The first few steps in solving the quadratic equation 9x2 + 49x = 22 − 5x by completing the square are shown. 9x2 + 49x = 22 − 5

Answer:

(Choice A) A 16:10

(Choice C) C 48:30

(Choice D) D 32:20

Step-by-step explanation:

The given ratio is

8:5

Select three ratios that correspond to 8:5

Check all options

(Choice A) A 16:10

= 16 / 10

Reducing by 2 yields

= 8 / 5

= 8:5

(Choice B) B 50:80

= 50 / 80

Reducing by 10 yields

= 5 / 8

= 5:8

(Choice C) C 48:30

= 48 / 30

Reducing by 6 yields

= 8 / 5

= 8:5

(Choice D) D 32:20

= 32 / 20

Reducing by 4 yields

= 8 / 5

= 8:5

(Choice E) E 64:35

= 64 / 35

The ratios equivalent to 8:5 are

(Choice A) A 16:10

(Choice C) C 48:30

(Choice D) D 32:20

The expression indicates that the total earnings of Mike over the two weeks amount to 2.05x dollars

Solution:

It is given that Mike earned x dollars during the first week at his new job,

While in the second week, he earned 5% more than the earnings of the first week.

To determine: Total earnings over the two weeks

From the information provided,

Earnings in the first week = "x" dollars

Earnings in the second week = 5% more than first week earnings

Thus,

Earnings in the second week = x + 5% of x

Therefore, earnings in the second week equal to 1.05x dollars

The total earnings over the two weeks:

Total earnings = Earnings from first week + Earnings from second week

Thus, the expression for the total earnings of Mike for both weeks is 2.05x dollars

The adjusted equation , indicating that the graph has been altered 4 units leftward and 6 units downward.

Clarification:

The parent equation is .

The transformed equation is .

Applying the function transformation rules, it's clear that the parent function has been modified into the function .

According to the function transformation rules,

indicates shifting the function b units to the left.

Thus, the transformed function reflects a shift 4 units to the left.

Additionally, from the function transformation rules, we understand that,

indicates shifting the function b units downward.

Consequently, the transformed function mirrors a shift of 6 units downward.

In summary, the adjusted equation , shows the graph shifted 4 units to the left and 6 units downward.

To find the maximum number of identical packs we see we have 72 pencils and 24 calculators.

This involves discovering the largest number that divides both 72 and 24 evenly,
which is known as the GCM or greatest common multiplier.

To determine the GCM, factor 72 into primes and group them:
72=2 times 2 times 2 times 3 times 3
24=2 times 2 times 2 times 3
Thus, the common grouping is 2 times 2 times 2 times 3, equating to 24.
Therefore, the maximum number of packs is 24.

For pencils:
72 divided by 24=3
Resulting in 3 pencils per pack.

For calculators:
24 divided by 24=1
So, 1 calculator per pack.

The outcome is 3 pencils and 1 calculator in each pack.

Answer:

Wyjaśnienie krok po kroku:

Załóżmy, że prostokąt ma wierzchołki (x,y,z) w dodatnim oktancie.  Prostokątny pudełko musi być symetryczne względem wszystkich trzech osi.

Wtedy jego boki to

Objętość =

Maksymalizuj objętość przy założeniu

tj.

Użyj mnożników Lagrange'a, mamy

przy maksimum

Dzieląc otrzymujemy

Podobnie

Zatem otrzymujemy

Stąd wymiary to

(2x,2y,2z)

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