Write an equation that can be used to find the atmospheric temperature T, at an altitude A.

The Table
Altitude- 0 2000 4000 6000 8000
Temp. - 88 81 74 67 60

Answer:

Step-by-step explanation:

Even though I have been teaching calculus and precalc for several years now, my mind automatically wants to think in degrees as opposed to radians.  So I converted the angle from radians to degrees to get 315.  This angle lies in QIV.  The reference angle is a 45 degree angle, since 360 - 315 = 45.  This is a 45 degree angle, but if you consider direction, measuring clockwise gives you a negative angle.  So it could be that the reference angle needs to be identified as -45 degrees.  It depends upon what lesson you are dealing with.  Regardless, because this is a 45-45-90 right triangle, both the legs measure the same length (because of the Isosceles Triangle Theorem), which is 1.  Therefore, if the angle is 45 degrees, then the tangent of it is 1/1 = 1.

Answer:

Step-by-step explanation:

They want you to translate N^3 into another form that would still be correct.

log N^3 = 3 * log N is the answer that I think you want.  Try it it.

Suppose N = 6

Then N^3 = 6*6*6 = 216

log 216 = 2.3345

Now try it the other way.

3*log(6) =  3*0.7782

3*log(6) = 2.3345

Same answer as before.

Answer:

x = 2

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS = Parenthesis, Exponents (& roots), Multiplication, Division, Addition, Subtraction,

and is the order in which you follow for order of operation questions.

First, subtract 5 from both sides.

2x + 5 (-5) = 9 (-5)

2x = 9 - 5

2x = 4

Isolate the x, Divide 2 from both sides:

(2x)/2 = (4)/2

x = 4/2

x = 2

x = 2 is your answer.

~

The volume of the rectangular prism is length x width x height:

Volume = 1 1/2 x 1/2 x 3/4 = 9/16 cubic units.

The volume of cube is length^3 = 1/4^3 = 1/64

Divide the volume of the rectangular prism by the volume of the cube:

Number of cubes = 9/16 / 1/64 = 36

The answer is 36

Answer:

[tex]\frac{f}{g}(x)=2x-1\\\\\frac{f}{g}(4)=7[/tex]

Step-by-step explanation:

[tex]\frac{f}{g}(x)=\dfrac{2x^2-5x+2}{x-2}=\dfrac{(x-2)(2x-1)}{(x-2)} =2x-1 \quad\text{x$\ne$2}\\\\\frac{f}{g}(4)=2\cdot 4-1=7 \qquad\text{fill in 4 for x and do the arithmetic}[/tex]

[tex]\left(\dfrac{f}{g}\right)(x)=\dfrac{2x^2-5x+2}{x-2}\\\\\left(\dfrac{f}{g}\right)(4)=\dfrac{2\cdot 4^2-5\cdot 4+2}{4-2}=\dfrac{32-20+2}{2}=7[/tex]

Final answer:

To determine how many miles Carlos drove, we subtract the one-time rental fee from the total cost and then divide by the per-mile charge, resulting in Carlos having driven 88 miles.

Explanation:

To find out how many miles Carlos drove the rental car, we need to use the information about the total cost and the cost structure provided by the rental company. The total cost includes a one-time fee and a charge per mile driven. We can set up an equation to represent this situation. Let m represent the number of miles driven.

The equation based on the given costs would be:
20 + 0.50m = 64

Now, solve for m:

m = 88

Carlos drove 88 miles with the rental car.

Answer:

Up

Step-by-step explanation:

Here the easy rules to remember the orientation of the parabolas are

a) If x is squared it opens up or down. And its coefficient of {[tex]x^{2}[tex] is negative it opens down.

b) If y is squared it opens side ways right or left. It its coefficient of [tex]y^{2}[/tex]

Hence in our equation of parabola

[tex]y = x^ 2-4[/tex]

x is squared and its coefficient is positive , hence it opens up towards positive y axis.

Answer:

D. 72 cm²

Step-by-step explanation:

The area of a square is given by ;

Area= l² where l = length

Given that the diagonal is 12 cm, let assume length of the square to be l

Apply the Pythagorean relationship where a=b=l

l² + l² = 12²

2 l² = 144

l²= 144/2

l²= 72

l =√72 =8.485 cm

⇒length of the square= l= 8.485 cm

⇒Area of the square= l² = 8.485² = 72 cm²

Answer:

36 cm2.

Step-by-step explanation:

The area of square A is 324 cm2. Since the dimensions of square A are three times larger than the dimensions of square B, the scale factor is 3.

To find the area of square B, first square the scale factor, 3.

3 squired =9

Next, divide the area of square A by 9.

324÷ cm2 ÷ 9 =36 cm2

Answer:

  $1034.75

Step-by-step explanation:

Mike's net pay is ...

  base pay + commission - deductions

  = $500 + 5%(23750 -10000) -152.75

  = 347.25 + 0.05×13750

  = $1034.75

Answer:

$1034.75

Step-by-step explanation:

Here we are given that the base salary of Mike is $500. He is also rewarded with some commission depending on sales. Hence we can bifurcate his gross pay as

Gross Pay = Base Pay + Commission

Commission = 5% of Sales over $10000

                     = 5% of (23750-10000)

                     = 5% of 13750

                     = 0.05*13750

                     = 687.50

Hence Gross pay = 500 + 687.50

                              = 1187.50

Also given that he has some deductions also i.e. $152.75 .

Therefor Net pay = Gross pay - Deductions

                             = 1187.50-152.75

                             = 1034.75

Hence Net Pay = $1034.75

Answer:

132 degrees.

Step-by-step explanation:

SR and PQ are both 48 degrees. A circle is 360 degrees.

360-96 because 48+48 is 96, is 264. PS and QR are also the same so 264/2 is 132.

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} \theta =87\\ s=14 \end{cases}\implies 14=\cfrac{\pi (87)r}{180} \\\\\\ 2520=87\pi r \implies \cfrac{2520}{87\pi }=\boxed{r} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r\qquad \qquad \implies C=2~~\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \left(\boxed{\cfrac{2520}{87~~\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}} \right)\implies C = \cfrac{5040}{87} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill C\approx 57.93~\hfill[/tex]

Final answer:

Ethan pays a total of 1.0355x dollars at the register for an item with an original price of x dollars, after applying a 5% discount and adding a 9% sales tax to the discounted price.

Explanation:

To calculate the total amount Ethan paid at the register, we need to take into account both the discount and the tax applied to the item's original price. First, we calculate the discounted price by subtracting the 5% off. Then, we add a 9% sales tax to that discounted price.

The original price is x dollars. The discount of 5% is 0.05x, so the discounted price is x - 0.05x, which simplifies to 0.95x. Next, we need to calculate the sales tax on the discounted price. The 9% tax on the discounted price is 0.09 * 0.95x, which is 0.0855x. Finally, to find the total amount paid, we add the sales tax to the discounted price:

Total Amount Paid = (0.95x) + (0.09 * 0.95x) = 0.95x + 0.0855x = 1.0355x

Answer: yes

Step-by-step explanation: Wall would be 60 feet wide. 60 / 5 = 12.

Answer:

Yes

Step-by-step explanation:

Given :

1/2 in = 1 foot

re-written as : 1 in = 2 feet

THe blueprint is drawn to be 30 inches long

this is equivalent to 30 in x 2 feet/in = 60 feet long

With a minimum width of 5 feet per stall,

the number of stalls in 60 feet = 60 feet / 5 feet = 12 stalls

Hence there will be enough room for 12 stalls.

Answer:

Explanation:

The function must meet the rule that the pay starts at $20 and it increases each hour by 4%.

A table will help you to visualize the rule or pattern that defines the function:

x (# hours)        pay ($) = p(x)

0                        20 . . . . . . . .  [starting pay]

1                         20 × 1.04 . . . [ increase of 4%]

2                        20 × 1.04² . . . [increase of 4% over the previous pay]

x                        20 × 1.04ˣ

Hence, the function is:     [tex]p(x)=20(1.04)^x[/tex]

The range is the set of possible outputs of the function. To find the range, take into account that this is a growing exponential function, meaning that the least output is the starting point, and from there the output will incrase.

The choices name x this output. Hence, the starting point is x = 20 and the upper bound is when the number of hours is 8: 20(1.04)⁸ = 27.37.

Then the range is from 20 to 27.37 (dollars), which is represented by 20 ≤ x ≤ 27.37 (option D from the choices).

Answer:

its D for shure

Step-by-step explanation:

Answer:

[tex]x =7\sqrt{3}[/tex]

Step-by-step explanation:

By definition, the tangent of a z-angle is defined as

[tex]tan(z) =\frac{opposite}{adjacent}[/tex]

For this case

[tex]opposite = 7[/tex]

[tex]adjacent = x[/tex]

[tex]z=30\°[/tex]

So

[tex]tan(30) =\frac{7}{x}[/tex]

[tex]x =\frac{7}{tan(30)}[/tex]

[tex]x =7\sqrt{3}[/tex]

Answer:

7√3 = x

Step-by-step explanation:

Arbitrarily choose to focus on the 30 degree angle.  Then the side opposite this angle is 7 and the side adjacent to it is x.

tan 30 degrees = (opp side) / (adj side), or (1√3) = 7 / x.

Inverting this equation, we get √3 = x/7.

Multiplying both sides by 7 results in 7√3 = x

Answer:

[tex]\dfrac{72}{19}[/tex]

Step-by-step explanation:

Consider triangle ABC. Segment AX is angle A bisector. Its length can be calculated using formula

[tex]AX^2=\dfrac{AB\cdot AC}{(AB+AC)^2}\cdot ((AB+AC)^2-BC^2)[/tex]

Hence,

[tex]AX^2=\dfrac{9\cdot 10}{(9+10)^2}\cdot ((9+10)^2-17^2)=\dfrac{90}{361}\cdot (361-289)=\dfrac{90}{361}\cdot 72=\dfrac{6480}{361}[/tex]

By the angle bisector theorem,

[tex]\dfrac{AB}{AC}=\dfrac{BX}{XC}[/tex]

So,

[tex]\dfrac{9}{10}=\dfrac{BX}{17-BX}\Rightarrow 153-9BX=10BX\\ \\19BX=153\\ \\BX=\dfrac{153}{19}[/tex]

and

[tex]XC=17-\dfrac{153}{19}=\dfrac{170}{19}[/tex]

By the Pythagorean theorem for the right triangles AXY and CXY:

[tex]AX^2=AY^2+XY^2\\ \\XC^2=XY^2+CY^2[/tex]

Thus,

[tex]\dfrac{6480}{361}=XY^2+AY^2\\ \\\left(\dfrac{170}{19}\right)^2=XY^2+(10-AY)^2[/tex]

Subtract from the second equation the first one:

[tex]\dfrac{28900}{361}-\dfrac{6480}{361}=(10-AY)^2-AY^2\\ \\\dfrac{22420}{361}=100-20AY+AY^2-AY^2\\ \\\dfrac{1180}{19}=100-20AY\\ \\20AY=100-\dfrac{1180}{19}=\dfrac{1900-1180}{19}=\dfrac{720}{19}\\ \\AY=\dfrac{36}{19}[/tex]

Hence,

[tex]XY^2=\dfrac{6480}{361}-\left(\dfrac{36}{19}\right)^2=\dfrac{6480-1296}{361}=\dfrac{5184}{361}\\ \\XY=\dfrac{72}{19}[/tex]

Answer:

Step-by-step explanation:

10-2= the number of cars that finished

Answer:

1/x

Step-by-step explanation:

1/x is rational because the x is in the denominator of the fraction.  x/2 could be rewritten as (1/2)x, which is linear.

Answer:  x² + 3x + 5

Step-by-step explanation:

f(x) = 3x + 5       g(x) = x²

(f + g)(x) = f(x) + g(x)

             = 3x + 5 + x²

             = x² + 3x + 5

Answer:

1 litre = 1000 millilitres (ml)

35 litres = 35×1000 => 35000 ml

So your fish tank holds 35000 ml of water

Answer:

Third choice from the top is the one you want

Step-by-step explanation:

This whole concept relies on the fact that if the index of a radical exactly matches the power under the radical, both the radical and the power cancel each other out.  For example:

[tex]\sqrt[6]{x^6} =x[/tex] and another example:

[tex]\sqrt[12]{2^{12}}=2[/tex]

Let's take this step by step.  First we will rewrite both the numerator and the denominator in rational exponential equivalencies:

[tex]\frac{\sqrt[4]{6} }{\sqrt[3]{2} }=\frac{6^{\frac{1}{4} }}{2^{\frac{1}{3} }}[/tex]

In order to do anything with this, we need to make the index (ie. the denominators of each of those rational exponents) the same number.  The LCM of 3 and 4 is 12.  So we rewrite as

[tex]\frac{6^{\frac{3}{12} }}{2^{\frac{4}{12} }}[/tex]

Now we will put it back into radical form so we can rationalize the denominator:

[tex]\frac{\sqrt[12]{6^3} }{\sqrt[12]{2^4} }[/tex]

In order to rationalize the denominator, we need the power on the 2 to be a 12.  Right now it's a 4, so we are "missing" 8.  The rule for multiplying like bases is that you add the exponents.  Therefore,

[tex]2^4*2^8=2^{12}[/tex]

We will rationalize by multiplying in a unit multiplier equal to 1 in the form of

[tex]\frac{\sqrt[12]{2^8} }{\sqrt[12]{2^8} }[/tex]

That looks like this:

[tex]\frac{\sqrt[12]{6^3} }{\sqrt[12]{2^4} }*\frac{\sqrt[12]{2^8} }{\sqrt[12]{2^8} }[/tex]

This simplifies down to

[tex]\frac{\sqrt[12]{216*256} }{\sqrt[12]{2^{12}} }[/tex]

Since the index and the power on the 2 are both 12, they cancel each other out leaving us with just a 2!  Doing the multiplication of those 2 numbers in the numerator gives us, as a final answer:

[tex]\frac{\sqrt[12]{55296} }{2}[/tex]

Phew!!!

ANSWER

A. Directrix y=-5, focus; (-2,6)

EXPLANATION

Answer:

Step-by-step explanation:

As with any equation involving fractions, you can multiply the equation by the least common denominator to eliminate fractions. Then solve in the usual way.

c) 1/a +b = c

  1 +ab = ac . . . . multiply by a

  1 = ac -ab . . . . subtract ab

  1 = a(c -b) . . . . . factor out a

  1/(c -b) = a . . . . divide by the coefficient of a

__

d) (a-b)/(b-a) = 1

  a -b = b -a . . . . . multiply by b-a

 2a = 2b . . . . . . . . add a+b

  a = b . . . . . . . . . . divide by the coefficient of a

Please be aware that this makes the original equation become 0/0 = 1. This is why a=b is not an allowed condition for this equation. As written, it reduces to -1 = 1, which is false. One could say there is no solution.

__

f) bc +ac = ab . . . . . multiply by abc

  bc = ab -ac . . . . . . subtract ac

  bc = a(b -c) . . . . . . factor out a

  bc/(b -c) = a . . . . . . divide by the coefficient of a

Answer:

interval notation: [-5,infinity)

or answer X=> -5

Step-by-step explanation:

For this case we must find the domain of the following function:

[tex]f (x) = \sqrt {x + 5}[/tex]

By definition, the domain of a function is given by all the values for which the function is defined.

The given function stops being defined when the argument of the root is negative. Thus, the domain is given by all values of "x" greater than or equal to -5.

Answer:

Domain: [tex]x\geq-5[/tex]

Answer:

(- 9, 4)

Step-by-step explanation:

A(3, 4) is 1 unit to the right of x = 2

Thus it's reflection will be 1 unit to the left of x = 2, that is

A(3, 4 ) → A'(1, 4) ← y- coordinate remains unchanged

--------------------------------------------------------------------

A'(1, 4 ) is 5 units to the right of x = - 4

Thus it's reflection will be 5 units to the left of x = - 4

A'(1, 4) → A''(- 9, 4 )

Under the 2 parallel reflections

A(3, 4) → A''(- 9, 4 )

Answer:

  y = 0.0018(x -105)² +7

Step-by-step explanation:

The vertex of the function is at (x, y) = (105, 7), so the equation will be of the form ...

  y = a(x -105)² +7

We can use x=0 to find the value of "a". At x=0, y=27, so ...

  27 = a(0 -105)² +7

  20 = 11025a

  20/11025 = a ≈ 0.0018

So, the model is ...

  y = 0.0018(x -105)² +7

Answer:

d

Step-by-step explanation:

Given.

-x + 3.9

Plug in.

-7.2 + 3.9 = -3.3

Answer.

-3.3

Answer:

11.1

Step-by-step explanation:

−(−7.2)+3.9

=7.2+3.9

=11.1

Answer:

B.  

Step-by-step explanation:

The parabola opens to the right since the focus is to the right of the vertex.  So the square part will definitely contain a y.  By elimination the answers can't be A or C.  The vertex is (2,3) so the answer is B.

Longer answer:

formula to use is (y-k)^2=4p(x-h) where the vertex is (h,k)

So (2,3) is our vertex so enter it in giving

(y-3)^2=4p(x-2)

p is 5 since 2 and 7 are 5 units apart

p is positive because again focus is right of vertex

the answer is

(y-3)^2=20(x-2)

Answer:

B

Step-by-step explanation:

Substitute a point in the equation:

(2,3)

(3 - 3)^2 = 20(2 - 2)

(3-3)^2 = 0

Which is True

You could also use y-y1=m(x-x1)

Answer:

  $2502.60

Step-by-step explanation:

The formula for the amount of an annuity due is ...

  A = P(1 +r/n)((1 +r/n)^(nt) -1)/(r/n)

where P is the monthly payment (100), r is the annual interest rate (.04), n is the number of compoundings per year (12), and t is the number of years (2). Given these numbers, the formula evaluates to ...

  A = $100(1.00333333)(1.00333333^24 -1)/0.00333333

  = $100(301)(0.08314296)

  = $2502.60

_____

This value is confirmed by a financial calculator. The given answer choices all appear to be incorrect. The closest one corresponds to an annual interest rate (APR) of 4.286%, not 4%.

Answer:

the values of the non-integral roots of the polynomial equation are:

4.73 and 1.27.

Step-by-step explanation:

To find the roots of the polynomial equation, we need to factorize the equation:

x^4 − 4x^3 = 6x^2 − 12x ⇒ x^4 − 4x^3 -6x^2 +12x = 0

⇒ x(x+2)(x -3 + sqrt(3))(x -3 - sqrt(3))

Then, the non integral roots are:

x1 = 3 - sqrt(3) = 1.26 ≈ 1.27

x2 = 3 + sqrt(3) =  4.73

Then, the values of the non-integral roots of the polynomial equation are:

4.73 and 1.27

The approximate values of the non-integral roots of the polynomial equation are:

                     1.27 and 4.73

We are given an algebraic equation as:

[tex]x^4-4x^3=6x^2-12x[/tex]

i.e. it could be written as:

[tex]x^4-4x^3-6x^2+12x=0\\\\i.e.\\\\x(x^3-4x^2-6x+12)=0[/tex]

Since, we pulled out the like term i.e. "x" from each term.

Now we know that [tex]x=-2[/tex] is a root of the term:

[tex]x^3-4x^2-6x+12[/tex]

Hence, we split the term into factors as:

[tex]x^3-4x^2-6x+12=(x-2)(x^2-6x+6)[/tex]

Now, finally the equation could be given by:

[tex]x(x-2)(x^2-6x+6)=0[/tex]

Hence, we see that:

[tex]x=0,\ x-2=0\ and\ x^2-6x+6=0\\\\i.e.\\\\x=0,\ x=2\ and\ x^2-6x+6=0[/tex]

[tex]x=0\ and\ x=2[/tex] are integers roots.

Now, we find the roots with the help of quadratic equation:

[tex]x^2-6x+6=0[/tex]

( We know that the solution of the quadratic equation:

[tex]ax^2+bx+c=0[/tex] is given by:

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] )

Here we have:

[tex]a=1,\ b=-6\ and\ c=6[/tex]

Hence, the solution is:

[tex]x=\dfrac{-(-6)\pm \sqrt{(-b)^2-4\times 1\times 6}}{2\times 1}\\\\i.e.\\\\x=\dfrac{6\pm \sqrt{36-24}}{2}\\\\i.e.\\\\x=\dfrac{6\pm \sqrt{12}}{2}\\\\i.e.\\\\x=\dfrac{6}{2}\pm \dfrac{2\sqrt{3}}{2}\\\\i.e.\\\\x=3\pm 3\\\\i.e.\\\\x=3+\sqrt{3},\ x=3-\sqrt{3}[/tex]

Now, we put [tex]\sqrt{3}=1.732[/tex]

Hence, the approximate value of x is:

[tex]x=3+1.732,\ x=3-1.732\\\\i.e.\\\\x=4.732,\ x=1.268[/tex]