A giant right triangular sculpture has two legs with lengths 20 meters and 40 meters. What is the measure of the smallest angle in this sculpture? Round your answer to the nearest degree.
15°
27°
30°
43°

The solution to the equation sqrt 2-3x / sqrt 4x = 2 is x = -2/3.

To solve the equation, we must first clear the denominators and simplify the equation. We can do this by multiplying both sides by sqrt(4x) and then squaring both sides. This gives us:
sqrt 2-3x = 4sqrt x
2 - 6x + 9x² = 16x
9x² - 22x + 2 = 0
Using the quadratic formula, we can find that x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in a = 9, b = -22, and c = 2, we get:
x = (-(-22) ± sqrt((-22)² - 4(9)(2))) / 2(9)
x = (22 ± sqrt(352)) / 18
x = (22 ± 4sqrt22) / 18
Simplifying this expression, we get:
x = (11 ± 2sqrt22) / 9
Therefore, the solution to the equation is x = -2/3.
To solve the equation sqrt 2-3x / sqrt 4x = 2, we must clear the denominators and simplify the equation. This involves multiplying both sides by sqrt(4x) and then squaring both sides.

After simplifying, we end up with a quadratic equation. Using the quadratic formula, we can find that the solutions are x = (11 ± 2sqrt22) / 9.

However, we must check that these solutions do not result in a division by zero, as the original equation involves square roots. It turns out that the only valid solution is x = -2/3.

Therefore, this is the solution to the equation.

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Answer: the answer is 7 dollars for 1 guest

Step-by-step explanation:

The required answers are 1) \($$A = x^2 + 28x + 192$$\) 2) 300000 3) \($$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$\).

area of the land purchased is given as 480m², and the dimensions of the land are (x+12)mx(x+16)m. Therefore, the area of the land can be expressed as:

\($$A = (x+12)(x+16)$$\)

Expanding this expression, we get:

\($$A = x^2 + 28x + 192$$\)

Hence, the area of the land purchased is given by the polynomial expression \($x^2 + 28x + 192$\).

The total budget for the expenses is Rs. 5,00,000. If Mr. Chand's daughter is ready to share 3/5 of the expenses, then the fraction of the expenses she will pay is:

\($\frac{3}{5}=\frac{x}{500000}$$\)

Simplifying this expression, we get:

\($x = \frac{3}{5}\times 500000 = 300000$$\)

Therefore, Mr. Chand's daughter will pay Rs. 3,00,000 towards the expenses.

We can solve the polynomial \($x^2 + 28x + 192$\) into different factors by using the quadratic formula:

\($x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$\)

Here, the coefficients of the polynomial are:

\($$a = 1, \quad b = 28, \quad c = 192$$\)

Substituting these values in the quadratic formula, we get:

\($x = \frac{-28 \pm \sqrt{28^2 - 4\times 1 \times 192}}{2\times 1}$$\)

Simplifying this expression, we get:

\($$x = -14 \pm 2\sqrt{19}$$\)

Therefore, the polynomial \($x^2 + 28x + 192$\) can be factored as:

\($$x^2 + 28x + 192 = (x - (-14 + 2\sqrt{19}))(x - (-14 - 2\sqrt{19}))$$\)

or

\($$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$\)

So, we have factored the polynomial into two factors.

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Answer:

-8x+21

Step-by-step explanation:

Use the distributive property.

Using simultaneous equation, the solution to the system of linear equations are 1223 $10 tickets, 1332 $20 tickets, and 763 $30 tickets were sold.

Let's solve the problem step by step.

Let:

x = number of $10 tickets sold

y = number of $20 tickets sold

z = number of $30 tickets sold

From the given information, we can form the following equations:

Equation 1: x + y + z = 3318 (Total number of tickets sold)

Equation 2: y = x + 109 (109 more $20 tickets than $10 tickets were sold)

Equation 3: 10x + 20y + 30z = 61760 (Total sales from ticket sales)

We can use these three equations to solve for the values of x, y, and z.

First, let's substitute Equation 2 into Equation 1:

x + (x + 109) + z = 3318

2x + 109 + z = 3318

2x + z = 3209 (Equation 4)

Now, let's substitute the value of y from Equation 2 into Equation 3:

10x + 20(x + 109) + 30z = 61760

10x + 20x + 2180 + 30z = 61760

30x + 30z = 59580

x + z = 1986 (Equation 5)

We now have a system of equations (Equations 4 and 5) with two variables (x and z). We can solve this system to find the values of x and z.

Multiplying Equation 4 by 30, and Equation 5 by 2, we get:

60x + 30z = 96270 (Equation 6)

2x + 2z = 3972 (Equation 7)

Now, subtract Equation 7 from Equation 6:

(60x + 30z) - (2x + 2z) = 96270 - 3972

58x + 28z = 92298

Simplifying, we have:

29x + 14z = 46149 (Equation 8)

Now, we can solve Equations 5 and 8 simultaneously:

x + z = 1986 (Equation 5)

29x + 14z = 46149 (Equation 8)

Multiplying Equation 5 by 14, and Equation 8 by 1, we get:

14x + 14z = 27804 (Equation 9)

29x + 14z = 46149 (Equation 8)

Now, subtract Equation 9 from Equation 8:

(29x + 14z) - (14x + 14z) = 46149 - 27804

15x = 18345

Divide both sides of the equation by 15:

x = 18345 / 15

x = 1223

Substituting the value of x into Equation 5, we can find z:

1223 + z = 1986

z = 1986 - 1223

z = 763

Now that we have the values of x and z, we can substitute them back into Equation 1 to find y:

1223 + y + 763 = 3318

y + 1986 = 3318

y = 3318 - 1986

y = 1332

Therefore, the solution to the problem is:

x = 1223 (number of $10 tickets sold)

y = 1332 (number of $20 tickets sold)

z = 763 (number of $30 tickets sold)

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Answer:

Step-by-step explanation:

Answer:

I think it is 20 percent

Step-by-step explanation:

Sorry if this is wrong

The dimensions of the rectangular slab are 16 meters in length and 2 meters in width.

Let's assume the length of the rectangular slab of concrete is L meters. According to the given information, the width is 14 meters less than the length, so the width would be L - 14 meters.

The formula for the area of a rectangle is A = length × width. In this case, the area is given as 32 m², so we can set up the equation:

32 = L × (L - 14)

Expanding the equation, we get:

32 = L² - 14L

Rearranging the equation, we have:

L² - 14L - 32 = 0

To solve this quadratic equation, we can either factorize it or use the quadratic formula. In this case, it's easier to use the quadratic formula:

L = (-b ± √(b² - 4ac)) / (2a)

Here, a = 1, b = -14, and c = -32. Substituting these values into the formula, we get:

L = (14 ± √((-14)² - 4 × 1 × (-32))) / (2 × 1)

Simplifying further:

L = (14 ± √(196 + 128)) / 2

L = (14 ± √324) / 2

L = (14 ± 18) / 2

Therefore, we have two possible values for L:

L₁ = (14 + 18) / 2 = 16

L₂ = (14 - 18) / 2 = -2

Since the length of the slab cannot be negative, we discard the negative value.

Thus, the length of the rectangular slab is 16 meters. To find the width, we subtract 14 meters from the length:

Width = 16 - 14 = 2 meters

Therefore, the dimensions of the rectangle are 16 meters by 2 meters.

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Answer: 0.40 and 40%

Answer:

40%

Step-by-step explanation:

Answer:

Question 1: A

Question 2: D

Step-by-step explanation:

I hope it helps

Answer:

depands

Step-by-step explanation:

sorry put sure yo can really just do 50 so

19%; 100% - 19% = 81% = .81

29,000(.81)^5 = $10,111.67

Answer:

x = 6

Step-by-step explanation:

We can solve for x in this circle using the intersecting chords theorem:

(x + 6)(x - 4) = 6 * 4

x² + 2x - 24 = 24

x² + 2x - 48 = 0

(x + 8)(x - 6) = 0

x = -8 or x = 6

Answer:

harmonica’s

Step-by-step explanation:

because it’s talking about multiple and it has apostrophe and an s

B

Step-by-step explanation:

The area of the triangle would be = 7.5 in²

A triangle is defined as the polygon that is characterized by having three sides and vertices and with a total internal angle of 180°.

The area of a triangle can be calculated using the formula of:

A = 1/2 base × height.

Base = 6 in

Height = 2.5 in

Area = 1/2 × 6 × 2.5

= 15/2

= 7.5 in²

Therefore the area of the given triangle = 7.5 In².

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The total area of the composite figure which has triangle and rectangle is  24.41 square inches

The given composite figure has two triangles and one rectangle

Area of rectangle =length × width

=4.6×3.15

=14.49 square inches

Area of left side triangle, it has base of 3.3 in and height 3.15 inches

Area of triangle = 1/2×3.3×3.15

=5.1975 square inches

Area of triangle on right side

Base = 3 in

Height = 6.3-3.15=3.15 in

Area of triangle = 1/2×3×3.15

=4.725 square inches

Total area = 14.49 + 5.1975  + 4.725

=24.41 square inches

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Answer:

3:2.

Step-by-step explanation:

They have 15 - 6 = 9 problems to do, so it is:

9:6

= 3:2.

Answer:

9/15

Step-by-step explanation:

15 - 6 = 9 as a fraction would be 9 meaning what is left and 15 as meaning how much they started with so it is 9/15 also called 9 over 15

Hope This Helped

The next three terms in the geometric sequence will be 24, 48 and 96.

We are given a geometric sequence:

3, 6, 12 …

We need to find the next 3 terms of the sequence.

We can see that:

a = initial term of the sequence

a = 3

r = common ratio between the consecutive terms.

r = 6 / 3 = 2

Now, nth term will be represented by:

aₙ = a rⁿ⁻¹

Substituting the values of a and r in the formula, we get that:

aₙ = 3 (2)ⁿ⁻¹

Now, the 4th term will be ( put n = 4)

a₄ = (3) (2)⁴⁻¹

a₄ = (3) (2)³

a₄ = (3) × (8)

a₄ = 24

The 5th term will be: (put n = 5)

a₅ = (3) (2)⁵⁻¹

a₅ = (3) (2)⁴

a₅ = (3) × (16)

a₅ = 48

6th term will be: (put n = 6)

a₆ = (3) (2)⁶⁻¹

a₆ = (3) (2)⁵

a₆ = (3) × (32)

a₆ = 96

Therefore, the next three terms in the geometric sequence will be 24, 48 and 96.

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Your question was incomplete. Please refer the content below:

The first three terms of a geometric sequence are 3, 6, 12. What are the next three terms?

Answer:naneeeeee

Step-by-step explanation:

It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of compounding periods per year

t = Number of years

In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.

We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.

Let's substitute the given values into the formula and solve for t:

56,398.43 = 500(1 + 0.06/2)^(2t)

Divide both sides by 500:

112.79686 = (1 + 0.03)^(2t)

Take the natural logarithm of both sides to eliminate the exponent:

ln(112.79686) = ln(1.03)^(2t)

Using the property of logarithms, we can bring down the exponent:

ln(112.79686) = 2t * ln(1.03)

Now, divide both sides by 2 * ln(1.03):

t = ln(112.79686) / (2 * ln(1.03))

Using a calculator, we find t ≈ 17.12.

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Answer:

c

Step-by-step explanation:

Answer:

C. 24:56

Step-by-step explanation:

3/7 * 8/8

3*8 = 24

7*8 = 56

24/56

Answer:

The unit rate is 6 pieces or candy per child.

Step-by-step explanation:

you would divide the number of pieces by the amount of children. 36÷6=6 candies. 6 candirs per child

Answer:

6

Step-by-step explanation:

36 pieces of candy among 6 children so 6 pieces for each

Step-by-step explanation:

\(47.1 = 2\pi \times r \\ r = \frac{47.1}{2\pi} = 7.4962996 \\ diameter = 2 \times r \\ = 14.99 = 15 \: feet\)

Answer:

8 ≥ m

Step-by-step explanation:

8 ≥ m is read as 8 is greater than or equal to m.

8, being the larger quantity is by the opening, showing it is greater than m. The underlined part represents m could also be equal to 8.

m could equal 8 or anything below the number 8.

Answer: 2,730

Step-by-step explanation:

Explained in mental math proccess:

In 455, the one value will be multiplied by 6. 5x6= 30.

In 455, the tens value will be multiplied by 6. 50x6= 300.

In 455, the hundreds value will be multipled by 6. 400x6= 2,400.

Find the sums of all products multiplied by 6. 30+300+2,400= 2,730.

455x6= 2,700

Following is the frequency distribution table:

0.720- 0.730

0.730- 0.740

0.740- 0.750

Any table that shows the frequency of values for one or more variables within a set of data. a table displaying each value of the variable and its accompanying frequency for a whole-number variable in a data set.

Given:

The lower limit is given as 0.720 inches.

and, The upper limit is 0.750 inches.

Also, the width of each class is 0.010 inches.

Thus, the intervals will be:

0.720- 0.730

0.730- 0.740

0.740- 0.750

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