Hi, thank you for posting your question.
This problem can be solved through ratio and proportion which can be applied to similar triangles like that shown in the figure. By ratio and proprotion,
MP/MN = MB/MA
81.9/67.2 = x/(67.2-32)
Thus, x = 42.9
An absolute value never equals to a negative number. The purpose of an absolute value is to remove the negative sign. So the absolute value of -5 is 5
Answer:
2 imaginary roots
Step-by-step explanation:
Answer:
Select 1, 4 and 5
The slope is -1/10
The x intercept is 100
The y intercept shows the initial amount on the card in dollars
Answer:
PQ = 34.4
Step-by-step explanation:
First, we know that the angles in a triangle add up to 180 degrees. Therefore, angle M = 48 and angle R = 74
Next, because there is a corresponding angle in each triangle, they are similar. This means that the ratios between corresponding sides are the same. For example, the side opposite angle O (MN) over the side opposite angle R (PQ) is equal to the side opposite angle N (OM) over the side opposite angle Q (RP)
This can be written as MN/PQ = OM/RP. Note that both the numerators are on the same triangle, and MN and PQ correspond, as well as OM and RP.
We are given MN, NO, and QR. Because NO is opposite a 48 degree angle (angle M) as well as QR (angle P), we can say that NO/QR = another ratio of a pair of corresponding sides. Because we want to find PQ, and both PQ and MN are opposite 74 degree angles, we can say that
NO/QR = MN/PQ
Thus,
11/27 = 14/PQ
multiply both sides by PQ to remove a denominator
PQ * 11/27 = 14
multiply both sides by 27 to remove the other denominator
PQ * 11 = 14 * 27
divide both sides by 11 to isolate the PQ
PQ = 14 * 27 /11
PQ = 34.4
