The graph of the function p(x) = −0.74x2 + 22x + 75 is shown. the function models the profits, p, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands:
graph of a parabola opening down passing through points negative 3 and 9 hundredths comma zero, zero comma 75, 5 and 6 tenths comma 175, 14 and 87 hundredths comma 238 and 51 hundredths, 24 and 13 hundredths comma 175, and 32 and 82 hundredths comma zero
if the company wants to keep its profits at or above $175,000, then which constraint is reasonable for the model?
a.)−3.09 ≤ x ≤ 5.6 and 24.13 < x ≤ 32.82
b.)0 ≤ x < 5.6 and 24.13 < x ≤ 32.82
c.)−3.09 ≤ x ≤ 32.82
d.)5.6 ≤ x ≤ 24.13

Kylie explained that (-4x+9)^2 will result in a difference of squares because (-4x+9)^2 (-4x+9)^2 =(-4x)^2+(9)^2=16x^2+81

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality

The length of a rectangle plus its width is 24 cm. the area is 143 square cm. what are the length and width of the rectangle?