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3 years ago

Given the equation 10x + 20y + 40 = 0, Find it’s gradient and intercept

Mathematics

1 answer:

jonny [76]3 years ago

8 0

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange the given equation into this form

10x + 20y + 40 = 0 ( divide all terms by 10 to simplify )

x + 2y + 4 = 0 ( subtract x + 4 from both sides )

2y = - x - 4 ( divide all terms by 2 )

y = - $\frac{1}{2}$ x - 2 ← in slope- intercept form

with slope m = - $\frac{1}{2}$ and y- intercept c = - 2

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Find DF AC=600 CB=480 AB=360

Mandarinka [93]

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6 0

3 years ago

Seeds are often treated with fungicides to protect them in poor-draining, wet environments. A small-scale trial, involving six t

alukav5142 [94]

Answer:

0.0076 = 0.76% probability that all five plants emerged from treated seeds

Step-by-step explanation:

The plants were chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

6 + 6 = 12 seeds, which means that $N = 12$

6 treated, which means that $k = 6$

Five sprouted, which means that $n = 5$

What is the probability that all five plants emerged from treated seeds?

This is P(X = 5). So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 5) = h(5,12,5,6) = \frac{C_{6,5}*C_{6,0}}{C_{12,5}} = 0.0076$

0.0076 = 0.76% probability that all five plants emerged from treated seeds

3 0

3 years ago

Find the distance between (-2,7) and (3, -3). Round to the nearest tenth. Geometry please help

yan [13]

Answer:

Step-by-step explanation:

The formula for distance when given vertices is

√(x2 - x1)² + (y2- y1)²

Where we have points (x1,y1) and (x2,y2)

So, (-2,7) and (3, -3)

Distance = √(3 -(-2))² + (-3 -7)²

= √5² + (-10)²

= √25 + 100

= √125

= 15

Therefore, the distance between (-2,7) and (3, -3) is 15

8 0

3 years ago

Find the indefinite integrals, if possible, using the formulas and techniques you have studied so far in the text.(a) 11 x4 dxTh

hoa [83]

Answer:

a) This integral can be evaluated using the basic integration rules. $\int 11x^{4}dx = \frac{11}{5} x^{5}+C$

b) This integral can be evaluated using the basic integration rules. $\int 8x^{1}x^{4}dx=\frac{4}{3}x^{6}+C$

c) This integral can be evaluated using the basic integration rules. $\int 3x^{31}x^{4}dx=\frac{x^{36}}{12}+C$

Step-by-step explanation:

a) $\int 11x^{4}dx$

In order to solve this problem, we can directly make use of the power rule of integration, which looks like this:

$\int kx^{n}=k\frac{x^{n+1}}{n+1}+C$

so in this case we would get:

$\int 11x^{4}dx=11 \frac{x^{4+1}}{4+1}+C$

$\int 11x^{4}dx=11 \frac{x^{5}}{5}+C$

b) $\int 8x^{1}x^{4}dx$

In order to solve this problem we just need to use some algebra to simplify it. By using power rules, we get that:

$\int 8x^{1}x^{4}dx=\int 8x^{1+4}dx=\int 8x^{5}dx$

So we can now use the power rule of integration:

$\int 8x^{5}dx=\frac{8}{5+1}x^{5+1}+C$

$\int 8x^{5}dx=\frac{8}{6}x^{6}+C$

$\int 8x^{5}dx=\frac{4}{3}x^{6}+C$

c) The same applies to this problem:

$\int 3x^{31}x^{4}dx=\int 3x^{31+4}dx=\int 3x^{35}dx$

and now we can use the power rule of integration:

$\int 3x^{35}dx=\frac{3x^{35+1}}{35+1}+C$

$\int 3x^{35}dx=\frac{3x^{36}}{36}+C$

$\int 3x^{35}dx=\frac{x^{36}}{12}+C$

6 0

3 years ago

An individual saves $5000 in a bank account at the beginning of each year for 10 years.

frozen [14]

Answer:

a) Amount saved if the interest is compounded annually is $5832

b) Amount saved if the interest is compounded semi-annually is $5849.5

Step-by-step explanation:

Principal Amount P = 5000

Time t = 10 years

Annual interest i = 8% = 0.08

We need to find amount saved if interest is compounded a) annually b) semi-annually

a) Amount saved if the interest is compounded annually

If interest compounded annually, n= 1

Using Formula: $A=P(1+\frac{r}{n})^{nt}$

Putting values:

$A=P(1+\frac{r}{n})^{nt} \\A=5000(1+\frac{0.08}{1})^{1*2}\\A=5000(1+0.08)^2\\A=5000(1.08)^2\\A=5000(1.1664)\\A=5832$

So, Amount saved if the interest is compounded annually is $5832

b) Amount saved if the interest is compounded semi-annually

If interest compounded semi-annually, n= 2

Using Formula: $A=P(1+\frac{r}{n})^{nt}$

Putting values:

$A=P(1+\frac{r}{n})^{nt} \\A=5000(1+\frac{0.08}{2})^{2*2}\\A=5000(1+0.04)^4\\A=5000(1.04)^4\\A=5000(1.1699)\\A=5849.5$

So, Amount saved if the interest is compounded semi-annually is $5849.5

4 0

3 years ago