X+x²=30
x²+x-30=0
(x+6)(x-5)=0
x=-6 or x=5
Answer:
the third option
Step-by-step explanation:
what does that mean ?
to "rationalize" it is to transform it into a rational number (that is a number that can be described as a/b, and is not an endless sequence of digits after the decimal point without a repeating pattern).
a square root of a not square number is irrational (not rational).
so, what this question is asking us to get rid of the square root part in the denominator (the bottom part).
for this we need to multiply to and bottom with the same expression (to keep the whole value of the quotient the same) that, when multiplied at the bottom, eliminates the square root.
what can I multiply a square root with to eliminate the square root ? the square root again - we are squaring the square root.
so, what works for 9 - sqrt(14) as factor ?
we cannot just square this as
(9- sqrt(14))² = 81 -2sqrt(14) + 14
we still have the square root included.
but remember the little trick :
(a+b)(a-b) = a² - b²
without any mixed elements.
so, we need to multiply (9-sqrt(14)) by (9+sqrt(14)) to get
81-14 = 67 which is a rational number.
therefore, the third answer option is correct.
<span>I can be wrong, but I think that the answer is: To find the values of p, q, r and s, you should start by finding all factor pairs of the leading coefficiant and constant term. </span>
Answer:
Store 2
Step-by-step explanation:
Given
1. $4.50 for 5 pounds
2. $1/5 for 1/3 pounds
3. $4.00 for 5 pounds
Required
Determine the store with the lowest unit rate
To do this, we simply divide the price by the weights in each store
For Store 1:
For Store 2:
For Store 3:
<em>Comparing the unit rates of the three stores, we can conclude that store 2 offers the least unit rate</em>
Answer:
option A: x + 1.5y ≤ 20
option C: x + 3y ≤ 36
option D: x ≥ 0
option H: y ≥ 0
Step-by-step explanation:
It says to assume x = the number of packages of pasta and y = the number of jars of pasta sauce.
Since the number of items can not be a negative number, we have x ≥ 0 and y ≥ 0.
Condition: He has $36, and can carry up to 20 pounds of food in his backpack.
Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar.
If he buys 'x' packs of pasta and 'y' jars of pasta sauce, then:-
Total cost = 1x + 3y ≤ 36 dollars.
and Total weight = 1x + 1.5y ≤ 20 pounds.
Hence, we have four inequalities:-
option A: x + 1.5y ≤ 20
option C: x + 3y ≤ 36
option D: x ≥ 0
option H: y ≥ 0
