MATHEMATICS MIDDLE SCHOOL

a flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 23 feet more than the length of the shortest side. Find the dimensions if the perimeter is 139 feet

Answers

Answer 1

Answer:

Let the short side be x

One side = 2x

And the third side = x+23

x+2x+x+23=139

4x=116

x=4

The other side = 5

The third side= 27

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What is the largest positive integer value of m such that the equation 3x^2 - mx + 7 = 0 has no real solutions?

Answers

use determinant
in form ax²+bx+c=0
when b²-4ac>0, it has 2 real roots
when b²-4ac=0, it has 1 real root
when b²-4ac<0, it has no real roots
so

we solve for no real roots
b²-4ac<0
a=3
c=7
b=-m

(-m)²-(4)(3)(7)<0
m²-84<0
add 84 both sides
m²<84
sqrt both sides
m<9.1 about
nearest integer
round down
m=9

answer is m=9

What are the domain and range of the relation (–4, 2), (0, 1), (0, 5), (8, 10)? A.Domain: {–4, 0, 8}; Range: {2, 1, 5, 10} B.Domain: {2, 1, 5, 10}; Range: {–4, 0, 8} C.Domain: {–4, 0, 5, 10}; Range: {2, 1, 8} D.Domain: {–4, 2, 0, 1, 5, 8, 10}; Range: {–4, 2, 0, 1, 5, 8, 10}