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3 years ago

Is (-1,4) a solution of the inequality y<2x+5?

1 answer:

6 0

Let's plug x= -1, y= 4 in the inequation, we have:
4< 2*(-1)+5
⇒ 4< -2+5
⇒ 4< 3 (false)

Therefore, (-1,4) is not a solution of the inequation y<2x+5~

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In the given right triangle, find the missing length.

mafiozo [28]

Answer:

The answer is 10

Step-by-step explanation:

$a=\sqrt{b^{2}-c^{2}}$

$a=\sqrt{26^{2}-24^{2}}$

$a=\sqrt{676-576}$

$a=\sqrt{100}$

a=10

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3 years ago

Lanny’s credit card has an apr of 33%, calculated on the previous monthly balance. His credit card record for the last 7 months

Softa [21]

The answer is A ( $83.39 )

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3 years ago

Read 2 more answers

Let f(x) = cxe−x2 if x ≥ 0 and f(x) = 0 if x < 0.

sergij07 [2.7K]

(a) If f(x) is to be a proper density function, then its integral over the given support must evaulate to 1:

$\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx = \int_0^\infty cxe^{-x^2}\,\mathrm dx=1$

For the integral, substitute u = x ² and du = 2x dx. Then as x → 0, u → 0; as x → ∞, u → ∞:

$\displaystyle\frac12\int_0^\infty ce^{-u}\,\mathrm du=\frac c2\left(\lim_{u\to\infty}(-e^{-u})-(-1)\right)=1$

which reduces to

c / 2 (0 + 1) = 1 → c = 2

(b) Find the probability P(1 < X < 3) by integrating the density function over [1, 3] (I'll omit the steps because it's the same process as in (a)):

$\displaystyle\int_1^3 2xe^{-x^2}\,\mathrm dx = \boxed{\frac{e^8-1}{e^9}} \approx 0.3678$

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3 years ago

What’s the hypotenuse?

Karolina [17]

Answer:

c = 10 feet

Step-by-step explanation:

Use the Pythagorean theorem: a^2 + b^2 = c^2

Step 1: Plug in the information

(6)^2 + (8)^2 = c^2

36 + 64 = c^2

100 = c^2

sqrt(100) = sqrt(c^2)

10 = c

Answer: c = 10 feet

7 0

3 years ago

4 people went to the movies. Each person spent $9.50 on a ticket and had the same amount of money leftover. They originally had

solong [7]

$2.50 was left for each person.

4(9.50) + x = 48

38 + x = 48

subtract 38 on both sides

x = 10

10$ was left in total by all 4 people

10/4 = 2.50

$2.50 was left over for each person

7 0

3 years ago