sin2x - căn 3 cos2x + 2 = 0

15 liters of the 10% acid solution must be used

55 liters of the 80% acid solution must be used

Let the volume of the 10% acid solution be x

Let the volume of the 80% acid solution be y

The combination of the two solutions gives 70 liters

x + y = 70..............................(1)

The 70 liters solution is equivalent to 65%

10x + 80y = 70(65)

10x + 80y = 4550..........................(2)

Make x the subject of the formula in equation (1)

x = 70 - y...............................(3)

Substitute equation (3) into equation (2)

10(70 - y) + 80y = 4550

700 - 10y + 80y = 4550

70y = 4550 - 700

70y = 3850

y = 3850/70

y = 55 liters

Substitute y = 55 into equation (3)

x = 70 - 55

x = 15 liters

Answer:

The answer is 126 \(cm^{3}\)

Step-by-step explanation:

The formula for the volume of a rectangle is L x W x H.

So you just plug in the numbers into the formula.

2 x 9 x 7

That equals 126.

If two trapezoids have respective surface areas of  \(432cm^2 and 48cm^2\), their similarity ratio is 3:1.

The ratio of the areas of similar figures is the square of the ratio of their corresponding side lengths.

Let's denote the ratio of similarity between the two trapezoids by "k".

The area of the first trapezoid is \(432 cm^2\), and the area of the second trapezoid is \(48 cm^2\).

Therefore, we can set up the equation:

(k * side length of first trapezoid)^2 / (k * side length of second trapezoid)^2 = 432/48

Simplifying the right-hand side of the equation gives:

(k * side length of first trapezoid)^2 / (k * side length of second trapezoid)^2 = 9

We can simplify the left-hand side of the equation by canceling out the "k" terms:

(side length of first trapezoid)^2 / (side length of second trapezoid)^2 = 9

Taking the square root of both sides gives:

(side length of first trapezoid) / (side length of second trapezoid) = 3

Therefore, the ratio of the corresponding side lengths of the two trapezoids is 3:1. Since the ratio of similarity is the square of the ratio of corresponding side lengths, we have:

k = (side length of first trapezoid) / (side length of second trapezoid) = 3/1 = 3

So, the ratio of similarity between the two trapezoids is 3:1.

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Answer:

liiiaaaarrrrrr

Step-by-step explanation:

Therefore, the football team scored 4 touchdowns, 2 field goals, and 1 safety in the game.

An equation is a mathematical statement that asserts that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and so on. An equation is often written with an equal sign (=) between the two expressions. The goal of solving an equation is to find the values of the variables that make the equation true. Equations are used extensively in mathematics, physics, engineering, and many other fields to describe relationships between different quantities.

by the question.

Let's denote the number of touchdowns scored by "T", the number of field goals scored by "F", and the number of safeties scored by "S".

From the problem, we know:

\(T + F + S = 8 (they scored points 8 times)\\7T + 3F + 2S = 38 (the total score was 38 points)\\T = F + S\) (they scored as many touchdowns as they did field goals and safeties combined)

Substituting the third equation into the first, we get:

\(F + S + F + S = 8\\2F + 2S = 8\\F + S = 4\)

We now have a system of three equations:

\(T + F + S = 8\\7T + 3F + 2S = 38\\T = F + S\)

Substituting the third equation into the first two, we get:

\(7(F + S) + 3F + 2S = 38\\8(F + S) = 21\)

Solving for F + S, we get:

\(F + S = 21/8\)

However, we also know that F + S = 4, so there must be a mistake somewhere. Looking back at the problem, we see that the statement "they scored as many touchdowns as they did field goals and safeties combined" implies that T = F + S + 1 (since a touchdown is worth 7 points and a field goal and safety combined are worth 4 points). Substituting this into the first two equations, we get:

\((F + S + 1) + F + S = 8\\7(F + S + 1) + 3F + 2S = 38\)

Simplifying, we get:

\(2F + 2S = 6\\10F + 9S = 31\)

Solving for F and S, we get:

\(F = 2\\S = 1\)

Substituting these values back into the equation T = F + S + 1, we get:

\(T = 4\)

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Answer:

a) 10 blue balls, b) 5/18

Step-by-step explanation:

a)

R=3, G=5, B=x (unknown)

probability of picking red = 1/6 and red = 3 so total = 3(6) = total is 18

3+5 = 8 so B=18-8 -> B=10

b) total is 18 and G=5 so green probability = 5/18

Answer:

4,320

Step-by-step explanation:

answer is 4,320

9x2x3x8x2x5

Answer:

66 km²

Step-by-step explanation:

To solve this, you should find the area of the rectangle as if it were complete and then subtract the area of the missing section.

Step one: Finding the area of the big rectangle

A =  length x width

A = 9 x 8

A = 72 km²

Step two: Find the area of the smaller rectangle

A = 2 x 3 = 6 km²

Step three: Subtract the area of the small rectangle from the area of the big rectangle

72 - 6 = 66

Answer:

8 bags altogether

Step-by-step explanation:

Again, without a photo, I can't choose the diagram. Very sorry.

k is Keith, s is Sean

k = 3s

substitute in bags Keith carried and solve for s

6 = 3s

divide both sides by 3

s = 2

Keith carried 6, Sean carried 2,

6 + 2 = 8 bags total

Answer:

40

Step-by-step explanation:

4*5=20

5*8=40

I hope you got it....

Answer:

\( {3}^{2} \)

Step-by-step explanation:

\(3^{ - 6} \times (3^4 \div 3^0)^2\)

\( \frac{1}{ {3}^{6} } \times ( {3}^{4} \div {3}^{0} {)}^{2} \)

\( \frac{1}{729} \times ( {3}^{4} \div {3}^{0} {)}^{2} \)

\( \frac{1}{729} \times ( {3}^{4} {)}^{2} \)

\( \frac{1}{729} \times 6561\)

\( \frac{1}{729} \times (729(9))\)

\(9\)

\( {3}^{2} \)

The value of Absolute maximum are (a) 8, (b) -30.36, (c) -10 and the Absolute minimum are (a) -10, (b) -362.39, (c) -362.39.

We are given a function:f(x) = x³ - 12x² - 27x + 8We need to find the absolute maximum and absolute minimum values of the function f(x) over each of the indicated intervals. The intervals are:

a) Interval = [-2, 0]

b) Interval = [1, 10]

c) Interval = [-2, 10]

Let's begin:

(a) Interval = [-2, 0]

To find the absolute max/min, we need to find the critical points in the interval and then plug them in the function to see which one produces the highest or lowest value.

To find the critical points, we need to differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 0].

Checking for x = 4 + √37:f(-2) = -10f(0) = 8

Checking for x = 4 - √37:f(-2) = -10f(0) = 8

Therefore, the absolute max is 8 and the absolute min is -10.(b) Interval = [1, 10]

We will follow the same method as above to find the absolute max/min.

We differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)

x = (24 ± √(888)) / 6

x = (24 ± 6√37) / 6

x = 4 ± √37

We need to check which critical point lies in the interval [1, 10].

Checking for x = 4 + √37:f(1) = -30.36f(10) = -362.39

Checking for x = 4 - √37:f(1) = -30.36f(10) = -362.39

Therefore, the absolute max is -30.36 and the absolute min is -362.39.

(c) Interval = [-2, 10]

We will follow the same method as above to find the absolute max/min. We differentiate the function:

f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:

f'(x) = 0

Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 10].

Checking for x = 4 + √37:f(-2) = -10f(10) = -362.39

Checking for x = 4 - √37:f(-2) = -10f(10) = -362.39

Therefore, the absolute max is -10 and the absolute min is -362.39.

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A rectangle contains the area of 60 inch² then the dimension is as follows:

length × width

60 × 1

30 × 2

20 × 3

15 × 4

12 × 5

10 × 6

The square inch unit provides the area. Given that the length and width of a rectangle are multiplied to determine its area, we can state that any pair of non-negative integers whose product is equal to 60 would be appropriate.

Area = length × Width

We can find those integer numbers for its dimensions:

(60 divisors)

width × length

60 × 1

30 × 2

20 × 3

15 × 4

12 × 5

10 × 6

length × width

60 × 1

30 × 2

20 × 3

15 × 4

12 × 5

10 × 6

And many other combinations for non integers like 40 × 1.5, 24 × 2.5 etc.

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Answer:

Area of the rectangle: 24 cm²

Area of the circle: 380.13 cm²

Area of between the circle and the rectangle: 356.13 cm²

Step-by-step explanation:

Answer:

397.39

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

p=(8)-3

p=5

Answer:

p=8-3

p=5

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Examples that would equal 3:

2 + 1 = 3 or 1 + 1 + 1 = 3

1.5 + 1.5 = 3

3 * 1 = 3

There you go the different ways to get 3

Given statement solution is :- We cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).

The given sequence is: 5 2 1 4 0 0 7 2 8 1 m m 7 m 5 m A.

To find the missing value, let's analyze the pattern in the sequence. We can observe the following pattern:

The first number, 5, is the sum of the second and third numbers (2 + 1).

The fourth number, 4, is the sum of the fifth and sixth numbers (0 + 0).

The seventh number, 7, is the sum of the eighth and ninth numbers (2 + 8).

The tenth number, 1, is the sum of the eleventh and twelfth numbers (m + m).

The thirteenth number, 7, is the sum of the fourteenth and fifteenth numbers (m + 5).

The sixteenth number, m, is the sum of the seventeenth and eighteenth numbers (m + A).

Based on this pattern, we can deduce that the missing values are 5 and A.

Now, let's calculate the missing value:

m + A = 5

To find a specific value for m and A, we need more information or equations. Without any additional information, we cannot determine the exact values of m and A. Therefore, we cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).

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Answer:

first you subtract 2 from both sides

-6x>18

then you divide

-6 by 18 which is -3 and since you divided with a decimal that flips your sign so your answer is X<-3

Answer:

x<-3

Step-by-step explanation:

First, write the equation and subtract 2 on both sides.

-6x+2>20

     -2  -2

-6x>18

Divide both sides by -6.

-6x>18

/-6  /-6

x<-3

(Remember, we have to flip the sign when multiplying or diving by a negative.)

Hope this helps! Have an amazing day C:

From the graph, the national debt in 1960 was 46%.

It was given that the national debt in 1960 is $0.3 trillion.

Let the GDP be represented by G. This means that 46% of this value is:

Equating this to the debt amount, we have:

Solving for G, we have:

Therefore, the GDP in 1960 was $0.65 trillion.

Answer:

D) 98/280 = p/100

Step-by-step explanation:

Since p is the missing percentage, it has to be OVER 100, so C is eliminated.

Total:

182 + 98 = 280

Spotted sheep probability:

98/280 = 0.35 or 35%

To check:

\(\frac{98}{280} =\frac{p}{100} \\\\280p=9800\\x=35\)

Answer:

$1.44

Step-by-step explanation:

Tax is a compulsory sum levied by the government. it increases the price of the good

tax paid = tax rate x price of the book

18 x 8%

18 x 0.08 = $1.44

The decibel value of the noise is 50 db.

What is meaning of intensity of sound?

The quantity of energy going across a unit area in a unit time in a direction that is opposite to the direction of the sound waves.

The unit that used to calculate intensity of sound is decibel.

Given equation that represents the relation between intensity of sound and the ratio of the sound to the human hearing threshold is

db = 10 log i

Where i = the ratio of the sound to the human hearing threshold.

Putting i = 100,000 in the given equation:

db = 10 log 100,000

Replace 100,000 by 10⁵ :

db = 10 log 10⁵

Applying the formula of logarithm log 10^{a} = a:

db = 10 × 5

db = 50

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Answer: Whatever the original balance was + 75

Step-by-step explanation:

You never gave a concrete value of what the balance of her account was before the new deposit so it is impossible for me to tell you the exact answer, but just add $75 to whatever it was before and you will be correct!  If you tell me the original value I would be more than happy to help you further :)  Have a great rest of your day!

The answer to Math.round(3.6) is D. 4.0. The Math.round() method is used to round a number to the nearest integer.

When we apply Math.round(3.6), it rounds off 3.6 to the nearest integer which is 4.

This method uses the following rules to round the given number:

1. If the fractional part of the number is less than 0.5, the number is rounded down to the nearest integer.

2. If the fractional part of the number is greater than or equal to 0.5, the number is rounded up to the nearest integer.

In the given question, the number 3.6 has a fractional part of 0.6 which is greater than or equal to 0.5, so it is rounded up to the nearest integer which is 4. Therefore, the correct answer to Math.round(3.6) is D. 4.0.

It is important to note that the Math.round() method only rounds off to the nearest integer and not to a specific number of decimal places.

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Answer:

volume of cylinder

= area of circle × height

= πr² × h

= (22/7 × 9²) × 20

= 254.57 × 20

= 5091.4 cm³

Answer:

5089.4 cm³

Step-by-step explanation:

The volume (V) of a cylinder is calculated as

V = Ah ( A is the area of the base and h the height ), thus

V = πr²h

   = π × 9² × 20 = π × 81 × 20 = 1620π ≈ 5089.4 cm³ ( to 1 dec. place )

Answer:

13 for 4 and 26 for 8 I believe is the answer

Step-by-step explanation:

The vertex form of the quadratic equation is:  y = a(x - h)² + k.

The standard form of quadratic equation is: y = ax² + bx + c.

In order to change the vertex form into standard form, you'll have to expand the squared binomial, (x - h)² through FOIL method before distributing the value of a, and adding the value of k.

Given the vertex form, y = 2(x - 2)² + 2:

We can transform the given vertex form into its standard form as follows:

(x - 2)² = (x - 2)(x - 2) = x² - 2x - 2x + 4 =  x² - 4x + 4.

y = 2(x - 2)² + 2

y = 2(x² - 4x + 4) + 2

y = 2(x² - 4x + 4) + 2

y = 2x² - 8x + 8 + 2

y = 2x² - 8x + 10  ⇒ This is the standard form of quadratic equation where a = 2, b = -8, and c = 10.  

Answer:

16.02 m

Step-by-step explanation:

the area (A) of a square is calculated as

A = s² ( s is the side length )

given A = 256.6404 , then

s² = 256.6404 ( take square root of both sides )

s = \(\sqrt{256.6404}\) = 16.02 m