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3 years ago

15 - 4x = 6 - 3xwhats the answer.

Mathematics

1 answer:

Makovka662 [10]3 years ago

5 0

Answer:9

Step-by-step explanation: First you add the 3x to both sides(the -4x and the -3x) and then you get 15-1x=6. Next you subtract 15 from 15 and 6, so you get -1x=-9. So then you divide both sides by -1 (do -1x over -1 equals -9 over -1). Last you do the dividing and you get x=9.

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Prove the divisibility of the following numbers:

Brut [27]

Answer:

Step-by-step explanation:

To prove divisibility, we need to factor the divident such that one of its factors matches the divisor.

(I use the notation x|y to denote that x divides y)

(A)

$75^{30}|45^{45}\cdot15^{15}\\45^{45}\cdot15^{15}=3^{45}\cdot 15^{45}\cdot 15^{15}=\\=3^{45}\cdot 15^{60}=3^{45}\cdot 15^{30}\cdot 15^{30}=3^{45}\cdot (3\cdot5)^{30}\cdot 15^{30}=\\=3^{45}\cdot 3^{30}\cdot(5\cdot 15)^{30}=3^{45}\cdot 3^{30}\cdot(75)^{30}\\\implies\\75^{30}|3^{45}\cdot 3^{30}\cdot75^{30}$

(B)

$72^{63}|24^{54}\cdot 54^{24}\cdot2^{10}\\24^{54}\cdot 54^{24}\cdot2^{10}=(2^{162}\cdot 3^{54})\cdot(2^{24}\cdot 3^{72}) \cdot 2^{10}\\=2^{196}\cdot 3^{126}$

In this case, it is easier to also factor the divisor to primes:

$72^{63}=2^{189}\cdot 3^{126}$

Both of these factor must be matched in the dividend in order to prove divisibility, and that indeed turns out to be true:

$2^{189}\cdot 3^{126}|2^{196}\cdot 3^{126}\implies\\2^{189}|2^{196}\,\,\mbox{and}\,\,3^{126}|3^{126}$

6 0

3 years ago

there are 270 at Colfax Middle School, where the ratio of boys to girls is 5:4. there are 180 students at Winthrop Middle School

ruslelena [56]

Colfax:

Add the ratio numbers together:

5 + 4 = 9

Divide total students by that:

270 / 9 = 30

Multiply each ratio by 30:

Boys = 30 *5 = 150

Girls = 30 * 4 = 120

Do the same for Winthrop:

4 +5 = 9

180 /9 = 20

Boys = 20 * 4 = 80

Girls = 20 * 5 = 100

Total students = 270 + 180 = 450

Total Girls = 120 + 100 = 220

Fraction that are girls = 220 / 450 which reduces to 22/45

4 0

3 years ago

Chase consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Chase's body

PIT_PIT [208]

Answer:

(a) The 5-hour decay factor is 0.5042.

(b) The 1-hour decay factor is 0.8720.

Step-by-step explanation:

The amount of caffeine in Chase's body decreases exponentially.

The 10-hour decay factor for the number of mg of caffeine is 0.2542.

The 1-hour decay factor is:

$1-hour\ decay\ factor=(0.2542)^{1/10}=0.8720$

(a)

Compute the 5-hour decay factor as follows:

$5-hour\ decay\ factor=(0.8720)^{5}\\=0.504176\\\approx0.5042$

Thus, the 5-hour decay factor is 0.5042.

(b)

The 1-hour decay factor is:

$1-hour\ decay\ factor=(0.2542)^{1/10}=0.8720$

Thus, the 1-hour decay factor is 0.8720.

(c)

The equation to compute the amount of caffeine in Chase's body is:

A = Initial amount × (0.8720)<em>ⁿ</em>

It is provided that initially Chase had 171 mg of caffeine, 1.39 hours after consuming the drink.

Compute the amount of caffeine in Chase's body 2.39 hours after consuming the drink as follows:

$A = Initial\ amount \times (0.8720)^{2.39} \\=[Initial\ amount \times (0.8720)^{1.39}] \times(0.8720)\\=171\times 0.8720\\=149.112$

Thus, the amount of caffeine in Chase's body 2.39 hours after consuming the drink is 149.112 mg.

4 0

3 years ago

The temperature in Alaska can reach -30 degrees Fahrenheit during the winter months it is colder in Antarctica than in the Alask

Fofino [41]

Answer:

B. -40°F

Step-by-step explanation:

its- clearly lower than -30

4 0

3 years ago

Read 2 more answers

A rule for a sequence of numbers is given.

Sliva [168]

D u got to add a lil bit and that you do division

6 0

3 years ago

15 - 4x = 6 - 3xwhats the answer. ​

15 - 4x = 6 - 3xwhats the answer.