Answer:
the larger number is 50
Step-by-step explanation:
Notice there are two unknown numbers. Let's address the smaller one as x and the larger one as y. now we can write two equations from translating the phrases given into algebraic expressions:
"the sum of two numbers is 80" can be written as:
Now the second phrase:
"The ratio of those two numbers is 3/5"
Notice here that in our ratio we need to use our small number (x) in the numerator of the quotient, and the larger number (y) in the denominator to make it in agreement with the small and larger numbers of the ratio 
, and solve for x:
Replace the value of x we just obtained in the first equation we wrote, so we obtain one equation with only one unknown hat we should be able to solve:
Therefore the larger number (y) equals 50.
Answer:
Step-by-step explanation:
Divide both sides by the square root of 2. If you are looking for an exact answer that is rationalized, it would be found by multiplying 6/sqrt(2) * sqrt(2)/sqrt(2) to get
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The domain is the horizontal extent. Since there are arrows on both ends of the graph, the horizontal extent is from -∞ to ∞.
The range is the vertical extent. The graph shows a minimum at y=-2, which value is in the range. Expressed in interval notation, it is [-2, ∞).
Please note that the "end behavior" of y tends to +∞ in for either direction of x.
__
The graph is "increasing" where it has positive slope, for 3 < x. It is "decreasing" where it has negative slope, for x < 3.
The graph is positive where it is above the x-axis. The points on the x-axis are not part of the "positive" interval(s). You will note there are two intervals where the graph is positive. It isn't difficult to find the answer choice that is a union of two intervals.
The graph is negative where hit is below the x-axis. Again, the points at x=1 and x=5 are not part of that interval, so it is expressed using curved brackets.
Answer:
1 - 9/7n
Explanation:
1/7 - 3(3/7n - 2/7)
<em>distribute</em><em> </em><em>the</em><em> </em><em>3</em><em> </em><em>with</em><em> </em><em>the</em><em> </em><em>2</em><em> </em><em>fractions</em><em> </em><em>inside</em><em> </em><em>the</em><em> </em><em>parenthesis</em>
1/7 - 9/7n + 6/7
<em>add</em><em> </em><em>like</em><em> </em><em>terms</em><em> </em><em>(</em><em>1</em><em>/</em><em>7</em><em> </em><em>+</em><em> </em><em>6</em><em>/</em><em>7</em><em>)</em>
7/7 - 9/7n
<em>or</em>
1 - 9/7n
First we note symmetry in the expression's coefficients.
We also note that 7*3=21, and 7+3=10.
From the rational roots theorem, we are tempted to try with 3 and 7 as coefficients of the factors.
Try
(7b+3)(3b+7)=21b^2+(49+9)b+21
By switching the sign of 3b+7 to 3b-7, we get the signs right, to check:
(7b+3)(3b-7)=21b^2+(9-49)b-21=21b^2-40b-21 ....right!
So
(7b+3)(3b-7)=21b^2-40b-21
