Usa ecuaciones simultáneas para resolver lo siguiente:
2x + 5y = 5

4x = 3y = 3

X =
Y =

The largest integer whose square has exactly digits when written in base is 28 in base 9 .

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z .

Largest base 9 three digit number = 888  

And it can be represented as 728 in base 10, largest square is 26^2       26 that is 28 in base 9.

Therefore the largest integer whose square has exactly digits when written in base is 28 in base 9 .

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20867

Final answer obtained is 2/3

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio. For instance, the geometric progression 2, 6, 18, 54, etc. has a common ratio of 3. Similar to that, the geometric series 10, 5, 2.5, 1.25,... has a common ratio of 1/2.

Powers [tex]r^{k}[/tex] of a given non-zero number r, like [tex]2^{k}[/tex] and [tex]3^{k}[/tex], are examples of a geometric sequence. A geometric sequence's basic structure is

[tex]ar,ar^{2},ar^{3}.ar^{4},-----[/tex]

where a is not equal to 0 is a scale factor that is equal to the initial value of the series and r is not equal to 0 is the common ratio.

A series is a sum, whereas a progression is a sequence. This is the difference between the two.

∑[tex]_{i=0}^{n}[/tex] [tex]ar^{i}=\frac{a(1+r^{n+1})}{1-r}[/tex]

We see that n= 99, r= -1/2, a=1

∑[tex]_{i=0}^{99}[/tex] [tex](\frac{-1}{2}) i=[/tex] [tex]\frac{1-(\frac{-1}{2})^{99+1} }{1-\frac{1}{2} }=\frac{1-(\frac{-1}{2})^{100} }{1+\frac{1}{2} }=\frac{1-\frac{1}{2}^{100} }{\frac{3}{2} }[/tex]

[tex]=\frac{\frac{2^{100}}{2^{100}} -\frac{1}{2^{100}} }{\frac{3}{2} } =\frac{2*(2^{100}-1)}{3*2^{100}}[/tex]

[tex]\frac{2*(2^{100}-1)}{3*2^{100}}[/tex]

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Answer:

B

it is the right equation

The evaluation of the expression gives -295/24. The correct option is the fourth option-   negative 295 over 24 (-295/24)

From the question, we are to evaluate the given expression

The given expression is,

7 3/8 × -1 2/3

To solve the expression, we will covert the fractions from mixed to improper fractions

7 3/8 × -1 2/3

59/8 × - 5/3

Multiplying, we get

-295/24

Hence, the evaluation of the expression gives -295/24. The correct option is the fourth option-   negative 295 over 24 (-295/24)

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Answer: 1.42 x 10^1

Step-by-step explanation:

Answer: 1.42x10

Step-by-step explanation:

Answer:niamh gets 15 and jack gets 35

Step-by-step explanation:

think of the raito 3:7 as 3x:7x. then we can do: 3x + 7x = 50, which means 10x = 50. then we can find x by dividing 50 by 10, so x is 5. then we can find 3x, whihc is 3x5 = 15. then find 7x, so 7x5 = 35. so niamh gets 15 and jack gets 35

Answer:

(a) 75 minutes

(b) 50 minutes

Answer:

y = [tex]\frac{1}{4}[/tex] x + 6

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 )

given

4x + y = 7 ( subtract 4x from both sides )

y = - 4x + 7 ← in slope- intercept form

with slope m = - 4

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex] , then

y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute )- 4, 5 ) into the partial equation

5 = - 1 + c ⇒ c = 5 + 1 = 6

y = [tex]\frac{1}{4}[/tex] x + 6 ← equation of perpendicular line

This rate in lb/s is 833.33 lb/s if a large dump truck can move 1,500 tons/h of gravel from one point to another on a work site.

The term "ton-hour" refers to a cooling service that provides 12,000 BTU of cooling, measured as a function of the amount of chilled water that flows through the Energy Transfer Station, the temperature difference between the chilled water at the Delivery Point, and the Return Point and the total BTU gain that occurs.

The imperial and US customary systems of measurement both utilize the unit of mass known as the pound (symbol: lb). The precise weight of the international avoirdupois pound, or today's standard pound, is 0.45359237 kilos. 16 avoirdupois ounces make up an avoirdupois pound.

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Answer:-41/4 try that

Answer:

1. 104F

2. 95F

Step-by-step explanation:

Formula for Celsius to Fahrenheit is

[tex](C*1.8) + 32 = F[/tex]

Question one:

40 times 1.8 = 72

72+32 = 104 Fahrenheit

Question two:

35 times 1.8 = 63

63+32 = 95 Fahrenheit

The measure of angle 2 and angle3 are 133 ad 47 degrees respectively

From the given diagram, the measure of angle 1 and 2 are congruent. (vertical angles)

Given he following parameters

m<1 = 133 degrees

Since m<1 = m<2, hence m<2 = 133 degrees

Also;

m<2 + m<3 = 180

133 + m<3 = 180

m<3 = 180 - 133

m<3 = 47 degrees

Hence the measure of angle 2 and angle3 are 133 ad 47 degrees respectively

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The eight machines can be arranged in the three available spaces in 336 ways.

Here we have 8 screw machines with 3 spaces. To find the different way, permutation will help.

Different ways = 8 P 3

= 8! / (8! -3!)

= 8! / 5!

= 8 x 7 x 6 x 5! / 5!

= 6x7x8 = 336.

Therefore, in 336 different ways the eight machines be arranged in the three spaces available.

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Answer:      10/3

Step-by-step explanation:

multiply the denominator, "3", by the mixed number "3", then add the numerator "1". So 3*3+1=10/3 (the denominator stays the same)

Answer: [tex]\frac{10}3}[/tex]

The solution to the system of equation is (-1, -6)

Given the system of equations

2x - 3y = 16

5x - 3y = 13

Subtract to have:

2x-5x = 16 - 13

-3x = 3

x = -3/3

x = -1

Substitute x = -1 into 1 to have:

2(-1) - 3y = 16

-2 - 3y = 16

-3y = 16 + 2

-3y = 18

y = -6

Hence the solution to the system of equation is (-1, -6)

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Answer:

Hello yeily, I think and believe they are all rational..

Step-by-step explanation:

Hope it helps <=/

Answer:

The first rectangle is 3x² - 6x + 13 more square feet then the second rectangle

Step-by-step explanation:

A rule for subtracting polynomials

Steps

At the end of the expression is (7x²- 4x + 12) + -4x² - 2x + 1

At this point you combine like terms like you do with adding polynomials so ( 7x² + (-4x²) is 3x², (-4x) + (-2x) is (-6x), and 12 + 1 is 13) so the final answer would be 3x²-6x+13

A component of the interval is x (π/4, 5π/4) when 5 sin(x) > 5 cos(x).

A relation in mathematics that compares two numbers or even other mathematical expressions in an unequal way is known as an inequality. When comparing two numbers on a number line, it is most frequently used to compare their sizes.

5 sin(x) > 5 cos(x)

To removing constant we divide both the side by 5:

5sin(x) > 5 cos(x)

sin(x) >  cos(x)

sin x > cos x;

sin x = cos x; tan x = 1; x = π/4 or x = 5π/4

sin x > cos x for x ∈ (π/4, 5π/4)

A component of the interval is x (π/4, 5π/4) when 5 sin(x) > 5 cos(x).

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I understand that the question you are looking for is:

Find all values of x in the interval [0, 2] that satisfy the inequality. (Enter your answer using interval notation.) 5 sin(x) > 5 cos(x)

GIVEN THE FOLLOWING:

Mario's car rate consumption. R = 24.5mile/gallon

Distance covered each day, D = 32.3 miles

Cost of gas $2.89/gallon

REQUIRED: (a) To calculate how much he spends on gas each week.

We proceed as follow:

Mario uses 1 gallon of gas for every 24.5 miles.

For 32.3 miles, he will use [tex]\frac{32.3}{24.5} ~gallons~ of gas=\frac{325}{245} ~gallons[/tex]

Now, a gallon of gas costs $2.89

[tex]\frac{325}{245}~gallons~will~cost =?[/tex]

[tex]\frac{325}{245} ~*2.89=3.81[/tex]

$3.81 is how much he spends each workday.

There are 5 working days in a week.

Therefore, for a week, he spends:

[tex]3.81~*~5~=19.05[/tex]

therefore, for each work week, he spends $19.05 on gas.

(B) To calculate how many miles he can drive with $15.00 worth of gas

We proceed thus:

A gallon of gas costs $2.89.

$15.00 will amount to:

$15.00/$2.89 = 5.19 gallons

Recall that Mario uses 1 gallon of gas for every 24.5 miles.

Therefore, 5.19 gallons will be used for:

[tex]5.19~*24.5=127.155 ~miles[/tex]

≈ 127 miles

Therefore, with gas worth $15.00, Mario will cover a distance of 127 miles

AshTheNeko

The total cost for going to the concert = $90.

The loss of value or benefit that'd result from engaging in a particular activity option in comparison to engaging in such an alternative activity which offers a higher come back on value or benefit is referred to as opportunity cost. The value of the best alternative picked during the decision-making process is provided.

We can select the best option out of all the options available with the aid of the idea of opportunity cost. It helps us use all of our resources as skillfully and productively as possible in order to maximize our financial gains.

For her part-time job, Karen receives a $10 hourly wage. The cost of the concert ticket after the discount is $50, so she decided to go.

It will cost money to take four hours off work. $10 x 4

                                                                           =$40

Opportunity costs of going to the concert = $50 + $40

                                                                      = $90

It is evident that the opportunity cost will be $90.

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I understand that the question you are looking for is:

Karen earn $10 per hour. she wants to go to a concert on Saturday and the price of the ticket is $75, but her friend sold her a ticket for $50. if Karen had to take 4 hours off of work to attend the concert ,What was her opportunity cost of attending the concert?

a.$40

b.$50

c.$75

d.$90

The length and width of rectangle is 160 feet and 100 feet.

The perimeter of the rectangle is calculated by the formula -

Perimeter = 2 × (length + width)

As per the given information, length = (60 + width)

Keep the values in formula to find the breadth of rectangle.

520 = 2 × (60 + width + width)

520 = 2 × (60 + 2 × width)

(60 + 2 × width) = [tex]\frac{520}{2}[/tex]

(60 + 2 × width) = 260

2 × width = 260 - 60

2 × width = 200

Width = [tex]\frac{200}{2}[/tex]

Width = 100 feet

Keep the value in formula to find the length of perimeter

520 =  2 × (length + width)

Length + 100 = [tex]\frac{520}{2}[/tex]

Length = 260 - 100

Length =  160 feet

Hence, the length and width of rectangle is 160 feet and 100 feet.

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The amount of silver that  should be added is 48% . A jeweler is said to have 5 rings that weigh 12 g apiece and are composed of an alloy of 20% silver and 80% gold.

What are linear equations?

An equation between two variables that, when plotted on a graph, produces a straight line.

The material will weigh 12 × 5 = 60 grams after melting all 5 rings.

The alloy's 20% silver and 80% gold content have been disclosed to us. Let's further say that the melted material receives an additional x grams of silver, resulting in a composition of 64% gold and 36% silver.

Thus, we can construct the following equation:

Amount of gold before = Amount of gold after mixing

So the equation we get

80% of 60 grams =64% of (X + 60) gram

0.80 × 60 = 0.64 (x + 60)

48 = 0.64x + 38.4

0.64x = 9.6

x = 9.6/0.64

x = 15

So

Amount of silver that needed to be added

= 0.64(15 + 60)

= 0.64(75)

= 48%

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Numbers in the first 20 rows of pascal's triangle are 210

Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra.

We have been given that:

Numbers of rows = 20

Pascal's triangle formula

1 + 2 + 3 + ….+ 19 + 20  = n (n + 1) / 2  

n=20

 (20)×(21)/ 2  = 210

Pascal's triangle patterns is its symmetry. Observe that in any row, if we read the consecutive numbers from the left, we will obtain the same as if we read them from the right.

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The cost of each spiral notebook is $3 and the cost of each book cover is $2

Given that Alexis and her sister bought school supplies. Alexis bought 5 spiral notebooks and 6 book covers for $27. Her sister bought 4 spiral notebooks and 2 book covers for $16 and asked to find out the cost of each spiral notebook and each book cover.

Let's assume spiral notebooks as "x"  and book covers as "y".

As a result, two linear equations in two variables will be formed.

⇒5x+6y=$27; Let's assume this equation as A

⇒4x+2y=$16; Let's assume this equation as B

Multiply equation B with 3

⇒12x+6y=$48; Let's assume this equation as C

Equation c- Equation A

⇒$48-$27=7x

⇒7x=$21

⇒x==$3

The cost of the spiral notebook is $3

From equation A

⇒5($3)+6y=$27

⇒$15+6y=$27

⇒6y=$12

⇒y=$2

The cost of the book cover is $2

Therefore,The cost of each spiral notebook is $3 and the cost of each book cover is $2

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The area of the parallelogram ABCD with the vertices is 40 square units

The vertices are given as

(2, 3), B (7, 3), C (8, -5), and D (3, -5)

From the graph, we have the following dimensions

Base = 5 units i.e. distance AB

Height = 8 units i.e. the distance between the parallel sides

The area of the parallelogram is then calculated as

Area = Base * Height

So, we have

Area = 5 * 8

Evaluate

Area = 40

Hence, the area of the parallelogram ABCD with the vertices is 40 square units

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Step-by-step explanation:

In the equation y = mx + b for a straight line, the number m is called the slope of the line. In the equation y = mx + b for a straight line, the. number b is called the y-intercept of the line.

The age of Mrs. Lee when her 2 children's combined age is [tex]\frac{5}{11}[/tex] of her age will be [tex]44[/tex] yrs. old

As per the question statement, Mrs. Lee, who is 40, has a son who is twice as old as her daughter. Mrs. Lee will be thrice her son's age when her daughter is 12-year old. We are asked that how old Mrs Lee be when her two children's combined ages are 5/11 of her own age.

This question is a classic example of forming and solving linear equations.

When Mrs. Lee was 40, her son was twice her daughter's age.

Let d = her daughter's age when Mrs. Lee was 40.

Then her son was 2d yrs. old when Mrs. Lee was 40.

When her daughter is 12, Mrs. Lee will be three times her son's age.

This means [tex](12 - d)[/tex] years have passed since Mrs. Lee was 40.

So, if her daughter was 12 at this time, that means her son was [tex]2d + (12 - d)[/tex]

And, Mrs. Lee's age at this time was [tex]40 + (12 - d)[/tex]

Mrs Lee was thrice her son's age at this time:

[tex]40 + (12 - d) = 3(2d + 12 - d))[/tex]

[tex]40+12-d=6d+36-3d\\4d=16\\d=4[/tex]

So, Mrs. Lee's age when her daughter was 12 is [tex]40 + 12 - 4 = 48[/tex] yrs. old

Her daughter was 8 yrs. old 4 years earlier.

Thus, Mrs Lee's age when her daughter was 20 was [tex]48 - 4= 44[/tex] years old.

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Blue whale is 15 times longer than otter.

To find how many times the blue whale is  longer than the otter, we will perform division. We will divide the length of blue whale by length of otter, which we will give us the desired result.

Now, performing calculation as per the above statements -

Number of times longer length = [tex]\frac{3*10^{4} }{2*10^{3} }[/tex]

Performing division of numbers. Also, as we know, on division the exponents are subtracted. Hence, subtracting the exponents to get the desired result.

Number of times longer length = 1.5*[tex]10^{4-3}[/tex]

The result will be -

Number of times longer length = 1.5*10

Performing multiplication -

Number of times longer length = 15

Hence, we get that blue whale is 15 times longer than otter.

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