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3 years ago

Anyone know the answer?

Mathematics

1 answer:

olganol [36]3 years ago

5 0

The last answer choice

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If 4 times a number is 48, what is the number?

Mars2501 [29]

The answer is 12 because 12 x 4 = 48

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2 years ago

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Which system of inequalities is represented by the graph?

alexgriva [62]

Answer:

$\left\{\begin{array}{l}y\ge -x-6\\ \\ y\le 2x+4\end{array}\right.$

Step-by-step explanation:

The diagram shows shaded region which boundary is bounded with two lines.

<u>Equation of the 1st line:</u>

This line passes through the points (-6,0) and (0,-6), so its equation is

$\dfrac{x-(-6)}{0-(-6)}=\dfrac{y-0}{-6-0}\\ \\\dfrac{x+6}{6}=\dfrac{y}{-6}\\ \\y=-x-6$

<u>Equation of the 2nd line:</u>

This line passes through the points (-2,0) and (0,4), so its equation is

$\dfrac{x-(-2)}{0-(-2)}=\dfrac{y-0}{4-0}\\ \\\dfrac{x+2}{2}=\dfrac{y}{4}\\ \\y=2x+4$

The origin belongs to the shaded region, so it must satisfy both inequalities, so

$-0-6=-6\le 0\Rightarrow$ correct inequality is $-x-6\le y$

$2\cdot 0+4=4\ge 0\Rightarrow$ correct inequality is $2x+4\ge y$

Note that signsare with notion "or equal to" because lines are solid.

Answer:

$\left\{\begin{array}{l}-x-6\le y\\ \\2x+4\ge y\end{array}\right.\Rightarrow \left\{\begin{array}{l}y\ge -x-6\\ \\ y\le 2x+4\end{array}\right.$

7 0

3 years ago

Determine the given pair of lines of parallel, perpendicular, or intersecting.

podryga [215]

$k:\ y=m_1\cdot x+b_1\ \ \ \ and\ \ \ \ l:\ y=m_2\cdot x+b_2 \\\\k\ ||\ l\ \ \ \Leftrightarrow\ \ \ m_1=m_2\ \ \ \ \ \ and \ \ \ \ \ \ k\ \bot\ l\ \ \ \Leftrightarrow\ \ \ \ m_1\cdot m_2=-1\\----------------------------\\1.\\ k:\ y= \frac{7}{3} x-8\ \ \ and\ \ \ l:\ y=\frac{7}{3} x+3\\\\m_1=m_2=\frac{7}{3}\ \ \ \Rightarrow\ \ \ k\ ||\ l$

$2.\\k:\ y=2x-1\ \ and\ \ l:\ -x+2y=6\ \Rightarrow\ \ 2y=x+6\ \ \Rightarrow\ \ y= \frac{1}{2}x+3 \\\\m_1 \neq m_2\ \ \ and\ \ \ m_1\cdot m_2 \neq -1\ \ \ \Rightarrow\ \ \ the\ lines\ intersect\\\\3.\\k:\ y= \frac{5}{2} x-17\ \ \ and\ \ \ l:\ y=- \frac{5}{2} x-1\ \ \ \Rightarrow\ \ \ the\ lines\ intersect\\\\4.\\k:\ y= \frac{5}{2} x-4\ \ and\ \ l:\ -5x+2y=6\ \Rightarrow \ 2y=5x+6\ \Rightarrow \ y= \frac{5}{2}x +3\\\\m_1=m_2= \frac{5}{2} \ \ \ \Rightarrow\ \ \ k\ ||\ l$

$5.\\k:\ y=- \frac{2}{3} x+12\ \ \ and\ \ l:\ y= \frac{3}{2} x+3\\\\m_1\cdot m_2=- \frac{2}{3}\cdot \frac{3}{2} =-1\ \ \ \Rightarrow\ \ \ k\ ||\ l\\\\6.\\k:\ y= \frac{1}{3}x-13\ \ \ and\ \ \ l:\ y=3x+2\ \ \ \Rightarrow\ \ \ the\ lines\ intersect \\\\7.\\k:\ y=-4x+5\ \ ,\ \ l: -x+4y=-16\ \Rightarrow\ 4y=x-16\ \Rightarrow\ y= \frac{1}{4}x-4 \\\\m_1\cdot m_2=-4\cdot \frac{1}{4} =-1\ \ \ \Rightarrow\ \ \ k\ \bot\ l$

$8.\\k:\ y= \frac{2}{3} x+3 \ ,\ \ l:\ -2x+3y=21 \ \Rightarrow\ \ 3y=2x+21\ \Rightarrow\ y= \frac{2}{3} x+7\\\\m_1=m_2= \frac{2}{3} \ \ \ \Rightarrow\ \ \ k\ ||\ l$

8 0

2 years ago

Which gives the best estimate and the exact product of (5.9)(8.28)? A: estimate: 40; exact product: 48.852

Evgesh-ka [11]

I think B gives the best estimate and exact product because

1). 5.9 x 8.28 is very similar to 6 x 8 which equals 48.

and

2. 5.9 x 8.28 = 48.852.

Hopefully that made sense. :)

5 0

3 years ago

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A phase modulator produces a maximum phase shift of 45 degrees. The modulation frequency range is 300 to 4000 Hz. What is the ma

sergejj [24]

Answer:

Maximum frequency deviation is 2616.29509 Hz

Maximum frequency deviation=(4000-3000)cos45

Max frequency deviation=2616.29509 Hz

8 0

3 years ago