Answer:
Q1: p = - 33
Q2: d = - 99
Q3: t = - 13
Step-by-step explanation:
Q1: 
We solve this taking LCM.
We get: 


Q4: 
Again we proceed like Q1 by taking LCM.
We get: 



Q7: 5t + 12 = 4t - 1
We club the like terms on either side.



Hence, the answer.
Answer: 23 degrees
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Explanation:
Using the inscribed angle theorem we can connect the central angle ABC and the inscribed angle ADC. The reason why is because they both cut off the minor arc AC
Angle ABC is given to be 46 degrees, the formula we use is shown below
central angle = 2*(inscribed angle)
angle ABC = 2*(angle ADC)
46 = 2*(angle ADC)
46/2 = 2*(angle ADC)/2 ... divide both sides by 2
23 = angle ADC
angle ADC = 23 degrees
Answer:
The length of each blue trim is 17.2 inches
Step-by-step explanation:
Given
See attachment for banner
Required
The length of each blue trim
Since all 4 triangles are equal, then the dimension of 1 triangle is:


The hypotenuse (x) of the triangle blue trim is represented by the blue trim
So:

This gives



Take square root


Check the picture below.
make sure your calculator is in Degree mode.
<h3>
Answer: -2w^2 + 25w = 25 or -2w^2 + 25w - 25 = 0</h3>
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Explanation:
Refer to the diagram below. The width is w. We have two opposite and parallel sides equal to this. The other two parallel congruent sides are L = 25-2w meters long. We start with the total amount of fencing, and then subtract off the two width values, so 25-w-w = 25-2w.
The area of the rectangle is
Area = length*width
Area = L*W
Area = (25-2w)*w
Area = 25w - 2w^2
Area = -2w^2 + 25w
Set this equal to the desired area (25 square meters) to get
-2w^2 + 25w = 25
and we can subtract 25 from both sides to get everything on one side
-2w^2 + 25w - 25 = 0
side note: The two approximate solutions of this equation are w = 1.0961 and w = 11.4039 (use the quadratic formula or a graphing calculator to find this)