pls pls helpIf the volume of a rectangle prism is 2x - 5x² - 12x. Given that the length is the longest side and width is the shortest side. Find the length, width and height.pls help i have a 9 week exan soon

The profit function is P(x) = -500.523x^2 + 600x - 200.

To find the profit function, P(x), we need to subtract the cost function, C(a), from the revenue function, R(x).

Given:

Cost function: C(a) = 500x^2 + 300

Revenue function: R(x) = -0.523x^2 + 600x - 200 + 300

Profit function, P(x), is obtained by subtracting the cost function from the revenue function:

P(x) = R(x) - C(a)

P(x) = (-0.523x^2 + 600x - 200 + 300) - (500x^2 + 300)

Simplifying the expression:

P(x) = -0.523x^2 + 600x - 200 + 300 - 500x^2 - 300

P(x) = -500x^2 - 0.523x^2 + 600x + 300 - 200 - 300

P(x) = -500x^2 - 0.523x^2 + 600x - 200

Combining like terms:

P(x) = (-500 - 0.523)x^2 + 600x - 200

Simplifying further:

P(x) = -500.523x^2 + 600x - 200

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Two stockpots are similar cylinders. The smaller stockpot has a height of 10 inches and a radius of 2.5 inches, the volume of larger one is 628.32 cubic inches.

We know that, to find volume:

Volume = π * \(r^2\) * h

For the smaller stockpot:

Radius (r) = 2.5 inches

Height (h) = 10 inches

Volume = π * (2.5)² * 10 ≈ 196.35 cubic inches

For the larger stockpot:

Radius (r) = 2.5 inches

Height (h) = 16 inches

Volume = π * (2.5)² * 16

             ≈ 628.32 cubic inches

Thus, the volume of larger one is 628.32 cubic inches.

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From the given numbers :

Integers: -50,000,000

Rational numbers : -1/2 and -1.5

Real numbers : −√5 , -1/2, -50, 000, 000 , -1.5.

As given,

Given numbers:

A. −√5 :It is an irrational number.

Therefore belongs to real numbers.

B. -1/2 :In p/q form .

It is a rational and real number.

C. -50,000,000

It is a negative integer and real number.

D. -1.5 =-15 /10

          =3/2

It is a rational and real number.

Therefore, from the given numbers :

Integers: -50,000,000

Rational numbers : -1/2 and -1.5

Real numbers : −√5 , -1/2, -50, 000, 000 , -1.5.

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Answer:

the answers for x and y are both 12

Answer:

A)

Each landing is about 17 inches.

B)

The vertical rise from Floor 1 to Floor 2 is about 7 feet.

Step-by-step explanation:

Please refer to the attachment below. (I accidentally wrote 30.30 instead of 30.20. Please ignore that and sorry for any confusion.)

Part A)

So, we want to find the length of \(\ell\).

Note that the angle of elevation, the vertical height, and \(\ell\) form a right triangle.

Since the vertical height opposite to our angle is 10, and we want to find the adjacent height, we can use the tangent ratio:

\(\displaystyle \tan(x^\circ)=\frac{\text{Opposite}}{\text{Adjacent}}\)

Therefore:

\(\displaystyle \tan(30.20)=\frac{10}{\ell}\)

Solve for \(\ell\). Cross-multiply:

\(\displaystyle \ell\tan(30.20)=10\)

So:

\(\displaystyle \ell=\frac{10}{\tan(30.20)}=17.1817...\approx17\text{ inches}\)

The landing space per step is about 17 inches.

Part B)

We know that there are a total of 12 feet of horizontal space total for each landing.

12 feet is equivalent to (12)(12) = 144 inches.

Since each landing is 17.1817... inches, this means that we have 144/(17.1817...) = 8.38... or about 8 steps.

Since the vertical rise of each step is 10 inches, the vertical rise from the 1st Floor to the second will be 8(10) or 80 inches or 80/12 = 6.666... or about 7 feet.

For an airplane has an airspeed of 530 kilometers per hour bearing N45 degrees E,  the ground speed of the plane and its direction is mathematically given as

Generally, the equation for the velocity of the plane is mathematically given as

\(Vp=Fcos\thetai+Fsin\theta j\)

Therefore

Vp=530cos45i+530sin45j

Vp= 374.76i+374.76j

For wind speed

Vm=80cos(90+30)i+80sin(90+30)j

Vm=-40i+69.28j

Hence, there resultant is

Vr=Vm +Vp

Vr=374.76i+374.76j + 40i+69.28j

Vr=334.77i+1444.05j

In conclusion, the Ground speed is

\(Vg=\sqrt{334.77^2+1444.05^2}\)

Vg=556.10km/hr

Direction

\(Tan \theta=\frac{444.05}{334.77}\)

\(\theta=52.99East\)

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The operations E-A,  A+E and B+D are defined for the matrices.

A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.

The number of rows of a matrix can be determined by counting from top to bottom and the number of columns can be determined by counting from left to right.

Matrices can only be added or subtracted only when they have the same dimensions, i.e. the same number of rows and the same number of columns. When adding or subtracting matrices, the corresponding elements of the matrices are added or subtracted.

Matrices A and E have the same dimensions i.e. They have 4 rows and 2 columns each.

Thus, the operations E-A (subtraction) and A+E (addition) are defined for the matrices.

Also, matrices B and D have the same dimensions i.e. They have 2 rows and 2 columns each.

Thus, the operations  B+D (addition) is defined for the matrices.

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The value of side EA is,

EA = 16.9

We have to given that;

Circle E with diameter CD and radius EA.

And, AB is tangent to E at A.

Here, AB = 34 and EB = 38

Hence, By using Pythagoras theorem we get;

AB² + AE² = EB²

34² + AE² = 38²

1156 + AE² = 1444

AE² = 1444 - 1156

AE² = 288

AE = √288

AE = 16.9

Thus, The value of side EA is,

EA = 16.9

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The angle m∠J  in the right angle triangle is 58.1 degrees.

One of the angle of a right tangle triangle is 90 degrees. The sum of

angles in a triangle is 180 degrees.

Therefore, the side length LK can be found using Pythagoras's theorem and the angle can be found using trigonometric ratios.

Hence,

tan ∠J = opposite / adjacent

tan ∠J = 15.1 / 9.4

∠J = tan⁻¹ 1.60638297872

∠J = 58.0909229196

Therefore,

m∠J = 58.1 degrees

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1. The scholar made a mistake in the last step

where he said x=3.5

\(0.5x = 7 \\ \frac{0.5x}{0.5} = \frac{7}{0.5} \\ x = 14\)

SCHOLA DIVIDED 7 BY 2 INSTEAD OF DIVIDING BY 0.5

2.TO CHECK IF 3 as a solution satisfies the equation I will first look in what the LHS is equal to by plugging in 3 in the place of n. SO THAT n=3 SATISFIES THE EQUATION LHS=RHS

\(lhs = - \frac{1}{2} (2(3) - 8) + 3 \\ lhs = - \frac{1}{2} (6 - 8) + 3 \\ lhs = - \frac{ 1}{2} ( - 2) + 3 \\ lhs = 1 + 3 \\ lhs = 4\)

Now I will check what The RHS IS EQUAL TO BY ALSO PLUGGING IN 3 IN THE PLACE OF n

\(rhs = \frac{1}{4} (8(3) - 4) - 1 \\ rhs = \frac{1}{4} (24 - 4) -1 \\ rhs = \frac{1}{4} (20) - 1 \\ rhs = 5 - 41\\ rhs = 4\)

FROM WHAT I FOUND LHS=RHS THIS MEANS THAT n=3 SATISFIES THE EQUATION BECAUSE IT IS BALANCED. WHAT IS ON THE LEFT HAND SIDE IS EQUAL WITH WHAT IS ON THE RIGHT HAND SIDE.

I HOPE THIS HELPS.

Answer:

17,190.79 cm ³

Step-by-step explanation:

24429.02 - 7238.23

Linear equations are represented by straight line.

The required graph is graph (a).

The given parameters are:

\(\mathbf{Rate =15}\)

Let x represents the number of weeks, and y represents the number of words in week x.

So, we have:

\(\mathbf{y = Rate \times x}\)

Substitute 15 for Rate

\(\mathbf{y = 15\times x}\)

\(\mathbf{y = 15x}\)

The above equation means that:

\(\mathbf{(x,y) = (0,0)(1,15),(2,30)....}\)

The graph that represents the above ordered pair is graph (a).

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Answer:

im lost

Step-by-step explanation:

;;..

The rank of the matrix is 3, since there are three linearly independent rows.

The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It is denoted by the symbol "rank(A)" for a matrix A.

To find the rank of the matrix:

[-2, -1, -3, -1] [ 1, 2, -3, -1] [ 1, 0, 1, 1] [ 0, 1, 1, -1]

We can perform row operations to reduce the matrix to row echelon form, which will help us determine the rank.

\(R_2 = R_2 + 2R_1 R_3 = R_3 + 2R_1 R_4 = R_4 + R_2\)

This gives us the following matrix:

[-2, -1, -3, -1] [ 0, 0, -9, -3] [ 0, -1, -1, 1] [ 0, 0, -4, -4]

We can see that the third row is not a linear combination of the first two rows, and the fourth row is not a linear combination of the first three rows. Therefore, the rank of the matrix is 3, since there are three linearly independent rows.

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Answer:

hfiwadhcase9iskoalsuhc;AJDSLASHDOIAWNHEOJOSED

Step-by-step explanation:

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Answer:

a + 50

Step-by-step explanation:

Step 1: Translate word into math

sum = +

fifty = 50

a = a

Step 2: Combine

a + 50

Answer:

a + 50

Step-by-step explanation:

Step 1: Translate word into math

sum = +

fifty = 50

a = a

Step 2: Combine

a + 50

Answer:

-2x^2-8x+12

Step-by-step explanation:

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

g(x)=5x^2+6x-8

(f-g) (x)= 3x^2-2x+4 - (5x^2+6x-8)

Distribute the minus sign

(f-g) (x)= 3x^2-2x+4 - 5x^2-6x+8

Combine like terms

          =-2x^2-8x+12

Answer:

\( - 2( {x}^{2} - 4x + 6)\)

Step-by-step explanation:

\( f(x)=3x^2-2x+4 \\ g(x)=5x^2+6x-8 \\ (f-g) (x) = 3 {x}^{2} - 2x + 4 - (5 {x}^{2} + 6x - 8) \\ = 3 {x}^{2} - 2x + 4 - 5 {x}^{2} - 6x + 8 \\ = - 2 {x}^{2} - 8x + 12 \\ = - 2( {x}^{2} - 4x + 6)\)

Answer:

123456789012345678901234567890123456678901234567890123445667890123456789012345678901234567890

Step-by-step explanation:

Answer:8

Step-by-step explanation:8x1=8

Answer:

True

Step-by-step explanation:

If the discriminant \(D=b^2-4ac < 0\), then there are two complex roots

If the discriminant \(D=b^2-4ac > 0\), then there are two real roots

If the discriminant \(D=b^2-4ac=0\), then there is only one real root

The correct way to calculate the percent change between the original value of $750 and the new value of $1,000 is option C.

C. (1,000 - 750)/750 = 250/750 = 1/3 ≈ 0.3333 = 33.33%

Therefore, the correct answer is option C, which represents a percent change of approximately 33.33%.

so correlation coefficient = σ^XY/σ^Xσ^Y = 1.225 / 1.36 = 0.9

Step-by-step explanation:                                                                          

a) We need to find the conditional p m f of X when Y = 1.

So, when Y = 1, there are only two X values: X =1 and X =2.

X can have any of the following values: 0, 1, 2, or 3                                                                                                        

so P(0) = 0/ 0.2 = 0          

P(1) = 0.1/(0.1+0.1) = 0.5

P(2) = 0.1/( 0.1+ 0.1) = 0.5

P(3) = 0/ 0.2 = 0

b)  The correlation coefficient of X and Y isρXY              

ρ^XY=(X,Y)=(X,Y)/σ^Xσ^Y=σ^XY/σ^Xσ^Y

We will calculate σ^X first by μ^x

f x(x) = 0.2; x = 0

= 0.2; x =1

= 0.2 ; x = 2

= 0.4 ; x = 3

μ^x = 0.2 * 0 + 0.2 * 1 + 0.2 * 2 + 0.4 * 3 = 1.8

σ^X^ 2 = 0.2 * 1.82 + 0.2 * 0.82 + 0.2 * 0.22 + 0.4 * 1.22 = 1.36

σ^X = 1.166

We will calculate σ^y first by μ^y

f^ x (X) = 0.2; y = 0

= 0.2; y =1

= 0.2 ; y= 2

= 0.4 ; y = 3

μ^y = 0.2 * 0 + 0.2 * 1 + 0.2 * 2 + 0.4 * 3 = 1.8

σ^y^ 2 = 0.2 * 1.82 + 0.2 * 0.82 + 0.2 * 0.22 + 0.4 * 1.22 = 1.36

σ^y = 1.166

Now we will calculate σ^XY

σ^2^XY = 0.4 * ( 3 - 1.8)* ( 3-1.8) + 0.2 *( 0 -1.8) * ( 0 - 1.8) + 0.1 * ( 1- 1.8) * ( 1- 1.8) + 0.1 * ( 2 -1.8) * ( 1 -1.8) + 0.1 * ( 1 - 1.8) * ( 2 - 1.8) + 0.1 * ( 2 - 1.8) * ( 2 - 1.8) = 1.26

σ^XY = 1.225        

so correlation coefficient = σ^XY/σ^Xσ^Y = 1.225 / 1.36 = 0.9

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(a) 45 tens is equal to 450. :- True

(b) 12.3 is equal to 123 ones. :- True

(c) 80 tens is greater than 6 hundreds. :- True

(d) 43,200 is less than 50 thousands. :- True

(e) 60 hundreds = 6,000 :- True

Consider the first statement,

45 tens are equal to 450

So, 45 tens mean 45 times 10 is written as:

45 × 10 = 450

Hence, it's true.

Consider the second statement,

12.3 is equal to 123 ones.

Now, 123 ones is equal to 123 times 1.

123 × 1 = 123

Hence, the statement is true.

Consider the third statement,

80 tens is greater than 6 hundreds.

Now 80 tens = 80 × 10 = 800

Now, 6 hundreds = 6 × 100 = 600

Now, 800 > 600

Hence, the statement is true.

Consider the fourth statement.

43,200 is less than 50 thousands.

Now, 50 thousands = 50 × 1000 = 50,000

We know,

50,000 > 43,200

Therefore, the statement is true.

Consider the fifth statement,

60 hundreds = 6000

Now, 60 hundreds = 60 × 100 = 6000

Therefore, the statement is true.

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Answer:

448 ft ^2

Step-by-step explanation:

\(A = \frac{b_{1} + b_{2}}{2} * h\\A = \frac{17 + 39}{2} * 16\\A = \frac{56}{2} * 16\\\\A = 28 * 16\\\\A = 448 ft^{2}\)

Hope this helps,

If best, mark brainliest, if not, hope it helps anyway.

Answer:

7 servings

Step-by-step explanation:

If you can make the spice rub with 2 tbsp, then divide 14 by 2 to get 7.

If you need reassurance multiply 7 x 2.

Answer:

6y +52

Step-by-step explanation:

6(2y + 8) - 2(3y - 2)

Distribute

12y + 48 - 6y +4

Combine like terms

6y +52

The equation which describes the relationship between the side length and shaded area of the quilt is y=0.5x²

Side length, x = 1,3,4,5,8

Shaded Area, y = 0.5, 4.5, 8, 12.5, 32

The relationship can be modeled as a quadratic function. Using a graphing calculator for the quadratic function written in the form y = ax² + bx + c

a = 0.5 ; b = 0 ; c = 0

Therefore, the quadratic function can be written as y = 0.5x²

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Answer:

Below in bold.

Step-by-step explanation:

A).  9.9^2 is close to 10^2 = 100

Round 1.79 to 1.8

So an estimate is 1.8 * 100

= 180.

B).  √97.5 / 1.96

( I am assuming that the square root is of 97.5 only).

is approximately equal to √100 / 2

= 10/2

= 5.

Betty spent $90 and Nan spent $ 30

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every area of mathematics, including coordinate geometry, calculus, and trigonometry. A straightforward algebraic expression is 2x + 4 = 8.

Given that :While shopping, Betty spent three times as much as Nan. And they spent a total of $120,

Let the Betty spent total $x and Nan spent total $Y

then,

x = 3y ....(i)

x +y =120 .....(ii)

put value of c from i equation to equation ii

4y = 120

y = 30

x = 90

Hence Betty spent $90 and Nan spent $ 30

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