MATHEMATICS HIGH SCHOOL

Simplify this imaginary number sqr -45?

Answers

Answer 1

Answer: √-45 = √45(-1) = √45 * √-1 = 5√9 * √-1 = 15i
Remember, i = √-1

Answer 2

Answer:

Answer:

3i√5

Step-by-step explanation:

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Simplify the expression: 1/1+cot^2xa.sec^2x
b.csc^2x
c.sin^2x
d.cos^2x
e.tan^2x

Answers

$\sin ^( 2 ){ x } +\cos ^( 2 ){ x } =1\n \n \frac { \sin ^( 2 ){ x } }{ \sin ^( 2 ){ x } } +\frac { \cos ^( 2 ){ x } }{ \sin ^( 2 ){ x } } =\frac { 1 }{ \sin ^( 2 ){ x } } \n \n 1+\cot ^( 2 ){ x } =\csc ^( 2 ){ x }$

Because of this...

$\frac { 1 }{ 1+\cot ^( 2 ){ x } } \n \n =\frac { 1 }{ \csc ^( 2 ){ x } }$

But...

$\frac { 1 }{ \csc ^( 2 ){ x } } =\sin ^( 2 ){ x }$

Therefore:

$\frac { 1 }{ 1+\cot ^( 2 ){ x } } =\sin ^( 2 ){ x }$

Answer:

(c)

Andy is one-fourth as old as his grandfather, who is 76 years old. Write an equation to determine whether Andy is 19 or 22 years old.

Answers

We know that if we multiply Andy's age by four we obtain 76. Lets assume that Andy's age its x. so
4*x=76
Now we have to solve equation
4*x=76 /:4 divide both sides by 4
x=19 - its the answer

A=Andy
G=Andy's Grandfather

A*4=G
G=76
A*4=76
/4
a=19

The area of a right triangle is 270 m². The height of the right triangle is 15 m. What is the length of the hypotenuse of the right triangle?

Answers

The area of a triangle is calculated by the expression given as:

Area = bh/2

where b is the base and h is the height.

We calculate as follows:

270 = b (15) / 2
b = 36

hypotenuse = sqrt ( 15^2 + 36^2 ) = 39

Answer:

hypotenuse = 39m

Step-by-step explanation:

Area of a triangle= 1/2 * base * height

where base = ?

height = 15

Plugin values into the formula:

270 = 1/2 base (15)

base = 270 (2)

base = 36

hypotenuse = √(base² + height²)

= √( 36² + 15² )

= 39

Peggy works as a busperson and earns \$7.50/h. She also receives 9\% of the gratuities earned by all the staff. In one week she worked 35 hours and the gratuities totalled \$1936.80. What was Peggy's gross pay?

Answers

Answer: $ 436.81

Step-by-step explanation:

Given: Hourly rate for Peggy= $7.50

Also, she receives 9% of the gratuities earned by all the staff.

Total hours she worked = 35 hours

Total gratuities = $1936.80

Gross pay = (Hourly rate ) x (Number of hours worked)+ 9% of (Total gratuities )

= $ [(7.50 ×35)+(0.09 ×1936.80)]

= $ (262.5 +174.31)

= $ 436.81

Hence, her gross pay = $436.81

Which expression is equivalent to (x²+3x-4)(x-5)1) x³+8x²-19x+20
2) x³-2x²-19x+20
3) x³-2x²-11x+20
4) x³-8x²-11x+20

Answers

$(x^2+3x-4)(x-5)=x^3-5x^2+3x^2-15x-4x+20=\n \n=x^3-2x^2-19x+20\ \ \ \Rightarrow\ \ \ Ans.\ B$

Write standard form of the equation of the line described.Through (2,0) parallel to y =2/3x

Answers

$y=(2)/(3)x , \ \ (2,0)\n \n m=(2)/(3) \n \n The \ slope \ of \ lines \ parallel \ is \ the \ same \n \n use \ y = mx + b \ and \ the \ point \ (2,0) \ to \ find \ b \n \n 0= -(2)/(3)\cdot 2+b$

$0=-(4)/(3) +b \n \nb=-(4)/(3) \n \ny=-(2)/(3)x+(4)/(3)$

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