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1 year ago

O GRAPHS AND FUNCTIONSGraphing a function of the form f(x) = ax + b: Integer slopeGraph the function h(x) = -5x +3.

Mathematics

1 answer:

Alborosie1 year ago

3 0

Graphs of linear functions

Since we are graphing a line, if we have two points we can plot the whole line

We evaluate the line in two points in order to locate two places where it passes through. We say y = h(x)

1. If x = 0 then

h(x) = - 5(0) +3

= 0 + 3

= 3

Then y = 3

2. If x = 2 then

h(x) = - 5(2) +3

= -10 + 3

= -7

Then y = -7

Now, we have two points: (0, 3) and (2, -7)

We locate them and then we plot the only straight line that passes through both points

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an arrow is shot vertically upward from a platform 33ft high at a rate of 174 ft/sec. when will the arrow hit the ground?

Cloud [144]

Answer:

h(t) = -16t2 + 186t + 43

at the ground h = 0

hence; -16t2 + 186t + 43 = 0

solving this quadratic equation using the quadratic formula ; a = -16, b = 186, c = 43 ; x = (-b +-(b2 - 4ac)1/2)/2a

gives t = 11.8 seconds to the nearest tenth (note that the negative root has no practical significance)

Step-by-step explanation:

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3 years ago

Find the area bounded by the given curves: y=2x−x2,y=2x−4

Andrej [43]

Answer:

$A = [\frac{32}{3}]$

Step-by-step explanation:

Given

$y_1 = 2x - x^2$

$y_2 = 2x - 4$

Required

Determine the area bounded by the curves

First, we need to determine their points of intersection

$2x - x^2 = 2x - 4$

Subtract 2x from both sides

$-x^2 = -4$

Multiply through by -1

$x^2 = 4$

Take square root of both sides

$x = 2$ or $x = -2$

This Area is then calculated as thus

$A = \int\limits^a_b {[y_1 - y_2]} \, dx$

Where a = 2 and b = -2

Substitute values for $y_1$ and $y_2$

$A = \int\limits^a_b {(2x - x^2) - (2x - 4)} \, dx$

Open Brackets

$A = \int\limits^a_b {2x - x^2 - 2x + 4} \, dx$

Collect Like Terms

$A = \int\limits^a_b {2x - 2x- x^2 + 4} \, dx$

$A = \int\limits^a_b {- x^2 + 4} \, dx$

Integrate

$A = [-\frac{x^{3}}{3} +4x](2,-2)$

$A = [-\frac{2^{3}}{3} +4(2)] - [-\frac{-2^{3}}{3} +4(-2)]$

$A = [-\frac{8}{3} +8] - [-\frac{-8}{3} -8]$

$A = [\frac{-8+ 24}{3}] - [\frac{8}{3} -8]$

$A = [\frac{-8+ 24}{3}] - [\frac{8-24}{3}]$

$A = [\frac{16}{3}] - [\frac{-16}{3}]$

$A = [\frac{16}{3}] + [\frac{16}{3}]$

$A = [\frac{16 + 16}{3}]$

$A = [\frac{32}{3}]$

Hence, the Area is:

$A = [\frac{32}{3}]$

7 0

4 years ago

A deck of cards contains 26 red and 26 black cards. The red cards are divided into 13 hearts and 13 diamonds. The black cards ar

mr_godi [17]

Answer:

Step-by-step explanation:

becouase its b

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3 years ago

Barry found a computer at Staples for $989. A week later, the computer went on sale for $849. What

JulijaS [17]

Barry found a computer at Staples for $989. A week later, the computer went on sale for $849. The percentage change is 14.156 % decrease

Solution:

Given that Barry found a computer at Staples for $989

A week later, the computer went on sale for $849

To find: percent of change

Percent change is the extent to which a variable gains or loses value. The figures are arrived at by comparing the initial (or before) and final (or after) quantities according to a specific formula.

THE PERCENT CHANGE IS GIVEN AS:

$\text{ percent change } =\frac{\text { final value - initial value }}{\text { initial value }} \times 100$

If the result is positive, it is percentage increase

If the result is negative, it is percentage decrease

Here initial value = 989 and final value = 849

Substituting the values in above formula,

$\begin{aligned}&\text { percent change }=\frac{849-989}{989} \times 100\\\\&\text { percent change }=-0.14155 \times 100=-14.156 \%\end{aligned}$

Here negative sign denotes percentage decrease

Thus percentage change is 14.156 % decrease

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3 years ago

Help? which one is it

Dennis_Churaev [7]

5 is the correct answer

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3 years ago