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PilotLPTM [1.2K]
3 years ago
9

Peter baked 18 cookies. He gave 2/3 of the cookies to his friend. How many cookies did Peter give to his friend

Mathematics
2 answers:
MissTica3 years ago
7 0

Peter had 18 cookies. He gave 2/3 of the cookies to his friend. How many cookies did Peter give to his friend?

Explanation: you divide 18 into 3 groups and you can split it into groups of 6. Peter gave his friend 2/3 which equals 12/18 cookies

Answer: Peter gave his friend 12 cookies



andre [41]3 years ago
4 0

Answer:

12

thStep-by-step explanation:

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Given: KPST is a trapezoid, KP=ST, MN is a midsegment, MN=20, h=15, PS:KT=3:7 Find: KS and KP
lions [1.4K]

Answer:

Length of KS = 25 units and

Length of KP = 17 units.

Step-by-step explanation:

Given: KPST is a trapezoid, KP =ST, MN is a mid segment, h is the height =15

Also it is given that, MN = 20 , h = 15 and PS:KT = 3:7.

  • If two sides of the trapezoid are equal then, it is an isosceles trapezoid.
  • Mid-segment of a trapezoid is a line segment which connects the midpoints of the non-parallel sides.
  • A trapezoid mid segment connects the midpoints of two congruent sides of the trapezoid and is parallel to the pair of parallel sides.
  • Length of the mid segment is the sum of two bases divide by 2

Since, the length of Mid-segment MN = 20.

Also, it is given: PS:KT = 3:7

Let  PS = 3x and KT = 7x respectively.

then;

\frac{PS+KT}{2} = 20

\frac{3x+7x}{2} = 20

\frac{10x}{2} =20

On Simplify, we get;

5x =20

Divide both sides by 5 we get;

x =4

Then:

Length of base PS = 3x = 3(4) = 12 and Length of base KT = 7x = 7(4) = 28.

Now, In triangle PLK

Using Pythagoras theorem to find KP;

It is given here, PL =h =15 and KL= 8 {you can see in the figure as shown below};

KP^2= PL^2 + KL^2

KP^2 = 15^2+8^2 =225 +64 = 289

KP = \sqrt{289}

Simplify:

KP = 17

therefore, the length KP = 17 units

To, construct a line: Join K and S

Now, in triangle KRS

KR = KL +LR = 8 +12 =20 and SR = h= 15

Using Pythagoras theorem in KRS to find KS;

KS^2 = SR^2+KR^2

KS^2 = 15^2 + 20^2 = 225 + 400 = 625

KS = \sqrt{625}

On simplify:

KS = 25

Therefore, the length of KS is, 25 units.

4 0
3 years ago
10. An arithmetic sequence has this recursive formula. What is the explicit formula?​
Mrrafil [7]

Answer:

a_{n}=45-3n

Step-by-step explanation:

Method 1:

Arithmetic sequence is in the form

a_{n} =a_{1} +(n-1)d\\

d is the common difference, can be found by:

d=a_{n}-a_{n-1}=-3

Subtituting the a_{1} and d

You get:

a_{n}=42+(-3)(n-1)=45-3n

Method 2 (Mathematical induction):

Assume it is in form a_{n}=45-3n

Base step: a_{1} =45-3(1)=42

Inducive hypophesis: a_{n}=45-3n

GIven: a_{n+1} =a_{n}-3

a_{n+1}=45-3n-3=45-3(n+1)

Proved by mathematical induction

a_{n}=45-3n

5 0
3 years ago
How do you describe the solution set to a system of linear inequalities?
Tatiana [17]

Answer:

How do you describe the solution set to a system of linear inequalities?

Step-by-step explanation:

The solutions of a system of linear inequalities are all the ordered pairs that make all the inequalities in the system true.

6 0
2 years ago
a box holds red pens and blue pens the ratio of red pens to blue pens is 1 to 4 The box holds 12 more blue pens than red pens wh
Genrish500 [490]

Answer:

20 pens

Step-by-step explanation:

if there is 1 red pen for every 4 blue pens

then

4 red pens would have 16 blue pens with it. makes a total of 20 pens, with 12 more blue pens than red pens

7 0
3 years ago
Add​​ using a number line.<br><br>-2 + 4<br><br>5__ 5
pogonyaev

Answer: i.. do.... not... know..

Step-by-step explanation:

6 0
1 year ago
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