MATHEMATICS HIGH SCHOOL

Which line is perpendicular to the line y=2/3x +3?Y=2/3x-1
Y=-2/3x+1
Y=3/2x+7
Y=-3/2x+7

Answers

Answer 1
Answer:

The line that is perpendicular to the given line, is:

y = (-3/2)*x + 7

How to get the perpendicular line?

Remember that two lines are perpendicular if the slope of one is equal to the opposite of the inverse of the other slope.

Here we start with the line:

y = (2/3)*x + 3

So the slope is 2/3.

The opposite of the inverse of that would be -(3/2). Then any line with a slope of -3/2 will be perpendicular to the given line. So we conclude that the correct option is:

Y = -(3/2)x+7

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In the diagram below, the top of each stair is parallel to the floor. What is the value of y?(Picture below.)

What three numbers can you multiply to get 24?

Answers

1x24, 2x12, 3x8 are 3 ways that get 24
Three numbers that are multiplied that = 24

2 * 2 * 6

Simplify

2*2 = 4
4*6 = 24

Answer would be : 2*2*6

Ok what next helppp i need 2

Answers

Answer:

3-2

Step-by-step explanation

A right triangle has legs with lengths 20 cm and 21 cm.What is the length of the hypotenuse?

Answers

The length of the hypotenuse of the given right-angled triangle is 29 cm.

What is the hypotenuse?

The longest side of a right-angled triangle, i.e. the side opposite the right angle, is called the hypotenuse in geometry.

Pythagorean theorem :

If p be the length of the hypotenuse of a right-angled triangle, q and r be the lengths of the other two sides, then

p² = q² + r²

How to solve this problem?

Here, the lengths of the other two sides of the given right-angled triangle are 20 cm and 21 cm. Put these values in the above theorem to get the desired result.

Now, p² = (20)² + (21)²

             = 400 + 441

             = 841

i.e. p = √(841)

         = 29

Therefore the length of the hypotenuse is 29 cm.

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c²=a²+b²
c²=20²+21²=400+441=841
c²=841
c=√841
c=29
Answer: 29 cm

Graham and Hunter are circus performers. A cable lifts Graham into the air at a constant speed of 1.5 ft/s. When Graham’s arms are 18 ft above the ground, Hunter, who is standing directly underneath Graham, throws Graham a ball as the cable continues to lift him higher. Hunter throws the ball from a position 5 ft above the ground with an initial velocity of 24 ft/s. Which system of equations can be used to model this situation?

Answers

The answer to the question above as to which system of equations can be used to model the situation of Graham and Hunter when a cable lifts Graham into the air at a speed of 1.5 ft/s and Hunter throws the ball from a position of 5 ft. above the ground with an initial velocity of 24 ft/s. the equation will be : H = 18t + 1.5t - 16t ^ 2
H = 5 + 24t - 16t ^ 2

The equation of Graham cable is h(t) = -16t² + 1.5t + 18 while The equation of Hunter ball is h(t) = -16t² + 24t + 5

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

The height of a projectile at time t is:

h(t) = -16t² + ut + h'

Where u is the initial velocity and h' is the initial height.

The equation of Graham cable is:

h(t) = -16t² + 1.5t + 18

The equation of Hunter ball is:

h(t) = -16t² + 24t + 5

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A bank offers a 3.7% annual interest rate for a retirement savings account. A worker puts $8,000 into the account. How much will be in the account after a year?

Answers

Answer:

$8,296

Step-by-step explanation:

(see attached for reference)

assuming simple interest, the final amount is given by

A = P(1 + rt), where

A = final amount (we are asked to find this)

P = principal amount = given as $8000

r = rate = 3.7% = 0.037

t = time = 1 year

substituting the known values into the formula,

A = P(1 + rt)

= 8,000 [ 1 + (0.037)(1) ]

= $8,296

Given:AB||CD .If the coordinates of point A are (8, 0) and the coordinates of point B are (3, 7), the y-intercept of AB is____ ? If the coordinates of point D are (5, 5), the equation of line CD is y___ = ___x + ____

Answers

(8,0)(3,7)
slope = (7-0) /(3-8) = -7/5

y = mx + b
slope(m) = -7/5
(3,7)

7 = -7/5(3) + b
7 = -21/5 + b
7 + 21/5 = b
35/5 + 21/5 = b
56/5 = b 

y = -7/5x + 56/5 <=== the y int of AB is 56/5

y = mx + b
slope(m) = -7/5
(5,5)

5 = -7/5(5) + b
5 = - 7 + b
5 + 7 = b
12 = b

y = -7/5x + 12 <=== equation of line CD

Answer:

first blank : 56/5

second blank : -7/5

third blank : 12

Step-by-step explanation:
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