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3 years ago

ABC is similar to APQ. Find x and y.

Mathematics

1 answer:

slavikrds [6]3 years ago

5 0

Answer:

x = 10.8

y = 11.2

Step-by-step explanation:

AB : AP = AC : AQ

5 :(5+9) = 6 : (6+x)

5: 14 = 6 :(6+x)

5(6+x) = 14*6

30 + 5x = 84

5x = 54

x = 10.8

AB : AP = BC :PQ

5 :14 = 4 : y

5y = 14*4

y = 11.2

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Answer:

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6 0

3 years ago

A cup of coffee contains about 100 mg of caffeine. Caffeine is metabolized and leaves the body at a continuous rate of about 12%

Mamont248 [21]

Answer:

a. $A = C_{0}(1-x)^t\\x: percentage\ of \ caffeine\ metabolized\\$

b. $\frac{dA}{dt}= -11.25 \frac{mg}{h}$

Step-by-step explanation:

First, we need tot find a general expression for the amount of caffeine remaining in the body after certain time. As the problem states that every hour x percent of caffeine leaves the body, we must substract that percentage from the initial quantity of caffeine, by each hour passing. That expression would be:

$A= C_{0}(1-x)^t\\t: time \ in \ hours\\x: percentage \ of \ caffeine\ metabolized\\$

Then, to find the amount of caffeine metabolized per hour, we need to differentiate the previous equation. Following the differentiation rules we get:

$\frac{dA}{dt} =C_{0}(1-x)^t \ln (1-x)\\\frac{dA}{dt} =100*0.88\ln(0.88)\\\frac{dA}{dt} =-11.25 \frac{mg}{h}$

The rate is negative as it represents the amount of caffeine leaving the body at certain time.

3 0

3 years ago

Hi do you want which is greater 0.75 x 81 or 0.9 x 81.

anygoal [31]

Answer:

0.9 x 81

Step-by-step explanation:

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5 0

4 years ago

Read 2 more answers

Which expression is the factorization of x2 + 10x + 21?

LiRa [457]

<h2>Solution:</h2>

Equation: x² + 10x + 21

Step 1: Find two numbers that can add up to 10 and be multiplied to 21. We have: 7 & 3, in the sense that 7+3=10, and 7×3=21. Replacing 10 with 7+3, the equation is now → x² + 7x + 3x + 21

Step 2: Get the new equation bracketed → (x² + 7x) (+3x + 21)

Step 3: Use 'x' in the equation. For the first part, we have 'x'. x² = x × x so, bring out one x out side the bracket, divide 7x by = 7 → x (x +7). Do the same for the second part by dividing 21 by 3 = 7, and then bringing out 3 from the bracket → 3 (x + 7).

Bringing everything together, we have: x(x+7) +3(x+7) → (x+3) (x+7)

<h3>Final answer:</h3>

(x+3) (x+7)

<h3 />

4 0

2 years ago

Add the following:

PIT_PIT [208]

Step-by-step explanation:

1) 7/23 + 11/23 + 9/23

7+11+9/23

27/23

= 1 4/23

2) 2 5/7 + 9 4/7

11 9/7

= 11.12

3) 9/20 + 3/5

9+12/20

21/20

= 1 1/20 or 1.05

8 0

4 years ago