Find the value of z.

Answer:

51.7661748226 degrees; 38.2338251774 degrees

Step-by-step explanation:

First, draw a diagram to illustrate this situation. Looking at angle A, Eric's height, 1.65 m, corresponds to OPPOSITE, and Eric's shadow, 1.30 m, corresponds to ADJACENT. Using SOH CAH TOA, the equation is:

tan(A) = 1.65/1.30

A = arctan(1.65/1.30)

A = 51.7661748226 deg

Looking at angle B, 1.65 m is ADJACENT and 1.30 m is OPPOSITE. Therefore, the equation is:

tan(B) = 1.30/1.65

B = arctan(1.30/1.65)

B = 38.2338251774 deg

The probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit is 25/52.

In the question, we are informed that a card is drawn at random from a standard 52-card deck.

We are asked the probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit.

We assume the event of drawing an odd card from the random pick to be A, and the event of drawing a card of spade suit to be B.

The number of outcomes favorable to event A = 16 {4 odd cards of each of the 4 suits, that is, 4*4 = 16}.

The total number of possible outcomes = 52 {The number of cards in the deck}.

Therefore, the probability of event A, P(A) = 16/52.

The number of outcomes favorable to event B = 13 {The 13 cards of spade suit}.

The total number of possible outcomes = 52 {The number of cards in the deck}.

Therefore, the probability of event B, P(B) = 13/52.

The number of outcomes favorable to events A and B both = 4 {4 odd cards of the spade suit}.

The total number of possible outcomes = 52 {The number of cards in the deck}.

Therefore, the probability of events A and B both, P(A ∩ B) = 4/52.

The probability that the randomly drawn card is an odd number or of spade suit is represented by P(A ∪ B), which is calculated by the formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 16/52 + 13/52 - 4/52 = 25/52.

Hence, the probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit is 25/52.

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Answer:

26

Step-by-step explanation:

Let's call the original two digit number xy, where x is the tens digit and y is the ones digit. An algebraic representation of this number is 10x + y.

The sum of the two digit number is 8: x+y=8

When the digits are reversed, the number increases by 36: (10y + x) - (10x + y) = 36

Now we have two equations and two unknown parameters, so we have enough information to find those parameters.

Solve for x:

X=8-y

plug in x:

(10y + 8-y) - (10(8-y)+ y) = 36

simplify:

(9y + 8) - (80-9y) = 36

18y - 72 = 36

y = 108/18 = 6

so if y=6, then x=8-y=8-6=2

so our number is 26. 62 is 36 greater than 26.

Answer:

75 / 192

Step-by-step explanation:

When it comes to multiplying fractions, you just multiply them straightforward. Multiply the numerator with the numerator, and the denominator with the denominator

Answer:

maximum 4 Mimimum I'm 0 or maximum 10 minimum 0

The quadratic equation u² - u - 6 = 0 where u = (x -4) is equivalent to (x-4)² – (x − 4) − 6 = 0 option (D) is correct.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a quadratic equation:

(x-4)² – (x − 4) − 6 = 0

Let (x - 4) = u

u² - u - 6 = 0

Thus, the quadratic equation u² - u - 6 = 0 where u = (x -4) is equivalent to (x-4)² – (x − 4) − 6 = 0 option (D) is correct.

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Answer:Option D on edge 2022

Step-by-step explanation:

The graphs of the transformations in each case are as follows;

a) f(x) = 5 -2 = 3

b) f(x) = 5

c) f(x) = 5

d) f(x) = 5+3 = 8.

The shifts, reflections, rotations and dilation operations are facilitated by transformation operations. On this note, it therefore follows that the graph of the given function as given is a straight horizontal line which is parallel to the x-axis and consequently, the transformations are as given above.

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Answer:

$9.92 (rounded off to nearest cent)

Step-by-step explanation:

Square of 7-inch radius pizza = [tex]7^{2}[/tex] = 49 inches

49 Inches = $6

Square of 9-inch radius pizza = [tex]9^{2}[/tex] = 81 inches

Given 49 Inches = $6

1 inch =$ [tex]$(\frac{6}{49} \\)[/tex]

I will leave it as a fraction as it is not the final answer, rounding it off will result in a loss of accuracy.

81 Inches = [tex]81* \frac{6}{49} \\[/tex]

= $9.92 (rounded off to nearest cent)

Answer:

Angle C = 68.7°

Step-by-step explanation:

The largest angle es angle C ([tex]\beta[/tex])

[tex]26^{2} =22^{2} +24^{2} -2(22)(24)cos\beta[/tex]

[tex]676=484+576-1056cos\beta[/tex]

[tex]676-1060=-1056cos\beta[/tex]

[tex]\frac{-384}{-1056} =cos\beta[/tex]

[tex]\beta =cos^{-1} (\frac{-384}{-1056} )=cos^{-1} (.36363)=68.676=68.7^{o}[/tex]

The Big O notation of the composite function 5N^3 O(N^2) is c. O(N^3).

A composite function of two capabilities combines the given two functions inside the given order. i.e., for any given functions f(x) and g(x), there may be four composite functions: f(g(x)) that is substituting g(x) into f(x) g(f(x)) that's substituting f(x) into g(x).

A composite characteristic is a function that relies upon any other feature. A composite characteristic is created while one characteristic is substituted for another feature. For instance, f(g(x)) is the composite function that is fashioned whilst g(x) is substituted for x in f(x). f(g(x)) is studied as “f of g of x”.

In Maths, the composition of a character is an operation wherein two capabilities say f and g generate a brand new feature say h in one of these manners that h(x) = g(f(x)). It method right here feature g is implemented to the function of x. So, basically, a feature is carried out to the result of every other feature.

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The answer to this question is A

The value of k are -5 and -7 if the distance between points (2,k) and (0,−6) is √5

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The question is:

Given the points (2,k) and (0,−6), for which values of k would the distance between the points be √5

[tex]\rm \sqrt{5}=\sqrt{(0-2)^2+(-6-k)^2}[/tex]

5 = 4 + (6 + k)²

After solving:

[tex]\rm 4+\left(6+k\right)^2-4=5-4[/tex]

(6 + k)² = 1

k = -5 or -7

Thus, the value of k are -5 and -7 if the distance between points (2,k) and (0,−6) is √5

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Answer:A.47.5 miles is 76

Step-by-step explanation:

in real life its like 76.44, but im rounding

The inequality that correctly represents this scenario is given as follows:

[tex]2x + 5y \leq 25[/tex]

The graph is given at the end of the question.

A system of inequalities is when two or more variables are related, and inequalities are built to find the values of each variable.

In this problem, the variables are given as follows:

Chocolate chips are $2 per pound and pecans are $5 per pound. She wants to spend at most $25, hence:

[tex]2x + 5y \leq 25[/tex]

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Answer:

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The simplified expressions are 2^-2 and 60^6

Expression (a)

We have:

2^3 * 2^-5

Apply the product law of indices

2^3 * 2^-5 = 2^(3 - 5)

Evaluate the difference

2^3 * 2^-5 = 2^-2

Expression (b)

We have:

(60^2)^3

Apply the power law of indices

(60^2)^3 = 60^(2 * 3)

Evaluate the product

(60^2)^3 = 60^6

Hence, the simplified expressions are 2^-2 and 60^6

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Answer:

20% gained

Step-by-step explanation:

25 - 20 = 5

5 / 25 * 100 = 20%

Answer:

(5a+5b+3ab)/15

Step-by-step explanation:

qquy đồng lên thôi !!

The number of lighter boards and heavier boards in the truck is 216 and 192 boards respectively.

let

Light board = x

Heavy board = y

x = y + 24

x + y = 408

(y + 24) + y = 408

y + 24 + y = 408

2y = 408 - 24

2y = 384

y = 384 / 2

y = 192 boards

So,

x = y + 24

= 192 + 24

x = 216 boards

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The plastic and the glass contain no water molecules. Plastic and glass have very different absorption frequencies from water, so they may not absorb any significant microwave energy and remain cool to the touch.

The absorption of electromagnetic radiation by water depends on the state of the water.

The absorption in the gas phase occurs in three regions of the spectrum. Rotational transitions are responsible for absorption in the microwave and far-infrared, vibrational transitions in the mid-infrared and near-infrared. Vibrational bands have rotational fine structure. Electronic transitions occur in the vacuum ultraviolet regions.

It is given that an empty plastic or glass dish being removed from a microwave oven can be cool to the touch, even when food on an adjoining dish is hot.

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The total weight of the two pieces together is 6 pounds.

A piece of raw silk that is 100 yards long by 1.25 yards wide weights 38lb.

Then, a piece that is 12.5 yards long (and still 1.25 yards wide) will weight:

M = (12.5/100)*38lb = 4.75 lb

And a piece of habotai silk that is 100 yards long by 1.25 yards wide weights 12lb.

Then, a piece that is 12.5 yards long will weigh:

M' = (12.5/100)*12lb = 1.5 lb

If we add these two, we get a total weight of:

M + M' = 4.5lb + 1.5lb = 6lb

The total weight of the two pieces together is 6 pounds.

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Answer: B , c, E

Step-by-step explanation:

Given that ,

∡J=90° , ∡k=30° , ∡L=60°

In the triangle ΔJKL,

 tan ∠L = tan 60°

⇒ JK÷JL= √3

⇒JK = √3JL

Thus, A is incorrect and B is correct

Again,

cos ∠L = cos60° =0.5

⇒JL/KL = 1÷2

⇒ JL = (1÷2)KL

⇒JL×2= KL

⇒ KL=2JL

Hence, F & D are incorrect and C is correct

Earlier we got,

JK = √3.JL

⇒JL=JK÷√3

and JL= (1÷2).KL

So, JK÷√3=(1÷2)KL

⇒JK÷√3×2 = KL

⇒2.JK= √3KL

⇒JK = (√3÷2).KL

hence E is correct

The choice which defines same arithmatic sequence using a Recursive Formula and an Explicit formula is (A) which is [tex]a_1= -23, a_n = a_{n-1}+ 12,a_n=-23 +12(n-1)[/tex]

If first term of a arithmatic sequence is a₁ and the common difference is d then,

By Explicit Formula, the n-th term of the sequence is given by,

[tex]a_n=a_1+(n-1)d[/tex]

By Recursive Formula,

[tex]a_n=a_{n - 1}+d[/tex]

In the first choice: a₁ = -23 and

[tex]a_n=a_{n-1}+12[/tex]

Then by recursive formula, it suggests arithmatic sequence with first term -23 and common difference 12.

and

[tex]a_n=-23+12(n-1)[/tex]

So by explicit formula it also suggests arithmatic sequence with first term -23 and common difference 12.

So it is one correct choice.

In second choice: a₁ = -100 and

[tex]a_n=a_{n-1}+1[/tex]

By recursive formula, it suggests arithmatic sequence with first term -100 and common difference 1.

[tex]a_n=100-1(n-1)[/tex]

By explicit formula, it suggests arithmatic sequence with first term 100 and common difference -1.

So it is not the correct choice.

In third choice: a₁ = -41 and

[tex]a_n=a_{n-1}+12[/tex]

By recursive formula, it suggests arithmatic sequence with first term -41 and common difference 12.

[tex]a_n=12-41(n-1)[/tex]

By explicit formula, it suggests arithmatic sequence with first term 12 and common difference -41.

So it is not the correct choice.

In fourth choice: a₁ = 50 and

[tex]a_n=a_{n-1}-4[/tex]

By recursive formula, it suggests arithmatic sequence with first term 50 and common difference -4.

[tex]a_n=50+4(n-1)[/tex]

By explicit formula, it suggests arithmatic sequence with first term 50 and common difference 4.

So it is not the correct choice.

Hence the option (A), the first choice is correct.

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Answer:

(-1,-4) is the vertex

x = -1 is the equation of symmetry;

Step-by-step explanation:

See attached image.

Answer:

(- 1, - 4 ) and x = - 1

Step-by-step explanation:

given a parabola in standard form

y = ax² + bx + c ( ax≠ 0 )

then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = x² + 2x - 3 ← is in standard form

with a = 1, b = 2 , then

x = - [tex]\frac{2}{2}[/tex] = - 1

substitute x = - 1 into the equation for corresponding y- coordinate

y = (- 1)² + 2(- 1) - 3 = 1 - 2 - 3 = - 4

vertex = (- 1, - 4 )

this is an upward opening parabola ( a > 0 )

the axis of symmetry is a vertical line passing through the vertex with equation

x = c ( c is the value of the x- coordinate of the vertex ), then equation is

x = - 1

Answer:

Step-by-step explanation:

2x squared, denoted (2x)2, is equal to 4x2. In general, we can raise a product to a power using the following product rule for exponents: (ab)n = an

Answer:

A

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

we know the thickness is x, so the sides are 3+2x and 4+2x

then we use foil:

(3+2x)(4+2x)=12+6x+8x+4x^2=4x^2+14x+12

we know the area is 15

4x^2+14x+12=15

4x^2+14x-3=0

So it is B

The shapes from the cross section are square, parallelogram, trapezium, kite, triangle and rectangle.

It is important to note that the cross section of a cube is a square.

From the cross section visible from the figure, we have the shapes;

Thus, the shapes from the cross section are square, parallelogram, trapezium, kite, triangle and rectangle.

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