For each figure below, determine if it has rotational symmetry.
If it does, give the smallest angle of rotation needed for the figure to appear unmoved.

Answer:

b

Step-by-step explanation:

Answer:

Keme lang bhie33

Step-by-step explanation:

The value of variables are,

1) h = - 3

2) r = 2

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We know that;

Diagonals of a parallelogram are equal to each other.

In figure 1;

We can formulate;

⇒ 2h + 2 = 2h + (h + 5)

⇒ 2h + 2 = 2h + h + 5

⇒ 2h + 2 = 3h + 5

⇒ 2 - 5 = 3h - 2h

⇒ - 3 = h

⇒ h = - 3

In figure 2;

We can formulate;

⇒ 5r + 5r = (5r - 2) + (4r + 4)

⇒ 10r = 5r - 2 + 4r + 4

⇒ 10r = 9r + 2

⇒ 10r - 9r =  2

⇒ r =  2

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The factors of the expression x² - x - 12 are 4 and -3.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

x² - x - 12

Using middle-term factorization.

x² - (4 - 3)x - 12

x² - 4x + 3x - 12

x(x - 4) + 3(x - 4)

(x - 4) (x + 3)

x - 4 = 0

x = 4

x + 3 = 0

x = -3

Thus,

The factors are 4 and -3.

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The simplified sum of the second and fourth integers is 2x + 4.

What is the whole number?

Whole numbers are numbers without fractions and it is a collection of positive integers and zeros. It is represented by the symbol “W” and the set of numbers is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,……………}.

Integers are whole numbers, and consecutive integers are whole numbers that are next to each other with a space of "1" between them,

i.e. 1, 2, 3, 4... or -2, 1, 0, 1...

Thus, if the first integer is "x" and the next is "x+1" then "x+2" and "x+3."

The sum = x+x+1+x+2+x+3 = 4x+6.

The sum of the second and fourth integers is:

= x+1 + x+3

= 2x + 4

Hence, the simplified sum of the second and fourth integers is 2x + 4.

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The value of the variable 'x' will be 60°. Then the correct option is B.

If the quadrilateral is inscribed in a circle then the quadrilateral is known as a cyclic quadrilateral. And the sum of opposite angles of the quadrilateral is 180 degrees.

In the diagram below, P is circumscribed about quadrilateral ABCD. Then the equation is given as,

x + 120° = 180°

Simplify the equation, then we have

x + 120° = 180°

x = 180° - 120°

x = 60°

The value of the variable 'x' will be 60°. Then the correct option is B.

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The given trigonometrical equation is solved and proved below.

In mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Given is a trigonometrical expression as -

tan(y) + cot (y)

The given expression is -

tan (y) + cot (y)

tan (y) + cot (y) = {sin(y) / cos(y) + cos(y) / sin(y)}

tan (y) + cot (y) = {sin²(y) + cos²(y)} / {sin(y) cos(y)}

tan (y) + cot (y) = 1 / {sin(y) cos(y)}

tan (y) + cot (y) = {1/sin(y) . 1/cos(y)}

tan (y) + cot (y) = cosec(y) sec(y)

L.H.S = R.H.S

Therefore, the given trigonometrical equation is solved and proved above.

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Rhyming scheme of "It rains, and the wind is never weary" is AABBA. Option (b) is correct.

A scheme is a well-organized plan for carrying out an action, particularly one that is dishonest or unlawful but will benefit you.

He paints his feelings and the storm raging around him as dark and gloomy in the poem's opening lines. The weather/depression cannot be avoided. He displays a yearning for the past, his youth, and possibly the dreams he had at that time.

He addresses his heart directly in the final verse, imploring it to calm down and accept what is happening. There will always be days when things seem more hopeless; that is just a fact of life.

Therefore, These quintains use the straightforward rhyme system AABBA, switching up the end sounds from stanza to stanza. Rain falls, but the wind never stops.

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The sampling distribution of the mean fuel efficiency will be approximately normal as the sample size is large.

The Central Limit Theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normal, regardless of the shape of the distribution of the population from which the sample is drawn.

In this case, you are taking a sample of 100 cars from a population with a mean fuel efficiency of 30 mpg and a standard deviation of 4 mpg. Since the sample size is sufficiently large, the sampling distribution of the mean fuel efficiency will be approximately normal.

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Answer:

To describe the shape of a cubic function, we need to consider its end behavior, any turning points it has, and any intervals over which it is increasing or decreasing.

For the cubic function 32. y = 3x³ - x - 3, the leading coefficient is 3, which means that the end behavior of the function will be determined by the sign of the term x³. Since the coefficient of x³ is positive, the function will approach positive infinity as x approaches positive infinity and negative infinity as x approaches negative infinity. This means that the graph of the function will curve upwards at both ends.

To find the turning points of the function, we can find the zeros (or roots) of the function. In this case, we can solve the equation 3x³ - x - 3 = 0 using the cubic formula or a numerical method. This will give us three real roots, which correspond to the x-values of the turning points of the function. The function will be concave upwards at the points between these roots and concave downwards at the points between the roots and the ends of the graph.

The function will be increasing on the intervals between the roots where the function is concave upwards and decreasing on the intervals between the roots where the function is concave downwards.

For the cubic function 33. y = -9x³ - 2x² + 5x + 3, the leading coefficient is -9, which means that the end behavior of the function will be determined by the sign of the term -9x³. Since the coefficient of x³ is negative, the function will approach negative infinity as x approaches positive infinity and positive infinity as x approaches negative infinity. This means that the graph of the function will curve downwards at both ends.

As with the previous function, we can find the zeros (or roots) of the function by solving the equation -9x³ - 2x² + 5x + 3 = 0 using the cubic formula or a numerical method. This will give us three real roots, which correspond to the x-values of the turning points of the function. The function will be concave upwards at the points between these roots and concave downwards at the points between the roots and the ends of the graph.

The function will be decreasing on the intervals between the roots where the function is concave upwards and increasing on the intervals between the roots where the function is concave downwards.

Step-by-step explanation:

the area is simply the product of its width and length, so hmmm before doing so, let's change all the mixed fractions to improper fractions and then multiply.

[tex]\stackrel{mixed}{4\frac{1}{5}}\implies \cfrac{4\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{21}{5}} ~\hfill \stackrel{mixed}{4\frac{2}{7}} \implies \cfrac{4\cdot 7+2}{7} \implies \stackrel{improper}{\cfrac{30}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{21}{5}\cdot \cfrac{30}{7}\implies \cfrac{21}{7}\cdot \cfrac{30}{5}\implies \cfrac{3}{1}\cdot \cfrac{6}{1}\implies \text{\LARGE 18}~in^2[/tex]

The area of the rectangle is 18 [tex]inch^{2}[/tex] and the perimeter is  [tex]16\frac{34}{35}[/tex] inches.

We know that, Area of a rectangle = l * b

        and Perimeter of a rectangle = 2(l + b)

 Where, l = length of the rectangle

             b = breadth of the rectangle

According to the question, l = [tex]4\frac{1}{5}[/tex] inch = [tex]\frac{21}{5}[/tex] inch

                                             b = [tex]4\frac{2}{7}[/tex] inch = [tex]\frac{30}{7}[/tex] inch    

Area of the given rectangle = l* b

                                              =   [tex]\frac{21}{5}[/tex] * [tex]\frac{30}{7}[/tex]

                                              = 18 [tex]inch^{2}[/tex]

The perimeter of the given rectangle = 2(l + b)

                                                              = 2( [tex]\frac{21}{5}[/tex] + [tex]\frac{30}{7}[/tex])

                                                              = 2 ([tex]\frac{297}{35}[/tex])

                                                              = [tex]\frac{594}{35}[/tex]

                                                              = [tex]16\frac{34}{35}[/tex] inch

Hence, the area of the rectangle = 18 [tex]inch^{2}[/tex]

and the perimeter =  [tex]16\frac{34}{35}[/tex] inch

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Check the picture below.

Answer:

THE ANSWER IS C

Step-by-step explanation: BECAUSE IT IS I

A proposition exists in this statement. Until we know if Jennifer will be late for the party and whether her cousin Zachary would become irate if she is, we cannot determine its true value. The right answer is C.

a. Because it is not a declarative sentence that can be either true or incorrect, this statement cannot be considered a proposition. Instead of expressing reality, it reflects hope or desire.

b. False. Fifteen is an odd number, not an even number.

c. A proposition exists in this statement. Unless we know if Jennifer will be late to the party and whether her cousin Zachary would become irate if she is, we cannot determine its veracity.

d. False. Chris Evert didn't win the French Open seven times on June 30, 1986; he only did so five times.

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Answer: 36.902 Seconds

Step-by-step explanation:

(1) --> To find the time that the rocket is at a height of more than 100 feet, you need to find the time when the height of the rocket is equal to 100 feet.

(2) --> do this by setting your equation equal to 100

[tex](-\frac{1}{2} )t^2 + 15t = 100[/tex]

[tex](-\frac{1}{2}) t^2 + 15t - 100 = 0[/tex]

(3) --> From here, use the quadratic formula to solve for t

Quadratic formula:

[tex]t = - \frac{-b+-\sqrt{b^2 - 4ac} }{2a}[/tex] (solving the b+ first)

[tex]t = \frac{(-15 + \sqrt{225 - 4(-\frac{1}{2}) (-100)}}{-1}[/tex]

[tex]= \frac{(-15 + \sqrt{475})}{-1}[/tex]

[tex]= \frac{(-15 + 21.902)}{-1}[/tex]

[tex]= \frac{6.902}{-1}[/tex]

[tex]= -6.902[/tex]

(solving b-)

[tex]t = \frac{-15 - \sqrt{475}}{-1}[/tex]

[tex]= \frac{-15-21.902}{-1}[/tex]

[tex]= \frac{-36.902}{-1}[/tex]

[tex]= 36.902[/tex]

HENCE: The first solution, -6.902, is not a valid time because it is negative. The second solution, 36.902, is the time when the rocket is at a height of 100 feet. Since the rocket is at a height of more than 100 feet for the entire time after it reaches a height of 100 feet, the rocket will be at a height of more than 100 feet for 36.902 seconds.

The value of angle m∠F is  42°.

What are the Exterior angle properties of triangle?

If in a triangle any side is extended, the outside angle or exterior angle formed results is equal to the sum of the two opposite internal angles.

Here we are given a triangle ΔGHF

m∠F = ∠HFG = 4x + 6

∠G = ∠FGH = 70°

and exterior angle ∠GHJ = -5 + 13x

Here side FH of ΔGFH is extended .

so by using exterior property of triangle i.e,

Exterior angle = sum of opposite interior angles.

∠GHJ =∠FGH + ∠GFH

-5 + 13x = 70 + (4x + 6)

13x - 4x = 70 + 6 + 5

9x = 81

x = 81/9

x = 9.

Therefore m∠F = ∠GFH = (4x+6)

m∠F = 4×9+6

m∠F = 42°

So we got the value of angle m∠F is  42°.

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Answer: B. 80%

Step-by-step explanation:

P(not green) means that Joseph will pick a marble that is either red, yellow, or purple.

First, we must find the total number of marbles by adding every marble of every color: 2 + 6 + 15 +7 = 30

Now, we need to find the total of marbles that are not green: 2 + 15 + 7 = 24

Now, to solve, we set up this fraction: not green/total marbles = 24/30 = 0.8

0.8 is equivalent to 80% when in percent form. Hope this helps!

Answer: B. 80%  

hope this helped :)

Answer:

The answer is a)2  and b)93

Step-by-step explanation:

we know that, x=3 and y=5

now, as per the question,

a) 4x-2y

=4(3)-2(5)

=12-10

=2

b) 2x^+3y^

=2(3)^+3(5)^

=2*9+3*25

=18+75

=93

therefore, a)2 and b)93

A corporation pays dividends to its stockholders in order to distribute profits to them.

A dividend, which is typically derived from the company's net profits, is a compensation given to shareholders for their investment in the equity of a company. In the United States, cash dividends—cash payments made to investors on a per-share basis—make up the majority of dividends.

For instance, if a business distributes a dividend at the rate of 20 cents per share, an investor holding 100 shares would get $20 in cash. An increase in the number of shares owned is a percentage of a stock dividend.

A dividend that is given to shareholders in the form of extra company shares is known as a stock dividend. Until the shares are sold by the owner, stock dividends are not subject to tax. Due to the issuance of additional shares, stock dividends, like stock splits, cause a decrease in the share price.

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2r+r+s+2s =2×r + r×1 + s×1 + 2×s

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, given that,

2r+r+s+2s

=2×r + r×1 + s×1 + 2×s

Hence,

each sum as the product of two factors 2r+r+s+2s =2×r + r×1 + s×1 + 2×s

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The value of g(1/2) for function g(x) = 5x² - 4x +3 will be 9/4.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

As given,

g(x) = 5x² - 4x +3

g(1/2)=5*1/2^2-4*1/2+3

=5/4-2+3

=5/4+1

g(1/2)=9/4

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Answer:

[tex] \frac{2x( \sqrt[4]{y}^{2}) }{3} [/tex]

Step-by-step explanation:

⁴√[(16x ^ 11 * y ^ 8)/(81x ^ 7 * y ^ 6)]=

=⁴√[(16x ^ 4 * y ^ 2)/81]=

=⁴√{[(4x ^ 2 * y)/9] ^ 2}=

=√[(4x ^ 2 * y)/9)]=

=[√(4x ^ 2 * y)]/3=

=(2x⁴√y²)/3

An equivalent expression for the given expression is 2x[tex]\sqrt[4]{y^2}[/tex]/3. Therefore, option B is the correct answer.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is [tex]\sqrt[4]{\frac{16x^{11}y^8}{81x^7y^6} }[/tex]

Here, [tex]\sqrt[4]{\frac{2^4x^{11}y^8}{3^4x^7y^6} }[/tex]

= [tex]\sqrt[4]{\frac{2^4x^{4}y^2}{3^4} }[/tex]

= 2x[tex]\sqrt[4]{y^2}[/tex]/3

Therefore, option B is the correct answer.

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The limit lim x → 0 (3x²/(1 - cos²(x/2)) = 0

A limit is the value of a function as the independent variable tends to a particular value.

Given the limit lim x → 0 (3x²/(1 - cos²(x/2))

We desire to evaluate the limit.

To evaluate the limit, we proceed as follows.

Since  lim x → 0 (3x²/(1 - cos²(x/2)), substituting x = 0 into the equation, we have that

lim x → 0 (3x²/(1 - cos²(x/2)) = (3(0)²/(1 - cos²(0/2))

= (3(0)/(1 - cos²(0)),

= ((0)/(1 - (cos(0)²))

= 0/(1 - 1)

= 0/∞

So, using l'hopital's rule which states that lim x → a f(x)/g(x) =  lim x → a f'(x)/g'(x)

So, lim x → 0 (3x²/(1 - cos²(x/2)) = lim x → 0 (d3x²/dx/d(1 - cos²(x/2))/dx,

= lim x → 0 2x/2cos(x/2)sin(x/2)

=  lim x → 0 2x/sinx

= 2(0)/sin0

= 0/0

Using l'hopital's rule again, we have that

lim x → 0 2x/sinx = lim x → 0 d2x/dx/dsinx/dx

= lim x → 0 2/cosx

= 2/cos(0)

= 2/1

= 2

So, we have that the limit lim x → 0 (3x²/(1 - cos²(x/2)) = 2

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The value of x is 16

A modulus function gives the magnitude of a number irrespective of its sign. It is also called the absolute value function. In mathematics, the modulus of a real number x is given by the modulus function, denoted by |x|. It gives the non-negative value of x. The modulus or absolute value of a number is also considered as the distance of the number from the origin or zero.

Given here, the equation x=|-16| but we know that modulus function only measures the magnitude therefore x cannot be negative thus x=16

Hence, The value of x is 16

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Answer: The sum that is equivalent to 3/5 + 1/6 is 18/30 + 5/30.

Step-by-step explanation:

This is because both 18/30 and 5/30 can be simplified to 3/5 and 1/6 respectively.

18/30 can be simplified by dividing both numerator and denominator by 6, which results in 3/5.

5/30 can be simplified by dividing both numerator and denominator by 5, which results in 1/6.

So 18/30 + 5/30 = 3/5 + 1/6.

The other options are not equivalent, 6/10 + 2/10 is equivalent to 4/5, 12/30 + 5/30 is equivalent to 17/30 and 3/11+4/11 is equivalent to 7/11

Answer:

c

Step-by-step explanation:

Choosing a sample from a population with some biasing would not represent the population well.

The entire group about whom you want to make conclusions is referred to as a population. The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole.

There are four types of sampling in statistics they are,

Simple random sampling, stratified sampling, cluster sampling, and systematic sampling are all types of probability sampling.

A random sample is such that the probability of choosing each sample is the same.

When we choose a sample biasedly then that sample might not represent the population sample well.

For example, choosing a sample from a population of trees for checking damages.

If we choose all the trees near to the side of the road it can happen that the trees just beside the road are more damaged.

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Answer:

10 hours

Step-by-step explanation:

7(y) + 5(x)=125

7(y) + 5(11) = 125

7(y) + 55=125

-55. -55

7(y)= 70

7/7 = 70/7

Y=10

The composite functions when solved accordingly gives us;

(f ° g)(x) = 75x³ + 140x²+ 87x + 18

(f ÷ g)(x) =  3x + 2

Composite functions are formed when the output of one function is used as the input of another.

Now, we are given the functions as;

f(x) = 15x² + 19x + 6

g(x) = 5x + 3

Let us factorize f(x) to get;

f(x) = 15x² + 19x + 6 = (5x + 3)(3x + 2)

(f ° g)(x) simply means; f[g(x)]

Thus, we have;

f.g(x) = (15x² + 19x + 6)(5x + 3)

f.g(x) = 75x³ + 95x² + 30x + 45x² + 57x + 18

f.g(x) = 75x³ + 95x² + 45x²+ 30x + 57x + 18

f.g(x) = 75x³ + 140x²+ 87x + 18

(f ÷ g)(x) = ((5x + 3)(3x + 2))/(5x + 3)

(f ÷ g)(x) =  3x + 2

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Answer:

im pretty sure 17

Step-by-step explanation: suhkmjnk