2) Distribute.

⇒ 5x ( x - 5 )

⇒ 5x² - 25x

Answer:

131,033.

Step-by-step explanation:

The growth factor is 1 + 0.2 %

= 1 + 0.002 = 1.002.

So in 3 years population

= 130,250(1.002)^3

= 131,033

Answer:

4 bulbs

Step-by-step explanation:

Answer:

Step-by-step explanation:

(0, 2) (2, 0)

(0-2)/(2-0)= -2/2= -1

y - 2 = -(x - 0)

y - 2 = -x + 0

y = -x + 2

The expression for the change of the variable z is Δz = (0.9 · x² + 0.6 · y²) · cos (x³ + y³).

In this question we must apply the concept of total differential to determine the change of the variable z in terms of the changes in variables x and y. That is:

[tex]\Delta z = \frac{\partial f}{\partial x}\cdot \Delta x + \frac{\partial f}{\partial y}\cdot \Delta y[/tex]     (1)

If we know that z = sin (x³ + y³), Δx = 0.3 and Δy = 0.2, then the expression for the change of z is:

[tex]\Delta z = 3\cdot \cos (x^{3}+y^{3})\cdot x^{2}\cdot (0.3)+3\cdot \cos (x^{3}+y^{3})\cdot y^{2}\cdot (0.2)[/tex]

Δz = (0.9 · x² + 0.6 · y²) · cos (x³ + y³)

The expression for the change of the variable z is Δz = (0.9 · x² + 0.6 · y²) · cos (x³ + y³).

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A change in the scale factor is to occur when an enlargement or a reduction in the dimensions of a building occurs to preserve the relationship between actual and mapped dimensions.

Scale factor is the factor which is used to enlarge or smaller the original figure.

Scale factor is the ratio of representation measurement of the figure to the original figures. An enlargement or a reduction in the dimensions of a building would cause a change in the scale factor.

This can be understood with the following points:

Thus, a change in the scale factor is to occur when an enlargement or a reduction in the dimensions of a building occurs to preserve the relationship between actual and mapped dimensions.

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