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grigory [225]
3 years ago
12

Solve the inequality 7(x+2)-5>3(x-1)

Mathematics
1 answer:
loris [4]3 years ago
3 0

Answer:

x>-3

Step-by-step explanation:

I used a calculator

You might be interested in
Options are<br><br> a) -2 and 12/5<br> b) 1 and 2<br> c)8/3 and 2<br> d) 3 and 4
tigry1 [53]
A) 1 and 2
That is the correct answer
6 0
2 years ago
Use the definition of continuity and the properties of limit to show that the function f(x)=x sqrtx/ (x-6)^2 is continuous at x=
jasenka [17]

Answer:

The function \\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}} is continuous at x = 36.

Step-by-step explanation:

We need to follow the following steps:

The function is:

\\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}

The function is continuous at point x=36 if:

  1. The function \\ f(x) exists at x=36.
  2. The limit on both sides of 36 exists.
  3. The value of the function at x=36 is the same as the value of the limit of the function at x = 36.

Therefore:

The value of the function at x = 36 is:

\\ f(36) = \frac{36*\sqrt{36}}{(36-6)^{2}}

\\ f(36) = \frac{36*6}{900} = \frac{6}{25}

The limit of the \\ f(x) is the same at both sides of x=36, that is, the evaluation of the limit for values coming below x = 36, or 33, 34, 35.5, 35.9, 35.99999 is the same that the limit for values coming above x = 36, or 38, 37, 36.5, 36.1, 36.01, 36.001, 36.0001, etc.

For this case:

\\ lim_{x \to 36} f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}

\\ \lim_{x \to 36} f(x) = \frac{6}{25}

Since

\\ f(36) = \frac{6}{25}

And

\\ \lim_{x \to 36} f(x) = \frac{6}{25}

Then, the function \\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}} is continuous at x = 36.

8 0
3 years ago
2. What is the equation in slope-intercept form of the line that passes through thepoints (-4, 47) and (2, -16)?O21 979y=-2*+ 21
trapecia [35]

hello

the points given are (-4, 47) and (2, -16)

let's find the intercept of this equation

\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ x_2=2 \\ y_2=-16 \\ y_1=47 \\ x_1=-4 \end{gathered}\begin{gathered} m=\frac{-16-47}{2-(-4)} \\ m=-\frac{21}{2} \\ slope=-\frac{21}{2} \end{gathered}

now, since we know the value of the slope, we can use that in the standard equation on a straight line

the standard equation of a straight line is given as

\begin{gathered} y=mx+c \\ m=\text{slope} \\ c=\text{intercept} \end{gathered}

we can pick any of the points and solve for intercept

let's use (2, -16)

\begin{gathered} x=2 \\ y=-16 \\ y=mx+c \\ m=-\frac{21}{2} \\ -16=-\frac{21}{2}(2)+c \\ -16=-21+c \\ \text{collect like terms} \\ c=-16+21 \\ c=5 \end{gathered}

now we know the value of intercept (c) = 5 and the slope (m) = 21/2

let's use this to write equation of the straight line

\begin{gathered} y=mx+c \\ y=-\frac{21}{2}x+5 \end{gathered}

from the calculations above, the equation of the straight line is given as y = -21/2x + 5

8 0
1 year ago
1) A prize is divided in the ratio 15:1 if the smaller share is £5 what is the total prize?
Alex777 [14]

Answer:

£80

Step-by-step explanation:

larger ratio is 15 and smaller ratio is 1

15 + 1 = 16

£5×16=£80

6 0
2 years ago
Drag the expression into the boxes to correctly complete the table
bazaltina [42]

Answer:

2nd and 3rd are polynomials, rest arent

Step-by-step explanation:

Polynomial has to have no ||s, sqrts, or variables in denominator of fraction

3 0
3 years ago
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