1. The concession stand is selling hot dogs and hamburgers during a game. At halftime, they sold a total of 78 hot dogs and hamburgers and brought in $105.50. how many of each item did they sell if hamburgers sold for $1.50 and hot dogs sold for $1.25?

Answers

Answer 1

Answer: 46 hotdogs ang 32 hamburgers

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Adina has a rectangular garden that measures 9 m wide by 13 m long. She wants to increase the area to 192 m^2 by increasing the width and length by the same amount. What will be the width (shorter dimension) of the new garden?Question 4 options: a) 14 m wide b) 13 m wide c) 12 m wide d) 11 m wide
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Two planes leave the airport at the same time. In one hour the plane that has flown north has traveled 400 miles. The plane that has flown southwest has traveled 250 miles. How far apart are the planes? LAW OF COSINES
GEOMETRY

Answers

$a^2=b^2+c^2-2\cdot b\cdot c\cdot cos \alpha \n---------------\n\nx^2=250^2+400^2-2\cdot250\cdot400\cdot cos135^0\n\nx^2=62,500+160,000-200,000\cdot cos(180^0-45^0)\n\nx^2=222,500-200,000\cdot(-cos45^0)\n\nx^2=222,500-200,000\cdot ( √(2) )/(2) \n\nx^2=222,500+100,000\cdot √(2) \n\nx^2=2500\cdot(89+40 √(2) )\n\n$

$x=50\cdot \sqrt{89+40 √(2)} \ \ \ \Rightarrow\ \ \ x\approx603.26\ [miles]\n\nAns.\ the\ distance\ is\ about\ 603.26\ miles$

This table represents the boiling point of water at different altitudes. Which equation represents water's boiling point (y) based on the change in altitude (x)? Altitude (thousands of feet) Boiling Point of Water (Fahrenheit) (sea level) 0 212 0.5 211.1 1.0 210 2.0 208.4 2.5 207.5 3.0 206.6 4.0 204.8 4.5 203.9

Answers

Answer:

The required equation is $y=-1.8x+212$ .

Step-by-step explanation:

We are given,

The table showing the boiling points of water at different altitudes.

We will find the slope of the equation using $m=(y_(2)-y_(1))/(x_(2)-x_(1))$ .

Taking points (0,212) and (0.5,211.1) and substituting in the formula,

Slope is $m=(211.1-212)/(0.5-0)$

i.e. Slope is $m=(-0.9)/(0.5)$

i.e. Slope is -1.8

Substituting slope and the point (0,212) in the equation $y=mx+b$ , we will find the value of y-intercept 'b'.

That is, $212=-1.8* 0+b$ i.e. b= 212

Thus, the required equation is $y=-1.8x+212$ .

If the exterior sides of two adjacent angles are opposite rays, then the angles are _____ angles. A. complementary
B. supplementary
C. vertical
D. right

Answers

The correct answer is B. Supplementary

That is the basic definition of what supplementary angles are and can be found in any textbook.

Answer supplementary

Step-by-step explanation:

Please solve the following simultaneous equation:
4x-3y=15
8x^2-27y^2=45

Answers

{ 4 x - 3y = 15
8 x² - 27 y² =45

Isolate y for 4 x - 3y = 15

4 x - 3y = 15 ( add 3y to both sides ):

4x-3y +3y = 15 + 3y

4x = 15 + 3y

Divide both sides by 4 :

4x / 4 = 15 + 3y / 4

x = 15+3y / 4

Plug the solutions x = 15+3y / 4 into : 8 x² - 27 y²=45

8 ( 15+3y / 4 )² - 27 y² = 45

1/2 ( 3y+15)² - 27 y² = 45

Multiply by LCD = 2

9 ( y+5)² - 54 y² = 90

-45 y² + 90 y + 225 = 90

- 45 y² + 90 y = 225 - 90

-45 y² + 90 y = 135 = 0

-45 ( y + 1 ) ( y - 3 ) = 0

Using the zero factor principle:

Solve ( y + 1 ) = 0

y = - 1

Solve ( y - 3 ) = 0

y = 3

y = -1 and y = 3

Plug the solution y = -1 , y = 3 into : 4 x - 3 y = 15

4 x - 3 y = 15 for - 1 :

4 x - 3 ( - 1 ) = 15

4 x + 3 = 15

4 x = 15 - 3

4 x = 12

x = 12 / 4

x = 3

For 3 :

4 x - 3 y = 15

4 x - 3 ( 3 ) = 15

4 x - 9 = 15

4 x = 15 + 9

4 x = 24

x = 24 / 4

x = 6

Therefore the final solution :

y = 3 , x = 6
y = - 1 , x = 3

hope this helps!

A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 140 lb and each box of books weighs 50 lb. The maximum capacity of the elevator is 830 lb. How many boxes of books can the delivery person bring up at one time?

Answers

We can model this with the following inequality

50x + 160 ≤ 1000 where x is the number of boxes....so, subtracting 160 from each side, we have

50x ≤ 840 divide both sides by 50

x ≤ 16.8 boxes ....but since he can't bring up partial boxes, round down to 16

the area of the U.S. is about 3.778 million square miles. Approximately670000 square miles are worked for food production. what percent of the U. S. is worked for food production?

Answers

$(670,000)/(3,778,000)$ × $100=9.71$ %

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