In shop class, Adriana makes a pyramid with a 4-inch square base and a height of 6 inches. She then cuts the pyramid vertically in half as shown. What is the area of each cut surface?

Step-by-step explanation:

formula

an = a1 + (n - 1) d

10 = a1

15 = a2

20 = a3

n = unknown number

d = difference between each sequence

a10 = 10 + (10 - 1) 5

a10 = 10 + (9)5

a10 = 10 + 45

a10 = 55

Answer:

The first answer choice is correct due to its Y-Intercept

Step-by-step explanation:

Of your 2 answer choices, the first answer choice is the best.

This is because your Y-Intercept is one of the most important things you look our first.

It should be (0,-4) which the first one clearly has.

Now, you could look at the growth, it is growing at a different rate that is increasing as opposed to a constant rate.

Both of them have that, but like I said the Y-Intercept Clearly exposed the right answer.

Therefore The first answer choice is correct.

Answer:

  (b)  0.3 microns or larger

Step-by-step explanation:

A particle of size 0.3 microns is judged to be the most penetrating particle size. So, a rating for the filtering of those particles will be a worst-case rating. For particles of any other size, the filter will perform better than for 0.3 micron particles. HEPA filters are rated based on their performance with particles ...

  0.3 microns or larger

Answer:

A = -18.

Step-by-step explanation:

We are given that y = 3x +9.

From this, we gather 3x - y = -9.

We then multiply both sides by 2 to get 6x – 2y = -18. Therefore, A = -18.

The value of x from the figure is 17.82 units

1) From the first figure.

Opposite side = x

Adjacent = 12

Using the SOH CAH TOA identity

tan53 = opp/adj

tan53 = x/12

x = 12tan53

x = 15.92 units

2) Using the SOH CAH TOA identity

cos27 = adj/hyp

cos27 = x/20

x = 20cos27

x =  17.82units

Hence the value of x from the figure is 17.82 units

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Answer:

a = -2

b =3

c =2

Step-by-step explanation:

f(x) = 2 + 3x – 2x²

Rewrite in descending powers of x

-2x^2 +3x+2

The form is ax^2 +bx +c

a = -2

b =3

c =2

Answer:

8

Step-by-step explanation:

Now consider an experiment of tossing three coins simultaneously. The possible outcomes will be HHH, TTT, HTT, THT, TTH, THH, HTH, HHT. So the total number of outcomes is 23 = 8.

Answer:

8

Step-by-step explanation:

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

Rewrite and add each vector:

[tex]p=\langle40cos70^\circ,40sin70^\circ\rangle\\q=\langle50cos270^\circ,50sin270^\circ\rangle\\r=\langle60cos235^\circ,60sin235^\circ\rangle\\p+q+r=\langle40cos70^\circ+50cos270^\circ+60cos235^\circ,40sin70^\circ+50sin270^\circ+60sin235^\circ\rangle\\p+q+r\approx\langle-20.73,-61.56\rangle[/tex]

Find the magnitude of the resulting vector:

[tex]||p+q+r||=\sqrt{x^2+y^2}\\||p+q+r||=\sqrt{(-20.73)^2+(-61.56)^2}\\||p+q+r||\approx64.96[/tex]

Therefore, the best answer is D) 64.959

Problem 2

Think of the vectors like this:

[tex]t=\langle7cos240^\circ,7sin240^\circ\rangle\\u=\langle10cos30^\circ,10sin30^\circ\rangle\\v=\langle15cos310^\circ,15sin310^\circ\rangle[/tex]

By adding the vectors, we have:

[tex]t+u+v=\langle7cos240^\circ+10cos30^\circ+15cos310^\circ,7sin240^\circ+10sin30^\circ+15sin310^\circ\rangle\\t+u+v\approx\langle14.8,-12.55\rangle[/tex]

Since the direction of a vector is [tex]\theta=tan^{-1}(\frac{y}{x})[/tex], we have:

[tex]\theta=tan^{-1}(\frac{y}{x})\\\theta=tan^{-1}(\frac{-12.55}{14.8})\\\theta\approx-40.3^\circ[/tex]

Don't forget to take into account that the resulting vector is in Quadrant IV since the horizontal component is positive and the vertical component is negative, so we will add 360° to our angle to get the result:

[tex]\theta=360^\circ+(-40.3)^\circ\\\theta=319.7^\circ[/tex]

Therefore, the best answer is D) 320°

Problem 3

Again, rewrite the vectors and add them:

[tex]u=\langle30cos70^\circ,30sin70^\circ\rangle\\v=\langle40cos220^\circ,40sin220^\circ\rangle\\u+v=\langle30cos70^\circ+40cos220^\circ,30sin70^\circ+40sin220^\circ\rangle\\u+v\approx\langle-20.38,2.48\rangle[/tex]

Using the direction formula:

[tex]\theta=tan^{-1}(\frac{y}{x})\\\theta=tan^{-1}(\frac{2.48}{-20.38})\\\theta\approx-6.94^\circ[/tex]

As the vector is located in Quadrant II, we need to add 180° to our angle:

[tex]\theta=180^\circ+(-6.94)^\circ\\\theta=173.06^\circ[/tex]

Therefore, the best answer is D) 173°

Problem 4

Using scalar multiplication:

[tex]-3u=-3\langle35,-12\rangle=\langle-105,36\rangle[/tex]

Find the magnitude of the resulting vector:

[tex]||-3u||=\sqrt{x^2+y^2}\\||-3u||=\sqrt{(-105)^2+(36)^2}\\||-3u||=111[/tex]

Find the direction of the resulting vector:

[tex]\theta=tan^{-1}(\frac{y}{x})\\\theta=tan^{-1}(\frac{36}{-105})\\\theta\approx-18.92^\circ[/tex]

As the vector is located in Quadrant II, we need to add 180° to our angle:

[tex]\theta=180^\circ+(-18.92)^\circ\\\theta=161.08^\circ[/tex]

Therefore, the best answer is C) 111; 161°

Problem 5

Using scalar multiplication:

[tex]5v=5\langle25cos40^\circ,25sin40^\circ\rangle=\langle125cos40^\circ,125sin40^\circ\rangle[/tex]

Since the direction of the angle doesn't change in scalar multiplication, it only affects the magnitude, so the magnitude of the resulting vector would be [tex]||5v||=125[/tex], making the correct answer C) 125; 200°

Answer:

a. maximum value

b. x = 5

c. domain = all reals , range = y is less than or equal to 72

Step-by-step explanation:

a. maximum because it is a negative function and thats the highest value

b. thats the x value of the vertex which is the highest point

Answer:

6 Cups

Step-by-step explanation:

3 cups of sugar to 9 cups of water

1 cups of sugar : 3 cups of water

2 X 3 = 6

Answer:

9n + 2

Step-by-step explanation:

Answer:

[tex]9p+2[/tex]

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Check the picture below.

Answer:

The graph is stretched horizontally by a factor of 4 and shifted up 1 unit

Step-by-step explanation:

The effect of transforming the function is (b) The graph is stretched horizontally by a factor of 4 and shifted up 1 unit

The functions are given as:

f(x) = 3sin(x)+1

g(x) = 3sin(x/4)+2

Start by stretching the function f(x) horizontally by a scale factor of 4.

So, we have:

f'(x) = 3sin(x/4) + 1

Next, shift the function f'(x) upward by 1 unit.

So, we have:

f'(x) = 3sin(x/4) + 1 + 1

Evaluate the sum

f'(x) = 3sin(x/4) + 2

Rewrite as:

g(x) = 3sin(x/4) + 2

Hence, the effect of transforming the function is (b) The graph is stretched horizontally by a factor of 4 and shifted up 1 unit

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Answer:

D, [tex]\frac{7(x-4)}{6}[/tex]

Step-by-step explanation:

Basically you have to simplify the (x² - 16). Since it is the difference of 2 squares, it's simplified as (x + 4)(x - 4). Now that everything is simplified, you can start doing the multiplication.

[tex]\frac{(x+4)(x-4)}{6x} *\frac{7x}{(x+4)}[/tex], You can cancel out the (x+4)'s

[tex]\frac{(x-4)}{6x} *{7x}[/tex], There is a common factor between 7x and 6x. The common factor is x. So cancel out both "x".

You end up with this, [tex]\frac{7(x-4)}{6}[/tex]

Answer:

12

Step-by-step explanation:

This thing to know about this question is that angle 1 and angle 3 are actually the same.

When two lines intersect, the opposite angles such as that shown in 1 and 3 are equal to each other.

So what you can do is set angle 1 and 3 equal to each other like so:

5x+10 = 70

Then solve for x

5x+10 = 70

5x = 60

x = 12

Answer:

24

Step-by-step explanation:

Volume to fill =  1 x 2 x 3/2 = 3  cm^3

Volume of cube to fill this volume  1/2 * 1/2 * 1/2 = 1/8 cm^3

3/ (1/8) = 24

The inequality for this situation is given as b + n ≥ 16 and 6b + 9n > 108

An inequality is an expression that shows the non equal comparison of two or more numbers and variables.

Let b represent the number of bracelets she sells, and let n represent the number of necklaces she sells.

Hence:

b + n ≥ 16  (1)

and:

6b + 9n > 108   (2)

The inequality for this situation is given as b + n ≥ 16 and 6b + 9n > 108

Find out more on inequality at: https://brainly.com/question/24372553

Answer:

1. The length is longer.

2. The length is longer.

Step-by-step explanation:

1. 7/10 = 0.70 > 0.67. Here, the length is greater than the width.

2. 9/10 of a yard is .9 * 36, or 32.4 inches. Here, the length is greater than the width.

Answer:

200g/0.2kg

Step-by-step explanation:

8 × 25g = 200g

The total mass of the pencil is 200 grams.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given that,

A pencil has a mass of 25 grams.

there are 8 pencils.

Total number of pencils = 8

Mass of each pencil = 25 grams

Total mass of the pencils = 8 × 25 = 200 grams

Hence the total mass is 200 grams.

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We will see that for Stuart the maximum height is 30ft, and for Francisco it is 46.0625 ft

In the case of Stuart it is simple, as we have a graph, we just need to see the largest y-value on the graph. We can see that it is y = 30, then for Stuart, the largest distance from the ground is 30ft.

In the case of Francisco, we need to find the maximum of:

g(x)= -16x^2 + 50x +7

Notice that this is a quadratic of negative leading coefficient, so the maximum is at the vertex.

x = -50/(2*-16) = 25/16

Evaluating the function in 25/16 we get:

g(25/16) = -16*(25/16)^2 + 50*(25/16) +7 = 46.0625 ft

If you want to learn more about quadratic functions, you can read:

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Answer:

20,442,240 account numbers are possible.

Step-by-step explanation:

The first character has 10 possible values.

The next 2 has 26 * 26 = 676 possible combinations.

The last 4 has 9*8*7*6 = 3024 possible combinations.

So the answer is 10 * 676 * 3024

= 20,442,240.

There exist 20,442,240 possible combinations if no digit appears more than once.

The first character contains 10 possible values.

The next 2 contains 26 [tex]*[/tex] 26 = 676 possible combinations.

The last 4 have 9 [tex]*[/tex] 8 [tex]*[/tex] 7 [tex]*[/tex] 6 = 3024 possible combinations.

The has 10 [tex]*[/tex] 676 [tex]*[/tex] 3024 = 20,442,240 possible combinations.

Therefore, there are 20,442,240 possible combinations if no digit appears more than once.

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a function is odd if f(-x) = - f(x)

f(x) = x³ + 2x

and

f(-x) = (-x)³ + 2 * (-x) = - x³ - 2x = - (x³+2x) = - f(x)

Answer:

Step-by-step explanation:

tlk here

Answer:

I will help you.

but first what is the problem

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Answer:

Help you with what??

whats the question????

In a parallelogram, angles that are opposite each other (as in, in opposite corners) are congruent. Angles that are next to each other (as in, on the same side) are supplementary.

It is very easy to solve for the value of y first because the expression is across from a known angle. Because these angles are opposite each other, they are congruent.

83 = 5y - 7

90 = 5y

y = 18

We can also use the same 83 degree angle to solve for the other two variables. 83 is on the same side as both of the remaining expressions, separately. As such 83 and another angle on the same side will add up to 180.

83 + -5x - 3 = 180

80 - 5x = 180

-5x = 100

x = -20

83 + z - 7 = 180

90 + z = 180

z = 90

Hope this helps!

Answer:

The skeletal system has many functions. Besides giving us our human shape and features, it:

Allows movement: Your skeleton supports your body weight to help you stand and move. Joints, connective tissue and muscles work together to make your body parts mobile.

Produces blood cells: Bones contain bone marrow. Red and white blood cells are produced in the bone marrow.

Protects and supports organs: Your skull shields your brain, your ribs protect your heart and lungs, and your backbone protects your spine.

Stores minerals: Bones hold your body’s supply of minerals like calcium and vitamin D.

Using the unit circle, it is found that the approximate decimal value of tan(α) is given by -3.274.

For an angle [tex]\alpha[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\alpha}, \sin{\alpha})[/tex].

In this problem, we have point (-0.292, 0.956), hence [tex]\cos{\alpha} = -0.292, \sin{\alpha} = 0.956[/tex].

Applying the definition of the tangent, we have that:

[tex]\tan{\alpha} = \frac{\sin{\alpha}}{\cos{\alpha}} = \frac{0.956}{-0.292} = -3.274[/tex].

Hence the second option is correct.

More can be learned about the unit circle at https://brainly.com/question/16852127

The answer: -3.274.
Hope you got it right! :)

Step 1 :

Find the mean of the data :

(2+4+6+8) / 4 = 20/4 = 5

Step 2 :

Find the distance between each data and mean.

Distance between 2 and 5 is 3

Distance between 4 and 5 is 1

Distance between 6 and 5 is 1

Distance between 8 and 5 is 3

Step 3 :

Add all the distances :

3+1+1+3 = 8

Step 4 :

Divide it by the number of data :

8 / 4 = 2

2 is the average absolute deviation.

"The beautiful thing about learning is that no one can take it away from YOU"

B.B.King

Answer:

It is B because

Step-by-step explanation:

3 x 9 x 4 = 108

Answer:

[tex]-45[/tex]

Step-by-step explanation:

add the negative numbers together, and the solution stays negative.
[tex](-14) + (-31) = -45[/tex]