In a local ice sculpture contest, one group sculpted a block into a rectangular based pyramid. The dimensions of the base were 3 m by 5 m, and the pyramid was 3.6 m high. Calculate the amount of ice needed for this sculpture.

Answer:

Options (B) and (C)

Step-by-step explanation:

The given expression is [tex](d^{\frac{1}{8}})^5[/tex]

By simplifying this expression,

[tex](d^{\frac{1}{8}})^5[/tex]

= [tex](\sqrt[8]{d})^{5}[/tex]

Option (B)

Similarly,

[tex](d^{\frac{1}{8}})^5[/tex]

= [tex]d^{\frac{5}{8}}[/tex]

= [tex](d^{5})^{\frac{1}{8}}[/tex]

Option (C)

Therefore, Options (B) and (C) will be the correct options.

To solve the equation, we need to let u = x²

A quadratic equation is an algebraic expression that takes the power of the second degree.

From the given parameter:

For us to be able to solve the given equation, we need to reduce the equation to a quadratic form.

This can be achieved by making an assumption that:

So, we will replace x² with u in the given equation.

By doing so, we have:

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Answer: Solve x4 – 17x2 + 16 = 0.Let u = xX 17x²✔ x²X -17x².

let u = x^2

Step-by-step explanation: just did it

Answer:

83.33 cajas estándar de frambuesas y 51.67 cajas de lujo de frambuesas.

Step-by-step explanation:

Representemos el número de cajas como

A = caja estándar de frambuesas

B = caja de lujo de frambuesas

Caja estándar de frambuesas = $ 7 Caja de lujo de frambuesas = 10.

A + B = 135 ......... Ecuación 1

B = 135 - A

7A + 10B = 1100 ........... Ecuación 2

Sustituir

135 - A para B en la ecuación 2

7A + 10 (135 - A) = 1100

7A + 1350 -10A = 1100

7A - 10A = 1100-1350

-3A = - 250

A = 250/3

A = 83.33 cajas

Sustituye 83.33 por A en la ecuación 1

A + B = 135

83,33 + B = 135

B = 135 - 83.33 = 51.67 cajas

Por lo tanto, vendió,

83.33 cajas estándar de frambuesas y 51.67 cajas de lujo de frambuesas.

Answer:

6th

Step-by-step explanation:

the chart says not, 7th has majority

Answer: Stratified Sampling

Step-by-step explanation: Stratified Sampling involves creating subdivisions of the population such that each subdivisions is seen as a subgroup or smaller chunk of the population which is split based on certain criteria or attribute. The stratified random sampling may be employed in delineating certain characteristics or to investigate further how a feature or characteristics vary between one subdivision to the other.

In the scenario above, the researcher made use of the stratified sampling by performing a random sampling selection of its subjects based on the different subdivisions of students available in the college

Answer:

Option A.3

Step-by-step explanation:

If its rise over run the fraction should be right 2 up 6 makeing a fraction of

6/2 which equals 3

The line has a slope of 3

Answer:

Option B

Step-by-step explanation:

When we compare the number of shirt with it's cost, we find out that 8 shirts cost $120.

For more understanding, see the attached file.

Answer:

76.

Step-by-step explanation:

It is given that N is a 2-digit number.

Last two digits of N^2 is the same as N.

We know that, a number is even if it ends with 0,2,4,6,8.

[tex]2^2=4,4^2=16,6^2=36,8^2=64[/tex]

If 0 is in end then we get two zeros in the square of that number.

It is clear that, number should ends with 6 to get the same number at the end.

[tex]16^2=256[/tex]

[tex]26^2=676[/tex]

[tex]36^2=1296[/tex]

[tex]46^2=2116[/tex]

[tex]56^2=3136[/tex]

[tex]66^2=4356[/tex]

[tex]76^2=5776[/tex]

[tex]86^2=7396[/tex]

[tex]96^2=9216[/tex]

It is clear that last two digits of (76)^2 is the same as 76.

Therefore, the required number is 76.

Answer:

Step-by-step explanation:

The equation of a linear function:

y = mx + b

m - slope

b - y-intercept

x = 3 - it's a vertical line. It's not equation of a linear function

y = 16 - it's a horizontal line. It's an equation of a linear function

where m = 0, b = 16

y = -3x + 10 - it's an equation of a linear function

where m = -3, b = 10

y = 3x² + 1 - it's a quadratic function ( x² ).

Answer:

y = 16 and y = -3x + 10

Step-by-step explanation:

hello

Answer:

[tex]A.\ \frac{4}{6} = \frac{6}{9} = \frac{8.5}{12.5}[/tex]

Step-by-step explanation:

Given

Let the two triangles be A and B

Sides of A: 4, 6 and 8.5

Sides of B: 6, 9 and 12.5

Required

Which set of ratio determines the dilation

To determine the dilation of  a triangle over another;

We simply divide the side of a triangle by a similar side on the other triangle;

From the given parameters,

A ------------------B

4 is similar to 6

6 is similar to 9

8.5 is similar to 12.5

Ratio of dilation is as follows;

[tex]Dilation = \frac{4}{6}[/tex]

[tex]Dilation = \frac{6}{9}[/tex]

[tex]Dilation = \frac{8.5}{12.5}[/tex]

Combining the above ratios;

[tex]Dilation = \frac{4}{6} = \frac{6}{9} = \frac{8.5}{12.5}[/tex]

From the list of given options, the correct option is A,

Answer:

a

Step-by-step explanation:

Answer:

second option

Step-by-step explanation:

Given

f(x) = (x - 7)(x + 4)(3x - 2)

To find the zeros let f(x) = 0, that is

(x - 7)(x + 4)(3x - 2) = 0

Equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x + 4 = 0 ⇒ x = - 4

3x - 2 = 0 ⇒ 3x = 2 ⇒ x = [tex]\frac{2}{3}[/tex]

zeros are x = - 4, x = [tex]\frac{2}{3}[/tex], x = 7

Answer:

(0,-3)

Step-by-step explanation:

Explanation:

The x intercepts here are -1, 2 and 3. This is where the graph crosses the x axis. We can determine these three values by solving f(x) = 0.

In other words, set (x-3)(x-2)(x+1) equal to zero and solve for x.

(x-3)(x-2)(x+1) = 0

x-3 = 0 or x-2 = 0 or x+1 = 0

x = 3 or x = 2 or x = -1

x = -1 or x = 2 or x = 3

When we expand out (x-3)(x-2)(x+1), there will only be one x^3 term and the coefficient for this term is positive 1. The positive leading coefficient indicates that the graph goes up forever as we move to the right. In other words, the graph grows forever after passing that dip between x = 2 and x = 3.

Another way you could phrase it is that "as x goes to infinity, y also goes to infinity". An informal way is to say "the graph rises to the right" to describe the end behavior.

Answer:

Step-by-step explanation:

Given the value of a family's home, in Camrose AB, given by the following exponential function f(x) = 130000(1.06)^x, where x is the number of years after the family purchases the house for $130,000. In order to calculate the best estimate for the instantaneous rate of change in the value of the home when the family has owned it for 5 years, we will have to substitute x =5 in the given function and solve as shown;

f(x) = 130000(1.06)ˣ

f(5) = 130000(1.06)⁵

f(5) = 130000*(1.06)⁵

f(5) = 130000*1.338226

f(5) = 173,969.38

Hence, the instantaneous rate of change in the value of the home when the family has owned it for 5 years is approximately  $173,969

Answer:

she walked 6 miles.

Step-by-step explanation:

We know that Ruth walks at a speed of 4 mph and it took her 1.5 hours to walk from her home to the library (from 9 to 10.30).

We can solve this using a rule of three:

If she walks 4 miles in 1 hour, how many hours did she walk in 1.5 hours?

1 hour           4 miles

1.5 hours       x miles

Solving for x we get:

[tex]x=\frac{1.5(4)}{1} =6[/tex] miles

Thus, she walked a distance of 6 miles

The distance between her home and the library is the number of meters between them.

The distance walked is 6 m

The speed is given as:

[tex]\mathbf{Speed = 4mph}[/tex]

The time spent walking is calculated as:

[tex]\mathbf{Time = 10:30am - 9:00am}[/tex]

[tex]\mathbf{Time = 1.5\ hrs}[/tex]

So, the distance is calculated as:

[tex]\mathbf{Distance = Speed \times Time}[/tex]

Substitute known values

[tex]\mathbf{Distance = 4mph \times 1.5hrs}[/tex]

[tex]\mathbf{Distance = 6m}[/tex]

Hence, the distance walked is 6 m

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Answer:

Option 3

Step-by-step explanation:

The curve goes infinitely downwards, so y is infinitely negative while x is limited at the y axis, or x=0 which is the asymptote.

Answer:

The completed table is

x | 0 | 6 | 12

y | 0 | 2 | 4

Step-by-step explanation:

It is given that y is (1/3) as large as x. That is,

y = (x/3)

x | 0 | 6 | 12

y | ? | ? | ?

y = (x/3)

When x = 0,

y = (0/3) = 0

when x = 6,

y = (6/3) = 2

when x = 12,

y = (12/3) = 4

The completed table is thus

x | 0 | 6 | 12

y | 0 | 2 | 4

Hope this Helps!!!

The values of x will be 0 , 18 , 36 respectively when the value of y is 0, 6, 12.

Given,

y is 1/3 times as large as x.

So, [tex]x=3y[/tex].

We have to calculate the value of x when y is given .

1. when [tex]y=0[/tex]

Then, [tex]x=0[/tex]

2.when, [tex]y=6[/tex]

Then, [tex]x=18\\[/tex]

3. When [tex]y=12[/tex]

[tex]x=3\times 12\\x=36[/tex]

Hence, the values of x will be 0 , 18 , 36 respectively when the value of y is 0, 6, 12.

For more details follow the link:

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Answer:

[tex]B. y=x^2+3 \\\\D.$ $x^2+3y=8[/tex]

Step-by-step explanation:

A quadratic function is a function in which the highest power of the unknown variable is 2.

Formally, a quadratic function is defined as a function of the form:

[tex]f(x)=ax^2+bx+c, a\neq 0[/tex]

From the given options, only B and D has the highest power as 2. Therefore, the equations that represent quadratic functions are:

[tex]B. y=x^2+3 \\\\D.$ $x^2+3y=8[/tex]

Answer:

8

Step-by-step explanation:

8^3 = 8*8*8 = 512

la base = base = 8

Answer:

Step-by-step explanation:

The given equation is expressed as

(x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12

Simplifying the right hand side of the equation, it becomes

[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)

x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)

(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)

4x/(x - 1)(x + 1)

Therefore,

4x/(x - 1)(x + 1) = 7/12

Cross multiplying, it becomes

4x × 12 = 7(x - 1)(x + 1)

48x = 7(x² + x - x - 1)

48x = 7x² - 7

7x² - 48x - 7 = 0

Applying the quadratic formula,

x = - b ± √(b² - 4ac)]/2a

from our equation,

b = - 48

a = 7

c = - 7

Therefore

x = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)

x = [48 ± √(2304 + 196]/14

x = (48 ± √2500)/14

x = (48 ± 50)/14

x = (48 + 50)/14 or x = (48 - 50)/14

x = 98/14 or x = - 2/14

x = 7 or x = - 1/7

Answer: The given equation is expressed as (x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12Simplifying the right hand side of the equation, it becomes[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)4x/(x - 1)(x + 1)Therefore, 4x/(x - 1)(x + 1) = 7/12Cross multiplying, it becomes4x × 12 = 7(x - 1)(x + 1)48x = 7(x² + x - x - 1)48x = 7x² - 77x² - 48x - 7 = 0Applying the quadratic formula,x = - b ± √(b² - 4ac)]/2a from our equation, b = - 48a = 7c = - 7Thereforex = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)x = [48 ± √(2304 + 196]/14x = (48 ± √2500)/14x = (48 ± 50)/14x = (48 + 50)/14 or x = (48 - 50)/14x = 98/14 or x = - 2/14x = 7 or x = - 1/7

Step-by-step explanation:

Answer:

9.48*

Step-by-step explanation:

This is a right triangle. The formula for solving the Hypotenuse, or the longest side of the right triangle is A^2 + B^2 = C^2. If we put the numbers from the problem into the formula this is what we get :

3^2 + 9^2 = C^2

9 + 81 = C^2

90 = C^2

9.48 = C

* This is rounded, the exact number is closer to 9.486832980505138. Your class should tell you what to round to.

Answer:

The answer would be A. 3√10 blocks

Step-by-step explanation:

I have had this question and its 3√10 blocks.
Hope this helps you other people :))

Answer:

(2x+15)(x−1)

Step-by-step explanation:

Factor 2x2+13x−15

2x2+13x−15

=(2x+15)(x−1)

Here is the answer good sir

Answer:

(x - 1)(2x + 15)

Step-by-step explanation:

Well let's make the square look at the image below ↓

By looking at the image we can tell that the given equation factored is

(x - 1)(2x + 15).

Hope this helps :)

Answer:

a^5.

Step-by-step explanation:

a^12 / a^7 = a^(12 - 7) = a^5.

Hope this helps!

Answer:  n< 3

Step-by-step explanation:

5n - 14 < 1 .  add 14 to both sides

5n -14 +14 < 1 + 14

5n +0 < 15

5n < 15   divide both sides by 5 .5n/5 = 15/5

n < 3

Answer:

4/5

Step-by-step explanation:

Slope(m) = (y2-y1)/(x2-x1)

Pick two points on your graph that are closest to clear values. (By that I mean you shouldn't pick points that aren't obvious unless you have to.)

For instance, I see the points (-2,0) and (3,4) to be clear; so we don't have to approximate anything.

You could plug these in in a any order but I'm going to let Point 1=(-2,0) and Point 2=(3,4). So:

m=(4-0)/(3--2)=(4/5)

Slope=4/5

Answer:

2 root 17

Step-by-step explanation:

The square root of 68 in simplest radical form is 2√17

From the question, we have the following parameters that can be used in our computation:

The square root of 68

Mathematically, we have

The square root of 68 = √68

Expand 68

So, we have

The square root of 68 = √(4 * 17)

So, we have

The square root of 68 = √4 * √17

Evaluate

The square root of 68 = 2 * √17

Evaluate the products

The square root of 68 = 2√17

Hence, the square root of 68 is 2√17

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Answer:

Geometric sequence

Step-by-step explanation:

Because this is not adding or subtraction, but multiplication, this would be a geometric sequence.

Answer:

It's the first option

Step-by-step explanation:

They've constructed two angle bisectors and have shown you where they meet. Their point of intersection is the center of the inscribed circle (the incenter). Therefore, the last step is finding the altitudes (perpendicular lines) from the incenter to all the sides.

Answer:

[tex]h=64t-4.9t^{2}[/tex]

Please refer to the attached graph.

Step-by-step explanation:

Given that

Initial velocity of rocket = 64 and is launched vertically.

To find:

Quadratic equation in time to represent the height of rocket in feet.

Solution:

Unit of initial velocity is not given in the question statement, let the velocity be in feet/second only.

Initial velocity, u  = 64 feet/s

The acceleration will be = -g because it is going opposite to gravitational force so it will be negative acceleration motion (speed will be decreasing) so -g will be the acceleration.

Formula for distance traveled is given as:

[tex]s=ut+\dfrac{1}{2}at^2[/tex]

Here Let us represent s by 'h'

a = -g = 9.8 m/[tex]s^2[/tex]

Let us put the known values in the formula:

[tex]h=64t+\dfrac{1}{2}(-9.8)t^2\\\Rightarrow h =64t-4.9t^2[/tex]

It is a quadratic equation, the equation represents the graph of a parabola.

Please refer to the attached graph.

Value of height is 0 at 0 second and ~13 seconds

Answer:

A. 3 Days

Step-by-step explanation:

Just took the test hope this helps :)

Answer:

the answer on edge is A.3