The line y = 2x + 6 cuts the x-axis at A and the y-axis at B. Find
(a) the length of AB,
(b) the shortest distance of O to AB, where O is the origin (0,0)​

Answer:

x = 5

Step-by-step explanation:

Sides of large triangle: 4x and 15

Corresponding sides of small triangle: 3x + 1 and 12

[tex] \dfrac{4x}{15} = \dfrac{3x + 1}{12} [/tex]

[tex] 60 \times \dfrac{4x}{15} = 60 \times \dfrac{3x + 1}{12} [/tex]

[tex] 16x = 15x + 5 [/tex]

[tex] x = 5 [/tex]

Answer:

c. y = -4x

Step-by-step explanation:

use slope formula

Answer:

c

Step-by-step explanation:

Answer:

a. 18

Step-by-step explanation:

AB+BC = AC

x + x = 36

2x = 36

x = 36/2

x = 18

Answer:

D=-90+22/7

Step-by-step explanation:

D= 22/7×d-90

D= -90+22d/7

Answer: X= 3/4

Simplified: 1/3

Answer:

C=20

Step-by-step explanation:

yes, it's a scaled version of a triangle with side lengths 3, 4 and 5.

by a factor of 20

a triangle with side lengths 3, 4 and 5 is a right triangle and it holds true for a²+b²=c², because 9+16=25

the 3,4,5-triangle is the simplest right triangle to calculate it's numbers seem somehow elegant.

the triangle in your problem is just a bigger version of it (wich means all angles stay the same).

My reasoning is lacking, but I'm sure

Answer:

1096 more water

Step-by-step explanation:

Let;

x = the water used in general

but used 3 times of the original = 3x

3*(548) = 1644 water a day

How much more water =New - original

where:

new = 1644

original= 548

1644 - 548

=1096 more water

Answer:

22

Step-by-step explanation:

1.) -2²-9(-2)

2.) -2(-2)+18

3.) 4+18

4.) 22

Answer:

The y-coordinate is 4. The point is (2,4)

Step-by-step explanation:

The point is 4 units above the x axis.

Answer:

y-coordinate=4

Step-by-step explanation:

Step-by-step explanation:

(1/2) / (1/3) = (1/2)(3/1) = 3/2 miles per hour = 1.5 miles per hour

Answer:

Step-by-step explanation:

to find the unit rate, which is what we are looking for, we have to divide the number of miles by the number of hours. Specifically:

[tex]\frac{\frac{1}{2} }{\frac{1}{3} }[/tex] and to work this out, we bring up the bottom fraction and flip it to multiply, giving us:

[tex]\frac{1}{2}[/tex] × [tex]\frac{3}{1}[/tex] which is [tex]\frac{3}{2}[/tex] miles per hour (which is the same thing as walking a mile and a half every hour). The choice you're looking for is the one that reflects 3/2 miles per hour. (I can't see which choice it is; they're too small!)

Answer:

y=-2x+12

Step-by-step explanation:

This is an equation in slope-intercept form:

y=mx+b (where m is the slope and b is the y-intercept)

We are given the slope, -2.

y=-2x+b

We plug in the values (5,2):

2=(-2)*5+b

2=-10+b

b=12

The equation is:

y=-2x+12

Answer:

126x9

Step-by-step explanation:

2^5 = 32

Hope this helps! :)

Answer:

32

Step-by-step explanation:

[tex]2^{5}[/tex]

= 2 × 2 × 2 × 2 × 2

= 4 × 4 × 2

= 16 × 2

= 32

Answer:

Slope = 4

Step-by-step explanation:

The slope of a linear equation can be calculated as;

m = y2-y1/x2-x1

What we have to do here is to select any two points ;

(x1,y1) = (3,8)

(x2,y2) = (6,20)

m = (20-8)/(6-3) = 12/3 = 4

Answer:

-2.76, -2.57, -2.5, -1.85, -1.58, 2.5, 2.85

Answer:

wht yr u in tis is too hard yk

Step-by-step explanation:

Given:

2.2 pounds = 1 kilogram

Weight of Mary = 120 pounds.

To find:

The weight of Marry in kilograms.

Solution:

We have,

2.2 pounds = 1 kilogram

Using this conversion, we get

1 pound = [tex]\dfrac{1}{2.2}[/tex] kilogram

120 pound = [tex]\dfrac{1}{2.2}\times 120[/tex] kilogram

                  = [tex]\dfrac{120}{2.2}[/tex] kilogram

                  [tex]\approx 54.54[/tex] kilogram

Therefore, the weight of Mary is about 54.54 kilograms.

Step-by-step explanation:

The question is not clear to me

Answer:

x = 3

Step-by-step explanation:

x + 9x + 5 = 35

=> x + 9x = 35 - 5

=> x + 9x = 30

=> 10x = 30

=> x = 30/10

=> x = 3

Answer:

x = 3

Step-by-step explanation:

Combine like terms. Like terms have same variable with same exponent.

Here x and 9x are like terms

x + 9x + 5  =  35

     10x + 5 = 35

Subtract 5 from both sides

10x + 5 - 5 = 35 - 5

       10x = 30

Divide both sides by 10

10x/10 = 30/10

x = 3

Answer:

P = 157.5 units

Step-by-step explanation:

Answer:

In this case, we can do substitution.

Step-by-step explanation:

For the first one, (s - t)(x) = ((x - 5) - 4x^2)(x) = x^2 - 21x

For the second one, (s*t)(x) = ((x - 5) *4x^2)(x) = 4x^4 - 20x^3

And for the last one,  (s+t)(-2) = ((x - 5) + 4x^2)(-2) = -8x^2 - 2x + 10

Hope your happy with the answer :)

Answer:

The value belonging to the green box is b

Step-by-step explanation:

QP uses the points Q and P

Q is (0,-a)

P is (b,-c)

The distance between the two points can be calculated using the distance formula;

D = √(x2-x1)^2 + (y2-y1)^2

(x1,y1) = (0,-a)

(x2,y2) = (b,-c)

D = √(b-0)^2 + (-c + a)^2

D = √(b)^2 + (-c + a)^2

Answer:

just do 64 * 118 = 7552

count the decimal points in BOTH the items 1 for the 6.4

and 2 in the 1.18 1+2 = 3

so starting from the right move in "3" positions and

put a decimal point

7.552

Step-by-step explanation:

Answer:

Step-by-step explanation:

cos x=sinx

divide by cos x

1=tan x

tan x=1

[tex]tan x=1=tan \frac{\pi }{4}=tan (n\pi +\frac{\pi }{4})\\x=n\pi +\frac{\pi }{4} ,\\where~n~is~an~integer.[/tex]