Solve each triangle – find any missing side and angle measures. Round answers to the nearest tenth.

The prediction of the author about the future of the earth's mantle is that it would affect the sea level rise.

This refers to the statement that contains a forecast about future events that is made.

Hence, we can see that from the complete text, there is the scientific explanation of the lead researcher about the future of the Earth's mantle and how this would affect sea levels as they would increase.

Yes, I support his guess because he made use of past events and current happenings to show the effects on the sea levels.

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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)

The actual payment Eric made to the bank at 175.00 for 36 months is 6,300

Actual payment to bank = Monthly payment × Number of months

= 175.00 × 36

= 6,300

Therefore, the actual payment made to the bank is 6,300.

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Answer:

Step-by-step explanation:

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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The answer to this question is A

Answer:

20% gained

Step-by-step explanation:

25 - 20 = 5

5 / 25 * 100 = 20%

Answer:

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The value of  y = -32 , x = -8 .

Direct Variation is when a variable is dependent on the other variable such that , on increasing one variable the other also increases.

It is given that

x and y are two variables

and they are in direct variation

y ∝ x

y = k x

where , k is the proportionality constant

From the given data , y = 76 when x = 19

76 = k * 19

k = 4

The value of x , when y = -32

-32 = 4 * x

x = -8

Therefore for y = -32 , x = -8 .

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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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Step-by-step explanation:

the solution is in the photo I sent

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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It will take 2/3 hour or 40 minutes to fill the tank if both pipes are used.

Let pi be pipe 1 and pi2 be pipe 2

pi = 1 / 1

pi2 = 1 / 2

together = 1/1 + 1/2 ;

3/2 time ; 2/3 hour.

It will take 2/3 hour or 40 minutes to fill the tank if both pipes are used.

Problem-solving is the act of defining a problem; figuring out the motive of the problem; identifying, prioritizing, and deciding on alternatives for a solution; and implementing an answer.

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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 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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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:

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:

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

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:

(-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:

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 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 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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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:

Answer:A.47.5 miles is 76

Step-by-step explanation:

in real life its like 76.44, but im rounding

Part 1

By the inscribed angle theorem, arc ZY measures 76 degrees.

Part 2

Since angles inscribed in the same arc are congruent, angle YXZ measures 38 degrees.

Part 3

Since diameters form semicircles and the arc of a semicircle measures 180 degrees, arc XYZ measures 180 degrees.

Part 4

Subtracting arc ZY from arc XYZ, we get 104 degrees.