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The  volume of the cube is  2744 cm³.

There are different quadrilaterals, for example: square, rectangle, rhombus, trapezoid and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example,  in a square all angles are 90° and all sides present the same value.

A square is a 2D figure, when the square is associated a 3D figure, the figure is called a cube. The cube presents 6 faces with length (l) , height (h) and width (w) equal. Thus, the cube presents congruent edges.

The volume is given from the formula V=a³, where a is a congruent edge.

The question gives:

Therefore,

V=a³

V=14³

V=14*14*14

V=2744 cm³

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Answer:

1. Correct

2. Incorrect

3. Correct

4. Correct

5. Incorrect

Step-by-step explanation:

For the ones you got wrong:

1 / (-3)² = 1/9

and

[tex]3^{-2}[/tex] = 1/9

Answer:

First one is correct

Second one is 1/9

Third one is -1/9

Fourth one is 1/9

Fifth one is 1/9

Step-by-step explanation:

Second one -

Fifth one - calculate 3 to the power of -2 to get

1/9

Answer: 25.1º

Explanation

As the given triangle is a right triangle, we can use trigonometric functions to find DF, specifically:

where the adjacent is the side adjacent to our angle and the hypotenuse is the longest side (side opposite to the 90º angle).

Based on this, we can replace the values as follows:

Solving for DF:

From the calculations, we could obtain the maximum speed of the car as 72.6 miles/hr.

The term proportionality gives us an idea of the nature of the relationship that does exist between the variables in a given situation. The proportionality could be;

1) Direct

2) Inverse

3) Joint

Given that  the stopping distance (D) varies directly as the speed (S), we could say;

D α S

Introducing the constant k

D = kS

k = D/S

k = 0.027 miles/40 mile/hr

k = 6.75 * 10^-4 hours

Maximum speed = D/k

= 0.049 miles/ 6.75 * 10^-4 hours

= 72.6 miles/hr

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Answer:

ab^4/b-a^2

Step-by-step explanation:

...........

Applying the Chain Rule, the derivatives are given as follows:

The function Z is defined as follows:

z = x^7y^7.

The variables x and y are functions of variables s and t, as follows:

Hence the derivative of z as a function of s is given as follows:

∂z/∂s = (dz/dx)(dx/ds) + (dz/dy)(dy/ds).

Hence, applying the derivative rules for the exponents, and for the exponents, we have that:

[tex]\frac{\partial z}{\partial s} = 7x^6y^7\cos{(t)} + 7y^6x^7\sin{(t)} = 7x^6y^6(y\cos{t} + x\sin{t})[/tex]

Replacing the values of x and y, we have that:

[tex]\frac{\partial z}{\partial s} = 7(s\cos{t})^6(s\sin(t))^6(y\cos{t} + x\sin{t})[/tex]

We follow the same logic as above, only that now the inside derivatives, that is, the derivatives of x and y, are as function of t and not of s, hence:

∂z/∂t = (dz/dx)(dx/dt) + (dz/dy)(dy/dt).

Then:

[tex]\frac{\partial z}{\partial t} = -7x^6y^7s\sin{(t)} + 7y^6x^7s\cos{(t)} = 7sx^6y^6(-y\sin{t} + x\cos{t})[/tex]

Then, replacing x and y as functions of s and t, we have that:

[tex]\frac{\partial z}{\partial t} = -7x^6y^7s\sin{(t)} + 7y^6x^7s\cos{(t)} = 7s(s\cos{t})^6(s\sin{t})^6(-y\sin{t} + x\cos{t})[/tex]

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The value of a, b, c and d are 25, 3, 14 and 7 such that the sum of all rows, columns and diagonals are 48.

Given to us a magic square in which the sum of all rows, columns and diagonals are same. Then, we have to complete the missing numbers i.e., a, b, c and d respectively.

Let's proceed to solve this magic square accordingly.

First let's calculate that what will be the sum of all rows, columns and diagonals.

From the figure of magic square one diagonal is completely filled from that we can easily calculate the sum of the diagonals.

Sum = 5+16+27 = 48

Then, we can find the value of a, b, c and d easily.

5+a+18 = 48

23+a = 48

a = 48-23

a = 25

Therefore, the value of a is 25.

29+16+b = 48

45+b = 48

b = 48-45

b = 3

Therefore, the value of b is 3.

Now, 5+29+c = 48

34+b = 48

c = 48-34

c = 14

Therefore, the value of c is 14.

Then, we have

c+d+27 = 48

14+d+27 = 48

41+d = 48

d = 48-41

d = 7

Therefore, the value of d is 7.

Hence, we have completed the magic square in which the sum of all rows, columns and diagonals are 48.

Therefore, the value of a, b, c and d are 25, 3, 14 and 7 respectively.

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Graph (D) shows a complex number with an imaginary component, i.

So, we are aware that a complex number is shown as:

Where x stands for a number's real value and y for a number's imaginary value.

As a result, the number I is written as:

This indicates that the symbol for the number I is a point (0,1).

Therefore, graph (D) shows a complex number with an imaginary component, i.

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The complete question is given below:

Which graph depicts a complex number with i as the imaginary part?

Answer:

21 Degrees.

Step-by-step explanation:

It was 22 degrees by noon, by then the temperature had already risen by
eight degrees, but since we are going back in time, we would subtract the eight degrees.

22 - 8 = 14.

Now we are at 9 A.M, it is 14 degrees. But, the temperature had doubled from 5-9 A.M, so we would divide our fourteen by two in order to half it.

14 ÷ 2 = 7.

Now we are at 5 A.M.

From midnight to 5 A.M the temperature dropped fourteen degrees so we would add that fourteen back into the equation.

7 + 14 = 21.

Hope this helped!!

Answer:

It is a function because circles are functions

Step-by-step explanation:

the formula for a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h,k) = center

r=radius

radius is 4 because diameter is 8

Center is (2,1)

plug it into the equation:

[tex](x-2)^2+(y-1)^2=16[/tex]

From trigonometric ratios we calculate the value of the cos C is 4/9 and the value of cosec C is 9/√65 .

Real functions known as trigonometric functions in mathematics connect right-angled triangle angles and the ratios of their two side lengths.

We know that sec C = 1/cos C

Hence the value of cos C = 4/9 .

Again we know that the value of sin C=1/cosec c

Therefore the value of cosec C is 9/√65 .

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Check the picture below.

[tex]\textit{internal division of a line segment using ratios} \\\\\\ S(-6,-5)\qquad R(-11,10)\qquad \qquad \stackrel{\textit{ratio from S to R}}{2:3} \\\\\\ \cfrac{S\underline{T}}{\underline{T} R} = \cfrac{2}{3}\implies \cfrac{S}{R} = \cfrac{2}{3}\implies 3S=2R\implies 3(-6,-5)=2(-11,10)[/tex]

[tex](\stackrel{x}{-18}~~,~~ \stackrel{y}{-15})=(\stackrel{x}{-22}~~,~~ \stackrel{y}{20}) \implies T=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-18 -22}}{2+3}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-15 +20}}{2+3} \right)} \\\\\\ T=\left( \cfrac{ -40 }{ 5 }~~,~~\cfrac{ 5}{ 5 } \right)\implies {\Large \begin{array}{llll} T=(-8~~,~~1) \end{array}}[/tex]

Answer:

33

Step-by-step explanation:

Answer:

[tex]x=-7i, 7i, 5/8, -5/8[/tex]

Step-by-step explanation:

[tex](64x^2-25)(x^2+49)=0 \\ \\ (8x-5)(8x+5)(x+7i)(x-7i)=0 \\ \\ x=-7i, 7i, 5/8, -5/8[/tex]

The slope of the line is indefinite (∞). Also, the line will be parallel to the x-axis.

It is given in the question that a line passes through the points (7, 10) and (7, 20).

We have to find the slope of the line.

We know that,

Slope of a line with coordinates (a,b)  and (c,d) is given by:-

(d - b)/( c - a)

Here,

a = 7,

b = 10,

c = 7 and,

d = 20

Hence, we can write,

Slope of the line = (20 - 10)/( 7 - 7) = 10/0 = ∞.

Hence, the slope of the line is indefinite.

Here, as the x -coordinate of both the points are same, this line will be parallel to the x - axis.

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To determine the missing number:

collect like terms

Therefore the missing number = -1

The option that best describes the elevation of Desert Shores is; A. Desert Shores is lower than 55 meters below sea level.

We are told that the elevation of Desert Shores, California, is less than -55 meters.

Now, an elevation of a natural landmass like this is usually given with reference to the sea level. If above sea level, it is positive but if below sea level, it is negative.

Now, the elevation is negative as we can see that it is given as -55 meters. Thus, we can easily conclude that Desert Shores is lower than 55 meters below sea level.

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Answer:

the answer is -5.0

Step-by-step explanation:

Tom subtracted -1.1 from -3.9 instead of adding them together

Answer:

Step-by-step explanation:

2/3 ÷ 4/9 What is the answer?

2/3 : 4/9 =

2/3 * 9/4 =

3/2

The true statement about the result is that D. The survey suffers from voluntary response bias and may not estimate true support for the extended hours

From the information, in order to measure support for extended hours, the citizen visits neighborhood homes and asks adults the research question.

This illustrates bias as the citizen wants to propose to the city council extending the hours at the local public library on some weekdays.

Therefore, the true support may not be illustrated. In conclusion, the correct option is D.

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He can buy $100  of gasoline that you can buy if you also get a car wash and can spend at most $30.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a b indicates that an is smaller than b.

When a > b is used, it indicates that an is bigger than b.

Given Data

The gas station charges $0.20 less per gallon of gasoline if a customer also gets a car wash. A car wash cost $10.

Inequality-

$0.2x + $10 = $30

0.2x = $20

x = 100

He can buy $100  of gasoline that you can buy if you also get a car wash and can spend at most $30.

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Answer:

3/5 is the smallest, 7/9 is in the middle and 5/6 is the biggest

Step-by-step explanation:

Brainlest, Please!

Answer: 3/5 is first, 7/9 is second, and 5/6 is last.

The two approximations of the region's area between the graph of the function and the x-axis over the given interval are 14.31 < AREA < 17.01

We have :
f(x) = 9 -x [ 2, 4 ], 6 rectangles.

Here, a = 2 and b = 4 , n = 6

The width of the rectangles will be

x' = [tex]\frac{b-a}{n}[/tex]

x' = [tex]\frac{4-2}{6} = \frac{2}{6} = \frac{1}{3} = 0.33[/tex]

Now, The given function is f(x) = 9 -x

[tex]f(x_{i}) = x_{i} - 9[/tex]

For [tex]x_{0} = 0[/tex], [tex]f(x_{0} ) = 9[/tex]

For  [tex]x_{1} = 0.3[/tex], [tex]f(x_{1} ) = 9 -0.3 = 8.7[/tex]

For [tex]x_{2} = 0.6[/tex], [tex]f(x_{2} ) = 9 -0.6 = 8.4[/tex]

For [tex]x_{3} = 0.9[/tex], [tex]f(x_{3} ) = 9 -0.9 = 8.1[/tex]

For [tex]x_{4} = 1.2[/tex], [tex]f(x_{4} ) = 9 -1.2 = 7.8[/tex]

For [tex]x_{5} = 1.5[/tex], [tex]f(x_{3} ) = 9 -1.5 = 7.5[/tex]

For [tex]x_{6} = 2.1[/tex], [tex]f(x_{3} ) = 9 -2.1 = 7.2[/tex]

Now, The area by using an approximation using 6 approximating rectangles and right endpoints is given by.

A = Sum of [tex]f_{i}x'[/tex] = [tex](f_{1} + f_{2} + f_{3} + f_{4} + f_{5} + f_{6})x'\\[/tex]

A = (8.7 + 8.4 + 8.1 + 7.8 + 7.5 + 7.2)*0.3

A = 47.7*0.3 = 14.31

The area by using an approximation using 6 approximating rectangles and left endpoints is given by:

A = Sum of [tex]f_{i}x'[/tex] = [tex](f_{0} + f_{1} + f_{2} + f_{3} + f_{4} + f_{5} + f_{6} } )x'\\[/tex]

A = (9+8.7 + 8.4 + 8.1 + 7.8 + 7.5 + 7.2)*0.3

A = 17.01

Thus  14.31 < AREA < 17.01

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Answer:

Answer bellow with explanations

Step-by-step explanation:

if Miriam buys 0.5 pounds of strawberries and 3 pounds of apples she will in total would have bought 3.5 pounds of fruit.

if you are looking for the price she had to pay for the fruits above the equation to solve that is as following.

0.5 x 3$ = 1.5$

3.0 x 3.25 = 9.75$

total for the fruits needed above would be 1.5$ + 9.75$ = 11.25$

if you are looking for the amount of pounds converted into the amount of fruit

0.5/3$ = 0.16(6) pounds of strawberries

3/3.25$= 0.92307692307 pounds of apples

total of pounds of fruit that have been purchased is equal to 0.16(6) + 0.92307692307 = 1.08974358973 pounds

If Miriam buys x pounds of strawberries and y pounds of apples

it can be shown in an equation using 2 unknown values

X(strawberries)

Y(apples)

x/3$ + y/3.25$

to calculate the amount of pounds that have been purchased

Answer:

225

Step-by-step explanation:

if it is 1/3 off, then it means it's at 2/3 the price. now, you have to divide 450/2 to get the answer. 2/3 divided by 2=1/3

450/2=225, and thats how much money you will save

From the question, we are asked to find the area.

Since all the sides of the figure are the same, then it is a square.

So we will be using the area of a square formula to solve it.

Formula for area of a square is:

Area = a x a = a²

a = 5 in

So,

Area = 5 x 5 = 5² = 25

Therefore, the area of the square is 25 in²

Answer:

(3, 0)

Step-by-step explanation:

I assume this means a clockwise rotation.

let's think this through logically :

the last option (0, 3) cannot be right, because that is F before the rotation. to go back to the original position requires a full rotation of 360° (remember, a circle has 360°, and that means to travel one complete time around the circle).

(0, -3) cannot be right, because this is just mirrored down, and would represent a turn of 180° (a half-circle).

for the other options imagine you use a math compass, put the pin on the origin, and the writing arm on F. and the you draw a circle through F.

(3, 0) is the result of the clockwise (right) turn of 90°, (-3, 0) would be the result of a counterclockwise (left) turn of 90°.

so, if my assumption above is incorrect, please pick (-3, 0) for the counterclockwise solution.

The given system of equations represented as a matrix is

[tex]\left[\begin{array}{ccc}2&3&5\\-1&0&4\\-6&-1&1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}9\\10\\12\end{array}\right][/tex]

From the question, we are to represent the given system of linear equations with a matrix.

The given system of equations is

2x + 3y + 5z = 9

-x + 4z = 10

-6x + z -12 = y

First, we will write the third equation in standard form

-6x + z -12 = y

This becomes

-6x - y + z = 12

Thus,

The system of equations becomes

2x + 3y + 5z = 9

-x + 4z = 10

-6x - y + z = 12

Thus,

The system of equations can be written as a matrix as shown below

[tex]\left[\begin{array}{ccc}2&3&5\\-1&0&4\\-6&-1&1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}9\\10\\12\end{array}\right][/tex]

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