Convert the rectangular coordinates (4, –4) into polar coordinates.

The answer is (B).

Draw any triangle ABC. Reflect this triangle across the line AB, creating triangle A'B'C' for which A'=A and B'=B. By definition of a reflection, sides B'C and B'C' are congruent. In addition, sides A'C and A'C' are congruent. The quadrilateral CA'C'B' has two pairs of consecutive sides that are congruent and no congruent opposite sides. By definition, this is a kite.

In literature, when a character meets a two-headed dragon, their response may vary based on the story's context. Dragons often symbolize challenges; thus, a character may respond with caution and respect. This concept, however, is symbolic and represents various elements in different literatures.

In literature, the response to meeting a two-headed dragon can vary greatly depending on the context of the story and the characteristics assigned to the creature. Dragons, particularly two-headed ones, often symbolize challenges or adversities. So, one way to respond practically when you meet a two-headed dragon would be with caution and respect.

For example, in fantasy literature, a protagonist might say 'Well met, noble dragon. What do you require of me?' This politeness and respect can often turn a potentially dangerous encounter into an opportunity for dialogue. Remember, in literature, fantastic creatures like headed dragons are often symbolic, representing something else entirely in the context of the story.

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Final answer:

The functions y=x and y=x+5 have the same slope but different y-intercepts. Their graphs are straight lines.

Explanation:

The functions y=x and y=x+5 are related in that they have the same slope of 1. This means that for every increase of 1 in the value of x, the value of y will also increase by 1. However, they have different y-intercepts. The function y=x has a y-intercept of 0, while the function y=x+5 has a y-intercept of 5.

Their graphs are related in that they are both straight lines. The graph of y=x is a line passing through the origin (0,0), while the graph of y=x+5 is a line shifted upward by 5 units compared to the graph of y=x.

The domain of Ethan's function f(x) = 2x² + 2x + 4  is all real numbers as it is a quadratic function.

The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value). In this case, the function f(x) = 2x² + 2x + 4 represents the temperature of a substance over time. Since temperature is a physical quantity and cannot be negative, the domain of the function must be restricted to non-negative values of x.

To determine the exact domain of the function, we can analyze the expression 2x² + 2x + 4. This expression is always non-negative for any real number x. Therefore, the domain of f(x) = 2x² + 2x + 4 is all real numbers x ≥ 0.

In mathematical notation, the domain of the function can be expressed as:

{x ∈ ℝ | x ≥ 0}

This indicates that the function is defined for all real numbers (ℝ) as long as the value of x is greater than or equal to 0 (x ≥ 0).

Answer with explanation:

The four options are

(A) log5 21 (B) log5 26 (C) log5 30 (D) log5 56

[tex]\rightarrow\log_{5}(4\times 7) +\log_{5}(2)\\\\ \rightarrow \log_{5}28+\log_{5}2\\\\\rightarrow \log_{5}(28 \times 2)\\\\=\log_{5}(56)\\\\ \text{Used this property of log}\\\\ \log_{m} a+\log_{m} b=\log_{m} ab[/tex]

Option D

Answer:

2/3 i got it right

Step-by-step explanation:

Final answer:

To find the scale factor between △ABC and △DEF, compare their corresponding side lengths and calculate the scale factor as 2.5 or 5/2.

Explanation:

To verify that two triangles △ABC and △DEF are similar, you need to check if their corresponding angles are congruent and their corresponding sides are proportional.

Calculate the scale factor using the corresponding sides of the triangles: AB/DE = BC/EF = CA/FD.

Substitute the values: 10/25 = 16/40 = 20/50. Simplify to find the scale factor.

Therefore, the scale factor of △ABC to △DEF is 2.5 or 5/2.

Answer: C) twelve over fifty one

Step-by-step explanation:

Formula for probability =[tex]\dfrac{\text{Favorable outcomes}}{\text{Total ouctomes}}[/tex]

We know that , a standard deck has 52 cards.

Number of hearts = 13  

If a heart was drawn on the first draw and not replaced, then the number of hearts left = 13-1=12          (favorable outcomes)

The total number of cards left = 52-1=51     (total outcomes)

Therefore, the probability of drawing a heart from a standard deck of cards on a second draw, given that a heart was drawn on the first draw and not replaced would be :-

[tex]\dfrac{\text{Number of hearts left}}{\text{Total cards left}}\\\\=\dfrac{12}{51}[/tex]

Hence, the correct answer is option C) twelve over fifty one

The number by which the circumference is multiplied is:

                               2

We know that the circumference of the circle in terms of the radius r is given by:

        [tex]\text{Circumference}=2\pi r[/tex]

Now, if the radius is doubled.

i.e.

[tex]r'=2r[/tex]

Hence, the circumference of the new circle is given by:

[tex]\text{Circumference of new circle}=2\pi (2r)\\\\i.e.\\\\\text{Circumference of new circle}=2(2\pi r)[/tex]

i.e.

[tex]\text{Circumference of new circle}=2\times \text{Circumference of original circle}[/tex]

The constant by which the circumference is multiplied is: 2

The function g(r) is a linear equation with a slope of -5 and a y-intercept of 13. You can find the value of g(r) by plugging in different values for r.

The student's question is regarding the function g(r)=−5r+13. However, the rest of the information provided appears to be disjointed and not directly related to the function in question.

To answer their question, g(r)=−5r+13 is a linear function where -5 is the slope and 13 is the y-intercept. In this equation, r is the independent variable, and g(r) is the dependent variable. You would insert a value for r to find the corresponding output of g(r). For example, if r = 2, then g(2) = -5(2) + 13 = -10 + 13 = 3.

Answer:

56 inches is the horizontal distance from the end of the ramp to the back of the truck.

Step-by-step explanation:

Height of the back of the truck =33 inches

Length of the ramp = 65 inches

Length of the end of ramp to the back of the truck =?

In triangle ABC:

AB = 33 inches

BC = ?

AC = 65  inches

[tex]AB^2+BC^2=AC^2[/tex] (Pythagoras theorem)

[tex](33 inches)^2+(BC)^2=(65 inches)^2[/tex]

BC = 56 inches

Answer:

440 miles.

Step-by-step explanation:

A rental company charges for rent a truck = $75 per day

and the charges per mile = 20 cents

100 cents = 1 dollar

20 cents =  [tex]\frac{20}{100}[/tex]

               = $0.20

Michael rents a truck for 2 days.

Let Michael drove the truck in 2 days = x miles

and his bill came to $238.

the equation will be : (75 × 2) + 0.20x = 238

150 + 0.20x = 238

0.20x = 238 - 150

0.20x = 88

x =  [tex]\frac{88}{0.20}[/tex]

x = 440

Michael drove the truck 440 miles in 2 days.

Answer:

2/5 and 3/5

Step-by-step explanation:

Complementary events have probabilities that sum to 100%, or 1.

28+82 = 110; this is not 100.

10+80 = 90; this is not 100.

1/7+2/7 = 3/7; this is not 1.

2/5+3/5 = 1; this is correct.

Answer:

 If ΔABC is similar to ΔDEF, therefore; m∠A = m∠D, m∠B=m∠E, and m∠C=m∠F,

though, if m∠A= 52, m∠D=52, and if m∠E=65, then m∠B=65, though to get m∠C;  

180- (52+65)

=  63 , so then, m∠C= 63

Step-by-step explanation: