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erma4kov [3.2K]

2 years ago

12

Find the equation of the line with slope 3/7 and that passes through the point (14, 0). Write your answer in the form y = mx + b

.

1 answer:

Allushta [10]2 years ago

7 0

Answer:

y = 3/7x - 6

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS
Equality Properties

<u>Algebra I</u>

Slope-Intercept Form: y = mx + b

m - slope

b - y-intercept

Step-by-step explanation:

<u>Step 1: Define</u>

Slope <em>m</em> = 3/7

Point (14, 0)

<u>Step 2: Find y-intercept </u><em><u>b</u></em>

Substitute: 0 = 3/7(14) + b
Multiply: 0 = 6 + b
Isolate <em>b</em>: -6 = b
Rewrite: b = -6

<u>Step 3: Write linear equation</u>

y = 3/7x - 6

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A farmer is tracking the amount of corn his land is yielding each year. He finds that the function f(x) = −x2 + 20x + 50 models

polet [3.4K]

Answer:

The crop yield increased by 9 pounds per acre from year 1 to year 10.

Step-by-step explanation:

To solve this we are using the average rate of change formula: $Av=\frac{f(x_2)-f(x_1)}{x_2-x_1}$ , where:

$x_2$ is the second point in the function

$x_1$ is the first point in the function

$f(x_2)$ is the function evaluated at the second point

$f(x_1)$ is the function evaluated at the first point

We know that the first point is 1 year and the second point is 10 years, so $x_1=1$ and $x_2=10$ . Replacing values:

$Av=\frac{-(10)^2+20(10)+50-[-(1)^2+20(1)+50]}{10-1}$

$Av=\frac{-100+200+50-[-1+20+50]}{9}$

$Av=\frac{150-[69]}{9}$

$Av=\frac{150-69}{9}$

$Av=\frac{81}{9}$

$Av=9$

Since $f(x)$ represents the number of pounds per acre and $x$ the number of years, we can conclude that the crop yield increased by 9 pounds per acre from year 1 to year 10.

6 0

3 years ago

Find the simplified product:<br> sqrt 2x^2 * sqrt18^5

makvit [3.9K]

Answer:

1944x^2.

Step-by-step explanation:

sqrt 2x^2 * sqrt18^5

= sqrt2x^2 * (sqrt(9^5*2^5))

= sqrt 2 x^2 * (sqrt9^5 * sqrt 2^5)

= sqrt2 x^2 * (243* sqrt2^5)

= 2^0.5 (243 * 2^2.5) x^2

= 2^3 * 243 x^2

= 1944x^2.

5 0

2 years ago

The International Coffee Association has reported the mean daily coffee consumption for U.S. residents as 1.65 cups. Assume that

Harman [31]

Answer:

The calculated value t = 1.3788 < 2.0262 at 0.05 level of significance

the null hypothesis is accepted

There is no significant difference between their counterparts across the nation

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given that the mean of the U.S residents = 1.65

Given that the size of the sample 'n' = 38

Mean of the sample = 1.84

Given that the standard deviation of the sample (S) = 0.85

<u><em>Step(ii):-</em></u>

<u><em>Null hypothesis:</em></u>H₀:

There is no significant difference between their counterparts across the nation

<u><em>Alternative Hypothesis:-</em></u>H₁:

There is a significant difference between their counterparts across the nation

Test statistic

$t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }$

$t = \frac{1.84-1.65}{\frac{0.85}{\sqrt{38} } }$

t = 1.3788

Degrees of freedom

ν = n-1 = 38-1 = 37

t₀.₀₅ ,₃₇ = 2.0262

The calculated value t = 1.3788 < 2.0262 at 0.05 level of significance

Null hypothesis is accepted

<u><em>Final answer:-</em></u>

There is no significant difference between their counterparts across the nation.

5 0

2 years ago