Hi, I need help solving and understanding this.
''Find two functions f and g such that h(x) = (f o g) (x).
h(x)=sqrt(7x+5)''

Answer:

x=14

Step-by-step explanation:

The length of the side using the Pythagoras theorem is 4 mi

What is Pythagoras theorem?

Pythagoras theorem says sum of squares of side is equal to the square of the hypotenuse.

We are given one side of the triangle is 3 mi

And hypotenuse of the triangle is 5 mi

Let the another side of the triangle is x mi

By Pythagoras theorem,

3^2 + x^2 = 5^2

9 + x^2 = 25

x^2 = 16

x =4 mi

Using Pythagoras theorem the length of side of another side is 4cm

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The factorized form of the given mathematical phrase 12x to the power of 3 - 4xsquared will be 4x²(3x - 1).

An algebraic factor is the multiplication of two algebraic terms.

The root of the quadratic equation formed by the algebraic factor is always real.

That term could be in form of summation multiplication or in subtraction.

As per the given phrase,

12x to the power of 3 - 4xsquared

12x³ - 4x²

Take x² as common,

x²(12x - 4)

Take 4 as common

4x²(3x - 1)

Hence "The factorized form of the given mathematical phrase 12x to the power of 3 - 4xsquared will be 4x²(3x - 1)".

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The graph has been shown where lines A and B meet each other at the coordinates (0.51, 5.2).

So, the coordinates where both lines meet are:

Coordinates for line A:

Coordinates for line B:

Now, plot the graph as follows:

(Refer to the graph attached below)

The coordinates where both lines meet are:

Therefore, the graph has been shown where lines A and B meet each other at the coordinates (0.51, 5.2).

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Answer:

-(x+1)²+4

Step-by-step explanation:

y = -x²-2x-3

= -[x²+2x+3]

= -[(x²+2x)+3]

{formulae to get the vertex form is add (b/2)² to the expression

(2/2)² = 1}

= -[(x²+2x+1)-1+3]

{we are adding so we have to subtract the same number as well}

= -[(x²+2x+1)+2]

thus vertex form,

y = -(x+1)²+2

The next step is 4004 x 4004. So option(b) is correct

The process of making something less complicated and thus easier to do or understand, or the result of such a process is a simplification.

Reduce the expression to 3/4x + y/2 (4x + 7). The given expression can be written as 3/4x + y/2 (4x) + y/2 using the distributive property.

Given that

44 x 44 = 1936

404 x 404 = 163216

We have to find the next step

In the first step only fours are there

In the next step 0 is included in between the fours

If we follow the same sequence there will be two zeros coming between fours

= 4004 x 4004

= 16032016

Therefore the next step is 4004 x 4004

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Answer:

3: alternate exterior angles 4: supplementary angles

Step-by-step explanation:

3: that are outside and are on dif sides

4: they are interior and add up to 180 degrees

The function with same rate of change as the function y = (7/4)x + 3 will be option C.

The rate of change for a function is nothing but rate of change of one thing over the second thing.

it can be calculated by  [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

For a equation written in y = mx + c , m is nothing but the slope / rate of change of function.

So for function  y = (7/4)x + 3

m = 7/4 which is the rate of change for this function.

Now let us find rate of change for each function.

For A rate of change will be = (-4 - 0) / (5 - 1)

= -4/3

For B it will be = ( 4 - 1) / (0 - (-1) )

= 3

For C it will be = (15 - 8) / (8 - 4)

= 7/4

For D it will be = (-2 - 0) / ( 0 - (-1) )

= -2

Therefore the rate of change which is same as the given function is of option C.

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The given statement in mathematical notation is Y≥2.

Given that the statement is Y is greater than or equal to 2.

We want to write the given statement in the mathematical notation.

In algebra, statements basically consist of true or false statements. These mathematical statements can consist of words and symbols.

The greater than in symbolic form is > and greater than or equal to ≥.

As it is given that Y is greater than or equal to 2 can be rewritten as Y≥2.

Hence, the given statement Y is greater than or equal to 2 is Y≥2.

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The liquid in this case is found to have a density of 900 g/L.

The term density has to do with the ratio of the mass to the volume of the object. The density of an object is an intrinsic property of the material and it can be used to identify the kind of material that we have.

In this case we have;

Mass of the empty bottle =  500g

Mass of the bottle and the liquid = 1400 g

Volume of the bottle = 1.0 L

Mass of liquid = 1400 g - 500g = 900 g

Density of the liquid = mass/ volume

=  900 g/1 L = 900 g/L

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Answer:

See below

Step-by-step explanation:

Present Value = 400

Period = 1 month      8 years is    n =   96 periods

Interest per period in decimal form     i =  .076 / 12 = .0063333

Fv = PV ( 1 + i)^n  

Fv = 400 ( 1 + .076/12)^96 = 733.29 dollars

The fraction of another vial could be filled with the leftover medicine is 125 / 128.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the company receives medicine in 1-gallon (128-ounce) jars and then sells the medicine in vials that hold 3 ounces

The fraction left will be:

= 1 - Amount filled

= 1 - 3/128

= 125 / 128

The fraction left is 125 / 128.

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Answer:

8(4-a)=2a

32-8a=2a

32=10a....dividing through by 10a we get..

32/10=10a/10

3.2=a

answer is 3.2

We know that the problem we are going to be dealing with is an equation. The big question is, what should we do? What steps should be taken to get to the answer? There are several steps. One of them is expanding the equation. We can't solve until we expand the left side. So the way we're going to do it is: the distributive property. This one states that if you have an [tex]a[/tex] term multiplied by the sum of  [tex]b[/tex] and [tex]c[/tex] (the last two terms are in parentheses), then, in a sense, [tex]a[/tex] gets "distributed" and what results is this:

[tex]\darkblue{ab+ac}[/tex]. So now we apply that to our problem: [tex]8(4-a)=32-8a[/tex]. Now we make the replacement: [tex]32-8a=2a[/tex]. Then, notice that we have [tex]a[/tex] terms on both sides. What we do is we subtract [tex]2a[/tex] from the right and left and subtract [tex]32[/tex] from the left and add to the right: [tex]-8a-2a=-32[/tex]. Now let me share a little trick with you. First, we can add the [tex]a[/tex] terms together: [tex]-10a=-32[/tex]. Next, if you have minus signs on both sides, you clear them: [tex]10a=32[/tex]. Now divide both sides by 10. Here another trick comes into play: If you divide by 10 you move the decimal sign 1 place to the left.

[tex]a=3.2[/tex]

Now for the checking - put [tex]3.2[/tex] for [tex]a[/tex] and simplify. The answer should be a statement true for all values of [tex]a[/tex]. Let's go.

[tex]8(4-3.2)=2(3.2)[/tex]

[tex]8(0.8)=6.4[/tex]

[tex]6.4=6.4[/tex] is the result. Since the statement is true, we understand that the solution WAS correct and that [tex]3.2[/tex] IS the value of [tex]a[/tex] in the equation [tex]8(4-a)=2a[/tex].

The value of x after solution of the equation 8x = -16 is -2 and it is not possible to solve this equation using multiplication.

According to the question,

We have the following equation:

8x = -16

Now, this equation can not be solved using multiplication because 8 is already in multiplication with x on the left hand side. If 8 would have been in division then it could be solved using multiplication.

So, dividing by 8 on both the sides:

x = -16/8

x = -2

Hence, the value of x after solution of the equation 8x = -16 is -2 and it is not possible to solve this equation using multiplication.

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Answer:

it may have an even chance

Trinomials that are perfect square trinomials are (C)  [tex]16z^{4}+48z^{2}+36[/tex] and (D) [tex]9m^{2}+36m+36[/tex].

[tex](a+b)^{2}=a^{2}+2ab+b^{2}[/tex]

We will check every trinomials in given options.

(A) [tex]25a^{2}-40a+64[/tex]

     [tex]25a^{2} = (5a)^{2}[/tex]

     [tex]64 = 8^{2}[/tex]

     [tex]-40a \neq 2(5a)(8)[/tex]

     Hence, its not a perfect square.

(B) [tex]x^{2}-6x-16[/tex]

     [tex]x^{2} = (x)^{2}[/tex]

     [tex]-16 \neq 4^{2}[/tex]

     [tex]-6x \neq 2(x)(4)[/tex]

     Hence, its not a perfect square.

(C) [tex]16z^{4}+48z^{2} +36[/tex]

     [tex]16z^{4} = (4z^{2} )^{2}[/tex]

     [tex]36 = 6^{2}[/tex]

     [tex]48z^{2}=2(4z^{2} )(6)[/tex]

    [tex]16z^{4}+48z^{2} +36 = (4z^{2}+6 )^{2}[/tex]

     Hence, its a perfect square.

(D) [tex]9m^{2}+36m+36[/tex]

     [tex]9m^{2} = (3m)^{2}[/tex]

     [tex]36 = 6^{2}[/tex]

     [tex]36m=2(3m)(6)[/tex]

    [tex]9m^{2}+36m+36 = (3m+6)^{2}[/tex]

     Hence, its a perfect square.

Therefore, only (C) and (D) are perfect square.

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Answer:

The 95% confidence interval for the mean tuition for all colleges and universities in the United States is between $15718 and $22882.

Step-by-step explanation:

Sample size greater than 30, which means that we use the normal distribution to find the interval.

We have that to find our  level, that is the subtraction of 1 by the confidence interval divided by 2. So:

α = (1 - 0.95) / 2

  = 0.025

Now, we have to find z in the table as such z has a pvalue of . So it is z with a pvalue of 1 - 0.025 = 0.975.

So, z = 1.96

Now, find M as such

M = z * (σ / √n )

In which σ is the standard deviation of the population and n is the size of the sample.

M = 1.96 * ( 10800 / √35 )

M = 3581.72

M ≈ 3582

The lower end of the interval is the sample mean subtracted by M. So it is 19300 - 3582  = $15718.

The upper end of the interval is the sample mean added to M. So it is  19300 + 3582  = $22882.

The 95% confidence interval for the mean tuition for all colleges and universities in the United States is between $15718 and  $22882.

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For the volume of through, the rate at which the water level (the depth) is decreasing, increases as more water is drawn from the trough and the rate at which water is being drawn from the through is 0.28cm/min

Volume:

Volume refers the mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Given,

A horizontal trough is 16 meters long, and its ends are isosceles trapezoids with an altitude of 4 m, a lower base of 4 m, and an upper base of 6 m.

Here we need to find the water level rising when the water is 2m deep if the water is being poured into the trough at the rate of10 m³/min.

While we looking into the given question we have identified that the values of length of the through, L = 16 m and the height of the through = 4 m

Lower base of the trapezoidal is a = 4 m

Upper base of the trapezoidal is b = 6 m

And the rate at which the water is decreasing at the depth of 3 m is 25 cm/min

Let us consider the length of the upper base at height is calculated as,

h = 4 + 2·x

So, the Volume of the through is,

=> Trapezoidal cross sectional area × Length

When we apply the value on the formula, then we get,

=> V = (4 + (4 + 2x)/2) x h

Now, if we include the water flow, then it can be written as,

=>  V = (4 + (4 + 2x)/2) x h x L

Apply the value of L as 16, then we get,

=>  V = (4 + (4 + 2x)/2) x h x 16

When we simplify this one then we get,

=> V = 8h (8 + 2x)

When we expand it then we get

=> V = 64h + 16hx

Here the value of x is  not given, however we can express x in terms of h from Figure 3 using

So, by using the similar Triangles concept, we can get the value f x as,

=> x/h=1/4

=> 4x=h

Therefore,  x = h/4

Now, Substituting x=h/4 into the Volume, V

=> V = 64h + 16h (h/4)

=> V = 64h + 4h²

When we differentiate this one, then we get,

=> dV/dt = 64 dh/dt + 8h dh/dt

Here we know that value of h=3m, dV/dt=25cm/min=0.25 m/min,

Then the equation is,

=> 0.25 = dh/dt (64 + 8 x 3)

=> 0.25 = 88 dh/dt

=> dh/dt = 0.002841m/min =0.28cm/min

Therefore, the rate is the water being drawn from the trough is 0.28cm/min.

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Answer:

376,404 copies sold.

Step-by-step explanation:

To find this answer, divide 33,500 copies by the 8.9%:

33,500 divided by 8.9% = 376404.494382

Now, if we round this number to the nearest whole number, it would be:

376,404 copies sold.

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The steps between the human resource department and accountant department are 85 steps.

What is Human Resource?

The group of individuals who work for a given organization, business sector, industry, or economy is referred to as its human resources.

As given in the question,

Randi must climb 51 steps from her office to get to the accounting department, and

The HR department is 34 steps below her office.

Since, the HR department is below her office and accountant department is above her office so, we need to add the steps taken from her office to reach both department.

So,

Steps between HR department and accountant department = Steps between her office and HR department + Steps between her office and accountant department

Steps between HR department and accountant department = 51 + 34

Therefore,

Steps between HR department and accountant department = 85 steps

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Answer:

The slope is 6

The slope-intercept form is y= 6x-1

Step-by-step explanation:

Answer:

  10.4 years

Step-by-step explanation:

Given the population of a small town is initially 13000 and decreasing at the rate of 4% per year, you want to know the number of years it will take for the population to reach 8500.

The equation for exponential decay is ...

  population = (initial population) · (1 - decay rate)^t

Here, the initial population is 13000, the decay rate is 4%, and the population of interest is 8500. This gives an equation we can solve for t.

  8500 = 13000 · (1 -0.04)^t

  8500/13000 = 0.96^t . . . . . . . divide by 13000

  log(17/26) = t·log(0.96) . . . . . take logs

  t = log(17/26)/log(0.96) ≈ 10.408

It will take about 10.4 years for the population to reach 8500 people.

 4 years is the total years will take to reach 8500 people.

 Hence, The total is equal to 4 years.

If a quantity is subject to exponential decay, it is declining at a rate proportionate to its current value.

Given the population of a small town is initially 13000 and decreasing at the rate of 4% per year, you want to know the number of years it will take for the population to reach 8500.

Exponential decay

The equation for exponential decay is ...

 population = (initial population) · (1 - decay rate)^t

Application

Here, the initial population is equal to 13000, the decay rate is equal to 4%, and the population of interest is 8500. This gives an equation we can solve for t.

 8500 =  13000 · (1 -0.04)^t

 8500/13000 = 0.96^t . . . . . . .

divide it by 13000

 log(17/26) = t·log(0.96) . . . . .

 take log

 t = log(17/26)/log(0.96) ≈ 10.408

 It will take about 10.4 years for the population to reach 8500 people.

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Answer: 71

Step-by-step explanation:

First, plug 11 in for x:  y=6(11)+5

Then, multiply 6 by 11:  6(11)=66

Finally, add 5:  66+5=71

The maximum height of the object is 88 feet and the time is 2.25 second(s) after launch

The function is given as

h(t) = -16t² + 72t + 7

Differentiate the above function

So, we have the following representation

h'(t) = -32t + 72

Set to 0

-32t + 72 = 0

So, we have

32t = 72

Divide by 32

t = 2.25

Hence, the time is 2.25 seconds

In (a), we have

t = 2.25

Substitute t = 2.25 in h(t) = -16t² + 72t + 7

h(2.25) = -16(2.25)² + 72(2.25) + 7

Evaluate

h(2.25) = 88

Hence, the maximum height is 88 feet

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The given expression is expressed in the form of 2(x + p)² + q as:

f(x) = (x + 5)² - 21.5

Given,

Express

2x² + 20x + 7

Step 1: Subtract both sides by 7

2x² + 20x = -7

Step: GCF and divide

2(x² + 10x) = -7

x² + 10x = -7/2

Step 3: Complete the Square

x² + 10x + 25 = -7/2 + 25

(x +5)² = 43/2

Step 4: Subtract 43/2 to both sides

(x + 5)² - 43/2

Hence we get the equation.

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The estimate of the tax when a purchase is made in her city with a sales tax of 9.05% are as follows;

a) 10% converted to a fraction is [tex]\dfrac{1}{10}[/tex]

b) An estimate of the amount Felipa pays as tax is $9.5

An estimate is a rough calculation that gives a value that is close to the actual value.

a)The sales tax in her city = 9.05

The sales tax is approximately 10%

To convert 10% to fraction we have;

10% = 0.1

[tex]0.1 = \dfrac{1}{10}[/tex]

[tex]10\% = \dfrac{1}{10}[/tex]

b) The estimate sales tax that Felipa would pay on a dress of $95 can be found as follows;

10% of $95 is found as follows;

[tex]\dfrac{1}{10} \times \$95 = \$9.5[/tex]

10% of $9.5 is found as follows;

The estimate of her tax is $9.5

The actual amount she pays as tax is found as follows;

[tex]\dfrac{1}{10} \times \$9.5 = \$0.95[/tex]

0.0005 = [tex]\frac{5}{10000}[/tex]

[tex]\dfrac{5}{10000} \times \$95 = \$0.0475[/tex]

9.05% = 0.0905

0.0905 = 0.10 - 0.01 + 0.0005

Her tax is $9.5 - $0.95 + $0.0475 = $8.5975

Felipa's tax if she buys a dress of $95 is $8.5975

Part of the question, based on a similar question online, includes;

a) To convert 10% into fractions

b) To provide an estimate of the tax payable on a $95 dress

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Answer:

[tex]b(5b^{3}+1)[/tex]

Step-by-step explanation:

[tex]-b(-b^{3} -1)+4b^{4} =b^{4}+b+4b^{4}[/tex]

                             [tex]= 5b^{4} + b[/tex]

                             [tex]= b(5b^{3}+1)[/tex]

The equation of the axis of symmetry will be x = -2 and the curve is drawn below.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation is given below.

y = -3(x + 2)² + 1

The equation of the axis of symmetry will be given as,

x + 2 = 0

x = - 2

The equation of the axis of symmetry will be x = -2 and the curve is drawn below.

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An expression for given sequence of operations is: j + 3^9

In this question, we need to write an expression for the sequence of operations described below.

raise 3 to the 9th power, then add the result to j

Consider the part of given statement,

raise 3 to the 9th power

We write this as: 3^9

then we add this result to j.

So, we get an expression: 3^9 + j

Therefore, an expression for given sequence of operations is: j + 3^9

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