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3 years ago

What polynomial should be subtracted from the polynomial y2–5y+1 to get the difference equal to 5

Mathematics

1 answer:

VMariaS [17]3 years ago

3 0

Answer: The polynomial

= y² - 5y - 4.

Step-by-step explanation:

Let the polynomial = f(y)

Therefore

y² -5y + 1 - f(y) = 5

f(y) = y² - 5y + 1 - 5

f(y) = y² - 5y - 4

The polynomial = y² - 5y - 4.

Check:

y² - 5y + 1 - ( y² - 5y - 4)

Open the bracket with the minus

y² - 5y + 1 - y² + 5y + 4

y² - y² - 5y + 5y + 1 + 4

= 0 - 0 + 5

= 5.

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What is the equation of the line that is perpendicular to the given line and passes through the point (3, 0)?

olga2289 [7]

Step $1$

Find the slope of the given line

Let

$A(-3,2)\ B(2,-1)$

slope mAB is equal to

$mAB=\frac{(y2-y1)}{(x2-x1)} \\ \\ mAB=\frac{(-1-2)}{(2+3)} \\ \\ mAB=-\frac{3}{5}$

Step $2$

Find the slope of the line that is perpendicular to the given line

Let

CD ------> the line that is perpendicular to the given line

we know that

If two lines are perpendicular, then the product of their slopes is equal to $-1$

$mAB*mCD=-1\\ mAB=-\frac{3}{5} \\ mCD=-\frac{1}{mAB} \\ mCD=\frac{5}{3}$

Step $3$

Find the equation of the line with mCD and the point (3,0)

we know that

the equation of the line in the form point-slope is equal to

$y-y1=m(x-x1)\\\\ y-0=\frac{5}{3} *(x-3)\\\\ y=\frac{5}{3} x-5$

Multiply by $3$ both sides

$3y=5x-15$

$5x-3y=15$

therefore

the answer is

the equation of the line that is perpendicular to the given line is the equation $5x-3y=15$

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3 years ago

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Vsevolod [243]

Answer:

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Step-by-step explanation:

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State the necessary value of nn that will make each statement true. 0.0004 × 0.002 = 8 × 10^n

vodka [1.7K]

Answer:

$-7 = n$

Step-by-step explanation:

$0,002 \times 0,0004 = 0,0000008$

$0,0000008 = 8 \times {10}^{-7}$

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3 years ago

A report by the US Geological Survey indicates that glaciers in Glacier National Park, Montana, are shrinking. Recent estimates

postnew [5]

Answer

a) C

b) B

c) C, E

d) 15.5

e) 0.7

f) 67.7

Step-by-step explanation

a) A linear equation can be written as $y=mx+c$ where $m$ is the slope and $c$ is the intercept on the $y$ -axis. The slope describes how $y$ changes when $x$ changes. A negative value means the it is a decreasing change. In our case, $y$ is $A$ and $x$ is $t$ . Thus, the slope of the equation is $m=-0.062$ . This means that the area of glacier is decreasing by $0.062 \text{km}{}^2 = 62000 \text{m}{}^2$ every year since 2000.

b) The $A$ -intercept (= 16.2 $\text{km}{}^2$ ) represents the area covered when $t=0$ . But $t=0$ starting from year 2000. This intercept then represents the area covered by glacier in the year 2000. Therefore, the area covered by glacier in 2000 was 16.2 $\text{km}{}^2$ .

c) $A=f(t)$ means the area covered after year 2000. Setting it to 12 means the area covered after $t$ years is 12 $\text{km}{}^2$ ). $t$ is therefore the number of years since 2000 that the total area covered will be 12 $\text{km}{}^2$ ).

d) $f(12)=16.2−0.062\times12 =16.2-0.744 = =15.456 15.5 \text{km}{}^2$ to 1 decimal place.

e) The term involving $t$ represents the disappearing area. In 12 years, the disappeared area is $0.062\times12=0.744 =0.7 \text{km}{}^2$ to 1 decimal place.