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andrew-mc [135]
3 years ago
11

Translate to a system of equations and solve.

Mathematics
2 answers:
hoa [83]3 years ago
5 0

Step-by-step explanation:

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luda_lava [24]3 years ago
5 0

Answer:

12 and 15

Step-by-step explanation:

Let the numbers be called x and y.  We know from the first sentence that:

x + y = 27.

From the second sentence we know that x + 3 = y. (In this problem it does not matter which is x and which is y.)

Substituting in x + 3 into the first equation, we have

x + x + 3 = 27

2x + 3 = 27

2x + 3 - 3 = 27 - 3

2x = 24

x = 12

y = x+ 3 = 15

Check: does x + y = 27?  Yes, 12 + 15 = 27

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Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar pe
vesna_86 [32]
Let
 x = loaves of bread
 y = batches of muffins
 You must make a system of two equations with two unknowns that describe the problem
 3.5x + 2.5y = 17 --- (1)
 0.75x + 0.75y = 4.5 --- (2)
 Resolving we have
 x = 6-y (from (2))
 replacing in (1)
 3.5 (6-y) + 2.5y = 17
 21 - 3.5y + 2.5y = 17
 y = 21-17 = 4
 Then substituting in (2)
 x = 6-y = 6-4 = 2
 Answer
 Helena could bake:
 2 loaves of bread
 4 batches of muffins
8 0
3 years ago
The ratio x:10 is equilvalent to 9:6. What is the value of x
Troyanec [42]

Answer: x=20/3=6.67

Step-by-step explanation:

To solve proportions, the most useful way is to use [cross multiplication], where we not multiply horizontally but as diagonally.

-----------------------------------------------------------------------------

Given

x:10=9:6

Cross Multiply

9·x=6·10

9x=60

Divide 9 on both sides

9x/9=60/9

x=20/3=6.67

Hope this helps!! :)

Please let me know if you have any questions

4 0
3 years ago
A city-wide gardening club is up of men, women and children in the ratio 5:4:11.
Sever21 [200]

Answer:

Women: 448  Men: 560  Children: 1232

Step-by-step explanation:

5+4+11 = 20/2240 = 112

Women = 4 x 112 = 448

Men = 5 x 112 = 560

Children = 11 x 112 = 1232

Total = 1232 + 560 +448 = 2240

3 0
3 years ago
What side is this a isosceles a scalene or equilateral
aksik [14]
The answer is a scalene
3 0
3 years ago
Someone ask me to solve this.
Semenov [28]
X=2h, y=3k

Substitute these values into equations.

y+2x = 4 ------> 3k+2*2h=4 ----->  3k +4h =4

2/y - 3/2x = 1-----> 2/3k -3/(2*2h) = 1 ------> 2/3k - 3/4h =1

We have a system of equations now.

 3k +4h =4          ------> 3k = 4-4h ( Substitute 3k in the 2nd equation.)
2/3k - 3/4h =1

2/(4-4h) -3/4h = 1
2/(2(2-2h)) - 3/4h = 1
1/(2-2h) -3/4h - 1=0

4h/4h(2-2h) -3(2-2h)/4h(2-2h) - 4h(2-2h)/4h(2-2h) =0

(4h- 3(2-2h) - 4h(2-2h))/4h(2-2h) = 0
Numerator should be = 0
4h- 3(2-2h) - 4h(2-2h)=0

Denominator cannot be = 0
4h(2-2h)≠0

Solve equation for numerator=0
4h- 3(2-2h) - 4h(2-2h)=0
4h - 6+6h-8h+8h² =0
8h² +2h -6=0
4h² + h-3 =0
(4h-3)(h+1)=0
4h-3=0, h+1=0
h=3/4  or h=-1

Check which
4h(2-2h)≠0
1) h= 3/4  , 4*3/4(2-2*3/4)=3*(2-6)= -12 ≠0, so we can use h= 3/4
2)h=-1, 4(-1)(2-2*(-1)) =-4*4=-16 ≠0, so we can use h= -1, also.

h=3/4, then  3k = 4-4*3/4 =4 - 3=1 , 3k =1, k=1/3
h=-1, then  3k = 4-4*(-1) =8 , 3k=8, k=8/3 

So,
if h=3/4, then  k=1/3,
and if h=-1, then  k=8/3 .




6 0
2 years ago
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