Advanced Algebra - Trig PLEASE HELP!!

Answer: A ≈ 127.31 units²

Step-by-step explanation:

     We can use the given formula for the area of a regular hexagon, where a is equal to a given side (here, that is 7).

        [tex]\displaystyle A=\frac{3\sqrt{3} }{2} a^2[/tex]

     We will substitute known values and solve by computing and simplifying.

        [tex]\displaystyle A=\frac{3\sqrt{3} }{2} a^2[/tex]

        [tex]\displaystyle A=\frac{3\sqrt{3} }{2} (7)^2[/tex]

        [tex]\displaystyle A=\frac{5.1961524}{2} 49[/tex]

        [tex]\displaystyle A=(2.59807621)(49)[/tex]

        [tex]\displaystyle A=127.3057[/tex]

        [tex]\displaystyle A\approx 127.31[/tex]

Answer:

9180 (cm³)

Step-by-step explanation:

area of cross-section (trapezium) = 0.5 X (12 + 22) X 9

= 0.5 X 34 X 9 = 153 cm²

then multiply that by the length (60)

153 X 60 = 9180 (cm³)

Answer:

To calculate the length of BC in the triangle ABC, we can use the trigonometric functions sine and cosine.

Given that ∠CAB = 90° and ∠ABC = 58°, we can determine that ∠BCA = 180° - 90° - 58° = 32°.

Using the sine function, we can find the length of BC:

sin(∠BCA) = BC / AB

Rearranging the formula, we have:

BC = AB * sin(∠BCA)

Substituting the given values:

BC = 9.3 * sin(32°)

Using a calculator or trigonometric table, we find:

BC ≈ 9.3 * 0.529 = 4.917

Rounding to three significant figures (SF), the length of BC is approximately 4.92 units.

Step-by-step explanation:

Answer:

I’m sorry but I don’t see any sentence below. Could you please provide me with the sentence?

The solution to the system of equations, using the Gauss-Jordan method, is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&14.28\\0&1&0&-21.4\\0&0&1&1.2\end{array}\right][/tex]

The matrix representing the system of equations is given as follows:

[tex]\left[\begin{array}{cccc}-5&-3&-4&-12\\0&-2&-7&38\\0&1&4&-22\end{array}\right][/tex]

First we want a value of 1 at line 1, column 1, hence we multiply the first line by -1/5, that is:

R1 -> -1/5R1

Hence:

[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&-2&-7&38\\0&1&4&-22\end{array}\right][/tex]

First we want a value of 1 at line 2, column 2, hence we multiply the second line by -1/2, that is:

R2 -> -1/2R2

Hence:

[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&1&1.5&-19\\0&1&4&-22\end{array}\right][/tex]

We want an element of zero at line 3, column 2, hence:

R3 -> R3 - R2

Hence:

[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&1&1.5&-19\\0&0&2.5&-3\end{array}\right][/tex]

First we want a value of 1 at line 3, column 3, hence we multiply the third line by 2.5, that is:

R3 -> 1/2.5R3

Hence:

[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&1&1.5&-19\\0&0&1&1.2\end{array}\right][/tex]

Then the solution to the system of equations is given as follows:

Hence the row-echelon form is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&14.28\\0&1&0&-21.4\\0&0&1&1.2\end{array}\right][/tex]

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Step-by-step explanation:

If side 1 and side 2 are LEGS of the triangle, then hypotenuse is found by

hyp^2 = 9^2 + 3^2     using pythagorean theorem

hyp^2 = 90

hyp = sqrt 90  = 3 sqt 10 =9.5 units

If hyp is 9   and  3 is one leg:

9^2 = 3^2 + L^2

L = 6 sqrt 2 =8.5 units

Answer: 40

Step-by-step explanation:

Answer:

The total number of possible outcomes for the math quiz is 16

Step-by-step explanation:

The remainder when dividing

[tex](10m^8 + 4m^6 + 10m^5) by (2m^2 + 5m^6 + 4m^4 + 10m^3)[/tex] is

[tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5.[/tex]

To find the remainder when dividing

[tex](10m^8 + 4m^6 + 10m^5) by (2m^2 + 5m^6 + 4m^4 + 10m^3),[/tex] we can use polynomial long division.

The dividend is[tex](10m^8 + 4m^6 + 10m^5)[/tex] and the divisor is [tex](2m^2 + 5m^6 + 4m^4 + 10m^3).[/tex]

Starting with the highest degree term, we divide ([tex]10m^8[/tex]) by ([tex]2m^2[/tex]) which gives us [tex]5m^6[/tex].

Next, we multiply the entire divisor [tex](2m^2 + 5m^6 + 4m^4 + 10m^3)[/tex] by [tex]5m^6[/tex], which gives us ([tex]10m^8 + 25m^{12} + 20m^{10} + 50m^9[/tex]).

We then subtract this product from the original dividend:

[tex](10m^8 + 4m^6 + 10m^5) - (10m^8 + 25m^{12} + 20m^{10} + 50m^9)[/tex] =[tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5.[/tex]

We repeat the process with the new dividend ([tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5[/tex]) and the divisor ([tex]2m^2 + 5m^6 + 4m^4 + 10m^3[/tex]).

Continuing the long division process, we eventually find the remainder to be: [tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5.[/tex]

Therefore, the remainder when dividing ([tex]10m^8 + 4m^6 + 10m^5[/tex]) by ([tex]2m^2 + 5m^6 + 4m^4 + 10m^3[/tex]) is [tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5[/tex].

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Note the full question is:

Divide. (10m8 + 4m6 + 10m5) ÷ 2m2 5m6 + 4m4 + 10m3 5m6 + 2m4 + 10m5 5m6 + 2m4 + 5m3 5m8 + 2m6 + 5m5

What is the reminder

The solution to all parts are shown below.

a) For a rectangle with a perimeter of 12 units, the dimensions that give the greatest area are 3 units by 3 units.

For a perimeter of 13 units, the dimensions are 3 units by 3.5 units.

For a perimeter of 14 units, the dimensions are 3.5 units by 3.5 units.

For a perimeter of 15 units, the dimensions are 3.5 units by 4 units.

For a perimeter of 16 units, the dimensions are 4 units by 4 units.

b) For a rectangle with a perimeter of 12 units, the dimensions that give the least area are 1 unit by 5 units.

For a perimeter of 13 units, the dimensions are 1 unit by 6 units.

For a perimeter of 14 units, the dimensions are 2 units by 5 units.

For a perimeter of 15 units, the dimensions are 2 units by 6 units.

For a perimeter of 16 units, the dimensions are 2 units by 7 units.

6. One possible figure made from square tiles where adding an additional tile decreases the perimeter is a "U" shape.

If you arrange 9 square tiles in the shape of a "U", the perimeter is 12 units. If you add another tile to the middle of the "U", the perimeter will decrease to 10 units.

7. Perimeter is a 1-dimensional measure because it only involves adding up the lengths of the sides of a shape. The student's claim that perimeter is a 2-dimensional measure is incorrect.

8. For a square, equilateral triangle, and circle each with a perimeter of 12 cm, the circle has the greatest area and the equilateral triangle has the least area.

To see this, we can use the formulas for the perimeter and area of each shape:

Its area is (3 cm)² = 9 cm².

Its area can be calculated using the formula A = (√(3)/4) x s², where s is the side length of the triangle.

Thus, the area is (√(3)/4) x (4 cm)² = 4sqrt(3) cm², which is approximately 6.9 cm².

Its radius can be calculated using the formula C = 2πr, where C is the circumference and r is the radius of the circle.

Thus, r = 6/(2π) cm, which is approximately 0.955 cm.

The area of the circle is πr², which is approximately 2.87 cm².

Therefore, the circle has the greatest area, followed by the square, and the equilateral triangle has the least area.

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Answer:

50%.

Step-by-step explanation:

If the die is perfectly balanced, the probability of rolling an odd number is 3 out of 6, or 50%.

Answer:

r(x) = x(x - 7)

Step-by-step explanation:

given the roots of a parabola x = a , x = b , then

the corresponding factors are (x - a) and (x - b)

from the graph the roots are where the graph crosses the x- axis

the graph crosses the x- axis at x = 0 and x = 7 , then

the corresponding factors are (x - 0) and (x - 7) , that is x and (x - 7)

the equation is then the product of the factors , that is

r(x) = x(x - 7)

Answer: 0.68

Step-by-step explanation:

The value of each angle 6x + 7 and 4x + 3 will be 55° and 35°, respectively.

Given that:

Angles, ∠1 = 6x + 7 and ∠2 = 4x + 3

Two angles are said to be complementary angles if their sum is 90 degrees.

The equation is given as,

∠1 + ∠2 = 90°

6x + 7 + 4x + 3 = 90°

10x + 10 = 90°

10x = 80°

x = 8

The value of each angle is calculated as,

∠1 = 6 * 8 + 7

∠1 = 55°

∠2 = 4 * 8 + 3

∠2 = 35°

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After using Gauss-Jordon elimination method, the solution for the system of equation is as follows;

[tex]\left[\begin{array}{cccc}1&0&0&-1\\0&1&0&-3\\0&0&1&-2\end{array}\right][/tex]

To solve the system of equation, its needs us to use the Gauss-Jordon elimination method. Therefore, the matrix

- 5  7  7  -30

1  -4   4    3

2   -4   6   -2  will be reduced to its echelon form as follows;

 R₁ ÷ 5                                   R₂ - R₁                       R₃ - 2× R₁

1  −1.4 −1.4   6                   1  −1.4 −1.4   6                1  −1.4 −1.4   6        

1   −4    4    3                    0  2.6  5.4  -3                0  2.6  5.4  -3

2 −4    6  −2                     2 −4    6  −2                  0  −1.2  8.8 −14

   R₂  ÷ -2.6                          R₃ - 1.2 R₂

1    −1.4    −1.4     6                1    −1.4    −1.4     6

0     1    -2.077  1.154            0     1    -2.077  1.154

0  −1.2     8.8    −14              0    0      1         -2

  R₁ - 1.4R₃                                 R₂ - 2.077R₃                 R₁ - 1.4R₂

1  -1.4  0  3.2                              1  -1.4  0  3.2               1   0    0   -1

0   1  -2.077  1.154                     0   1     0   -3               0   1     0   -3

0  0   1  -2                                  0   0    1    -2               0   0    1    -2          

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The mean of the distribution of the sample means (sampling distribution) for all possible samples of size 81 that could be drawn from the parent population of GPAs is equal to the mean of the parent population of GPAs.

The mean of the distribution of the sample means (sampling distribution) for all possible samples of size 81 that could be drawn from the parent population of GPAs is equal to the mean of the parent population. This is due to the central limit theorem, which states that as the sample size increases, the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Therefore, if we were to take all possible samples of size 81 from the population of GPAs and calculate the mean of each sample, the distribution of these means would be approximately normal with a mean equal to the population mean of GPAs. This means that if we take a large number of samples of size 81 and calculate the mean of each sample, the average of these means will be very close to the population mean of GPAs.
In conclusion, the mean of the distribution of the sample means (sampling distribution) for all possible samples of size 81 that could be drawn from the parent population of GPAs is equal to the mean of the parent population of GPAs.

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Answer:

The total cost of the two toys before the discount is VND 45,000 + VND 25,000 = VND 70,000.

Step-by-step explanation:

The discount is 10% of the total cost, which is 0.1 x VND 70,000 = VND 7,000.

Therefore, the final cost after the discount is VND 70,000 - VND 7,000 = VND 63,000.

Nam will have to pay VND 63,000 to buy the two toys after the discount.

The solution to the equation is x = 28/9

Given data ,

To solve the equation 3x/4 = 7/3, you can follow these algebraic steps:

Step 1 :
Multiply both sides of the equation by 4 to eliminate the fraction in the denominator of the left side:

(4) (3x/4) = (4) (7/3)

3x = (4/1) (7/3)

Step 2:
Simplify the right side of the equation:

3x = 28/3

Step 3 :
Divide both sides of the equation by 3 to isolate x:

(1/3) (3x) = (1/3)(28/3)

x = (28/3) / 3

Step 4 :

Simplify the right side of the equation:

x = 28/9

Hence , the solution to the equation 3x/4 = 7/3 is x = 28/9

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Answer:

14

Step-by-step explanation:

used a calculator to check the answer

Answer:37.5 average

Step-by-step explanation:I think

Answer:

12) x = 6. 13) not tangent

Step-by-step explanation:

12) x² - 5 = 31 (since they are both tangents)

x²  = 31 + 5 = 36

x = ±6

x = +6 (has to be positive since it's a length).

13) if it was tangent, angle BAC would be 90°.

that would also mean AB²  = BC² - AC²

                                            =  15² - 5²

                                            = 225 - 25

                                           = 200

AB = √200 ≠ 14.

Since the values are different, AB is not a tangent to the circle

The requried probability that the mean of a sample of 70 computers would differ from the population means by less than 1.9 months is 0.8671, rounded to four decimal places.

The mean of the sampling distribution of the sample means is:

u = 105

and the variance of the sampling distribution of the sample means is:

σ² = 81/70

We can standardize the distribution of the sample means by using the z-score formula:

z = (x - u) / (σ/ √(n))

where x is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.

We want to find the probability that the sample mean differs from the population mean by less than 1.9 months, or |x - u| < 1.9. This is equivalent to finding the probability that the standardized sample mean falls within the range:

-1.9 / (σ/ √(n)) < z < 1.9 / (σ/ √(n))

Substituting the values we have, we get:

-1.9 / (9 / √(70)) < z < 1.9 / (9 / √(70))

Simplifying, we get:

-1.1158 < z < 1.1158

Using a standard normal distribution table, we can find the probability that the z-score falls within this range:

P(-1.1158 < z < 1.1158) = 0.8671

Therefore, the probability that the mean of a sample of 70 computers would differ from the population means by less than 1.9 months is 0.8671, rounded to four decimal places.

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The value of w is 9.

We can use the slope formula to find the value of w.

The slope formula is:

m =[tex](y_2 - y_1) / (x_2 - x_1)[/tex]

where m is the slope of the line and [tex](x_1, y_1)[/tex]and [tex](x_2, y_2)[/tex] are two points on the line.

We know that the slope of the line is 7, and the two points on the line are (-5, -5) and (-3, w). So we can plug in these values into the slope formula and solve for w:

7 = (w - (-5)) / (-3 - (-5))

Simplifying the right-hand side, we get:

7 = (w + 5) / 2

Multiplying both sides by 2, we get:

14 = w + 5

Subtracting 5 from both sides, we get:

w = 9

Therefore, the value of w is 9.

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Answer: what subject, and i got you.

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

I will just calculate the population of every detail for ease.
800 total students.
800 * 60% or 0.6 = 480
480 girls.
480 * 50% or 0.5 = 240
240 music class girls.
240 * 10% or 0.1 = 24
24 music class girls.
so 24 music class girls that are into volleyball and 32 team girls.
32-24 = 8
8 of the team girls are not into music.

The matrices after the row operations are given as follows:

a) [tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex]

b) [tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\-6&-5&-2&-3\end{array}\right][/tex]

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\2&5&-6&-4\end{array}\right][/tex]

When we multiply a matrix row by a constant, each element of the row is multiplied by the constant.

Hence the resulting matrix after we multiply row 3 by 2 is given as follows:

[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex]

We can also exchange rows of the matrix, hence the resulting matrix after rows 1 and 3 are exchanged is given as follows:

[tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\-6&-5&-2&-3\end{array}\right][/tex]

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The amount of fluid ounces of water the water bottle can hold is 48 fluid ounces.

Annabel's water bottle holds 6 cups of water.  Therefore, the amount in fluid ounces the bottle water can hold can be calculated as follows:

Therefore,

1 cup = 8 fluid ounces

6 cups = ?

cross multiply

Hence,

number of fluid ounces of water the water bottle can hold = 8 × 6

number of fluid ounces of water the water bottle can hold = 48 fluid ounces.

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Answer:36000

Step-by-step explanation:

He saves 36000 dollars

The height of the cylinder is determined as 36.2 inches.

The height of the cylinder is calculated by applying the formula for surface area of a cylinder as shown below;

S.A = 2πr(r + h)

where;

The height of the cylinder is calculated as follows;

2,285.92 = 2π x 8.2 (8.2 + h)

2,285.92 = 51.52(8.2 + h)

8.2 + h = 2,285.92/51.52

8.2 + h = 44.37

h = 36.2 inches

Thus, the height of the cylinder for the given radius and surface area is determined by using the equation for surface area of a cylinder.

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The complete question is below:

The surface area of a cylinder is 2,285.92 square inches. What is the height? if the radius of the cylinder is 8.2 inches.