*the length of the shorter altitude and the shorter side of a parallelogram are 9cm and 82 cm. the length of a longer diagonal is 15 cm. what is the area of this parallelogram?

Refer to the image attached.

Given: Altitude AC = 9 cm, Diagonal AD = 15 cm, side AB = 82 cm.

To find: Area of parallelogram

Solution:

Since, area of parallelogram = base height

=

We have to determine the base BD.

Consider the triangle ABC,

by Pythagoras theorem,

BC = 81.5 cm

Now, Consider the triangle ACD,

by Pythagoras theorem,

CD = 12 cm

Now, base BD = BC + CD

= 81.5+12

= 93.5 cm

Area of parallelogram = BD

= 93.5 x 9

= 841.5 square centimeters.

Therefore, the area of parallelogram is 841.5 square centimeters.

the ratio of grapes to blueberries she should use is 12: 3

step-by-step explanation:

if mandie is making 15 cups of fruit salad, the ratio of grapes to blueberries she should use is 12: 3.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."