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2 years ago

Solve the system using substitution.

Mathematics

1 answer:

GaryK [48]2 years ago

4 0

Answer: x = 7, y = -3, z = 1

Step-by-step explanation:

EQ 1: 3x + 4y - z = 8 solve for z

+z -8 +z - 8

3x + 4y - 8 = z

EQ 3: 5x + y - 2z = 30 substitute 3x + 4y - 8 for z and solve for x

5x + y - 2(3x + 4y - 8) = 30

5x + y - 6x - 8y + 16 = 30

-x - 7y + 16 = 30

-16 -16

-x - 7y = 14

+7y +7y

-x = 7y + 14

x = -7y - 14

EQ 2: x - 5y + 2z = 24 substitute 3x+4y - 8 for z and -7y - 14 for x

(-7y - 14) - 5y + 2(3x + 4y - 8) = 24

-7y - 14 - 5y + 6(-7y - 14) + 8y - 16 = 24

-7y - 14 - 5y - 42y - 84 + 8y - 16 = 24

-46y - 114 = 24

+114 +114

-46y = 138

÷-46 ÷-46

y = -3

x = -7y - 14

= -7(-3) - 14

= 21 - 14

= 7

z = 3x + 4y - 8

= 3(7) + 4(-3) - 8

= 21 - 12 - 8

= 1

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Which graph represents the function over the interval [−3,3] ? f(x)=⌈x+1⌉

CaHeK987 [17]

Answer: The correct graph is the bottom left graph.

Step-by-step explanation:

Given function is f(x)=ceil(x+1)

To plot graph of f(x) in interval of(-3,3) :

ceil(x+1) is ceiling function

The output of ceil(x) is least integer greater than x

for example ceil(5.5)=6

For an interval of (-3,-2):

Take x=(-2.4)

x+1=(-1.4)

y=f(x)=ceil(x+1)=(-1)

Similarly,

For an interval of (-2,-1):

Take x=(-1.4)

x+1=(-0.4)

y=f(x)=ceil(x+1)=(0)

For an interval of (-1,0)

y=f(x)=1

For an interval of (0,1)

y=f(x)=2

For an interval of (1,2)

y=f(x)=3

For an interval of (2,3)

y=f(x)=4

Thus, The correct graph is the bottom left graph.

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2 years ago

Patricia owned so many posters that she decided to sell 77 of them to her friends.after selling the posters she still had 186 le

allochka39001 [22]

Answer:

Patricia initially had 263 posters.

Step-by-step explanation:

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3 years ago

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3 less than g is less than or equal to 17.

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Answer:

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Step-by-step explanation:

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3 years ago

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3 years ago

Sean earns 6.70 per hour working after school.He needs at least $155 to buy a new video game.Write an inequality that describes

Scorpion4ik [409]

Answer:

The inequality representing how many hours he should work in order to reach his goal would be

$x\geq 23.14$

where $x$ represents the number of hours Sean works.

Step-by-step explanation:

Hourly earnings of Sean from after school job = $6.70

Let Sean work for $x$ hours in order to earn at least $155.

We will use unitary method to find earning for $x$ hours.

If 1 hour earnings = $6.70

∴ in $x$ hours earnings in dollars would be = $6.70\times x=6.7x$

Now, we know Sean needs at least $155 to buy a new video game.

This means his earnings working $x$ hours must be at least $155.

Thus, the inequality representing how many hours he should work in order to reach his goal would be

$6.7x\geq 155$

Dividing both sides by 6.7.

$\frac{6.7x}{6.7}\geq \frac{155}{6.7}$

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Thus, Sean should work a minimum of 23.14 hours to earn at least $155.

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