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Final answer:

The logarithmic function F(x) = logb x is an increasing function when the base b is greater than 1, because the value of logb x increases as x increases for b > 1.(Option D)

Explanation:

The question asks for what values of b will F(x) = logb x be an increasing function. To determine this, we need to understand the behavior of logarithmic functions based on their base value (b). A logarithmic function is increasing if the base of the logarithm is greater than 1. This is because as x increases, the value of logb x increases when b>1. Conversely, if b<1 (but b>0), the function is decreasing because the power to which b must be raised to produce x decreases as x increases. We also know that the base of a logarithm cannot be negative or zero, as this would not produce a valid logarithmic function.

Therefore, the correct answer is D. b > 1, where the logarithmic function F(x) = logb x is an increasing function.

In this question it has been clearly indicated that AZB is to be taken as an arc. This is because there is the arc symbol on top of AZB. Thus, we have [tex] \overarc{AZB} [/tex] and we need to answer what does the arc [tex] \overarc{AZB} [/tex] represent.

As we can see from the diagram, by visual inspection, that AZ is the chord which is lesser than the diameter and AZB is the segment on that lesser side of the circle. Therefore, the arc [tex] \overarc{AZB} [/tex] must be the minor arc.

Therefore, Option A, minor arc is the correct answer.

The zero of the quadratic function is therefore x = 1. Since both factors give the same zero, we have a repeated zero and f(x) only touches the x-axis at one point, x = 1.

The zeros of the quadratic function f(x) = 4x^2 - 12x + 8 are the values of x that make f(x) = 0. In this function, we can factor by finding two numbers that multiply to give the constant term (8 times 4, the coefficient of x^2) and add to give the coefficient of x (-12). Here, those numbers are -4 and -4, so we rewrite the middle term -12x as -4x - 4x, and factor by grouping:

4x^2 - 4x - 4x + 8 = 0

4x(x - 1) - 4(x - 1) = 0

(4x - 4)(x - 1) = 0

Now we have two factors equal to zero, which gives us two equations to solve:

4x - 4 = 0 or x - 1 = 0

x = 1

The slope - intercept form of the equations are : [tex]y = \frac{3}{4} x - 7 [/tex] and [tex]y = - \frac{2}{5} x + 2[/tex]

Given the standard form of the equations :

The General form of a slope - intercept equation :

For equation (1) :

3x - 4y = 28

Make y the subject

-4y = 28 - 3x

Divide both sides by - 4 to isolate y

y = -7 + 3/4x

[tex]y = \frac{3}{4} x - 7 [/tex]

For equation (2) :

4x + 10y = 20

Make y the subject

10y = 20 - 4x

Divide through by 10 to isolate y

y = 2 - 2/5x

[tex]y =- \frac{2}{5} x + 2[/tex]

Hence, the slope - intercept equations are : [tex]y = \frac{3}{4} x - 7 [/tex] and [tex]y = - \frac{2}{5} x + 2[/tex]

Learn more :

C. 31 pi over 5

~sbcardinals :)

hello there

your answer would be

C, 31 pi over 5

hope it helps

thank you

best regards Queen Z

The scale factor from the smaller figure to the larger figure is found by taking the cube root of the ratio of their volumes, which is the cube root of 216/343.

The student asked: Which of the following could represent the scale factor of the smaller figure to the larger figure? When comparing the volumes of two geometric figures, we can determine the scale factor of their linear dimensions by understanding the relationship between volume and linear scale factor.

Given that the smaller figure's volume is 216 cubic inches and the larger figure's volume is 343 cubic inches, we are looking for the cube root of the ratio of these volumes to find the linear scale factor.

To find the scale factor from the smaller figure to the larger figure, divide the volume of the smaller figure by the volume of the larger figure and then calculate the cube root: Scale factor = ∛(216/343). This calculation will give you the scale factor of the linear dimensions from the smaller figure to the larger figure.

Answer:

[tex](x+6)^{2}+2x=189[/tex]  

and

[tex]x^{2}+14x+36=189[/tex]

Step-by-step explanation:

Let

x -----> the number

we know that

The equation that represent the situation is

[tex](x+6)^{2}+2x=189\\ \\x^{2} +12x+36+2x=189\\ \\x^{2}+14x+36=189[/tex]

therefore

The equations that could be used are

[tex](x+6)^{2}+2x=189[/tex]  and [tex]x^{2}+14x+36=189[/tex]

Answer:

(x+6)^{2}+2x=189  

and

x^{2}+14x+36=189

Step-by-step explanation:

APEX APEX APEX APEX APEX APEX APEX APEX APEX APEX

More than $0 but less than $4100

A(2/7:5)

B(10:39)

The slope is 7/2.

The slope of the line y=3.5x+4 is 3.5, and the missing coordinates will be filled as a(0.28, 5) and b(10, 9)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given equation of line is y=3.5x+4

When we compare this with slope intercept form y=mx+b.

slope m=3.5

We need to find the value of x when y is 5

5=3.5x+4

1=3.5x

Divide both sides by 3.5

x=0.28

So a coordinates are (0.28, 5)

Now let us find y value when x is 10

y=3.5(10)+4

y=39

So b coordinates are (0.28, 39)

Hence, the slope of the line y=3.5x+4 is 3.5, and the missing coordinates will be filled as a(0.28, 5) and b(10, 9)

To learn more on slope of line click:

https://brainly.com/question/14511992

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Answer:

In first blank : y = - 2,

In second blank : ( 0, 1 )

Step-by-step explanation:

Given function is,

[tex]f(x)=3^{x+1}-2[/tex]

The horizontal asymptote of the function f(x),

[tex]y=lim_{x\rightarrow \infty} f(x)[/tex]

[tex]y=lim_{x\rightarrow \infty} 3^{x+1}-2[/tex]

[tex]y=3^{\infty+1}-2[/tex]

[tex]y=3^\infty - 2[/tex]

[tex]y=0-2[/tex]

⇒ y = -2

First option is correct.

Also, the function has no vertical asymptote,

2. For finding the y-intercept, x = 0,

[tex]f(0)=3^{0+1}-2=3-2=1[/tex]

Hence, the y-intercept = (0,1)

Third option is correct.

Final answer:

The function f(x) = 3x + 1 – 2 is a linear function and does not have an asymptote, contrary to the options provided. The y-intercept is found by setting x to 0, which results in the point (0, – 1).

Explanation:

The function in question is f(x) = 3x + 1 – 2. To determine its asymptote and y-intercept, we analyze its structure.

Since this is a linear function and not a rational function, it does not have an asymptote like those found with rational functions, whose denominators can become zero. Instead, the original function is a modification of the function f(x) = 3x, with vertical shifts up by 1 and down by 2, effectively canceling each other out. Therefore, the asymptote is essentially the x-axis, which can be represented by the equation y = 0. However, since none of the provided options include y = 0, and the function we are analyzing is, in fact, linear without any asymptotes, there must be an error in the question regarding this part.

To find the y-intercept, we set x equal to 0 and solve for f(0):

f(0) = 3(0) + 1 – 2 = 1 – 2 = – 1.

Therefore, the y-intercept of the function is the point (0, – 1).

The given arithmetic series is

[tex] \sum_{t=1}^{18} (3t-4) [/tex]

When t =1, we will get the first term,a, which is

[tex] 3(1)-4 =3-4=-1 [/tex]

When t =18, we will get the last term,l , which is

[tex] 3(18)-4 = 50 [/tex]

Now we use the formula of sum of n terms which is

[tex] S = \frac{t}{2} (a+l) [/tex]

Substituting the values of t,a and l, we will get

[tex] S = \frac{18}{2} (-1+50) = 9*49 =441 [/tex]

Consider the arithmetic series [tex] _{t=1}\Sigma^{t=18} (3t-4) [/tex]

Let t=1 in the given series, we get

first term = [tex] a_{1} [/tex] = 3-4 = -1.

Let t=2 in the given series, we get

second term = [tex] a_{2} [/tex] = [tex] (3 \times 2)-4 = 2 [/tex]

Let t=3 in the given series, we get

third term = [tex] a_{3} = (3 \times 3)-4=5 [/tex]

Now, let t=18 in the given series, we get

last term = l = [tex] l = (3 \times 18)-4 = 50 [/tex]

We get the series as

-1, 2, 5,..... 50

Sum = [tex] \frac{n}{2}(a+l) [/tex]

= [tex] \frac{18}{2}(-1+50) [/tex]

= [tex] = 9 \times 49 [/tex]

= 441

Therefore, the sum of the given arithmetic series is 441.

Answer:

The value of the given function is 25 for x = 2.

Step-by-step explanation:

Given function is,

[tex]F(x) = 4x^3 - x^2 - 5x + 7[/tex]

At x = 2,

The value of the function is,

[tex]f(2)=4(2)^3-(2)^2-5(2)+7[/tex]

[tex]=4(8)-4-10+7[/tex]

[tex]=32 - 7[/tex]

[tex]=25[/tex]

Hence, the value of the given function is 25 for x = 2.