Use the Distributive Property to evaluate each expression.
1. 3(5 + 6) =
2. (6 + 4)(-12) =
3-619 - 4) =

Answer:

Just multiply two of the same numbers together twice

Step-by-step explanation:

Find the closest square number to the Square root of 31 which is 36. The square root of 36 is 6. So since 31 is smaller than 36, it must be between 5 and 6. Do this for the rest of the questions.

The measure of the largest angle in the kite is 26.67 (approx)°.

The given problem states that you cut out a piece of fabric in the shape of a kite so that the congruent angles of the kite are each 100°. The other two angles of the kite are not equal. If one of the angles is 4 times the size of the other, then the larger angle is 4x, and the smaller one is x.

We need to determine the measure of the largest angle in the kite. In order to find out the measure of the largest angle in the kite, we need to know the sum of all the angles in the kite. Let's recall the sum of angles in a kite. A kite is a quadrilateral whose four sides can be grouped into two pairs of adjacent sides that are equal in length. A kite has two opposite pairs of equal angles. The sum of the angles of a kite is 360°.In a kite, the angles can be represented as a, a, b, and c where a is the congruent angle and b and c are non-congruent angles.

Then, 2a + 2b = 360°2a + 2x + 4x = 360°2a + 6x = 360°2a = 360° - 6x2a = 180° - 3xa = (180° - 3x)/2

Since a = 100°, we can substitute it in the equation above, a = (180° - 3x)/2 and find the value of x.

Substituting a = 100° in the above equation, we get:

100 = (180 - 3x)/2100 × 2 = 180 - 3x200 = 180 - 3x20 = -3x/-3x = -20/(-3)x = 6.67 (approx)

Now we can substitute this value of x in the expression for the larger angle to find its measure. The larger angle is 4x, so it is equal to 4(6.67) = 26.67 (approx)°.

Therefore, the measure of the largest angle in the kite is 26.67 (approx)°.

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The differentiation of the function  f(x) = sin⁻¹(3x⁵) is  \(15x^4/\sqrt{1-9x^{10}}\).

Function is a combination of different types of variable and constants.

A function is denoted by f(x).

The given function is,

f(x) = sin⁻¹(3x⁵)

Differentiate the given function with respect to x

f'(x) = d/dx(sin⁻¹(3x⁵))

The differentiation of sin⁻¹x is  \(1/\sqrt{1-x^2}\),

f'(x) =\(1/\sqrt{1-(3x^5)^2}\cdot d/dx(3x^5)\)

     = \(1/\sqrt{1-9x^{10}}\cdot 15x^4\)

     = \(15x^4/\sqrt{1-9x^{10}}\)

The differentiation of f(x) = sin⁻¹(3x⁵) is  \(15x^4/\sqrt{1-9x^{10}}\).

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Answer:

139.93

Step-by-step explanation:

i used a online calculator

https://www.omnicalculator.com/physics/maximum-height-projectile-motion

The maximum height attained by the arrow will be 1,700 feet.

What is mean by Quadratic equation?

A polynomial which has a power two then its called a Quadratic equation.

Given that;

An arrow is launched upward with a velocity of 320 feet per second from the top of a 100-foot structure.

Let the equation for the height of the arrow at time t is;

h (t) = - 16t² + 320t + 100.

Here, The arrow is follow the path of a parabola that curves downwards.

The value of t for the vertex = - b / 2a

                                            = - 320/2×-16

                                            = 10

Substitute t = 10 in above equation, we get;

h (t) = - 16t² + 320t + 100.

h (t) = - 16 × 10² + 320 × 10 + 100

h (t) = -16 × 100 + 3200 + 100

h (t) = - 1600 + 3200 + 100

h (t) = 1,700

Therefore, The maximum height attained by the arrow will be 1,700 feet.

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Answer:

b = 31°

Step-by-step explanation:

b + 59 = 90

b = 90 - 59

b = 31°

Answer:

31

angles on a line = 180°

so, 90-59-b=180°

Answer:

43.6 has 3 significant figures.

Answer:

  {2, 4, 6, 8}

Step-by-step explanation:

Even numbers are of the form 2n, where n is any integer. If you want positive even numbers less than 10, you require ...

  0 < 2n < 10

  0 < n < 5 . . . . . . divide by 2

That is, n = {1, 2, 3, 4}, so 2n = {2, 4, 6, 8}.

The positive even integers less than 10 are {2, 4, 6, 8}.

In such cases some time positive no. is less than 10 either more than ten

Step-by-step explanation:

for example 2 is less than ten and 2 is a positive even no.

2nd example 12 is also a positive even no. but more than 10

so we can say for 1 to 9 positive no. are less that ten but 11to infeniti is more than ten

If my answer is correct so like me

Answer:

1. First box, the missing fraction = 1/10

2. For the 2nd box

a. The missing fraction = 3/10

b. Percentage = 30%

3. For 7/10

Percentage = 70%

Step-by-step explanation:

From the question given above, the following data were obtained:

The strip is divided into 10 equal parts.

1. For the first box:

The missing fraction = 1/10

2. For the 2nd box

a. The missing fraction = 3/10

b. Percentage = 3/10 × 100 = 30%

3. For 7/10

Percentage = 7/10 × 100 = 70%

Answer:

7

Step-by-step explanation:

9x + 1 = 7x - 9 + 5x - 11

9x + 1 = 12x - 20

9x + 1 - 1 = 12x - 20 - 1

9x = 12x - 21

9x - 12x = 12x - 12x -21

-3x = -21

-3x/3 = -21/-3

x = 7

Hope that helps!

Answer:

Solving gives us the result, x = 2, y = -1

Step-by-step explanation:

The system of equations is,

y = 2x-5

y=-2x+3

equating the two equations, we get,

(since y = y)

\(2x-5 = -2x + 3\\4x -5 = 3\\4x = 3+5\\4x=8\\x=8/4\\x=2\)

and then since y = 2x-5

\(y=2(2)-5\\y=-1\)

so, x =2, y = -1

Answer:

Step-by-step explanation:

The integers are: x, x+2

Them, x + x+ 2 = 36

2x +2 = 36

The round trip distance in miles from city 1 to city 3 is given as follows:

30 miles.

The matrix corresponding to the distances between each of the cities is given by the image presented at the end of the answer.

Looking at row 1, column 3, we have that the distance from city 1 to city 3 is of 15 miles.

For the round trip distance, we have to go back from city 3 to city 1, more 15 miles, hence the distance is given as follows:

2 x 15 = 30 miles.

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Answer:

30

Step-by-step explanation:

you have to look at carefully

Answer: 1 73/90 if the decimal is 1.81 and the one is repeating

If the .81 is repeating then 1 9/11

Step-by-step explanation:

Answer:

20/11

Step-by-step explanation:

let 0.(81) = x

--> 100x = 81.(81)

--> 100x - x = 81.(81) - 0.(81)

--> 99x = 81

--> x = 81/99 = 9/11

1.(81) = 1 + 0.(81) = 1 + x = 1 + 9/11 = 20/11

Answer:

we are going to place 2 at the place where x is

Step-by-step explanation:

5(2)-5

10-5

5 is your answer I believe

Answer:

3:1

Step-by-step explanation:

employees with children studying in grade school=30

employees with no children=10

So ratio of employees who have children studying in grade school to employees with no children =

30

__ =3:1

10

a. Assuming no additional restrictions, there are  800 possible three-digit area codes.

b. Considering ERCs, there are  80 ERCs.

c. For the seven digits after the area code, there are \(8 \times 10^6 = 8,000,000\)  possible seven-digit phone numbers.

d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers is 800 \(\times\) 8,000,000 = 6,400,000,000.

a. For three-digit area codes, the first digit cannot be 0 or 1.

Assuming no additional restrictions, there are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining two digits (0-9). Therefore, the total number of three-digit area codes possible under this plan is \(8 \times 10 \times 10 = 800.\)

b. For an ERC (Easily Recognizable Code), the second and third digits of the area code must be the same, and the first digit cannot be 0 or 1. There are 8 possibilities for the first digit (2-9) and 10 possibilities for the third digit (0-9).

Since the second digit must be the same as the third digit, there is only 1 possibility.

Therefore, the total number of ERCs is \(8 \times 1 \times 10 = 80.\)

c. For the seven digits after the area code, the first digit of the three-digit local prefix cannot be 0 or 1.

There are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining six digits (0-9).

Therefore, the total number of seven-digit phone numbers possible is 8 * \(10\times 10 \times 10 \times 10 \times 10 \times 10 = 8,000,000.\)

d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers can be calculated by multiplying the number of possibilities for each digit position.

For the area code (part a), there are 800 possibilities.

For the seven digits after the area code (part c), there are 8,000,000 possibilities.

Therefore, the total number of ten-digit phone numbers possible is 800 * 8,000,000 = 6,400,000,000.

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Answer:

STo solve for m in the equation -319.45 = m, we can isolate the variable m by adding 319.45 to both sides of the equation:

-319.45 + 319.45 = m + 319.45

This simplifies to:

0 = m + 319.45

Finally, we can subtract 319.45 from both sides to solve for m:

0 - 319.45 = m + 319.45 - 319.45

-319.45 = m

Therefore, the value of m is -319.45.tep-by-step explanation:

The temperature at 8:00 A.M. was 15°C.

Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.

We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C

3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.

Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C

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Answer:

$17,204.28

Step-by-step explanation:

So first of all you want to start by finding what P, r and t would be.

Once I found all of those I put them into the equation (l = Prt) and solved (by putting it into a calculator obviously). That is how I came up with my answer. Check the screenshot provided to see what P, r and t would be and to see all my work! :)

Hope this helps! :)

Have a great day!

Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

The angles are formed by a transversal and two parallel lines in the figure. By applying congruent angles and vertical opposite angle property, ∠1 ≅∠3 ≅ ∠5 ≅ ∠7; ∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8. Therefore option B is correct.

Congruent angles are identical to each other and have the same measure. The angles formed by the transversal in corresponding corners are called corresponding angles and they are congruent.

Therefore, ∠1 ≅ ∠5, ∠3 ≅ ∠7----------(1)

At a vertex if two angles are opposite to each other, then they are vertically opposite angles, they are equal and congruent to each other.

Therefore, ∠1 ≅ ∠3, ∠5 ≅ ∠7----------(2)

Combining (1) and (2), we get:

∠1 ≅∠3 ≅ ∠5 ≅ ∠7
Similarly we can find,

∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8.

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Answer:

Let's denote:

- the amount of money Helen Weller needs to invest in the account that pays 15% interest as x,

- the total amount of money in both accounts as y = $10,000 + x.

According to the problem, the total interest from the two investments should be equal to the interest from a single investment at a 13% rate. This translates to the following equation:

(12% * $10,000) + (15% * x) = 13% * y.

Substituting y = $10,000 + x into the equation gives us:

(12% * $10,000) + (15% * x) = 13% * ($10,000 + x).

Now we can solve this equation to find the value of x.

Let's convert all percentages to decimals (12% = 0.12, 15% = 0.15, 13% = 0.13) and solve for x:

0.12 * $10,000 + 0.15x = 0.13 * ($10,000 + x),

$1,200 + 0.15x = $1,300 + 0.13x,

0.02x = $100,

x = $100 / 0.02,

x = $5,000.

Therefore, Helen Weller needs to invest an additional $5,000 in the account that pays 15% interest to ensure the total interest from both investments is equal to a single investment at a 13% rate.

Answer:

Step-by-step explanatio

The perfect square form the given numbers is 25.

Perfect squares are defined as the number which is the result of the multiplication of another number, likely integers, to itself two times.

For example, 4 = 2 × 2

So 4 is a perfect square of 2.

Here the given numbers are,

20, 21, 24, 25.

We need the perfect squares as the squares of integers.

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

So 25 is a perfect square.

20, 21 and 24 cannot be written as the square of an integer.

Hence the correct number is 25.

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The inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

Inverse of a function can be calculated by following the steps mentioned below -

According to the question, the equation given is as follows

y = f(x) = 2x + 5

y = 2x + 5

Replace 'y' with 'x', we get -

x = 2y + 5

Now, solve for y -

2y = x - 5

y = (x/2) - (5/2)

Replace 'y' with f⁻¹(x) -

f⁻¹(x) = (x/2) - (5/2)

Hence, the inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

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Answer:yes!!

Step-by-step explanation:suprisingly this website gives you the tools to get an answer for anything. People will find ur stuff and give an answer, or sometimes multiple people.

Answer:

Step-by-step explanation:

LM=2x+24

MN= x+28

LN=31

LN=(2x+24)+(x+28)

31=(2x+24)+(x+28)

solve

31=(2x+24)+(x+28)

31-24-28 = 2x +x

-21=3x

-7=x