solve the inequality. use interval notion to state the solution (x+3)^2>2(x^2+7)
Answers
Answer:
we conclude that:
[tex]x^2+6x+9>2x^2+14\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:1<x<5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(1,\:5\right)\end{bmatrix}[/tex]
Hence, (1, 5) is the solution in interval notation.
Please also check the attached graph.
Step-by-step explanation:
Given the inequality expression
[tex]\left(x+3\right)^2>\:2\left(x^2+7\right)[/tex]
as
(x + 3)² = x² + 6x + 9
2(x² + 7) = 2x² + 14
so
[tex]\:x^2+6x+9\:>\:2x^2+14[/tex]
rewriting in the standard form
[tex]-x^2+6x-5>0[/tex]
Factor -x² + 6x - 5: - (x - 1) (x - 5)
[tex]-\left(x-1\right)\left(x-5\right)>0[/tex]
Multiply both sides by -1 (reverse the inequality)
[tex]\left(-\left(x-1\right)\left(x-5\right)\right)\left(-1\right)<0\cdot \left(-1\right)[/tex]
Simplify
[tex]\left(x-1\right)\left(x-5\right)<0[/tex]
so
[tex]1<x<5[/tex]
Therefore, we conclude that:
[tex]x^2+6x+9>2x^2+14\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:1<x<5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(1,\:5\right)\end{bmatrix}[/tex]
Hence, (1, 5) is the solution in interval notation.
Please also check the attached graph.
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Answer:
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Step-by-step explanation:
3(2x-1)+7=-44
3(2x)+3(-1)+7
6x-3+7=-44
6x-3+3+7
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Answers
Answer:
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Answers
Answer:
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Step-by-step explanation:
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What is the solution to the system of equations:
x=2y-8
4x+y=13
Answers
Answer:
x=2, y=5
Step-by-step explanation:
Replace all occurrences of x with 2y−8 in each equation.
9y−32=13
x=2y−8
Solve for y in the first equation.
y=5
x=2y−8
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Answers
Answer:
a x (23a+5a^4 - 11)
Step-by-step explanation:
(a x (13a - 6a^4 - 2) + 10a^2 + 11a^5 - 9a
rewite the expression and remove any unnecessary parentheses.
a x (13a - 6a^4 -2) + 10a^2 +11a^5 - 9a
factor the expression.
a x (23a - 6a^4-2+11a^4-9)
connect like terms.
your welcome
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Answers
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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O (x, y) - (y, x)
O (x, y) - (-y, x)
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Answer:
I am assuming you are asking for what percent correct she got. She got 46% correct.
Step-by-step explanation:
You divide the answers correct by the total questions. She got 69 out of 150, so dividing that is .46
To turn a decimal into a percentage, just move the decimal two places to the right, thus getting 46 %
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
hope it is correct (did it really fast) and hope it helps
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
998-98=900
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Answer:
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Step-by-step explanation:
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Answer:
85 + 2.5v ≥ 115
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Step-by-step explanation:
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I really need help with this question.
A landscaper needs to fill a path measuring 2 feet by 6 feet with patio stones.
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options. She cannot cut or overlap the stones, and they all must fit inside the
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Answer:
I also need the answer
Step-by-step explanation:
What's the sum of an infinite geometric series if the first term is 156 and the common ratio is 2∕3?
Answers
Answer:
468
Step-by-step explanation:
Formula for infinite sum of geometric series is;
S_∞ = a1/(1 - r)
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a1 = 156
r = ⅔
Thus;
S_∞ = 156/(1 - ⅔)
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Answers
Answer:
25%
Step-by-step explanation:
We can first divide and multiply by 100% to obtain the pecentage:
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Answers
Answer:
20,615
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Forty-five students chose to have their school pictures retaken. If this represents
1/5 of the students in the school, write and solve an
equation to determine x, the number of students
in the school.
А: 1/5x=45 Solution: 225students
B: 1/5+x=45 Solution:
44 4/5students
C: x-1/5=45 Solution:
44 1/5students
D: None of the above
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Answers
Answer:
A
Step-by-step explanation:
So if 45 students represent 1/5 of the school, and x is the number of students in the school, then 45 will simply represent 1/5 of x.
This means that the equation is 1/5x = 45.
Now, you have to solve the equation.
[tex]\frac{1}{5} x = 45[/tex]
Multiply both sides of the equation by 5
[tex]\frac{1}{5}x * 5 = 45 * 5\\x = 225[/tex]
This means that there are 225 students.
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Answers
Answer:
x= 3,-5
Step-by-step explanation:
Answer: x=3, -5
Step-by-step explanation: Solve for
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x
by simplifying both sides of the equation, then isolating the variable.
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Answers
Answer:
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Step-by-step explanation:
Answer:
-32
Step-by-step explanation:
(7x(6))-(5x(-2))=-32
