Mathematics, 07.01.2021 18:40, brisamauro27

The area of a square tile is 1.56 square feet. What is the area of a floor covered with 103 tiles?

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answered: Guest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

answered: Guest

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.

$\bf \textit{hyperbolas, vertical traverse axis } \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} [-0.35em] \rule{34em}{0.25pt} \begin{cases} h=0\\ k=0\\ a=\sqrt{5}\\ c=3 \end{cases}\implies c=\sqrt{a^2+b^2}\implies 3=\sqrt{(\sqrt{5})^2+b^2}\implies 3^2=5+b^2$

$\bf 3^2-5=b^2\implies 9-5=b^2\implies 4=b^2\implies \sqrt{4}=b\implies \boxed{2=b} [-0.35em] ~\dotfill \cfrac{(y-0)^2}{(\sqrt{5})^2}-\cfrac{(x-0)^2}{2^2}=1\implies \cfrac{y^2}{5}-\cfrac{x^2}{4}=1$

answered: Guest

Idk but keep trying

answered: Guest

step-by-step explanation:

you just have to add the 15 + 9 to get 24

you do this bc you want to find the total of the whole line and those two numbers make up the line

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