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vodomira [7]
2 years ago
8

The slope of the line whose equation is 2x + 5y + 1 = 0 is

Mathematics
1 answer:
natita [175]2 years ago
6 0

Answer:

the slope is -2/5

Step-by-step explanation:

Solve for y.

2x + 5y + 1 = 0

5y = -2x - 1

y = -2/5 x - 1/5

Compare to

y = mx + b, where m is the slope.

m = -2/5

Answer: the slope is -2/5

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How to evaluate question number 4
ANTONII [103]

There are 2 ways that spring to mind.

One is to use the definition of the derivative at a point:

f'(c)=\displaystyle\lim_{x\to c}\frac{f(x)-f(c)}{x-c}

In this case, c=0 and f(x)=\sqrt{5-x}. Then

f'(x)=-\dfrac1{2\sqrt{5-x}}\implies f'(0)=\displaystyle\lim_{x\to0}\frac{\sqrt{5-x}-\sqrt5}x=-\dfrac1{2\sqrt5}

- - -

If you don't know about derivative yet (I would think you do, considering this is for a midterm in AP Calc, but I digress), the other way is to rely on algebraic manipulation. Multiply the numerator and denominator by the conjugate of the numerator to get

\dfrac{\sqrt{5-x}-\sqrt5}x\cdot\dfrac{\sqrt{5-x}+\sqrt5}{\sqrt{5-x}+\sqrt5}=\dfrac{\left(\sqrt{5-x}\right)^2-\left(\sqrt5\right)^2}{x\left(\sqrt{5-x}+\sqrt5\right)}=-\dfrac x{x\left(\sqrt{5-x}+\sqrt5\right)}=-\dfrac1{\sqrt{5-x}+\sqrt5}

This is continuous at x=0, so the limit is the value of the expression at x=0:

\displaystyle\lim_{x\to0}\frac{\sqrt{5-x}-\sqrt5}x=-\lim_{x\to0}\frac1{\sqrt{5-x}+\sqrt5}=-\frac1{2\sqrt5}

5 0
3 years ago
Which statement best describes a many-to-one function?
r-ruslan [8.4K]

Answer:

B

Step-by-step explanation:

many different values of x lead to the same value of y.

hence, many-to-one.

but it does not mean that all values of x have to lead to the same value of y. it could be, but it is not demanded. so, it is not necessarily a horizontal line.

and this does not give us any information about the power of x involved. so, we cannot make any statement about linear or non-linear function.

8 0
3 years ago
Write an equation of the line with a slope of 7 and y-intercept of 2. y =​
scZoUnD [109]

Answer:

Y = 7X + 2

Step-by-step explanation:

Y = mx + b .... slope intercept form of a line.

m - Slope

b = Y - intercept.

8 0
2 years ago
Need help ASAP!!!!!!
Mnenie [13.5K]

Answer:

Mean = 2.95

Median = 3

Step-by-step explanation:

The mean of the number of visits of 40 adults to the gym is

\dfrac{0\cdot 4+1\cdot 3+2\cdot 12+3\cdot 5+4\cdot 8+5\cdot 5+6\cdot 2+7\cdot 1}{40}=\\ \\=\dfrac{3+24+15+32+25+12+7}{40}=\dfrac{118}{40}=2.95

The median of the data is the average number between 20th and 21th terms (because 40 is even number, so the middle term is the average between two middle terms).

20th term = 3 visits

21th term = 3 visits

Hence, median is 3 visits

6 0
3 years ago
Find the area of a sundown that measures 3 yards by 3/4 yard.
juin [17]
To find this you multiply the 2 numbers together. 3*3/4=2.25.

2.25 in fraction form is 2 \frac{1}{4}
3 0
3 years ago
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