MATHEMATICS HIGH SCHOOL

Can someone help me answer this pls.

Answers

Answer 1

Answer:

Scale shows weight = 193

Weight of assistant = 135

Weight of dog = x

x = 193 - 135

x = 58

The dog weighs 58 pounds.

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Simplify $(1-3i)(1-i)(1+i)(1+3i)$

Answers

$(1-3i)(1-i)(1+i)(1+3i)=\n(1^2-(3i)^2)(1^2-i^2)=\n(1+9)(1+1)=\n10\cdot2=20$

Answer:

$\huge\boxed{(1-3i)(1-i)(1+i)(1+3i)=20}$

Step-by-step explanation:

$(1-3i)(1-i)(1+i)(1+3i)\n\n\text{use the commutative property}\n\n=(1-3i)(1+3i)(1-i)(1+i)\n\n\text{use the associative property}\n\n=\bigg[(1-3i)(1+3i)\bigg]\bigg[(1-i)(1+i)\bigg]\n\n\text{use}\ (a-b)(a+b)=a^2-b^2\n\n=\bigg[1^2-(3i)^2\bigg]\bigg[1^2-i^2\bigg]\n\n=\bigg(1-9i^2\bigg)\bigg(1-i^2\bigg)\n\n\text{use}\ i=√(-1)\to i^2=-1\n\n=\bigg(1-9(-1)\bigg)\bigg(1-(-1)\bigg)\n\n=\bigg(1+9\bigg)\bigg(1+1\bigg)\n\n=(10)(2)\n\n=20$

Write an expression that represents "the product of a number and 12".

Answers

Answer:

x = 12y

Step-by-step explanation:

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 are the common factors of 60 36 and 24?

Answers

1, 2, 3, 4, 6, 12 :)

When Ava bought her car, it was worth $19,340. It was expected to decrease at a rate of 12.5% each year.What is best prediction for the value of Ava’s car 10 years after she bought it?
(Points : 5)

Answers

To do this, you must do 12.5% of $19,340, then 12.5% of that sum, and so one 10 times. Your answer:
12.5% X $19,340 = 241,750/100 = $2,417.5.
$19,340 - $2,417.5 = $16,922.5 X 12.5% = 211,531.25/100 = $2,115.3
$16,922.5 - $2,115.3 = $14,807.2
Repeated 8 more times... and you get your answer...
Hope that helps:) Sorry that I didnt give you the answer...

A softball thrown into the air has a parabolic trajectory. After reaching a maximum height of 28 feet, the ball covers a ground distance of 4 feet before hitting the ground. Which equation describes the ball’s trajectory?

Answers

If the take the origin as the starting point of the ball, then the vertex would be (4,28) and the parabola would be facing downwards. Using the general form of the parabola which is (x-h)^2 = 4p(y-k) where h and k are taken from the coordinate of the vertex (h,k).
So, the equation would be, (x-4)^2)=4p(y-28). To determine 4p, we can substitute either of the two points: (0,0) or (0,8). The second coordinate is taken from the given that the ball covers a distance of 4 ft after it reaches a maximum height. The total distance traveled by the ball is twice that, which is 8 ft.
After substituting, 4p = -4/7. Plugging this into the equation and after expanding and simplifying, the equation of the ball's trajectory is:
y = (-4/7)x^2+14x

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1,000^8=10^w what does w equal