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2 years ago

(9x-4y) x (-2) + (3x+2y)

Mathematics

2 answers:

Mama L [17]2 years ago

7 0

Answer: $-18x^{2} +8yx+3x+2y$

Step-by-step explanation:

aleksklad [387]2 years ago

4 0

Answer:(3x-2y)(3x+2y)

Step-by-step explanation:

IT is this one

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The equation 3.5x + 1.5y = 21 represents the cost for a family to

Alexus [3.1K]

Answer:

Hey there!

The x-intercept is (6,0) meaning that if no children attend, 6 adults will attend.

The y-intercept is (0,14) meaning that if no adults attend, 14 children will attend.

Let me know if this helps :)

7 0

3 years ago

Convert 45 miles/h equals how many ft/sec

nlexa [21]

Can you show your original question

8 0

3 years ago

A diver dives from a cliff with a height of 144 feet. His height, h, in feet is given by the equation h=-16t^2+144 , where t is

Deffense [45]

Answer:

It takes 3 seconds for the diver to reach the water.

Step-by-step explanation:

The height, in feet, is given by the following equation:

$h(t) = -16t^{2} + 144$

How many seconds will it take for the diver to reach the water?

He reaches the water when his height is 0, that is, when h(t) = 0. So

$h(t) = -16t^{2} + 144$

$0 = -16t^{2} + 144$

$16t^{2} = 144$

$t^{2} = \frac{144}{16}$

$t^{2} = 9$

$t = \pm \sqrt{9}$

$t = \pm 3$

There are no negative instant of time, so just t = 3.

It takes 3 seconds for the diver to reach the water.

6 0

3 years ago

A steady wind blows a kite due west. The kite's height above ground from horizontal position x = 0 to x = 80 ft is given by y =

GaryK [48]

Answer:

The distance travelled by the kite is 122.8 ft ( approx )

Step-by-step explanation:

Here, the given function,

$y=150-\frac{1}{40}(x-50)^2$

Differentiating with respect to x,

$y'=-\frac{1}{20}(x-50)$

∵ arc length of a curve is,

$L=\int_{a}^{b} \sqrt{1+y'^2}dx$

Where, y shows the height of the curve for a ≤ x ≤ b,

Thus, the arc length of the given curve is,

$L=\int_{0}^{80} \sqrt{1+(-\frac{1}{20}(x-50)^2}dx$

Put $-\frac{1}{20}(x-50)=tan\theta$

$\implies -dx=-20 sec^2\theta d\theta$

$\implies L=-20\int_{0}^{80} \sqrt{1+tan^2\theta}sec^2\theta d\theta$

$=-20\int_{0}^{80} (sec \theta ) sec^2\theta d\theta$

By integration by parts,

$=|-\frac{20}{2}(sec \theta tan\theta +ln|sec\theta +tan\theta |) |^{x=80}_{x=0}$

If x = 80, $tan \theta = -\frac{1}{20}(30-50)=\frac{3}{2}$

$sec \theta = \frac{\sqrt{13}}{2}$

$\implies \theta = \frac{1}{20}(0-50)=\frac{5}{2}$

$sec \theta = \frac{\sqrt{29}}{2}$

Thus, the length of the curve is,

$=-10(\frac{\sqrt{13}}{2}(-\frac{3}{2}) +ln|\frac{13}{2}-\frac{3}{2}|) + 10(\frac{5\sqrt{29}}{4} + ln |\frac{29}{2} + \frac{5}{2} |)$

$\approx 122.8\text{ feet}$

8 0

3 years ago

Show that the equation 2x^2+5hx=3k has real and distinct roots for all positive values of k.

saveliy_v [14]

The given equation is quadratic and nature of roots of quadratic equation are dependant on its discriminant. Writing the equation in standard form:

$2 x^{2} +5hx-3k = 0$

Finding the discriminant:

$Discriminant = (5h)^{2} - 4(2)(-3k) = (5h)^{2}+24k$

The roots of a quadratic equation are real and distinct if the value of its discriminant is greater than 0.

If we observe the value of discriminant, it is a sum of two terms in this case. The first term is square of (5h), which will always be a positive term or zero if h is zero. The second term is 24k. The value of 24k will always be positive for positive values of k.

Thus for positive values of k, the discriminant of given equation is always positive and thus we can say the root of given equation will always be real and distinct for positive values of k.

3 0

3 years ago