The area of triangle ABC is 24 square centimeters. If B = 30° and a = 6 cm, what is the measure of side c? 4 cm 8 cm 16 cm 32 cm

The quotient of 3/5 and 9/10 is the value obtained by dividing both values, Hence, the quotient of the division is 2/3

The division operation can be expressed thus :

3/5 ÷ 9/10

Take the reciprocal of the denominator and change the sign to multiplication ;

Reciprocal of 9/10 = 10/9

Hence, we have ;

3/5 × 10/9 = 30/45

Therefore, the quotient is 2/3

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Final answer:

The weight of the red marble is 16 grams, and the weight of the blue marble is 18 grams, based on the solution of the system of linear equations derived from the given total weights of the marbles.

Explanation:

To solve the problem of determining the weight of each marble, we can set up a system of linear equations based on the given information:

Let r be the weight of a red marble in grams.

Let b be the weight of a blue marble in grams.

The total weight of 3 red marbles and 2 blue marbles is 84g.

The total weight of 12 red marbles and 5 blue marbles is 282g.

Based on these statements, we can write two equations:

3r + 2b = 84 (1)

12r + 5b = 282 (2)

We can solve this system of equations by multiplying equation (1) by 4 to eliminate variable b.

(4)(3r + 2b) = (4)(84)

12r + 8b = 336 (3)

Subtract equation (2) from equation (3) to solve for r:

(12r + 8b) - (12r + 5b) = 336 - 282

3b = 54

b = 18 (weight of blue marble)

Substitute value of b in equation (1) to solve for r:

3r + 2(18) = 84

3r + 36 = 84

3r = 48

r = 16 (weight of red marble)

Therefore, the weight of the red marble is 16 grams and the weight of the blue marble is 18 grams.

Answer:

Option A. 44°

Step-by-step explanation:

In a given triangle FGH sides have been given as FG = 7 yards, FH = 6 yards, and GH = 5 yards.

We have to calculate the approximate value of ∠F.

We apply the cosine rule in the given triangle.

5² = 7² + 6² - 2×7×6×cosF

25 = 49 + 36 - 84× cosF

25 = 85 - 84 cosF

84cosF = 85 - 25 = 60

[tex]cosF=\frac{60}{84}=0.71428[/tex]

[tex]F=cos^{-1}( 0.71428) = 44.4[/tex]

F = 44°

Therefore option A. 44° is the correct answer.

To determine the quotient and remainder for (5x^2+38x+18) divided by (x+7), polynomial long division must be used, involving dividing terms, multiplying and subtracting until the remainder is obtained.

To find the quotient and remainder of the division of polynomials (5x2+38x+18) by (x+7), we can use polynomial long division.

By doing this, you will obtain the quotient and the specific remainder for this division.

3 x squared:) hope this helps

The sum of two consecutive numbers is 131. What are the two numbers?

Answer is provided in the image attached.

Answer:

The length of the hypotenuse is 3√3 units.

Step-by-step explanation:

It is given that the length of the legs of a right triangle are 5 units and √2 units.

According to the Pythagoras theorem, in a right angled triangle

[tex](hypotenuse)^2=(leg_1)^2+(leg_2)^2[/tex]

Substitute leg₁=5 and leg₂=√2 in the above formula.

[tex](hypotenuse)^2=(5)^2+(\sqrt{2})^2[/tex]

[tex](hypotenuse)^2=25+2[/tex]

[tex](hypotenuse)^2=27[/tex]

Taking square root both the sides.

[tex]hypotenuse=\sqrt{27}[/tex]

[tex]hypotenuse=3\sqrt{3}[/tex]

Therefore the length of the hypotenuse is 3√3 units.

Answer:

C) x³ -4x² - 24x + 21.

Step-by-step explanation:

Given : (x – 7)(x² + 3x – 3).

To find : Multiply the polynomials.

Solution : We have given  (x – 7)(x² + 3x – 3).

Distributes x over (x² + 3x – 3) and  -7 over (x² + 3x – 3).

Then

x (x² + 3x – 3) -7(x² + 3x – 3).

x³ + 3x² -3x - 7x² - 21x +21.

Combine like terms

x³ + 3x² - 7x² -3x -21x + 21.

x³ -4x² - 24x + 21.

Therefore, C) x³ -4x² - 24x + 21.

Answer:

x³ -4x² - 24x + 21.

Step-by-step explanation:

Ape-x

First you take the $139.50 and divide it by $15.50

139.50 / 15.50 = 9

Then you take the 9 and multiply it by 3, be cause there are 3 shirts per $15.50

9 x 3 = 27

You can buy a total of 27 shirts with $139.50

Answer:

[tex]6(-7x+1)[/tex]

Step-by-step explanation:

Given: The equation [tex]6-42x[/tex].

To find: Factorize the given equation.

Solution:

The given expression is:

[tex]6-42x[/tex]

which can be rewritten as:

[tex]-42x+6[/tex]

Upon solving the above expression and Taking 6 common from both the terms of the expression ,we get

[tex]6(-7x+1)[/tex]

which is the required factorized form of the given expression.

Answer:

The middle term of the product of (x - 4)(x - 3) is -7

Step-by-step explanation:

Consider the given expression (x - 4)(x - 3)

We have to find the middle term of the product of (x - 4)(x - 3).

First multiply the given terms, we get,

[tex](x - 4)(x - 3)=x(x-3)-4(x-3)[/tex]

Simplify, we get,

[tex]x(x-3)-4(x-3)=x^2-3x-4x+12[/tex]

Simplify further, we get,

[tex]x^2-3x-4x+12=x^2-7x+12[/tex]

Thus, the middle term of the product of (x - 4)(x - 3) is -7

Answer:

Dependent

Step-by-step explanation:

[tex]y=-3x+4[/tex] and [tex]6x+2y=8[/tex]

Lets solve the second equation for y and then substitute it in first equation

[tex]6x+2y=8[/tex]

Subtract 6x on both sides

[tex]2y=-6x+8[/tex]

Divide by 2 on both sides

[tex]y=-3x+4[/tex]

Now we plug it in first equation for y

[tex]-3x+4=-3x+4[/tex]

Add 3x on both sides

[tex]4=4[/tex]

Both sides are same, they are equal. the system has infinite solutions.

They are said to be dependent

The correct order of operations for simplifying the expression (x+3)^2 - [tex](x^2+9)/2x^2[/tex] is as follows:
1. Square the binomial (x+3) to get x^2 + 6x + 9.
2. Divide each term in (x^2+9) by [tex]2x^2[/tex] to get [tex]1/2 + 9/2x^2[/tex].
3. Substitute the simplified expressions back into the original expression: [tex]x^2 + 6x + 9 - (1/2 + 9/2x^2).[/tex]

The correct order of operations for simplifying the expression (x+3)^2 - (x^2+9)/2x^2 is as follows:

1. Start by simplifying the expression within the parentheses: (x+3)^2. This means squaring the binomial (x+3). To do this, you multiply the binomial by itself: (x+3) * (x+3). This results in [tex]x^2 + 6x + 9.[/tex]

2. Next, simplify the expression within the second set of parentheses: (x^2+9).

3. Now, divide [tex](x^2+9)[/tex] by 2x^2. To do this, divide each term in (x^2+9) by 2x^2. This gives us [tex](x^2/2x^2)[/tex] [tex]+ (9/2x^2)[/tex]. Simplifying further, we get 1/2 + [tex]9/2x^2[/tex].

4. Finally, substitute the simplified expressions back into the original expression: [tex]x^2 + 6x + 9 - (1/2 + 9/2x^2).[/tex]

yes; Reflections and translations are rigid motions. Rigid motions preserve the size of the original image.

Final answer:

To find the inverse of the function f(x) = 3x - 8, you swap x and y and solve for y, resulting in the inverse function f^-1(x) = (x + 8) / 3.

Explanation:

To find the inverse function f-1(x) for the given linear function f(x) = 3x - 8, we will follow these steps:

Replace f(x) with y: y = 3x - 8.

Swap x and y to make it x = 3y - 8.

Solve for y to get the inverse function.

Starting with x = 3y - 8, we add 8 to both sides to obtain x + 8 = 3y. Then, we divide both sides by 3 to isolate y, resulting in y = (x + 8) / 3. Therefore, the inverse function is f-1(x) = (x + 8) / 3.

We get the approximate value of [n] as 5.

        [tex]$\log_{b}({b^x})=x[/tex]

We have 31,100 is rounded to the nearest power of 10 and [N] represents a power of 10.

We can write -

10ⁿ = 31100

10ⁿ = 311 x 10²

10ⁿ ⁻ ² = 311

log(10ⁿ ⁻ ²) = log(311)

(n - 2) log 10 = log (311)

n - 2 = log(311)/log(10)

n - 2 = 2.5

n = 4.5

n = 5 (approx.)

Therefore, we get the approximate value of [n] as 5.

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When rounding 31,100 to the nearest power of 10, we get the value of n is 4.

To find the value of n when 31,100 is rounded to the nearest power of 10, we first need to determine which powers of 10 are closest to 31,100. The nearest powers of 10 to 31,100 are 104 (10,000) and 105 (100,000). Since 31,100 is closer to 104 than to 105, we round it down to 104.

Therefore, when 31,100 is rounded to the nearest power of 10, the value of n is 4.

The process involves converting the number into scientific notation and then adjusting the exponent, which represents the number of places the decimal point moves. In our case, to convert 31,100 to a number between 1 and 10, we would express it as 3.11 × 104, confirming that the value of n is 4.