Answer:
The prime factorization of 42 is 2 × 3 × 7
Step-by-step explanation:
John gets 12, Walt, Matt, and Richie get 4 each
Y = 15
180 = 142 + 2y + 8
180 = 150 + 2y
30 = 2y
y = 15
x = 30.5
142 = 4x + 20
122 = 4x
x = 30.5
Answer:
The the equation of the line through the points (8, -2) and (5, 5) in slope-intercept form is
![y=-\frac{7}{3} x+\frac{50}{3}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B7%7D%7B3%7D%20x%2B%5Cfrac%7B50%7D%7B3%7D)
Step-by-step explanation:
Let's start by calculation the slope of the line by finding the slope of the segment that joins the two given points (8, -2) and (5, 5):
![slope=\frac{y_2-y_1}{x_2-x_1} \\slope=\frac{5-(-2)}{5-8}\\slope=\frac{7}{-3} \\slope=-\frac{7}{3}](https://tex.z-dn.net/?f=slope%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%5C%5Cslope%3D%5Cfrac%7B5-%28-2%29%7D%7B5-8%7D%5C%5Cslope%3D%5Cfrac%7B7%7D%7B-3%7D%20%5C%5Cslope%3D-%5Cfrac%7B7%7D%7B3%7D)
Now we use this slope in the general slope-intercept form of a line;
![y=mx+b\\y=-\frac{7}{3} x+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5Cy%3D-%5Cfrac%7B7%7D%7B3%7D%20x%2Bb)
and then we calculate the value of the intercept "b" by using one of the given points through which the line must pass (for example (5,5) ), and solving for b:
![y=-\frac{7}{3} x+b\\5=-\frac{7}{3} (5)+b\\5=-\frac{35}{3} +b\\b=5+\frac{35}{3}\\b=\frac{50}{3}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B7%7D%7B3%7D%20x%2Bb%5C%5C5%3D-%5Cfrac%7B7%7D%7B3%7D%20%285%29%2Bb%5C%5C5%3D-%5Cfrac%7B35%7D%7B3%7D%20%2Bb%5C%5Cb%3D5%2B%5Cfrac%7B35%7D%7B3%7D%5C%5Cb%3D%5Cfrac%7B50%7D%7B3%7D)
The the equation of the line is
![y=-\frac{7}{3} x+\frac{50}{3}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B7%7D%7B3%7D%20x%2B%5Cfrac%7B50%7D%7B3%7D)
Answer:
Unable to be determined.
Step-by-step explanation:
AA postulate : 2 corresponding angles that are congruent.
SSS theorem : 3 sides of a triangle that are equal to another triangle's 3 sides.
SAS postulate: 2 sides and their included angle are congruent to another triangle's 2 sides and their included angle.
This would seem to follow the SAS postulate at first, but the angle we are provided is not the included angle of the sides. In triangle ABC, we are analyzing lines AB and AC. Their included angle is A, but we are given the measure for angle B.
Same with DEF; we analyze DE and DF, who share angle A, but we are given angle E as a measure.
Therefore, we cannot determine if the triangles are similar or not.