We have to simplify and get the value of x from this inequality given:
Given inequality,

Now let's simplify by using distributive property,

We need to find x, so let's isolate x to the letter side of the inequality for calculation at ease.


Now, dividing -2 from both sides.
Note : As we are dividing a negative number from both sides, the sign of the inequality will be <u>reversed</u>.


Now subtracting -7 from both sides,


Or, Interval of the equal ![(- \infin, -7 ]](https://tex.z-dn.net/?f=%28-%20%5Cinfin%2C%20-7%20%5D)
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Answer:
The jeweler made 11 bracelets and 7 necklaces.
Step-by-step explanation:
Given that a jeweler had a fixed amount of gold to make bracelets and necklaces, and the amount of gold in each bracelet is 6 grams and the amount of gold in each necklace is 16 grams, knowing that the jeweler used 178 grams of gold and made 7 more necklaces than bracelets, to determine a system of equations that could be used to determine the number of bracelets made and the number of necklaces made, the following mathematical reasoning should be considered:
(16 - 6) x 7 = 70
178 - 70 = 108
108/6 = 18
18 - 7 = 11
(11 x 6) + (7 x 16) = X
66 + 112 = X
178 = X
Thus, the jeweler made 11 bracelets and 7 necklaces.
Answer:
27
Step-by-step explanation:
Let <em>g </em>be Gabrielle's age and <em>m </em>be Mikhail's age.
We can turn the statements the problem gives us into mathematical expressions to help us solve.
Gabrielle's age is two times Mikhail's age:
<em>g </em>= 2<em>m</em>
The sum of their ages is 81:
<em>g </em>+ <em>m </em>= 81
This gives us a system of equations that will allow us to solve for Gabrielle's age.
<em>g </em>+ <em>m </em>= 81
(2<em>m</em>)<em> </em>+ <em>m </em>= 81
3<em>m </em>= 81
<em>m</em> = 
<em>m </em>= 27
If we need to solve for Gabrielle's age, we can do the following.
<em>g </em>= 2<em>m</em>
2(27)<em> </em>= <em>g</em>
54 = <em>g</em>
g = 54
Mikhail's age is 27.
Gabrielle's age is 54.
Answer:
The answer is option C
Step-by-step explanation:
f(x) = x³ + 2x² + 3x + 4
To find f(-1) substitute the value of x that's
- 1 into f(x)
That's
<h3>

</h3>
We have the final answer as
<h3>

</h3>
Hope this helps you
Answer:
C
Step-by-step explanation:
Given f(x) then f(x + h) represents a horizontal translation of f(x)
• If h > 0 then a shift to the left of h units
• If h < 0 then a shift to the right of h units
Here the shift is 5 units right, thus g(x) = (x - 5)²
Given f(x) then f(x) + c represents a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Here the shift is 3 units down, thus g(x) = f(x) - 3
Hence
g(x) = (x - 5)² - 3 → C