Find the domain of the function. Write the answer in interval notation.

Answer:

18 pencils in 3 packs.

Step-by-step explanation:

Assuming that each pack will have the same amount of pencils. It is given that there are 36 pencils in all when one has 6 packs. Find the amount in each pack by dividing (total amount of pencils)/(amount of packs) = Amount of pencils per pack:

36/6 = 6

There are 6 pencils in each pack.

Now, Elsa wants to know how much pencils are in 3 packs. Multiply the amount of packs with the amount of pencils in each pack:

Total amount of pencils = amount of packs (3) x amount of pencils per pack (6)

                                       = 3 x 6

                                       = 18

There are 18 pencils in 3 packs.

~

Answer:

67°

Step-by-step explanation:

Answer:

49

Step-by-step explanation:

The probability of choosing a red marble is equal to the number of red marbles over the number of total marbles there are.

Therefore, let the number of red marbles be [tex]x[/tex].

We have the following equation:

[tex]\frac{x}{84}=\frac{7}{12}[/tex]

Cross-multiplying, we get:

[tex]12x=7\cdot 84,\\x=\frac{84\cdot 7}{12},\\x=\boxed{49}[/tex]

Therefore, there are 49 red marbles in the bag.

Answer:

3520 steps

Step-by-step explanation:

The first thing we must do is figure out how many inches are in a mile. (There are 63,360 inches in one mile). With that out of the way, we can now divide these inches by 18, since each of Eric's steps are 18 inches long, and we want to determine how many steps he would have to take. 63,360 divided by 18 is 3520. This means our answer is 3520 steps, and that is how many steps he must take to walk 1 mile. I hope you understood and please let me know if you still need help!

Answer: 3520 steps

Step-by-step explanation:

Use proportions and set x = number of steps in a mile:

[tex]\frac{1}{18 in}=\frac{X}{63360 in}[/tex]

18x = 63360

x = 63360 ÷ 18 = 3520 steps.

Answer:

Step-by-step explanation:

The easiest way to solve this is with calculus, believe it or not. The position function is

[tex]s(t)=-16t^2+64t[/tex]. The first derivative of this is the velocity function:

v(t) = -32t + 64. From physics, we know that at the max height of an object's path, the velocity is equal to 0, so setting this velocity equation equal to 0 and solving for time, will tell us the time it took to get to the max height (which we don't know yet, but we will in a bit):

0 = -32t + 64 and

-64 = -32t so

t = 2 seconds. It takes 2 seconds to reach a max height. Plugging that 2 in for t in the position function will tell you the max height that corresponds to this time:

[tex]s(2)=-16(2)^2+64(2)[/tex] and

s(2) = 64 feet.

So the max height is 64 feet and it is reached at 2 seconds after launching.

Also from physics we know that at halfway through a parabolic path, which is also the max height, we are halfway through time-wise as well. That means that if it takes 2 seconds to reach the max height from the ground, it will take another 2 seconds to fall to the ground.

So the total time the rocket is in the air is 4 seconds: 2 seconds to reach the max height and another 2 to fall back down.

Answer:

Step-by-step explanation:

find the DB =[tex]\displaystyle\bf \sqrt{17^2-8^2} =15[/tex]  ; now find AD=AB-DB=21-15=6  .Then                AC=[tex]\displaystyle\bf \sqrt{AD^2+CD^2} =\sqrt{6^2+8^2} =10[/tex]  

Answer:

C

Step-by-step explanation:

Using Pythagoras' identity in both right triangles

To find BD

BD² + CD² = BC²

BD² + 8² = 17²

BD² + 64 = 289 ( subtract 64 from both sides )

BD² = 225 ( take the square root of both sides )

BD = [tex]\sqrt{225}[/tex] = 15

Then

AD = AB - BD = 21 - 15 = 6

To find AC

AC² = AD² + CD²

AC² = 6² + 8² = 36 + 64 = 100 ( take the square root of both sides )

AC = [tex]\sqrt{100}[/tex] = 10 → C

Answer:

A’ will be located on ray Ray B A.

B and B’ are the same point.

Line segment A B and Line segment BC will be part of the image’s sides.

Step-by-step explanation:

Given that the dilation is made through point B, B and B’ are the same point, A’ will be located on Ray BA, C’ will be located on Ray BC, line segment B'C' will be double than line segment BC, line segment B'A' will be double than line segment BA, and the pre-image (triangle ABC) will be inside the image (triangle A'B'C').

Answer:

A B D is your answer

Step-by-step explanation:

Answer:

The answer is 3x-y-2=0

Step-by-step explanation:

Answer:

2nd option

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate the slope using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 1) and (x₂, y₂ ) = (2, 4) ← 2 points on the line

m = [tex]\frac{4-1}{2-1}[/tex] = 3

The line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = 3x - 2 ← in slope- intercept form

subtract y from both sides

0 = 3x - y - 2 , that is

3x - y - 2 = 0 ← in general form

Answer:

60%

Step-by-step explanation:

27/45 = .6

.6 = 60%

Answer:

For two vectors to be orthogonal it means that their dot product must be equal to zero.

Usually dot product of perpendicular vectors is zero and thus all perpendicular vectors are orthogonal.

Answer: second choice!

Step-by-step explanation:

Answer:

Given

length of rectangular sheet of paper is 12 (1/2) i.e. (25/2)

Breadth of rectangular sheet of paper is 10 (2/3) i.e. (32/3)

But we know that perimeter of rectangle = 2 (length + breadth)

Perimeter of rectangular sheet = 2 [(25/2) + (32/3)]

LCM of 2 and 3 is 6,

by taking this and simplifying we get

Perimeter = 2[(25 × 3)/6 + (32 × 2)/6]

= 2[(75/6) + (64/6)]

= 2(139/6) = (139/3)

= 46 (1/3) cm

Answer:

Perimeter of rectangular sheet = 2 [(25/2) + (32/3)]

LCM of 2 and 3 is 6,

by taking this and simplifying we get

Perimeter = 2[(25 × 3)/6 + (32 × 2)/6]

= 2[(75/6) + (64/6)]

= 2(139/6) = (139/3)

= 46 (1/3) cm

Step-by-step explanation:

Answer:

1441.08 in^3

Step-by-step explanation:

Volume of rectangular prism = 15 * 9 * 9 = 1215 in^3

radius = 3 in

Volume of the cylinder = 3^2 * 3,14 * 8 = 226.08 in^3

Total volume = 1215 + 226.08 = 1441.08 in^3

Answer:

HJHJGHJHG

Step-by-step explanation:

JGHU45565677689789

Answer: (a) P = 6W + 2

(b) L = 2W + 1

(c) Width = 13cm

Length = 27cm

Step-by-step explanation:

The formula for perimeter of a rectangle is 2(length + width). Since the length is 1 cm more than twice its width, then the length will be:

L = (2 × W) + 1

(b) L = 2W + 1

Therefore, P = 2(L + W)

P = 2( 2W + 1) + 2W

P = 4W + 2 + 2W

(a) P = 6W + 2

Since perimeter is given as 80cm. Therefore,

P = 6W + 2

6W + 2 = 80

6W = 80 - 2

6W = 78

W = 78/6

W = 13

Width is 13cm

Length = 2W + 1

Length = 2(13) + 1

Length = 27cm

The width of the rectangle is 13cm and the length is 27cm.

A rectangle is a quadrilateral. Opposite sides are equal. The four angles in a rectangle is equal to 90 degrees.

The formula for determining the perimeter of a rectangle = 2x (length + width)

P = 2(L + W)

80 = 2(1 + 2w + w)

80 = 2(1 + 3w)

40 = 1 + 3w

40 - 1 = 3w

39 = 3w

w = 13cm

Length = 1 + 2(13) = 27cm

To learn more about rectangles, please check: https://brainly.com/question/16595449

Answer:

x = 24

Step-by-step explanation:

mathematically, in a cyclic quadrilateral, two opposite angles are supplementary

what this mean is that they add up to be 180

From what we have in the question, the two angles are supplementary and that means they add up to equal 180 degrees

thus, we have it that;

(4x + 9) + (3x + 3) = 180

4x + 3x + 9 + 3 = 180

7x + 12 = 180

7x = 180-12

7x = 168

x = 168/7

x = 24

Answer:

D

Step-by-step explanation:

Answer:

t ≈ 3.65 s

Step-by-step explanation:

Let the distance the object travels after leaving the balloon be x.

Using Newton's equation of motion, we have;

s = ut + ½gt²

We are given;

s = 30 m

u = -10 m/s (negative because it is an upward motion)

Thus;

30 = -10t + ½(10)t²

30 = -10t + 5t²

5t² - 10t - 30 = 0

Using quadratic formula, we have;

t ≈ 3.65 s

Given function:

Find

Substitute x with r = 5:

g(r + 5) = 5(r + 5) + 3 = 5r + 25 + 3 = 5r + 28

Answer:

G ( r + 5 ) = 5r + 28

Step-by-step explanation:

Given ;

G ( x ) = 5x + 3

To Find :-

G ( r + 5 )

Solution :-

plug r + 5 as x in the function.

distribute 5

combine like terms

Answer:

-1

Step-by-step explanation:

1. Sets the exponents equal

3b-1 = b-3

2. collect like terms and calculate it

3b-b=1-3

2b= -2

(divide both side by 2)

b=-1

Answer:

The answer is y= - ⅓x + 5 in slope intercept form and y-7 = - ⅓ (x + 6) in point slope form.

Answer:

1/root(3)

Step-by-step explanation:

the steps are in the pic above.

The value of tan pi/6 is 0.5773502.

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

Given that, what is the exact value of tan pi/6,

To find the value of tan π/6 using the unit circle:

Rotate ‘r’ anticlockwise to form pi/6 angle with the positive x-axis.

The tan of pi/6 equals the y-coordinate(0.5) divided by the x-coordinate(0.866) of the point of intersection (0.866, 0.5) of unit circle and r.

Hence, the value of tan pi/6 = y/x = 0.5774 (approx)

Learn more about trigonometric functions click;

https://brainly.com/question/6904750

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Answer:

2 sheep

Step-by-step explanation:

If you have 36 sheep  and you sell:

first day    1/2 of them  you sold               18

second day  1/3  them you sold                12

On thhe third day  1/9  them you sold       4

Therefore you sold 18 + 12  + 4  = 34

And you still have  2 sheep

Answer:

Step-by-step explanation:

Answer:

Solution given:

it is a right angled isosceles triangle

so

perpendicular [p]=base[b]=3

hypotenuse [h]=x

we have

by using Pythagoras law

p²+b²=h²

3²+3²=h²

18=h²

h=[tex]\sqrt{18}[/tex]

x=[tex]\bold{3\sqrt{2}}[/tex]

Answer:

Only 10 base units to learn

Step-by-step explanation:

The metric system is a decimal based system developed to be universally acceptable by making use of base units from obtained from nature and the use of prefixes for multiples and submultiples of the base units, decimal ratios, which allows easy representation of quantities, as well as having a coherent structure of base and derived units which are obtained from the base units

During conversion in the metric system, which is decimal based, it is only required to move the decimal point

The prefixes which are used to specify multiples and submultiples are the same through out

The decimal system is based on the powers of ten

The number of base units to learn are 7 including; 1. Meter (m), 2. Kilogram (kg), 3. Second (s), 4. Ampere (A), 5. Kelvin (k), 6. Candela (cd), and 7. mole (mol)

Therefore the metric system has several advantages that include all of the following except; Only 10 base units to learn

Answer:

Multiples of 120 are 120, 240, 360, 480, 600, 720, 840 etc; Multiples of 150 are 150, 300, 450, 600, 750, 900 etc; Therefore, the least common multiple of 120 and 150 is 600.

Least common multiple (LCM) of 19600 and 19619 is 384532400.

Answer: 19600

Step-by-step explanation:

19600/120 = 160

Answer:

156

Step-by-step explanation:

area = 4*4 + 14 * 10

        = 16 + 140

        =156 cm²

Answer:

a = 4

b = -2

Step-by-step explanation:

If the given function is continuous at x = 1

[tex]\lim_{x \to 1^{-}} f(x)=(x+1)[/tex]

                     [tex]=2[/tex]

[tex]\lim_{x \to 1^{+}} f(x)=ax+b[/tex]

                     [tex]=a+b[/tex]

[tex]\lim_{x \to 1} f(x)=ax+b[/tex]

                   [tex]=a+b[/tex]

And for the continuity of the function at x = 1,

[tex]\lim_{x \to 1^{-}} f(x)=\lim_{x \to 1^{+}} f(x)=\lim_{x \to 1} f(x)[/tex]

Therefore, (a + b) = 2 -------(1)

If the function 'f' is continuous at x = 2,

[tex]\lim_{x \to 2^{-}} f(x)=ax+b[/tex]

                     [tex]=2a+b[/tex]

[tex]\lim_{x \to 2^{+}} f(x)=3x[/tex]

                     [tex]=6[/tex]

[tex]\lim_{x \to 2} f(x)=3x[/tex]

                   [tex]=6[/tex]

Therefore, [tex]\lim_{x \to 2^{-}} f(x)=\lim_{x \to 2^{+}} f(x)=\lim_{x \to 2} f(x)[/tex]

2a + b = 6 -----(2)

Subtract equation (1) from (2),

(2a + b) - (a + b) = 6 - 2

a = 4

From equation (1),

4 + b = 2

b = -2