Resolva as expressões a seguir e registre os resultados na forma fracionária e na forma decimal

The ordered pair of solutions is (11/5, 2).

What is the linear equations?

A linear equation is a mathematical equation that represents a straight line when graphed on a coordinate plane. It has the form of ax + b = y, where a and b are constants and x and y are variables. The coefficient "a" determines the slope of the line, and the constant "b" determines the y-intercept.

The elimination method is a method of solving a system of linear equations by adding or subtracting the equations to eliminate one of the variables.

Here is the solution for the system of equations 2x - 2y = 2 and 5x + 2y = 12 using the elimination method:

Multiply the first equation by 5: 10x - 10y = 10

Add the two equations: 15x - 8y = 22

Solve for x by dividing both sides of the equation by 15: x = 22/15 = 11/5

Substitute the value of x back into one of the original equations to solve for y:

2x - 2y = 2

2(11/5) - 2y = 2

22/5 - 2y = 2

22/5 - 2y = 2

22/5 = 2 + 2y

22/5 - 2 = 2y

20/5 = 2y

10/5 = y

The solution to the system of equations is (x, y) = (11/5, 10/5) = (11/5, 2).

So, the ordered pair of solutions is (11/5, 2).

To learn more about linear equations, Visit

https://brainly.com/question/2030026

#SPJ1

The ordered pair of solutions is written in the format (x, y) is (11/5, 2) .

When plotted on a coordinate plane, a linear equation is a mathematical equation that resembles a straight line. It takes the form axe + b = y, with a and b acting as constants and x and y as variables. The line's slope is determined by the coefficient "a," whereas the y-intercept is determined by the constant "b."

A system of linear equations can be solved using the elimination approach by adding or removing equations to get rid of one of the variables.

Here is the elimination technique solution for the system of equations 2x - 2y = 2 and 5x + 2y = 12:

The first equation is multiplied by 5: 10x - 10y = 10.

Equational sum: 15x - 8y = 22

Divide both sides of the equation by 15 to find the value of x: x = 22/15 = 11/5

To find the value of y, add the value of x back into one of the initial equations:

2x - 2y = 2

2(11/5) - 2y = 2

22/5 - 2y = 2

22/5 - 2y = 2

22/5 = 2 + 2y

Simplify the equation

22/5 - 2 = 2y

20/5 = 2y

10/5 = y

The system of equations has a solution of (x, y) = (11/5, 10/5) = (11/5, 2).

The pair of answers that are in order is (11/5, 2).

To learn more about system of equations refer to:

https://brainly.com/question/13729904

#SPJ1

Answer:

1) 9

2) 27

3) Read explanation below!

Step-by-step explanation:

1) Use the Pythagorean theorem to find AD. Show your working

To find '?' we first have to expand the indices...

Now work out '?'

2) Find AC. Show your working

We have found out that AD is 9 and to find AC we have to add 18!

3) Is ΔABC a right triangle? Explain

We can that ΔABC is not a right angle as none of the angles in the triangle are 90°!  If it was a right angled triangle we would see the ∟sign on one of the angles. Even though there are two of those in the middle it does not count as the question is asking about ΔABC!!

Have a lovely day :)

The temperature at noon is equal to -0.1°C.

Mathematically, the standard form or slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Note: Let x represent the time.

Next, we would write an equation that models the situation based on the rate of change (slope) and y-intercept (initial value) as follows;

y = mx + c

y = -0.8x - 2.5

y = -0.8(3) - 2.5

y = -2.4 - 2.5

y = -0.1°C

Read more on rate of change here: brainly.com/question/18569635

#SPJ1

The slope-intercept form of the function described by this table is y = x + 1

From the question, we have the following parameters that can be used in our computation:

x   y

0   1

From the above table of values, we can see that

The difference between the x and the y value is 1

Mathematicallly, this can be represeted as

y - x = 1

Add x to both sides

y = x + 1

The above equation is in the slope intercept form, y = mx + c

Hence, the equation is y = x + 1

Read more about linear equation at

https://brainly.com/question/2030026

#SPJ1

Answer:

they started trip at 10:00 am

Step-by-step explanation:

Let's call the starting time "S".

The arrival time is 11:37AM,

difference in time after break to park arrived : 11:37 am - 10:48 am = 49 minutes

remaining time : 97-49= 48 minutes

starting time= 10:48 am -48 minutes = 10:00 am

The area for each part of the figure is given as follows:

The area of a right triangle is given by half the multiplication of it's sides.

Triangle A has the side lengths given as follows:

Hence the area is given as follows:

A = 0.5 x 4 x 10 = 20 units squared.

Triangle D is has the side lengths given as follows:

Hence the area is given as follows:

D = 0.5 x 2 x 6 = 6 units squared.

The total area is given by the sum of the areas of each part of the figure, hence:

20 + 2 + 4 + 6 = 32 units squared.

More can be learned about areas at https://brainly.com/question/21735282

#SPJ1

Answer:pls brainly award

Step-by-step explanation:

The 330 feet of rope is equivalent to 330/3 = 110 yards.

The cost of the rope at SportsStuff.com is 110 * $5.50 = $605.

The cost of the rope at OutdoorHaven.com is 110 * $5.20 + $12.25 = $604.45.

Therefore, the cheapest price you can pay is $604.45.

Answer:

The number with the highest sum of prime factors is 27, as it has only two prime factors: 3 and 3. The sum of its prime factors is 6, so if you choose 27, you can move 6 spaces. The number 25 has two prime factors as well, but only 5 + 5 = 10. 26 is not a prime number, so it wouldn't be the best choice. So, if you want to move as many spaces as possible, you should choose 27.

The original amount of water is 15 cups.

The change in David's water intake is 3 cups.

And, The percent change is 20%. This is a percent decrease.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

David is tracking the amount of water he drinks each day.

Here, On Thursday, he drinks 15 cups of water.

And, On Friday, he drinks 12 cups of water.

Hence, We get;

The original amount of water = 15 cups.

And, The change in David's water intake = 15 - 12

                                                               = 3 cups

And, The percent change in his water intake is,

⇒ Percent = 3 / 15 × 100

⇒ Percent = 20%

Thus, The original amount of water is 15 cups.

The change in David's water intake is 3 cups.

And, The percent change is 20%. This is a percent decrease.

Learn more about the percent visit:

https://brainly.com/question/24877689

#SPJ1

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is given as follows:

0.5874 = 58.74%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 17.2, \sigma = 2.5, n = 40, s = \frac{2.5}{\sqrt{40}} = 0.3953[/tex]

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is the p-value of Z when X = 18.1 subtracted by the p-value of Z when X = 17.1, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (18.1 - 17.2)/0.3953

Z = 2.28

Z = 2.28 has a p-value of 0.9887.

Z = (17.1 - 17.2)/0.3953

Z = -0.25

Z = -0.25 has a p-value of 0.4013.

Hence:

0.9887 - 0.4013 = 0.5874 = 58.74%.

More can be learned about the normal distribution at https://brainly.com/question/25800303

#SPJ1

Factored form of -3n⁶ +12n⁴ - 6n² would be, (n² + 1)(-3n² + 6).

What is factorization?

The process of writing a number or any mathematical object as a product of several factors, usually smaller or simpler objects of the same kind, is known as factorization or factoring.

In mathematics, factorization is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number.

The factored form of -3n^6 +12n^4 - 6n² is:

-3n² (n⁴ - 2) + 6n² (1 - n²)

= -3n² (n⁴ - 2) + 6n² - 6n⁴

= -3n² (n⁴ - 2 + 2n²) + 6n²

= -3n² (n² + 1)² + 6n²

= (n² + 1)(-3n² + 6).

So, Factored form of -3n⁶ +12n⁴ - 6n² would be, (n² + 1)(-3n² + 6).

To know more about factorization visit,

https://brainly.com/question/25829061

#SPJ1

Answer:

The length of the train can be calculated using the formula:

Length of the train = Speed x Time / 2

Where,

Speed = 60 km/hr = 60 x 1000/60 = 1000 m/min

Time = 9 sec = 9 / 60 min = 0.15 min

So,

Length of the train = 1000 x 0.15 / 2 = 75 m

Therefore, the length of the train is 75 meters.

Answer:

Length of the train shold be 75m

Step-by-step explanation:

The statements that are true are:

Clayton could use the relationship (x, y) right-arrow (y, x) to find the points of the image.

Clayton could negate both the x and y values in the points to find the points of the image.

C’ will move because all points move in a reflection.

The image and the pre-image will be congruent triangles.

The image and pre-image will not have the same orientation because reflections flip figures.

Options A, B, D, E, and F.

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

Clayton could use the relationship (x, y) → (y, x) to find the points of the image.

This is the y = x reflection rule.

This is true.

Clayton could negate both the x and y values in the points to find the points of the image.

Reflection of (x, y) along the x-axis and y-axis consecutively will give us

(-x, -y).

This is true.

C’ will remain in the same location as C because it is on the line of reflection.

This is not true.

C’ will move because all points move in a reflection.

This is true.

The image and the pre-image will be congruent triangles.

This is true.

The image and pre-image will not have the same orientation because reflections flip figures.

This is true.

Thus,

All statements are true except the statement:

C’ will remain in the same location as C because it is on the line of reflection.

Learn more about reflections here:

https://brainly.com/question/12463306

#SPJ1

This is a problem finding the slope of a line at some point "a"

It accomplishes this by doing an average rate of change formula over an area approaching 0.

We must know the format of this type of equation.

See first image.

The variables in this example don't match up.

Let the function input be x, and the limit being a --> 0

a = 2

f(x) = x^5

Answer:

[tex]\displaystyle{f(x)=x^4 \ \: \text{and} \ \: a =2}[/tex]

Step-by-step explanation:

The first principal of derivative:

[tex]\displaystyle{f'(x) = \lim_{h\to 0} \dfrac{f(x+h)-f(x)}{h}}[/tex]

Since the given problem represents f'(a), meaning:

[tex]\displaystyle{f'(a) = \lim_{h\to 0} \dfrac{f(a+h)-f(a)}{h}}[/tex]

If we compare:

[tex]\displaystyle{f'(a) = \lim_{h\to 0} \dfrac{f(a+h)-f(a)}{h}}[/tex]

and

[tex]\displaystyle{ \lim_{h\to 0} \dfrac{(2+h)^4-16}{h}}[/tex]

which can be rewriten as:
[tex]\displaystyle{f'(a) = \lim_{h\to 0} \dfrac{(2+h)^4-2^4}{h}}[/tex]

We can conclude by comparing that:

This would mean that:

[tex]\displaystyle{f(x)=x^4}[/tex]

Therefore:

[tex]\displaystyle{f(x)=x^4 \ \: \text{and} \ \: a =2}[/tex]

The amount that will be in the account in 25 years is $16,282.298.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

Given that,

Principal amount, P = $3000

Rate of interest, r = 7% = 0.07

Number of years, n = 25

The final amount in a compound interest where the interest is compounded annually is,

A = P (1 + r)ⁿ

Substituting the given values,

A = 3000 (1 + 0.07)²⁵

   = 3000 (1.07)²⁵

   = 16,282.298

Hence the final amount after 25 years is $16,282.298.

Learn more about Compound Interest here :

https://brainly.com/question/29335425

#SPJ1

Therefore , the solution of the given problem of probability comes out to be likelihood that the full batch will be approved is therefore 0.832.

Probability theory is an area of mathematics that focuses on calculating the probability that a claim is accurate or that a particular occurrence will occur. Chance can be represented by any number range between 0 and 1, where 1 often denotes certainty and 0 typically denotes possibility. A probability diagram shows the possibility that a specific event will occur. The numerals 0 and 1, fractions with a ranging of 0% to 100%, or a few more characters can all be used to indicate probabilities.

Here,

Given that we've done it

Amount of CDs: 2100

50 faulty CDs total.

If every component of the sample is acceptable, the complete batch is accepted.

Therefore, we shall apply the "Binomial Theorem"

If there is no flaw, let p be the likelihood of success.

So, => p = 2100 - 50 / 2100

=> p = 2050/2100

=> p =0.97

q is the likelihood of a failure, or defect.

So,

=> q = 50/2100

=> q = 0.02

hence, the number of CDs chosen is 6.

Consequently, it is => P(X=6) = (0.97)6 = 0.832.

The likelihood that the full batch will be approved is therefore 0.832.

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ1

Answer: 11

Step-by-step explanation:

3x2=6

6+5=11

a. The perimeter of the figure is:  61.4 cm

b. The area of the figure is: 160.69 cm²

The figure consists of two semicircles which makes one full circle and a rectangle. Therefore:

a. The perimeter of the given figure = circumference of a circle + 2w.

d = 8.6 cm

Circumference of the circle = 2 * pi * r = 2 * 3.14 * (8.6/2) = 27.00 cm

Perimeter = 27.00 + 2(17.2)

Perimeter = 61.4 cm

b. Area = area of circle + area of rectangle = 2πr + (length * width)

r = 7.9/2 = 3.95 cm

length = w = 17.2 cm

width = d = 7.9 cm

Area = 2*3.14*3.95 + (17.2*7.9) = 160.69 cm²

Learn more about the area and perimeter of a figure on:

https://brainly.com/question/443376

#SPJ1

The equity of Company X's is $13,291.

The difference between assets and liabilities is the equity.

The equity is the portion of assets belonging to the owners.

Initial investment = $12,000

Retained Earnings = $1,291

Long-term loan = $9,982 ($12,000 - $2,018)

Land and building = $8,878

Equipment = $4,230

Cash $8,250

Inventory = $1,225

Accounts Receivable = $675

Accounts Payable = $485

Short-term loan = $500

Company X

As of current date

Cash                                 $8,250

Inventory                            1,225

Accounts Receivable          675  $10,150

Long-term investment  $1,000

Land and building          8,878

Equipment                      4,230    $14,108

Total Assets                               $24,258

Accounts Payable         $485

Short-term loan               500       $985

Long-term loan                         $9,982

Total liabilities                         $10,967

Initial capital           $12,000

Retained earnings       1,291  $13,291

Total liabilities and equity   $24,258

Learn more about the equity at https://brainly.com/question/14032844

#SPJ1

Determine Company X's equity?

The number of sophomores in the class is 35.

The number of Juniors in the class is 19.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of sophomores = x + 16

Number of Juniors = x

Now,

Number of students in the class = 54

This means,

x + x + 16 = 54

2x + 16 = 54

2x = 54 - 16

2x = 38

x = 19

Thus,

Number of sophomores = 19 + 16 = 35

Number of Juniors = 19

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The required amount invested in accounts with 8% and 12% are $1470 and $1820 respectively.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Lydia has money in two savings accounts one rate is 8% and the other is 12%  and the total interest is $336. Let the amount invest in accounts be x and y respectively.
According to the question,
0.08x + 0.12y = 336 - - - - - -(1)

Again,
she has $350 more in 12% account
y = x + 350 - - - - - -(2)

Put y in equation 1,
0.08x + 0.12[x + 350] =336
0.08x + 0.12x + 42 = 336
0.20x = 336 - 42
x = 294/0.20
x = $1470

Now

y = 1470 + 350
y = $1820

Learn more about models here:
https://brainly.com/question/22591166
#SPJ1

Answer:

b

Step-by-step explanation:

:)

Answer:

0.2

Step-by-step explanation:

as 0.2 is greater than 1

Answer:

0.2

Step-by-step explanation:

The diagram = 0.1

0.1 < 0.2

The value of cosα is 2/5.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Given that, tanα= -2/5 and α is quadrant IV.

We know that, tan(−θ) = − tan(θ)

α= 2/5

As we know cos(−θ) = cos(θ)

cosα =2/5

Therefore, the value of cosα is 2/5.

Learn more about the trigonometric ratios here:

brainly.com/question/25122825.

#SPJ1

Answer:

8

Step-by-step explanation:

f(4) = 3(4) - 4

f(4) = 12 - 4

f(4) = 8

After 3 3/5 weeks, they will have the same number of pictures.

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, Yuki and Roman are photographers for the yearbook. Yuki starts with 20 photos. She then takes 60 photos each week. Roman starts with 110 photos. He then takes 35 photos each week.

Let "w" the number of weeks they collected the pictures

For Yuki,

The total picture he has after 0 weeks = is 20

The total picture he has after 1 week = 20 + 60

The total picture he has after 2 weeks = 20 + 60*2

The total picture he has after w weeks = 20 + 60*w

For Roman,

The total picture he has after 0 weeks = is 110

The total picture he has after 1 week = 110 + 35

The total picture he has after 2 weeks =110 + 35*2

The total picture he has after w weeks = 110 + 35*w

To calculate the number of weeks when they have equals pictures:

20 + 60*w = 110 + 35*w

25w = 90

w = 3 3/5

Therefore, After 3 3/5 weeks, they will have the same number of pictures.

Learn more about proportionalities here:

https://brainly.com/question/3254974

#SPJ1

Answer:

[tex]\text{Choice C: }\boxed{b\le 1 \dfrac{7}{10}\\\\}[/tex]

Step-by-step explanation:

We are given inequality:

[tex]\dfrac{7}{2}\ge \:b\:+\:\dfrac{9}{5}[/tex]