Answer:
1 ± √47
Step-by-step explanation:
Combine like terms in 2x^2 +3 x-7 =x^2 +5x +39:
2x^2 - x^2 = x^2 (first term);
3x - 5x = -2x (second term);
-7 - 39 = -46 (third term)
Then we have, all on the left side, x^2 - 2x - 46, which is a quadratic equation. Here the coefficients are a = 1, b = -2 and c = -46.
Then the discriminant, b^2 - 4ac, is:
(-2)^2 - 4(1)(-46) = 4 + 184.
The roots are:
-(-2) ±√188 2 ± √4√47
------------------- = -------------------
2 2
= 1 ± √47 (last of the answer choices)
=
x = ------------------
Answer:
Alan would need 13.2 gallons of gas to drive 286 miles.
Step-by-step explanation:
This question can be solved in a number of ways. First, you can find the unit rate, or the approximate amount of miles that Alan can drive per gallon of gas. Since we know that Alan drove 260 miles using 12 gallons of gas, we can divide the number of miles by the number of gallons to get the amount of miles per gallon: 260 ÷12 = 21.67miles per gallon. In order to find the amount of gas needed to drive 286, we take the total mileage divided by the unit rate: 286 ÷ 21.67 = 13.2 gallons. The other way to solve is using a proportion with a variable, for example: 260/12 = 286/x. Using cross-multiplication and divide, we get 260x = 3432, divide both sides of our equation by 260 to isolate the variable and solve for x = 13.2 Either method will result in the same answer.
<em>Directed numbers</em> are numbers that have either a <u>positive</u> or <u>negative </u>sign, which can be shown on a <em>number line</em>. Therefore, point F is Fifteen-halves of line <em>segment</em> DE.
A <u>number line</u> is a system that can show the positions of <em>positive</em> or <em>negative</em> numbers. It has its <em>ends</em> ranging from <em>negative infinity</em> to <em>positive infinity</em>. Thus any <em>directed</em> number can be located on the line.
Directed numbers are numbers with either a <u>negative</u> or <u>positive </u>sign, which shows their direction with respect to the <em>number line.</em>
In the given question, the <u>distance</u> between points D and E is <em>9 units</em>. So that <em>dividing</em> 9 units in the ratio of 5 to 6, we have;
x 9 = 
= 
Therefore, the <em>location</em> of point F, which <u>partitions</u> the directed line segment from d to E into a 5:6 ratio is . Thus the<em> answer</em> is <u>Fifteen-halves.</u>
For further clarifications on a number line, visit: brainly.com/question/23379455
#SPJ1
Answer: 364 with a remainder of 28
Step-by-step explanation:
14952/41
41 goes into 149 3 times
149 - (41 *3)
149 - 123 = 26
41 goes into 265 6 times
265 - (41*6)
265 - 246 = 19
41 goes into 192 4 times
192 - (41*4)
192 - 164 = 28
So 14952/41 = 364 with a remainder of 28
