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You're welcome  !!!

Circumference  =  2 * pi * r  = 2 * 3.14 * r  = 2 * 3.14 * 5.2   =  32.656 ft

Thank you so much for your help!

y = -0.000488x^2  + 0.656x

We have the form  y  =  ax^2  + bx

The x coordinate of the vertex  is =  -b / [ 2 *a ] =      - 0.656  / [ 2 *  -0.000488 ] ≈  672.13

To find the  height above the river, put this value back into  the function and we  get

y  = -0.000488(672.13)^2  + 0.656(672.13) ≈ 220.5 ft

The section of the bridge above the arch will be the difference between  the intercepts of the function and the x axis

But  (0,0)  is one intercept...and using the fact that this parabola is symmetric bout its vertex point....the other  intercept occurs at   2 ( 672.13)  = 1344.26 ft ≈  1344.3 ft.

See the graph, here :  https://www.desmos.com/calculator/jd1toj6pak

[The line y = 220.5  represents  the bridge span  between the two  x intercepts  ]

Thank you!!

The sum of the interior angles of a triangle  = 180°

Let  x  be the unknown angle...so we have...

55 + 80  +  x  = 180

135 + x  = 180     subtract  135 from both sides

x  = 45°

Well look who joined the parade …the one and only Blarney Master. Longtime no see. (Not long enough, though.)

----

^{please take this into consideration}

Why of course, that’s a very reasonable thing to ask.

^{We all make mistakes, including you, and it's very hypocritical for you to attack others for getting math problems wrong when your posts show that you make mistakes too.}

Why, far be it from me to be a hypocrite. And of course I’ll excuse the decomposing rat in your kitchen, because well, all kitchens have germs--even mine. You’ll understand if I don’t indulge. We chimps enjoy tasty rats and voles, but I prefer mine on the fresh side. Though, if I turn in to Chimp Hyde, I might.

^{Keep in mind that many users here are high school students- they're here to learn, and cussing them isn't going to help anyone}

The only high school student I’ve (knowingly) trolled is Max Wong. It wasn’t for his math (the kid is brilliant), it was for juvenile rudeness. My troll post was more rude than he was. Alan hid it, as I was editing it. Max never saw it.    

^{Ginger, i have to agree with the guest- you are very quick to judge others,}

1)

The question clearly says "factors", not "prime factors", so let's try and answer the question. Firstly, what are the factors of 72? A factor is an integer that divides the number without leaving a remainder, so 1 and 72 are factors, as are 2,3,4,6,... and so on. In fact the prime factorization of 72 is \(2^3\times 3^2\), so you can create a factor of 72 by taking an integer power of 2 between \(2^0\) and \(2^3\)(inclusive) and multiplying it by a power of 3 between \(3^0\) and \(3^2\). Since there are 4 of the first and 3 of the second there are exactly \(4\times3=12\) factors: 1,2,3,4,6,8,9,12,18,24,36 and 72. To get multiples of 72 you can multiply by 2 to get \(2\times72=2^4\times3^2=144\) which has \(5\times3=15\) factors or 3 to get \(3\times72=2^3\times3^3=216\) has \(4\times4=16\) factors. Using larger powers of 2 or 3 or including more prime multipliers will produce way too many factors, so:

\(3\times72=2^3\times3^3=216\) is the least (and only) integer multiple of 72 with exactly 16 factors.

Suppose a function f(x) is defined on the domain [-8,4] . If we define a new function g(x)

by g(x) = f(-2x), then what is the domain of g(x)? Express your answer in interval notation.

\(-8\le -2x \le 4\\ -8\le -2x\qquad and \qquad -2x \le 4\\ \quad 4\ge x\qquad \quad and \qquad \qquad  x \ge -2\\ \quad x \le 4\qquad \quad and \qquad \qquad  x \ge -2\\ -2 \le x \le 4\)'

domain is

[-2,4]

1/2 divided by 5/8

How many 5/8 of a chocolate bar is in 1/2 a chocolate bar

is in 1/2 a chocolate bar

Well it fits less than 1 time.

I can see that it fits only 4/5 times

Check:

\(\frac{1}{2}\div \frac{5}{8}\\ =\frac{1}{2}\times \frac{8}{5}\\ =\frac{4}{5}\)

that is great :)

As follows:

  \(\text{Start as follows: }\frac{2x-y}{x+y}=\frac{2}{3}\\ \text{ Then multiply both sides by }3(x+y)\\ 3(2x-y)=2(x+y)\text{ or }6x-3y=2x+2y\\\text{Collect like terms together: }4x=5y\\\text{Divide both sides by }4y\\\frac{x}{y}=\frac{5}{4}\)

A rectangle has a base of 6x+7 and a height of 7. The area of the rectangle is 133in^2.

Solve for the missing sides.

\(\begin{array}{|rcll|} \hline A &=& \text{base} \times \text{height} \\ A &=&(6x+7) \times 7 \quad & | \quad A =133\ \text{in}^2 \\ 133 &=&(6x+7) \times 7 \quad & | \quad :7 \\ 19 &=& 6x+7 \\ \mathbf{6x+7} & \mathbf{=} & \mathbf{19} \\ \hline \end{array}\)

The missing side is 19.

Sally found that one dozen eggs costs $1.20 at Super-X. However, she could get 2.5 dozen of the same eggs at Limitless for $3:15. When buying 5 dozen eggs, how many cents would she save by shopping at the less expensive store?

Find the price per egg and compare the two as follows:

dozen = 12

$1.20 / 12 =$0.10 cents per egg at the Super-X store.

$3.15 /(2.5 x 12)

$3.15 / 30 = $.105 cents per egg at the Limitless store.

$0.105 - $0.10 =$0.005 or 1/2 cent per egg cheaper at Super-X store.

5 dozen x 12 = 60

60 x $0.005 =$0.30 - or 30 cents that Sally would save by buying the 5 dozen eggs at Super-X.

 2x + 2y =6x -3y, solve for x/y
2x - 6x = -3y -2y
-4x = -5y
-4x / -5y =1
x/y =5/4

0.135 x 1,000 / 1,000 =135 / 1000  divide both top and bottom by 5 =27/200. That is it. It cannot be reduced any further.

-7/18 - This also cannot be reduced any further as a fraction, because 7 is a prime number. You can express it as a decimal = -0.38888.........etc.

-15/36 - You can divide both top and bottom by 3 and you should get:

-5/12 - and this cannot be reduced any further, because 5 is a prime number. You can also express it as a decimal: -0.4166666.......etc.

It is rational of course, because "rational" means "it can be expressed as a ratio". So, once you put one natural number over another, that automatically means the resulting fraction is rational.

Help please.

Force to to keep car from rolling down the hill... =   5300 sin (8°) ≈ 737.6 lbs

Force  perpendicular to the hill  =  5300 cos (8°) ≈  5248 4 lbs

 -2(s - 7) > 4s + 8   simplify the  left side

-2s + 14 > 4s + 8          add  2s to  both sides, subtract 8 from both sides

6 > 6s       divide both sides by 6

1 > s       which  means the same thing as     s < 1

So....the answer  is   ( - infinity, 1 )

If AK is an  altitude, then angle AKC  is   a right angle

By the Pythagorean Theorem...

AK  = √  [ AC^2  - CK^2 ] = √ [ 9^2  - 4^2 ] = √ [ 81 - 16] = √65

Also...angle  AKB is right....which implies that

AB  = √ [ AK^2 + BK^2 ] = √ [  (√ 65)^2 + (√5)^2 ] =  √ [65 + 5 ] =    √70  units^2

Triangle  ABC  is isosceles with  AB  = AC

AD  is an altitude which is also  a median to BC...so  DC  = DB  = 6

And  DE is parallel to AB

So  angle EDC  = angle ABC

And angle ACB  = angle ECD

So...by AA congruency, ΔABC  ~ Δ  EDC

Since the area  of  Δ  ABC = 180....we can  find the altitude AD thusly

180  = (1/2) (AC) (AD)

180  = (1/2) (12) (AD)

180 = 6  (AD)   divide each side by 6

30  = AD

Now  Δ ABC  and Δ EDC  are similar.... and BC  = 2DC

So......the altitude of Δ ABC  is also twice that of  Δ EDC...so  the altitude of Δ  EDC   = 15

And the area of Δ EDC  = (1/2)DC( altitude of EDC)  = (1/2)(6)(15)  = .45

So...the area  of ABDE  = area of  Δ ABC  -  area  of Δ  EDC  =   180  - 45  =  135  units^2

Let A  = (0,8)   B  =(0,0)   C  = (15,0)  and M  = (0,4)

So CM  = √ [ (15 - 0) ^2  + ( 0 - 4)^2 ] =   √ [15^2 + 4^2 ]   =  √ [ 225 + 16]  = √241 ≈ 15.52 units

Look  at "C'

If we multiply   25 * 1 hour  + 40   we get  1 * 25  + 40  = 25  + 40  = 65

If we multiply 2 * 2 hours + 40  we get 2 *25  + 40  = 50 + 40  = 90

This seems to  be the rule....check it yourself for 3 hours, 4 hours and 5 hours to see that this rule is correct....!!!

B.  the product of 7  and a  number x   [ "product"  means "multiply" ]