Graph the logarithmic function g(x) = log₂ (x+2) −3.

Answer: (0,0)   (12,0)

Step-by-step explanation:

y=4x³-96x²+576x

Let y=0

Hence,

4x³-96x²+576x=0

Divide both parts of the equation by 4:

x³-24x²+144x=0

x(x²-24x+144x)=0

x=0

Thus, (0,0)

x²-24x+144=0

x²-2(x)(12)+12(12)=0

x²-2(x)(12)+12²=0

(x-12)²=0

x-12=0

x=12

Thus, (12,0)

Supoose a<1 compared to the parent function then parabola is wider than the parent function.

An equation is an expression that shows the relationship between two or more numbers and variables.

Direction the parabola opens the value of p as positive, the parabola opens up.

The focus and vertex both have the same x position, so the distance would be in terms of the y-coordinates only.

Supoose a<1 compared to the parent function then parabola is wider than the parent function

If "a" is a fraction less than one, therefore the parabola becomes wider.

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Answer:

39

Step-by-step explanation:

The given function to us is ,

[tex]\longrightarrow f(x) = 3x^3 + 1\\ [/tex]

We need to find the average rate of change between [tex] x=1 [/tex] and [tex] x=3[/tex] .

We can calculate the average rate of change as ,

[tex]\longrightarrow A(x) =\dfrac{f(b)-f(a)}{b-a} [/tex]

So that ,

[tex]\longrightarrow A(x) =\dfrac{f(3)-f(1)}{3-1}\\ [/tex]

[tex]\longrightarrow A(x) =\dfrac{ \{ 3(3)^3 +1 -(3(1)^3+1)\}}{2}\\ [/tex]

[tex]\longrightarrow A(x) = \dfrac{ 81 +1 - 3 -1 }{2}\\[/tex]

[tex]\longrightarrow A(x) = \dfrac{78}{2}\\ [/tex]

[tex]\longrightarrow\underline{\boxed{ A(x) = 39}} [/tex]

The two possible locations of L are (-2,-1) and (14/3, -5/3).

According to the question,

We have the following information:

JK has endpoints J(-10, 1) and K(2, -2). Point L divides JK into two parts with lengths in a ratio of 2:1.

We know that the following formulas are used to find the coordinates of a point:

x = [tex]\frac{(mx2+nx1)}{(m+n)}[/tex] and x = [tex]\frac{(mx2-nx1)}{(m+n)}[/tex]

y = [tex]\frac{(my2+ny1)}{(m+n)}[/tex] and y = [tex]\frac{(my2-ny1)}{(m+n)}[/tex]

In this case, we have the following values:

x1 = -10 and y1 = 1

x2 = 2 and y2 = -1

m = 2 and n = 1

So, we have:

x = {2*2+1*(-10)}/(2+1)

x = (4-10)/3

x = -6/3

x = -2

For the negative sign:

x = {2*2-1*(-10)}/3

x = (4+10)/3

x = 14/3

x = 4.67

The values of y:

y = {2*(-2)+1*1}/3

y = (-4+1)/3

y = -3/3

y = -1

For the negative sign:

y = {2*(-2)-1*1}/3

y = (-4-1)/3

y = -5/3

y = -1.67

Hence, the two possible locations of L are (-2,-1) and (14/3, -5/3).

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Answer:

164 pillows

Step-by-step explanation:

Equation: 124 + 5(8)

Answer: h = 46.25

Step-by-step explanation:

You can use the formula below to calculate the value of its interior angle:

       [tex]\frac{(n-2)*180}{n} =\frac{(18-2)*180}{18} =\frac{16*180}{18} =160[/tex]

So, each one of its interior angles is equal to 160°. Set that equal to the given angle measure and solve:

[tex]160=4h-25\\\\4h=160+25=185\\\\h=46.25[/tex]

The solution to 4 divided by 3.48 is 0.87

Division in mathematics is the method of dividing large numbers into smaller numbers or par

Step 1: Rewrite the question in mathematical terms then

[tex]\frac{3.48}{4}[/tex]= 0.87

Therefore, answer to the division  is 0.87

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The number of tiles is 96

From the question, we have

The width of the room is 16 feet, 8 inches and the client has chosen a square tile that measures 4 inches on each side.

16 feet = 192 inches

Number of tiles = (192*8)/(4*4)

= 96 tiles

The number of tiles is 96.

Multiplication:

The product of two or more numbers is computed by mathematicians using multiplication. In everyday life, it is a basic mathematical operation that is frequently used. We employ multiplication when we must combine groups of like sizes. The operation of multiplication serves as a representation of the fundamental idea of adding the same number repeatedly. The product of two or more numbers is what is obtained when those numbers are multiplied, and the factors are the quantities that are multiplied. Multiplying the numbers simplifies the process of adding the same number repeated.

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The value of the function when the value of x is 5 is 29.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

[tex]f(x)= \left \{ {{x^3 \;\;\;\;\;\; x < -3} \atop {2x^2-9\;\;\;-3\leq x < 4}} \atop {5x+4\;\;\;x > 4}}\right.[/tex]

As the value of the function is to be found when the value of x is 5.

So, we can write the function as,

f(5) = 5x + 4

f(5) = 5(5) + 4

f(5) = 29

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The nth-degree polynomial that satisfies the aforementioned conditions is the polynomial p (x) = -3 (x + 9) (x - 1 - 6i) (x - 1 + 6i).

Given that:

p is of degree 3.

1 + 6i and -9 are zeros of p.

Since 1 + 6i is an imaginary number equal to zero so 1 - 6i must also be the one equal to zero.

So, p (x) = A (x + 9) (x - (1 + 6i)) (x- (1-6i))

p (x) = A (x + 9) (x - 1 - 6i) (x - 1 + 6i) ........ (Z)

Using formula:

(a-b) (a+b) = a² - b²

(a-b)² = a² - 2ab + b²

Assume, x - 1 = a, 6i = b  

p (x) = A (x + 9) (x² - 2x + 1 + 36)

As i² = -1

p (x) = A (x + 9) (x² - 2x + 37)

Solving this equation we get,

p (x) = A (x³ - 2x² + 37x + 9x² - 18x + 333)

p (x) = A (x³ + 7x² + 19x + 333) ....... (1)

Given that:

p(2) = -1221

Putting the value of x = 2 and p(2) = -1221 in equation (1).

p(2) = A (2³ + 7(2²) + 19(2) + 333)

=> -1221 = A (8 + 28 + 38 + 333)

=> A = -1221/407

=> A = -3

Putting the value of A = -3 in equation (Z).

Hence, the polynomial p (x) = -3 (x + 9) (x - 1 - 6i) (x - 1 + 6i).

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Answer:

a) -3x + y = 8

Step-by-step explanation:

Now we have to,

→ find which of these equations is linear.

Format of linear equation,

→ Ax + By = C

Then the linear equation is,

→ Ax + By = C

→ -3x + y = 8

Hence, answer is -3x + y = 8.

Answer:

A. -3x + y = 8

Step-by-step explanation:

Definition of a Linear Equation:

This is a linear equation as the highest power of its variables is one, and each variable is multiplied by a constant only.

This is not a linear equation as the highest power of the term in x is 2.

This is not a linear equation as the highest power of the term in x is 3.

This is not a linear equation as the x and y variables are multiplied by each other rather than by a constant.

Answer:

Step-by-step explanation:

220.5-(12.8+20.25+18.2+25.5)

220.5-(76.25)

143.75 lbs of ice left

The "key" for a combination padlock involves a 210 combination.

What is a combination?

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.

Here, we have

A combination padlock has 10 digits to choose from for each of the

four sections of the lock.

so,  we apply a combination

¹⁰C₄ = 10! / (6! × 4!)

      = (10 × 9 × 8 × 7 × 6!) / (6! × 4!)

      =  (10 × 9 × 8 × 7)/ 4!

     = (10 × 9 × 8 × 7)/ (4 × 3 × 2 × 1)

  =  210

Hence, the "key" for a combination padlock involves a 210 combination.

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Answer:

[tex] {2}^{ - 5} [/tex]

Step-by-step explanation:

Please see picture on how to do it

[tex]4x+7=1+2(2x+3)[/tex]

⇒ Our goal is to solve for x. We can do this by moving everything else to the other side of the equation.

⇒ Open up the parentheses:

[tex]4x+7=1+4x+6[/tex]

⇒ Simplify:

[tex]4x+7=4x+7[/tex]

Because both sides are equal, we end up with x = x.

In this case, we can say that all values of x are true.

All values of x are true.

The total amount of purchases of Rollie is $1,251. Rollie's available credit card limit after spending $1,251 from $4,000 is $2,749.

We are given:

Rollie has a credit card limit of $4,000.

He made the following purchases: $425.36, $358.33, $377.11, and $90.20.

We need to find the total amount of purchases and Rollie's available credit card limit.

To find the total amount of purchases, we need to perform the addition that is add all the expenses:

The total amount of purchases

= addition of all purchases

= $425.36 + $358.33 + $377.11 +  $90.20

= $1251

We need to subtract the total amount of purchases from the credit card limit to get Rollie's available credit card limit.

So,

Rollie's available credit card limit

= credit card limit - the total amount of purchases

= $4000 - $1251

= $2749

Thus, the total amount of purchases of Rollie is $1,251. Rollie's available credit card limit after spending $1,251 from $4,000 is $2,749.

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Kyra takes 105 minutes to cover a distance of 7 miles if she walks at  a speed of 1/15 miles per minute.

Given,

Kyra is participating in a fundraiser walk-a-thon.

She walks 2 miles in 30 minutes

We have to find the time taken by Kyra to cover 7 miles if she continues the same rate of speed;

Here,

2  miles in 30 minutes

Then,

Speed = distance / time

Speed = 2 / 30

Speed = 1/15 miles per minute

Now,

The time taken to cover 7 miles;

Speed = distance / time

1/15 = 7 / t

t = 7 x 15

t = 105 minutes

That is,

Kyra takes 105 minutes to cover a distance of 7 miles if she walks at  a speed of 1/15 miles per minute.

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Answer:

d. If corresponding angles are congruent, then the lines are parallel

Step-by-step explanation:

This is an example of two lines intersected by a transversal. If corresponding angles on both lines are equal, then the lines must be parallel! Think about it! If both of the two-mark angles were 30 degrees, both lines would be pointing in the exact same direction - parallel!

If corresponding angles are congruent, then the lines are parallel thus option (d) is correct.

Two lines in the same plane that are equally spaced apart and never cross each other are said two lines in the same plane that are equally spaced apart and never cross each other to be parallel lines.

As per the given two parallel lines and one transversal.

The angle with a single mark is collectively known as the corresponding angle.

If the corresponding angle is the same insure that both lines which intersect at single lines will be parallel.

Hence "If corresponding angles are congruent, then the lines are parallel".

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The cost of the labor per hour is $ 45

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The total cost of the parts is = $ 141

The total number of hours worked by the technician = 4.25 hours

The total cost of repair = $ 332.25

Let the cost of the labor be = y

The total cost of labor =
Cost of the labor per hour x Number of hours worked by the technician

The total cost of labor = 4.25y

Now ,

The total cost of repairing the computer =
Total cost of labor  + Total cost of the parts

The total cost of repairing the computer = 141 + 4.25y

332.25 = 141 + 4.25y

Subtracting 141 on both sides , we get

4.25 y = 191.25

Divide by 4.25 on both sides , we get

y = $ 45

Therefore cost of labor per hour y = $ 45

Hence , the total cost of labor per hour is $ 45

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The number of subsets contained in Q if Q={x∣∣x is an even, positive integer and x < 27] is 13.

A subset implies a part of the mathematical concept that's referred to as the set. The set is the collection of the elements that are grouped in the curly braces.

In this case, since x is an even number and less than 27, this will be:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, and 26.

Therefore, the numbers are 13.

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Answer:

[tex]y=-\dfrac{1}{8}x^3[/tex]

Step-by-step explanation:

If a function is symmetrical about the origin, when y is replaced with (-y) and x is replaced with (-x), the resulting function will be equal to the original function.

Original function:

[tex]y=-\dfrac{1}{8}x^3[/tex]

Replace y with (-y) and x with (-x):

[tex]\implies -y=-\dfrac{1}{8}(-x)^3[/tex]

[tex]\implies -y=-\dfrac{1}{8}\cdot -x^3[/tex]

[tex]\implies -y=\dfrac{1}{8}x^3[/tex]

Multiply both sides by -1:

[tex]\implies y=-\dfrac{1}{8}x^3[/tex]

Therefore, as the function is equal to the original function, this function is symmetric with respect to the origin.

A model of the given expression on a number line is represented by a number line with open circle on point negative 11 over 2 (-11/2) and arrow shaded to the left.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

From the information provided, we have the following mathematical expression:

x = -3 - 2 1/2

x = -3 - 5/2

x = -11/2 or -5.5.

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15/4 days take 20 men to complete the task.

Given,

In the question:

The number of days worked is inversely proportional to the number of people.

If it takes 15 people to collect and pile sand for the construction of a classroom in five days.

To find the how many days take it 20 men to complete the task?

Now, According to the question:

Based on the given condition:

Formulate:

5 x 15 ÷ 20

Calculate :

5x 15/ 20

Cross out the common factor:

=15/4

Hence, 15/4 days take 20 men to complete the task.

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The number of revolutions = Total distance divided by its circumference

The radius of the tire is 1.167 yards.

A circle is a two-dimensional figure with a radius and circumference of
2πr.

The area of a circle is given as πr².

We have,

The number of revolutions = Total distance divided by its circumference

Total distance = 200 yards

Revolutions = 27.28

A tire is in the form of a circle.

So,

The circumference of the tire.

= 2πr

Now,

27.28 = 200 yards / 2πr

2πr = 200 yards / 27.28

r = 200/(27.28 x 2 x 3.14)

r = 200 / 171.32

r = 1.167 yards.

The radius of the tire is 1.167 yards.

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The passenger train traveling at 30 mi/hr faster than the freight train and traveling 3 times the distance traveled by the freight train, through the kinematic equations, indicates that the speed of the freight train is 15 mi/hr and the speed of the passenger train is 45 mi/hr.

Kinematics is the study of the motion of an object without reference to the force that causes the motion.

The speed of the passenger train = 30 + The speed of the freight train

Distance traveled by the passenger train in 6 hours = 3 × The distance traveled by the freight train

Let v represent the speed of the freight train and let d represent the distance traveled by the freight train in 6 hours

From kinematic equations, we get;

Speed of the passenger train = 30 + v

Distance traveled by the passenger train in 6 hours = 3 × d

(30 + v) × 6 = 3•d

6•v = d

Which gives; (30 + v) × 6 = 3 × 6•v

180 + 6•v = 18•v

12•v = 180

v = 180 ÷ 12 = 15

The speed of the freight train is v = 15 mi/hr

The speed of the passenger train = 30 + v

The speed of the passenger train is (30 + 15) mi/hr = 45 mi/hr

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The p-value of this sample proportion is equal to 0.0360.

At the 0.01 (1%) significance level, there isn't enough evidence to conclude that freshmen students study less than 2.5 hours per day, on an average.

For this statistical study, we would use a t-test statistic and the null and alternative hypotheses would be given by:

H₀: p ≥ 150 minutes

H₁: p < 150 minutes

Mathematically, the t-test statistic can be calculated by using this formula:

[tex]t=\frac{x\;-\;\mu}{\frac{\delta}{\sqrt{n} } }[/tex]

Where:

Substituting the given parameters into the formula, we have;

t-test, t = (135 - 150)/(44/√30)

t-test, t = (-15)/8.0333

t-test, t = -1.8672

From the t distribution table, the p-value is given by:

p-value = P(t < -1.8672)

p-value = 0.0360

Since the p-value (0.0360) is greater than the significance level (0.01), we fail to reject the null hypothesis because there is insufficient evidence to claim that the mean time of the freshman students is less than 2.5 hours per day.

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