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2 years ago

Find the distance between the two points on the graph.

Mathematics

1 answer:

puteri [66]2 years ago

8 0

let's take a peek at the graph, it has the points of (-5 , 3) and (-2 , -3), so then

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-2-(-5)]^2+[-3-3]^2}\implies d=\sqrt{(-2+5)^2+(-3-3)^2} \\\\\\ d=\sqrt{3^2+(-6)^2}\implies d=\sqrt{45}\implies d\approx 6.71$

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Put it in order yes or no?and how do yk if it is or not

Serggg [28]

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Answer:

yes, yes, no, no

Step-by-step explanation:

An equation is linear if no term has a variable with an exponent other than 0 or 1. There can be no products of variables.

The equations with terms x³ or x² will not be linear.

(a, b) linear (yes)

(c, d) not linear (no)

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2 years ago

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nadya68 [22]

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2 years ago

Find the vertex of y=-x^2+6x-12

Debora [2.8K]

You find the x coordinates using x = -b/2a = -6/2(-1) = 3

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2 years ago

The equation h(t) = -16t² + 80t + 64 represented the height, in feet, of a potato t seconds after it has been launched.

Lyrx [107]

Answer:

Part A) The potato hit the ground at t=5.70 seconds (see the explanation)

Part B) The potato is 40 feet off the ground at the time t=5.28 seconds (see the explanation)

Step-by-step explanation:

we have

$h(t)=-16t^2+80t+64$

where

h(t) is the height of a potato in feet

t is the time in seconds

Part A) Write an equation that can be solved to find when the potato hits the ground. Then solve the equation

we know that

When the potato hit the ground, the value of h(t) must be equal to zero

For h(t)=0

$-16t^2+80t+64=0$

Solve the quadratic equation

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^2+80t+64=0$

$a=-16\\b=80\\c=64$

substitute in the formula

$t=\frac{-80\pm\sqrt{80^{2}-4(-16)(64)}} {2(-16)}$

$t=\frac{-80\pm\sqrt{10,496}} {-32}$

$t=\frac{-80+\sqrt{10,496}} {-32}=-0.70$

$t=\frac{-80-\sqrt{10,496}} {-32}=5.70$

therefore

The potato hit the ground at t=5.70 seconds

Part B) Write an equation that can be solved to find when the potato is 40 feet off the ground. Then solve the equation

For h(t)=40 ft

substitute in the quadratic equation

$-16t^2+80t+64=40$

$-16t^2+80t+24=0$

Solve the quadratic equation

we have

$a=-16\\b=80\\c=24$

substitute in the formula

$t=\frac{-80\pm\sqrt{80^{2}-4(-16)(24)}} {2(-16)}$

$t=\frac{-80\pm\sqrt{7,936}} {-32}$

$t=\frac{-80+\sqrt{7,936}} {-32}=-0.28$

$t=\frac{-80-\sqrt{7,936}} {-32}=5.28$

therefore

The potato is 40 feet off the ground at the time t=5.28 seconds

3 0

2 years ago

Find the 19th term of the arithmetic sequence whose common difference is =d5 and whose first term is =a12.

emmasim [6.3K]

An=a1+d(n-1)
a1=first term
d=common difference
n=which term

common difference is 5 first term is 2
an=5+2(n-1)
19th term is n=19
a19=5+2(19-1)
a19=5+2(18)
a19=5+36
a19=41

19th term is 41

4 0

3 years ago