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3 years ago

Solve the system by substitution 3x+y=-16 and y=-x-4

Mathematics

1 answer:

kap26 [50]3 years ago

7 0

Solution,

y = -x-4......(i)

3x + y =- 16.......(ii)

Now,

Substituting the value of y in equation (ii)

or, 3x + (-x-4)= -16

or,3x - x - 4 = -16

or, 2x= -16 +4

or, x = -12/2

: x = -6

Then,

Substituting the value of x in (i) equation;

or,y= -(-6) - 4

or,y= 6 - 4

: y =2

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Select the correct answer.

Likurg_2 [28]

Answer:

Step-by-step explanation:

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5 0

3 years ago

Solve (x + 1)2 – 4(x + 1) + 2 = 0 using substitution.

solniwko [45]

For this case we have to:

Let $u = x + 1$

So:

$u ^ 2-4u + 2 = 0$

We have the solution will be given by:

$u = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}$

Where:

$a = 1\\b = -4\\c = 2$

Substituting:

$u = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (1) (2)}} {2 (1)}\\u = \frac {4 \pm \sqrt {16-8}} {2}\\u = \frac {4 \pm \sqrt {8}} {2}\\u = \frac {4 \pm \sqrt {2 ^ 2 * 2}} {2}\\u = \frac {4 \pm2 \sqrt {2}} {2}$

The solutions are:

$u_ {1} = \frac {4 + 2 \sqrt {2}} {2} = 2 + \sqrt {2}\\u_ {2} = \frac {4-2 \sqrt {2}} {2} = 2- \sqrt {2}$

Returning the change:

$2+ \sqrt {2} = x_ {1} +1\\x_ {1} = 1 + \sqrt {2}\\2- \sqrt {2} = x_ {2} +1\\x_ {2} = 1- \sqrt {2}$

Answer:

$x_ {1} = 1 + \sqrt {2}\\x_ {2} = 1- \sqrt {2}$

3 0

2 years ago

Read 2 more answers

Which of the following illustrates the truth value of the given conditional statement?

Blababa [14]

Answer:

Option A. F T → F

Explanation:

A conditional is represented by:

p → q

Where p is called the antecedent, and q is the consequent.

Thus, a conditional states that if the antecedent is true, its consequent is also true; also, if the consequent is false, then the antecedent must be false.

On the other hand, if the antecedent is true, the consequent can be either true or false.

1. State the antecedent of the conditional and is truth value

Antecedent: 6 > 10

Truth value: False, because 6 is not greater than 10.

2. State the consequent of the conditional and its truh value

8 • 3 = 24

Truth value: True, because 8 times 3 is 24.

3. Truth value of the conditional

Hence, the truth value of the conditional is:

False Truth → Truth, or

F T → T

Which is the option A.

6 0

2 years ago

Read 2 more answers

PLZZZZ HELP The Lakeview city council is considering two different plans to help reduce the amount of pollution in the city. Pla

sdas [7]

1. The two equations follow the slope-intercept form which y=mx + b. They have the same y-intercept which is equal to 900.

2. Suppose x= 10
Plan Alpha: y=-7x+900=-7(10)+900=830
Plan Foxtrot: y = -17x+900 = -17(10)+900=730

Between the 2 plans, the lower value is 730. Plan Foxtrot is better for reduction of pollution.

3. The city council should choose Plan Foxtrot because the reduction of pollution is much greater. Their goal would be reached faster if they go with faster reduction of pollution.

5 0

2 years ago

The perimeter of a rectangular sandbox is 28ft. The length is six times the width.

VLD [36.1K]

Let the width =x
length = 6x
p=14x
28=14x
x=2

7 0

3 years ago