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Zepler [3.9K]
3 years ago
10

x + 18" alt="3(x + 5) \leqslant 3x + 18" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
klemol [59]3 years ago
8 0

3(x+5)\leq 3x+18\\\\3x+15\leq 3x+18\\\\15\leq 18\\\\x\in\mathbb{R}

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Find the value of k and x2<br> x^2+ 13x + k = 0, x1=-9
Anarel [89]

Given:

The quadratic equation is:

x^2+13x+k=0

x_1=-9

To find:

The value of k and x_1.

Solution:

We have,

x^2+13x+k=0                ...(i)

Putting x=-9, we get

(-9)^2+13(-9)+k=0

81-117+k=0

-36+k=0

k=36

Putting k=36 in (i), we get

x^2+13x+36=0

Splitting the middle term, we get

x^2+9x+4x+36=0

x(x+9)+4(x+9)=0

(x+9)(x+4)=0

x=-9,-4

Here, x_1=-9 and x_2=-4.

Therefore, the required values are k=36 and x_2=-4.

3 0
3 years ago
No work needed!! Just answers, thank you! 25 points!!
Maurinko [17]

Answer:

Step-by-step explanation:

S_{31} = 9 \cdot 31 + [-0.5 \cdot \frac{31(31-1)}{2}] = 46.5

S_{40} = 40 + [-3 \cdot \frac{40(40-1)}{2}] = -2300

3 0
3 years ago
NEEd help! Will help alot tysm!
xz_007 [3.2K]

Answer:

3rd one

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Tell whether the ordered pair is a solution of the given system. (-2,-4) {y=1/2x -3, y=-2x-8}
kompoz [17]

Answer:

The ordered pair (-2,\, -4) is indeed a solution to the system:

\left\lbrace\begin{aligned} & y = \frac{1}{2}\, x - 3 \\ & y = -2\, x - 8\end{aligned}\right..

Step-by-step explanation:

Consider a system of equations about variables x and y. An ordered pair (x_{0},\, y_{0}) (where x_{0} and y_{0} are constant) is a solution to that system if and only if all equations in that system hold after substituting in x = x_{0} and y = y_{0}.

For the system in this question, (-2,\, -4) would be a solution only if both equations in the system hold after replacing all x in equations of the system with (-2) and all y with (-4).

The \texttt{LHS} of the equation y = (1/2)\, x - 3 would become (-4). The \texttt{RHS} of that equation would become (1/2) \, (-2) - 3. The two sides are indeed equal.

Similarly, the \texttt{LHS} of the equation y = -2\, x - 8 would become (-4). The \texttt{RHS} of that equation would become (-2)\, (-2) - 8. The two sides are indeed equal.

Thus, x = (-2) and y = (-4) simultaneously satisfy both equations of the given system. Therefore, the ordered pair (-2,\, -4) would indeed be a solution to that system.

8 0
2 years ago
Steven starts a savings account with $10,000. He earns 7% annual interest. How much will be in the account after 6 years. Round
sveta [45]

So the equation is A = P(1+rt)
A = 10,000(1+0.07*6)
A = 10,000(1+0.42)
A = 14,200.00

7 0
3 years ago
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