What are the key features of the quadratic function f(x) = 2(x - 3)2 + 4

Bacterial growth is expressed by an exponential function with the formula of [bacteria]=ae^[time]b

The minimum electric rate in cents per kwh for which the 12-year total cost will be less for the first freezer is 8.61 cents

Let x =  minimum electric rate (Cents/kWh)

Total months in 12 years is 12*12 = 144 m

1st freezer

Total cost over 12 years is

623.95 (cost) + (90 kWh/m)*(144 m)(x/100 $/kWh)

= 623.95 + 129.6x

2nd freezer

Total cost over 12 years is

500 + 100*144*(x/100)

= 500 + 144x

For the 1st freezer to cost less over 12 years,

623.95 + 129.6x < 500 + 144x

123.95 < 14.4x

8.61 < x

The minimum rate is 8.61 cents per kWh

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Answer:

[tex]k = -\frac{7}{3}[/tex]

Step-by-step explanation:

Given :

p(x) = 2x² − 3kx + 5

Since, -1 is a zero for p then :

p(-1) = 0

Solving the equation p(-1) = 0 for k :

p(-1) = 0

⇔ 2(-1)² − 3k(-1) + 5 = 0

⇔ 2 + 3k + 5 = 0

⇔ 3k = -5 - 2

⇔ 3k = -7

⇔ k = -7/3

NOTE :

If -1 is a zero of p

[tex]\Longrightarrow k = -\frac{7}{3}[/tex]

[tex]\Longrightarrow p(x) = 2x^2 - 3(\frac{-7}{3}) x + 5\\\Longrightarrow p(x) = 2x^2+ 7x + 5[/tex]

That's great for Rachel! I would love a gift card as well where is this at?

The probability of rolling an odd number and then rolling a 2 is 1/12.

Option C is true.

What is Probability?

Probability is measure of the likelihood of an event to occur.

Given that;

A six - sided dice is rolled twice.

The sides are labelled 1-6.

Now,

In a dice odd number are 1, 3, 5

Hence, The probability of rolling an odd number = 3/6

And, The probability of rolling a 2 = 1/6

So, The probability of rolling an odd number and then rolling a 2

= 3/6 x 1/6

= 1/12

Hence, The probability of rolling an odd number and then rolling a 2 is 1/12.

Option C is true.

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Based on the accounts and the benefits they offer, Kate should choose B. College Savings, because she meets the minimum deposit and it earns more interest

Kate should pick the college savings account for two reasons with the first being that the $5,000 she wants to deposit meets the minimum deposit amount of $1,000.

The second reason is that the account earns more interest than other account.

Even though it is simple interest, the 9% is still much higher than the compound interest of 1% that the regular account gives.

Kate should choose college savings.

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Answer:

a function is a rule or correspondence by which each element x is associated with a unique element y.

hope this was helpful!

The density in ounces per liter is 3.57826 rounding off = 3.58

Density of a substance can be defined as a relationship between the mass and the volume of that substance.

[tex]Density=\frac{Mass}{Volume}[/tex]

For Example if a metal have a mass 0f 7gm and volume as [tex]5cm^{3}[/tex]

[tex]Density=\frac{7}{5} = 1.4g/cm^{3}[/tex]

we know that 1 gram/fluid ounce of volume = 1.19275 ounces/liter

1 gm/fluid ounce =1.19275 ounces/liter

3 gm/fluid ounce = 3*1.19275 ounces/liter

So 3 gm/fluid ounce = 3.57826 ounces/liter

On rounding it to nearest hundredth we get 3.58 ounces/liter

Therefore the density of the material which weighs 3 gm/fluid ounce in ounces/liter is 3.58.

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It is found that Margo are going to be using sampling.

• sampling in statistics may be a a part of the sampling technique within which each sample has an equal probability of being chosen. In other words, a sample chosen randomly is an unbiased representation of the entire population.

Sample strategies is also classified as :

1) Convenient: The sample that is taken from a pool that is readily accessible.

2) Random : When all options are into a hat and draw a number of team

3) Systematic : Every kth element

4) Cluster : once we divide population into groups called clusters, and every element of cluster is surveyed.

5) Stratified : In stratified also divides the population into groups, However just some of the weather of the group are surveyed. per the question Marbles are taken from the bag, and after they're taken they're again placed back within the bag so it depicts sampling.

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Answer:

y=2

Step-by-step explanation:

6 times y and six times 3

6y+18=30

    -18  -18

6y=12

divide both sides by 6 and you will get y=2

Answer:

length is 9 and width is 6

Step-by-step explanation:

List the factors of 54 and choose the numbers that only have a difference of 3. In this case it is 6 and 9, then put them in the order they go based on the instructions.

Answer:

please solve this question 4²×3³×(-1)¹²²

Answer:

-27

here is the answer for you

Answer:

[tex]5x^2y^5z[/tex]

Step-by-step explanation:

Hello!

Expand the cube root:

Use exponent rule:

The answer is [tex]5x^2y^5z[/tex].

Answer:

this question is impossible!11!1!!!!

Step-by-step explanation:

none

Answer:

30,70,110

Step-by-step explanation:

12. acute

13. acute

14. obtuse

Answer:

14 is an obtuse angle

Step-by-step explanation:

An obtuse angle is an angle that is bigger than 90° degrees but doesn’t reach a straight line at 180°.

32 Quartz to 48 Quartz is 2/3 Quartz

The quart is a measurement which is use to find the capacity of liquid. Or we can say Quart is a unit of liquid volume which is measured in gallon. There are different measurements into which we can convert the unit such as ounces and liters. These conversion values are as below :

Mathematically, we can write :

          1 quart = 32 fluid ounces

          1 quart = 0.94 US liters = 4 cups (approx.)

According to given question,  32 Quartz to 48 Quartz is the ratio of 32 and 48 Quartz value.

Mathematically, we can write :

[tex]\frac{32 \ Quartz }{48 \ Quartz}\\ \\= \frac{2 \ Quartz}{3 \ Quartz} \\\\or, = \frac{2}{3} Quartz[/tex]

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Answer:

10 squared is 100 so 10 squared is greater than 5.

Step-by-step explanation:

Hope its corrects and it helps you!

Answer:

v = 4.875

Step-by-step explanation:

Anytime you have a proportion (a fraction = a fraction)

you can cross multiply to change the equation (get rid of the fractions!) and solve.

see image.

3/v = 8/13

8v = 39

v = 4.375

see image.

Answer: 0.51639777..

Step-by-step explanation:

Using translation concepts, we have that:

4. The type is f(x + k), with k = 3, and a horizontal shift.

5. The type is kf(x), with k = 5 and a vertical stretch.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For graph 4, we have function g(x) is a shift left of 3 units of function f(x), hence:

The type is f(x + k), with k = 3, and a horizontal shift.

For graph 5, we have that for each value of x, g(x) = 5f(x), hence:

The type is kf(x), with k = 5 and a vertical stretch.

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The dimensions of the kitchen are 11m × 8m.

In geometrical mathematics, a polygon with four sides is referred to as a quadrilateral, while a quadrilateral with two opposed, parallel, and equal sides is referred to as a rectangle.

A rectangle has four equal-sized angles. There are four angles in a rectangle.

A rectangle has 90° angles on all sides.

The rectangle's diagonal is the separation or length of a line segment that connects any two opposed vertices.

Let l and w represent the length and breadth of the rectangular kitchen, respectively.

we know that area of a rectangle = length × width

perimeter of a rectangle = 2(l ₊ b)

Given that the rectangular kitchen has an area of 88 m².

A = 88 m²

l × w = 88 m² ....eq(1)

The perimeter of the rectangle is 38 m.

Perimeter (P) = 38 m

2(l+w) = 38 m

l+w = 19 m

l = 19 - w .....eq(2)

substitute eq(2) in eq(1).

l × w = 88 m²

(19 - w)w = 88

19w - w² = 88

-w²+19w-88 = 0

w²-19w+88 = 0

By factorization method, we get:

w²-11w-8w+88 = 0

w(w-11)-8(w-11) = 0

(w-11)(w-8)

w = 11 or w = 8

If w = 11,

then l = 19-11 = 8m

and If w = 8m

then, l =  19-8 = 11m

so the dimensions are 11m×8m

Hence we get the dimensions of the kitchen are: 11m×8m

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Answer:

find the three postive consecutive integers such that the product of the smallest and the largest is 17 more than 3 times the median intger

Answer: 5, 6, 7

Step-by-step explanation:

Let three positive consecutive integers equal to x, x+1, x+2

Hence,

[tex]\displaystyle\\x(x+2)-3(x+1)=17\\x^2+2x-3x-3=17\\x^2-x-3-17=17-17\\x^2-x-20=0\\x^2-5x+4x-20=0\\x(x-5)+4(x-5)=0\\(x-5)(x+4)=0\\x-5=0\\x-5+5=0+5\\x=5\in\ (x > 0)\\x+4=0\\x+4-4=0-4\\x=-4\notin\ (x > 0)\\5+1=6\\5+2=7[/tex]

Every day that John rides on the bus, he loses $3

if he rides on the bus for 17 days, it can be solved like this
(3 x 2)17 = 102$
The change is John's money is -$102 over a span of 17 days

Hope this helped