First of all we can draw a parallel line to divide the figure into a triangle and a rectangle as shown in the figure. To find the area of our rectangle, remember that the area of a rectangle is length times width, so
. Since we know for our figure that the length and width of our rectangle are 13cm and 6cm respectively, lets replace those values in our formula to get its area:
Similarly, the area of a triangle is one half times base times height, so
. Since we know that our base is 8cm and our height 6cm, lets replace those values in our equation to find the area of our triangle:
Now the only thing left is add our areas:
We can conclude that the correct answer is <span>
A. 102</span>
<h3>
Answer: True</h3>
Explanation:
Technically you could isolate any variable you wanted, from either equation. However, convention is to pick the variable in which isolating it is easiest, and most efficient.
The key thing to look for is if there's a coefficient of 1. This is found in the second equation for the y term. Think of -4x+y = -13 as -4x+1y = -13. Due to the coefficient of 1, when solving for y we won't involve messy fractions.
If you were to solve for y, then you'd get y = 4x-13, which is then plugged in (aka substituted) into the first equation. That allows you to solve for x. Once you know x, you can determine y.
Answer:
If the price of a product decreases from $10 to $8, leading to an increase in quantity demanded from 40 to 60 units.
Step-by-step explanation:
Answer:
Step-by-step explanation:
f(x) = x^2 + 4x + 4
f(x + a) = (x + a)^2 + 4(x + a) + 4
f(x + a) = x^2 + 2ax + a^2 + 4x + 4a + 4 Now combine like terms and use the distributive property.
f(x + a) = x^2 + (2a + 4)x + a^2 + 4a + 4
We are told that f(x + a) = x^2 - 6x + 9
So that means that
2a + 4 = - 6 Subtract 4 from both sides.
2a = - 6 - 4
2a = - 10 Divide by 2
a = - 10/2
a = - 5.
But you are not finished. You have to check the last part.
a^2 + 4x + 4 = 9
(a + 2)^2 = 9
Take the square root of both sides
sqrt(a+ 2)^2 = +/- 3
a+2 = 3
a = 1.
Does this work or is it extraneous? It is extraneous because it will not work for 2(a) + 4 = - 6
You get 6 = - 6 which is not correct. But you did give the second best answer.
a + 2 = - 3
a = - 3 - 2
a = - 5 which agrees with your previous answer.
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This is an extremely hard or tricky or sneaky problem. It takes a lot of conniving to get the right answer and 1 is not a left field answer. It just does not happen to be correct.
Given the angle:
-660°
Let's find the coterminal angle from 0≤θ≤360.
To find the coterminal angle, in the interval given, let's keep adding 360 degrees to the angle until we get the angle in the interval,
We have:
Coterminal angle = -660 + 360 = -300 + 360 = 60°
Therefore, the coterminal angle is 60°.
Since 60 degrees is between 0 to 90 degrees, is is quadrant I.
60 degrees lie in Quadrant I.
Also since it is in quadrant I, the reference angle is still 60 degrees.
ANSWER:
The coterminal angle is 60°, which lies in quadrant I, with a reference angle of 60°
