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german
3 years ago
6

If P and S are rational numbers and R and Q are irrational numbers, which of these statements is true?

Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
8 0

Answer: B. The product of P and S is always a rational number.

Step-by-step explanation: The product AND sum of two rational numbers will ALWAYS be rational.

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Are the expressions 3/4a + 8 - 1/4a - 2 and 1/2(a + 12) equivalent? Show why or why not.
natta225 [31]

Answer:Yes they are equivalent.

Step-by-step explanation:

3/4a + 8 - 1/4a - 2 1/2(a + 12)

Combine like terms Distributive property

2/4a+6 1/2a+6

2/4=1/2 (simplify)

1/2+6=1/2+6

4 0
3 years ago
Pls help with this!! no wrong answers pls
Juliette [100K]

Answer:

x = 40

Step-by-step explanation:

180 = 100 + x +x

180-100= 2x

80 = 2x

x = 40

4 0
3 years ago
Find the equation of a line that is perpendicular to y = 3x – 5 and passes through the point (1, -3).
Svetradugi [14.3K]

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \qquad y = \stackrel{\stackrel{m}{\downarrow }}{3}x-5

well then therefore

\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{3\implies \cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}

so we're really looking for the equation of a line with slope of -1/3 and that passes through (1, -3 )

(\stackrel{x_1}{1}~,~\stackrel{y_1}{-3})\qquad \qquad \stackrel{slope}{m}\implies -\cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{-\cfrac{1}{3}}(x-\stackrel{x_1}{1})\implies y+3=-\cfrac{1}{3}x+\cfrac{1}{3} \\\\\\ y=-\cfrac{1}{3}x+\cfrac{1}{3}-3\implies y=-\cfrac{1}{3}x-\cfrac{8}{3}

6 0
2 years ago
I’m pretty confused on this question. Anyone know the answers?
Afina-wow [57]

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

• If m > 0, then the line slopes upwards from left to right ( increases )

• If m < 0, then the line slopes downwards from left to right ( decreases )

(a)

y + x = 3 ( subtract x from both sides )

y = - x + 3 ← in slope-intercept form

with m = - 1 ⇒ decreasing from left to right

(c)

y = 4x + 8 ← is in slope-intercept form

with m = 4 ⇒ increasing from left to right

the equation of a line in the form x = c represents a vertical line, where c is the value of the x-coordinates the line passes through

(b)

x - 5 = 0 ( add 5 to both sides )

x = 5 ← is a vertical line

the equation of a line in the form y = c represents a horizontal line, where c is the value of the y-coordinates the line passes through

(d)

\frac{y}{4} = - 6 ( multiply both sides by 4 )

y = - 24 ← is a horizontal line


3 0
3 years ago
How many ways can 4 people sit in a row of 7 ​chairs?
Ghella [55]

7\cdot6\cdot5\cdot4=840

6 0
3 years ago
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