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3 years ago

(a+b)^2–(b+c)^2 as a product of two polynomials

Mathematics

1 answer:

vovikov84 [41]3 years ago

8 0

Hey there!!

In order to solve this problem, we will need to use the identity a² - b²

∴ a² - b² = ( a + b ) ( a - b )

According to the question,

a = a + b

b = b + c

( a + b )² - ( b + c )²

... ( a + b + b + c ) ( a + b - b - c )

... ( a + 2b + c ) ( a - c )

Now, we will need to solve this using distributive property.

Distribute a with a , 2b , c and distribute -c with a , 2b and c and then combine all the like terms.

... ( a² + 2ab + ac ) + ( -ac - 2bc - c² )

... ( a² + 2ab + ac - ac - 2bc - c² )

... ( a² + 2ab - bc - c² )

Hope my answer helps!!

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What is an equation of a line which passes through (6,9) and is perpendicular to the line whose equation is 4x − 6y = 15?

Svetllana [295]

Given:

The equation of the line passes through the point (6,9) and is perpendicular to the line whose equation is $4 x-6 y=15$

We need to determine the equation of the line.

Slope:

Let us convert the equation to slope - intercept form.

$-6 y=15-4x$

$y=\frac{2}{3}x-\frac{5}{2}$

From the above equation, the slope is $m_1=\frac{2}{3}$

Since, the lines are perpendicular, the slope of the line can be determined using the formula,

$m_1 \cdot m_2=-1$

$\frac{2}{3} \cdot m_2=-1$

$m_2=-\frac{3}{2}$

Therefore, the slope of the equation is $m=-\frac{3}{2}$

Equation of the line:

The equation of the line can be determined using the formula,

$y-y_1=m(x-x_1)$

Substituting the point (6,9) and the slope $m=-\frac{3}{2}$ in the above formula, we get;

$y-9=-\frac{3}{2}(x-6)$

Simplifying the terms, we get;

$2(y-9)=-3(x-6)$

$2y-18=-3x+18$

$3x+2y=36$

Thus, the equation of the line is $3x+2y=36$

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3 years ago

Kim rode her bicycle 135 miles in 9 weeks riding the same distance each week. eric rode his bicycle 102 miles in 6 weeks riding

zysi [14]

The answer is a because you divide 135÷9=15 and 102÷6=17 . 17-15=2

6 0

3 years ago

g (15 points) Suppose 42 out of 600 rats exposed to a potential carcinogen develop tumors. A control group of 350 rats not expos

vazorg [7]

Answer:

a) The relative risk is 1.8 $\overline{846153}$

b) The attributable risk is $0.69 \overline{047619}$

c) There is a relationship between exposure and tumor risk

Step-by-step explanation:

The number of exposed rats that develop tumors, a = 42

The number of rats exposed to the carcinogen = 600 rats

The number of exposed rats that did not develop tumors, b = 600 - 42 = 558

The number of not exposed rats in the control group = 350 rats

The number of rats that develop tumors in the control group, c = 13 tumors

The number of not exposed rats that did not develop tumors, d = 350 - 13 = 337 rats

a) The relative risk, RR = a/(a + b)/(c/(c + d))

∴ RR = (42/(42 + 558))/(13/(13 + 337)) = 49/26 = 1.8 $\overline{846153}$

b) The attributable risk = (a - c)/a

∴ The attributable risk = (42 - 13)/42 = $0.69 \overline{047619}$

c) The odds ratio = (a·b)/(c·d)

∴ The odds ratio = 42 × 558/(13 × 337) = 23439/4381 ≈ 5.35

Given that the result of attributable risk is positive, there is an indication that there is a higher probability to develop tumor when exposed to the potential carcinogen, therefore, there is a relationship between exposure and tumor risk

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3 years ago

Can anyone help me find the value pls?

Flauer [41]

The inside angle for B, which is labeled x is the same as the outside angle of D which is labeled as 72, so we know x = 72.

In a parallelogram two angles next to each other equal 180, so angle A and angle B equal 180.

We know B = 72, so A = 180-72 = 108

Angle A is divided in 2 by angle y, so y = 108/2 = 54

Answers: x = 72

Y = 54

4 0

3 years ago

Maria plans to use fencing to build an enclosure or enclosures for her two horses. A single enclosure would be square shaped and

Gala2k [10]

Step 1
find the perimeter of a single enclosure
perimeter of a square=4*b
where b is the long side of a square
area square=b²
area square=2025 ft²
b²=2025-------> b=√2025-----> b=45 ft
so
perimeter=4*45-------> 180 ft

step 2
find the perimeter of a two individual enclosure
perimeter=4*20+3*40------> 200 ft
area=20*40*2------> 1600 ft²

therefore
fencing singular enclosure < fencing two individual enclosure
180 ft < 200 ft

area singular enclosure > area two individual enclosure
2025 ft² > 1600 ft²

the answer is the option
a The singular enclosure would minimize cost because it requires 180 feet of fencing.

5 0

3 years ago

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