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3 years ago

Find the slope of the line represented by the data on the picture

Mathematics

1 answer:

arsen [322]3 years ago

4 0

Answer:

slope = - 4

Step-by-step explanation:

Calculate the slope m using the slope formula and any 2 ordered pairs from the table.

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 8) and (x₂, y₂ ) = (- 1, 4) ← 2 points from the table

m = $\frac{4-8}{-1+2}$ = $\frac{-4}{1}$ = - 4

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The length of a rectangle is 5 cm more than the width and the perimeter is at least 61cm. What are the smallest possible dimensi

aleksandrvk [35]

I think the length is 17.75cm and the width is 12.75 cm

I'm not entirely sure whether it's the smallest possible length but it works on the calculator

17.75*2+12.75*2=61

6 0

3 years ago

A firework is fired into the air from the top of a barn. Tis hight (h) above the ground in yards after (t) seconds is given by t

Grace [21]

The given function for the height of the firework is a quadratic function

1. Time at which the firework reaches the maximum height is 1 seconds

2. The maximum height of the firework, is 25 yards

3. Time after which the firework will fall to the ground is (1 + √5) seconds

Reason:

The given function that represents the height of the fireworks with time is

presented as follows;

h(t) = -5·t² + 10·t + 20

1. The time at which the firework reaches its maximum height is given by

the maximum point of the given function as follows;

The x-value of the maximum point of a quadratic function is $x = \dfrac{b}{2 \cdot a}$

Where;

a, and b, are the coefficient of x² and x, in the general form of a quadratic function f(x) = a·x² + b·x + c

By comparison, we have;

$t = -\dfrac{10}{2 \times (-5)} = 1$

The time at which the firework reaches the maximum height is t = 1 seconds

2. The maximum height is given by plugging in the value of t, at the maximum point into the given function as follows;

h(1) = -5×1² + 10×1 + 20 = 25

The maximum height of the firework, f(1) = 25 yards

3 The time at which the firework will fall to the ground, is given by the zero of the function as follows;

When the firework falls to the ground, h(t) = 0 = -5·t² + 10·t + 20

Dividing both sides by (-5) gives;

$\dfrac{0}{-5} = \dfrac{ -5 \cdot t^2 + 10 \cdot t + 20}{-5} = t^2 - 2 \cdot t - 4$

t² - 2·t - 4 = 0

By the quadratic formula $x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}$ , we get;

$t = \dfrac{2\pm \sqrt{(-2)^{2}-4\times 1\times (-4)}}{2\times 1} = \dfrac{2\pm \sqrt{20}}{2\times 1} = \dfrac{2\pm 2 \times \sqrt{5}}{2\times 1} = 1 \pm \sqrt{5}$

Therefore;

The time after which the firework will fall to the ground, t = 1 + √5 seconds

Learn more here:

brainly.com/question/20628403

3 0

3 years ago

Can someone help me with this truth table. I just don't understand how to do it.

RUDIKE [14]

An implication $(p\implies q)$ is true if either the premise $(p)$ is false, or both the premise and conclusion $(p\text{ and }q)$ are both true, and false otherwise.

$\begin{array}{c|c|c|c|c|c|c}p&q&p\implies q&\neg q&(p\implies q)\land\neg q&\neg p&(p\implies q)\land\neg q\implies\neg p\\T&T&T&&&&\\T&F&F&&&&\\F&T&T&&&&\\F&F&T&&&&\end{array}$

Negation $(\neg q)$ is straightforward; if a statement is true, then its negation is false, and vice versa.

$\begin{array}{c|c|c|c|c|c|c}p&q&p\implies q&\neg q&(p\implies q)\land\neg q&\neg p&(p\implies q)\land\neg q\implies\neg p\\T&T&T&F&&F\\T&F&F&T&&F\\F&T&T&F&&T\\F&F&T&T&&T\end{array}$

A conjunction $(p\land q)$ is true if both premises are true, and false otherwise.

$\begin{array}{c|c|c|c|c|c|c}p&q&p\implies q&\neg q&(p\implies q)\land\neg q&\neg p&(p\implies q)\land\neg q\implies\neg p\\T&T&T&F&F&F\\T&F&F&T&F&F\\F&T&T&F&F&T\\F&F&T&T&T&T\end{array}$

Finally, by the rules of implication, we can fill the last column:

$\begin{array}{c|c|c|c|c|c|c}p&q&p\implies q&\neg q&(p\implies q)\land\neg q&\neg p&(p\implies q)\land\neg q\implies\neg p\\T&T&T&F&F&F&T\\T&F&F&T&F&F&T\\F&T&T&F&F&T&T\\F&F&T&T&T&T&T\end{array}$