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2 years ago

Write the inequality given in the diagram below

Mathematics

1 answer:

11111nata11111 [884]2 years ago

4 0

Answer:

x ≥ - 1

Step-by-step explanation:

the solid circle above - 1 on the number line indicates that x can equal - 1

the arrow points right indicating x is greater than or equal to - 1 , that is

x ≥ - 1

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Help please, will mark brainiest!

VARVARA [1.3K]

Answer:

A) 9^7

Step-by-step explanation:

For this type of problem, since they both have the same base, you can add the exponents together and have the base remain the same. So you would have 5+2 = 7.

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3 years ago

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A line passes through (3, -2) and (6, 2). a. Write an equation for the line in point-slope form. b. Rewrite the equation in stan

koban [17]

Answer:

(a)

Given: A line passes through the points (3, -2) and (6, 2)

Point slope form: An equation of line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

$y -y_1=m(x-x_1`)$ .....[1] where m is the slope of the line.

Calculate first the slope of the line:

Slope(m) = $\frac{y_2-y_1}{x_2-x_1}$

Substitute the given points;

$m = \frac{2-(-2)}{6-3}=\frac{2+2}{3} =\frac{4}{3}$

Substitute the value of m in [1] ;

$y - (-2) = \frac{4}{3}(x-3)$

$y+2=\frac{4}{3}(x-3)$ ......[1]

therefore, the equation of line in point slope form is, $y+2=\frac{4}{3}(x-3)$

(b)

to find the standard form of the equation [1]

Multiply both sides by 3 in [1] we get;

$3(y+2) = 4(x-3)$

using distributive property; $a\cdot (b+c) = a\cdot b + a\cdot c$

3y + 6 = 4x -12

Subtract 3y to both sides we get;

3y + 6 -3y = 4x - 12 - 3y

Simplify:

6 = 4x - 3y -12

Subtract 6 from both sides we get;

0 = 4x - 3y -12-6

Simplify:

4x - 3y - 18 =0

Therefore, the standard form of the equation is; 4x - 3y - 18 =0

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3 years ago

Aidan has $65 in his bank account. His brother Michael also has a bank account. They want to calculate the amount of money in bo

stepan [7]

Answer:

C because they won't know unless they know what Michael has

Step-by-step explanation:

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3 years ago

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Samuel's sister is 39. She is 6 years older than Samuel's age tripled. How old is Samuel?

Thepotemich [5.8K]

Answer:

Step-by-step explanation:

39-6=33

33/3=11

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3 years ago

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Integrate xe^(-x^2).

Gekata [30.6K]

You can easily integrate it using a simple substitution:

$\large\begin{array}{l} \mathsf{\displaystyle\int\!x\,e^{-x^2}\,dx}\\\\ =\mathsf{\displaystyle\int\!\left(-\frac{1}{2}\right)\cdot (-2)x\,e^{-x^2}\,dx}\\\\ =\mathsf{\displaystyle-\,\frac{1}{2}\int\!\,e^{-x^2}\cdot (-2x)\,dx\qquad\quad(i)}\\\\ \end{array}$

$\large\begin{array}{l} \textsf{Let}\\\\ \mathsf{-x^2=u,}\quad\textsf{then}\quad\mathsf{-2x\,dx=du}\\\\\\ \textsf{so (i) becomes}\\\\ =\mathsf{\displaystyle-\,\frac{1}{2}\int\!e^u\,du}\\\\ =\mathsf{\displaystyle-\,\frac{1}{2}\cdot e^u+C}\\\\ =\mathsf{\displaystyle-\,\frac{1}{2}\cdot e^{-2x}+C}\\\\\\ \boxed{\begin{array}{c} \mathsf{\displaystyle\int\!x\,e^{-x^2}\,dx=-\,\frac{1}{2}\,e^{-x^2}+C} \end{array}}\qquad\checkmark \end{array}$

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$\large\textsf{I hope it helps. :-)}$

Tags: <em>integrate substitution indefinite integral exponential composite calculus</em>

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4 years ago