Approximately how many gallons are in
7 liters? (1 L 0.26 gal.)
Group of answer choices

1.8 gallons

6.7 gallons

7.3 gallons

46 gallons

The width of the rectangle is equal to 3.42 meters

Let the width of the rectangle be represented by the variable x

thus from the question we can say that the length of the rectangle is 3 + x

Given is the area of the rectangle

we know that the area of the rectangle is Length × Breadth

Given area of the rectangle = 22 square meters

thus Area = Length × Breadth

On substituting the value we get

22 = ( 3 + x ) ( x )

x² + 3x = 22

x² + 3x - 22 = 0

b² - 4ac = 9 + 88 = 97

thus - b ± \(\sqrt{b^{2} -4ac}\) / 2a

= - 3 ± 9.84 / 2

Thus the two values of x we will get are :

x= -12.84 / 2 = -6.42 which is rejected because width cant be negative

thus the value of x = 6.84 / 2 =3.42 meters

Thus we get values of x as

x =  3.42 meters

Thus the required width of the rectangle = 3.42 meters

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Consider the same figure as given above. It is observed that DP/PE = DQ/QF and also in the triangle DEF, the line PQ is parallel to the line EF.

So, ∠P = ∠E and ∠Q = ∠F.

Hence, we can write: DP/DE = DQ/DF= PQ/EF.

The above expression is written as

DP/DE = DQ/DF=BC/EF.

It means that PQ = BC.

Hence, the triangle ABC is congruent to the triangle DPQ.

(i.e) ∆ ABC ≅ ∆ DPQ.

Thus, by using the AAA criterion for similarity of the triangle, we can say that

∠A = ∠D, ∠B = ∠E and ∠C = ∠F.

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The solution of the given initial-value problem would be  y(x) = 3 cos(3x) + 2 sin(3x).

We are required to solve the given initial-value problem.

The initial value problem isy″ + 9y = 0, y(0) = 3, y′(0) = −6

To solve the initial-value problem, we follow these steps:

Step 1: We find the characteristic equation to be r² + 9 = 0.The roots of this equation are r = ±3i.Therefore, the general solution is

y(x) = c1 cos 3x + c2 sin 3x.

Step 2: We will use the initial conditions to find the values of c1 and c2.We know that y(0) = 3. Therefore,

3 = c1 cos 0 + c2 sin 0 ⇒ 3 = c1.

Using the second initial condition,y′(x) = -3c1 sin 3x + 3c2 cos 3x.

We know that y′(0) = −6.

Therefore,−6 = -3c1 sin 0 + 3c2 cos 0 ⇒ −6 = 3c2.

Therefore, c2 = −2.

Substituting the values of c1 and c2 in the general solution, we get

y(x) = 3 cos 3x − 2 sin 3x = 3 cos(3x) + 2 sin(3x).

Therefore, the solution of the given initial-value problem is

y(x) = 3 cos(3x) + 2 sin(3x).

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The coordinate for the R' is (3, -4) if the R(-4, 3) is reflected in the line y = x option (D) is correct.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have:

Image of R(-4, 3) after a reflection in the line y = x

The rule for the reflection over y = x is:

(x, y) = (y, x)

(-4, 3) = (3, -4)

Thus, the coordinate for the R' is (3, -4) if the R(-4, 3) is reflected in the line y = x option (D) is correct.

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The pair of rectangle that will prove Carly's statement incorrect is: Option 3: A rectangle with length 4 and width 3. A rectangle with length 3 and width 2.

Dilation of a figure will leave its sides get scaled (multiplied) by same number.

Thus, suppose if a rectangle is dilated, and its sides were of length = L and width = W, then its dilated version would be having length = Ln, and width = Wn where n is the factor of scaling.

Thus, we get:

\(n = \dfrac{Ln}{L} = \dfrac{Wn}{W}\\\\or\\\\\text{Ratios of corresponding dilated sides are equal}\)

For the given cases, checking all the given pairs:

Getting length to length and width to width ratio:

\(\dfrac{L_1}{L_2} = \dfrac{4}{8} = \dfrac{1}{2}\\\\\dfrac{W_1}{W_2} = \dfrac{2}{4} = \dfrac{1}{2}\\\\\\Thus, \dfrac{L_1}{L_2} = \dfrac{W_1}{W_2}\)

Pair given are dilated version of each other.

Getting length to length and width to width ratio:

\(\dfrac{L_1}{L_2} = \dfrac{4}{6} = \dfrac{2}{3}\\\\\dfrac{W_1}{W_2} = \dfrac{2}{3} \\\\\\Thus, \dfrac{L_1}{L_2} = \dfrac{W_1}{W_2}\)

Pair given are dilated version of each other.

Getting length to length and width to width ratio:

\(\dfrac{L_1}{L_2} = \dfrac{4}{3}\\\\\dfrac{W_1}{W_2} = \dfrac{3}{2} \\\\\\Thus, \dfrac{L_1}{L_2} \neq \dfrac{W_1}{W_2}\)

Pair given are not dilated version of each other.

Getting length to length and width to width ratio:

\(\dfrac{L_1}{L_2} = \dfrac{4}{2} = \dfrac{2}{1}\\\\\dfrac{W_1}{W_2} = \dfrac{3}{1.5} = \dfrac{2}{1}\\\\\\Thus, \dfrac{L_1}{L_2} = \dfrac{W_1}{W_2}\)

Pair given are dilated version of each other.

Thus, the pair of rectangle that will prove Carly's statement incorrect is: Option 3: A rectangle with length 4 and width 3. A rectangle with length 3 and width 2.

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Answer:

c

Step-by-step explanation:

The algebraic expression that represents the total cost of buying one carton of strawberry ice cream and one carton of chocolate ice cream is 4.00 + 4.00 = 8.00.

Let's break down the given information step by step. The grocery store is offering a sale on ice cream, and each carton of any flavor costs 4.00. Cecy wants to buy one carton of strawberry ice cream and one carton of chocolate ice cream.

To represent the total cost algebraically, we need to add the cost of the strawberry ice cream to the cost of the chocolate ice cream. Since each carton costs 4.00, we can write the expression as 4.00 + 4.00.

By adding the two terms, we get 8.00, which represents the total cost of buying one carton of strawberry ice cream and one carton of chocolate ice cream.

Therefore, the algebraic expression 4.00 + 4.00 = 8.00 represents the total cost of buying the ice cream.

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Answer:

30ft

Step-by-step explanation:

It says that triangle DEF is equal to triangle GHJ, meaning they are congruent. This would automatically mean that the side length of the triangles would be the same. The side length of triangle DEF is 30ft so that would be the same in triangle GHJ.

Answer:

The length of the diagonal from P to Q is

\( \sqrt{ {9}^{2} + {12}^{2} + {8}^{2} } = \sqrt{289} = 17\)

Answer:

35

Step-by-step explanation:

3:5

21;35

as it must be * by 7 as 3*7=21

so therefore we times 5*7 as well

so they has 35 loses

If a book has 276 pages and Amina had read 1/3 of the book, then 184 pages are left for Amina to read.

If a book has 276 pages and Amina has already read 1/3 of the book, we need to find out how many pages are left for her to read. To calculate the number of pages Amina has already read, we can multiply the total number of pages by the fraction she has read:

1/3 x 276 = 92 pages

Therefore, Amina has already read 92 pages of the book.

To determine how many pages are left for Amina to read, we subtract the number of pages she has already read from the total number of pages:

276 - 92 = 184 pages

So, there are 184 pages left for Amina to read in the book.

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The yearly difference in median income for males versus females with less than a high school diploma is $9,302.

This means that, on average, males with less than a high school diploma earn about $9,302 more per year than their female counterparts.

The yearly difference in median income between males and females with less than a high school diploma can be determined from the latest available data from the U.S. Census Bureau.

According to the U.S. Census Bureau's report on Income and Poverty in the United States: 2020, the median earnings for full-time, year-round workers with less than a high school diploma were as follows:

Males: $29,846

Females: $20,544

To calculate the yearly difference in median income, we simply subtract the median earnings for females from the median earnings for males:

$29,846 - $20,544 = $9,302.

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Answer:

64.9 degrees I'd say. may not be exact

Answer:

12-9x

Step-by-step explanation:

Here, we want to write an algebraic expression from the given statement

Let us start with the product of 9 and a number x

What this mean is that we want to multiply 9 and x

That gives 9 * x = 9x

Now, 12 is decreased by this product means we are to subtract 12 from it

we have this finally as;

12-9x

Expression of the collection of variables and constant. The value of the given expression 2x² - y¹ + 3x⁰ for x = 3 and y = 5 will be 16.

An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.

Expression is very useful to determine the end or root value of constraint.

As per the given expression,

2x² - y¹ + 3x⁰

Substitute, x = 3 and y = 5

2(3)² - 5 + 3(1) = 18 - 5 + 3 = 16.

Hence "The value of the given expression 2x² - y¹ + 3x⁰ for x = 3 and y = 5 will be 16".

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The selection depends on individual needs, preferences, and the intended use of the tiny house.

a) To find the amount of space inside each house, we need to calculate the volume for each design.

House on the left:

Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³

Triangular house:

Volume of a triangular prism = (base area x height) / 2

Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²

Volume = (20 m² x 7 m) / 2 = 70 m³

b) When comparing the environmental impacts of each house, several factors need to be considered:

Positive impacts:

1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.

2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.

3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.

Negative impacts:

1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.

2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.

3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.

c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:

The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.

The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.

Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.

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\(3(x - 2) + 7x = \frac{1}{2} (6x - 2) \)

\(3(x - 2) + 7x = \frac{1}{2} (6x - 2) \\ \\ \implies3x - 6 + 7x = ([\frac{1}{2} \times 6 \: x] - [\frac{1}{2} \times 2]) \\ \\ \implies10x - 6 = ([\frac{1}{ \cancel2} \times \cancel 6 \: x] - [\frac{1}{ \cancel2} \times \cancel2]) \\ \\ \implies 10x - 6 = 3x - 1 \\ \\ \fbox{Bringing (3x )to left side whereas( - 6 )in right side} \\ \\ \implies10x - 3x = - 1 + 6 \\ \\ \implies7x = 5 \\ \\ \therefore x = \frac{5}{7} \)

The Solution is = \( \frac{5}{7}\)

\(\text\red{One Solution set is possible.}\)

Answer:

6

Step-by-step explanation:

From the table given defining a function, the values of "x" on the table represents the input of the function, which gives us an output, f(x), which can be labelled as "y" in some instances.

Thus, the value of f(0), is simply the output value we would get, given an input value of "0".

So therefore, f(0) = 6. That is, at x = 0, f(x) = 6.

Answer: 6

Step-by-step explanation:

Answer:

x^-3=1/x^3

This is how we do it.

Answer:

Take the reciprocal. 1/x^3

Step-by-step explanation:

When you take the reciprocal of a number or a variable, the exponent changes sign.

The simplified form of the expression 1/5 divied by 2 as a fraction is 1/10.

Given the expression in the question;

1/5 divied by 2

1/5 ÷ 2

To simplify, multiply 1/2 by the reciprocal of 2

1/5 ÷ 2

1/5 × 1/2

Simplify

( 1 × 1 ) / ( 5 × 2 )

( 1 ) / ( 5 × 2 )

Multiply 5 and 2

( 1 ) / ( 10 )

1/10

Therefore, the simplified form is 1/10.

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Answer:

Ill help you if you come help me with mine c:

Step-by-step explanation:

here is mine:

The values of f(x) and g(x) are shown for selected values of x in the table below.

x f(x) g(x)

0 0 1

1 3 2

2 6 4

3 9 8

4 12 16

Of these two functions, one is exponential and the other is linear. Determine which of the functions is linear, and explain why this must be the case.

Determine guest's expected number of phone calls after a week by simplifying equation, calculating 0.5793, and dividing by 17.38.

To find out how many phone calls the guest should expect after a week, we can substitute d = 7 into the equation y = 30(0.92)d:

y = 30(0.92)7

Simplifying this equation, we get:

y = 30(0.92)^7

Using a calculator, we can calculate that (0.92)^7 is approximately 0.5793.

Substituting this value back into the equation, we have:

y = 30 * 0.5793

Multiplying 30 by 0.5793, we get:

y ≈ 17.38

Therefore, the guest should expect approximately 17.38 phone calls after a week. Since we cannot have a fraction of a phone call, the closest whole number is 17. So the answer is not listed among the given options.

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The solution of the given inequality is t ≤ -10.

When two values are not equal to one another, there is an inequality between them, which is a mathematical concept. It is a claim that one value exceeds or falls short of another.

Mathematical symbols for inequalities include (less than), > (greater than), (less than or equal to), and (greater than or equal to).

Given that,

t - 4 ≤ -14

The inequality can be solved as below,

t - 4 ≤ -14

t ≤ -14 + 4

t ≤ -10

Therefore, the solution to the inequality is t ≤ -10.

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Answer:

x = 3 (see below)

Step-by-step explanation:

To solve for x, you need to isolate the variable to one side of the equation. To do that, you need to use reverse operations. For example, the reverse operation of subtraction is addition.

In this case, we have:

15 = 5x

5x is the same thing as 5 (x) or 5 times x. This means the reverse operation is division. So, we need to divide both sides of the equation by 5:

15 = 5x

-----   ----

5       5

--------------

3 = x

x = 3

Answer:

See below

Step-by-step explanation:

Best way to do this is to convert the equation to vertex form and that will tell you several points you can graph:

\(y=x^2-4x-1\\y+5=x^2-4x-1+5\\y+5=x^2-4x+4\\y+5=(x-2)^2\\y=(x-2)^2-5\)

Here, we can see that the vertex of the parabola is (2,-5) and that the axis of symmetry is x=2. You can also quickly get the y-intercept since plugging in x=0 gets you (0,-1). Finding a few more points should be pretty simple from here on out since your equation is more condensed.

8723.36's hexadecimal equivalent is 2233.C5.

To convert the hexadecimal number BEBE.FAFA into decimal, we can use the following method:

BE.BD = (11 x 16^1) + (14 x 16^0) = 189.

FA.FA = (15 x 16^1) + (10 x 16^0) = 250.

BEBE.FAFA = (189 x 16^2) + (250 x 16^(-4))= 48894.98047 (in decimal).

Therefore, the decimal equivalent of hexadecimal number BEBE.FAFA is 48894.98047.8.

To convert the decimal number 8723.36 into octal, we can use the following steps:

Divide the number by 8, and write the remainder from right to left until the quotient is less than 8.8723 ÷ 8 = 109 .Quotient109 ÷ 8 = 13 Remainder 5

Quotient 13.

Write down the remainder on the left of the last remainder.

13 ÷ 8 = 1 Remainder 5

Quotient 1.

Write down the remainder on the left of the last remainder.

Since the quotient of 1 is less than 8, we stop writing down remainders.

The octal equivalent of 8723.36 is 20725.64.9.

To convert the decimal number 8723.36 into binary, we can use the following method:

Convert the integer part to binary by repeated division by 2. 8723 ÷ 2 = 4361

Remainder 1 4361 ÷ 2 = 2180

Remainder 1 2180 ÷ 2 = 1090

Remainder 0 1090 ÷ 2 = 545

Remainder 0 545 ÷ 2 = 272

Remainder 1 272 ÷ 2 = 136

Remainder 0 136 ÷ 2 = 68

Remainder 0 68 ÷ 2 = 34

Remainder 0 34 ÷ 2 = 17

Remainder 1 17 ÷ 2 = 8

Remainder 1 8 ÷ 2 = 4

Remainder 0 4 ÷ 2 = 2

Remainder 0 2 ÷ 2 = 1

Remainder 0 1 ÷ 2 = 1

Remainder 1

Write down the remainders from the last to first, and add zeroes to make up for any missing digits: 10001000101011.0111011111010

Therefore, the binary equivalent of 8723.36 is 10001000101011.0111011111010.10.

To convert the decimal number 8723.36 into hexadecimal, we can use the following method:

Convert the integer part to hexadecimal by repeated division by

16. 8723 ÷ 16 = 545

Remainder 3 545 ÷ 16 = 34

Remainder 1 34 ÷ 16 = 2

Remainder 2 2 ÷ 16 = 0

Remainder 2

Write down the remainders from the last to first: 2233.

Convert the fractional part to hexadecimal by repeated multiplication by 16 and recording the integer part at each step.0.36 x 16 = 5.76 (integer part 5)0.76 x 16 = 12.16 (integer part 12 = C)

Therefore, the hexadecimal equivalent of 8723.36 is 2233.C5.

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Answer:

The height of the right circular cylinder is 4.55 inches ⇒ b

Step-by-step explanation:

The formula of the surface area of a right circular cylinder is

S.A = 2πrh + 2πr², where

∵ The surface area of a right circular cylinder is 300 square inches

∴ S.A = 300 in.²

∵ Its radius is 5 inches

∴ r = 5 in.

∵ π = 3.14

→ Substitute them in the rule above

∵ 300 = 2(3.14)(5)(h) + 2(3.14)(5)²

∴ 300 = 31.4h + 157

→ Subtract 157 from both sides

∵ 300 - 157 = 31.4h + 157 - 157

∴ 143 = 31.4h

→ Divide both sides by 31.4

∵ 4.554140127 = h

∴ 4.55 = h

∴ The height of the right circular cylinder is 4.55 inches

Answer:

B.) 4.55

Step-by-step explanation:

Edge 2021