Pythagorean theorem
c2 = a2 + b2
58^2 = 42^2 + b2
3364 = 1764 + b2
1600 = b2
b = 40
Answer:
x=7−√10 or x=7+√10
Step-by-step explanation:
−5(x−7)2+30=−20
Step 1: Simplify both sides of the equation.
−5x2+70x−215=−20
Step 2: Subtract -20 from both sides.
−5x2+70x−215−(−20)=−20−(−20)
−5x2+70x−195=0
For this equation: a=-5, b=70, c=-195
−5x2+70x+−195=0
Step 3: Use quadratic formula with a=-5, b=70, c=-195.
x=
−b±√b2−4ac
2a
x=
−(70)±√(70)2−4(−5)(−195)
2(−5)
x=
−70±√1000
−10
x=7−√10 or x=7+√10
Answer:
Let's define:
A = # of students in group A
B = # of students in group B
C = # of students in group C.
"The total number of students who could attend a field trip is represented by the variable t."
This can be written as:
A + B + C = t.
"The number of students in Group A is less than the number in Group B."
Here we have a strictly "less than", then this is written as:
A < B.
"Group A has 6 students more than 1/4 the total number of students"
A = t/4 + 6
"Group B has 3 less than the total number of students"
B = t - 3.
Then we have the equations:
A + B + C = t.
A = t/4 + 6
B = t - 3.
A < B.
We could replace the second and third equatio in the fourth one, to get:
t/4 + 6 < t - 3.
t/4 + 9 < t
9 < t - t/4
9 < t*(4/4 - 1/4)
9 < t*(3/4)
(4/3)*9 < t
12 < t.
Then we found an inequality that defines the minimum possible value of t,
Answer: for number 1, Begin at the point, draw a vertical line either up or down to the x-axis to get the x-coordinate.
Begin at the point, draw a horizontal line either to the left or right of the y-axis to get the y-coordinate.
And for number 2, if the image is smaller than the pre image, it is an enlargement. If the image is larger than the pre image, it is a reduction. :)
Step-by-step explanation:
In a two-dimensional plane, coordinates of a point define its exact location. The coordinate plane has two axes that are perpendicular to each other which are known as the x and y axis.
To find out the coordinates of a point in the coordinate system, follow the following procedure.
Begin at the point, draw a vertical line either up or down to the x-axis to get the x-coordinate.
Begin at the point, draw a horizontal line either to the left or right of the y-axis to get the y-coordinate.
The x-coordinate and the y-coordinate determine the new coordinates of a point.
