The logarithmic function j(x) is defined as j(x)=log(x+5)−1. The graph below shows the logarithmic function k(x).
Which statement about the two functions is true?

A
Both functions have the same vertical asymptote.

B
Both functions have a domain of all real numbers.

C
The x-intercept of k(x) is greater than the x-intercept of j(x).

D
Function j(x) is greater than function k(x) for all values of x.

See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2

Area models are shapes used to model or illustrate products, multiplications, divisions and quotients

The equation is given as:

4x^2+12x+9 = (2x+3)^2

Express (2x+3)^2 as the product of (2x+3) and (2x+3)

4x^2+12x+9 = (2x+3) * (2x+3)

The above means that the area model is a square.

So, the side lengths of the model must be equal, where the side lengths are 2x + 3 and the area of the square is 4x^2+12x+9

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Answer:

The first option:

[tex]6x^{2} -4x+6[/tex]

Step-by-step explanation:

Trust me I am right.

If you need work please ask!

Have a nice day!

The (B) arithmetic mean is the best estimate of next year's return.

Therefore, the (B) arithmetic mean is the best estimate of next year's return.

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The correct question is shown below:

The ______ mean is the best estimate of next year's return. multiple choice question.

(A) the average of the arithmetic and geometric mean

(B) arithmetic

(C) geometric

The linear function of the table of values is y = -1.5x + 25

The table of values is given as:

Sequence One       Sequence Two       Ordered Pair        

6                                         16                           (6, 16)

8                                         13                           (8, 13)

10                                        10                           (10, 10)

12                                         7                            (12, 7)

14                                         4                            (14, 4)

From the above table of values, we can see that:

This means that the table represents a linear function, and the slope of the function is

m = -3/+2

This gives

m = -1.5

A linear function is represented as:

y = mx + c

This gives

y = -1.5x + c

Using the table of values, we have

16 = -1.5 * 6 + c

Evaluate the product

16 = -9 + c

Add 9 to both sides

c = 25

Substitute c = 25 in y = -1.5x + c

y = -1.5x + 25

Hence, the linear function of the table of values is y = -1.5x + 25

See attachment for the graph of the table

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Let the mass of the object exists at 60 N and the height exists at 3m then work

exists in 1764.

What is work?

The work done by a force exists determined to be the product of a component of the force in the direction of the displacement and the magnitude of this displacement.

Work can be estimated by multiplying Force and Distance in the direction of force as follows.

W = F × d. Unit.

Given data:

m = mass of the object = 60 N

h = height = 3 m

Work = Fh = mgh

g = gravity = 9.8 m/s²

work = Fh = mgh

[tex]= 60*3*9.8[/tex]

= 1764

Therefore, the work exists in 1764.

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Hello,

[tex]3x + 4 = 8[/tex]

[tex]3x + 4 - 4 = 8 - 4[/tex]

[tex]3x = 4[/tex]

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

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

one of the properties of a cyclic quad (four sided shape in eucliean geometry) is that the opposite sides add up to 180°

So in this case to get x we= 180°-105°=285°

therefore x is 285°

[tex]a = \frac{\pi.r {}^{2} }{4} = \frac{3.14 \times 10 {}^{2} }{4} = \frac{3.14 \times 100}{4} [/tex]

[tex]a = 78.5[/tex]

Answer:

12×h=p

Step-by-step explanation:

if she works for 12 dollars per hour you multiply the 12 dollars buy the hours she worked to get the p

Answer: 8/33

Step-by-step explanation:

So the probability of picking a purple marble is 8/12, after that there are 11 marbles left in the box

Now the probability of picking a green marble without placing the first marble back is 4/11

So the probability of doing both is 8/12 x 4/11 = 8/33

Answer:

24/25

Step-by-step explanation:

use tan^-1 to find the angle

tan^-1(3/4)=36.86989765°

A =36.86989765°

2A= 2×36.86989765

=73.73979529°

sin2A>>>>sin(73.73979529°)

=24/25 or 0.96

Answer:

sin2A = [tex]\frac{24}{25}[/tex]

Step-by-step explanation:

using the identity

sin2A = 2sinAcosA

given

tan2A = [tex]\frac{3}{4}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]

then this is a 3- 4- 5 right triangle with

hypotenuse = 5, opposite = 3 , adjacent = 4 , then

sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{5}[/tex] and cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex]

Then

sin2A = 2 × [tex]\frac{3}{5}[/tex] × [tex]\frac{4}{5}[/tex] = [tex]\frac{2(3)(4)}{5(5)}[/tex] = [tex]\frac{24}{25}[/tex]

Answer:

Step-by-step explanation:

To graph by hand I would first convert both equations into y=mx+b.

We start with:

[tex]\left \{ {{2x-2y=4} \atop {x+2y=8}} \right.[/tex]

Solve for y for 2x-2y=4

[tex]2x+2y=4\\2y=4-2x\\y=2-x[/tex]

Solve for y for x+2y=8

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

Giving the new but equal system of equations:

[tex]\left \{ {{y=2x-x} \atop {y=4-\frac{x}{2} }} \right.[/tex]

From this point on you can graph the two functions to find where the two lines intersect, thats your solution.

I've gone ahead and graphed it on desmos for you

Answer:

-93312a²

Step-by-step explanation:

1) Simplify 36³ to 46656.

-2a² × 46656

2) Simplify 2a² × 46656 to 93312a².

-93312a²

Answer: [tex]\Large\boxed{y-1=\frac{4}{5} (x+2)}[/tex]

Step-by-step explanation:

Given the requirement for function

Point-slope form : y - y₁ = m (x - x₁)

Given information

m = 4/5

Point = (x₁, y₁) = (-2, 1)

Substitute values into the function form

y - y₁ = m (x - x₁)

y - (1) = (4/5) (x - (-2))

Simplify the function

[tex]\Large\boxed{y-1=\frac{4}{5} (x+2)}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Graph b.

Step-by-step explanation:

B is not a function because it fails the vertical line test.
To be a function any vertical line drawn must pass through the graph at one point only. That is not true for graph B - a line can pass through 2 points on this graph.

(D) 80°, 140°, and 70° group of segments cannot form a triangle.

To find which group of segments cannot form a triangle:

Therefore, (D) 80°, 140°, and 70° group of segments cannot form a triangle.

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Answer:

80, 140, 70

Step-by-step explanation:

From the given sample data in the table on the backpack weight, we have;

(a) The means of the samples are;

(b) The range is 0.25

(c) The true statements are;

(a) The sample means of each of each of the three samples are found as follows;

[tex]Mean = \frac{ \sum \: x}{n} [/tex]

Where;

x = The value of a data point

[tex] \sum \: x = Sum of the data [/tex]

n = Sample size

The mean of the first sample, S1, data is therefore;

[tex]Mean \: S1 = \frac{3 + 7 + 8 + 3 + 7 + 9 + 6 + 8}{8} [/tex]

3+7+8+3+7+9+6+8 = 51

Which gives

[tex]Mean \: S1 = \frac{51}{8} = \mathbf{6.375\[/tex]

Similarly, we have;

[tex]Mean \: S2 = \frac{8 + 6 + 4 + 7 + 9 + 4 + 6 + 7}{8} [/tex]

8 +6+4+7+9+4+6+7 = 51

Which gives;

[tex]Mean \: S2 = \mathbf{\frac{51}{8}} = 6.375 [/tex]

Mean of the second sample = 6.375

[tex]Mean \: S3 = \frac{9 + 4 + 5 + 8 + 7 + 5 + 9 + 6}{8} [/tex]

9+4+5+8+7+5+9+6 = 53

Which gives;

[tex]Mean \: S3 = \frac{53}{8} = \mathbf{6.625} [/tex]

(b) The range of the means of the sample means is found as follows;

Range = Largest value - Smallest value

Which gives;

(c) The population mean is given by the mean of the sample means. That is, a very good estimate of the sample mean is given by the mean of the sample means.

The true statements are therefore;

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Answer:

no

Step-by-step explanation:

So you can express a polynomial in factored form as such: [tex]a(x)*b(x)*c(x)...[/tex] where a(x), b(x), and c(x), each represent a polynomial which are each factors of the equation. It's important to note that each factor is being multiplied by each other, meaning if any of the factors output 0, the entire thing is 0, no matter the value of the other factors, since 0 * some value = 0. For this reason, if we plug in the value that makes (x+1) 0, into the polynomial, and the polynomials value is 0, that means it is a factor.

x + 1 = 0

x = -1

The value that makes the factor 0, is -1. This means that if it is a factor of the polynomial, then plugging in -1 as x into the polynomial should make the value 0.

Original Equation:

[tex]12x+5x+3x^2-5[/tex]

Plug in -1 as x

[tex]12(-1)+5(-1)+3(-1)^2-5[/tex]

Multiply values

[tex]-12-5+3(1)-5[/tex]

Simplify:

[tex]-17+3-5\\-14-5\\-19[/tex]

Since the value of the polynomial is not 0, this means x+1 is not a factor

You can also solve this use the Remainder Theorem and Factor Theorem which essentially uses the same logic

Remainder Theorem:

   If a polynomial P(x) is divided by x-a, the remainder is P(a)

Using the remainder theorem, if x-a is indeed a factor, then that means the remainder should be 0, just as 11 is a factor of 77, and 77/11 has a remainder of 0. This is what the factor theorem essentially states

Factor Theorem:

   The expression "x-a" is a factor of P(x) if and only if P(a) = 0

The absolute value exists its distance from zero on the number line.

⇒ f(x) = |x| exits f(x) = x for f(x) ≥ 0 and f(x) = -x for x < 0

⇒ Hence: f(x) = |x+8| exists f(x) = x+8 for x+8 ≥0 and x > -8

⇒ f(x) = -x+8 exists x + 8 < 0 i.e. x < -8

The function containing an algebraic expression inside absolute value symbols exists comprehended as an absolute functional form, and the calculation exists as pursues:

An absolute functional form has an algebraic expression inside absolute value symbols.

Remember that a number's absolute value exists its distance from zero on the number line.

⇒ f(x) = |x| exits f(x) = x for f(x) ≥ 0 and f(x) = -x for x < 0

⇒ Hence: f(x) = |x+8| exists f(x) = x+8 for x+8 ≥0 and x > -8

⇒ f(x) = -x+8 exists x + 8 < 0 i.e. x < -8

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The total area of the composite figure is 176 ft

The area of a composite figure can be found as follows;

Therefore,

Total area = area of rectangle + area of triangle

area of rectangle = lw

where

Therefore,

area of a rectangle = 16 × 8

area of a rectangle = 128 ft²

area of triangle = 1 / 2 bh

where

Therefore,

area of triangle = 1 / 2 × 12 × 8

area of triangle = 48 ft²

Total area of the composite figure = 48 + 128 = 176 ft

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Answer:

343.608 million to nearest thousand.

Step-by-step explanation:

Projected annual percent of growth = 3%  ( from the values 1.03 in the equation)

Worth is 2012 ( 12 years after 2000) is:

241(1.03)^12

= 343.608 million

[tex]c^2 = a^2 + b^2 - 2ab \cos C \\ \\ 55^2 = 24^2 + 40^2 - 2(24)(40)\cos C \\ \\ \cos C=\frac{55^2 - 24^2 - 40^2}{-2(24)(40)} \\ \\ C=\cos^{-1} \left(\frac{55^2 - 24^2 - 40^2}{-2(24)(40)} \right) \\ \\ \cos C=-\frac{283}{640} \\ \\ C=\boxed{\arccos \left(\-frac{283}{640} \right)}[/tex]

[tex]C=\boxed{\arccos \left( - \frac{283}{640} \right)}[/tex]

Answer:

6pi

Step-by-step explanation:

First, find the circumference of the circle with radius 9. The formula is C = 2*pi*r, so C = 2*pi*9 = 18pi. Since arc is intercepted by the 120 degree central angle, the arc length is essentially 120/360 = 1/3 of the circumference. So, the arc length is 18pi*1/3 = 6pi, or approximately 18.850.

Answer:

x + y = 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = E (4, 3 ) and (x₂, y₂ ) = A (6, 1 )

m = [tex]\frac{1-3}{6-4}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1 , then

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, 3 )

3 = - 4 + c ⇒ c = 3 + 4 = 7

y = - x + 7 ← equation in slope- intercept form ( add x to both sides )

x + y = 7 ← equation in standard form

The length of arc AB is 3π given that radius of the circle is 27 units and the angle made by the arc AB at the center of the circle is 20°. This can be obtained using the formula to find arc length.

Formula used for finding arc length:

⇒ L = 2 π r (θ/360°)

where r is the radius of the circle and θ is the angle made by the arc at the center of the circle.

⇒ L = r × θ

where r is the radius of the circle and θ is the angle made by the arc at the center of the circle.

Here in the question it is given that,

r = 27 units

θ = 20°

Since the angle made by the arc at the center of the circle is in degrees, the formula to find the length of the arc is,

⇒ L = 2 π r (θ/360°)

L = 2 π (27) (20°/360°)

L = π (27) (20°/180°)

⇒ L = 3 π

Hence the length of arc AB is 3 π given that radius of the circle is 27 units and the angle made by the arc AB at the center of the circle is 20°.

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Answer:

the answers are -243 and 729

Step-by-step explanation:

you multiply each by -3. 1x-3 gives you -3. -3x-3 gives you 9. -3x9 gives you -27. -27x-3 gives you 81. 81x-3 gives you -243 and -243x-3 gives you 729. i hope this helps.

The distance from the center to where the foci are located exists 8 units.

The formula associated with the focus of an ellipse exists given as;

c² = a² − b²

Where c exists the distance from the focus to the center.

a exists the distance from the center to a vertex,

the major axis exists 10 units.

b exists the distance from the center to a co-vertex, the minor axis exists 6 units

c² = a² − b²

c² = 10² - 6²

c² = 100 - 36

c² = 64

[tex]c = \sqrt{64}[/tex]

c = 8

Therefore, the distance from the center to where the foci are located exists 8 units.

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The first five terms of the sequence are 1/5, 2/5, 3/5,4/5, 1

Recursive functions are functions that is used to determine the next term of a given sequence giving the common difference.

Given the recursive function shown below;

f(1) = 1/5

f(n) = f(n-1) + 1/5

For the second term;

f(2) = f(1) + 1/5

f(2) = 1/5 + 1/5

f(2) = 2/5

For the third term;

f(3) = f(2) + 1/5

f(3) = 2/5 + 1/5

f(3) = 3/5

For the fourth term;

f(4) = f(3) + 1/5

f(4) = 3/5 + 1/5

f(4) = 4/5

For the fifth term;

f(5) = f(4) + 1/5

f(5) = 4/5 + 1/5

f(5) = 5/5 = 1

Hence the first five terms of the sequence are 1/5, 2/5, 3/5,4/5, 1

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