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3 years ago

Which of the following is a solution of y - x < -3? A. (6, 2) B. (2, 6) C. (2, -1)

Mathematics

1 answer:

timurjin [86]3 years ago

3 0

For this case we have the following inequality:

$y-x$

We must evaluate each of the points and verify if the inequality is met:

$(6,2)\\2-6$

The inequality is met!

$(2,6)\\6-2$

It is not fulfilled!

$(2, -1)\\-1-2$

It is not fulfilled!

Thus, the point that meets the inequality is (6,2)

Answer:

Option A

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Gimme the answer because I have no idea how to do this it makes no sense to me

kati45 [8]

Answer:

C, D, B

Step-by-step explanation:

the mode is if a number is repeated more than one time

EX. 15, 23, 15, 23, 15

C because 15 is repeated 3 times and 19 is too.

D because 42 is repeated 2 times and so is 18.

B because 87 is repeated 2 times and 32 is too.

5 0

2 years ago

Can someone please solve this problem for me?

statuscvo [17]

Answer:

5 and 7.

Step-by-step explanation:

Hey! So to start you need to create an algebraic expression. You can express this problem through the following equation:

*Note: if x is an odd integer, x + 2 is the next consecutive odd integer.

$x *(x+2)=35$

Expanding, you get:

$x^{2}+2x = 35.$

And moving the 35 to the other side, you get a simple quadratic.

$x^{2}+2x -35 =0.$

Solving by factoring:

$(x+7)(x-5)$

This means two possible solutions for the smaller consecutive number are -7 and 5. However the question asks for two positive odd integers, so one of the numbers must be 5. The next will be 7(as its x + 2).

5 0

2 years ago

A) Two angles are adjacent if their measures add up to 90°.

slavikrds [6]

Answer:

A) False

B) False

Step-by-step explanation:

A. Two angles whose measures add up to 90° are said to be complementary, while two angles are adjacent when formed beside each other. So, adjacent angles might be complementary or supplementary. Thus, the answer to the first part of the question is false.

B. When two angles share a side, they are said to be adjacent to each other. But supplementary angles add up to $180^{o}$ . Since adjacent angles might be complementary or supplementary, then the answer to the second part of the question is false.

4 0

2 years ago

Convert 86.25 into hexadecimal.

Romashka-Z-Leto [24]

Answer:

56.4

Step-by-step explanation:

To convert decimal number 86.25, we convert its integer and fraction part individually and then add them to get the equivalent hexadecimal number, as below:

To convert integer 86 to hexadecimal, follow these steps:

Divide 86 by 16 keeping notice of the quotient and the remainder. Continue dividing the quotient by 2 until you get a quotient of zero.

Then just write out the remainders in the reverse order to get the equivalent hexadecimal number.

86 / 16 = 5 with remainder 6

5 / 16 = 0 with remainder 5

Here is the answer to 86 decimal to hexadecimal number:

For converting decimal fraction 0.25 to hexadecimal number, follow these steps:

Multiply 0.25 by 16 keeping notice of the resulting integer and fractional part. Continue multiplying by 16 until you get a resulting fractional part equal to zero (we calcuclate upto ten digits).

Then just write out the integer parts from the results of each multiplication to get equivalent hexadecimal number.

0.25 × 16 = 4 + 0

Here is the answer to 0.25 decimal to hexadecimal number:

0.4

Therefore, decimal number 86.25 converted to hexadecimal is equal: 56.4

8 0

2 years ago

Read 2 more answers

The graphs of the polar curves r = 4 and r = 3 + 2cosθ are shown in the figure above. The curves intersect at θ = π/3 and θ = 5π

Gennadij [26K]

(a)

$\displaystyle \frac{1}{2} \cdot \int_{\frac{\pi}{3}}^{\frac{5\pi}{3}} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

or, via symmetry

$\displaystyle\frac{1}{2} \cdot 2 \int_{\frac{\pi}{3}}^{\pi} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

____________

(b)

By the chain rule:

$\displaystyle \frac{dy}{dx} = \frac{ dy/ d\theta}{ dx/ d\theta}$

For polar coordinates, x = rcosθ and y = rsinθ. Since
r = 3 + 2cosθ, it follows that

$x = (3 + 2\cos\theta) \cos \theta \\ 
y = (3 + 2\cos\theta) \sin \theta$

Differentiating with respect to theta

$\begin{aligned}
\displaystyle \frac{dy}{dx} &= \frac{ dy/ d\theta}{ dx/ d\theta} \\
&= \frac{(3 + 2\cos\theta)(\cos\theta) + (-2\sin\theta)(\sin\theta)}{(3 + 2\cos\theta)(-\sin\theta) + (-2\sin\theta)(\cos\theta)} \\ \\
\left.\frac{dy}{dx}\right_{\theta = \frac{\pi}{2}}
&= 2/3
\end{aligned}$

2/3 is the slope

____________

(c)

"distance between the particle and the origin increases at a constant rate of 3 units per second" implies dr/dt = 3

Angle θ and r are related via r = 3 + 2cosθ, so implicitly differentiating with respect to time

 $\displaystyle\frac{dr}{dt} = -2\sin\theta \frac{d\theta}{dt} \quad \stackrel{\theta = \pi/3}{\implies} \quad 3 = -2\left( \frac{\sqrt{3}}{2}}\right) \frac{d\theta}{dt} \implies \\ \\ \frac{d\theta}{dt} = -\sqrt{3} \text{ radians per second}$

5 0

2 years ago