A painter needs 5 gallons of paint to finish a house. He has 3 quarts and 1 pint. How much more paint does he
need?
Make a Selection:
A. 3 gallons
B. 4 gallons, 1 pint
C. 3 gallons, 1 pint
D. 4 gallons, 1 quart
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Answer:

Step-by-step explanation:

The equation is simplified by combining "like" terms. The terms "2x" and "2x" are "like" not just because they are identical, but because the only variable (x) is raised to the same power (1) in each term. We can use the distributive property to help combine those terms:

  2x +2x = (x)(2+2) = 4x

Of course, the constants on the left can be simply added: 3 + 5 = 8.

Now, the simplified form of the equation is ...

  4x + 8 = 16

__

To solve this, we note that all the numerical values are multiples of 4, the x-coefficient. Then we can divide all of them by 4 to give ...

  x + 2 = 4

You know the value of x already at this point, since you're familiar with your addition facts. However, to complete the solution algebraically, we subtract 2 from both sides of the equation:

  x = 2

_____

Comment on this solution

You will usually get instruction to "separate the variable terms from the constant terms," so the simplified equation would usually have 8 subtracted from both sides to give ...

  4x = 8

Then, you would divide by the x-coefficient to get x=2.

I elected to do it the way shown above for a couple of reasons:

Answer:

Step-by-step explanation:

Solve each equation individually, using substitution or elimination.

A. x + 3y = 3

   2x - y = -2

Substitute:

2(3-3y) - y = -2

6-6y-y = -2

6-7y = -2

y = 8/7

plug it back in to the first equation:

x + 24/7 = 3

x = -0.4285, approximately, and since this rounds to -0.4 and 8/7 approximately equals 1.1,

A is your answer.

The system of equations has a solution of approximately (-0.4,1.1) is x+3y=3 and 2x-y=-2.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

here,
To determine whether (-0.4, 1.1) is the solution of which equation,
So, put the solution in the equation of Option A,
x+3y = 3
-0.4 + 3(1.1) = 3
2.9 ≈ 3

And,
2x-y=-2
2(-0.4) - 1.1 = -2
-0.8 - 1.1 = -2
-1. 9 ≈ -2

Thus, the system of equations has a solution of approximately (-0.4,1.1) is x+3y=3 and 2x-y=-2.

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Answer:

B

Step-by-step explanation:

In the composition of f and g, the equation is telling us to place the function f inside g. Observing in B that f is (x + 4), then this can be put in place of the x in 3x^2, making it 3(x + 4)^2 and finally the minus 5.

Answer:

Anything you own that has value and can be turned into cash.

Step-by-step explanation:

Unless there is a passage that refers to the word, the second option would be the best answer due to Google's online dictionary.

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept → (0, b)

We have the equation y = 6x + 8. Therefore

m = 6

b = 8

Answer: A: (0,8)

Step-by-step explanation:

Answer:

Option 1

Step-by-step explanation:

Before answering the question, we should define what the like radicals are.

The radicals which have the same expression under the root and same root number. There can be numerical multiples outside the radical but we have to compare the root number and same expression under the root.

In the given question, only option one has the same root number to the radical given in the question and the same expression under the root ..

Answer:

Assuming your asking what is 4.82 hours to minutes, the answer to this is 289.2 minutes

Answer:

∠2 = 52°

Step-by-step explanation:

Since 1 angle = 90° then the sum of the other 2 angles = 90°, that is

∠2 + ∠3 = 90 ← substitute values

3x + 1 + 2x + 4 = 90

5x + 5 = 90 ( subtract 5 from both sides )

5x = 85 ( divide both sides by 5 )

x = 17

Hence

∠2 = 3x + 1 = (3 × 17) + 1 = 51 + 1 = 52°

Answer:

60 m2

Step-by-step explanation:

Since they are congruent SQ=MP, NM=RQ, RS=NP. The formula to find the area of a triangle is  1/2 bh. So you do 8 times 15 divided by 2. 8 times 15 is 120. 120 divided by 2 is 60 m2.

Answer:60m^2

Step-by-step explanation:

MNP is a triangle and area of a triangle = 1/2* base *height

From the figure height = 15 and base = ?

So we solve for the base using Pythagoras theorem

.: MP = square root of 17^2 - 15^2

MP = 8m =the base

Area of MNP = 1/2*8*15

Area = 60m^2

For this case we have that if and it varies directly with x, we can write the equation as:

[tex]y = kx[/tex]

Where:

k: It is the constant of proportionality.

According to the table:

[tex]-3 = k (1)[/tex]

Clearing k:

[tex]k = -3[/tex]

Then,[tex]y = -3x[/tex]

Answer:

Option C

Answer:

y varies directly with x

[tex]k = -3[/tex]

The equation is:

[tex]y = -3x[/tex]

Step-by-step explanation:

We can say that and it varies directly with x if it is fulfilled that

[tex]y = kx[/tex]

Where k is a constant known as the constant of variation.

So

[tex]\frac{y}{x} = k[/tex]

This means that if y varies with x then the division of y between x should always be equal to a constant value k.

We must test this for the values shown in the table

[tex]\frac{-3}{1} = -3[/tex]

[tex]\frac{-9}{3} = -3[/tex]

[tex]\frac{-15}{5} = -3[/tex]

The quotient of [tex]\frac{y}{x}[/tex] is always equal to [tex]-3[/tex]. Then [tex]k = -3[/tex] and the variation of y with x is direct

The equation is:

[tex]y = -3x[/tex]

Answer:

A = 3.4 cm

Step-by-step explanation:

The length of line segment AB is 3.4cm.

The area of octagon is given as 2a^2(1+sqrt{2})  

Where a is the side of octagaon. All sides of octagon are same.

As, 2a^2(1+sqrt{2}) = 54cm

Then, a^2 = 54/2(1+sqrt{2})

a^2 = 54/4.828

a^2 = 11.19

a = 3.4 cm

We can notice that 731.8 is the Greatest among all numbers because 731 is always greater than 730

Now consider the remaining numbers : 730.38 , 730.1 , 730.63

★  730.1 can be written as 731.10

As the Number part of remaining numbers is same (730), we need to consider the decimal parts of the numbers in order tell which number is greatest among them

★ Decimal part of 730.38 is 38

★  Decimal part of 730.10 is 10

★  Decimal part of 730.63 is 63

As 63 > 38 > 10 :

We can say that : 730.63 > 730.38 > 730.10

So, Arrangement of given numbers from greatest to least is :

★  731.8 > 730.63 > 730.38 > 730.10

Answer:

Third week, 15 words per minute

Step-by-step explanation:

First week: 10 words per minute

Second week

10 * 20% = 10*.2 = 2

It is an increase, so we add the 2 to the original amount

10+2 = 12 word per minute

Third week

12 * 25% = 12 *.25 = 3

It was an increase, so we add the 3 to the amount in week 2

12+3 = 15 words per minute

Hello There!

50*50 is 2,500

Answer:

1000

Step-by-step explanation:just multiply

Answer:

82%

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

Given

[tex]\sqrt{-x+4}[/tex] = x - 4 ( square both sides )

- x  4 = (x - 4)² ← expand

- x + 4 = x² - 8x + 16 ( subtract - x + 4 from both sides )

0 = x² - 7x + 12 ← in standard form

0 = (x - 3)(x - 4) ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 4 = 0 ⇒ x = 4

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions

x = 3 : [tex]\sqrt{-3+4}[/tex] = [tex]\sqrt{1}[/tex] = 1

right side = 3 - 4 = - 1

left side ≠ right side ⇒ extraneous solution

x = 4 : [tex]\sqrt{-4+4}[/tex] = 0 and right side = 4 - 4 = 0

left side = right side ⇒ x = 4 is the solution

ANSWER

Option D.

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} [/tex]

The new function is

[tex]g(x) = f(5x)[/tex]

This implies that,

[tex]g(x) = {(5x)}^{2} [/tex]

This gives us:

[tex]g(x) = {25x}^{2} [/tex]

We can that the graph of g(x) will shrink by a factor of 25 compared to f(x).

The graph will open upwards and shrink towards the y-axis.

Answer:

The answer is D

Step-by-step explanation:

* Lets revise some transformations

- A horizontal compression is the squeezing of the graph toward

 the y-axis.

- If the graph is y = f(x) and its image is y = f(k•x)

∴ The graph is horizontally compressed if k > 1 that means divide

   each of its x-coordinates by k.

∴ The graph is horizontally stretched if 0 < k < 1, that means divide

   each of its x-coordinates by k.

* Now lets solve the problem

∵ f(x) = x²

∵ g(x) = f(5x)

- Substitute the value of x in f(x) by 5x

∴ f(5x) = (5x)²

∴ g(x) = (5x)²

∵ The image of f(x) = x² is g(x) = (5x)²

∴ k = 5

∵ 5 > 1

∴ The graph of f(x) is compressed horizontally

- divide each x-coordinates of the points on the graph by 5

∴ The graph becomes narrow to the y-axis

- Look to the attached graph for more understanding

# The red graph is f(x) = x²

# The blue graph is g(x) = (5x)²

* The answer is the last graph D

For this case we must simplify the following expression:

[tex]\sqrt {\frac {2160x ^ 8} {60x ^ 2}}[/tex]

We rewrite the expression:

[tex]\sqrt {\frac {60 * 36 * x ^ 8} {60x ^ 2}} =[/tex]

We eliminate common terms:

[tex]\sqrt {\frac {36 * x ^ 8} {x ^ 2}} =[/tex]

For division of powers of the same base, the same base is placed and the exponents are subtracted:

[tex]\sqrt {36x ^ {8-2}} =\\\sqrt {36x ^ {6}} =[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

[tex]6x ^ {\frac {6} {2}} =\\6x ^ 3[/tex]

Answer:

Option C

Answer:

156 sq in

Step-by-step explanation:

If you have a rectangle measuring 13 inches by 12 inches, you will consider the side with 13 inches as the length of the rectangle and the one with 12 inches as the width of the rectangle.

The area of a rectangle is obtained by multiplying the length by the width... so, you'll get:

A = 13 in x 12 in = 156 square inches

Answer:

(y + 14)(y - 14)

Step-by-step explanation:

A difference of squares has the general form

a³ - b² and factors as

(a + b)(a - b)

Given

y² - 196

y² = (y)² ⇒ a = y and 196 = 14² ⇒ b = 14

y² - 196

= y² - 14² = (y + 14)(y - 14) ← difference of squares

Answer:

B

Step-by-step explanation:

We can use the law of sines to form a proportion.

The law of sines state that any side length divided by the sin of the opposite angle measure will be equal.

Let's form a proportion.

[tex]\frac{25}{sin(90)}=\frac{b}{sin(35)}[/tex]

Simplify.

b ≈ 14.34

The value of b from the diagram is 14

From the given diagram we have the following

hypotenuse = 25

using the SOH CAH TOA identity, hence;

sin 35 = b/25

b = 25sin35

b = 14.34

The value of b from the diagram is 14.34

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Answer:

f(n) = 64(3/4)^(n-1).

Step-by-step explanation:

The common ratio  is  48/64 = 36/48 =  3/4.

For a GS  nth term = a1 r^(n-1) where r = the common ratio, a1 = the first term, and n = the number of peaks reached.

The axplicit function is   64(3/4)^(n-1).

Answer:

f(x) = 64(three-fourths) Superscript x minus 1

Step-by-step explanation:

A bouncing toy reaches a height of 64 inches at its first peak, 48 inches at its second peak, and 36 inches at its third peak. The explicit function is f(x) = 64(three-fourths) Superscript x minus 1

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}5x-3y=6\\x+y=2&\text{multiply both sides by 3}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}5x-3y=6\\3x+3y=6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad8x=12\qquad\text{divide both sides by 8}\\.\qquad x=1.5\\\\\text{put the value of x to the second equation:}\\\\1.5+y=2\qquad\text{subtract 1.5  from both sides}\\y=0.5[/tex]

Answer:

Your answer would be A.) 5x − 3y = 6  and 6x − 2y = 8

when a graphed line is vertical, it indicates that the relation is not a function

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

We can visually identify functions by their graphs using the vertical line test. If any vertical line intersects the graph more than once, then the graph does not represent a function.

The vertical line represents a value in the domain, and the number of intersections with the graph represent the number of values to which it corresponds.

As we can see, any vertical line will intersect the graph of y=|x|−2 only once.

Therefore, it is a function.

A vertical line can cross the graph of x=|y|+1 more than once.

therefore, it is not a function.

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Answer:

3x + 7y = 31

-3x - 2y = -1

____________________

5y = 30

y = 6

____________________

3x + 42 = 31

3x = -11

x = - 11/3

____________________

x = -11/3; y = 6

For this case we have by definition, that the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We need two points through which the line passes to find the slope:

[tex](0, -2)\\(-3,0)[/tex]

We found the slope:

[tex]m = \frac {y2-y1} {x2-x1}\\m = \frac {0 - (- 2)} {- 3-0} = \frac {2} {- 3} = - \frac {2} {3}[/tex]

So, the equation is of the form:

[tex]y = - \frac {2} {3} x + b[/tex]

We substitute a point to find "b":

[tex]-2 = - \frac {2} {3} (0) + b\\-2 = b[/tex]

Finally, the equation is:

[tex]y = - \frac {2} {3} x-2[/tex]

Answer:

Option C

Answer:

Step-by-step explanation:

In math, a term is a combination of coefficients, constants and /or variables, each combination being separated by either a + sign or a - sign.

A term's definition provides an explanation of its meaning, often found in dictionaries but should also consider context and usage for a well-rounded understanding. Terms are often constructed from roots, prefixes, and suffixes that each convey a portion of the term's complete meaning. In textbooks, 'Key Terms' are important words paired with their definitions, as used in context.

The definition of a term refers to the explicit and clear explanation of what a particular term or word represents or means. This explanation is often found in dictionaries, but for full comprehension, it's important to also consider context and usage. While a dictionary provides a basic description based on common usage of a term, sometimes this common usage might lack precision or accuracy. It becomes essential to reflect on the term's meaning within a larger understanding of the world.

Consider anatomical terms used in biology, their definitions are composed of roots, prefixes, and suffixes - each part offering a piece of the term's overall meaning. For example, 'hypertension' is made from hyper- which means high and -tension which means pressure. Together it represents abnormally high blood pressure.

Meanwhile, in the context of a school textbook, 'Key Terms' are words of importance that are highlighted (usually in bold) and then followed by a definition. This way, the term syntax is given in the context in which it is used in the text. This makes understanding easier and seamless.

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Answer:

If one factor is (x-10) then the other factor is (x+2).

Step-by-step explanation:

We need to factorize the term x^2-8x-20

For factorization we need to break the middle term.

Middle term : -8x

Product of first and last term: -20x^2

Factors: -10x, +2x

Solving:

x^2-8x-20

x^2-10x+2x-20

x(x-10)+2(x-10)

(x-10)(x+2)

So, if one factor is (x-10) then other factor is (x+2)