Which function has a domain of (-1, ∞) and a range of (-∞, ∞)?
O A. f(x) = log₂x - 1
OB. f(x) = log₂ (x-1)
C. f(x) = log₂(x + 1
D f(x) = log₂ x+ 1

The coordinates of Z are (-11.5, 5)

When a point on a line segment divides it into two segments, the formula used to determine the coordinates of that point is known as the section formula. Let us say, we have a point P(x,y) that divides the line segment with marked points as A (x1,y1) and B(x2,y2). To find the coordinates, we use the section formula, which is mathematically expressed as:

P(x, y) =  (m[tex]x_2[/tex] + n [tex]x_1[/tex] / m+ n, m [tex]y_2[/tex] +n[tex]y_1[/tex] /m+ n)

Given coordinates:

XY:XZ is 2:3

X is located at (6,10) and Y is located at (-1,8).

let the coordinates of Z(x, y)

using section formula

-1 = (2x + 18)/ 5

-5 = 2x +18

2x = -23

x= -11.5

and, 8 = 2y + 30 /5

40 = 2y + 30

2y= 10

y=5

Hence, the coordinates of Z are (-11.5, 5)

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The value of a is 20.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Given that,

HL is perpendicular to HJ

m ∠2 = (a + 15)°

and

m ∠3 = (a + 35)°

If HL and HJ are perpendicular,

Then,

m ∠2 + m ∠3 = 90°

(a + 15)°  +  (a + 35)° = 90°

Now, solve for a

(a + 15)°  +  (a + 35)° = 90°

a + 15 + a + 35 = 90

a + a = 90 - 15 - 35

2a = 40

a = [tex]\frac{40}{2}[/tex]

a = 20.

Hence, the value of a is 20

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The inequality equation is = 15x +10y>=110. This equation represents the possible values for the number of hours lifeguarding and the number of hours washing cars = 15x +10y >= 110

Hourly wage of Cooper working as a lifeguard = $15

Hourly wage of Cooper washing cars = $10

Minimum income required this week = $110

Let x be the number of hours Cooper works as a lifeguard and y be the number of hours Cooper works washing cars

Income from working as a lifeguard based on the number of hours = 15x

Income from working washing cars based on the number of hours = 10y

Formulating the inequality equation we get the following:

15x + 10y >=110

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The expansion and simplified form of the expression [(x+3)(2x-1)(x+4)] will be (2x³ + x² - 25x - 12).

As per the question statement, we are provided with the expression of [(x+3)(2x-1)(x+4)] where three separate factors of the variable "x" are multiplied with each other.

We are required to expand and simplify the above-mentioned expression to obtain our desired answer.

Given, [(x + 3)(2x - 1)(x + 4)]

= [{(x + 3)*(2x - 1)}(x + 4)]

= [{(x*2x) - (x*1) + (3*2x) - (3*1)}(x + 4)]

= [(2x² - x - 6x -3)(x + 4)]

= [(2x² - 7x -3)(x + 4)]

= [(2x²*x) + (2x²*4) - (7x*x) - (7x*4) - (3*x) - (3*4)]

= [2x³ + 8x² - 7x² - 28x - 3x - 12]

= [2x³ + (8x² - 7x²) - (28x + 3x) - 12]

= (2x³ + x² - 25x - 12)

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Answer:

No, 9 is not a factor of 76 and 46.

Step-by-step explanation:

No, 9 is not a factor of 76 and 46. 9 is a factor of 72 and 45.

I hope this helps!

The perimeter of each pool is 92 ft.

What is perimeter?

A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter.

Given, the triangles are congruent so,

20x-15 = 15x+15

=> 20x-15x = 15+15

=> 5x = 30

=> x = 30/5 = 6

Therefore, perimeter = (4x-4) + (5x+1) + 41

                                    = (4x6 - 4) + (5x6 + 1) + 41

                                    = 20 + 31 + 41

                                    = 92

Hence, the perimeter of each pool is 92 ft.

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The surface area of the given pyramid is equivalent to 760 square inches.

The surface area of a figure is the sum of the area of the surfaces of such figure.

The given pyramid is made up of 5 big rectangles and 2 small rectangles

Surface area = Area of 4 large rectangles + 2(area of small rectangles)

Surface area = 2(22 * 10) + 2(22 * 5) + 2(10 * 5)

Surface area = 440 + 220 + 100

Surface area  = 760 square inches

Surface area = 760 square inches

Hence the surface area of the rectangular based pyramid is 760 square inches

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Neither graph in this problem represents a proportional relationship, as they have different rates of change. Examples are as follows:

1. Different rates between days 0-10 and 30-40.

2. Different rates between hours 0 - 1 and 2 - 3.

A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, as the rule below shows.

y = kx

Hence, a function will only be proportional if the rate of change is constant for all intervals.

For item 1, we have that:

Hence it is not a proportional relationship, due to the different rates.

For item 2, we have that:

For the same reason as item 1, of the different rates, it does not represent a proportional relationship.

The graphs are missing and are given by the image at the end of the answer.

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Answer:

Subtract 8 from both sides

Step-by-step explanation:

You want to isolate the term with the variable you want to solve for.

Answer:

Subtract 8 from both sides.

We have to evaluate the expressions.

We have to solve each operation in the correct order: first the operations within the parenthesis, and within them, first the powers, then the multiplication/quotients and lastly the adds/subtractions. Then, we apply the same sequence for the terms outside the parenthesis.

a)

b)

c)

Answer: a) 146, b) 4 c) 29

Answer:

maybe, probably 20mph

Step-by-step explanation:

The average rate of change is equal to 10 miles per hour.

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

Given that the function is changing from point (30,2) to (20,1). The average rate of the change will be calculated as,

The average rate of change = ( 30 - 20) / ( 2 - 1)

Average rate of change = 10 miles per hour

Therefore, the average rate of change is equal to 10 miles per hour.

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Step-by-step explanation:

my name is my name is mikiyas

Answer:

he has travelled nine blocks

Step-by-step explanation:

four blocks + two blocks + three blocks

=nine blocks

the area of triangle cod is 6 sq. inch

A trapezoid is also as a trapezium, is a flat closed shape having 4 straight  

sides, with one pair of parallel sides . a trapezium can also a  parallel legs .

Point O (the point of intersection of diagonals )divides two diagonals AC and BD into parts that are proportional:

AO/CO = DO/BO

Then AO x BO = CO xDO

Consider triangle ABO. The area of this triangle is

Aabo  = 1/2 x AO x BO x sin ∠AOB

Consider triangle COD. The area of this triangle is

Acod = 1/2 x CO x DO x sin ∠COD

Since  AO x  BO = CO x DO and angles AOB and COD are congruent as vertical angles

Acod = 1/2 x BO x AO x sin ∠ AOB = Aaob = 6. inc.sq.

hence ,

the area of traiangle cod is 6 sq. inc.

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Answer:

10 bags would cost $30

Step-by-step explanation:

We have been given we can get 2 bags for $6

so we need to how many bags we would get for a dollar =

6/2 = 3

now we need the value for 10 bags =

10 times 3 =

$30

I have attached a image which makes the equation much more pleasing to look at, do check it out. :)

(Hi fyi this answer took a lot of time & effort to make sure it was accurate, precise and to the point to be produced, so if you could opt this answer as the brainliest it would mean the world to me,)

Stay positive and Take care,

A fellow mate,

Cheers !

The most appropriate choice for equation of line in slope intercept form will be given by-

x intercept = 0 and y intercept = 0

This means that  if Ryan do not work at all, he will not be paid.

The graph is positive throughout

This means to get paid, Raid will have to spend some time doing .

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here,

x intercept = 0 and y intercept = 0

This means that  if Ryan do not work at all, he will not be paid.

The  graph is throughout positive.

This means to get paid, Raid will have to spend some time doing .

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Answer:

31.42cm

Step-by-step explanation:

We know that C = πd. Since the diameter is 10cm, we know that C = π x 10cm = 31.42cm (to 2 decimal places).

Answer:

31.42 centimeters.

Step-by-step explanation:

Are we in the same class? I had this same question and its due.

Answer:8%

Step-by-step explanation:

The integer solutions of the system of inequalities are x >= 1 and b <= 0

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

System of inequalities 1

Here, we have

3 - 18x < 0

0.2 - 0.1x > 0

Rewrite as

0 < 0.2 - 0.1x

The above means that

3 - 18x  < 0.2 - 0.1x

Collect the like terms

So, we have

3 - 0.2 < 18x + 0.1x

Evaluate the like terms

So, we have

2.8 < 18.1x

Divide both sides by 18.1

So, we have

0.155 < x

Rewrite as

x > 0.155

The integer value greater than 0.155 is at least one

Hence, the integer solution of the system is x >= 1

System of inequalities 2

Here, we have

6 - 4b > 0

3b - 1 > 0

The above means that

6 - 4b > 0 < 3b - 1

Collect the like terms

So, we have

-4b > - 6 + 0 + 1< 3b

Evaluate the like terms

So, we have

-4b > -5 < 3b

Solve for b

b < -1.25 or -1.67 < b

The integer values in this case are 0

So, we have

b <= 0

Hence, the integer solution of the system is b <= 0

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The measure of an exterior angle of a regular octagon is 45 degrees

Angles are formed when two or more lines intersect.

This in other words means that angles is the measure of space between the intersection of rays or lines

The given parameters are:

Shape: regular octagon

A regular octagon has 8 sides, and the total sum of angles is 360

So, we have

Exterior angle = Total sum of angles/Number of sidee

This gives

Exterior angle = 360/8

Evaluate the quotient

Exterior angle = 45

Hence, the measure of the angle is 45 degrees

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The coordinates of the roots of the equation 3+2x-x^2=0 is (- 1, 0 ) and (3, 0 ).

A quadratic equation  can be described as the algebraic equation  that posses the second degree of x which can be seen in the form of ax2 + bx + c = 0 and this can be followed in solving the equation.

We were given:

3+2x-x^2=0

This equation can be re arranges as :

-x^2 +  3+2x=0

This can be factorized as :

(x + 1)(x - 3)

Hence the  coordinates of the roots can then be written as  (- 1, 0 ) and (3, 0 ).

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[tex]p < 10-4\\p < 6[/tex]

P<6 is the solution

Be reminded <> change direction when you divide or multiply by a negative number.

Answer:

x = 118 text messages

Step-by-step explanation:

Since the total cost of $59.50 is comprised of the flat fee of $30 plus $0.25 for each text message, we can write

$59.50 = $30 + $0.25x

$29.50 = $0.25x

x = 118 text messages

Answer:

[tex]\dfrac{\dfrac{3}{5}x + \dfrac{7}{10}y}{x + y}[/tex]  

where x = number of students in Zankers class and y = number of students in Haynes' class

If the number of students in these classes are equal then the average fraction is 13/20

Step-by-step explanation:

Let x = number of students in Zanker's class

Then number of students who went for the trip is [tex]\dfrac{3}{5}x[/tex]

Let y  be the number of students in Haynes' clas

Number of students who went = [tex]\dfrac{7}{10}y[/tex]

Total number of students who went on the trip = [tex]\dfrac{3}{5}x + \dfrac{7}{10}y[/tex]

Total number of students in both classes = x + y

So average fraction

=
= [tex]\dfrac{\textsf {Total Number of Students On Trip}}{\textsf {Total Number of Students}}\\\\= \dfrac{\dfrac{3}{5}x + \dfrac{7}{10}y}{x + y}[/tex]

Without knowing how many students are in each class we can only come up with an equation

If we assume the same number of students in each class
Then we get total students who went on trip =  [tex]\dfrac{3}{5} N + \dfrac{7}{10}N[/tex][tex]= \left( \dfrac{3}{5} + \dfrac{7}{10}\right)N= \left(\dfrac{13}{10}\right)N[/tex]

where N = total number of students

Since the total in 2 classes is 2N the average fraction

[tex]= \left(\dfrac{13}{10}\right)N \div 2N = \dfrac{13}{20}[/tex]

The transformations that maps polygon jklm to polygon nopq are described as follows:

C. Reflection across the y-axis, translation 2 units left and 6 units up, dilation with center (0,0) and scale factor 1/2.

The first transformation was a reflection, changing the orientation of the polygon.

Due to the orientation assumed with the equivalent vertices, NL, KO, PJ and MQ, the reflection was over the y-axis, with vertex O assuming coordinates (2,-2).

Since vertex O is at the y-axis, the polygon was translated 2 units left and 6 units up, with O assuming coordinates (0, 4).

The final coordinates of O are (0,2), hence the polygon was dilated with a scale factor of 1/2, as 4 x 1/2 = 2, which is the final y-coordinate of O.

The problem is incomplete, and the complete problem is given by the image at the end of the answer.

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