show that the value of cos30 degrees x tan60 degrees + sin30 degrees is an integer

Answer:

Step-by-step explanation: 2x+12x = 14x

14x=70

70/14 = 5

x = 5

Answer: x=29

Step-by-step explanation:

12=70-2x

12=-2x+70

Subtract 70 from both sides: 12-70=-2+70-70

-58=-2x

Divide both sides by the same factor: -58/-2=-2x/-2

x=29

Answer:   68.5

Step-by-step explanation:

6 cm + 6 cm + 18 cm+ 9.5cm + 3cm + 11cm+ 9cm+ 6cm= 68.5

~Hope this helps ;0~

The slower stone will take 3.33 seconds if the faster stone takes 10s to return to the ground.

It is defined as the rate of change in linear velocity with respect to time. It is also known as linear acceleration.

From the motion equation:

s = ut + at²/2

From the data given:

s = 0

0 = 3u(10) - 9.8(10)²/2

After solving:

u = 16.33 m/s

To calculate for time:

s = ut + at²/2

s = 0

u = 16.33

0 = 16.33t + 9.8t²/2

t = 3.33 seconds

Thus, the slower stone will take 3.33 seconds if the faster stone takes 10s to return to the ground.

The complete question is:

Two stones are thrown vertically upward from the ground, one with three times the initial speed of the other.

(a) If the faster stone takes 10s to return to the ground, how long will it take the slower stone to return?

Learn more about linear acceleration here:

https://brainly.com/question/13723307

#SPJ4

The ladder reaches 24 feet high on the building.

The given parameters are:

Length of ladder (l) = 30 feet

Base of the ladder (b) = 18 feet

The height (h) of the ladder on the wall of the building is calculated as

h^2 =l^2 - b^2

This gives

h^2 = 30^2- 18^2

Evaluate

h^2 = 576

Take the square rots

h = 24

Hence, the ladder reaches 24 feet high on the building.

Read more about Pythagoras theorem at

https://brainly.com/question/2437195

#SPJ1

The expression that iis equivalent to 8x³ − 64 when factored completely will be A. (2x − 4)(4x² + 8x + 16)

It should be noted that (2x − 4)(4x² + 8x + 16) will be:

= (2x − 4)(4x² + 8x + 16)

= 8x³ + 16x² + 32x - 16x² - 32x - 64

= 8x³ - 64

Therefore, the correct option is A.

Learn more about expressions on:

brainly.com/question/25968875

#SPJ1

Answer: (-235, -5.8)

Step-by-step explanation:

elimination

∠AHF is the exterior angle to the triangle GHI, so m∠AHF = 116°.

What is exterior angle?

When one side of a triangle is stretched, an external angle is generated. An external angle of a triangle is a non-straight angle (one that is not merely an extension of a side) that is outside the triangle but next to an interior angle.

From figure, m∠CIH = 105° (given)

so, m∠GIH = (180° - m∠CIH) = (180° - 105°) = 75° (complementary angles)

And m∠BGD = 41°

So, m∠IGH = M∠BGD = 41° (vertically opposite angles)

Now, m∠AHF = m∠GIH + m∠IGH (exterior angle)

                       = 75° + 41°

                       = 116°

To learn more about exterior angles, click on the link

https://brainly.com/question/28029291

#SPJ1

Answer:

x = 3

Step-by-step explanation:

2(4 + 3x) + 6 = 32 ( subtract 6 from both sides )

2(4 + 3x) = 26 ( divide both sides by 2 )

4 + 3x = 13 ( subtract 4 from both sides )

3x = 9 ( divide both sides by 3 )

x = 3

As a check

substitute x = 3 into the left side of the equation and if value obtained is equal to the right side (32) then it is a solution to the equation.

2(4 + 3(3)) + 6

= 2(4 + 9) + 6

= 2(13) + 6

= 26 + 6

= 32

left side = right side

then x = 3 is the solution to the equation

Answer:

[tex] \sf \: x = 3[/tex]

Step-by-step explanation:

[tex] \sf \rightarrow \: 2(4 + 3x) + 6 = 32[/tex]

Apply the distributive property

[tex] \sf \rightarrow8 + 6x + 6 = 32[/tex]

Combine like terms

[tex] \sf \rightarrow 14 + 6x = 32[/tex]

Rearrange variables to the left side of the equation

[tex] \sf \rightarrow 6x = 32 - 14[/tex]

Calculate

[tex] \sf \rightarrow 6x = 18[/tex]

Divide both sides by the coefficient of 6

[tex] \sf \rightarrow \frac{6x}{6} = \frac{18}{6} [/tex]

Calculate

[tex] \sf \rightarrow x = \frac{18}{6} [/tex]

[tex] \sf \rightarrow \: x = 3[/tex]

∠6 = 43°

If two angles sum to 90 degrees, they are said to be complementary angles. In other terms, a right angle is created when two complementary angles are combined (90 degrees). Angles 1 and 2 are complementary if their total of angles equals 90 degrees (i.e., ∠1 + ∠2 = 90°), and as a result, they are referred to as each other's complements.

Now as per the question the given angle is

∠8 = 47°

It is also given that ∠6 and ∠8 form are complementary angles. Therefore it means that the sum of both the angles will be 90°

∠6 + 47° = 90°

Now subtracting 47 from both sides we will get :

∠6 = 90 - 47 = 43°

Therefore, ∠6 = 43°

To know more about complementary angles, refer to this link :

https://brainly.com/question/15592900?referrer=searchResults

The output value of f(11) in the given function f(x) = ( x − 2 )2 + 15 is 33

Given the data in the question;

To determine the output value of f(11), replace all the occurrence of x with 11 in the function.

f(x) = ( x − 2 )2 + 15

f(11) = (11−2)2 + 15

f(11) = (9)2 + 15

Remove the parenthesis

f(11) = 9×2 + 15

f(11) = 18 + 15

f(11) = 33

Therefore, the output value of f(11) in the given function f(x) = ( x − 2 )2 + 15 is 33.

Learn more about composite function here: https://brainly.com/question/20379727

#SPJ1

Answer:

s = 3 cm

Step-by-step explanation:

the volume (V) of a cube is calculated as

V = s³ ( s is the side length )

here V = 27 cm³ , then

s³ = 27 ( take cube root of both sides )

[tex]\sqrt[3]{s^3}[/tex] = [tex]\sqrt[3]{27}[/tex]

s = 3

the length of each edge of the cube is 3 cm

The value of x when y=3 is x=-3.

y ∝ x

y=kx

where k is the constant of proportionality.

put x=-2, y=2

2=k*-2

k=-1

now it's given that y=3 putting in the equation

y=kx

3=-1*x

x=-3

The value of x when y=3 is x=-3.

For more information on the proportionality constant click on the link below:

https://brainly.com/question/24868934

#SPJ4

The probability that a car is red is 1/3

The given parameters are

P(Car has two doors, given that it is red) = 0.6

P(car has two doors and is red) = 0.2

The probability that a car is red is

P(Red) = P(car has two doors and is red)/P(Car has two doors, given that it is red)

This gives

p(Red) = 0.2/0.6

Evaluate

p(Red) = 1/3

Hence, the probability that a car is red is 1/3

Read more about probability at

https://brainly.com/question/24756209

#SPJ1

Answer:

Step-by-step explanation:

ur dad

Answer:

Step-by-step explanation:

The answer is I.D.K

The first term of the geometric sequence is a(1) = 7.

The nth term of a geometric sequence is given by:

a(n) = a(1) . rⁿ⁻¹

Where:

a(1) = the first term

r = ratio

Parameter given in the problem:

a(5) = 112

Plug n = 5 into the formula

a(1) . r⁵⁻¹ = 112

a(1) . r⁴ = 112    ....... (1)

a(7) = 448

Plug n = 7 into the formula

a(7) = a(1) . r⁶

448 = a(1) . r⁶  ..... (2)

Divide (2) by (1)

448 : 112 = r⁶ : r⁴

4 = r²

Since  r² = 4, then r⁴ = ( r² )² = 4² = 16.

Substitute r⁴ = 16 into equation (1):

a(1) . 16 = 112

a(1) = 112/16 = 7

Learn further on geometric sequence here:

https://brainly.com/question/1509142

#SPJ4

The digits in millions period of the number is 468 as the digit 8 is in the ones million place, 6 is in the tens million place and 4 is in the hundred millions place.

Given the number is 21,468,127,471.

The digits in which are given in the large numbers are in groups of three places. The groups are called periods. Commas are usually used to separate the periods.

The groups of numbers are 3 digit group and which is starting from the right to left.

As we all know that we read the group of periods as ones, tens, hundreds, thousand, ten thousand, hundred thousand, million, ten million, hundred million, billion etc.

From  the above, we find that the given number 21,468,127,471 contains digit 1 is in the ones place, 7 is in the tens place, 4 is in the hundredth place, 7 is in the thousand place, 2 is in the ten thousand place, 1 is in the hundred thousand place, 8 is in the million place, 6 is in the ten million place, 4 is in the hundred million place , 1 is the billion place and 2 is in the ten bilion.

Hence, the digits in millions period of the given number 21,468,127,471 is 468 as the digit 8 is in the ones million place, 6 is in the tens million place and 4 is in the hundred millions place.

Learn more about millions from here brainly.com/question/17806392

#SPJ9

Answer: Maybe D I'm not sure

Step-by-step explanation:

The triangles are congruent by the SAS theorem not the HL Theorem

The statement is given as

Yama stated that △KLM≅△PLN by the HL Theorem

From the figure, we can conclude that the triangles are truly congruent

This is evident by the marks on the corresponding angle and the corresponding sides of the triangles

From the figure, we have

1 corresponding angle

2 corresponding sides

This means that the triangles are congruent by the SAS theorem not the HL Theorem

Hence, the triangles are congruent by the SAS theorem not the HL Theorem

Read more about congruent triangles at

https://brainly.com/question/1675117

#SPJ1

Using the Fundamental Counting Theorem, the number of pairs are given as follows:

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For matching pairs, we have that:

Hence the number of pairs is:

N = 2 x 20 x 19 = 760.

For the non-matching pair, we have that there are 20 red and 20 blue to choose, hence the number of pairs is:

N = 20 x 20 = 400.

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866

#SPJ1

Answer:

2x6x6+7+j

34+67897790+b,xyy

1. The sequence will be 13 + 2( n - 1).

2. The sequence will be 22 + 6(n - 1).

1. It should be noted that the common difference is 15 - 13 = 2

First term = 13

Therefore, the sequence will be:

= a + (n - 1)d.

a = first term

d = difference

n = numbers

= 13 + 2( n - 1).

2. Common difference = 28 - 22 = 6

First term = 22

The sequence will be:

a + (n - 1)d

= 22 + 6(n - 1)

Learn more about expressions on:

brainly.com/question/22048677

#SPJ1

Answer:

I think it is 23.333

Step-by-step explanation:

I added 16 to both sizes and got 3x=70

then divide 70 by 3 and got 23.333

The missing term of the GP is: 1530.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: 9180, ___, 255.

To find: the missing term of the geometric sequence.

Finding:

The geometric mean of a geometric sequence is used to find the term between two term of a geometric sequence.

Thus, Let the missing term by x.

Then, x = [tex]\sqrt{9180\times255} = \sqrt{2340900}=1530.[/tex]

Hence, the missing term of the geometric sequence is 1530,

To learn more about geometric progression, refer to the link: https://brainly.com/question/15978376

#SPJ4

Answer:

x=4

Step-by-step explanation:

This line has an undefined slope since it goes straight up

The line falls on the x coordinate 4

A function is defined as a relation between a set of inputs having one output each.

The inputs are called the domain and the outputs are called the range.

The range for the function f(x) = |x| + 3 is {y | 3 ≤ y < ∞}.

A function is defined as a relation between a set of inputs having one output each.

The inputs are called the domain and the outputs are called the range.

We have,

f(x) = |x| + 3

We need to find the range of f(x).

We can have x values of any real numbers.

For x = 0,

f(0) = 0 + 3 = 3

For x = 1,

f(1) = 1 + 3 = 4

For x = 2,

f(2) = 2 + 3 = 5

For x = 3

f(-3) = |-3| + 3 = 6

For x = -1,

f(-1) = |-1| + 3 = 1 + 3 = 4

For x = -2,

f(-2) = |-2| + 3 = 2 + 3 = 5

For x = -3,

f(-3) = |-3| + 3 = 3 + 3 = 6

We see that,

If we take x = 0, 1, 2, 3, 4, .... the f(x) values increases from 3, 4, 5, 6 and so on.

If we take x = 0 , -1, -2, -3, ..... the f(x) values increases from 3, 4, 5, 6 and so on.

This means that f(x) values are from 3 to infinity for x ∈ R

[ R = real numbers ]

Thus the range for the function f(x) = |x| + 3 is {y | 3 ≤ y < ∞}.

Learn more about functions here:

https://brainly.com/question/17440903

#SPJ2

Answer:

Step-by-step explanation: i think C is the answer

Answer:

36 degrees

Step-by-step explanation:

this a complementary angle. This means that both sides add up to 90 degrees. 90-54=36

Answer:

36°

Step-by-step explanation:

These angles are complimentary, meaning they add to 90°. You know this by the little square marking.

a + 54° = 90°

a = 36°