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2 years ago

Solve the inequality.

Mathematics

1 answer:

Lady bird [3.3K]2 years ago

4 0

Answer:

x $\leq$ -3

Step-by-step explanation:

Make common denominators

$\frac{2x}{6}$ - $\frac{3x-3}{6}$ $\geq$ $\frac{6}{6}$

Use the numerators only

2x - (3x - 3) $\geq$ 6

Distribute

2x - 3x + 3 $\geq$ 6

-x + 3 $\geq$ 6

Subtract 3 from both sides

-x $\geq$ 3

x $\leq$ -3

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You randomly draw a marble from a bag of marbles that contains 7 blue marbles, 2 green marbles, and 1 red

statuscvo [17]

Answer:

0.3 chance of not drawing a blue marble.

Step-by-step explanation:

This problem can be found using the theoretical probability formula.

The formula is: P (desired outcome) = # of desired outcomes

total number of outcomes

Now all you have to do is input the numbers into the equation.

P(not drawing a blue marble) = 3

3/10 is equal to 0.3 as a decimal.

5 0

2 years ago

Pythagorus' Theroem

stellarik [79]

C x c = a x a + b x b
c x c = 6 x 6 + 2 x 2
c x c = 36 + 4
square root of c x c = 40
c = 6.32
therefore, the rope is 6.32m

hope that helped ☺️

7 0

2 years ago

The profile of the cables on a suspension bridge may be modeled by a parabola. The central span of the bridge is 1210 m long and

brilliants [131]

Answer:

The approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.

Step-by-step explanation:

The equation of the parabola is:

$y=0.00035x^{2}$

Compute the first order derivative of y as follows:

$y=0.00035x^{2}$

$\frac{\text{d}y}{\text{dx}}=\frac{\text{d}}{\text{dx}}[0.00035x^{2}]$

$=2\cdot 0.00035x\\\\=0.0007x$

Now, it is provided that |x | ≤ 605.

⇒ -605 ≤ x ≤ 605

Compute the arc length as follows:

$\text{Arc Length}=\int\limits^{x}_{-x} {1+(\frac{\text{dy}}{\text{dx}})^{2}} \, dx$

$=\int\limits^{605}_{-605} {\sqrt{1+(0.0007x)^{2}}} \, dx \\\\={\displaystyle\int\limits^{605}_{-605}}\sqrt{\dfrac{49x^2}{100000000}+1}\,\mathrm{d}x\\\\={\dfrac{1}{10000}}}{\displaystyle\int\limits^{605}_{-605}}\sqrt{49x^2+100000000}\,\mathrm{d}x\\\\$

Now, let

$x=\dfrac{10000\tan\left(u\right)}{7}\\\\\Rightarrow u=\arctan\left(\dfrac{7x}{10000}\right)\\\\\Rightarrow \mathrm{d}x=\dfrac{10000\sec^2\left(u\right)}{7}\,\mathrm{d}u$

$\int dx={\displaystyle\int\limits}\dfrac{10000\sec^2\left(u\right)\sqrt{100000000\tan^2\left(u\right)+100000000}}{7}\,\mathrm{d}u$

$={\dfrac{100000000}{7}}}{\displaystyle\int}\sec^3\left(u\right)\,\mathrm{d}u\\\\=\dfrac{50000000\ln\left(\tan\left(u\right)+\sec\left(u\right)\right)}{7}+\dfrac{50000000\sec\left(u\right)\tan\left(u\right)}{7}\\\\=\dfrac{50000000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+5000x\sqrt{\dfrac{49x^2}{100000000}+1}$

Plug in the solved integrals in Arc Length and solve as follows:

$\text{Arc Length}=\dfrac{5000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+\dfrac{x\sqrt{\frac{49x^2}{100000000}+1}}{2}|_{limits^{605}_{-605}}\\\\$

$=1245.253707795227\\\\\approx 1245.25$

Thus, the approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.

7 0

3 years ago

A jacket that originally sold for $60.00 was on sale for 10% off. When it didn't sell after several weeks, the sale price was di

sammy [17]

The final price of the jacket was $32.40 after both the 10% and 40% discount. The total discount is NOT equal to a 50% discount. When 10% off, the price was $54, bringing the next 40% off to a whole different number, not necessarily off the original price.

I don't know if that makes sense to you, sorry xD

7 0

2 years ago

Use the ditributive property for -8 (x / 3)

ioda

Greetings!

"Use the distributive property for $-8 (x / 3)$ ."

The distribute property is used to simplify an expression/equation. This is done by multiplying the contents of the parenthesis by the number outside of bracket.

 $-8 (x / 3)$
$=(-8*x / -8*3)$
Simplify.
 $=(-8x/-24)$

Hope this helps.
-Benjamin

4 0

3 years ago