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inessss [21]
3 years ago
5

What is the answer to: y=-2x-5,4x+3y=15 using substitution to solve it..??

Mathematics
1 answer:
MrRa [10]3 years ago
4 0

Answer:

Step-by-step explanation:

Plug the first equation into the second

4x+3(-2x-5)=15\\4x-6x-15=15\\-2x=30\\x=-15

y=-2(-15)-5

=30-5

=25

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The range of all real numbers x such that 2x − 5 < 7 and 4x + 10 > 6 is . The range of all real numbers x such that 2x − 5
lisov135 [29]

Solution for Part 1:

2x − 5 < 7 and 4x + 10 > 6 is called a compound inequality. To find the range we need to solve each of the inequality and range would be the values of x which will make both the inequality TRUE.

Solving inequality 2x - 5 < 7:

2x - 5 < 7 {adding 5 on both sides}

2x - 5 + 5 < 7 + 5 {Combining like terms in either side of inequality}

2x < 12 {Dividing 2 on both sides}

2x/2 < 12/2 {Simplifying fraction in either side of inequality}

x < 6

Solving inequality 4x + 10 > 6:

4x + 10 > 6 {Subtracting 10 on both sides of inequality}

4x + 10 - 10 > 6 -10 {Combining like terms on either side}

4x > -4 {Dividing by 4 on both sides}

4x/4 > -4/4 {Simplifying each fraction}

x > - 1

Range of 2x − 5 < 7 and 4x + 10 > 6 will be all the x value which satisfy both the inequality x < 6 and x > -1.

Conclusion Part 1:

The range of all real numbers x such that 2x − 5 < 7 and 4x + 10 > 6 is can be given by interval notation (-1, 6)

Solution for part 2:

2x − 5 < 7 or 4x + 10 > 6 is called a compound inequality. To find the range we need to solve each of the inequality and range would be the values of x which The solution is same as part 1, with a small difference.

Range of 2x − 5 < 7 or 4x + 10 > 6 will be all the x value which satisfy any one of the inequality x < 6 or x > -1.

Conclusion Part 2:

The range of all real numbers x such that 2x − 5 < 7 or 4x + 10 > 6 is can be given by interval notation (-∞, ∞)

Note:

(i) When two inequalities are joined by the word and, the solution of the compound inequality occurs when both inequalities are true at the same time. It is the overlap, or intersection, of the solutions for each inequality.

(ii) When the two inequalities are joined by the word or, the solution of the compound inequality occurs when either of the inequalities is true. The solution is the combination, or union, of the two individual solutions.

6 0
3 years ago
What are the answers for a-c... Need the answers asap...thank you
xxMikexx [17]
For Letter C You Need to Count The Squares in the Pond And the Half Squares are a Half. The Answer for C is 33 Because The Half and the Other Half is a Whole So I Made 3 New Wholes and Added it to the 30.
7 0
3 years ago
F(x)=2x^2-x-6 g(x)=4-x (f+g)(x)
Semenov [28]

\large  \boxed{(f + g)(x) = f(x) + g(x)}

The property above is distribution property where we distribute x-term in the function.

Substitute both f(x) and g(x) in.

\large{ \begin{cases} f(x) = 2 {x}^{2}   -  x - 6 \\ g(x) =  4 - x \end{cases}}  \\  \large{f(x) + g(x) = (2 {x}^{2}  - x - 6) + (4 - x)} \\  \large{f(x) + g(x) = 2 {x}^{2}  - x - 6 + 4 - x}

Évaluate/Combine like terms.

\large{f(x)  + g(x) = 2 {x}^{2}  - 2x - 2}

The function can be factored so there are two answers. (Both of them work as one of them is factored form while the other one is not.)

\large{(f + g)(x) = 2 {x}^{2}  -2x -2}

<u>Alternative</u>

\large{(f + g)(x) = 2({x}^{2}  -x - 1)}

<u>Answer</u>

  • (f+g)(x) = 2x²-2x-2
  • (f+g)(x) = 2(x²-x-1)

Both answers work. The second answer is in factored form.

Let me know if you have any doubts!

8 0
2 years ago
Find the measure of ∠AED for m∠BEC = 118
mylen [45]

dang nobody answered.. and this question is on an assignment  

7 0
3 years ago
HELPPPPP ASAP!!!! Thx!! and NOOO FILESSSS!! it's on KHAN ACADEMY!!
Black_prince [1.1K]

Answer:

32

Step-by-step explanation:

x=\dfrac{180-116}{2}=\dfrac{64}{2}=32

7 0
3 years ago
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