MATHEMATICS HIGH SCHOOL

The difference of two numbers is 11 and their product is 42.find these numbers.

Answers

Answer 1
Answer: \left\{\begin{array}{ccc}x-y=11&\to x=y+11\nx\cdot y=42\end{array}\right\n\n(y+11)y=42\ny^2+11y-42=0\ny^2+14y-3y-42=0\ny(y+14)-3(y+14)=0\n(y+14)(y-3)=0\iff y=-14\ \vee\ y=3\n\nx=-14+11=-3\ \vee\ x=3+11=14\n\nAnswer:-3\ and\ -14\ or\ 14\ and\ 3
Answer 2
Answer: a-b=11\n a=11+b \n ab=42 \n(11+b)*b=42 \n b^2+11b=42 \n b^2+11b-42=0 \n b^2 +14b-3b -42=0 \n b(b+14)-3(b+14)=0 \n (b+14)(b-3)=0 \n b+14=0 \ b-3=0 \nb= -14 \ b=3 a=11+b \n 1)a=11-14 \na=-3 \n 2)a=11+3 \n a=14

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1. If Ronnie paid $40 for 8 hamburgers, find the unit price of a hamburger.

Answers

Answer:

The burger is $5 each.

Step-by-step explanation:

8x = 40

x = 5

Answer:

the unit price would be $5

Step-by-step explanation:

40÷8=5

5×8=40

Adam is going to cook a turkey for 14 people and wants to allow ¾ lb of turkey for each person. 1lb = 450 g
How much would a turkey cost for 14 people? £

Answers

Missing info:
Turkey Sizes: 
small - 2kg - 3.9kg 
medium - 4kg - 5.4kg 
large - 5.5kg - 7.2kg 
extra large - 7.3kg - 9.2kg 

Turkey Prices: 
Small / Medium - £5.99 per kg 
Large / Extra Large - £4.99 per kg 

3/4 lb x 14 persons = (3*14)/4 = 42/4 = 10.5 lbs

1 lb = 450 grams

10.5 lbs * 450grams/lb = 4,725 grams

1 kg = 1000 grams

4,725 grams * 1kg/1000 grams = 4725 kg / 1000 = 4.725 kg.

4.725 kg is under the Medium size of the Turkey.

Medium sized turkey costs £5.99 per kg.

4.725 kg * £5.99 per kg = £28.30

A turkey would cost  £28.30 for 14 people.

How to solve this
The minimum value of f is f×3=-5 and f×1=2

Answers

F ========== 2....................

Final answer:

The question provides two equations involving the variable f. By isolating f in these equations, we derive two possible values for f. The minimum value for f is the smaller of these two derived values, which is -5/3.

Explanation:

To solve this we can use the principle that if two different values of f multiply with different numbers to equal different constants, we can set up a system of equations to find those values of f.

The given equations are f×3=-5 and f×1=2. Let's denote f×1 as f₁ and f×3 as f₂.

  • From f×1=2, we get f₁=2/1=2
  • From f×3=-5, we get f₂=-5/3

So, the minimum value of f, that is f_min would be the smaller of f₁ and f₂. As -5/3 is smaller than 2, f_min = -5/3.

Learn more about Solving System of Equations here:

brainly.com/question/31653301

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Is. 1.2/3 and 1.8/4.5 proportional or not?

Answers

Answer:proportional

Step-by-step explanation: i took the test!

if it takes juwan exactly 35 minutes by car to get to his grandmother's. the nearest parking area is a 4-minute walk from her apartment.one week, he realized that he spent 5 hours and 12 minutes traveling to her apartment, and then back Home. how many round trips did he make to visit his grandmother's?

Answers

He made 4 round trips to visit his grandmother.

Further Explanation

Step 1

Amount of time he spent to get to his grandmother’s = 35 minutes and extra 4-minute walk (and can be expressed as 35 + 4)

= 35 + 4  

= 39

Step 2

To complete a round trip, the amount of time he spent to his grandmother’s will be multiply by 2

Therefore,

= 39 x 2

= 78

Total amount of time of a round trip = 78

Step 3

Amount of time he spent on a trip to her apartment and back home = 5 hours and 12 minutes

To determine that, 5 hours will be added to 12 minutes

Therefore,

Since 1 hour = 60,

Then, (5 x 60) +12

= (5 x 60) + 12

= 300 + 12

= 312

Amount of time he spent on a trip to her apartment and back home = 312

Step 4

To determine how many round trip he made, the amount of time he spent on a trip to her apartment and back home (312) will be divided by the total amount of time of a round trip (78) i.e. 312 ÷ 78

= 312 ÷ 78

= (312)/(78)

= 4

Therefore Juwan made a total of 4 round trips to his grandmother’s place.

LEARN MORE:

KEYWORDS:

  • juwan
  • apartment
  • 4-minute walk
  • grandmother
  • parking area
  • round trips
1 Round Trip = 2(35 min + 4 min) = 78 min

Total time spent travelling:
(5 hrs * 60 min/hr) + 12 min = 312 min

Number of Round Trips:
(312 min)/(78 min) = 4 round trips

What is the general solution for (cosX + sinX)(1 - 2sinX)=0

Answers

1. square both sides, a straight forward method. 
2. hand plot 
3. calculator plot, not recommended.Let Y=sin x + cos x -1 
Y=0, find x=? 
4. Substitute 1=sin^2(x) + cos^2(x) on the right hand side 
Y1=sin^2(x) - sin(x) 
Y2=cos^2(x) - cos(x) 
Y1 + Y2=0, Y1=0, Y2=0, 
a(a-1)=0, so, a=0, a=1, where a=sin(x), or cos(x), 
so x=0, pi/2 
Have a good day!
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