Question

5 questions for algebra please help!!!

Answer 1

where are the questions
one by one

Answer 2

1.What is the slope of the line that passes through the pair points (-7/2,-3) and (-5,5/2)
a.6/22
b.-6/22
c.22/6
d-22/6
2.tell whether the lines for each pair of equations are parallel,perpendicular,or niether
Y=-3x+7
-2x+6y=3
a.parallel
b.perpendiclar
c.neither
3.tell whether the lines for each pair of equations are parallel,perpendicular,or neither
Y=-1/4x+10
-2x+8y=6
a.parallel
b.perpendicular
c.neither
4. the table shows the number of miles driven over time.
Time(hours)|distance(miles)
4 232
6 348
8 464
10 580

Express the relashionship between distance and time in simplified form as a unit rate. Determine which statement correctly interprets this relashionship.
a. 232; your care travels 232 miles.
b. 1/58; your car travels 58 miles in 1 hour.
c. 58/1; your car travels 58 miles in 1 hour
d. 1/10; your car travels for 10 hours
5. For the data in the table, does y vary directly with x? if it does write an equation for the direct variation.
X | Y
10 12
15 18
20 24
a. Yes; y=1.2x
b. Yes; y=2x
c. Yes; y=x+1

Answer 3

@dayakar

Answer 4

hint:
the slope \(m\) of a line which passes at points:
\[\left( {{x_1},{y_1}} \right),\quad \left( {{x_2},{y_2}} \right)\]
is given by the subsequent formula:
\[m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\]

Answer 5

Yea i know the slope formula but when i did it i got none of the anwsers so im confused

Answer 6

let's suppose this:
\[\left( {{x_1},{y_1}} \right) = \left( { - 5,5/2} \right),\quad \left( {{x_2},{y_2}} \right) = \left( { - 7/2, - 3} \right)\]

Answer 7

so -7/2-(-5)/-3-5/2 right?

Answer 8

then after a simple substitution, we get:
\[\huge \begin{gathered}
m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{ - 3 - \frac{5}{2}}}{{ - \frac{7}{2} - \left( { - 5} \right)}} = \hfill \\
\hfill \\
= \frac{{\frac{{\left( {\left( { - 3} \right) \cdot 2} \right) - 5}}{2}}}{{\frac{{ - 7 + \left( {5 \cdot 2} \right)}}{2}}} = ...? \hfill \\
\end{gathered} \]

Answer 9

i got -5 1/2/1 1/2

Answer 10

that's right!

Answer 11

such result can be rewritten as follows:
\[\huge \begin{gathered}
m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{ - 3 - \frac{5}{2}}}{{ - \frac{7}{2} - \left( { - 5} \right)}} = \hfill \\
\hfill \\
= \frac{{\frac{{\left( {\left( { - 3} \right) \cdot 2} \right) - 5}}{2}}}{{\frac{{ - 7 + \left( {5 \cdot 2} \right)}}{2}}} = \frac{{ - \frac{{11}}{2}}}{{\frac{3}{2}}} \hfill \\
\end{gathered} \]

Answer 12

now, please multiply both numerator and denominator, of last side, by \(4\)

Answer 13

it would be -22/6 right?

Answer 14

that's right!

Answer 15

Can you help me with number 2?

Answer 16

second question:
two lines, for example:
\(y=m_1x+q_1\) and \(y=m_2x+q_2\) are parallel if \(m_1=m_2\)

Answer 17

so is number 2 perpendicular

Answer 18

we have this:
the first line is \(y=-3x+7\), so the first slope is \(m_1=-3\)
whereas the second line is \(y=(1/3)x+1/2\)
so the second slope is \(m_2=1/3\)

Answer 19

now, please what is the product: \(m_1 \times m_2=...?\)

Answer 20

m1=1/2 m2 m2=1/2 so they have the same y intercept correct?

Answer 21

for #2 you have to put both equations in slope intercept for and if they have the same y intersept then it perp if it has the same slope its par.

Answer 22

so im correct the second one is perpendicular because it has the same slope just reciprocal of each other and the y intercept is the same?

Answer 23

hint:
we can write this:
\[\huge {m_1} \times {m_2} = \frac{1}{3} \times \left( { - 3} \right) = ...?\]

Answer 24

-1

Answer 25

that's right they are perpendicular. Nevertheless the y-intercept of the first line is 7, whereas the y-intercept of the second line is 1/2

Answer 26

and im guessing number 3 is paralell

Answer 27

i think number 3 is parallel because the slopes are the same but the y intercepts are different am i wrong?

Answer 28

we can rewrite the second equation as below:
\(y=(1/4)x+3/4\)
so the slope of the second line is \(1/4\), whereas the slope of the first line is \(-1/4\)

Answer 29

now we can see that:
\(m_1\) is different from \(m_2\), furthermore \(m_1 \times m_2=-1/16\), so what can you conclude?

Answer 30

paralell

Answer 31

are you sure? parallel lines have the same slope

Answer 32

ohh so it would be neither

Answer 33

that's right!

Answer 34

i didnt see the negative sign for the second slope ;)

Answer 35

ok! :)

Answer 36

now, for the fourth exercise, we can see that the ratio:
\[\frac{{{\text{distance}}}}{{{\text{time}}}}\]
is constant for each ordered pair. Please what is the value of such constant?

Answer 37

namely, please compute these ratios:
\[\Large \begin{gathered}
\frac{{232}}{4} = ...? \hfill \\
\hfill \\
\frac{{348}}{6} = ...? \hfill \\
\hfill \\
\frac{{464}}{8} = ...? \hfill \\
\hfill \\
\frac{{580}}{{10}} = ...? \hfill \\
\end{gathered} \]

Answer 38

they all equal 58

Answer 39

so the anwser is.... 58/1 or 1/58 i got confused on that

Answer 40

yes! correct!
so the requested relation is:
\[\large \frac{{{\text{distance}}}}{{{\text{time}}}} = 58\]
or:
\[\large {\text{distance}} = 58 \times {\text{time}}\]

Answer 41

now, if \(time = 1\) hour, what is the \(distance\)?
\[\large {\text{distance}} = 58 \times {\text{time}} = 58 \times 1 = ...?\]

Answer 42

58/1

Answer 43

that's right!

Answer 44

for 5 im really confused

Answer 45

im not good at direct variations

Answer 46

5. For the data in the table, does y vary directly with x? if it does write an equation for the direct variation.
X | Y
10 12
15 18
20 24
a. Yes; y=1.2x
b. Yes; y=2x
c. Yes; y=x+1
d. No; ydoes not vary directly with x.

Answer 47

hint:
again please compute these ratios:
\[\huge \begin{gathered}
\frac{{12}}{{10}} = ...? \hfill \\
\hfill \\
\frac{{18}}{{15}} = ...? \hfill \\
\hfill \\
\frac{{24}}{{20}} = ...? \hfill \\
\end{gathered} \]

Answer 48

oooooh 1.2 so ye=1.2x

Answer 49

that's right!

Answer 50

Thanks ;) you are a really good helper

Answer 51

:)

Answer 52

can i ask you another question? @Michele_Laino

Answer 53

ok!

Answer 54

For the data in the table does y vary directly with x? if it does, write an equation for the direct variation
X | Y
40 32
28 16
16 12
a. Yes; y=2x
b. Yes; y= 0.5x
c. Yes’ y=1.5x
d. No; y does not vary directly with x

Answer 55

@Michele_Laino

Answer 56

Desribe how the graphs of y=|x| and y=|x+5| are related
a. The graphs have the same shape. The y intercept of y=|x| is 0 and the y intercept of the second graph is 5
b. The graphs have the same shape. The y intercept of y =|x| is 0 and the y intercept of the second graph is -5
c. The two graphs are the same.
d. The graphs have the same shape. The y intercept of y=|x| is 0 and the x intercept if the second graph is 5

Answer 57

Desribe how the graphs of y=|x| and y=|x|-5 are related
a. The graphs have the same shape. The y intercept of y=|x| is 0 and the y intercept of the second function is 5
b. the functions have the same y intercept. The second function is steeper tha y=|x|
c. The two functions are the same.
d. The graphs have the same shape. The y intercept of y=|x| is 0 and the x intercept if the second function is - 5

Answer 58

For the first one, i would suggest multiplying your x's in to your equations.

Answer 59

i think it is D

Answer 60

it doesnt vary directly with x @Lovelarap

Answer 61

yup

Answer 62

as we can see the y-coordinate of the graph \(y=|x|-5\) is 5 points less than the corresponding graph \(y=|x|\)

Answer 63

for the last two, try this document:

Answer 64

so my anwser is d. The graphs have the same shape. The y intercept of y=|x| is 0 and the x intercept if the second function is - 5

Answer 65

that's right! I think that in your textbook there is a typo, since the correct statement is:
The graphs have the same shape. The y intercept of y=|x| is 0 and the \(y\) intercept if the second function is - 5

Answer 66

oh i wrote it wrong it said y intercept

Answer 67

ok! :)
it is option d

Answer 68

and for
Desribe how the graphs of y=|x| and y=|x|-5 are related
a. The graphs have the same shape. The y intercept of y=|x| is 0 and the y intercept of the second graph is 5
b. the functions have the same y intercept. The second functions is steeper tha y|x|
c. The two graphs are the same.
d. The graphs have the same shape. The y intercept of y=|x| is 0 and the x intercept if the second graph is 5
my anwser is either a or d but im not sure

Answer 69

oops
i ment y=|x| and y=|x+5| are related

Answer 70

a. The graphs have the same shape. The y intercept of y=|x| is 0 and the y intercept of the second graph is 5
b. The graphs have the same shape. The y intercept of y =|x| is 0 and the y intercept of the second graph is -5
c. the two graphs are the same.
d. The two graphs are the same. d. The graphs have the same shape. The y intercept of y=|x| is 0 and the x intercept if the second graph is 5

Answer 71

in order to find the y.intercept, we have to replace \(x=0\). So the y-intercept of the first graph,is:
\(y=|x|=|0|=...?\)
whereas the y-intercept of the second graph is:
\(y=|x+5|=|0+5|=...?\)