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Inessa [10]
2 years ago
10

The mapping diagram shows a functional relationship.

Mathematics
1 answer:
xxTIMURxx [149]2 years ago
8 0

Answer:

you already know the answer?

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One Endpoint is 9,18 and the midpoint is 14,16 what the other end point
Valentin [98]
\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ 9}}\quad ,&{{ 18}})\quad 
%  (c,d)
&({{ x}}\quad ,&{{ y}})
\end{array}\qquad
%   coordinates of midpoint 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)

\bf \left( \cfrac{x+9}{2}~,~\cfrac{y+18}{2} \right)=\stackrel{\textit{midpoint}}{(14,16)}\implies 
\begin{cases}
\cfrac{x+9}{2}=14\\\\
x+9=28\\
\boxed{x=19}\\
-------\\
\cfrac{y+18}{2}=16\\\\
y+18=32\\
\boxed{y=14}
\end{cases}
7 0
3 years ago
At the beginning of a snowstorm, Grayson had 10 inches of snow on his lawn. The snow then began to fall at a constant rate of 0.
maxonik [38]

Answer:

  • Grayson had 10 inches of snow in his lawn
  • the snow falls at a constant rate of 0.5 inches per hour
  • no snow was melting
  • the snow has fallen for 3 hours  

Let y be the height of the snow in the lawn

Grayson had 10 inches at the beginning (at t=0) so y= 10

3 hours passed so y= 10 + 3*0.5 = 11.5 inches

Grayson had 11.5 inches after three hours

Assuming that the snow continued to fall for an unkhown time t

y = 0.5*t + 10

we had 10 at the beginning so we add 10 (+10)

the snow is growing by 0.5 inches in the single hour so we multiply by 0.5

t is the time and it can 4, 5, 6 ...... hours

Just like a function :

  • 0.5 is the slope
  • t is the variable
  • 10 is the y-intercept

3 0
3 years ago
How many solutions does an equation of the form x^2- k^2= 0 have?
N76 [4]
1. Use Difference of squares: a^2-b^2=(a+b)(a-b)
(x+k)(x-k)=0

2. Solve for x and k
x=+-k
k=+-x
8 0
3 years ago
Find the exact value of sin2 theta given sin theta =5/13, 90°<theta <180°
Zepler [3.9K]
Now, we know that 90°< θ <180°, that simply means the angle θ is in the II quadrant, where sine is positive and cosine is negative.

\bf sin(\theta )=\cfrac{\stackrel{opposite}{5}}{\stackrel{hypotenuse}{13}}\impliedby \textit{now let's find the \underline{adjacent side}}&#10;\\\\\\&#10;\textit{using the pythagorean theorem}\\\\&#10;c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\qquad &#10;\begin{cases}&#10;c=hypotenuse\\&#10;a=adjacent\\&#10;b=opposite\\&#10;\end{cases}

\bf \pm\sqrt{13^2-5^2}=a\implies \pm\sqrt{144}=a\implies \pm 12 =a \implies \stackrel{II~quadrant}{-12=a}&#10;\\\\\\&#10;therefore \qquad cos(\theta )=\cfrac{\stackrel{adjacent}{-12}}{\stackrel{hypotenuse}{13}}&#10;\\\\&#10;-------------------------------\\\\&#10;sin(2\theta )\implies 2sin(\theta )cos(\theta )\implies 2\left(\frac{5}{13}  \right)\left( \frac{-12}{13} \right)\implies -\cfrac{120}{169}
3 0
3 years ago
A survey of pet owners found that on average, they spend $1,225 annually per pet, with a standard deviation of $275. Between whi
earnstyle [38]

Answer:

B.$675 and $1,775

Step-by-step explanation:

8 0
3 years ago
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