MATHEMATICS HIGH SCHOOL

2. Stephen Curry's record during the 2017 – 2018 NBA final game is made up of 2-point shots and 3-points.His total points scored for the final game was 45 points with 19 shots made. How many 2-point shots did
he make? How many 3-point shots did he make?

Answers

Answer 1
Answer:

Answer:

He made 7 3-point shots.

Step-by-step explanation:

x+y=19

2x+3y=45

y=19-x

2x+3*(19-x)=45

2x+57-3x=45

-x=45-57

-x=-12

x=12

y=19-12

y =7

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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.

Find the distance between point P(2, -1) and Q(10,-7)

Answers

The distance between the two points is 10.

Sam rotated parallelogram ABCD 90° clockwise around the origin. If angle A is 130° and angle B is 50°, what is the degree measurement of angle A'?

Answers

Answer-

The measurement of angle A' will be 130° .

Solution-

Transformations like - rotations, reflections, and translations are isometric.  That means that these transformations do not change the size of the figure.  If the size and shape of the figure is not changed, then the figures are congruent.

It doesn't matter the order or how much degree of rotation has taken place, the final image will be congruent to the original image.

So, even after the rotation of 90° clockwise around the origin, the measurement of angle A will be 130° and so do all the rest of the angles.

Answer:

B, 130 degrees.

Step-by-step explanation:

The longest side of an obtuse triangle measures 20 cm. The two shorter sides measure x cm and 3x cm

Answers

Obtuse triangle is a triangle that has an angle that is greater than 90°.

longest side: 20 cm
two shorter sides: x cm and 3x cm

choice given: 6.3   6.4   7.0   7.1

Obtuse triangle Pythagorean Theorem

c² > a² + b²

20² > x² + 3x²
400 > 4x²
÷4      ÷4
 100 > x²
   10 > x
  
400 > 4(7.1)²
400 > 4(50.41)
400 > 201.64

The greatest possible value of x is 7.10

There is a discrete relationship between the number of workers and the number of bricks layed on a wall. Use this information to answer problems 9-11. What is the domain for the function that models the relationship between workers and bricks laid on the wall?

Answers

Answer: The domain of a function represents all the possible input values or independent variables that can be used in the function. In this case, the function models the relationship between the number of workers and the number of bricks laid on the wall.

To determine the domain, we need to consider what values the number of workers can take on in this relationship. Since the number of workers is discrete, it means that only whole numbers can be used to represent the number of workers. For example, you cannot have 2.5 workers.

Therefore, the domain of the function would be a set of whole numbers. We can represent this using interval notation as {0, 1, 2, 3, ...}, where the ellipsis (...) indicates that the pattern continues indefinitely.

Solve the following simultaneous equations : 5m - 3n = 19; m - 6 = -7​

Answers

Answer:

m = -1

n= -8

Step-by-step explanation:

5m -3n = 19

m - 6 = -7

solve for m:

m = -7+6

m = -1

plug in m

5(-1) - 3n = 19

-5 - 3n = 19

-3n = 24

n = -8
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