5. 25 it takes gallons of paint to paint a fence. How much paint is needed for 3/5 of the fence?

The unknown measures are given as follows:

BC = 2.52, AB = 1.28, m < C = 27º.

The three trigonometric ratios are defined as follows:

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle C is given as follows:

63 + 90 + m < C = 180

m < C = 27.

Side BC is opposite to the angle of 63º, while the hypotenuse is the square root of 8, hence it is obtained as follows:

sin(63º) = BC/sqrt(8)

BC = square root of 8 x sine of 63 degrees

BC = 2.52.

Side AB is opposite to the angle of 27º, hence it's length is given as follows:

sin(27º) = AB/sqrt(8)

AB = square root of 8 x sine of 27 degrees

AB = 1.28.

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He makes $8/49 for every 7 cups of juice, so his overall profits will be some multiple of $8/49.

Finding the worth of one unit of a quantity, then using this value to determine the value of a specified number of units of the quantity, is known as the unitary technique. When solving issues involving rates, ratios, and proportions, this approach is helpful. The fundamental tenet of the unitary technique is that we can use the value of one unit of a quantity to determine the value of any number of additional units of the same quantity.

given

Let's symbolise the cost of a cup of apple juice by the variable x.

So, a cup of lemon juice is sold for 3/2 times x, or (3/2)x.

Mr. Tan offers 5 cups of apple juice for every 2 cups of lemon juice. This indicates that there are 2.5 sales of lemon juice for every 1 sales of apple juice.

Assume Mr. Tan sells 5y cups of apple juice and 2y cups of lemon juice.

Based on the information provided, we can conclude that apple juice generates $12 more revenue than lemon juice.

in order to create an equation:

5yx = 2(3/2)x + 12

Simplifying:

5yx = 3x + 12

adding two to both sides:

10yx = 6x + 24

x(10y - 3) = 12

x = 12 / (10y - 3) (10y - 3)

We can now re-use this number of x to represent the revenue from apple juice in the equation:

5yx = 3x + 12

5y(12 / (10y - 3)) = 3(12 / (10y - 3)) + 12

Therefore, Mr. Tan charges $1/7 for each cup of apple juice and (3/2)($1/7) Equals $3/14 for each cup of lemon juice.

He charges (5/7)($1/7) = $5/49 for 5y = 5(1/7) = 5/7 glasses of apple juice.

For a sum of (2/7)($3/14) = $3/49, he sells 2y = 2(1/7) = 2/7 cups of lemon juice.

For each 7 cups of juice sold, Mr. Tan makes a sum of $5/49 + $3/49 = $8/49.

Consider that he offers 2n cups of lemon juice and 5n glasses of apple juice. (2n)($3/14) + (5n)($1/7) = $6n/49 + $5n/49 = $11n/49

He makes $8/49 for every 7 cups of juice sold, so his overall profits will be some multiple of $8/49.

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Answer:

y < 2x + 4

Step-by-step explanation:

y+4<-2(x-4)

y + 4 < -2x +8

y < 2x + 4

Answer:

218.88

Step-by-step explanation:

Answer:

10mins for 35 photos

Step-by-step explanation:

If it takes 8mins to produce 28photos, that is ratio 1:3.5

For 7 photos, divide by 3.5, that is 2mins

For 4mins, multiply by 3.5, that will be 14photos

For 21 photos, divide by 3.5, that will be 6 mins

The volume of the rectangular prism whose surface area is 250 cm square is 250cubic centimeters.

The surface area of a rectanular prism is calculates by the formula

= 2( length*width + length*height + width*height ) square units

Let the length of the given prism be l centimeters.

Given, width is 5 centimeters and height is 10 centimeters of the rectangular prism.

The surface area of the rectangular prism is 250 cm square.

Thus by the above formula,

250 = 2 ( l*5 + l*10 +10*5)

⇒250 = 2 (15*l +50)

⇒ 250= 30*l + 100

⇒ 150 = 30*l

⇒l = 150/30 = 5 (centimeters)

Thus the volume of the given rectangular prism is calculated as

= ( length*width*height) cubic units

= (5*5*10) cubic centimeters

= 250 cubic centimeters

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The given statement, "by the Invertible Matrix Theorem if the equation [tex]Ax^{(0)}[/tex]has only the trivial solution, then the matrix is invertible. Thus, A must also be row equivalent to the identity matrix," is true (T).

This is because the theorem states that a square matrix is invertible if and only if it can be transformed into the identity matrix by a sequence of elementary row operations. And if the equation [tex]Ax^{(0)}[/tex] only has the trivial solution, then the matrix must be row equivalent to the identity matrix, implying that it is invertible.

The Invertible Matrix Theorem is a powerful result in linear algebra that allows us to determine whether a square matrix is invertible or not. It states that a square matrix is invertible if and only if its determinant is nonzero, which is equivalent to saying that the matrix can be transformed into the identity matrix by a sequence of elementary row operations.

If the matrix is not invertible, then its determinant is zero, and it is said to be singular. In this case, the equation [tex]Ax^{(0)}[/tex] will have infinitely many solutions or no solutions at all, depending on the specific values of the right-hand side vector.

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Answer:

312 square inches

Step-by-step explanation:

To find the surface area of a cake baked in a rectangular pan with an 8-inch by 12-inch base and a volume of 288 cubic inches, we need to find the dimensions of the pan. We can do this by dividing the volume by the area of the base, which gives us the height of the pan. Once we know the height, we can use the dimensions of the base and the height to find the surface area of the cake.

pool = length x width x height

pool = 15 x 9 x ?

270 = 135x

x = 2

the height is 2 meters.

We can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.

Sine formula is used to calculate the sine angle of a right-angled triangle which is the ratio of the opposite side and the hypotenuse.

Given is that a 40-ft-wide house has a roof with a 6-12 pitch (the roof

rises 6 ft for a run of 12 ft). The owner plans a 14-ft-wide addition that will

have a 3-12 pitch to its roof.

We can write the measure of length AB as -

AB = 6 + √(9 + 296)

AB = 6 + 17.46

AB = 23.46 ft

We can write the measure of length BC as -

BC = 6 + 1/4 x 12

BC = 6 + 3

BC = 9 ft

Therefore, we can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.

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Answer:

  32°

Step-by-step explanation:

You want the measure of the smaller angle of the linear pair marked (3g+23) and (7g+127).

The angles of a linear pair total 180°, so we have ...

  (3g +23) +(7g +127) = 180

  10g = 30 . . . . . . . . . subtract 150

  g = 3 . . . . . . . . . divide by 10

The smaller angle is ...

  ∠PKT = (3·3 +23)°

  ∠PKT = 32°

Answer:

2:35

Step-by-step explanation:

Answer:

There are different methods to express a two logarithm into a single logarithm, depending on the specific form of the logarithms involved. Here are some examples:

Logarithms with the same base:

If you have two logarithms with the same base, you can use the following logarithmic identity:

log_a(x) + log_a(y) = log_a(xy)

Using this identity, you can express a sum or difference of logarithms with the same base as a single logarithm:

Example 1: log_2(3) + log_2(5) = log_2(3*5) = log_2(15)

Example 2: log_5(7) - log_5(2) = log_5(7/2)

Logarithms with different bases:

If you have two logarithms with different bases, you can use the following change of base formula to express them with a common base:

log_a(x) = log_b(x) / log_b(a)

Using this formula, you can rewrite a logarithm with a base a as a logarithm with a base b:

Example 1: log_2(7) = log_10(7) / log_10(2)

Example 2: log_5(2) = log_2(2) / log_2(5)

Once you have expressed both logarithms with the same base, you can apply the logarithmic identity from method 1 to simplify them into a single logarithm.

The cost of 5 pounds of bananas in 1939 would have been $2.709.

According to the US Bureau of Labor Statistics, the cost of 1 pound of bananas is $0.63/lb. In 1939, the cost of bananas was 14% lower. Therefore, to find the cost of bananas in 1939, we need to calculate 14% of $0.63/lb and then subtract it from $0.63/lb.

Calculate 14% of $0.63/lb
0.14 * $0.63/lb = $0.0882/lb

Subtract $0.0882/lb from $0.63/lb to get the cost of bananas in 1939
$0.63/lb - $0.0882/lb = $0.5418/lb

Multiply the cost of bananas in 1939 by the number of pounds Pam buys
$0.5418/lb * 5 lb = $2.709

Therefore, the cost of 5 pounds of bananas in 1939 would have been $2.709.

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The three consecutive integers whose sum is 360 are 119, 120, and 121.

To find three consecutive integers whose sum is 360, we can use algebra to set up an equation and solve for the first integer. Let x be the first integer, then the next two consecutive integers will be x+1 and x+2. The sum of these three integers is 360, so we can write the equation:

x + (x+1) + (x+2) = 360

Simplifying the equation gives us:

3x + 3 = 360

Subtracting 3 from both sides gives us:

3x = 357

Dividing both sides by 3 gives us:

x = 119

So the first integer is 119. The next two consecutive integers are 120 and 121. Therefore, the three consecutive integers whose sum is 360 are 119, 120, and 121.

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In  linear equation, 7/10 did he buy .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                            Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

multiply the fractions by each other.

7/8*4/5

7*4=28

8*5=40

28/40

"B" would be the correct answer but, it the fraction should be reduced to 7/10.

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The trigonometric value of sin 14° to 4 decimal places is sin 14° = 0.241.

The value of sin 14° to 4 decimal places is 0.2419.

An angle is the measure that determines two straight lines, which when joined together create a point of origin, which is called the vertex of the angle.

The unit of measurement associated with angles is degrees.

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Answer:

It’s a right triangle

Step-by-step explanation:

15 squared plus 8 squared equals 17 squared which 289=289

The width of the rectangular field is 51 m. To find the width of the rectangular field, we can use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.

Given:
P = 294 m
L = 96 m

Substituting the given values into the formula, we get:

294 = 2(96) + 2W

Simplifying the equation, we get:

294 = 192 + 2W

Subtracting 192 from both sides of the equation, we get:

102 = 2W

Dividing both sides of the equation by 2, we get:

W = 51

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Answer:

Step-by-step explanation:

30x453.6=13608 grams

The exponential functions y=1.2ˣ  shows exponential growth and y=0.71ˣ shows exponential decay.

What exactly are exponential functions?

Exponential functions are functions that involve a variable exponent. They are of the form f(x) = aˣ, where "a" is a positive constant base and "x" is the variable exponent.

Exponential functions exhibit rapid growth or decay, depending on the value of "a" and the sign of "x". For example, if "a" is greater than 1, the function grows rapidly as "x" increases, while if "a" is between 0 and 1, the function decays rapidly as "x" increases.

Now,

As stated above that for exponential function y=aˣ

when a>1 it shows exponential growth

and when a<1 it shows decay.

hence,

          The exponential functions y=1.2ˣ  shows exponential growth and y=0.71ˣ shows exponential decay.

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The length of the body of the guitar is represented by the radical expression 24√3.

We can start by simplifying 8√147.

8√147 = 8√(49 × 3) (since 49 is a perfect square)

= 8 × 7√3

= 56√3

Next, we need to find the length of the body of the guitar, given that the neck measures 8√48. We know that the total length of the guitar is 56√3, so we can set up an equation:

total length = length of neck + length of body

56√3 = 8√48 + length of body

To solve for the length of the body, we can start by simplifying 8√48:

8√48 = 8√(16 × 3) (since 16 is a perfect square)

= 8 × 4√3

= 32√3

Substituting this back into the equation:

56√3 = 32√3 + length of body

Simplifying:

length of the body = 24√3

Therefore, the answer is A) 24√3.

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The question is -

Suppose the total length of the guitar is given by the expression 8√147. Which radical expression represents the length of the body if the neck measures 8√48? A) 24√3 B) 12√3 C) 8√3 D) 9√9

Step-by-step explanation:

addition and subtraction:

y + z - z = y

b. multiplication and division:

When y ≠ 0:

yz / y = z

When z ≠ 0:

y / z * z = y

It is answer choice (C). 7 and 8!

Really hope this helped! brainliest would be very appreciated!

~HAPPY DAYZ~

In this expression, Q+bar (D) is a polynomial, and we are asked to compare the degree of R with that of the polynomial (c^(3)+2c^(2)-5c-2)/(c^(2)+c-4).

The degree of a polynomial is determined by the highest power of the variable. The highest power of c in (c^(3)+2c^(2)-5c-2)/(c^(2)+c-4) is 3, so this polynomial has a degree of 3.

To compare it to the degree of R, we need to know the highest power of R in our expression. If the degree of R is less than the degree of (c^(3)+2c^(2)-5c-2)/(c^(2)+c-4), then the expression Q+bar (D) will have a degree of 3.

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The answer are LCD (least common denominator) of the set of fractions (7)/(20) and (9)/(40) is 40.

Here is a step-by-step explanation on how to find the LCD:

1. Find the multiples of each denominator.

- Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200...

- Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400...

2. Compare the multiples of each denominator and find the smallest number that appears in both lists.

- The smallest number that appears in both lists is 40.

3. The smallest number that appears in both lists is the LCD.

- Therefore, the LCD of the set of fractions (7)/(20) and (9)/(40) is 40.

So the answer to the question "Find the LCD (least common denominator) of the set of fractions. Do not combine the fractions; only find the LCD. (7)/(20) and (9)/(40)" is 40.

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The answer is (-14x)/(9).

To simplify the given expression, we need to find a common denominator for all the fractions, which is 18. We can then multiply the numerators and denominators of each fraction by the same number to get the same denominator for all the fractions. Once we have the same denominator, we can combine the numerators using addition and subtraction. Finally, we can simplify the resulting fraction if possible.

The expression is: (x)/(3)+(2x)/(18)-(6x)/(3)

First, find a common denominator for all the fractions. The smallest common denominator is 18.

Next, multiply the numerators and denominators of each fraction by the same number to get the same denominator for all the fractions:

(x)/(3) * (6)/(6) = (6x)/(18)

(2x)/(18) * (1)/(1) = (2x)/(18)

(6x)/(3) * (6)/(6) = (36x)/(18)

Now, we can combine the numerators using addition and subtraction:

(6x)/(18) + (2x)/(18) - (36x)/(18) = (6x + 2x - 36x)/(18) = (-28x)/(18)

Finally, we can simplify the resulting fraction by dividing both the numerator and denominator by 2:

(-28x)/(18) = (-14x)/(9)

So the simplified expression is: (-14x)/(9)

Therefore, the answer is (-14x)/(9).

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The simplified expression of (1)/(13)(13y)  is 169y.

To simplify the expression (1)/(13)(13y) using the commutative or associative property, we can rearrange the terms and group them together.

Using the commutative property, we can rearrange the terms so that the two 13's are next to each other:

(1)(13)(13y) = (13)(13y)(1)

Now, using the associative property, we can group the two 13's together and simplify:

(13)(13y)(1) = (13*13)(y)(1) = (169)(y)(1)

Finally, we can simplify further by multiplying the 169 and 1 together:

(169)(y)(1) = (169y)(1) = 169y

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The value οf x is 1000 kg/m³ and the cοrrespοnding value οf y in lb/ft³ is 62.0 lb/ft³. The value οf x is 2000 lbs/yard³ and the cοrrespοnding value οf y in lb/ft³ is 74 lb/ft³.

Quantities and measurements are essential cοmpοnents οf the study οf mathematics and the physical sciences. A quantity is any prοperty οr characteristic that can be measured οr expressed in numerical terms, such as length, mass, time, temperature, and vοlume.

Frοm the prοject research part 2: Densities in lb/ft3 (pοunds per cubic fοοt). Cοnvert the densities as belοw,

Cοnvert kilοgrams per cubic meter tο the pοunds per cubic fοοt by multiplying by 0.062:

(x kg/m³) (0.062) = y lb/ft³

If we have a value οf x, we can multiply it by 0.062 tο get the cοrrespοnding value οf y in lb/ft³.

Let's say we have x = 1000 kg/m³. We can find y in lb/ft³ as fοllοws:

y lb/ft3 = (1000 kg/m3) (0.062) = 62.0 lb/ft3

Therefοre, the value οf x is 1000 kg/m3 and the cοrrespοnding value οf y in lb/ft3 is 62.0 lb/ft³.

Anοther questiοn is, Cοnvert pοunds per cubic yard tο pοunds per cubic fοοt by multiplying by 0.037:

(x lbs/yard³) (0.037) = y lb/ft³

Let's say we have x = 2000 lbs/yard³. We can find y in lb/ft³ as fοllοws:

y lb/ft³ = (2000 lbs/yard³) (0.037) = 74 lb/ft³

Therefοre, the value οf x is 2000 lbs/yard³ and the cοrrespοnding value οf y in lb/ft³ is 74 lb/ft³.

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The correct order of the fractions is: (1)/(5), (1)/(2), (4)/(5), 1(3)/(10), 1(9)/(10).

To order the fractions using the number line, we need to compare each fraction and determine which one is smaller or larger. Here are the steps to do this:

1. Find the least common denominator (LCD) of all the fractions. In this case, the LCD is 10.

2. Convert each fraction to an equivalent fraction with the LCD as the denominator. This means multiplying the numerator and denominator of each fraction by the same number to get the LCD as the new denominator.

- (1)/(2) = (1*5)/(2*5) = (5)/(10)
- (4)/(5) = (4*2)/(5*2) = (8)/(10)
- (1)/(5) = (1*2)/(5*2) = (2)/(10)
- 1(3)/(10) = (13)/(10)
- 1(9)/(10) = (19)/(10)

3. Now that all the fractions have the same denominator, we can compare the numerators to determine the order of the fractions.
4. Arrange the fractions from smallest to largest according to their numerators:
- (1)/(5) = (2)/(10)
- (1)/(2) = (5)/(10)
- (4)/(5) = (8)/(10)
- 1(3)/(10) = (13)/(10)
- 1(9)/(10) = (19)/(10)

In conclusion, to order the set of fractions (1)/(2),(4)/(5),(1)/(5),1(3)/(10),1(9)/(10) using the number line, we need to find the least common denominator, convert each fraction to an equivalent fraction with the LCD as the denominator, and then compare the numerators to determine the order of the fractions.

The correct order is (1)/(5), (1)/(2), (4)/(5), 1(3)/(10), 1(9)/(10).

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