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3 years ago

HELP!!!!!

Mathematics

1 answer:

Elis [28]3 years ago

7 0

Line 1 and line 4 are parallel

Step-by-step explanation:

Two lines are said to be parallel if they have same slope.

In order to compare the lines given, we have to write them all in the same form, and then compare their slopes.

Line 1:

$y=\frac{1}{3}(x+6)$

Applying distributive property,

$y=\frac{1}{3}x+2$

Line 2:

$y-6 = 3x\\\rightarrow y=3x+6$

Line 3:

$y=-3(x-4)$

Applying distributive property,

$y=-3x+12$

Line 4:

$3y+18=x$

re-arranging,

$3y=x-18\\y=\frac{1}{3}x-6$

Now we have rewritten all the lines in the form $y=mx+q$ , where m is the slope. By comparing the values of m, we see:

$m_1 = \frac{1}{3}\\m_2=3\\m_3 = -3\\m_4=\frac{1}{3}$

Therefore, the lines which are parallel are line 1 and line 4.

Learn more about parallel and perpendicular lines:

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A university is trying to determine if certain remedial classes need to be offered to their incoming class. To do so, they give

lora16 [44]

Answer:

The experiment is identifying whether a student gets less than a 75% on the entrance exam.

The trial is one exam being taken.

An outcome is a student scoring 80%.

Step-by-step explanation:

An experiment occurs when an intervention is made by a researcher and its effect are studied, thus the experiment here is identifying whether a student gets less than a 75% on the entrance exam.

The trial is the one exam being taken.

While an outcome is the aftermath of the experiment which includes a student scoring 80%.

8 0

3 years ago

A line has a slope of –3 and a y-intercept of (0, –1). What is the equation of the line that is parallel to the given line and p

givi [52]

Well, the first line has a slope of -3, and runs through 0, -1.

a line parallel to that one, will have the same exact slope of -3.

now, we know about this other parallel line that it runs through -3,1, and of course, since is parallel, it has a slope of -3

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1\\
&&(~ -3 &,& 1~)
\end{array}
\\\\\\
% slope = m
slope = m\implies -3
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-1=-3[x-(-3)]
\\\\\\
y-1=-3(x+3)
\implies 
y-1=-3x-9\implies y=-3x-8$

6 0

3 years ago

Allen opens a retirement savings account with an initial deposit of $5,000. He makes annual contributions to the account, and at

Lera25 [3.4K]

Answer:

He gained 3,650 dollars over 5 years of saving his retirement money

Step-by-step explanation:

Just subtract 5,00 from 8,000 and u get 3,000 so then just add 650 to the 3,000 and thats your answer 3,650!!

3 0

3 years ago

HELP PLEASE!!!!

kumpel [21]

Answer:

The rational numbers are $\frac{11}{3}, 6.25, 0.01045,\sqrt{\frac{16}{81}},0.\bar{42}$ and the irrational functions are $\sqrt{48},\sqrt{\frac{3}{16}}$ .

Step-by-step explanation:

A rational number can be expressed in the form of $\frac{p}{q}$ , where p and q are integers and q is not equal to 0. For example $2,3.5,\frac{2}{5},...$ .

An irrational function can not be expressed in the form of $\frac{p}{q}$ , where p and q are integers and q is not equal to 0. For example $\sqrt{2},\sqrt{3},\sqrt{5},...$ .

If any number is multiplied by a irrational number then the resultant number is an irrational number.

By the above definition we can conclude that:

The number $\frac{11}{3}$ is a rational number.

$\sqrt{48}=\sqrt{16\times 3}=4\sqrt{3}$

Therefore $\sqrt{48}$ is an irrational number.

$6.25=\frac{625}{100}=\frac{25}{4}$

Therefore 6.25 is a rational number.

$0.01045=\frac{1045}{100000}=\frac{209}{20000}$

Therefore 0.01045 is a rational number.

$\sqrt{\frac{16}{81}}=\frac{4}{9}$

The number $\frac{16}{81}$ is a rational number.

$\sqrt{\frac{3}{16}}=\frac{\sqrt{3}}{4}$

The number $\frac{3}{14}$ is an irrational number.

$0.\bar{42}=\frac{42}{99}$

Therefore $0.\bar{42}$ is an irrational number. The numbers with recursive bar are always rational numbers.

3 0

3 years ago

suppose you deposit $1000 in a savings account that pays 4.8% interest compounded monthly. Write an exponential function to mode

zubka84 [21]

Answer:

The exponential function is $A(t) = 1000(1.004)^{12t}$ .

You will have $1,100.55 in the account after 2 years.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Deposit $1000 in a savings account that pays 4.8% interest compounded monthly.

This means that $P = 1000, r = 0.048, n = 12$ . So