1) Solve the equation: 15(7x-6) = 3x-5
My answer is (-85/108)
2) Mary and her brother collect coins. Mary has 4 times the number of coins that her brother has. Together they have 175 coins. How many does Mary have?
My answer is 140
3) Perform the indicated operations. Express the answer as a single polynomial in standard form.
(x-1)(x^2 + 2x -3)
My answer is x^3 + x^2 - 5x + 3
4) Determine which values must be excluded from the domain.
x / x^2 - 9
My answer is x=3 and x=-3
5) Solve the equation. The letters a,b,c are constants.
ax-b=c; a is not equal to 0.
My answer is x=b + c / a
6) Find c in the following.
For 4x^2 - 12x + c to be a perfect square, c must be?
The choices are 9 , 3 ,-9, 0, or noe of the above.
My answer is none of the above.
7) Write the statment using symbols.
The sum of four and x is the product of 5 and y.
My answer is 4+x = 5y
8) write the number as a decimal.
3.875 x 10^-9
My answer is 0.000000003875
Are these answers correct?
all ok, except #5 and #6
in #5 write it as (b+c)/a or else only b is divided by a
#6 should be 9 so that
4x^2 + 12 + 9 = (2x+3)^2
Thank you!
(x-2)(x+2)
___________
2(x-3)
I need to see the work for the problem 2/5x2875....I know the answer is 1725...but i need to see the process in order to answer the other questions.
Let's go through each question and check the answers:
1) Solve the equation: 15(7x-6) = 3x-5
To solve this equation, we distribute the 15 to get: 105x - 90 = 3x - 5.
Combining like terms, we have: 105x - 3x = 90 - 5.
This simplifies to: 102x = 85.
Dividing both sides by 102 gives us: x = 85/102.
Simplifying the fraction, we get x = 17/20.
So, your answer of (-85/108) is incorrect.
2) Mary and her brother collect coins. Mary has 4 times the number of coins that her brother has. Together they have 175 coins. How many does Mary have?
Let's say the number of coins Mary's brother has is represented by 'x'.
Since Mary has 4 times the number of coins her brother has, Mary will have 4x coins.
Together, they have 175 coins, so we can write the equation: x + 4x = 175.
Combining like terms, we have: 5x = 175.
Dividing both sides by 5 gives us: x = 35.
So, your answer of 140 is correct.
3) Perform the indicated operations. Express the answer as a single polynomial in standard form.
(x-1)(x^2 + 2x -3)
To multiply the given polynomials, we use the distributive property.
First, distribute (x-1) to each term within (x^2 + 2x -3):
(x^2 + 2x -3)(x) + (x^2 + 2x -3)(-1)
Expanding each term, we get:
x^3 + 2x^2 - 3x - x^2 - 2x + 3
Simplifying further, we combine like terms:
x^3 + (2x^2 - x^2) + (2x - 2x) - 3
This simplifies to:
x^3 + x^2 - 3
So, your answer of x^3 + x^2 - 5x + 3 is incorrect.
4) Determine which values must be excluded from the domain.
x / (x^2 - 9)
To find the values that must be excluded from the domain, we need to identify any values of 'x' that would make the denominator zero. In this case, the denominator is (x^2 - 9).
We set the denominator equal to zero and solve for 'x':
x^2 - 9 = 0
(x - 3)(x + 3) = 0
From this, we see that x = 3 and x = -3 make the denominator zero. Therefore, we must exclude those values from the domain.
So, your answer of x = 3 and x = -3 is correct.
5) Solve the equation. The letters a, b, c are constants.
ax - b = c; a is not equal to 0.
To solve this equation for 'x', we need to isolate 'x' on one side of the equation.
First, add 'b' to both sides:
ax - b + b = c + b
ax = c + b
Next, divide both sides by 'a':
(ax)/a = (c + b)/a
x = (c + b)/a
So, your answer of x = (b + c)/a is correct.
6) Find 'c' in the following.
For 4x^2 - 12x + c to be a perfect square, 'c' must be?
The choices are 9, 3, -9, 0, or none of the above.
To make 4x^2 - 12x + c a perfect square, we need to have a perfect square trinomial. This means that the square of the second term (-12x) should be equal to four times the product of the first and third terms (4x^2 * c).
From this, we can set up the equation:
(-12x)^2 = 4(4x^2)(c)
Simplifying, we have:
144x^2 = 16cx^2
Dividing both sides by x^2:
144 = 16c
Finally, dividing both sides by 16:
c = 9/4
So, your answer of none of the above is incorrect. The correct answer is c = 9/4.
7) Write the statement using symbols.
The sum of four and x is the product of 5 and y.
The sum of four and x can be represented as: 4 + x.
The product of 5 and y can be represented as: 5y.
So, the statement can be written as: 4 + x = 5y.
Your answer of 4 + x = 5y is correct.
8) Write the number as a decimal.
3.875 x 10^-9
To write the number as a decimal, we can multiply 3.875 by 10 raised to the power of -9, which effectively shifts the decimal point 9 places to the left.
This gives us: 0.000000003875
So, your answer of 0.000000003875 is correct.
Overall, you have provided correct answers for questions 2, 4, 5, 7, and 8. The answers for questions 1, 3, and 6 are incorrect.