Solve the Equations in terms of X:
a. x/a = b/c
b. s=xt^2/2
d. 4= 10/x
e. 5= 5/x-5
f. 40=2((x10)2-5)
g. x(y+2)/ (5y +8)
1.What is the average of 2/9 and 4/5?
2. Subtract 4.20 x 10^-5 from 6.468 x 10^-4
3.Given: D= density; M= Mass; V= Volume; and D= M/V
a) If an object has a density of 1.5g/cm cubed and a volume of 3 cm cubed, how much it weigh?
b) If an object has a density of 1.5g/cm cubed and a mass of 4.5g, what is its volume?
4. A car travels in 125 miles in 2 and a half hours. What is its average speed?
Thanks in advance and will appreciate it work is shown so i can be able to learn and do it myself the next time...
a thoough g are basic algebra questions. If you cannot do any of them, you should not be taking physics. Show us your work so someone can explain where help is needed.
1. The average of two numbers is their sum divided by 2.
2. Write the numbers so that the exponent of 10 is the same. The subtract the mumbers in front.
6.468x10-4
-0.042x10^-4
------------
6.426 x 10^-4
3a M = V*D
3b V = M/D
4. 125 / 2.5 = __ mph?
and g is not an equation..
a. To solve the equation x/a = b/c in terms of x, we can cross multiply and then solve for x.
First, cross multiplying gives us xc = ab.
To solve for x, divide both sides of the equation by a:
x = (ab)/c.
Therefore, x = (ab)/c.
b. To solve the equation s = xt^2/2 in terms of x, we can isolate x by multiplying both sides of the equation by 2/t^2:
2/t^2 * s = 2/t^2 * (xt^2/2)
This simplifies to:
2s/t^2 = x
Therefore, x = 2s/t^2.
c. To solve the equation 4 = 10/x in terms of x, we can isolate x by multiplying both sides of the equation by x:
4 * x = 10 * x/x
This simplifies to:
4x = 10
To solve for x, divide both sides of the equation by 4:
x = 10/4
Simplifying further, we have:
x = 5/2
Therefore, x = 5/2.
d. To solve the equation 5 = 5/(x - 5) in terms of x, we can start by multiplying both sides of the equation by x - 5:
5 * (x - 5) = 5/(x - 5) * (x - 5)
This simplifies to:
5x - 25 = 5
To solve for x, add 25 to both sides of the equation:
5x = 30
To isolate x, divide both sides of the equation by 5:
x = 30/5
Simplifying further, we have:
x = 6
Therefore, x = 6.
e. To solve the equation 40 = 2((x*10)^2 - 5) in terms of x, we can begin by simplifying the expression within the parentheses:
((x*10)^2 - 5) = (x^2 * 100) - 5
Next, multiply by 2:
2((x*10)^2 - 5) = 2((x^2 * 100) - 5)
Distributing the 2, we get:
2(x^2 * 100) - 2*5 = 2x^2 * 200 - 10
Now, rewrite the equation:
40 = 2x^2 * 200 - 10
To solve for x, isolate the x^2 term by adding 10 to both sides:
40 + 10 = 2x^2 * 200
50 = 2x^2 * 200
Divide both sides by 200:
50/200 = 2x^2
Simplify:
1/4 = x^2
To find x, take the square root of both sides:
sqrt(1/4) = x
Simplify:
1/2 = x
Therefore, x = 1/2.
f. To solve the equation x(y + 2)/ (5y + 8) in terms of x, we can start by multiplying both sides of the equation by (5y + 8):
x(y + 2) = (5y + 8)
Next, distribute x:
xy + 2x = (5y + 8)
To isolate x, subtract xy from both sides:
2x = (5y + 8) - xy
Finally, divide both sides by 2:
x = ((5y + 8) - xy)/2
Therefore, x = ((5y + 8) - xy)/2.
1. To find the average of 2/9 and 4/5, add the two fractions together and then divide by 2:
(2/9 + 4/5)/2
To add the fractions, we need a common denominator. The least common multiple of 9 and 5 is 45, so we can rewrite the fractions with a denominator of 45:
(2*5/9*5 + 4*9/5*9)/2
Simplifying the numerators:
(10/45 + 36/45)/2
Adding the fractions:
46/45 /2
To divide by 2, we can multiply by the reciprocal:
(46/45) * (1/2)
Simplifying:
46/90
This can be further simplified by dividing both numerator and denominator by their greatest common divisor, which is 2:
23/45
Therefore, the average of 2/9 and 4/5 is 23/45.
2. To subtract 4.20 x 10^-5 from 6.468 x 10^-4, we need to have the same exponent.
First, let's convert both numbers to scientific notation with the same exponent of 10, using the same exponent of 10^-4:
6.468 x 10^-4 - 4.20 x 10^-5
To subtract, we can now subtract the coefficients:
6.468 - 4.20 = 2.268
Now, keep the exponent of 10^-4:
2.268 x 10^-4
Therefore, the result is 2.268 x 10^-4.
3.a) Given the density formula D = M/V, where D is density, M is mass, and V is volume, we can solve for the mass (M) when D and V are given.
We know that D = 1.5 g/cm^3 and V = 3 cm^3.
Substituting these values into the formula, we have:
1.5 g/cm^3 = M/3 cm^3
To solve for M, we can cross multiply:
1.5 g/cm^3 * 3 cm^3 = M
Simplifying:
4.5 g = M
Therefore, the object weighs 4.5 grams.
3.b) Given the same density formula D = M/V, but with D = 1.5 g/cm^3 and M = 4.5 g, we can solve for the volume (V).
Substituting these values into the formula, we have:
1.5 g/cm^3 = 4.5 g/V
To solve for V, we can cross multiply:
1.5 g/cm^3 * V = 4.5 g
Divide both sides of the equation by 1.5 g/cm^3:
V = 4.5 g / 1.5 g/cm^3
Simplifying:
V = 3 cm^3
Therefore, the volume of the object is 3 cm^3.
4. To find the average speed of a car that travels 125 miles in 2.5 hours, we can use the formula:
Average Speed = Distance / Time
Plugging in the values, we have:
Average Speed = 125 miles / 2.5 hours
To simplify, divide the numerator by the denominator:
Average Speed = 125 miles / 2.5 miles/hour
Simplifying further, we have:
Average Speed = 50 miles/hour
Therefore, the average speed of the car is 50 miles per hour.