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3 years ago

Your family goes to a Southern-style restaurant for dinner. There are 6 people in your family.

Mathematics

1 answer:

Viktor [21]3 years ago

4 0

Answer:

Number of people who order chicken dinner = 1

Number of people who order the steak dinner = 5

Step-by-step explanation:

Let

x = number of people who order chicken dinner

y = number of people who order the steak dinner

x + y = 6 (1)

14x + 17y = 99 (2)

From (1)

x = 6 - y

Substitute into (2)

14x + 17y = 99 (2)

14(6 - y) + 17y = 99

84 - 14y + 17y = 99

- 14y + 17y = 99 - 84

3y = 15

y = 15/3

y = 5

Substitute y = 5 into (1)

x + y = 6 (1)

x + 5 = 6

x = 6 - 5

x = 1

Number of people who order chicken dinner = 1

Number of people who order the steak dinner = 5

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Alla [95]

$\bf \begin{array}{clclll}
3^{1001}&\qquad &4^{1002}\\
\uparrow &&\uparrow \\
a&&b
\end{array}\\\\
-----------------------------\\\\
(a+b)^2-(a-b)^2\implies (a^2+2ab+b^2)-(a^2-2ab+b^2)
\\\\\\
a^2+2ab+b^2-a^2+2ab-b^2\implies 2ab+2ab\implies 4ab
\\\\\\
now\qquad 4(3^{1001})(4^{1002})=k12^{1001}\qquad 
\begin{cases}
12^{1001}\\
(4\cdot 3)^{1001}\\
4^{1001}\cdot 3^{1001}
\end{cases}$

$\bf \\\\\\
4(3^{1001})(4^{1002})=k(4^{1001}\cdot 3^{1001})\implies \cfrac{4(3^{1001})(4^{1002})}{4^{1001}\cdot 3^{1001}}=k
\\\\\\
4\cdot \cfrac{3^{1001}}{3^{1001}}\cdot \cfrac{4^{1002}}{4^{1001}}=k\implies 4\cdot 4^{1002}4^{-1001}=k\impliedby 
\begin{array}{llll}
\textit{same base}\\
\textit{add the}\\
exponents
\end{array}
\\\\\\
4\cdot 4^{1002-1001}=k\implies 4\cdot 4^1=k\implies 16=k$

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3 years ago

Solve by graphing y<7/3x + 5 and x<-3

Molodets [167]

Slope : -7/3

Y-Intercept: 4

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3 years ago

(WILL GIVE BRAINLIEST)

weeeeeb [17]

Answer:

m<I=57

m<J=57

m<K=66

Step-by-step explanation:

All the angles in a triangle add up to 180 degrees.

m<I= 3x+18

m<K= 5x+1

m<I is congruent to m<J.

We can plug the information we already know into the equation.

3x+18+3x+18+5x+1=180

11x+37=180

Subtract 37 from both sides.

11x=143

x=13

Now, we can find out what the angles are.

m<I= 3x+18

m<I=3(13)+18

m<I=39+18

m<I=57

We know that m<I=m<J, so they are both equal to 57 degrees.

m<J=57

Now for m<K:

m<K=5x+1

m<K=5(13)+1

m<K=65+1

m<K=66

We know this is correct because 57+57+66=180.

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