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4 years ago

13. 11 = 2b +17 14. 5 = 4a -7

1 answer:

3 0

$13.\ 2b+17=11\qquad|-17\\\\2b=-6\qquad|:2\\\\\boxed{b=-3}\\\\14.\ 4a-7=5\qquad|+7\\\\4a=12\qquad|:4\\\\\boxed{a=3}\\\\16.\ 2g-3=-19\qquad|+3\\\\2g=-16\qquad|:2\\\\\boxed{g=-8}\\\\17.\ 5x-9=16\qquad|+9\\\\5x=25\qquad|:5\\\\\boxed{x=5}\\\\19.\ 5+\dfrac{y}{8}=-3\qquad|-5\\\\\dfrac{y}{8}=-8\qquad|\cdot8\\\\\boxed{y=-64}$

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A country has two political parties, the Demonstrators and the Repudiators. Suppose that the national senate consists of 100 mem

IRISSAK [1]

Answer:

(a) 4.148 x 10^(12) ways

(b) 5,827,360 ways

Step-by-step explanation:

Number of Demonstrators (D) = 44

Number of Repudiators (R) = 56

(a)

5 senate members must be Repudiators and 5 must be demonstrators, assuming that the order at which they are selected is irrelevant:

$N= C^{D}_{5} * C^{R}_{5}\\N=\frac{56!}{5!(56-5)!} *\frac{44!}{5!(44-5)!} \\N=3,819,816*1,086,008\\N=4.148 *10^{12}$

(b)

Since there are two different positions, (speaker and vice speaker), order is important in this situation, and the total number of ways to select two senators from each party is:

$N= P^{D}_{2} * P^{R}_{2}\\N=\frac{56!}{(56-2)!} *\frac{44!}{(44-2)!} \\N=3,080*1,892\\N=5,827,360$

6 0

4 years ago

The family of solutions to the differential equation y ′ = −4xy3 is y = 1 √ C + 4x2 . Find the solution that satisfies the initi

slega [8]

Answer:

The correct option is 4

Step-by-step explanation:

The solution is given as

$y(x)=\frac{1}{\sqrt{C+4x^2}}$

Now for the initial condition the value of C is calculated as

$y(x)=\frac{1}{\sqrt{C+4x^2}}\\y(-2)=\frac{1}{\sqrt{C+4(-2)^2}}\\4=\frac{1}{\sqrt{C+4(4)}}\\4=\frac{1}{\sqrt{C+16}}\\16=\frac{1}{C+16}\\C+16=\frac{1}{16}\\C=\frac{1}{16}-16$

So the solution is given as

$y(x)=\frac{1}{\sqrt{C+4x^2}}\\y(x)=\frac{1}{\sqrt{\frac{1}{16}-16+4x^2}}$

Simplifying the equation as

$y(x)=\frac{1}{\sqrt{\frac{1}{16}-16+4x^2}}\\y(x)=\frac{1}{\sqrt{\frac{1-256+64x^2}{16}}}\\y(x)=\frac{\sqrt{16}}{\sqrt{{1-256+64x^2}}}\\y(x)=\frac{4}{\sqrt{{1+64(x^2-4)}}}$

So the correct option is 4

8 0

3 years ago

Read 2 more answers

Find the area of the shaded region.

Lyrx [107]

1)
Area of bigger rectangle
A = (x+1)(x+1) = x^2 + 2x + 1

2)
Area of smaller rectangle
A = 5(x - 7) = 5x - 35

3)
The difference:
(x^2 + 2x + 1) - (5x - 35)
= x^2 + 2x + 1 - 5x +35
= x^2 - 3x + 36

area of the shaded region = x^2 - 3x + 36

6 0

4 years ago

Read 2 more answers

The area of a rectangle is 35ft^2 , and the length of the rectangle is 3 ft more than twice the width. Find the dimensions of th

allsm [11]

Answer:

1228 is your answer

Step-by-step explanation:

3 0

3 years ago

Please help me with this question :)<br>

zlopas [31]

Answer:

q>27/61

Step-by-step explanation:

50*q+43-(>11*q+70)>0

Step 1. Divied both sides by 61 q-(27/61)

Step 2. Add 27/61 to both sides q >27/61

Step 3. Inequality plot for 61.000q -27.000 > 0

Answer: q>27/61 or 27/61

8 0

3 years ago