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mihalych1998 [28]
3 years ago
13

Catarina is buying supplies for a party. She plans to spend at least $100 on food and at least $50 on party favors. She can spen

d no more than $250 total on food and party favors.
Write three inequalities, how much Catarina plans to spend on food, party favors and food.
Mathematics
1 answer:
harkovskaia [24]3 years ago
3 0

Answer:

food \geq 100

favors \geq 50

total \leq 250

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A circle passes through points A(7,4), B(10,6), C(12,3). Show that AC must be the diameter of the circle.
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so we have three points, A, B and C, if indeed AC is the diameter of the circle, then half the distance of AC is its radius, and the midpoint of AC is the center of the circle, morever, since B is also on the circle, the distance from B to the center must be the same radius distance.

in short, half the distance of AC must be equals to the distance of B to the midpoint of AC, if indeed AC is the diameter.

\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{12}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{12+7}{2}~~,~~\cfrac{3+4}{2} \right)\implies \left( \cfrac{19}{2}~~,~~\cfrac{7}{2} \right)=M\impliedby \textit{center of the circle}

now, let's check the distance from say A to the center, and check the distance of B to the center, if it's indeed the center, they'll be the same and thus AC its diameter.

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AM=\sqrt{\left( \frac{19}{2}-7 \right)^2+\left( \frac{7}{2}-4 \right)^2} \\\\\\ AM=\sqrt{\left( \frac{5}{2}\right)^2+\left( -\frac{1}{2} \right)^2}\implies \boxed{AM\approx 2.549509756796392} \\\\[-0.35em] ~\dotfill

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{10}~,~\stackrel{y_1}{6})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}}) \\\\\\ BM=\sqrt{\left( \frac{19}{2}-10 \right)^2+\left( \frac{7}{2}-6 \right)^2} \\\\\\ BM=\sqrt{\left( -\frac{1}{2}\right)^2+\left( -\frac{5}{2} \right)^2}\implies \boxed{BM\approx 2.549509756796392}

6 0
3 years ago
PLEASE HELP! I WILL GIVE BRAINLIEST!!!! (no trolls) PLEASE SHOW WORK OR GIVE EXPLANATION!!!!!!
IgorLugansk [536]

explanation:

The fastest way to find the missing endpoint is to determine the distance from the known endpoint to the midpoint and then performing the same transformation on the midpoint.  In this case, the x-coordinate moves from 4 to 2, or down by 2, so the new x-coordinate must be 2-2 = 0.  The y-coordinate moves from 4 to -5, or down by 9, so the new y-coordinate must be -5-9 = -14.

 

An alternate solution would be to substitute (4,4) for (x1,y1) and (2,-5) for (x,y) into the midpoint formula:

x=(x1+x2)/2

y=(y1+y2)/2

Solving each equation for (x2,y2) yields the solution (0,-14).

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3 years ago
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Then, look in the Fed Tax tables (
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Therefore, calculate the income tax due: 35.70 + (752.1 - 521) × 15 ÷ 100 = 70.37$

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myrzilka [38]

The volume of a rectangular prism is given by the multiplication of its three dimensions: if w, h, l are the width, height and length of the prism, the volume is

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lesantik [10]

Answer: 77.05

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2 years ago
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