in two or more complete sentences, explain how to solve the cube root equation, ^3sqrt+1 -2 =0

Using the given information sin(x) = 5/7 and x in quadrant 2, the exact values are:

sin(x/2) = √[(1 - √24/7)/2],

cos(x/2) = -√[(1 + √24/7)/2],

tan(x/2) = (√[(1 - √24/7)/2]) / (-√[(1 + √24/7)/2]).

To determine the exact values of sin(x/2), cos(x/2), and tan(x/2) when sin(x) = 5/7 and x is in quadrant 2, we can utilize the half-angle formulas. These formulas allow us to express the trigonometric functions of an angle in terms of the trigonometric functions of half that angle.

Given sin(x) = 5/7, we can find cos(x) using the Pythagorean identity:

cos(x) = √(1 - sin^2(x)) = √(1 - (5/7)^2) = √(1 - 25/49) = √(24/49) = √24/7.

To find sin(x/2), we use the half-angle formula for sine:

sin(x/2) = ±√[(1 - cos(x))/2] = ±√[(1 - √24/7)/2].

Since x is in quadrant 2, sin(x) is positive. Therefore, sin(x/2) is also positive. Thus, we have:

sin(x/2) = √[(1 - √24/7)/2].

Similarly, we can find cos(x/2) using the half-angle formula for cosine:

cos(x/2) = ±√[(1 + cos(x))/2] = ±√[(1 + √24/7)/2].

Since x is in quadrant 2, cos(x) is negative. Therefore, cos(x/2) is also negative. Thus, we have:

cos(x/2) = -√[(1 + √24/7)/2].

Lastly, we can find tan(x/2) using the half-angle formula for tangent:

tan(x/2) = sin(x/2) / cos(x/2) = (√[(1 - √24/7)/2]) / (-√[(1 + √24/7)/2]).

Combining these results, the exact values for sin(x/2), cos(x/2), and tan(x/2) when sin(x) = 5/7 and x is in quadrant 2 are:

sin(x/2) = √[(1 - √24/7)/2],

cos(x/2) = -√[(1 + √24/7)/2],

tan(x/2) = (√[(1 - √24/7)/2]) / (-√[(1 + √24/7)/2]).

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The two planes are approximately 200 miles apart, rounded off to the nearest integer.

Using the Law of Cosines formula,

The distance between the two planes can be determined.

The formula for the Law of Cosines is as follows: c^2 = a^2 + b^2 - 2ab*cos(C), where c is the side opposite the angle C and a and b are the other two sides.

Using the formula, the distance between the two planes after one hour can be calculated as follows:

[tex]c^2[/tex] = [tex]200^2[/tex] + [tex]300^2[/tex] - 2(200)(300)cos(50°)[tex]c^2[/tex]

= 40,000 + 90,000 - 120,000cos(50°)[tex]c^2[/tex]

= 130,000 - 89,873.86c

= sqrt(40,126.14)c

= 200.315 miles

Therefore, after one hour, the two planes are approximately 200 miles apart, rounded off to the nearest integer.

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sum angel measure of angles in triangle is 180° according to this rule

(n-2)180 , n is the no. of sides

so E+D+F=180

72+D+63=180

135+D=180

D=180-135

D=45°

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Answer:

The graph is not shown.

x² - x - 6 = (x - 3)(x + 2)

The answer is:

B. This equation has no real solution

Work/explanation:

To solve this equation, we square-root both sides:

[tex]\sf{x^2=-81}[/tex]

[tex]\sf{\sqrt{x^2} =\sqrt{-81}}[/tex]

And here things begin to happen. We cannot take the square root of a negative number.

So this leads us to the conclusion that this equation doesn't have a solution in the "Real Numbers" set.

However, we do have a solution in the "Complex Numbers" set.

Answer:

Excise tax

Step-by-step explanation:

Correct me if I'm wrong <3

2mL of water must be added to 16mL of 9% alcohol solution to reduce the concentration to 8%.

To reduce the concentration of 16mL of 9% alcohol solution to 8%, we need to calculate the amount of water that must be added.

Here are the steps to follow:

The initial amount of alcohol in the solution

To calculate the initial amount of alcohol, we multiply the initial volume of the solution (16mL) by its initial concentration (9%):

Initial amount of alcohol = 16mL x 9%

= 1.44mL

Determine the final volume of the solutionWe can use the following formula to determine the final volume of the solution:

Initial amount of alcohol/ final concentration of alcohol = Final volume of solution

1.44mL / 8% = Final volume of solution

Final volume of solution = 18mL

The amount of water to addThe amount of water to add is the difference between the final volume of the solution and the initial volume of the solution:

Amount of water to add = Final volume of solution - Initial volume of solution

Amount of water to add = 18mL - 16mL

Amount of water to add = 2mL

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Answer: 9

Step-by-step explanation:

Step-by-step explanation:

When finding (x) not relating to a y=mx+b equation, start by setting your equation up to equal zero.

2x+7=0

Next you want to "isolate" the variable (get it by itself) as best as possible. Start by removing your extra number from the side of the equation where x resides. You may do this by opposing its symbol. ALWAYS MAKE SURE TO DO SOMETHING ON BOTH SIDES OF THE EQUAL SYMBOL!!

2x+7=0 -> subtract 7 from each side of the equal symbol so that the value still exists within the equation.

This would show:

(2x+7)-7=0-7

2x=-7

From here you want to continue isolating the variable.

Divide each side of the equal symbol by 2, so that we get rid of the coefficient, and arrive at what x truly equals by itself.

This would show:

2x/2=-7/2

x=[tex]\frac{-7}{2}[/tex]

In conclusion, the value of x is -7/2 (negative 7 halves)

The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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Answer:UNIT 1.7 - ALGEBRA 7 - SIMULTANEOUS LINEAR EQUATIONS. 1.7.1 Two ... 2. x−1(4x − x2) − 6(1 − 3x) ≡ 4 − x − 6 + 18x ≡ 17x − 2. ... (3)] we obtain.

Step-by-step explanation:

The range for which the graph of the exponential is greater than the quadratic function is the required range which is -0.5≤x<1

The parabolic curve drawn on the graph represents the quadratic function while the other curved line represents the exponential function.

The required range is where the exponential curve is above the quadratic curve. At this range the value of the exponential function would be greater than that of the quadratic function.

Hence, the required interval is -0.5≤x<1

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The graph is bounded and does not extend to infinity, the range is the subset of real numbers within that constraint.

To create a table of values for the given function graph, we will identify the x-values and their corresponding y-values.
Reading the graph from left to right, the x-values in order from least to greatest are: -10, -5, 0, 5.
By looking at the graph, we can determine the corresponding y-values for each x-value.

Let's say the y-values are y1, y2, y3, and y4 respectively.
Now, we can create the table of values:
x   |   y
-10 |   y1
-5  |   y2
0   |   y3
5   |   y4
To state the domain and range of the function, we need to consider the set of all possible x-values and the set of all possible y-values.
In this case, the domain of the function is the set of x-values, which is {-10, -5, 0, 5}.
The range of the function is the set of y-values, which corresponds to {y1, y2, y3, y4}.
It is important to note that without specific values for y1, y2, y3, and y4, we cannot provide the exact range of the function.

The domain of the function is {-10, -5, 0, 5}, which is the set of all possible x-values.

Regarding the scope of the function, since you said that the y values ​​correspond to {y1, y2, y3, y4}, it i not possible to determine the exact scope of the function since there are no specific values. y4 function for y1, y2, y3.

However, based on the chart and the information given, we can say that the range will be a series of real numbers, depending on how the chart behaves.

If the graph extends infinitely in both the positive y-direction and the negative y-direction, the range consists entirely of real numbers.

However, we can say that the range will be a set of real numbers depending on the behavior of the graph.

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Answer: We have f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16

                        (f-g)(x)= 3x⁵-2x⁴-x²+x-21

Step-by-step explanation:

Here we have,

Given : f(x)=3x⁵+6x²-5 and g(x)= 2x⁴+7x²-x+16

We know,

(f-g)(x)= f(x)-g(x)

= (3x⁵+6x²-5 ) - ( 2x⁴+7x²-x+16)

On subtracting g(x) from f(x) we get,

(f-g)(x)= (3x⁵+6x²-5  - 2x⁴-7x²+x-16)

On simplify,

 (f-g)(x) =3x⁵-2x⁴-x²+x-21

Hence,

(f-g)(x) = f(x) - g(x) = 3x⁵-2x⁴-x²+x-21

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The extraneous solution for the rational expression 2 · x² - 2 = (x - 1) · (x - 2) is equal to x = 1.

In this problem we must determine whether an extraneous solution exist to a given rational expression. The procedure is now summarized. First, use algebra properties to eliminate denominators:

1 / (x - 1) = (x - 2) / (2 · x² - 2)

2 · x² - 2 = (x - 1) · (x - 2)

Second, expand and simplify the expression until a polynomial in standard form is found:

2 · x² - 2 = x² - 3 · x + 2

x² + 3 · x - 4 = 0

Third, factor the quadratic equation:

(x + 4) · (x - 1) = 0

x = - 4 or x = 1

Fifth, check in initial expression:

1 / (- 4 - 1) = (- 4 - 2) / [2 · (- 4)² - 2]

- 1 / 5 = - 6 / 30

- 1 / 5 = - 1 / 5

1 / (1 - 1) = (1 - 2) / (2 · 1² - 2)

1 / 0 = - 1 / 0 (EXTRANEOUS)

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Answer: [m and n], and [o and p]

Step-by-step explanation:

The parallel groups of lines are m and n, and the group o and p.

The number of values in the data-set in this problem is given as follows:

n = 33.

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:

4|5 = 45.

The number of values in the data-set is given by the number of leafs of the plot.

Hence the number of values in the data-set in this problem is obtained as follows:

11 + 14 + 5 + 3 = 33.

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The total of 50 leaves in the given stem-and-leaf plot. There are 50 data values in this dataset.

A stem-and-leaf plot is a method for displaying data.

It is commonly used to depict the distribution of a dataset.

Determining the number of data values ​​in a given dataset requires counting the individual data points represented by the stem-leaf diagram.

In a stem-and-leaf plot, each data value is split into a stem and a leaf, which is then arranged in order.

In the given stem-and-leaf plot, the data values are:

5 0 0, 0 1, 2 3 3 3, 4 7 8, 6 0 1 1 1 2, 4 4 5 7 7 8 8 8, 7 0 3 5 7 9, 8 6 6 7

There are different methods to determine the number of data values in a dataset.

Looking at the stem-and-leaf graph, we can see that each digit represents a data point.

Counting the digits in each stem gives:

stem 5: 1 digit

stem 6: 5 digits

stem 7: 4 digits

stem 8: 3 digits

Summing the digits of each stem gives:

1 + 5 + 4 + 3 = 13

So there are 13 data values ​​in this dataset.

The simplest method is to count the number of data values by looking at the stem-and-leaf plot.

By counting the number of leaves in the plot, we can determine the number of data values in the dataset.

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[tex] - 13 = \frac{w}{9} - 6 \\ - 13 + 6 = \frac{w}{9} \\ - 7 = \frac{w}{9} \\ w = - 63[/tex]

so only -63 is the solution, the rest three are NOT solution for this equation.

The correct option is (iii) the distance between points X and Z. Distance between points Y and Z: 2 units

We can find the distance between points on the line segment by finding the difference between their coordinates.

The correct option is the distance between points X and Z, which is equal to 6.

There are four points that partition the directed line segment from A to B.

The partition ratio at each point is as follows:

Point P partitions the directed line segment from A to B into a 3:4 ratio.

Point Q partitions the directed line segment from A to B into a 4:3 ratio.Point R partitions the directed line segment from A to B into a 2:5 ratio.

Distance between points Y and Z:

Again, the number line does not provide the exact coordinates of the points Y and Z. However, the line segment from A to B is split 5:2 at point S, so the distance can be concluded as: Between Y and Z is 2 units.

So the distance between the given points is:

Distance between points W and X: 5 units

Distance between points X and Y: 4 units

Distance between points X and Z: 5 units

Distance between points Y and Z: 2 units

Point S partitions the directed line segment from A to B into a 5:2 ratio.

Here, we have to measure the distance of each of the following:

(i) The distance between points W and X

(ii) The distance between points X and Y

(iii) The distance between points X and Z

(iv) The distance between points Y and ZThe distance between points X and Z is 6 units.

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The distances are described as follows:

The distance between points W and X is 5 units.

The distance between points X and Y is 4 units.

The distance between points X and Z is 8 units.

The distance between points Y and Z is 4 units.

The distance between points W and X is gotten:

We  subtract the coordinates of point W from the coordinates of point X to get the distance

Distance = X - W = (-3) - (-8) = 5 units.

The distance between points X and Y shown as :

we will also  subtract the coordinates of point X from the coordinates of point Y.

Distance = Y - X = 1 - (-3) = 4 units.

The distance between points X and Z is :

We also  subtract the coordinates of point X from the coordinates of point Z.

Distance = Z - X = 5 - (-3) = 8 units.

The distance between points Y and Z:

Finally, we subtract the coordinates of point Y from the coordinates of point Z.

Distance = Z - Y = 5 - 1 = 4 units.

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The value of n can be determined by finding the number of visible arcs in the pattern, which is 30 in this case.

To determine the value of n, we need to find the relationship between the total length of visible areas and the number of circles (n).

In the given pattern, each circle contributes to the visible area twice: once as its circumference and once as the overlapping part with the adjacent circles. Since the circumference of each circle is 1 unit, the visible area contributed by each circle is 2 units.

Therefore, the total length of visible areas can be expressed as 2n. Given that the total length is 60 units, we can set up the equation:

2n = 60

Solving this equation, we find:

n = 60/2 = 30

Thus, the value of n is 30.

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Answer:

approximately 28.26 square feet

Step-by-step explanation:

The formula for the area of a circle is A = pi(r)^2. So, the radius is half of the diameter, meaning it's 3 feet. Then we square it to get 9, and multiply by pi, or 3.14. This leads us to the approximated answer of 28.26 square feet.

The area is:

28.27 square feet

Work/explanation:

Since the tabletop is circular, we use the formula for a circle's area, which is: [tex]\bf{A=\pi r^2}[/tex].

We have the diameter, and to find the radius, we divide the diameter by 2, which gives us 6 ÷ 2 = 3 feet, so the radius of the tabletop is 3 feet.

Now, here's a diagram for you;

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 3\ ft}\end{picture}[/tex]

Plug in the data:

[tex]\sf{A=\pi\times3^2}[/tex]

[tex]\sf{A=\pi\times9}[/tex]

[tex]\sf{A=28.27\:ft^2}[/tex]

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Answer:

no solutions

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

Answer:

x = 1

Step-by-step explanation:

given 2 secants to a circle from an external point , then

the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant, that is

8(8 + 10x) = 9(9 + 7x) ← distribute parenthesis

64 + 80x = 81 + 63x ( subtract 63x from both sides )

64 + 17x = 81 ( subtract 64 from both sides )

17x = 17 ( divide both sides by 17 )

x = 1

Answer:

Step-by-step explanation:

Compound interest is interest on interest.

To calculate the time for compound interest,

we can use the formula  -  A = P (1 + r/n)^(nt) ,

where A ⇒ future value of the investment,

P ⇒  the principal amount,

r ⇒  the annual interest rate,

n ⇒ is the number of times interest is compounded per year and

t ⇒ the number of years.

Given that,

P = 750$,

A = 1405$,

r = 7% and

n = 12  (since interest is compounded monthly).

We can solve for t by plugging in these values into the formula and solving for t :

1405 = 750(1 + 0.07/12)^(12t)

⇒ t ≈ 6.5 years

Therefore, the money was in the bank for approximately 6.5 years.

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An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.

An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.

This function is one-to-one because for every element x in P, there is a unique element 2x in Q. It is onto because every element y in Q has a preimage x in P such that f(x) = y (e.g., y/2 = x).

Furthermore, this function preserves the group structure between P and Q, as it satisfies the properties of an isomorphism. In this case, the group structure is addition, and the function f preserves addition: f(x + y) = 2(x + y) = 2x + 2y = f(x) + f(y) for all x, y in P.

Therefore, the function f: P -> Q defined as f(x) = 2x is an example of a one-to-one function that is an isomorphism between sets P and Q.

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In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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At most, 9 students could be going on the field trip.

Let's denote the number of students going on the field trip as "x". We know that the total number of bottles of water ordered is 25.

The teachers receive 6 bottles of water altogether. Therefore, the number of bottles allocated to the students is 25 - 6 = 19.

Since each student needs 2 bottles of water, we can set up the equation:

2x = 19

To find the maximum number of students, we divide 19 by 2:

x = 19/2

The result is x = 9.5, which indicates that the maximum number of students going on the field trip can be 9 students. Since we can't have a fractional number of students, we round down to the nearest whole number. Therefore, at most, 9 students could be going on the field trip.

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Answer: [tex](-3+18)+(i+5i)[/tex]

Step-by-step explanation:

The commutative property of addition states that the order in which numbers are added does not change the sum. In the context of complex numbers, this means that you can rearrange the real and imaginary parts separately.

So, the expression that demonstrates the use of the commutative property of addition in the first step of simplifying the expression [tex](-3+i)+(18+5i)[/tex]

would be:

[tex](-3+18)+(i+5i)[/tex]