A rectangular pool is 20 feet by 30 feet. The depth of the pool is 60 inches, but the depth of the water is 3/4 of the depth of the pool. Find each measure to the nearest tenth. (Lesson 1-7)
b. the volume of water in the pool

The value of x = 2.

Three points of collinear are A, B, and C. Here point B is between A and C.

The properties of collinear point are,

a>The slope of AB is equal to the slope of BC,

b>Line AB + BC = AC

c>The area is equal to 0.

As the three points are collinear, and from the second property we have

AB + BC= AC

Where, AB = 4x + 3

            BC = 3x + 2

So we have,

(4x + 3) + (3x + 2) =19

7x + 5=19

7x = 14

x=2

Therefore we get the value of x =2.

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Answer: x = -1, 15

Step-by-step explanation:

15 = x²- 14x

⇒ x²- 14x-15 = 0

⇒  x²- 15x+x-15 = 0

⇒ x (x-15) + (x-15) = 0

⇒ (x-15) (x+1) = 0

Now,

x= -1, 15

The following expression i.e.[tex]x^{\frac{10}{3} }[/tex] is rewritten as [tex](x^{3} )\sqrt[3]{x}[/tex]

Expression:

An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

You can think of expression as being comparable to phrases. A phrase in language may contain an action on its own, but it does not constitute a whole sentence.

⇒ [tex]x^{\frac{10}{3} }[/tex] { given a exponential expression }

⇒ [tex]x^{\frac{9+1}{3} }[/tex] { spliting the power into parts }

⇒[tex]x^{3+\frac{1}{3} }[/tex]

⇒ [tex]x^{3}[/tex]×[tex]\sqrt[3]{x}[/tex]  { spliting the terms by using properties of exponent }

⇒  [tex](x^{3} )\sqrt[3]{x}[/tex]

Hence,   [tex](x^{3} )\sqrt[3]{x}[/tex] is rewritten form of the given expression  i.e.[tex]x^{\frac{10}{3} }[/tex]

Therefore,The following expression i.e.[tex]x^{\frac{10}{3} }[/tex] is rewritten as [tex](x^{3} )\sqrt[3]{x}[/tex]

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The ratio of the largest element of the set to the sum of the other ten elements of the set is closest to which integer.

A ratio in mathematics describes how many times one number is contained in another. For instance, the ratio of oranges to lemons in a dish of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of oranges to the total amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8 (or 3:4). (or 4:7).

The quantities in a ratio can be of any kind, such as counts of people or things, measures of lengths, weights, or times, etc. Both numbers must be positive in the majority of situations.

Explanation:

The requested ratio is[tex]\[\dfrac{10^{10}}{10^9 + 10^8 + \ldots + 10 + 1}.\][/tex]

Using the formula for a geometric series, we have[tex]\[10^9 + 10^8 + \ldots + 10 + 1 = \dfrac{10^{10} - 1}{10 - 1} = \dfrac{10^{10} - 1}{9},\][/tex]

which is very close to [tex]$\dfrac{10^{10}}{9},$[/tex] so the ratio is very close to 9.

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Answer:

What's the question?

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

we just have to see the units to determine the terms

the terms are, a², ab, b, b², 1 has no terms, but imagine it as [tex]x^{0}[/tex]

Mark me brainliest if it helped

Answer:

bhe ganyan din

akin

Step-by-step explanation:

please help us

Answer:

G(x)=-9 when x=5

Step-by-step explanation:

Replace X with 5

3x -x^2+1 becomes 3*5-5^2+1

Then solve

15-25+1=-9

Given that statements 1 and 2 are true statements, the conclusion agrees with the laws of syllogism.

In syllogism, we have a pattern of reasoning in which the flow is that the premise must lead to the conclusion. This implies that reasoning must be logically sound and unbiased.

Now let us look at the statements that we have here;

Statement 1 - .If the measure of an angle is between 90-180 , then it is obtuse

Statement 2 - If an angle is obtuse, then it is not acute.

We know that these are true syllogisms because mathematically, we define the obtuse angle as an angle that is greater than 90 degrees but less than 180 degrees.

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The expression which represents the sales price of the bracelet in terms of the sticker price is; s = 0.65p and the evaluation for a sticker price of $60 is; $39.

It follows from the task content that the bracelet has been discounted 35% from its sticker price.

Hence, the sales price of the bracelet is therefore; (100 - 35)% of sticker price, p.

Therefore, we have;

s = (65/100) × p

s = 0.65p.

Ultimately, the evaluation for a sticker price of $60 is; s = 0.65(60).

s = $39.

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Dimensions of new rectangle after getting scaled by factor of 5 are 10cm by 15cm. Option  (B) is correct.

What is scale factor?

In two similar geometric figures the ratio of their corresponding side is scale factor let the old dimension be x and scale  factor be a then new dimension will be a*x

If a>1 then their will be enlargement in the geometric figures

Given that rectangle that is 2 cm by 3 cm has been scaled by a factor of 5

It means scale factor be 5

New dimensions of given rectangle will be found by multiplying by 5

New length and breadth are 2*5=10

                                               3*5=15

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Answer:

RS = 33

Step-by-step explanation:

from the number line

RT = RS + ST ( substitute values )

46 = RS + 13 ( subtract 13 from both sides )

33 = RS

Answer:

RS = 33

Step-by-step explanation:

Given that,

→ ST = 13

→ RT = 46

Then the value of RS will be,

→ RS + ST = RT

→ RS + 13 = 46

→ RS = 46 - 13

→ [ RS = 33 ]

Hence, the value is 33.

Answer:

choice 2,5,6

Step-by-step explanation:

Answer:

i took it like 2 years ago. i think its MNP, N, 1, and PNM?

Answer: 23 x 10,000

Step-by-step explanation:

23 multiplying with 10,000

you will get 230,000

Answer:

23 * 10000 or 23 * [tex]10^{4}[/tex]

Step-by-step explanation:

23 * 10000 or 23 * [tex]10^{4}[/tex]

The proof of the given algebra equation is; x = -40

We are given the algebra equation as;

(8 - 3x)/4 = 32

Using multiplication property of equality, multiply both sides by 4to get;

8 - 3x = 128

Using subtraction property of equality, subtract 8 from both sides to get;

-3x = 120

Using division property of equality, divide both sides by -3 to get;

x = -40

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The surface area of the sandbox assuming there is no lid is 21.3 feet

From the question, we are to determine the surface area of the sandbox

From the given information,

The dimension of the box is 3 feet by 4 feet

Thus,

Length = 4 feet

Width = 3 feet

and

The depth of the box is 8 inches

That is,

Height = 8 inches = 8/12 feet

Height = 2/3 feet

Now,

Using the formula for the surface area of a box

Surface area = (2lw + 2lh + 2wh)

If there is no lid,

The surface area becomes

Surface area = (lw + 2lh + 2wh)

Thus,

Surface area = (4×3 + 2×4×2/3 + 2×3×2/3)

Surface area = (12 + 16/3 + 4)

Surface area = (12 + 5.3 + 4)

Surface area = 21.3 feet

Hence, the surface area of the sandbox assuming there is no lid is 21.3 feet

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Basically, a sequence is a function whose domain is set of natural numbers and co-domain is set of real numbers.

Function:

A function relates each element of a set with exactly one element of another set (possibly the same set)

Real numbers:

Real numbers can be defined as the union of both rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”.

Domain

Domain is the set of all possible inputs of a function.

Co - Domain:

Co - domain is the set of its possible outcomes or results.

Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position.

That's why, every sequence must be the function itself.

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10 boxes will be required by the printing company

Company can fit 7000 calendars in 1 box

7000 calendars = 1 box

1 calendar = 1/7000

70000 calendar = 1/7000 * 70000

= 10 boxes

10 boxes will be required by the printing company

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The equation is 6.5 (r-1) + 5.5  = 259 or 6.5 r - 1 = 259.

In this case, r stands for the overall number of rows.

The answer indicates that each row is 6.5 cm tall.

A formula known as an equation uses the equals sign (=) to express how two expressions are equal. The word "equation" and its cognates in other languages may have slightly different meanings. For instance, in French, an equation is defined as having one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. The task of solving an equation with variables entails figuring out which values of the variables cause the equality to hold true. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions. Identity equations and conditional equations are the two types of equations.

The height of the top row is 6.5 - 1 = 5.5 cm.

Except for this row, there are total rows of = (r-1)

So, 6.5 is the total length of these rows (r-1)

The overall length of the wall is therefore equal to the sum of the (r-1) row and the top row.

However, once more in line with the inquiry,

Exactly 259 centimeters must be on the wall.

⇒ 259 = 6.5(r-1) + 5.5

⇒ 6.5(r-1) + 5.5 = 259

⇒ 6.5 r - 6.5 + 5.5 = 259

⇒ 6.5 r - 1 = 259

Which is the required equation for finding the number of rows (r).

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The correct answer is false.

A rational number also includes the sum of two rational numbers.

a/b-c/d=ad-bc/bd

Since a/b and c/d are integers, and we know that a, b, c, and d are all rational numbers. Since ad and bc are both integers under our rule, it follows that ad - bc is also an integer. As a result, our rule states that ad, bc, and bd are all integers. As a result, we know that ad - bc and bd are integers and that the difference between two rational numbers is a number of the type a/b-c/d=ad-bc/bd is the precise definition of a rational number, where ad - bc and bd are integers. Thus, we may conclude that a rational number is the difference between two rational numbers.

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According to the solving the distance between two points is:

= 14.77

In coordinate geometry, the distance formula is used to calculate the actual distance between two points. The formula for calculating the distance between two locations (x1,y1) (x 1, y 1) and (x2,y2) (x 2, y 2) is D=(x2x1)2+(y2y1)2 D = (x 2 x 1) 2 + (y 2 y 1) 2.

The length of a line segment seems to be the distance between two locations. Congruent segments are those with the same length. By drawing a line with a ruler, we may compute the approximate distance between two points.

Given points: (-4, 6) and (3, -7)

X₁ = -4
Y₁ = 6
X₂ = 3
Y₂ = -7

We know that the distance between two points:

distance = √((x₂ - x₁)²+(y₂ - y₁)²)

              = √((3 - (-4))²+((-7) - 6)²)

              = √((3 + 4)²+(-13)²)

              = √((7)²+(-13)²)

              = √((49)+(169))

              = √(218)

             = 14.77

According to the solving the distance between two points is:

= 14.77

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Answer:

Step-by-step explanation:

6x - 32 = 4x + 16

2x - 32 = 16

2x = 48

x = 24

6(24) - 32 = 144 - 32 = 112

4(24) + 16 = 96 + 16 = 112

Using a system of equations, it is found that there were 3 associates and 5 partners assigned to the case.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

The firm assigned a total of 8 lawyers to the case, hence:

x + y = 8

x = 8 - y.

The firm was able to charge the client $6500 per day for these lawyers' services, hence, considering the costs:

500x + 1000y = 6500.

Since x = 8 - y, we have that:

500(8 - y) + 1000y = 6500.

500y = 2500

y = 5.

x = 8 - 5 = 3.

The firm assigned 3 associates and 5 partners to the case.

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Answer:

8.

Step-by-step explanation:

Using Order of operations PEMDAS.

Arithmetic operations are done in the following order:

Parentheses, Exponents, Multiply, Divide, Add, Subtract.

So, we have:

-18 - 7(-10 + 8) + 12

= -18 - 7 * -2 + 12

= -18 + 14 + 12

= -4 + 12

= 8.

well, we can say that the function will be y = (50% of "x") - 8.

wait a minute! what's the 50% of "x" anyway?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{50\% of x}}{\left( \cfrac{50}{100} \right)x}\implies 0.5x~\hfill {\LARGE \begin{array}{llll} g=0.5x - 8 \end{array}}[/tex]

She has  27 quarters and 73 dimes.

Write a system of equations.

Let x be the number of quarters, and y be the number of dimes.

x+y=100

0.25x+0.10y=14.05

Solve by substitution:y=100−x

∴0.25x + 0.10(100 - x) = 14.05

0.25x+10−0.10x=14.05

0.15x+10=14.05

0.15x=4.05

x=27

Solve for y now:

y+27=100

y=100−27

y=73

Hence, She has 27 quarters and 73 dimes.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The meanings of the word equation and its cognates in various languages can vary slightly. For instance, in French, an equation is defined as having one or more variables, whereas, in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.

Finding the values of the variables that cause the equality to hold true is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions. Equations come in two varieties: identities and conditional equations.

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Answer:

Hi, here are the remaining values in order.

Answer: option c

Step-by-step explanation:

hope this helps

Answer: 102

Step-by-step explanation:

[tex]x=-2\ \ \ \ \ y=4\\\\8x^2-xy+y^2-xy^2+14=\\\\8(-2)^2-(-2)(4)+(4)^2-(-2)(4)^2+14=\\\\8(-2)(-2)-(-8)+(4)(4)-(-2)(4)(4)+14=\\\\32+8+16+32+14=\\\\102[/tex]