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State the X- and Y- intercepts of each function. 4x – 6y = 12

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The answer, my friend, is not A, not B, so it has to be C or D. Which in this case it is C.

Study Solutions

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State the X- and Y- intercepts of each function. 4x – 6y = 12

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**Answer:**

**Option b is correct**

**Step-by-step explanation:**

The direct variation says that:

, then the equation is of the form:

where, k is the constant of variation.

**As per the statement:**

If y varies directly as x.

By direct variation:

….[1]

If y = 18 when x = 5

Substitute these values in [1] we have;

**Divide both sides by 5 we have;**

or

⇒ ……[2]

**We have to find the value of y when x = 11.**

Substitute x = 11 in [2] we have;

**Therefore, the value of y is, **

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When the function is given in vertex form y=a(x-h)2+k, how is the vertex found?

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Okay so you need to distribute the -7.

1.) -7 times 3e which equals -21e

*negative times a positive equals a negative

2.) -7 times -2f which will equal to 14f

*negative times a negative equals a positive

3.) -7 times 4 which equals -28

1.) -7 times 3e which equals -21e

*negative times a positive equals a negative

2.) -7 times -2f which will equal to 14f

*negative times a negative equals a positive

3.) -7 times 4 which equals -28

which leaves you with the equation -21e + 14f -28 + 6e – 2

now just combine like terms, like -21e and 6e or -28 and -2

1.) -21e + 6e will equal to -15e

2.) -28 + -2 will equal to -30

So at the end it will be simplified down to

Answer: -15e + 14f – 30

Hope this helps

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Pronouns in the nominative case may function as?

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Y=x²+x-6 (original form ax²+bx+c)

1) this is a parabola open upward since the coefficient of x² is positive

so it has a minimum.

2) Its symmetry line = -b/2a = -1/2 & for x=-1/2, y= 23/4

So its minimum is (-1/2, 23/4)

3) Now to see if the parabole intercepts the x-axis we calculate the roots of

x²+x-6. As you will notice Δ <0 so there is no roots & consequently it doesn’t intersect with x-axis

Your graph is wrong, and the parabola should be above the x-axis & it will intersect with the y-axis at y=23/4 =5.75nunits

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i would just make this into an equation!!

t for the number of turkey sandwiches

s for the number of steak sandwiches

t for the number of turkey sandwiches

s for the number of steak sandwiches

it’s 4 dollars for every turkey sandwich and 6 for every steak sandwich, so:

4t + 6t = 4524

you can call this your “profit” equation. it just tells you how much money they made. however many sandwiches they sold at those rates gave them the outcome of 4524

then you need a second equation, to account for the number of sandwiches, and instead of worrying about profit you need to focus on the number of sandwiches sold (which is why they gave you the number 925)

t + s = 925

the number of turkey sandwiches plus the number of steak sandwiches adds up to a total of 925 sandwiches.

so you have two equations:

4t + 6s = 4524

t + s = 925

to figure out the number of turkey sandwiches sold, you want to solve for the variable t. this can be done a few ways with your two equations, but the easiest to follow will probably be substitution in this case.

first, isolate your variable t in one of the equations. it’ll be easier with the second one.

t = 925 – s

then you plug that into your first equation:

4(925 – s) + 6s = 4524

then solve it like normal.

4(925 – s) + 6s = 4524

3700 – 4s + 6s = 4524

3700 + 2s = 4524

2s = 824

s = 412

so now you know your s variable. plug that back into the following equation, and you have the number of turkey sandwiches sold:

t = 925 – s

t = 925 – (412)

t = 513

513 turkey sandwiches were sold

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**Answer:**

**Global maxima are (3, 0) and (-3, 0),**

**Local minima is (0, -1.62)**

**Step-by-step explanation:**

Here, the given function,

Differentiating with respect to x,

For maxima or minima,

Thus, the critical points of the function f(x) are 0, -3 and 3,

Since, f'(x) > 0 on the left side of x = -3 and f'(x) < 0 on the right side of x = -3,

⇒ x = -3 is local maxima,

Also, f(-3) = 0,

⇒ **f(x) has maxima at (-3, 0)**,

f'(x) < 0 on the left side of x = 0 and f'(x) > 0 on the right side of x = 0,

⇒ x = 0 is the local minima,

Also, f(0) = -1.62

⇒ **function f(x) has minima at (0, -1.62)**,

Hence, the **global maxima** are** (3, 0)** and **(-3, 0),**

**Local minima** is** (0, -1.62).**

f'(x) > 0 on the left side of x = 3 and f'(x) < 0 on the right side of x = 3,

⇒ x = 3 is local maxima,

Also, f(3) = 0,

⇒** function f(x) has maxima at (3, 0)**.

**Note :** function f(x) has no global minima because its end behaviour is,

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The correct answer is – D. globalization.

The globalization is a relatively recent trend, and it has become a dominant trend only in the past few decades. As a process, the globalization is connecting the countries, regions, continents, people, around the world in pretty much every aspect, be it economy, politics, music, social trends, fashion…

This process has its good sides and bad sides, thus it has critics for and critics against it, but it seems that most of the countries in the world are in favor of it, and it seems that it will continue to grow and spread.

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The answer, my friend, is not A, not B, so it has to be C or D. Which in this case it is C.

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All you have to do is compare both types of deductions. Calculate first Nedages’ total deductions:

Total deductions = $2,150 + $826 + $3,133 + $1,331

Total deductions = $7,440

This is less than the standard deduction which is $8,350. So, let’s determine by how much.

$8,350 – $7440 = $910

So, standard deduction is much better by $910. The answer is C.

How to solve f(x)=x^2+1, g(x)= 5x how to solve

(f + g)(x) = f(x) + g(x) = [3x + 2] + [4 – 5x] = 3x – 5x + 2 + 4 = –2x + 6(f – g)(x) = f(x) – g(x) = [3x + 2] – [4 – 5x] = 3x + 5x + 2 – 4 = 8x – 2(f×g)(x) = [f(x)][g(x)] = (3x + 2)(4 – 5x) = 12x + 8 – 15×2 – 10x= –15×2 + 2x + 8

Find f(6) if f(x) = x2 ÷ 3 + x.

**Answer:**

**The value of f(6) is, 18**

**Step-by-step explanation:**

Given the function:

…..[1]

**We have to find the value of .**

Put x = 6 in [1] we have;

⇒

⇒

**Simplify:**

**Therefore, the value of f(6) is, 18**

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If h(x) = −2x − 10, find h(−4). −2 −18 −3 −16

**Answer:**

The correct option is (a) i.e.

h(-4) = -2

**Step-by-step explanation:**

The mathematical expression is given as :

……(1)

Where

h(x) is dependent on x

**We need to find the value of h(x) at x = -4 . Putting the value of x in equation (1) we get :**

h(-4) = -2

**The value of h(-4) is -2. So, the correct option is (a). Hence, this is the required solution.**

What is the 22nd term in the arithmetic sequence in which a4 is 73 and a10 is -11?

For A.P nth term’s formula is

An=a1+(n-1)d

An=a1+(n-1)d

5.) a4=31, a10=85

put n=4 into general term (given above)

a4=a1+(4-1)d

31=a1+3d (putting values of a4)

a1=31-3d ====> (1)

Now put n=10

a10=a1+(10-1)d

85=31-3d+9d (putting values of a10, and a1)

85=31+6d

6d=85-31

6d=54

d=54/6

d=9

Now put the value of ‘d’ into eq (1)

a1=31-3d

a1=31-3(9)

a1=31-27

a1=4

Thus the series will be

a2=a1+d=4+9=13

a3=a2+d=13+9=22

and so on

4,13,22,…..

And the same process for your second question

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State the importance of examining a function analytically as well as graphically.?

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**Explanation:**

The term **isoelectronic** means same number of electrons.

Then you need to count the number of electrons in the given species** NO₂⁻.**

You have to **count the number of electrons of N (nitrogen) atoms, the number of electrons of two O (oxygen) atoms, and the adjust for the negative charge of the ions.**

The atomic number of **N** is 7, meaning that each atom has 7 protons and **7 electrons**.

The atomic number of **O** is 8, meaning that each atom has 8 protons and **8 electrons**.

The negative charge of the **ion** means that it has **one extra electron**, which is the responsible for the** negative charge**.

Therefore the total number of electrons of the ion NO₂⁻ is **7 + 2 (8) + 1 = 24.**

Note that that **24 = 3 x 8**, so 24 is the number of electrons in **3 atoms of oxygen**.

The moleucle **O₃ is an allotrope of the oxygen**. (an allotrope is a a form of an element with different structure and physical properties in the same physical state).

Therefore, **the allotrope of oxygen isoelectronic with NO₂⁻ is O₃ (ozone)**

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Which set of ordered pairs does not describe a function

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**Answer:**

The maximum number of acres of barley the farmer can plant and still be under budget would be of 123 acres.

**Step-by-step explanation:**

The farmer grows two types of seeds, with a budget of $10,000. He has spent $4,200 in wheat seed, and wants to know the maximum number of barley he is able to plant.

First of all, as $10,000 – $4,200 is equal to $5,800, that is the amount of money he is able to spend in barley seeds.

As every acre of barley seed costs $47 to plant, in order to know how many acres he can plant we have to do the following calculation:

5,800 / 47 = maximum of acres the farmer can plant

5,800 / 47 = 123.40

The maximum number of acres of barley the farmer can plant and still be under budget would be of 123 acres.

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**Answer:**

a. providing child care

**Explanation:**

**Manifest functions** are those that are intended functions of a particular society. For example, the manifest function of schools is to educate children, which means that as society, this is the reason why we have created schools. **Latent functions** are the ones that are not intended, but that still happen. In this case, child care is intended to provide “care” for children (manifest). However, as an unintended product, it also provides education (latent).

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**Answer:**

** option C has smallest rate of change**

**Step-by-step explanation:**

given points x = 0 and x = 1

hence putting value in equation y = 3x

y = 0 and y = 3

rate of change of =

from equation A) y = 8 x + 2

at x = 0 y = 2 and at x = 1 y = 10

rate of change =

B) y = 3 x + 2

at x = 0 y = 2 and at x = 1 y = 5

rate of change =

C) y = 2 x

at x = 0 y = 0 and at x = 1 y = 2

rate of change =

hence,** option C has smallest rate of change**

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**Answer:**

Hazel has to spend $36.36

$36 and 36 cents.

**Step-by-step explanation:**

The given box is a rectangular box. To find the felt needed to cover the box, we need to find the surface area of the rectangular prism.

Surface area of a rectangular prism = 2(l*w + w*h + h*l), where “l” is the length, “w” is the width and “h” is the height of the rectangular prism.

Given: l = 11 inches; w = 8 inches; and h = 6 inches.

Now plug in these given values in the above formula, we get

Surface area of the rectangular prism = 2 (11* 8 + 8*6 + 6*11)

Let’s simplify it.

= 2(88 + 48 + 66)

= 2(202)

= 404

The surface area of the rectangular prism = 404 square inches.

The felt cost 9 cents square inches.

Convert 9 cents to dollar.

9 cents = $0.09

To find the cost of the felt needed to cover prism multiply 404 by 0.09

The total cost = 404*0.09 = $36.36

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█ **Question** █

A volcanic eruption takes place under the ocean. Huge waves crash against the shores and destroy houses of people. Which Earth systems interact during this process?

█ **Answer: **Hydrosphere █

**Explanation —> **The hydrosphere effects the earth system, causing natural disasters.

Hope that helps! ★ If you have further questions about this question or need more help, feel free to comment below or leave me a PM. -UnicornFudge aka Nadia

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There are four variables which govern changes in population size.

births

deaths

immigration

emigration

A population gains individuals by birth and immigration and loses individuals by death and emigration.

births

deaths

immigration

emigration

A population gains individuals by birth and immigration and loses individuals by death and emigration.

Biotic Potential

Populations vary in their capacity to grow. The maximum rate at which a

population can increase when resources are unlimited and environmental

conditions are ideal is termed the population’s biotic potential. Each

species will have a different biotic potential due to variations in

the species’ reproductive span (how long an individual is capable of reproducing)

the frequency of reproduction (how often an individual can reproduce)

“litter size” (how many offspring are born each time)

survival rate (how many offspring survive to reproductive age)

There are always limits to population growth in nature. Populations

cannot grow exponentially indefinitely. Exploding populations always

reach a size limit imposed by the shortage of one or more factors such

as water, space, and nutrients or by adverse conditions such as disease,

drought and temperature extremes. The factors which act jointly to

limit a population’s growth are termed the environmental resistance. The interplay of biotic potential and density-dependent environmental resistance keeps a population in balance.

Carrying Capacity

For a given region, carrying capacity is the maximum number of

individuals of a given species that an area’s resources can sustain

indefinitely without significantly depleting or degrading those

resources. Determining the carrying capacities for most organisms is

fairly straightforward. For humans carrying capacity is much more

complicated. The definition is expanded to include not degrading our

cultural and social environments and not harming the physical

environment in ways that would adversely affect future generations.

For populations which grow exponentially, growth starts out slowly,

enters a rapid growth phase and then levels off when the carrying

capacity for that species has been reached. The size of the population

then fluctuates slightly above or below the carrying capacity.

Reproductive lag time may cause the population to overshoot the carrying

capacity temporarily. Reproductive lag time is the time required for

the birth rate to decline and the death rate to increase in response to

resource limits. In this scenario, the population will suffer a crash

or dieback to a lower level near the carrying capacity unless a large

number of individuals can emigrate to an area with more favorable

conditions. An area’s carrying capacity is not static. The carrying

capacity may be lowered by resource destruction and degradation during

an overshoot period or extended through technological and social

changes.

An example of dieback occurred in Ireland after a fungus infection

destroyed the potato crop in 1845. During this potato famine

approximately 1 million people died and 3 million people emigrated to

other countries. Increased food production due to improved agricultural

practices, control of many diseases by modern medicine and the use of

energy to make historically uninhabitable areas of Earth inhabitable are

examples of things which can extend carrying capacity. The question is

how long will we be able to keep increasing our population on a planet

with finite size and resources?

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**Answer**;

FADH2

**Explanation**;

Glycolysis involves the breaking down of a sugar; generally glucose, although fructose and other sugars may be used; into more manageable compounds in order to produce energy.

Glycolysis produces 2 ATP, 2 NADH, and 2 pyruvate molecules: Glycolysis, or the aerobic catabolic breakdown of glucose, produces energy in the form of ATP, NADH, and pyruvate, which itself enters the citric acid cycle to produce more energy.

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**Answer: **The answer is** (B), (C) and (E).**

**Step-by-step explanation: **We are given five options out of which we are to select all those which can be modelled by exponential functions.

We can see that the options (A) and (D) cannot be modelled by exponential functions, because the rate of increasing or decreasing are not calculating compoundly.

But, in options (B), (C) and (E), the rate is increasing or decreasing each year.So, these three can be modelled by exponential functions.

In fact, the options (B) and (E) will show exponential growth because the number is increasing and option (C) will show exponential decay as the number is decreasing.

**Thus, (B), (C) and (E) are the correct options.**

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**Answer:**

**The average rate of change A(x) over interval [a, b] is given by:**

…..[1]

**As per the statement:**

The table of values represents a polynomial function f(x).

For interval [7, 9]

f(7) = 1920

f(9) = 5760

then

**using equation [1] we have;**

Substitute the given values we have;

**Next:**

For interval [4, 6]

f(4) =105

f(6) =945

then

**using equation [1] we have;**

Substitute the given values we have;

⇒

⇒

**Therefore,1500 greater is the average rate of change over the interval [7, 9] than the interval [4, 6]**

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**Answer: **Hello there!

we have the equation y = 1.09x, that describes the number of yards y in x meters.

a) Yes, if you have negative numbers of x (this means negative meters, this is used usually to denothe something that is behind the observer) then the equation transform them into negative yards.

b) in this case you want to know how many meters are in 40yd, then we replace y by 40yd in the equation:

40 = 1.09x

x = 40/1.09 = 36.7 meters

so in a 40yd race, there are 36.7 meters.

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Passive Transport: Simple Diffusion

Diffusion across a cell membrane is a type of passive transport, or transport across the cell membrane that does not require energy. Remember that the cell membrane is a phospholipid bilayer. Although the inside and the outside of a cell are both water-based, there is a hydrophobic region in the middle, and this is an important barrier to anything large, charged, or hydrophilic. Molecules that are hydrophobic, just like the hydrophobic region, can pass through the cell membrane by simple diffusion.

Therefore, simple diffusion is the unassisted passage of small, hydrophobic, nonpolar molecules from a higher concentration to a lower concentration. Very small molecules can slip through the cell membrane, too, even if they are hydrophilic – just like a few ants might crawl through a crack in the wall just because they’re tiny.

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