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3 years ago

Find the slope of the line that passes through (4,2) and (9,1)?

Mathematics

2 answers:

pshichka [43]3 years ago

8 0

Answer:

The slope of the line is $\displaystyle -\frac{1}{5}$ .

Step-by-step explanation:

We are given two coordinate points:

$(4, 2)$
$(9, 1)$

We are asked to find the slope of the line.

We can use the rise-over-run formula to solve for the slope of the line.

$\displaystyle \text{slope} = \frac{\text{rise}}{\text{run}}\\\\\text{slope} = \frac{y_2-y_1}{x_2-x_1}$

However, we firstly need to name our coordinate points.

In math, we can label our coordinates using the following label system:

$(x_1, y_1), (x_2, y_2)$

Therefore, we can also label our coordinates as such:

$x_1 = 4$
$y_1 = 2$
$x_2 = 9$
$y_2 = 1$

Now, we can supply these values into the formula and solve for our slope, or a better known variable, m.

$\displaystyle m = \frac{1 - 2}{9 - 4}\\\\m = \frac{-1}{5}\\\\m = -\frac{1}{5}$

Therefore, our slope is $\displaystyle -\frac{1}{5}$ .

Nataly [62]3 years ago

8 0

Answer: m= -1/5

Step-by-step explanation:

Find the Slope (4, 2) and (9, 1)

Slope is equal to the change in y over the change in x, or rise over run.

change in y

m = _________

change in x

The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise). y₂ − y₁

m = _____

x₂ − x₁

Substitute in the values of x and y into the equation to find the slope.

1 − (2)

m = _____

9 − (4)

Simplify the numerator.

−1

m = _____

9 − (4)

Simplify the denominator.

−1

m = _____

Move the negative in front of the fraction.

−1

m = _____

− 5

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Alexxandr [17]

Answer:

Step-by-step explanation:

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3 years ago

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Given the two functions, which statement is true?

tia_tia [17]

Answer:

Option D

Step-by-step explanation:

f(x) = $\text{log}_{15}x$

Transformed form of the function 'f' is 'g'.

g(x) = $\frac{1}{2}\text{log}_{15}(x+4)$

Property of vertical stretch or compression of a function,

k(x) = x

Transformed function → m(x) = kx

Here, k = scale factor

1). If k > 1, function is vertically stretched.

2). If 0 < k < 1, function is vertically compressed.

From the given functions, k = $\frac{1}{2}$

Since, k is between 0 and $\frac{1}{2}$ , function f(x) is vertically compressed by a scale factor $\frac{1}{2}$ .

g(x) = f(x + 4) represents a shift of function 'f' by 4 units left.

g(x) = f(x - 4) represents a shift of function 'f' by 4 units right.

g(x) = $\frac{1}{2}\text{log}_{15}(x+4)$

Therefore, function f(x) has been shifted by 4 units left to form image function g(x).

Option D is the answer.

8 0

3 years ago

Using the formula in model 1, choose the correct answers for the total amount and amount of interest earned in the following com

DIA [1.3K]

The total amount is $ 1015.82 and interest amount is $ 165.82

Solution:

The formula for amount when interest is compounded annually is:

$\mathrm{A}=P\left(1+r}\right)^{n}$

Where,

"A" is the total amount

"P" is the principal

"r" is the rate of interest in decimal form

"n" is the number of years

From given, $850 at 2% for 9 years, compounded annually

P = 850

t = 9 years

$r = 2 \% = \frac{2}{100} = 0.02$

Substituting the given values we get,

$A = 850(1+0.02)^9\\\\A = 850 \times 1.02^9\\\\A = 850 \times 1.1950\\\\A = 1015.82$

Thus total amount is $ 1015.82

Interest amount = Total amount - principal

Interest amount = 1015.82 - 850

Interest amount = 165.82

Thus total amount earned is $ 1015.82 and interest amount is $ 165.82

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3 years ago

Sylvia has a circular table cloth. The area of the table cloth is 254.34 in2

yaroslaw [1]

Answer:

The answer is C

Step-by-step explanation:

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2 years ago

Simplify the expression.

Marizza181 [45]

$\bf \textit{Cofunction Identities}
\\ \quad \\
sin\left(\frac{\pi}{2}-{{ \theta}}\right)=cos({{ \theta}})\qquad 
\boxed{cos\left(\frac{\pi}{2}-{{ \theta}}\right)=sin({{ \theta}})}
\\ \quad \\ \quad \\
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\\ \quad \\ \quad \\
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$\bf \\\\
-------------------------------\\\\
sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta )
\\\\\\
\boxed{cos(\theta )=\sqrt{1-sin^2(\theta )}}$

$\bf \\\\
-------------------------------\\\\
\cfrac{cos^2\left(\frac{\pi }{2}-x \right)}{\sqrt{1-sin^2(x)}}\implies \cfrac{\left[ cos\left(\frac{\pi }{2}-x \right)\right]^2}{cos(x)}\implies \cfrac{[sin(x)]^2}{cos(x)}\implies \cfrac{sin(x)sin(x)}{cos(x)}
\\\\\\
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3 years ago

Find the slope of the line that passes through (4,2) and (9,1)￼?

Find the slope of the line that passes through (4,2) and (9,1)?