I need help with this geometry question

Juan must add a volume of 7 cubic feet for the enlarged sandbox.

The volume occupied by the sandbox (V), in cubic feet, is represented by the volume formula for a parallelpiped:

V = w · l · h

Where:

Juan wants to know the additional amount of sand required for the enlarged sandbox. If we know that the initial volume is equal to a cubic foot and each length is double, then we find that the resulting volume for sandbox is:

V' = (2 · w) · (2 · l) · (2 · h)

V' = 8 · (w · l · h)

V' = 8 · V

V = 8 ft³

The addition of sand is found by the following subtraction:

ΔV = V' - V

ΔV = 8 ft³ - 1 ft³

ΔV = 7 ft³

An additional volume of 7 cubic feet is needed for the sandbox.

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The area of the rectangle is given by the formula below:

A = 18x^2 - 27x + 7

For a rectangle of width W and length L, the area is given by the formula:

A = W*L

Here we know that the dimensions of a rectangle are 6x-7 and 3x-1, then we can define:

L = 6x - 7

W = 3x - 1

Replacing that in the area formula above we will get:

A = (6x - 7)*(3x - 1)

Now we can expand that product:

A = (6x)*(3x) + (6x)*(-1) + (-7)*(3x) + (-7)*(-1)

A = 18x^2 - 6x - 21x + 7

A = 18x^2 - 27x + 7

That is the formula for the area in terms of x.

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Answer:

b = 5

Step-by-step explanation:

Add 8b to both sides :

2+6b = 5b+7

Subtract 5b from both sides :

2+b = 7

Subtract 2 from both sides :

b = 5

Let's check :

-8(5) + 2 +6(5) = -3(5) + 7

-40 + 2 + 30 = -15 + 7

-38 + 30 = -8

-8 = -8

Correct

Hope this helped and have a good day

Answer:

b = 5

Step-by-step explanation:

to solve this you must first combine like terms

-8b + 2 + 6b = -3b + 7

combine (add) -8b and 6b

that makes -2b

-2b + 2 = -3b + 7

now add 3b to both sides to put b on one side

-2b + 2 + 3b = -3b + 3b + 7

b + 2 = 7

now subtract 2 to both side

b + 2 - 2 = 7 - 2

b = 5

that is your answer

Answer:

Step-by-step explanation:

The answer for this can be an inequality or an interval notation or a graph

* Subtraction of (1) in both sides of the inequality

* Let's call part A: [tex]X+1\geq 3[/tex]

* Let's call part B: [tex]\frac{4}{3} X < -8[/tex]

* Solve part A first:

Do the subtraction of (1) on both sides of the inequality.

X ≥ 3 −1

X ≥ 2

Subtract

* Solve part B now:

Multiply  for 3/4 both sides of the inequality  to eliminate the [tex]\frac{4}{3}[/tex]

[tex]\frac{4}{3} X (\frac{3}{4} < -8 (\frac{3}{4})[/tex])

X < -24/4

X < -6

Answer

Inequality Form:

x < −6 or x ≥ 2

Interval Notation:

( − ∞,−6)∪[2,∞)

In Graph:

See the attach

The figure given can be classified into; rhombus, quadrilateral, square.

The correct answer option is option c

Quadrilateral: This is a polygon with four sides.

Rhombus: This is a parallelogram having all sides of equal length.

Rectangle: A quadrilateral having opposing sides parallel and four right angles.

Square: A polygon with four sides of equal length and four right angle.

Parallelogram: This is a convex quadrilateral in which each pair of opposite edges are parallel and of equal length.

In conclusion, the figure can be classified into quadrilateral, rhombus and square.

Complete question:

The complete question is in the attached image.

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Answer:

Store B

Step-by-step explanation:

Store A: $2.50 ÷ 2 = $1.25

Store B: $3.25 ÷ 3 = $1.08 (to nearest cent)

Store B offers the better deal.

Answer:

2.6

Step-by-step explanation:

2 7/12

12x2=24

24+7=31

31/12=2.583333

Answer:

its 262.5%

Step-by-step explanation:

In the proportional relationship table, x would represent distance and y, weight.

The complete table is given in the explanation below.

If two variables that have quantities that vary proportionately are x and y, then the constant of proportionality that lies between both varies can be calculated as k = y/x. The equation for the proportional relationship would be expressed as y = kx.

x represents distance (cm)

y represents weight (newtons).

Using the pair of value that is given in the table, (20, 28), the constant of proportionality, k, would be:

k = y/x = 28/20

k = 1.4

The equation would be y = 1.4x.

Use the equation to complete the table by substituting the value of each missing variables:

Row 2, when x = 55:

y = 1.4(55)

y = 77

Row 3, when y = 140:

140 = 1.4x

140/1.4 = x

100 = x

x = 100

Row 4, when x = 1:

y = 1.4(1)

y = 1.4

The table would be:

           Distance (cm)     Weight (newtons)          

Row 1        20                     28

Row 2       55                     77

Row 3       100                    140

Row 4        1                        1.4              

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The product of 17×7 using the difference of two squares is 119.

= 17×7

=(12+5)(12-5)

=12(12-5)+5(12-5)

=12×12-12×5+5×12-5×5

=12²-5²

=144-25

=119

The difference between two squares is a theorem that tells us if a quadratic equation can be written as a product of two binomials, in which one shows the sum of the square roots and the other one is the difference of the square root.

I hope this answer helps.

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Answer:

143

Step-by-step explanation:

The reminder of the equation using the long division method is 70X - 12.

long division method :

Four main steps to solving this problem:

[tex]x^2 - 3$\overline{)x^5 + 24x^3- 5x - 12}$( x^3 + 25x\\\\[/tex]

           x₅ + 3 x³

          (-)    (-)                              

                 25x³ - 5x   -   12

                 25x³ - 75x

                 (-)      (+)                          

                            70x  - 12              

here

divisor - (x² - 3)

dividend - (x⁵ + 2x12x² - 5x - 12)

quotient - (x³ +25x)

the given question is incomplete the correct question is

Use long division to divide.

(x⁵ + 2x12x² - 5x - 12) / (x² - 3)

The reminder of the equation using the long division method is 70X - 12.

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The given linear equation has only one solution i.e. x = 3/4

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

A linear equation in one variable has

(a) Only one solution

(b) Two solutions

(c) More than two solutions

(d) No solution

Here,

On solving we have 8x - 6 = 0 or x = 3/4. The above linear equation is only true if x = 3/4 and

Hence, the given linear equation has only one solution i.e. x = 3/4.

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Answer: : (4 – 5) – (13 – 18 + 2).

Step-by-step explanation:

hoped dat helped

The two equations combined is

Eliminating one variable gives

the variables are

The equation formed is a consistent independent set of equation with two variables solved by elimination method as follows

Elimination of one of the variable

3x + y = 20      (1)

10x + y = 55     (2)

subtracting (1) from (2)

10x - 3x + y - y = 55 - 20

7x + 0 = 35

7x = 35

x = 5

substituting to find y

3x + y = 20

3 * 5 + y = 20

15 + y = 20

y = 20 - 15

y = 5

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Answer:44/52

Step-by-step explanation:There are four aces in a deck of 52 cards, so the probability of not drawing an ace is 44/52 =

Answer:

[tex]( \frac{1}{2} )^5 = \frac{1}{32}[/tex]

Step-by-step explanation:

The probability of "not a tail" is 1/2.  The five tosses are independent, so the probability of "not a tail" 5 times in succession is

[tex]\left(\frac{1}{2}\right) \cdot \left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right)[/tex]

The rate of spray at both times is 40 gallons/hour and it is the same.

What is the rate of change?

How quickly something changes over time is referred to as its rate of change, or ROC. Thus, it is the acceleration or deceleration of changes (i.e., the rate) rather than the magnitude of individual changes.

We have,

spray 20 gallons of water in 1/2 hour.

30 gallons and 3/4 hours (it's not 347 hours).

We simply calculate the rate for one hour:

1/2 hour = 20 gallons

3/4 hours = 30 gallons

Then for 1 hour,

1 hour = 20 * 2 = 40 gallons

1 hour = 30 * 4/3 = 40 gallons

Hence, the rate of spray at both times is 40 gallons/hour and it is the same.

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Answer:

13 Remainder 44

Step-by-step explanation:

The solution after divide is, 13 and remainder = 44

We have to given that;

954 divided by 70 by using long division and with a remainder.

Now, We can divide as,

⇒ 954 divided by 70

70 ) 954 ( 13

     -70

   ----------

      254

    - 210

     ----------

         44

Therefore, The solution is, 13 and remainder = 44

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Answer:

0.150985

Step-by-step explanation:

You add the two decimals together which gives you 120788.

Then, you move the decimal 4 places which is 12.0788.

Then you divide 12.0788 by 2 which gives you 6.0394.

Finally, you divide 6.0394 by 40 which gives you 0.150985.

The budget of KT's Restaurant for newspaper advertising for the coming year is $58,533,500

Given,

The length of advertisement of KT's Restaurant in Vidalia Times in week days = 5,000

The length of advertisement of KT's Restaurant in Vidalia Times in Saturdays = 10,000

The cost of daily column = $27.55 per column inch

The cost of Saturdays = $29.35 per column inch

We have to find the budget of KT's Restaurant for newspaper advertising for the coming year;

Here,

There are approximately 53 Saturdays in a year.

So,

365 - 53 = 312

Then,

The budget of advertisement on daily column = 312 × 5000 × 27.55 = $42,978,000

The budget of advertisement on Saturday column = 53 × 10,000 × 29.35 = $1,555,500

Therefore,

The total budget for advertisement = 42,978,000 + 1,555,500 = $58,533,500

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Answer:

$ 1.38

Step-by-step explanation:

5.50 ÷ 4 = 1.375. rounded to 2 dp: 1.38

The range of market return is 15.9% and the mean of market return is 2.94%

Productive Investments Limited provided the returns for Laska stocks for 2017 to 2021.

Year         Laska return

2017         -2.2%

2018          -3.4%

2019         12.5%

2020         -0.8%

2021          8.6%

The range of market return = Highest return - lowest return

= 12.5 - (-3.4)

= 15.9%

mean market return = (-2.2 +(-3.4) + 12.5 +(-0.8) + 8.6)/5

mean market return = 2.94%

Therefore, the range of market return is 15.9% and the mean of market return is 2.94%

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Answer:

B(a) = a/6 - 9

Step-by-step explanation:

The equation that represents the function B(a) as the length of the side parallel to the base is B(a) = a/6 - 9, as per the area of a trapezoid.

What is the area of a trapezoid?

If the length of two parallel sides of a trapezoid is 'a', 'b' and the height of that trapezoid is 'h', then the area of a trapezoid can be represented as

= [(a + b)h]/2

Given, the base of the trapezoid is 9 and the height of the trapezoid is 12.

Therefore, 'b' is the parallel side of the base.

The given function that represents the area of the trapezoid is:

A(b) = [12(b + 9)]/2

Let, A(b) = a.

Therefore, a =  [12(b + 9)]/2

⇒ 2a = 12(b + 9)

⇒ a = 6(b + 9)

⇒ a = 6b + 54

⇒ 6b = a - 54

⇒ b = (a - 54)/6

⇒ b = a/6 - 9

If we assume the length of the side parallel to the base 'b' = B(a), therefore, the equation will be:

B(a) = a/6 - 9

The number of yes votes on whether to raise property taxes, using proportions, was of 3345, considering that 6183 total votes.

A proportion is a fraction of a total amount, and equations are built with these fractions and the rates in the context of a problem to find the desired measures in the problem using basic arithmetic operations such as multiplication and division.

One application of proportions is for ratio problems, as one ratio between two amounts a and b is given by the division of a by b, and over the total, these rates are:

The ratio of yes votes to no votes was 5 to 4, hence the fraction of yes votes is given as follows:

5/(5 + 4) = 5/9.

The total number of votes was of 6183, hence the number of yes votes is calculated as follows:

5/9 x 6183 = 3435 total yes votes.

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Answer:

2x-2y=4 that is the best way u can write it

The required image of points (-4, 6) is (-6, -4) as per the given condition,

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,

As the image of the point (5, -1) is mapped as, (1, 5),
Which implies a function that (x, y) mapped as (-y , x)
So for (-4, 6) mapped as (-6, -4)

Thus, the required image of points (-4, 6) is (-6, -4) as per the given condition,

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The root of the quadratic equation is 2x² + 7x + 6 is x = -2 and x = -3 / 2.

The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.

The equation to find the roots, is a quadratic equation.

Hence,

2x² + 7x + 6

2x² + 3x + 4x + 6

x(2x + 3) + 2(2x + 3)

Hence,

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

Therefore,

x + 2 = 0    or 2x + 3 = 0

x = -2 or x = -3 / 2

The roots of the equation is x = -2 and x = -3 / 2

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The x and y table of all 5 points in this graph include the following:

x                   y

1                   1

2                  2

3                  3

4                  4

5                  5

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).

Additionally, the graph of any proportional relationship is always modeled by a straight line with the data points passing through the origin (0, 0).

In this scenario, we can reasonably and logically deduce that all of the data points in this graph are represented by the red symbols.

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The value of pH of the coffee is 4.89

pH is a measure of hydrogen ion concentration, a measure of the acidity or alkalinity of a solution

Given:  The formula pH= -log₁₀ C,

where is the concentration of hydronium ions in the solution measured in moles per litre

The concentration(C) of Hydronium ions type of coffee is 1.3 x 10⁻⁵ moles per liter

To calculate the pH, we will substitute the value of the concentration (C) into the given formula:

pH= -log₁₀ C                     (C = 1.3 x 10⁻⁵ moles per liter)

pH = -log₁₀(1.3 x 10⁻⁵) = 4.89

Therefore, the pH of the coffee is 4.89

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