The graph of an absolute value function has a vertex of (3, 6) and crosses the x-axis at (-3,0) and (9,0). What is the equation of the absolute value function?

The population of the dark city in 2015 will be 449,245.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

The dark city had a population of 350,000 in 1990 and has increased exponentially since then, to 475,000 in 2008. Then the equation will be

350,000 = a(b)      ...1

475,000 = a(b)¹⁸      ...2

From equations 1 and 2, then we have

475,000 / 350,000 = b¹⁷

b = 1.018

Then the value of the variable a will be

350,000 = 1.018a

a = 343768.87

Then the equation will be

y = 343,768.87 (1.018)ˣ

The population in 2015 will be

y = 343,768.87 (1.018)¹⁵

y = 343,768.87 x 1.3068

y = 449,245

The population of the dark city in 2015 will be 449,245.

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Answer:

\(1.345 * 10^{10\)

Step-by-step explanation:

= 13450000000

Putting the decimal point after first non-zero digit

=> \(1.345 * 10^{10\)

Answer:

1.345 × 10^10

Step-by-step explanation:

Put the decimal point after 1.

1.345

Multiply by a number that makes the decimal to 13450000000.

That number is 10^10.

Answer:

2,3,4,5,6,7,8

Step-by-step explanation:

In words, the expression 2 ≤ x ≤ 8 translates to

"values of x between and inclusive of 2 and 8"

since we are being asked for integers,  the possible values that match this description are 2,3,4,5,6,7,8

Answer:

The correct answer is 3,4,5,6,7

Step-by-step explanation:

The signs < and > infer that the correct answer can it be either of these.

Because x is greater than two but less that eight, the number 3,4,5,6, and 7 are the only possible answers for x

Answer:

C

Step-by-step explanation:

Answer:

In expanded form:

2^3 = 2 * 2 * 2 = 8

In standard form :

2^3

Step-by-step explanation:

Given the numbers in range (0 to 10)

Write an exponential expression :

Choosing from the range for the Base and the exponent

Base = 2

Exponent = 3

where ; 2 = base. ; 3 = exponent

In expanded form:

2^3 = 2 * 2 * 2 = 8

In standard form :

2^3

Answer:

16..............................

Answer:

The slope for this equation is m=5/6.

Answer:

the sample is biased

Step-by-step explanation:

The number 357 in binary is 101100101 and x^2 - 3x - 10 when factored is (x - 5)(x + 2). Other solutions are below

The triangle and the loci are attached

(a) To convert 357 to a binary number, we can use the division-by-2 method:

357/2 gives 178 R 1

178/2 gives 89 R 0

89/2 gives 44 R 1

44/2 gives 22 R 0

22/2 gives 11 R 0

11/2 gives 5 R 1

5/2 gives 2R1

2/2 gives 1R0

1/2 gives 0 R 1

Therefore, 357 in binary is 101100101

(b) To factorise x^2 - 3x - 10, we have

x^2 - 3x - 10 = (x - 5)(x + 2)

(c) To solve 5x^2 - 7x + 1 = 0 using completing the square, we have:

x^2 - (7/5)x + 1/5 = 0 -- make the coefficient of x^2 equals 1

So, we have

x^2 - (7/5)x = -1/5

Next, we have

x^2 - (7/5)x + (7/10)^2 = -1/5 + (7/10)^2

Factorize

(x - 7/100)^2 = -1/5 + (7/10)^2

Simplifying the right-hand side, we get:

(x - 7/10)^2 = 29/100

Taking the square root of both sides, we get:

x - 7/10 = ±√29/10

Adding 7/10 to both sides, we get:

x = 7/10 ±√29/10

So, we have

x = 7/10 + √29/10 or x = 7/10 - √29/10

Evaluate

x = 1.24 or x = 0.16

Therefore, the solutions are x = 0.160 and x = 1.24, rounded to 2 decimal places.

(a) To evaluate 102 (mod 4), we divide 102 by 4 and find the remainder:

102 divided by 4 gives a quotient of 25 with a remainder of 2.

Therefore, 102 (mod 4) is 2.

(b) First, we need to find the volume of the bucket. We can do this by treating it as a frustum of a cone:

The radius of the top of the frustum is 10m, the radius of the bottom is 6m, and the height is 16 m.

The volume of a frustum of a cone is given by:

V = (1/3)πh(R^2 + r^2 + Rr),

Plugging in the values, we get:

V = (1/3) * 3.14 * 16 * (10^2 + 6^2 + 10*6)

V = 3282.35 m^3

Finally, we can find the depth of water in the rectangular tin by using the formula for volume:

V = Bh

where B is the area of the base of the tin and h is the height of the water in the tin.

Plugging in the values, we get:

3282.35 m^3 = 48 cm^2 h

So, we have

3282.35 m^3 = 0.0048 m^2 h

Solving for h, we get:

h = 683822.916667 m

Approximate

h = 683822.92 m

Therefore, the depth of water in the tin is 683822.92 m

The area of a sector of a circle is given by:

A = (θ/360)πr^2,

So, we have

300 = (θ/360)

300 = (θ/360) * (22) * 112

Solving for θ, we get:

θ = 300 * 360 * 1/(22 * 112)

θ ≈ 43.83 degrees

The perimeter of the sector is the sum of the arc length and the lengths of the two radii that form the sector.

The arc length is given by:

s = (θ/360)2πr

Plugging in the values, we get:

s = (43.83/360)(2)(22/7)(28)

s ≈ 21.43 cm

The length of each radius is 28 cm. Therefore, the perimeter of the sector is:

P = 2(28) + 21.43

P ≈ 77.43 cm

Therefore, the perimeter of the sector is 77.43 cm, rounded to 2 decimal places.

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The equation 3/2x - 5/3x = 2 can be solved as follows:

x = 12

To solve the equation 3/2x - 5/3x = 2, we need to isolate the variable x.

First, we'll simplify the equation by finding a common denominator for the fractions. The common denominator for 2 and 3 is 6. Thus, we have:

(9/6)x - (10/6)x = 2

Next, we'll combine the like terms on the left side of the equation:

(-1/6)x = 2

To isolate x, we'll multiply both sides of the equation by the reciprocal of (-1/6), which is -6/1:

x = (2)(-6/1)

Simplifying, we get:

x = -12/1

x = -12

To check the solution, we substitute x = -12 back into the original equation:

3/2(-12) - 5/3(-12) = 2

-18 - 20 = 2

-38 = 2

Since -38 is not equal to 2, the solution x = -12 does not satisfy the equation.

Therefore, there is no solution to the equation 3/2x - 5/3x = 2.

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The total number of bacteria in the dish is 31457280

The expression is given as:

Total = (32)^4 * 30

Start by evaluating the exponent

Total = 1048576 * 30

Next, evaluate the product

Total = 31457280

Hence, the total number of bacteria in the dish is 31457280

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Answer:

A (3^8)

Step-by-step explanation:

I have this question on my test. I'm just assuming the person didn't put ^.

(3^2)^4 times 3^0

Answer: 25% of 12 is 3

Step-by-step explanation:

Since there 25% is 1/4 of 100%, you'd need to divide.

There are 12 pints of berries.

If 1/2 of 25% is 6 since \(2 \sqrt{12}=6\), you can say that the percentage would be 2/4.

Now, divide 12 by 4: \(4\sqrt{12}=3\)

3 in this case would be the 1/4 and the 1/4 is substituting 25%

So there are 3 pints of blueberries.

Answer:

look at the photo I have sent

you wearing a mask right now???

The line that is tangent to the circle D is: line segment AB.

The straight line that "just touches" the curve at a particular location is known as the tangent line (or simply tangent) to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.

At any given location, a line that is tangent to a circle contacts the curve of the circle.See image 1 below, which explains what a tangent is.

According to the second diagram's representation of circle D, line segment AB touches circle D's curve at point B.

As a result, line segment AB is the line that is perpendicular to the circle D.

Your question is incomplete but most probably your full question was

Circle D is shown. Line segment F E goes through point D. Line segment C D is shown. Line segment G H goes from one side of the circle to the other side. Line segment A B is outside of the circle and intersects the circle at point B. In circle D, which is tangent to the circle? Line G H Line segment A B CD EF

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Answer:

B

Step-by-step explanation:

Line segment AB

60 percent of the sandwiches were not pastrami with work showing.

What do you mean by percentage?

percentage, a comparative figure denoting one-hundredth of any quantity. One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified, percentage.

The total number of sandwiches sold by the deli owner is 90

total number of pastrami is 36.

total number of pastrami is 54.

so, the percentage of sandwiches sold that were NOT pastrami is,(54/90)×100

Hence, 60 percent pastrami with work showing.

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Step-by-step explanation:

4/3 pi r^3  = volume of sphere      diameter = 8 ft then radius = 4 ft

  sub in the values, calculate and round answer:

4/3 (3.14)(4^3) = 268.08 ft^3

Answer: 267.95

Step-by-step explanation: 4/3 * 3.14 * 4^3 = 267.95

The area of the square is 36units²

A square is a plane figure with four equal sides and four right (90°) angles.

The area of a square is expressed as;

A = l× l = l²

the length of the square = √ 3-(-3)²+ -3-3)²

= √6²

= 6 units

Therefore the side length of the square is 6units

area of the square = l²

= 6² = 36 units²

Therefore the area of the square is 36units²

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The evaluation of the expression is 2, if the expression is x - y + z(x + w).

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

Given that x = 1, y = 1, w = 1, and z = 1

We have been given expression

⇒ x - y + z(x + w)

Substitute the values of x = 1, y = 1, w = 1, and z = 1 in the above expression,

⇒ 1 - 1 + 1(1 + 1)

⇒ 0 + 1(2)

⇒ 2

Hence, the evaluation of the expression is 2.

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Your question is incomplete, probably the missing part is:

Given x = 1, y = 1, w = 1, and z = 1 and this expression x - y + z(x + w): what is the evaluation of the logical expression?

Answer:

k = 45

The angles are 45 , 45, 90

Step-by-step explanation:

The sum of the angles of a triangle are 180

45+ k+2k = 180

Combine like terms

45+3k = 180

Subtract 45 from each side

45+3k-45 = 180-45

3k = 135

Divide by 3

3k/3 = 135/3

k =45

The angles are 45, k,2k

The angles are 45 , 45, 90

Answer:

\(k = 45 \: \: degrees \\ 2k = 90 \: \: degrees\)

Step-by-step explanation:

\(45 + 2k + k = 180 \\ 45 + 3k = 180 \\ 3k = 180 - 45 \\ 3k =13 5 \\ \frac{3k}{3} = \frac{135}{3} \\ k = 45 \\ 2k = 45 \times 2 \\ \: \: \: \: \: \: \: \: = 90\)

Answer:

in a monthly shy much $3500

in a weekly she much $807.69

Step-by-step explanation:

Answer:

Below! : )

Step-by-step explanation:

$3,500 monthly

$807.69 per week

$1,615.38 biweekly

Hope this helps! : )

The maximum number of glasses that can fit between two shelves in Monica's kitchen cabinet is 4.

option B.

To find the maximum number of glasses that can fit between two shelves, we need to subtract the height of two stacks of glasses from the distance between the shelves and divide by the height of a single stack.

Let's call the height of a single glass "h".

Then the height of a stack of 8 glasses would be 8h, and the height of a stack of 2 glasses would be 2h.

We know that:

8h = 42 cm

2h = 18 cm

So,

h = 42 cm / 8

h = 5.25 cm

And,

h = 18 cm / 2

h = 9 cm

Now, we can calculate the maximum number of glasses that can fit between two shelves as follows:

= ( 36 cm - 42 cm - 18 cm ) / 5.25 cm

= ( 36 cm - 60 cm ) / 5.25 cm  

= -24 cm / 5.25 cm

= -4.5 stacks

Since a stack must have a whole number of glasses, we can conclude that the maximum number of glasses that can fit between two shelves in Monica's kitchen cabinet is 4.

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Answer:

Or you could also find the area of 2 triangles and one rectangle.

Area of a triangle = bh/2

1st triangle = 6 x 2 = 12

12 ÷2 = 6

2nd triangle = 6x2= 12 ÷ 2 = 6

Area of a rectangle

A=bh

b = 4

h= 6

6x4=24

Now add all the areas to find out the area of the shape, so

6+6+24 =

\(36 {ft}^{2} \)

The area of the plot of land, expressed in terms of the width (x) in standard form, is (x)(x+2).

Let's consider the width of the plot of land as x meters. According to the given information, the length of the plot is 2 more than the width. Therefore, the length can be expressed as (x + 2) meters.

To calculate the area of a rectangular plot of land, we multiply the length by the width. In this case, the area can be calculated as (x)(x + 2).

Expanding the expression, we have:

Area = x(x + 2)

        = \(x^2 + 2x\)

Thus, the area of the land is given by the quadratic expression \(x^2 + 2x\), which represents the area in terms of the width (x) in standard form.

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Answer:

A = 73 , B = 9 , C = 13

Step-by-step explanation:

the value of A corresponds to x = 8, in the interval x ≤ 10 , then

f(x) = 9x + 1 , that is

f(8) = 9(8) + 1 = 72 + 1 = 73 = A

the value of B corresponds to x = 10, in the interval x > 10 , then

f(x) = 2x - 11 , that is

f(10) = 2(10) - 11 = 20 - 11 = 9 = B

the value of C corresponds to x = 12, in the interval x > 10 , then

f(x) = 2x - 11 , that is

f(12) = 2(12) - 11 = 24 - 11 = 13

Answer:

f(5) = 21

Step-by-step explanation:

Given:

\(f(0)=1\)

\(f(n)=f(n-1)+n+1\)

\(\implies f(1)=f(0)+1+1=1 + 1 + 1=3\)

\(\implies f(2)=f(1)+2+1=3 + 2 + 1=6\)

\(\implies f(3)=f(2)+3+1=6+3+1=10\)

\(\implies f(4)=f(3)+4+1=10+4+1=15\)

\(\implies f(5)=f(4)+5+1=15+5+1=21\)

Answer:

x-axis

Step-by-step explanation:

The coaster starts at a height of 250, then drops down to 0 at x=500, and then rises back up to a height of 250. The bump is located at x=500 and is the highest point on the coaster.

y = -0.0005(x-500)² + 250

The coaster starts at the highest point (y=250) when x=0 and then drops down to x=500 by following the equation y=ax(x-1000). To create the bump, we need to make the coaster rise before it falls, so we use a quadratic equation that has a vertex at x=500 and y=250 (the initial height).

The equation y = -0.0005(x-500)² + 250 is a downward-facing quadratic equation with a maximum value of y=250 at x=500. This means that as the coaster approaches x=500, it starts to rise, and then falls down again. The coefficient -0.0005 controls the steepness of the coaster's drop and the height of the bump.

Here's a graph of the coaster:

         ^

       260|                               *

          |                          *    

          |                     *  

          |                *    

          |            *  

 height   |        *      

          |     *          

          |  *            

        0 +--------------->

            0      500    1000   x-axis

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Answer:

D. (2.1)

A. (3.2)

B. (1.4)

C. (1.4)

Answer: \(\sqrt{20}\) or 4.4721...

Step-by-step explanation:

Let's pretend to draw a diagonal line straight from A to C, for a visual reference.

Point A is at (-3, 2)

Point C is at (1, 4)

You could use the distance formula... \(d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}\)

or you could use Pythagorean Theorem, \(a^{2}+b^2=c^2\), which might seem easier.

The rise of our diagonal line is 2 units, and the run is 4.

2^2=4 and 4^2= 16

4+16=20

\(\sqrt{20}\) = 4.4721...