In ΔPQR, p = 4.7 inches, ∠P=76° and ∠Q=57°. Find the length of q, to the nearest 10th of an inch.

a) The value of 8^1/3 is 2

b) The value of 8^2/3 is 4

c) The value of 16^3/4 is 8

Information given in the problem

a)   the value of 8^1/3

b)  the value of 8^2/3

c) the value of 16^3/4

This equation represents exponents in fraction form and the basics for the calculation is from

a^(b/c) =

[tex]\sqrt[c]{a}^{b}[/tex]

Rewriting the expression is done as below

8^1/3

=∛8

= 2

8^2/3

= ∛8²

= 2²

= 4

16^3/4

[tex]\sqrt[4]{16}^{3}[/tex]

= 2³

= 8

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Isolate one of the two variables in one of the equations.

(- 2, - 4 )

- 4x + 4y = - 8 → (1)

4x - 6y = 16 → (2)

adding (1) and (2) term by term will eliminate x

0 - 2y = 8

- 2y = 8 ( divide both sides by - 2 )

y = - 4

substitute y = - 4 into either of the 2 equations and solve for x

substituting into (2)

4x - 6(- 4) = 16

4x + 24 = 16 ( subtract 24 from both sides )

4x = - 8 ( divide both sides by 4 )

x = - 2

solution is (- 2, - 4 )

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Answer: To find the number of liters of water in the first pool after x minutes have passed, we can use the formula:

972 + 17x

To find the number of liters of water in the second pool after x minutes have passed, we can use the formula:

44x

Note that both of these formulas assume that the pools are being filled continuously, without any interruptions. If the flow of water into either pool is interrupted at any point, the actual amount of water in the pools may be different from what these formulas predict.

Answer:

a)

17x + 972

44x

b)

972 + 17x = 44x

Step-by-step explanation:

Answer:

-7x(to the power of 2)-2x-16

Explanation:

Option (C) is the proper choice, both set A and B  

Describe a function.

It is described as a particular kind of relationship, and each value in the domain is associated to exactly one value in the range according to the function.

These are the ordered pairs:

Set A: (-1, 0), (-2, 1), (4, 3), (3, 4) (3, 4)

Set B: (1, 4), (2, 3), (3, 2), (4, 1) (4, 1)

Set C: (2, 1), (3, 2), (2, 3), (1, 4) (1, 4)

Sets A and B are both functions since they both have sets of x values that are all distinct. Set C is not a function because it repeats the x value of 2, while also providing two distinct y values.

As a result, the function option (C) is the proper choice and the set C: (2, 1), (3, 2), (2, 3), and (1, 4) does not represent the function.

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Therefore ,the answer that states, "Infinitely many solutions, both sides are equivalent expressions" is the one that should be selected in this case.

Equations are mathematical expressions that have two algebraic expressions on either side of an equals (=) sign.  For an unknown quantity represented by an unknown variable, equations can be solved to determine its value.

Here,

The number of solutions is unlimited if there are more variables than linear independent equations.

A single solution or no solution is possible if there are the same number of linearly independent equations and variables.

In the following scenarios, we are at a loss for solutions:

y = x + 3

y = x - 3

this causes:

x + 3 = x - 3

+3 = -3

Consequently, this system lacks a solution.

The first set of equations is

y = x + 5

y = 2x + 5

You can see that there is only one solution for this system because there are only two variables and two linear independent equations.

Thus, "One solution, the graph of these lines should connect at one point" is what we have here. The key idea is (0, 5)

Another system is:

y =x+x+5 = 2x + 5

y = 2x+ 5

Since both equations are identical and there are just two variables in this situation, there are an endless number of solutions to the system.

The answer that states, "Infinitely many solutions, both sides are equivalent expressions" is the one that should be selected in this case.

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The distance from the the point on the ground bellow the hot air balloon is 1039 feet

Distance here talks about how far the person stands from a point

The given parameters are

The angle of depression from the point 30⁰

Height of the air balloon = 600 feet

The distance from the the point on the ground bellow the hot air balloon = x

To find x we use the trigonometric ratio:

TanB = opposite/Adjacent

Tan30 = 600/x

This implies that x*tan30 = 600

Making x the subject we have 600/tan30

⇒x = 600/0.5774

x=1034 feet

In conclusion, the distance from the the point on the ground bellow the hot air balloon is 1039 feet

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The following is not the same across classification and regression decision trees is a . type of predicted variable .

Given :

which of the following is not the same across classification and regression decision trees a. type of predicted variable b. impurity measure/ splitting criteria .

What is classification and regression decision trees ?

CART is a predictive algorithm used in Machine learning and it explains how the target variable's values can be predicted based on other matters.

The  not same across classification and regression decision trees is type of predicted variable .

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The constant of proportionality (p) for the data points on this graph would then be determined as follows: [tex]p = y/xp = 420/6 = 560/8p = 70.[/tex]

following equation: y = px

Where:

p is the constant of proportionality.

y represents the gems collected.

x represents the game levels.

The constant of proportionality (p) for the data points on this graph would then be determined as follows: [tex]p = y/xp = 420/6 = 560/8p = 70.[/tex]

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Step-by-step explanation:

let the number be x

So,

(x - 6) × 2 = 22

2x - 12 = 22

2x = 34

x = 17

Thus, the answer is 17

Answer:

Part A: $32.10

Part B: 156 miles

Step-by-step explanation:

Part A:

$0.05 per mile. 0.05 times 42 = $2.10

30 + 2.10 = $32.10

Part B:

The rent cost a day is $30

37.80 - 30 = $7.80

7.80 is the money for miles

7.80 divided by 0.05 = 156 miles

Brace's boat is 225 feet from the bottom of the lighthouse.

What do you mean by trignoemtry?

Trigonometry (“triangles” and “measures”) is the branch of mathematics that studies the relationship between the side lengths and angles of triangles.

Trigonometry is one of the important branches in the history of mathematics that studies the relationship between the sides and angles of right triangles.

Trigonometric ratios of triangles are also called trigonometric functions. Sine, cosine, and tangent are three important trigonometric functions, abbreviated sin, cos, and tan.

It is given that Dontaya is at the top of a lighthouse which is 250 feet above sea level. From the top, the measure of the angle of depression to Brace's boat on the water is 48 degrees

Let Brace's boat is x feet from the bottom of the lighthouse.

Using trignometric ratios,

tan 48 = [tex]\frac{P}{B}=\frac{250}{x}[/tex]

1.11 = [tex]\frac{250}{x}[/tex]

x = [tex]\frac{250}{1.11} = 225.23[/tex] ≈ 225 feet

Therefore, Brace's boat is 225 feet from the bottom of the lighthouse.

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Answer:

353340 + x + 33

Step-by-step explanation:

real life sum situation

Answer:

$3.45

Step-by-step explanation:

To find the unit price, there must be one gallon of gas

24.82 : 7.2

?  : 1

Cross multiply: 24.85 = 7.2(?)

divide: 3.45138889 = ?

Round: 3.45

Answer: A trend line is a line on a scatter plot, drawn near points, that approximates the association between the data sets.

Step-by-step explanation:

2. The linear trend in precipitation is the dominant trend type. The nonlinear trends occur much less frequently and more widely scattered over the globe. However, the nonlinear trends are credible patterns of change in precipitation.

3. The trend is the component of a time series that represents variations of low frequency in a time series, the high and medium frequency fluctuations having been filtered out. This component can be viewed as those variations with a period longer than a chosen threshold

4. The trend component represents changes in time-series data that are unpredictable and cannot be associated with a seasonal, cyclical, or random component. OB. The trend component is the long-term increase or decrease in a variable being measured over time.

5. The trend is the component of a time series that represents variations of low frequency in a time series, the high and medium frequency fluctuations having been filtered out.

6. The trend component is the long-term increase or decrease in a variable being measured over time.

Answer: A.-20

Step-by-step explanation:

f(4)=-2(4)^2+12

f(4)=-2(16)+12

f(4)=-32+12

f(4)=-20

(a) This is the factored form of the equation.

(b) The x - intercepts are  (√2, 0) and (-√2, 0).

(c) The value of f(-1) is -8.

What is x - intercept?

We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable. Set x = 0 and then solve for y to find the y-intercept.

(a)  Consider, the given equation

f(x) = 8x^2 - 16

First to factor the equation.

Take 8 common from both the terms,

f(x) = 8(x^2 - 2)

This is the factored form of the equation.

(b) Now to find the x- intercept.

Let y = 8x^2 - 16

Set y = 0

So,

0 = 8x^2 - 16

8x^2 - 16 =0

x^2 - 2 = 0

x^2 = 2

x = ±√2

Hence, the x - intercepts are  (√2, 0) and (-√2, 0).

(c) Now to find the value of f(-1)

plug x = -1 in the given equation.

f(-1) = 8(-1)^2 - 16

f(-1) = 8(1) - 16

f(-1) = 8 - 16

f(-1) = -8

Hence, the value of f(-1) is -8.

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Answer: [tex]y+3=-\frac{3}{5}(x+5)[/tex]

Step-by-step explanation:

The equation of the given line can be rearranged as follows:

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

Parallel lines have the same slope, so the slope of the line we need to find is -3/5.

Substituting into point-slope form, the equation of the line is [tex]y+3=-\frac{3}{5}(x+5)[/tex].

Answer: [tex]\displaystyle \frac{-1}{3}[/tex]

Step-by-step explanation:

       The slope of a perpendicular line will always be the reciprocal of the original line's slope. Here, the reciprocal of -3 is [tex]\frac{-1}{3}[/tex].

The reciprocal of 7 3/7 is 7/52

Answer: I'm pretty sure it's 7/52

Step-by-step explanation:

7*7 is 49, plus the 3 is 52, then the reciprocal of that. 7/52 is already in it's simplest form. Hope this helps!

Answer:

c is correct

Step-by-step explanation:

take 8 common bro

Answer:

a = 16

Step-by-step explanation:

6 = [tex]\frac{a}{4}[/tex] + 2 ( subtract 2 from both sides )

4 = [tex]\frac{a}{4}[/tex] ( multiply both sides by 4 to clear the fraction )

4 × 4 = a , that is

a = 16

By solving equations we know that he should mix 4 grams and 16 grams of the 30% and 60% bottles, respectively.

In mathematical equations, the equals sign is used to show that two expressions are equal.

According to algebra, an equation is a statement that shows the equality of two mathematical expressions.

For instance, the formulas 3x + 5 and 14, which together make the equation 3x + 5 = 14, are separated by the word "equal."

So, John requires a total of 20 grams.

Let x equal the 30% that he requires.

Let 20-x equal 60% of what he needs.

So, we have:

(x/20 * 30) + (20-x/20 * 60) = 54

Evaluate as follows:

1.5x + 60 -3x = 54

-1.5x = -6

x = 4 grams

20-x = 16 grams

Therefore, by solving equations we know that he should mix 4 grams and 16 grams of the 30% and 60% bottles, respectively.

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Answer:

Step-by-step explanation:

for the first car  374/17 = 22 m per second

for bus  414/23 = 18  m per second

so the car is moving faster

car is moving faster than (22-18)=4 m per second from the bus

Answer: Car: 22 meters per second, Bus: 18 meters per second. The bus travels faster at 4 meters per second.

Step-by-step explanation: First, you should write a proportional relationship for meters per second so the car would be 374/17 and the bus would be written as 414/23. This is so you can know that you divide 374 by 17 to get 18, and 374 by 17 to get 22. So, you had it backward, the bus is faster by 4 meters per second, I hope this helped, for me (a 7th grader) this was review math, so I hoped this helped you.

Answer:

400

Step-by-step explanation:

403.1 rounded is 400

Answer:

x = -2/3; -20/9 so A

Step-by-step explanation:

im 100% percent sure:)

For the given similar triangle the value of x will be 9 inches.

It is required by law to demonstrate that two triangles are identical in shape, although size is not a requirement. The comparable angles are congruent and the ratio of the respective sides is in the same proportions.

It is given that, the unknown side is x, from the observation it is obtained that the two triangles are similar

The derived formula is, because the sides of the similar triangles are all equal in ratio.

8/6=12/x

x=12×6 / 8

x=9 inches

Thus, for the given similar triangle the value of x will be 9 inches.

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Answer: point A will stay where it is.

Step-by-step explanation: point A is the point of rotation

The value of x is 0.636.

What is logarithms?

The opposite of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.

f(x) = [tex]log_{a}x[/tex] (r) y = [tex]log_{a}x[/tex], where a > 0. It is the inverse of the exponential function a^y = x. Log functions include natural logarithm (ln) or common logarithm (log).

Given equation is

e^(5x) = 24

taking log with base e on both sides:

ln e^(5x) = ln 24

Applying the formula ln e^a = a

5x = ln 24

Divide both sides by 5:

x = 0.636

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