Answer:
The perimeter (to the nearest integer) is 9.
Step-by-step explanation:
The upper half of this figure is a triangle with height 3 and base 6. If we divide this vertically we get two congruent triangles of height 3 and base 3. Using the Pythagorean Theorem we find the length of the diagonal of one of these small triangles: (diagonal)^2 = 3^2 + 3^2, or (diagonal)^2 = 2*3^2.
Therefore the diagonal length is (diagonal) = 3√2, and thus the total length of the uppermost two sides of this figure is 6√2.
The lower half of the figure has the shape of a trapezoid. Its base is 4. Both to the left and to the right of the vertical centerline of this trapezoid is a triangle of base 1 and height 3; we need to find the length of the diagonal of one such triangle. Using the Pythagorean Theorem, we get
(diagonal)^2 = 1^2 + 3^2, or 1 + 9, or 10. Thus, the length of each diagonal is √10, and so two diagonals comes to 2√10.
Then the perimeter consists of the sum 2√10 + 4 + 6√2.
which, when done on a calculator, comes to 9.48. We must round this off to the nearest whole number, obtaining the final result 9.
Depending on the values of 'r', 't', and 'e', the numerical value of that expression
might have many factors.
For example, if it happens that r=5, t=1, and e=4 for an instant, then, just
for a moment, (r + t)(e) = (5+1)(4) = 24, and the factors of (r+t)(e) are
1, 2, 3, 4, 6, 8, 12, and 24 . But that's only a temporary situation.
The only factors of (r+t)(e) that don't depend on the values of 'r', 't', or 'e' ,
and are always good, are (<em>r + t</em>) and (<em>e</em>) .
Classic Algebra and its unnecessarily complicated sentence structure. As you may have probably known, Algebra has its own "vocabulary set".
"the length of a rectangle exceeds its width by 6 inches" -> length is 6 in. longer than width -> l= w + 6
Since we're solving for the length and width, let's give them each variables.
length = l = w+6
width = w
The next bit of information is "the area is 40 square inches"
Applying the formula for the area of a rectangle we can set up:
l x w = 40
replace "l", or length, with it's alternate value.
(w+6) x w = 40
distribute
+ 6w = 40
subtract 40 from both sides
+ 6w - 40 = 0
factor
(w - 4)(w + 10) = 0
solve for w
w= 4, or -10
So great, we have 2 values; which one do we choose? Since this problem is referring to lengths and inches, we will have to choose the positive value. There is not such thing as a negative distance in the real world.
We now have half of the problem solved: width. Now we just need to find the length which we can do but substituting it back into the original alternate value of l.
l = w + 6
w=4
l = 4 + 6 = 10
The length is 10 in. and the width is 4 in. Hope this helps!
The answer is 16. To solve this problem, it will look like this:
5 n + n = 24
So, 6(4) = 24. n=4
With this equation, you can see that 4 kids walk to school and 20 take the bus. Then you need to do 20 - 4 = 16. So 16 more kids take the bus than walk to school.
Another way to look at it...
We know there are 5 times as many bus kids as there are walkers.
walkers - n
bus kids - n+n+n+n+n
6n = 24 (the total number of students), which can translate to 6 x n = 24. We know that 6x4=24, so n=4. The number of kids that walk is 4. The number of kids on the bus is 20. So subtract the bus kids from the walking kids, and that leaves us the answer. 16 more students ride the bus than those who walk. I hope that helped.
Answer:
Richard is making $9.6 per hour now
Step-by-step explanation:
Given:
Initial amount Richard was earning = $10/hr
Due to lass in productivity 20% pay was cut
Amount Richard was earning after 20% pay cut = $8/hour.
After few again due to increase in productivity Diane gave a 20% raise.
To Find:
How much is Richard making now = ?
Solution:
Let the amount that Richard is making now be x
Then
x = 8+ 20% of 8
x =
x =
x =
x = 9.6