Answer:there are 14 5point problems and 15 2point problems on the test.
Step-by-step explanation:
x represents number of 5 point questions and y represents questions worth 2 points.
The total number of questions in the test is 29. It means that
x + y = 29
x = 29 - y
Mr. Martin’s math test is worth 100 points. It means that
5x + 2y = 100 - - - - - - - - -1
Substituting x = 29 - y into equation 1, it becomes
5(29 - y) + 2y = 100
145 - 5y + 2y = 100
- 5y + 2y = 100 - 145
- 3y = - 45
y = - 45/-3
y = 15
x = 29 - y = 29 - 15
x = 14
The area of a triangle can be calculated as half the product of base length and height. We want the area to be no greater than 10 in².
a) (1/2)(4)(2x-3) ≤ 10
b) 4x -6 ≤ 10 . . . . . simplify
... 4x ≤ 16 . . . . . . . .add 6
... x ≤ 4 . . . . . . . . . divide by the coefficient of x
c) The maximum value of (2x -3) in is (2·4 -3) in = 5 in.
The triangle should be no more than 5 in high to have an area less than 10 in².
Answer:
m<F = 79 degrees
Step-by-step explanation:
As per the given information;
m<E = 22, the triangle EDF (the one that is given in the picture) is isosceles (meaning that the sides are congruent).
In an isosceles triangle, (a triangle where the sides are congruent) the base angles (the angles opposite to the two congruent sides) are also congruent. One should also know, that in an isosceles triangle, like in any triangle, the sum of the measures of the angles equals 180 degrees.
Using this we can say that
m<D = m<F
To keep it simple while solving the problem, let's say that they have a value of x degrees.
So,
m<E + m<D + m<F =180
Subsitute
22 + x + x = 180
Simplify and inverse operations
22 + x + x = 180
-22 -22
2x = 158
/2 /2
x = 79
So the measure of <D and <F is 79 degrees.
Answer:
The answer is A.
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
2+6m+7=57
6m=57-7-2
6m=50-2
6m=48
m=48/6
m=8
