Solving steps for 2x + 14 = 34 ? I know the answer but it's asking me to label the steps

To match the graphs of cylinders a and b to cylinders P and Q, we need to analyze the relationship between the height of the water and the volume of water in each cylinder.

Cylinder P would correspond to graph b, while Cylinder Q would correspond to graph a.

The reasoning behind this is as follows:

Cylinder P, corresponding to graph b, shows a steeper increase in height with increasing volume. This indicates that the water level rises quickly as more volume is added, suggesting that the cylinder has a smaller cross-sectional area. Since height is directly proportional to volume for a cylinder, a smaller cross-sectional area would result in a higher rise in height for the same volume of water.

Cylinder Q, corresponding to graph a, shows a slower increase in height with increasing volume. This implies that the water level rises more gradually as more volume is added, indicating a larger cross-sectional area. A larger cross-sectional area would result in a smaller increase in height for the same volume of water.

In summary, the steeper graph b matches Cylinder P with a smaller cross-sectional area, while the gentler graph a matches Cylinder Q with a larger cross-sectional area.

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SOLUTION:

Step 1:

In this question, we are given the following:

Which of the following equations shows "Five times a number minus 40 is 50"?

Step 2:

The details of the solution are as follows:

The correct answer is:

Answer:

Step-by-step explanation:

1 white 1 green 1 blue + 2 reds = 5 balls

5 seen as a percentage

5%

The solution to Assignment problem is given below.

The goal of the assignment problem, a particular kind of linear programming issue, is to reduce the time or expense of having several tasks completed by multiple people.

Step-1: Find out the each row minimum element and subtract it from that row

   1   2   3   4   5    

A  12 0 11 12 16 (-11)

B  5 0 4 5 5 (-1)

C  6 1 4 7 0 (-3)

D  0 9 2 22 0 (-13)

E  7 4 0 2 4 (-2)

Step-2: Find out the each column minimum element and subtract it from that column.

   1   2   3   4   5    

A  12 0 11 10 16

B  5 0 4 3 5

C  6 1 4 5 0

D  0 9 2 20 0

E  7 4 0 0 4

   (-0) (-0) (-0) (-2) (-0)

Step-3: Make assignment in the opporunity cost table

(1) Rowwise cell (A,2) is assigned, so columnwise cell (B,2) crossed off.

(2) Rowwise cell (C,5) is assigned, so columnwise cell (D,5) crossed off.

(3) Rowwise cell (D,1) is assigned

(4) Columnwise cell (E,3) is assigned, so rowwise cell (E,4) crossed off.

Step-5: Cover the 0 with minimum number of lines

(1) Mark(✓) row B since it has no assignment

(2) Mark(✓) column 2 since row B has 0 in this column

(3) Mark(✓) row A since column 2 has an assignment in this row A.

(4) Since no other rows or columns can be marked, therefore draw straight lines through the unmarked rows C,D,E and marked columns 2.

Step-4: Number of assignments = 5, number of rows = 5

Which is equal, so solution is optimal

Optimal assignments are

   1   2   3   4   5    

A  9 [0] 8 7 13

B  2 0 1 [0] 2

C  6 4 4 5 [0]

D  [0] 12 2 20 0

E  7 7 [0] 0 4

Optimal solution is

Work Job Cost

A           2 11

B           4 6

C           5 3

D           1 13

E           3 2

       Total 35

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P Q P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q

T T T T T F F F F F T    T

F T T F F T T T T T F    F

P F T F F T T T T T F     F

-P T T F F T T T T T F     F

-Q T T T T F T F F F T     T

-P V -Q T T F F T T T T T F

-P -> Q T T F F T T T T T F

-P -> -Q T T F F T T T T T F

P <-> Q T T T T F T T T T F

Here is a more detailed explanation of how I filled out the table:

P | Q : This column is simply the truth value of P and Q. If P and Q are both true, then the entry in this column is T. If P is true and Q is false, then the entry in this column is F. If P is false and Q is true, then the entry in this column is F. And if P and Q are both false, then the entry in this column is T.

P V Q : This column is the truth value of P or Q. If P is true, then the entry in this column is T. If Q is true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P ^ Q : This column is the truth value of P and Q. If P and Q are both true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P -> Q : This column is the truth value of P implies Q. If P is true and Q is false, then the entry in this column is F. And if P is false or Q is true, then the entry in this column is T.

-P : This column is the negation of P. If P is true, then the entry in this column is F. And if P is false, then the entry in this column is T.

-Q : This column is the negation of Q. If Q is true, then the entry in this column is F. And if Q is false, then the entry in this column is T.

-P V -Q : This column is the truth value of not P or not Q. If P and Q are both true, then the entry in this column is F. If P and Q are both false, then the entry in this column is T. And if P or Q is true, then the entry in this column is T.

-P -> Q : This column is the truth value of not P implies Q. If P is true and Q is false, then the entry in this column is T. And if P is false or Q is true, then the entry in this column is F.

-P -> -Q : This column is the truth value of not P implies not Q. If P and Q are both true, then the entry in this column is T. If P is false or Q is false, then the entry in this column is T. And if P is true and Q is true, then the entry in this column is F.

P <-> Q : This column is the truth value of P if and only if Q. If P and Q are both true or P and Q are both false, then the entry in this column is T. And if P and Q have different truth values, then the entry in this column is F.

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The two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

To solve the system of equations, let's assign variables to the two integers. Let the first integer be represented by 'x' and the second integer by 'y'.

According to the given information:

a. Fourteen more than twice the first integer gives the second integer:

This can be expressed as: 2x + 14 = y

b. The second integer increased by one is the square of the first integer:

This can be expressed as: y + 1 = x^2

Now, we have a system of equations:

1) 2x + 14 = y

2) y + 1 = x^2

To solve this system, we can substitute the value of 'y' from equation 1) into equation 2):

2x + 14 + 1 = x^2

2x + 15 = x^2

Rearranging the equation, we have:

\(x^2 - 2x - 15 = 0\)

Factoring the quadratic equation, we get:

(x - 5)(x + 3) = 0

Setting each factor equal to zero:

x - 5 = 0   -->   x = 5

x + 3 = 0   -->   x = -3

Substituting the values of 'x' back into equation 1), we can find the corresponding values of 'y':

For x = 5:

2(5) + 14 = y

10 + 14 = y

y = 24

For x = -3:

2(-3) + 14 = y

-6 + 14 = y

y = 8

Therefore, the two pairs of integers that satisfy the given conditions are (-3, 8) and (5, 24).

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The value of x in 7-3(2x-1)= 2x+26 is -4

Linear equation is is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line. The solutions of linear equations will generate values, which when substituted for the unknown values, make the equation true. In the case of one variable, there is only one solution. For example, the equation x + 3= 0 has only one solution as x = -3.

To find x in 7-3(2x-1)= 2x+26 ,we solve the parentheses first which will give

7- 6x+3= 2x+26

collect the like terms

-6x-2x=26-3-7

-8x= 16

divide both side by -8

-8x/-8= 16/-8

therefore x= -2

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Answer: -21

Step-by-step explanation:

Answer: 7 and 17

Step-by-step explanation:

Since the area of a rectangle is the product of the two sides, the product of these two numbers must be 119.

The factors pairs of 119 are 1 and 119, and 7 and 17.

x+7 and x-3 have a difference of 10. The difference of 7 and 17 is also 10. Hope this helped!

In the future, please take a less blurry photo because I had to guess the part where I think it said x-3.

Answer:

A football pass of 9 yards

Step-by-step explanation:

-9 AKA negative 9. Negative can also mean down or left or backwards even.

A hold 9 feet deep is dug down

9 dollars withdrawn from the bank means your down 9 dollars

A pass of 9 yards is positive yardage

9 below 0 is a temperature of negative nine

The only one that isn't negative, but is positive is a football pass of 9 yards

Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000 \cdot 0.12 \cdot 6\)

\(I=24000 \cdot 6\)

\(I=144000\)

Therefore, the return on Ayanda's investment using Option 1 is R144000.

\(\hrulefill\)

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000(1+0.095)^6-200000\)

\(I=200000(1.095)^6-200000\)

\(I=200000(1.72379142...)-200000\)

\(I=344758.28426...-200000\)

\(I=144758.28426...\)

\(I=144758.28\)

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

\(\hrulefill\)

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

Given:

\(F_{1}x=F_{2}(d-x)\)

\(F_{2}=27Ibs\)

\(d=10in\)

\(x=0.15 in\)

Find:

\(F_{1}\)

To find the force, replace the variables \(F_{2}=27\), \(d=10\), \(x=0.15\) and solve for \(F_{1}\).

=> \(F_{1}x=F_{2}(d-x)\\\)

=> \(F_{1}(.15)=(27)((10)-(.15))\\\)

=> \(F_{1}(.15)=(27)(9.85)\\\)

=> \(F_{1}(.15)=265.95\)

=> \(F_{1}=1773Ibs\)

Thus the answer is 1773 Ibs.

Using the concept of percentage, she earned a total of $1091 last week

A percentage is a number or ratio that can be expressed as a fraction of 100. Percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

To determine the amount she earned last week, we need to calculate the amount in commission and add it with her weekly salary.

She received 3% commission on her sales and she made a sale of $29700.

Let's find 3% of 29700

3 / 100 = x / 29700

0.03 = x / 29700

x = 29700 * 0.03

x = 891

The amount she earns will be 891 + 200 = 1091

Janelle earned $1091 last week

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Assuming \(f(x)=x^2\).

\(y=x^2\\x=-\sqrt y \vee x=\sqrt y\)

Since \(x\geq0\) only \(x=\sqrt y\) is valid.

Therefore

\(f^{-1}(x)=\sqrt{x}\)

The area of the composite figure is the sum of the area of the sector and the triangle . Therefore, the area of the composite figure is 95.52 cm².

This composite figure is created by placing a sector of a circle on a triangle. The area of the composite figure can be found as follows:

The composite figure is a combination of a sector and a right triangle. Therefore, the area of the composite figure is the sum of the area of the sector and the area of the right triangle.

area of the composite figure = area of the triangle + area of the sector

Hence,

area of the composite figure =  1 / 2 bh + ∅ / 360 × πr²

area of the composite figure = 1 / 2 × 6 × 8 + 82 / 360 × 3.14 × 10²

area of the composite figure = 48 / 2 + 25748 / 360

area of the composite figure = 24 + 71.5222222222

area of the composite figure = 95.5222222222

Therefore,

area of the composite figure = 95.52 cm²

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Answer:

Step-by-step explanation:

When you divide two negative numbers, the negative sign cancels. So you just get an answer of 6.

Answer:

6

Step-by-step explanation:

-54 / -9

ok so first of all we can just change them to positive

54 / 9

this is what goes on in my head

the 2 digits equal 9

a number times 9 is just that number less then that number times 10

54 / 9 = 6

-54 / -9 = 6

Answer:

A.

B.

C.

Step-by-step explanation:

all three are used in 3 dimensional objects hence the name 3 dimensions.

Answer:

B = 50 & C = 130

Step-by-step explanation:

I really don't know how to explain but 180 - 50 = 130 for C and 50 is the measurement for B

Answer:

S₁₆ = 344

Step-by-step explanation:

the sum to n terms of an arithmetic sequence is

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = - 1 and d = a₂ - a₁ = 2 - (- 1) = 2 + 1 = 3 , then

S₁₆ = \(\frac{16}{2}\) [ (2 × - 1) + (15 × 3) ]

     = 8 (- 2 + 45)

     = 8 × 43

     = 344

Answer:

59

Step-by-step explanation:

Round 59.3506494 to the first 2 sig figs which is 59 since the number next to the decimal isnt over or 5, so it stays as 59 instead of 60.

this is literally kindergarten math smh

its 21

Answer:

the answer is D because all of the other ones are completely different expressions. but D is the expression that's in the problem, except they combine 6x and 7x because they're like terms

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The answer is D because you want to add the same variables together (6x+7x) to simplify. and you would leave the 5 alone because it does not have the same variable.

Answer:

D 13x+5

Replace x in the equation for f(x) with -5:

|2x +9| = |2(-5) +9| = |-10 +9| = |-1| = 1

Now find x 1 and see where the graph of G(x) crosses the Y :

It crosses ay Y = 5

The answer is A. 5

Answer:

The correct answer is A. 5.

Step-by-step explanation:

I got it right on the Edmentum test.

Answer:

It’s 0.12

Step-by-step explanation:

Took test

Answer:

3,805 pounds of cement for $266.35 is a better buy

Step-by-step explanation:

3,805 pounds of cement for $266.35

266.35 : 3,805= 0.07

check your work:  3,805 x 0.07 = 266.35

so for the first offer you will be paying $0.07 per pound

5 tons of cement for $1,400.00

1 ton = 2000 pounds

5 tons = 10000 pounds

1,400.00 : 10000 = 0.14

for the second offer you will be paying $0.14 per pound of cement. 3,805 pounds of cement for $266.35 is a better buy because you will be paying half of the price for each pound.

hope this helps!

After evaluating the integral answer is 85/4. thus, option A is the answer.

The given transformation is a change of variables from (x, y) to (u, v). To evaluate the integral using the transformation, we need to use the Jacobian determinant. The Jacobian determinant is the absolute value of the determinant of the matrix of partial derivatives of the transformation.

du/dx = 1, du/dy = 1

dv/dx = -2, dv/dy = 1

The determinant of the matrix of partial derivatives is det(J) = du/dx * dv/dy - du/dy * dv/dx = (1)(1) - (1)(-2) = 3

So the Jacobian determinant is |J| = |3| = 3.

The integral becomes:

R\int \int 5y dx dy = (1/3) R\int \int 5v du dv

where R is the region in the uv-plane that corresponds to the region in the xy-plane bounded by the lines y= -x+1, y=-x+4, y= 2x+2, y= 2x+5

The integral evaluates to (1/3) R\int \int 5v du dv = (1/3) * 85/2 = 85/6 = 85/4

Therefore the correct answer is 85/4

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Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.