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3 years ago

Solve for x, where x > 0 and 84x(x + 2) = 90-13x. Express your answer as a simplified common fraction.

Mathematics

1 answer:

icang [17]3 years ago

7 0

84x(x+2) = 84x² + 168x

84x² + 168x = 90 - 13x

84x² +181x - 90 = 0

bhaskara formula

$\frac{-181+-\sqrt{181^{2}- 4.84.(-90) } }{168 } }$

$\frac{-181+-\sqrt{32.761 +30.240} }{168}$

$\frac{-181+-251}{168}$

since its a positive number, we can't use the minus

so, $\frac{70}{168}$

they're both dividable by 14, so

x = $\frac{5}{12}$ is your answer

hope it helps :)

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How many ways can the words in d-r-a-g-o-n-f-l-y be arranged

GarryVolchara [31]

Answer:

362880 ways

Step-by-step explanation:

The word dragonfly has 9 different letters.

So, to find how many ways this word can be arranged, we just need to calculate the factorial of 9:

First letter has 9 possibilities

Second letter has 8 possibilities (one used)

Third letter has 7 possibilities (two used), and so on.

So the number of ways is:

9*8*7*6*5*4*3*2*1 = 362880 ways

7 0

3 years ago

Math help ( 20 pts )

Nimfa-mama [501]

A) The answer is 24 m

x - the distance from the spot on the beach to the parking lot

Triangles that are divided by x distance is similar, and therefore:
x : 18 = 32 : x
x * x = 18 * 32
x² = 576
x = √576
x = 24

Thus, the distance the spot on the beach from the parking lot is 24 m.


b) The answer is 40 m.

x - the distance from the spot on the beach to the parking lot
b - distance from the parking lot to the refreshment stand.

First, find the horizontal leg (a) of the biggest right triangle. According to the Pythagorean theorem:
a² + b² = c²
a = ?
b = ?
c = 32 m + 18 m = 50 m

Find a from the right triangle which sides are a (as a hypotenuse), x, and 18 m.
x² + 18² = a²
x = 24
24² + 18² = a²
576 + 324 = a²
900 = a²
a = √900
a = 30 m

Now, find b:
a² + b² = c²
30² + b² = 50²
900 + b² = 2500
b² = 2500 - 900
b² = 1600
b = √1600
b = 40 m

Thus the distance from the parking lot to get the refreshment stand is 40 m.

6 0

3 years ago

Riverside elementary school is holding a schoolwide election to choose a color. 5/8 of the votes were for blue. 5/9 of the remai

sleet_krkn [62]

Answer:

There were 180 votes for blue.

Step-by-step explanation:

Given:

Riverside elementary school is holding a schoolwide election to choose a color. 5/8 of the votes were for blue. 5/9 of the remaining votes were for green and the remaining 48 votes were for red.

Now, to find the votes for blue.

Let the total votes be $x.$

The votes for blue:

$\frac{5}{8} \ of\ x$

$=\frac{5}{8} \times x$

$=\frac{5x}{8}$

Remaining votes are:

$x-\frac{5x}{8} \\\\=\frac{8x-5x}{8} \\\\=\frac{3x}{8}$

The votes for green:

$\frac{5}{9} \ of\ \frac{3x}{8} \\\\=\frac{5}{9} \times \frac{3x}{8} \\\\=\frac{15x}{72}$

The remaining votes for red = 48.

Now, the total votes are:

$\frac{5x}{8} +\frac{15x}{72} +48=x\\\\\frac{45x+15x+3456}{72}=x\\\\\frac{60x+3456}{72}=x$

Multiplying both sides by 72 we get:

$60x+3456=72x$

Subtracting both sides by 60 $x$ we get:

$3456=12x$

Dividing both sides by 12 we get:

$288=x\\\\x=288.$

Thus, the total votes = 288.

Now, to get the votes for blue:

$\frac{5}{8} \ of\ 288\\\\=\frac{5}{8}\times 288\\\\=0.625\times 288\\\\=180.$

Therefore, there were 180 votes for blue.

8 0

4 years ago

What is the value of b2 - 4ac for the following equation? 2x2 - 2x - 1 = 0 -4 12 0

Daniel [21]

Answer:

I think you mean the equation is

$2 {x}^{2} - 2x - 1 = 0$

And you must find

$delta = {b}^{2} - 4ac = 4 + 8 = 12$

5 0

3 years ago

Use either the substitution or elimination method to solve the following word problem. Your answer should include two equations

vichka [17]

Let w represent the number of weeks passed.

The amount of money Ed saved is 6w - 1 (I'm subtracting the one dollar that he owes to someone)

His sister saved 6w + 2.66 (I'm adding the money she already saved).

What value of w makes both expressions equal?
We need to solve the equation 6w - 1 = 6w + 2.66

Let's solve it.
If we subtract 6w from both sides, we get -1 = 2.66
So, there is no solution. They will never have saved the same amount.
This makes sense because they started out with different amounts of money saved, but they are saving at the same rate.

7 0

4 years ago

Read 2 more answers