Wilda can do the job in 4 hours ... she does 1/4 (or 0.25) of it each hour.
Karla can do it in 5 hours ... she does 1/5 (or 0.2) of it each hour.
Wilda worked alone for 1 hour ... 0.25 of the job was done before her helper
arrived. So only 0.75 of the job remained to be done together.
Working together, they accomplish (0.25 + 0.2) = 0.45 of the job in 1 hour.
How many times do they need to do 0.45 of the job in order to finish
the 0.75 of it that remains ? That's the number of hours it will take them,
working together.
0.75 / 0.45 = <em>1 and 2/3</em>
After Wilda worked alone for 1 hour and Karla came along to join her, it will
take them another <em>1 hour and 40 minutes</em> to finish the job and go for a swim.
Answer:
MNK = TRP
MN is congruent to TR.
X = 6.3
Step-by-step explanation:
MNK is congruent to TRP because the two triangles are congruent, which is a given statement. This also means that all side and angle measures will be congruent. Because of this, it can be inferred that MN is congruent to TR and they have equal side length measures. This means that TR measures 20. This means that 3X - 1 = 20. By solving we can get 6.33.
Okay. so I'm gonna assume you know what factor out means--were gonna take out 5/6. what we need to know is, how does that affect our ending number 2/3? well, we're gonna have 5/6 times some stuff first off, right?
5/6 ( )
so what's in the parenthesis? well, if we distribute in our mind, S would just have to be by itself for it to work out. so we have
5/6 ( s )
but what about 2/3? well, if we're multiplying everything on the inside by 5/6, how can be get it to cancel and leave 2/3 alone? we could divide 2/3 by 5/6, right?
5/6 ( s + (2/3) / (5/6) )
now, when we distribute our 5/6, we'll have just 2/3 at the end. now let's simplify that end term so it looks a little better. if we divide by a fracion, that's the same as multiplying by the flipped version, so let's do that.
2/3 / 5/6 = 2/3 × 6/5 = 2 (6) / 5 (3) = 12/15
we can reduce 12/15 by dividing the top and bottom by three.
= 4/5
so our final answer would be:
5/6 [S + 4/5] you can redistribute to make sure it matches. Anyway, hope that helps!
Answer:
y = 5x+7
Step-by-step explanation:
Parallel lines have the same slope so y = 5x+9 is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 5
The new line will have a slope of 5
y = 5x+b
We know a point on the line (-2,-3)
Substitute this point into the equation
-3 = 5(-2)+b
-3 = -10+b
-3+10 = b
7 = b
y = 5x+7
We are given the following:
- parabola passes to both (1,0) and (0,1)
<span> - slope at x = 1 is 4 from the equation of the tangent line </span>
<span>First, we figure out the value of c or the y intercept, we use the second point (0, 1) and substitute to the equation of the parabola. W</span><span>hen x = 0, y = 1. So, c should be equal to 1. The</span><span> parabola is y = ax^2 + bx + 1 </span>
<span>Now, we can substitute the point (1,0) into the equation,
</span>0 = a(1)^2 + b(1) + 1
<span>0 = a + b + 1
a + b = -1 </span>
<span>The slope at x = 1 is equal to 4 which is equal to the first derivative of the equation.</span>
<span>We take the derivative of the equation ,
y = ax^2 + bx + 1</span>
<span>y' = 2ax + b
</span>
<span>x = 1, y' = 2
</span>4 = 2a(1) + b
<span>4 = 2a + b </span>
So, we have two equations and two unknowns,<span> </span>
<span>2a + b = 4 </span>
<span>a + b = -1
</span><span>
Solving simultaneously,
a = 5 </span>
<span>b = -6</span>
<span>Therefore, the eqution of the parabola is y = 5x^2 - 6x + 1 .</span>
