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Oduvanchick [21]
3 years ago
8

Solve the system

Mathematics
1 answer:
konstantin123 [22]3 years ago
7 0
Use substitution. 

y = 2 - x and y = 4x + 7 can become

2 - x = 4x + 7

Now solve for x

-5 = 5x

-1 = x

Now plug -1 for x in either equation.

y = 2 - x -> y = 2 - (-1) -> y = 3
y = 4x + 7 -> y = 4*-1 + 7 -> y = -4 + 7 -> y = 3

So C) is the correct answer.
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James has a certain amount of money. If he buys $3$ pens and $2$ pencils, he will have $\$2$ left over. If he buys $2$ pens and
labwork [276]

The cost of pen and pencils are related to the number that can be bought

with a given amount of money.

  • <u />\underline{The \ ordered  \ pair \  (a,  \, b)  \ is  \ (6, \,  2)}<u />

Reasons:

The given parameters are;

If  the number number of pens and pencils James buys = 3 pens and 2 pencils, the amount James will have left = $2

If the number of pens and pencils James buys = 2 pens and 3 pencils, the amount James will have left = $6

The amount of money Judith has = The amount of money with James

The number of pens and pencil James and Judith can buy = 6 pens and 6 pencils

The cost of one pen = a

The cost of one pencil = b

Required:

To find the ordered pair (a, b)

Solution:

Let <em>X</em> represent the initial amount of money James has, we get;

X - (3·a + 2·b) = 2...(1)

X - (2·a + 3·b) = 6...(2)

2·X = 6·a + 6·b...(3)

Therefore;

X = (6·a + 6·b) ÷ 2 = 3·a + 3·b

Which from equation (1) gives;

3·a + 3·b - (3·a + 2·b) = 2

3·a + 3·b - 3·a - 2·b = 2

3·b - 2·b = 2

b = 2

Subtracting equation (1) from equation (2) gives;

(X - (2·a + 3·b)) - (X - (3·a + 2·b)) = 6 - 2 = 4

-2·a - 3·b + 3·a + 2·b = 4

a - b = 4

a = 4 + b

∴ a = 4 + 2 = 6

a = 6

<u />

<u />

\underline{The \ ordered  \ pair \  (a,  \, b)  \ is  \ (6, \,  2)}<u />

Learn more about word problems and simultaneous equations here:

brainly.com/question/14294864

8 0
2 years ago
A forester wishes to predict the volume (in cubic feet) of usable lumber in a certain species of tree using the height (in feet)
alex41 [277]

Answer: The response variable = Volume

and explanatory variable(s) in this study are: Height and Diameter.

Step-by-step explanation:

Important definitions:

  • The explanatory variable is a type of independent variable manipulated by the experimenter for the ongoing experimental study.
  • The response variable is a type of dependent variable which depends on the explanatory values provided by the experimenter.

Given: A forester wishes to predict the volume (in cubic feet) of usable lumber in a certain species of tree using the height (in feet) and diameter (in inches) of the trees.

Here, Volume directly depends upon the height and diameter of the tree.

Also, forester ( Experimenter) wants to predict volume by cutting tree that means it is an response variable and it depends on height and diameter , so height and diameter are explanatory variable.

Hence, The response variable = Volume

and explanatory variable(s) in this study are: Height and Diameter.

7 0
3 years ago
How would you convert 0.91 repeating into a fraction?
Eva8 [605]

It has to be a little greater than 91/100

so try dividing by 99:-

91 / 99 = 0.919191..

Answer 91/99

5 0
3 years ago
What is the sequence of transformations that maps abc to a’b’c’ ?
JulsSmile [24]

Answer:

In Step 1: option D is correct

And in step 2: option A is correct.

Step-by-step explanation:

We have been given the graph

The figure in fourth quadrant after rotating 90 degrees counterclockwise about the origin will shift in first quadrant.

And after translating 4 units left will give the figure shown in second quadrant.

Therefore, In Step 1: option D is correct

And in step 2: option a is correct.

5 0
3 years ago
Use the word below to make a sentence
boyakko [2]

Answer:

The prize for the first one to brake that glass in the grass during a train moving will get a free VIP pass to the tourtament of cricket, also it will need to bring a towel to dry yourself in the pool included.

5 0
3 years ago
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