Answer: The answer is 8.
Step-by-step explanation: The first step is to convert the expression into figures. We shall call the unknown number Y. So if we are told “the square of a number,” that means Y squared, or better still, Y^2. Further we are told “the difference between the square of a number and 40” and that can be written as;
Y^2 - 40.
Next we are told that this expression is equal to 3 times that number (that is 3Y). That can now be written out as follows,
Y^2 - 40 = 3Y
If we move all expressions to one side of the equation, what we would have is,
Y^2 - 3Y -40 = 0
(Remember that when a positive value crosses to the other side of an equation it becomes negative and vice versa)
We now have a quadratic equation
Y^2 -3Y - 40 = 0
By factorizing we now have
(Y -8) (Y + 5) = 0
Therefore Y - 8 = 0 or
Y + 5 = 0
Hence, Y = 8 or Y = -5
Since we are asked to calculate the positive solution, Y = 8
Preeeeetty sure it's just 16 for that.
Are you sure you submitted the whole problem?
Angle DAC = 180-25 = 155 degrees
Angle ABC = 180 - 146 = 34 degrees
Angle ADC = 180 - 149 = 31 degrees
ABCD is a quadrilateral and angles in quadrilateral add up to 360 degrees
Angle BCD = 360 - (155 + 34 + 31)
= 360 - 220
= 140 degrees
Answer:
The scale factor for the resultant rectangle is
units.
Step-by-step explanation:
Given two rectangles with sides 3 units and 7.5 units.
We have to find the scaling factors so that we can obtain bigger rectangle of 7.5 units from smaller rectangle of 3 units.
Scale factor is defined as the ratio of corresponding side of given figure to the corresponding side of resulting figure.
That is 
Here, 
Hence, the scale factor for the resultant rectangle is units.
Answer:
≈ 62.8
Step-by-step explanation:
Using the equal ratios of
= 
, that is
= 
= 5, thus
5 × sector = 100π ( divide both sides by 5 )
sector = 20π = 20 × 3.14 = 62.8 units²
