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1 year ago

1. Show your work algebraically for full credit. Circle your answer (8 points - from lesson 3.04)

Mathematics

1 answer:

melomori [17]1 year ago

5 0

The required equation of the line is $3x-4y=6$

What is an equation?

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.

Slope of the line, m is

$=\frac{x_{2}-x_{1} }{y_{2} -y_{1} }$ $=\frac{3-(-3)}{6-(-2)}$ $=\frac{6}{8}$ $=\frac{3}{4}$

then, the equation of the line is given by

$y-y_{1}=m(x-x_{1} )$

$or, y-3=\frac{3}{4} (x-6)$

$or, 4y-12=3x-18$

$or, 3x-4y=6$

Hence, the required equation of the line is $3x-4y=6$

To know more about equations, click on the link

brainly.com/question/28196676

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Given a rectangle with an area of 20 square units, if the width is x units and the length is x + 1 units, what is the difference

ollegr [7]

Answer: 1unit.

Step-by-step explanation:

Area of the rectangle

A = length × width

Since the area = 20 and the width is x and the length is x + 1.

We now substitute for the values in the above formula and solve for x

20 = x × x + 1

20 = x( x + 1 ), we now open

20 = x² + x , then re arrange.

x² + x - 20 = 0, this is a quadratic equation.we solve for x using quadratic means

Here, I am going to solve using factorization by grouping

x² + x - 20 = 0

x² + 5x - 4x - 20 = 0

x( x + 5 ) - 4( x + 5 ) = 0

( x + 5 )( x - 4 ). = 0

Therefore, the solution for x will be

x = -5 or 4, but x can not be -5 ( negative), so x = 4.

Now the difference between width and the length can easily be calculated from the above,

Width = 4 (x) , and length = 5 (4 + 1),

Now difference will be

5 - 4 = 1unit.

5 0

3 years ago

A plane flew 500 miles in 40 minutes. How long would it take to fly 1 mile

mina [271]

I believe it’s 12.5 miles

3 0

2 years ago

The price of tickets for the dance was 1 ticket for $6 or 2 tickets for $8 she looked inside the cash box and found $200 and tic

Aleks04 [339]

We can say that exchanging one couple's ticket for an individual's ticket would increase the money in the cash box from 200 to 202 and it would result in an even number of couples tickets sold.

Step-by-step explanation:

Let the number of tickets sold to the individuals = s

Let the number of tickets sold to the couples = c

According to the question,

s + c = 46 ( Equation 1)

Since each individual's ticket is $6, the total amount of money made by selling tickets to individuals is 6s.

Similarly, since each ticket sold to couples is $8, the total amount of money made by selling tickets to couples is 8c.

So,

6 s + 8 c = 200 ( Equation 2)

On solving both the equations, we get

c = 38 and s = 8

Therefore, 8 tickets were sold to individuals and 38 tickets were sold to the couples.

5 0

2 years ago

A computer can be classified as either cutting dash edge or ancient. Suppose that 94% of computers are classified as ancient.

taurus [48]

Answer:

(a) 0.8836

(b) 0.6096

(c) 0.3904

Step-by-step explanation:

We are given that a computer can be classified as either cutting dash edge or ancient. Suppose that 94% of computers are classified as ancient.

(a) Two computers are chosen at random.

The above situation can be represented through Binomial distribution;

$P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 2 computers

r = number of success = both 2

p = probability of success which in our question is % of computers

that are classified as ancient, i.e; 0.94

LET X = Number of computers that are classified as ancient

So, it means X ~ $Binom(n=2, p=0.94)$

Now, Probability that both computers are ancient is given by = P(X = 2)

P(X = 2) = $\binom{2}{2}\times 0.94^{2} \times (1-0.94)^{2-2}$

= $1 \times 0.94^{2} \times 1$

= 0.8836

(b) Eight computers are chosen at random.

The above situation can be represented through Binomial distribution;

$P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 8 computers

r = number of success = all 8

p = probability of success which in our question is % of computers

that are classified as ancient, i.e; 0.94

LET X = Number of computers that are classified as ancient

So, it means X ~ $Binom(n=8, p=0.94)$

Now, Probability that all eight computers are ancient is given by = P(X = 8)

P(X = 8) = $\binom{8}{8}\times 0.94^{8} \times (1-0.94)^{8-8}$

= $1 \times 0.94^{8} \times 1$

= 0.6096

The above situation can be represented through Binomial distribution;

$P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 8 computers

r = number of success = at least one

p = probability of success which is now the % of computers

that are classified as cutting dash edge, i.e; p = (1 - 0.94) = 0.06

LET X = Number of computers classified as cutting dash edge

So, it means X ~ $Binom(n=8, p=0.06)$

Now, Probability that at least one of eight randomly selected computers is cutting dash edge is given by = P(X $\geq$ 1)

P(X $\geq$ 1) = 1 - P(X = 0)

= $1 - \binom{8}{0}\times 0.06^{0} \times (1-0.06)^{8-0}$

= $1 - [1 \times 1 \times 0.94^{8}]$

= 1 - $0.94^{8}$ = 0.3904

Here, the probability that at least one of eight randomly selected computers is cutting dash edge is 0.3904 or 39.04%.

For any event to be unusual it's probability is very less such that of less than 5%. Since here the probability is 39.04% which is way higher than 5%.

So, it is not unusual that at least one of eight randomly selected computers is cutting dash edge.

7 0

2 years ago

What is the y-intercept of a line that has a slope of 1/4 and passes through point (8,3)

exis [7]

Answer:

Step-by-step explanation:

Y-y1=m(x-x1)

Y- 3= 1/4(x- 8)

Y-3= 1/4x- 2

Y= 1/4x+1

Y intersept= 1

6 0

3 years ago