What is the correct label for the angle?

Answers

Answer 1

Answer: That is an acute angle

Answer 2

Answer: angle TRS or angle SRT

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Which expression is a difference of cubes? 9w^33-y^12 18p^15-q^21 36a^22-b^16 64c^15- a^26

Answers

we know that

A polynomial in the form $a^(3)-b^(3)$ is called adifference of cubes. Both terms must be a perfect cubes

Let's verify each case to determine the solution to the problem

case A) $9w^(33) -y^(12)$

we know that

$9=3^(2)$ ------> the term is not a perfect cube

$w^(33)=(w^(11))^(3)$ ------> the term is a perfect cube

$y^(12)=(y^(4))^(3)$ ------> the term is a perfect cube

therefore

The expression $9w^(33) -y^(12)$ is not a difference of cubes because the term $9$ is not a perfect cube

case B) $18p^(15) -q^(21)$

we know that

$18=2*3^(2)$ ------> the term is not a perfect cube

$p^(15)=(p^(5))^(3)$ ------> the term is a perfect cube

$q^(21)=(q^(7))^(3)$ ------> the term is a perfect cube

therefore

The expression $18p^(15) -q^(21)$ is not a difference of cubes because the term $18$ is not a perfect cube

case C) $36a^(22) -b^(16)$

we know that

$36=2^(2)*3^(2)$ ------> the term is not a perfect cube

$a^(22)$ ------> the term is not a perfect cube

$b^(16)$ ------> the term is not a perfect cube

therefore

The expression $36a^(22) -b^(16)$ is not a difference of cubes because all terms are not perfect cubes

case D) $64c^(15) -a^(26)$

we know that

$64=2^(6)=(2^(2))^(3)$ ------> the term is a perfect cube

$c^(15)=(c^(5))^(3)$ ------> the term is a perfect cube

$a^(26)$ ------> the term is not a perfect cube

therefore

The expression $64c^(15) -a^(26)$ is not a difference of cubes because the term $a^(26)$ is not a perfect cube

I'm adding a new case so I can better explain the problem

case E) $64c^(15) -d^(27)$

we know that

$64=2^(6)=(2^(2))^(3)$ ------> the term is a perfect cube

$c^(15)=(c^(5))^(3)$ ------> the term is a perfect cube

$d^(27)=(d^(9))^(3)$ ------> the term is a perfect cube

Substitute

$64c^(15) -d^(27)=((2^(2))(c^(5)))^(3)-(d^(9))^(3)$

therefore

The expression $64c^(15) -d^(27)$ is a difference of cubes because all terms are perfect cubes

The expression $\boxed{64{c^(15)} - {d^(27)}}$ is a difference of cubes.

Further Explanation:

Given:

The options are as follows,

(a). $9{w^(33)} - {y^(12)}$

(b). $18{p^(15)} - {q^(21)}$

(c). $36{a^(22)} - {b^(16)}$

(d). $64{c^(15)} - {a^(26)}$

(e). $64{c^(15)} - {d^(27)}$

Calculation:

The cubic formula can be expressed as follows,

$\boxed{{a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)}$

The expression is $9{w^(33)} - {y^(12)}.$

9 is not a perfect cube of any number, ${w^(33)}$ can be written as ${\left( {{w^(11)}} \right)^3}$ and ${y^(12)}$ can be represents as ${\left( {{y^4}} \right)^3}.$

$9{w^(33)} - {y^(12)}$ cannot be written as the difference of cube. Option (a) is not correct.

The expression is $18{p^(15)} - {q^(21)}.$

18 is not a perfect cube of any number, ${p^(15)}$ can be written as ${\left( {{p^5}} \right)^3}$ and ${q^(21)}$ can be written as ${\left( {{q^7}} \right)^3}.$

$18{p^(15)} - {q^(21)}$ cannot be written as the difference of cube. Option (b) is not correct.

The expression is $36{a^(22)} - {b^(16)}.$

36 is not a perfect cube of any number, ${a^(22)}$ is not perfect cube and ${b^(16)}$ is not a perfect cube.

$36{a^(22)} - {b^(16)}$ cannot be written as the difference of cube. Option (c) is not correct.

The expression is $64{c^(15)} - {a^(26)}.$

64 can be written as ${\left( {{2^2}} \right)^3}, {a^(26)}$ is not perfect cube and ${c^(15)}$ can be written as ${\left( {{c^5}} \right)^3}.$

$64{c^(15)} - {a^(26)}$ cannot be written as the difference of cube. Option (d) is not correct.

The expression is $64{c^(15)} - {d^(27)}.$

64 can be written as ${\left( {{2^2}} \right)^3}, {d^(27)}$ can be written as ${\left( {{d^9}} \right)^3}$ and ${c^(15)}$ can be written as ${\left( {{c^5}} \right)^3}.$

$\boxed{64{c^(15)} - {d^(27)} = {{\left( {{2^2}{c^5}} \right)}^3} - {{\left( {{d^9}} \right)}^3}}$

$64{c^(15)} - {d^(27)}$ can be written as the difference of cube. Option (e) is correct.

The expression $\boxed{64{c^(15)} - {d^(27)}}$ is a difference of cubes.

Learn more:

1. Learn more about unit conversion brainly.com/question/4837736

2. Learn more about non-collinear brainly.com/question/4165000

3. Learn more aboutbinomial and trinomial brainly.com/question/1394854

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Exponents and Powers

Keywords: Solution, factorized form, expression, difference of cubes, exponents, power, equation, power rule, exponent rule.

What is the measure ofA
30°
C

Answers

Answer:

120°

Step-by-step explanation:

X + y = 155x - y = 9
Elimination method

(4, ? )

what number is the ?

Answers

The ? Is 11.

You add the equations to get rid of one variable, then you have 6x=24 then you divide both sides and you have x=4, then you substitute the given value of x and you are left with 5*4 - y = 9. And the solution or well possible solution is y = 11 which gives youuuuu. (x , y) = (4 , 11)

4 + y = 15....1
20 - y = 9.....2

....1*5
20 + 5y = 75....3

....3 - .....2
4y = 60
y = 15

the answer for (?) is 15
i’m not sure if this 100% correct but i’m trying my best to help you

1. Each of 9 friends chooses her favorite positive integera. The median of the chosen number is 91, what is the smallest the average of the 9 chosen numbers could be?

b. The median of the chosen number is 91, is there an limit to how large the aerge of the chosen numbers can be? If so, what is the largest the average can be?

c. The average of the chosen number is 91, what is the smallest the median of the 9 chosen numbers could be?

d. The average of the chosen numbers is 91. What is the largest the median of the chosen numbers could be?

Answers

Answer:

a) 1

b) There is no limit to which the largest number can be because we are only given information about the median.

c) 1

d) 90

Final answer:

The smallest average is 49 and the largest average is 91. The smallest median is 91 and the largest median is also 91.

Explanation:

a. Since the median is 91, at least 5 friends must choose numbers greater than or equal to 91, and at most 4 friends can choose numbers less than 91. To minimize the average, let's assume the four friends choose the smallest possible numbers less than 91 (1, 2, 3, and 4). The remaining five friends can then choose 91, 91, 91, 91, and 91. The average of the nine chosen numbers is (1 + 2 + 3 + 4 + 91 + 91 + 91 + 91 + 91)/9 = 49.

b. There is no limit to how large the average of the chosen numbers can be. The nine friends can all choose the same number, such as 91, which would make the average 91.

c. Since the average is 91, let's assume the eight friends choose the smallest possible numbers less than 91 (1, 2, 3, ..., 8). The remaining friend can then choose a number greater than or equal to 91. To minimize the median, the friend can choose the smallest possible number greater than or equal to 91, which is 91. So, the smallest median would be 91.

d. Since the average is 91, let's assume the eight friends choose the largest possible numbers less than 91 (84, 85, ..., 91). The remaining friend can then choose a number greater than or equal to 91. To maximize the median, the friend can choose the largest possible number greater than or equal to 91, which is 91. So, the largest median would also be 91.

Learn more about median and average of chosen numbers here:

brainly.com/question/33899535

#SPJ2

A circle cuts the x-axis at (4,0) and (14,0), and cuts the y-axis at (0,6) and (0,8). Find it's equation

Answers

It is not a circle but you can find the equation of the ellipse.
To do this we need to work out the major and minor radii and the centre
The centre is at (9, 7)
The major (y) radius is 1 and the minor (x) radius is 5
Therefore the equation is (x-9)/5 + (y-7)/1 = 1

What is the product?

2x(x – 4)

Answers

Keywords:

Product, factors, polynomial, distributive property

For this case we must find the product of two factors of a polynomial. To do this, we must apply the distributive property, which states: $a (b + c) = ab + ac.$