What is the interval in which both f (x) and g(x) are positive?
A. (–1, ∞)
B. (2, ∞)
C. (3, ∞)
D. (–∞, 2) ∪ (2, ∞)

Answer: The answer is x < 5/2 and x > -5.

Step-by-step explanation:

First you need to separate the inequality and keep x on one side to maintain consistency. For instance the problem-

[tex]\frac{5-2x}{3} > 0\\\frac{5-2x}{3} < 5\\[/tex]

Now solve as normal.

*Note: When dividing a side or multiplying a side by a negative number, the sign of the inequality switches (this will be shown when I do the equation if it doesn't make since how I word it).

[tex]5-2x > 0*3\\5-2x < 5*3[/tex]

[tex]-2x > 0-5\\-2x < 15-5[/tex]

[tex]x < \frac{-5}{-2} =x < \frac{5}{2} \\x > \frac{10}{-2} =x > -5[/tex]

So, x < 5/2 and x > -5.

If anything is confusing about the procedure just leave a comment, and I'll try to explain further.

The equation of the line with points (2,10) and (0,0) is: y = 5x.

The line given has two points which are stated as:

(2,10) and (0,0).

Find the slope(m):

Slope (m) = change in y / change in x = (10 - 0)/(2 - 0)

Slope (m) = 10/2

Slope (m) = 5

The y-intercept (b) = 0

Substitute m = 5 and b = 0 into y = mx + b

y = 5x + 0

y = 5x

The equation of the line is: y = 5x.

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Answer:

K

Step-by-step explanation:

(1*500 * 5) + (10 * 3*500)

Answer:

i think the answer is the second one D and A

Answer:

3

Step-by-step explanation:

Slope of a line between any two points (x1,y1) and (x2,y2) is given by the equation:
[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

let's take (x1,y1) as (4,4) and (x2,y2) as (5,7)

So slope = [tex]\frac{7-4}{5-4}[/tex] = 3

Answer:

y = 3x - 8

Step-by-step explanation:

y = Mx + c

m = 3 / 1

4 = 3(4) + c

4 - 12 = c

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Answer:  [tex]\textsf{3955cm}[/tex]

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Given: [tex]\textsf{Tree = 4m and 25cm, Pole = 70cm shorter}[/tex]

Find: [tex]\textsf{The height of the pole}[/tex]

Solution: The first step that we must take is to convert the tree height to centimeters and after doing so we would just subtract 70 cm from that to get the pole height.

Convert to cm

Combine

Subtract 70 from the tree height

Using the information from the problem the height of the pole would be 3955cm.

Answer:

A. 15

Step-by-step explanation:

9 12 15 is a

3 4 5 right triangle

Pythagorean Theorem

9^2+12^2=c^2

81+144=c^2

225

√225=√c^2

15=c

The slope of the given line is -2, and since perpendicular lines have negative reciprocal slopes, the slope of the line we want to find is 1/2.

Substituting into point-slope form,

[tex]y+4=\frac{1}{2}(x-8)\\\\y+4=\frac{1}{2}x-4\\\\\boxed{y=\frac{1}{2}x-8}[/tex]

Answer:

Equation of line perpendicular to y= -2x-9 is y=x/2-8 .

Step-by-step explanation:

The slope of a line gives the measure of its steepness and direction. The slope of a curve at a point is equal to the slope of the straight line that is tangent to the curve at that point.

The general equation of a line is y = mx + c, where m is the slope of the line and c is the y-intercept. It is the most common form of the equation of a straight line that is used in geometry.

The product of slopes of two perpendicular lines gives (-1).

m1m2=(-1)

(-2)m2=(-1)

m2=1/2

y=m2x+c

Point (8,-4) satisfies the given equation :

(-4)=1/2 x 8 + c

c = (-8)

Line perpendicular to y= -2x-9 will be -

y=x/2-8

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The domain of gof(x) is {x ∈ ℝ| x ≠ −2, 1} .

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.

given function:

f(x) = x² + x -3

g(x) = 1/x+1

Now, solving the equation

gof = g(f(x))

=g( x² + x -3)

=1/(x² + x -3)+1

=1/ x² + x -2

= 1/ x² +2x - x -2

= 1/ x( x+ 2) - (x +2)

=1/ (x+2)(x-1)

Hence, the domain of gof(x) is {x ∈ ℝ| x ≠ −2, 1} .

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Since everything to the right of the line is shaded, the linear inequality which represents the graph is equal to: A. y ≥ 1/3x - 4.

In order to determine the linear inequality which represents the graph, we would find the slope of the given points.

Mathematically, the slope of a straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

[tex]Slope = \frac{-4\;-\;(-5)}{0\;-\;(-3)}\\\\Slope = \frac{1}{3}[/tex]

Slope = 1/3.

From the standard equation, we have:

y - y₁ = m(x - x₁)

y - (-5) = 1/3(x - (-3))

y + 5 = 1/3x + 1

y = 1/3x + 1 - 5

y = 1/3x - 4

y ≥ 1/3x - 4.

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Answer:

x = +1

x = -1

Step-by-step explanation:

x^4-1=0​

x^4=+1​

fourth root of x^4= fourth root of +1​

x = +1

x = -1

Answer: 31 cm.

explanation:

Given, Radius = 5 cm (near to)

this means the radius is near 5 cm. It can be 4.9, 4.99, 4.999.....or 5.01,5.001,5.001...... and so on.

So, the circumference of the circle is given by:-

Circumference = 2× [tex]\pi[/tex] × r

⇒ 2 × 22/7 × 5    (for the smallest value, we'll consider r as 5 and then round off the circumference to the smallest value)

⇒ 220/7 ≈ 31.43 cm

rounding off to the smallest integer, we have

Circumference = 31 cm.

The smallest value that the circumference could have is 10 [tex]\pi[/tex]cm

Using Formula,

Circumference = 2 [tex]\pi \\[/tex] r

Radius = 5 cm

So, C = 2 [tex]\pi[/tex] 5

C = 10 [tex]\pi[/tex]cm

Therefore circumference is 10 [tex]\pi[/tex]cm.

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Answer:

6/x2

Step-by-step explanation:

Answer:

[tex]\mathsf {\frac{6}{x^{2}}}[/tex]

Step-by-step explanation:

[tex]\mathsf {\frac{2}{x^{2}} + \frac{4}{x^{2}} }[/tex]

[tex]\mathsf {\frac{2+4}{x^{2}}}[/tex]

[tex]\mathsf {\frac{6}{x^{2}}}[/tex]

i beilive this is unknown

Answer:

a, b, d

Step-by-step explanation:

its one of those

Answer:

A, the first one

Answer:

True

Step-by-step explanation:

-77 is less than -76. Since the symbol refers to less than or equal to, this statement will be true.

Answer:

-300

Step-by-step explanation:

113-413=-300

Answer:

1780

Step-by-step explanation:

multiply the length value by 1760

and then divide the length value by 3

Answer:

all real numbers

Step-by-step explanation:

the answer is all real numbers.

we know this since if you plug in any value for x we will get a real number.

hope this helps

The value of x will be 3

From given diagram, triangle ABC and EDC meet at a common vertex C.

So, triangle ABC and EDC both are congruent to each other.

Applying the similarity property of congruence, ratio of the congruent triangles' corresponding sides will be equal.

Therefore,

[tex]\frac{AB}{ED} = \frac{AC}{EC} = \frac{BC}{CD}[/tex]

[tex]\frac{AC}{EC} = \frac{BC}{CD}[/tex]

Simplifying the expression,

We get

(18-x)/x = 25/5

(18-x)/x = 5

18-x = 5x

18-x-5x = 0

18 - 6x = 0

- 6x = -18

x = 3

Hence, the value of x is 3.

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The correct answer is the last choice .

The parent quadratic function is f(x) = x² it's just like the image above .

if you look at the graph horizontal translation has happened two units to right , it means we have -2 inside a bracket next to x , then vertical translation has happened 4 units to up it means we have +4 outside the bracket and after x

there's also a reflection on the graph which means there's a negative before the bracket .

HOPE IT HELPS

PLEASE GIVE BRAINLIEST

Answer:

[tex]\frac{1}{18}[/tex]

Step-by-step explanation:

The best way to solve this problem is to simplify each factorial one by one!

Starting at the numerator, the factorial for 2! is just 2, while the factorial for 5 is 120.

At the denominator, the factorial of 6! is 720, while the factorial for 3 is 6.

To write this out, we're given: [tex]\frac{(2) (120)}{(720) (6)}[/tex]

Just simply multiply and then divide, and we are given 1/18

Answer:

For section A, the average rate of change is 12. For section B, the average rate of change is 300. The average rate of change in Section B is greater than Section A by 25. The rate of change keeps on increasing because the slope of the function is increasing.

Step-by-step explanation:

Concept: For a function f(x), the rate of change is given by [tex]\frac{f(x_{2})-f(x_{1}) }{x_{2}-x_{1} }[/tex]. Given function is h(x) = 3(5∧x).

For x = 0 to x = 1, the value of function would be f(0) = 3 to f(1) = 15.

The rate of change would be (15-3) / (1-0) = 12.

For x = 2 to x = 3, the value of function would be f(2) = 75 to f(3) = 375.

The rate of change would be (375-75) / (3-2) = 300.

The average rate of change in Section B is greater than Section A by

300 / 12 = 25.

Looking at the function, that is h(x) = 3(5∧x), we see that this function is an increasing function. The slope of an increasing function keeps on increasing with the value of x. The rate of increase is also a slope. That is why the rate keeps on increasing.

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