Write 2.5 as a mixed number and as an improper fraction. Write your answers in simplest form.

Answer:

40.5

Step-by-step explanation:

The vertex, focus and axis of symmetry of the given function are (3, 4), (3, 33/8) and 3 respectively.

The given quadratic function is f(x) = 2(x - 3)² + 4.

We need to find the key features of the given quadratic function.

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. A quadratic function has a minimum of one term which is of the second degree.

Now, the key features of the given quadratic function as follows:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (3, 4)

Focus: (3, 33/8)

Axis of Symmetry: x=3

Directrix: y=31/8

Plot these points (1, 12), (2, 6), (3, 4), (4, 6) and (5, 12) on the graph.

Therefore, the vertex, focus and axis of symmetry of the given function are (3, 4), (3, 33/8) and 3 respectively.

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Answer:

8 nickels and 14 pennies

Step-by-step explanation:

Let p = number of pennies

Let n = number of nickels

p + n = 22             .01p + .05n =.54

Take the second equation and multiple it through by 100 to clear the decimals.

100(.01p + .05n( = .54(100)

p + 5 n = 54  Multiply this through by -1 so that I can add it to the first equation.

-p  -5n = -54

p + n = 22   Add these together

    -4n = -32  Divide both sides by -4

n = 8  We have solved for n.  We have 8 nickels.

Plug 8 in for n in the first equation and solve for p.

p + n = 22

p + 8 = 22  Subtract both sides by 8

p  = 14  There are 14 pennies.

Check:

p + n = 22

14 + 8 = 22

22 = 22  Checks

.01p + .05n = .54

.01(14) + .05(8) = .54

.14 + .40 .54

.54 .54 check

The function rule for g(x) is g(x) = -4x

The function is given as

f(x) = 4x

The transformation is given as reflection across the x-axis

The rule of this transformation is

(x, y) = (x, -y)

So, we have

g(x) = -f(x)

This gives

g(x) = -4x

Hence, the function rule for g(x) is g(x) = -4x

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Answer:2

Step-by-step explanation:

The simplified form of the expression (2⁴)⁻¹ is 1/2⁴ (one over two raised to the power of four).

The integers exponents are the exponents that should be an integer. It can be either a positive integer or a negative integer. In this, the positive integer exponents describe how many times the base number should be multiplied by itself.

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

It is given that the expression is (2⁴)⁻¹

Now,

using the integer exponent properties,

=> (2⁴)⁻¹  

=> (2)⁴* ⁻¹

=> (2)⁻⁴

=> 1/2⁴

Therefore, the answer is 1/2⁴ (one over two raised to the power of four) derived using the properties of integer exponents.

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Answer:

544 miles

Step-by-step explanation:

160 miles= 5 hours in order to see how much she traveled in 1 hour you need to divide so do 160 divided by 5 = 32 then do 32x17 which would be 544.

I hope it helps you!

~XxBells is a cute girlxX~

Kaylee would travel 544 miles in 17 hours if she continued at the same rate.

A mathematical number is known as distance measures "how much ground an object has traveled" while moving. Distance is defined as the product of speed and time.

distance = rate × time

We know that Kaylee drove 160 miles in 5 hours, so her rate is:

rate = distance / time = 160 miles / 5 hours = 32 miles/hour

Now we can use this rate to find out how far she would travel in 17 hours:

distance = rate × time

distance = 32 miles/hour × 17 hours

distance = 544 miles

Therefore, Kaylee would travel 544 miles in 17 hours if she continued at the same rate.

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By using Heron's formula and standard formula for the area of a triangle, the area of the composite figure is 921006.497 square meters.

In this problem we must determine the area of a composite figure, which consists in subtracting the area of an isosceles triangle from the area of the equilateral triangle:

Big triangle

The area of the big triangle is determined by Heron's formula:

s = [3 · (520 m)] / 2

s = 780 m

A = √[(780 m) · (1560 m - 520 m)³]

A ≈936693.077 m²

Small triangle

H = (520 m) · sin 60°

H ≈ 450.333 m

h = 450.333 m - 390 m

h = 60.333 m

A = 0.5 · (520 m) · (60.333 m)

A = 15686.580 m²

Then, the area of the composite figure is 921006.497 square meters.

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It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.

In the given statement is:

λ = 2.5 x 10^-2 [tex]min^{-1}[/tex]is the rate constant of the nucleus

To solve this problem, we use

N(t) = [tex]N_{0}[/tex]e^-λt

and since we are looking for the time it takes to decay the nucleus to one -fourth of its original amount, we set

N(t) = 1/4 [tex]N_{0}[/tex] = 0.25[tex]N_{0}[/tex]

We can substitute this in the decay equation:

0.25[tex]N_{0}[/tex] =[tex]N_{0}[/tex] e^-λt

Cancel the like terms

0.25 = e ^-λt

Take the natural logarithm of both sides:

㏑(0.25) =㏑(e^-λt)

㏑(0.25)= -λt

Solve for the time t:

t = - ㏑(0.25)/λ

Substitute the given rate constant :

t = ㏑(0.25) / 2.5 x 10^-2 [tex]min^{-1}[/tex]

t = -1.3863 /2.5 x 10^-2 [tex]min^{-2}[/tex]

t = 55.452mins

It takes approximately 55 mins for the sample to decay to one - fourth of its original amount.

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Answer:

positive the answer is 3

Step-by-step explanation:

Step-by-step explanation:

just draw what I have done

The length with scale factor to form quadrilateral 1/2, A'B' is √5 units when AB is √20.

The formula to find the distance between the two points is usually given by

d=√((x2 – x1)² + (y2 – y1)²).

Given :

Quadrilateral ABCD is dilated at the center (0,0) with a scale factor of 1/2 to form quadrilateral A'B'C'D'.

Points - A(0,4), B(4,2), C(4,-4), and D(-2,-2).

So, the points of the quadrilateral ABCD becomes:

So,  length of A'B'

AB = √(4-0) ² +(2 -4)²

AB = √16 + 4

AB = √20

AB = 2√5

A'B' = 1/2 AB

A'B' = √5

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The minimum wage per hour = $2

Here we need to find the value of minimum wage per hour in 1975

As is given that the earning minimum wage is $80 for working 40 hours.

40-hour work gives = $80

1-hour work gives = $80/40

                             = $2

Therefore the minimum wage per hour in 1975 is $2

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Lindsay Bedford should embroider 73 caps.

Let us assume the number of number of caps needed to be embroidered for desired earning be x. Now, forming the equation to solve for x, thus, finding the required number of caps.

Equation -

6.50*8 + 0.45*x = 85

Now solving this equation for the value of x.

Performing multiplication of numbers on Left Hand Side

52 + 0.45x = 85

Shifting the product from Left Hand Side to Right Hand Side

0.45x = 85 - 52

Performing subtraction on  Right Hand Side to find the value of x

0.45x = 33

Shifting 0.45 to denominator on  Right Hand Side

x = 33÷0.45

Performing division to find the value of x

x = 73.3

The number of caps can not be in fraction. So, we will round off the digit to find exact number of caps.

Number of caps = 73

Therefore, Lindsay Bedford needs to embroider 73 caps.

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The complete question is -

Lindsay Bedford works at a baseball cap shop. She is paid $6.50 per hour plus $0.45 for each cap she embroiders. How many caps must she embroider to earn at least $85 in an 8-hour day?

Except for x = 3, the set of x values for that y will become a real number as per Y=8/x-3 contains all real numbers.

A real number is any number which can be found with in real world. Numbers can be found all around us.

Now according to the question;

In actuality, the expression Y=8/x-3 stops producing a real numerical value for y when the denominator has become zero.

When the denominator is zero, the y value is undefined and thus not a real number.

As a result, if we set;

x - 3 = 0

x = 3

Therefore, except for x = 3, the set of x values for which y is a real number per the Y=8/x-3 includes all real numbers.

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The complete question is-

Y=8/x-3

Identify the set of values x for which y will be a real number

The total cost of the ski weekend comes out to be $250.

Total expenses for just a given period are the sum of all gross cash expenditures and furthermore any pending subsidiary items like operating expenses, reward fees, interest, & taxes.

Some key features regarding the total cost are-

Now, according to the question;

The cost of all spending are-

$50 for transportation

$50 for lodging

$50 for ski lift tickets

$100 for waiter.

Total cost = transportation cost + lodging cost +  ski lift tickets cost + waiter cost.

Total cost = $50 + $50 + $50 + $100

Total cost = $250.

Therefore, the total spending in the ski weekend are $250.

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Answer:

Step-by-step explanation:

3 3/4 = 15/4

15/4 divided by 3/4 = 5

Answer:

Step-by-step explanation:

the number is y

you are told

y+0.5y=27

Therefore,

1.5y = 27.

If you divide by 1.5 on both sides, you'll get 18 which is your answer.

18+9=27

Based on the fact that Raven is trying to decide between two plumbing services, the costs of the service charge are:

The Service cost for Service provider A is:

= 50 x  1.5 + (50 x ((1.75 / 1.5) - 1)

= $83.33

Service cost for Service provider B is:

= Number of hours x Cost per hour

= 60 x 1.75

= $105

The cheaper plumber is Service provider A.

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Answer:

$8.60

Step-by-step explanation:

Let x = the tip

80 - x = 9(5.85 + 1.25) + 5(1.50)

80 -x = 63.90 + 7.5

80 - x = 71.40  Subtract 80 from both sides

-x = -8.60  Divide both sides by -1

x = 8.60

For the bucket to hold the 10 litres, then it s said to contains 2.64 gallons.

A multi-step procedure encompassing multiplication as well as division by a mathematical factor is known as unit conversion. We can measure weight, length, and temperature in a variety of ways.

Now, per the given question;

The total amount a bucket contains is 10 litres.

Noe, the conversion of litres in gallons is given as;

1 litres = 0.26 gallons.

Thus, 10 litres = 10×0.264

= 2.64 gallons.

Therefore, the bucket will contain 2.64 gallons.

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The function that Ngozi's salary s(t) in dollars, t years after she starts to work as an interpreter is given by [tex]S = 24000 * (1.035)^t[/tex].

What is a function?

You can use the fact that the raise is done on the previous year's salary.

Let the initial salary be P = $24000

After 1 year, her salary increased by R = 3.5% which, thus,

Total salary = P + increment

Similarly going on, we get

[tex]P_t = P(1+ \frac{R}{100})^t = S[/tex] (we can say)

Putting values of P(value of P) and R(value of R), we get

[tex]S = 24000(1 + 0.035)^t = 24000 *(1.035)^t[/tex]

Thus,

The function that Ngozi's salary s(t) in dollars, t years after she starts to work as an interpreter is given by

[tex]S = 24000 * (1.035)^t[/tex]

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Answer:

they should produce 225 software programs and 225 video games per week.

Step-by-step explanation:

limit 450

there are 2 factors the software and video games.

450•2= 225

The measure of the speed during the time is 63. 64 miles per hour

The formula for speed is expressed as;

Speed = distance/ time

Given that;

Let's convert the time in minutes to hour

60 minutes = 1 hour

20 minutes = x hour

cross multiply

x = 20/ 60

x = 0. 33 hours

Substitute the values

Speed = 21/ 0. 33

Speed = 63. 64 miles per hour

Thus, the measure of the speed during the time is 63. 64 miles per hour

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Answer: the second one

Step-by-step explanation:

The inequality that represents buying n notebook with a calculator and a maximum amount of $37 to spend:

37 ≥ 2n + 24

Option D is the correct answer.

It is a statement of an ordered relationship

- greater than,

- greater than or equal to,

- less than,

- less than or equal to between two numbers or algebraic expressions.

We have,

Cost of the calculator = $24

Cost of a notebook = $2

Total amount to spend = $37

Number of notebooks = n

The inequality that represents buying n notebook with a calculator and a maximum amount of $37 to spend:

37 ≥ 24 + 2n

The number of possible notebooks to buy:

37  24 + 2n

37 - 24 ≥ 2n

13 ≥ 2n

13/2 ≥ n

6.5 ≥ n

The number of notebooks can be 6 or fewer.

Thus,

The inequality that represents buying n notebook with a calculator and a maximum amount of $37 to spend:

37 ≥ 2n + 24

Option D is the correct answer.

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The length of the base will be equal to 65.99 centimeters.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The formula for the Pythagorean theorem is given below:-

H² = B² + P²

Given that in a right triangle if the hypotenuse is 70 cm and the shorter leg is one-third the length of the longer leg.

P = 70/ 3 cm

H = 70 cm

The value of the leg will be calculated as:-

H² = B² + P²

70² = B² + (70/3)²

B² = 70² -  (70/3)²

B = √4355

B = 65.99 cm

Therefore, the length of the base will be equal to 65.99 centimeters.

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Answer:

26.2

Step-by-step explanation:

7 + (2x3) 5-6 (9/5)

7 + 6*5-6*1.8

7 + 30-10.8

37 - 10.8

26.2

The trigonometric function that can be used to find the value of x is 12 / tan ( 25 ) . The correct values of a and b will be 12 and 25 resp . .

Given :

A right angle triangle , one angle = 25 ° and side opposite given angle = 12 units .

Trigonometric Formula for Tan θ

tan θ = perpendicular / base , tan θ = ( sin θ / cos θ ) , tan θ = ( 1 / cot θ ) .

where θ = 25 , perpendicular = 12 , base = x .

Substituting values in above first formula ,

tan 25 = 12 / x

Therefore , x = 12 / tan ( 25 ) .

Hence , a = 12 and b = 25 .

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Answer:

slope=y2-y1/x2-x1

=-6-(-6)/9-6

=0/3

any fraction in which numerator is 0 is 0.