Triangle RST is drawn inside rectangle RSNM. Point T is halfway between points M and N on the rectangle. The length of side RS is 9 in. and the length of side RM is 8 in. Show your work

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Triangle RST is drawn inside rectangle RSNM. Point T is halfway between points M and N on the rectangle. The length of side RS is 9 in. and the length of side RM is 8 in.

1) What is the area of triangle RST?

2)What is the ratio of area of  triangle RST to area of triangle RMT?

3) What is the area of rectangle RSMN to area of triangle TSN?

Diagram is attached.

1) 36 sq.in

2) 2:1

3) 4:1

Step-by-step explanation:

1) Area of triangle is; ½ × base × height.

For triangle RST, base = 9 in and height = 8 in

Thus, area of triangle RST = ½ × 9 × 8

= 36 sq.in

2)Area of triangle RMT = ½ × 8 × 9/2

= 18 sq.in

Ratio of area of RST to area of RMT = 36/18 = 2:1

3)Area of triangle TSN = ½ × 8 × 9/2 = 18 sq.in

Area of Rectangle RSNM = Length x width = 9 × 8 = 72 sq.in

Ratio of Area of Rectangle RSNM to Area of triangle TSN  = 72/18 = 4:1

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

the answer is b: 18

step-by-step explanation:

use the pythagorean theorem to .

a^2+b^2=c^2

plug 18 for "r"

the 2 legs are 18 and 24

18^2+24^2=c^2

324+576=c^2

900=c^2

c=30

30-12=18

18 is the radius

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