Answer:
26 rows
Step-by-step explanation:
this is like a rectangle length×width situation.
seats per row = s
number of rows = r
s × r = 884
s = r + 8
so, we can use e.g. the second equation in the first :
(r + 8) × r = 884
r² + 8r = 884
r² + 8r - 884 = 0
the general solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = r
a = 1
b = 8
c = -884
r = (-8 ± sqrt(8² - 4×1×-884))/(2×1) =
= (-8 ± sqrt(64 + 3536))/2 = (-8 ± sqrt(3600))/2 =
= (-8 ± 60)/2 = -4 ± 30
r1 = -4 + 30 = 26
r2 = -4 - 30 = -34
a negative number did not make any sense for the number of rows, so r = 26 is our answer.
Answer: Choice A
The triangles are congruent because both the corresponding sides of the triangles and the corresponding angles of the triangles are congruent.
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Explanation:
Congruent triangles are identical copies of one another. This means the corresponding pieces must be the same.
It's like saying two houses are identical, so that means the all the various parts (eg: front door, windows, etc) must be identical. If let's say the two front doors were different, then the houses wouldn't be completely identical.
Going back to the triangles, we know that the sides are congruent by the tickmarks
- side MN = side RS (single tickmark)
- side NP = side ST (double tickmarks)
- side MP = side RT (triple tickmarks)
That takes care of the first part of choice A.
And similarly, the angle markers tell us which angles are congruent
- angle M = angle R (single arc)
- angle N = angle S (90 degree angle marker)
- angle P = angle T (double arc)
That concludes the second part of choice A.
By the graph of a straight line through the origin with a slope equal to the unit rate
Answer:
Y-intercept is (0, -13)
X-intercept is at (13/5, 0)
Step-by-step explanation:
When it's in this form, y = mx + b, you automatically know what the y-intercept is (b).
So the y-intercept is (0, -13)
To algebraically find this, you'd plug in a 0 for x, since the y intercept is when it crosses the y-axis, which is located at x = 0.
To find the x intercept, you'd do the opposite of the y-intercept, which is plugging in a 0 for y and solving for x. The x-axis is located at y = 0.
0 = 5x - 13
13 = 5x
x = 13/5
The x-intercept is at (13/5, 0)
I hope this helped!
