The American College of Sports Medicine considers age as one factor when it recommends low and
high heart rates during workout sessions.
For safe and efficient exercise, your heart rate should be between 55% and 90% of the maximum
heart rate level. The maximum heart rate is calculated by subtracting a person's age from 220
beats per minute.
(Let a represent a person's age and h represent the person's recommended heart rate.)
1. The following equation represents the low value for heart rate. Simplify the equation.
h = .55(220-a)
2. The following equation represents the high value for heart rate. Simplify the equation.
h = .90(220-a)
3. Use these two expressions to write a system of inequalities that represents the heart rate range
for safe and efficient exercise. (Hint: you need to write two separate inequalities)

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)