Kyle is making a frame for a rectangular piece of art. The length of the frame is 3 times the width, as shown below. If Kyle use
s 18 feet of wood to make the frame, what is the length of the frame?
1 answer:
Answer:
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6.75 feet |
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Step-by-step explanation:
Let the width be x. If the width is x, the the length has to be 3x because in the question it says that the length is 3 times the width.
Since this is a rectangle, the opposite side has the same measure, like in the attachment below.
To find the perimeter, you would add up all the sides.
3x+3x+x+x
=6x+2x
=8x
It is also given in the question that he uses 18 feet. Which means that the perimeter is 18 feet. But you figured out that 8x is ALSO the perimeter. This means that you can say: 8x=18.
Solve for x, 18/8=9/4=2.25.
You want the length, which is 3x. So 3(2.25) is your answer.
3(2.25) = 6.75
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We have the following data:
Margin of Error = E = 2.7 % = 0.027
Sample size = n = 900
Proportion of adults in favor = p = 60% = 0.6
We need to find the confidence level. For this first we need to find the z value.
The margin of error for a population proportion is given as:
Using the values, we get:
As, seen from the z table, z=1.65 corresponds to the confidence level 90%. So, the answer to this question is option B
Margin of Error = E = 2.7 % = 0.027
Sample size = n = 900
Proportion of adults in favor = p = 60% = 0.6
We need to find the confidence level. For this first we need to find the z value.
The margin of error for a population proportion is given as:
Using the values, we get:
As, seen from the z table, z=1.65 corresponds to the confidence level 90%. So, the answer to this question is option B
Step-by-step explanation:
by switching the places of x and y ans solving for y
Answer:
Step-by-step explanation:
The quadratic formula for a equation of form
ax²+bx + c = 0 is
For the first equation,
x²+3x-4=0,
we can match that up with the form
ax²+bx + c = 0
to get that
ax² = x²
divide both sides by x²
a=1
3x = bx
divide both sides by x
3 = b
-4 = c
. We can match this up because no constant multiplied by x could equal x² and no constant multiplied by another constant could equal x, so corresponding terms must match up.
Plugging our values into the equation, we get
as our possible solutions
Plugging our values back into the equation, x²+3x-4=0, we see that both f(-4) and f(1) are equal to 0. Therefore, this has 2 real solutions.
Next, we have
x²+3x+4=0
Matching coefficients up, we can see that a = 1, b=3, and c=4. The quadratic equation is thus
Because √-7 is not a real number, this has no real solutions. However,
(-3 + √-7)/2 and (-3 - √-7)/2 are both possible complex solutions, so this has two complex solutions
Finally, for
4x² + 1= 4x,
we can start by subtracting 4x from both sides to maintain the desired form, resulting in
4x²-4x+1=0
Then, a=4, b=-4, and c=1, making our equation
Plugging 1/2 into 4x²+1=4x, this works as the only solution. This equation has one real solution