a = 4, b= 9. Explanation: Since all of it is to the power of 3, we can divide the exponents to of the results (right side of the equation). 12/3=4, 27/3=9. Hope this helps.
Answer:
x = 28
Step-by-step explanation:
Triangle ABP and triangle CDR are similar. Thus, we can solve this problem for x using an equation of proportions:
hypotenuse leg length
15+42 10+x
---------------- = ----------
42 x
Then (15+42)x = 42(10+x) after cross multiplication
57x = 420 + 42x
Subtracting 42x from both sides, we get
15x = 420.
Dividing both sides by 15 results in
x = 28
Answer: Choice C) -11
-----------------------------------
Explanation:
The first equation given is y = 3 - 1/2x
In other words, y is the same as 3 - 1/2x.
We can replace y in the second equation with 3 - 1/2x
This is known as substitution (think of a substitute teacher who is a temporary replacement for your teacher)
Doing this leads to...
3x+4y = 1
3x+4*y = 1
3x+4*( y ) = 1
3x+4*( 3 - 1/2x ) = 1 <<--- y has been replaced with 3-1/2x
3x+4*(3) +4*(-1/2x) = 1
3x+12-2x = 1
3x-2x+12 = 1
x+12 = 1
x+12-12 = 1-12 <<-- subtracting 12 from both sides
x = -11
Which is why the answer is choice C) -11
x - Ram's age now
Ram is half his father's age now, so his father's age is two times Ram's age:
2x - Ram's father age now
x - 10 - Ram's age ten years ago
2x - 10 - Ram's father age ten years ago
ten years ago he was one third his father's age so his father's age was three times Ram's age:
2x - 10 = 3•(x - 10)
2x - 10 = 3x - 30
-10 + 30 = 3x - 2x
20 = x
2x = 2•20 = 40
Answer:
<u>Ram is 20 years old now, Ram's father is 40 years old now.</u>
Equation of a line is in the form y = mx+c, where m is the gradient and c is the y-intercept.
First step is to find the gradient.
m = (y2-y1)/(x2-x1)
= ( 5- -8)/(8-4) = 13/4
We have y = (13/4)x + c
Now we replace one of the coordinates to find c. Let’s replace (4,-8)
We have: -8 = (13/4)*4 + c
-8=13+c
c=-8-13= -21
Therefore, equation of line is:
y = (13/4)x - 21