how much more is 1/2 than 1/3

As we can conclude from the graphical method that this system has no common intersection point they have no solution.

Graphical solutions of a system of equations are way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Given system of equations are x + 2y = 4, 3x + 6y = 6, 3x - y = 5 and

6x - 2y = 10.

The graphical representation of these equations are attached in the image below.

As we can observe , 3x - y = 5(green line)  and 6x - 2y = 10(purple line) are coinciding with each other so they have infinite no. of solutions.

x + 2y = 4(red) and 3x + 6y = 6(blue) are parallel to each other and hence have no solution.

And in together all these 4 lines have no common intersection point so they have no solution.

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Answer:

m = - 3

Step-by-step explanation:

since the line passes through (1, 3 ) then the coordinates of the point make the equation true.

substitute x = 1, y = 3 into the equation and solve for m

3 = m + 6 ( subtract 6 from both sides )

- 3 = m

The constant of proportionality that relates the cost in 72 dollars as y, to the number of gallons of unleaded gasoline in 22.5 gallons of unleaded gasoline as x is $3.20 per gallon of unleaded gasoline.

The constant of proportionality is the ratio of the so-called proportional relationship that relates two given values ​​to each other.

Other names for the constant of proportionality are constant ratio, constant rate, unit rate, variable constant, and even rate of change.

The relationship between two variables, X and Y, is directly proportional if it can be expressed in terms of Y/X = k or Y = Xk.

y/x = k

k is the constant of proportionality.

Given that:

y = $72 and x = 22.5 gallons.

So, the value of the constant of proportionality (k) = 72/22.5

=> k = 720/225

Dividing both by the numerator and denominator by 45. We get,

=> k = 16/5

The value of the constant of proportionality (k) = $3.20 per gallon of unleaded gasoline.

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Answer:

  m∠6 = 61°

Step-by-step explanation:

Given a transversal crossing parallel lines AB and CD, you want the measure of angle 6 given that angle 2 is 61°.

Where a transversal crosses parallel lines, corresponding angles and vertical angles are congruent. This has the effect of making all acute angles congruent, and all obtuse angles congruent.

Acute angle 6 is congruent to acute angle 2, which measures 61°. (They are "corresponding" angles.)

  m∠6 = 61°

The measurement of m∠1 and m∠3 is 52° when a is parallel to b.

According to the question,

We have the following information:

The line a is parallel to b and they are being cut a line m.

m∠6 = 128°

We know that when two parallel lines are cut by another line then the sum of consecutive interior angles is 180°. And we also know that vertically opposite angles are equal.

m∠1 and m∠3 are vertically opposite angles.

m∠3 and m∠6 are consecutive interior angles.

∠3+∠6 = 180°

∠3 = 180-128

∠3 = 52°

So, we have:

∠1 = ∠3 = 52°

Hence, the measurement of m∠1 and m∠3 is 52° when a is parallel to b.

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Answer:

x<2

Step-by-step explanation:

8+3x<14

3x<6

3x/3<6/3

x<2

To write the point-slope form of the line that passes through (1, -5) and is parallel to a line with a slope of 1.

A perpendicular line will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So if we have a slope of 1 or 1/1. our perpendicular line needs a slope of -1.

y - y1 = m(x - x1)

slope(m) = -1

(1,-5)...x1 = 1 and y1 = -5

now we sub...pay close attention to your signs

y - (-5) = -1(x - 1)....not done yet

y + 5 = -1(x - 1)...or it can also be written as : y + 5 = - (x - 1)

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The interest on principle $775 over eight year at rate 1.47% is  $91.14

Simple interest is a interest which is only based on principle amount, it does not imply on yearly interest.

The given principle, p = $775 ,

Rate r = 1.47 %,

and Time = 8 year.

To find interest I, Use formula,

I=(p × r × t)/100,

I=775 ×1.47 ×8/100,

I = $91.14

So the interest is I = $91.14

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a) The distance travelled on the cycle in the first 14 seconds is; 96 m

b) The acceleration in the first 4 seconds is; 2 m/s²

The velocity time graph for a cycle is as attached.

The distance covered will be the area under the curve.

Formula for area of trapezium is;

A = (1/2)(sum of parallel sides) * height

Area for 0 to 14 sec is a trapezium formed with parallel sides as 14 and  10 while distance between them is 8 is solved as;

Area = (1/2)(14 + 10) * 8  

Area = 24 * 4  = 96  

Thus;

Distance covered = 96 m

Distance travelled on the cycle in the first 14 seconds is 96 m.

Therefore, the acceleration in first 4 seconds = (8 - 0)/(4 - 0)

= 8/4 = 2 m/s²

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Kate bakes 20-inch by 18-inch pan of cornbread and divide it into 2 in x 2 in pieces. The number of pieces is 90.

The problem can be solved using associative property in multiplication and division. That is the factors can re-group and it will not change the product.

The given problem can be translated into an algebraic expression:

(20 x 18) : (2 x 2)

Let

length of cornbread pan = 20

wide of cornbread pan = 18

To cut the cornbread 2 inches by 2 inches means we divide the length by 2 inches and the wide by 2 inches. Hence, the algebraic expression can be re-group into:

(20 x 18) : (2 x 2) = (20 : 2) x (18 : 2)

                           = 10 x 9 = 90

Hence, the pan contains 90 pieces of cornbread.

Complete question:

Kate bakes 20-inch by 18-inch pan of cornbread. the cornbread is cut into pieces that measure 2 inches by 2 inches. how many pieces of cornbread does the pan contain?

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Correctly complete the statement about the distance traveled by the water in 3 minutes and number of complete cycles the water makes in 3 minutes.

The water travels 450 feet and completes 15 cycles in 3 minutes.

Define distance.

A measurement of how far apart two objects or points are can be quantitative or occasionally qualitative is called distance. In mathematics, distance refers to the length that separates two points on a line or line segment. The fact that distance is a scalar quantity means that it is independent of an object's motion. Metre is the SI unit of distance.

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Answer:

it's I'd b yes so ya hope you do great

Step-by-step explanation:

Answer:

they all are odd numbers

Step-by-step explanation:

trick question they all are odd numbers, unless you can divide or subtract  the numbers

Answer:3716

Step-by-step explanation: any number landing in an even number is even

The equation for the function r (2) in general form is r(2) = 12.5.

Given:

f (x) = 4x

r (x) = f(x) + 4.5

substitute f(x) in r(x)

r(x) = f(x) + 4.5

r(x) = 4x + 4.5

r(2) means x = 2

r(2) = 4*2 + 4.5

r(2) = 8 + 4.5

r(2) = 12.5

Therefore The equation for the function r (2) in general form is r(2) = 12.5.

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The sphere with the volume 1436.03 m³ has 7m long radius.

To find out the approximate length of its radius by using the formula to calculate volume of sphere is:

V= 4πr³/3

The value of π is 22/7 or 3.14.

So, V = 4 × 3.14 × r³ / 3

Volume of the sphere is given which is 1436.03 m³.

Thus, r³ = 1436.03×3 / 4×3.14

r = ³√ 4308.09/12.56 = ³√343 = 7 m.

Hence, the radius of the given sphere is 7 m.

The cube root of a number is the factor that we multiply by itself three times to get that number.

For example, the cube root of 27 is 3.

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Tracking the food Timber eats and how many miles she runs each week is an example of Self-Supervision.

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After using the Simplification method we will get the value (x - 3) / (x + 5)

What is Simplification?

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. We can —

By eliminating all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form, fractions can be made simpler.

By combining and grouping like terms, mathematical expressions can be made simpler. This makes the phrase simple to comprehend and to solve.

Given,

(x^2-x-6) / (x^2+7x+10)

This equation can be separated into two parts, the top and the bottom, which we can simplify further.

Simplifying the top part

x² - x - 6

This can be factored into the following:

x² + 2x - 3x - 6

x(x + 2) - 3(x + 2)

(x + 2)(x - 3)

Now, Simplifying the bottom part

x²+7x+10

x² + 2x + 5x + 10

x(x + 2) + 5(x + 2)

(x + 2)(x + 5)

Now, we can write the new numerator and denominator

(x + 2)(x - 3) / (x + 2)(x + 5)

(x - 3) / (x + 5)

Hence, (x - 3) / (x + 5) is the answer when simplifying

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The possible length of the rectangular garden is L ≥ 6225ft which has a perimeter of 540 feet,

The interior angles of a four-sided polygon are all 90 degrees. At each corner or vertex, the two sides meet at a right angle. The rectangle varies from the square in that its two opposite sides are of equal length.

Let L represent the garden's length.

Let W represent the garden's width.

The perimeter is 540 feet.

The rectangle's perimeter is equal to 2(L + W) = 540

L + W = 270      ....(i)

W = 270 - L      ....(ii)

The rectangle's area is equal to its length times its width, which is given  12000 square feet.

L × W ≤ 12000  ....(iiI)

Substitute the value of equation (ii) into (iii)

(270 - L)(L)   ≤   12000

270l  -  L²  ≤   12000

0   ≤  L²  -  270l +  12000

L²  -  270l  +  1200  ≥  0

Solving the quadratic inequality above, and we get

L ≥  6225

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Four fifth times and eight ninth times would be simplified as 32/45.

What is a fraction?

A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.

To simplify four-fifth times and eight-ninth times, we have to use the fractions,

Simplifying, we get

                           [tex]=\frac{4}{5}* \frac{8}{9}\\\\=\frac{4*8}{5*9}\\\\\=\frac{32}{45}[/tex]

Hene, four fifth times and eight ninth times would be simplified as 32/45.

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The percentage value of puppies weighing over 6 pounds is 25%

What is Percentage?

Percentage is a relative number that represents the hundredth part of any quantity. One percent (symbolised 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount.

Solution:

Given that there are 12 puppies in total and 3 of them weighted above 6 pounds

To calculate the percentage we need to divide 3 by 12 and then multiply it by 100

= (3/12) * 100

= 25%

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Answer:

False

A saver has much more positives. It means you'll have more money in your future :)

Answer:

3:10 ratio of mangos to rest of the fruits or 15:50 unsimplified

Step-by-step explanation:

There are 50 fruits in total with 15 of them being mangos. Simplify this (divide by both numbers by 5) to get 3:10

The half life of the substance is 828.37

The period of time it takes for one-half of a radioactive isotope to decay is known as the half-life. An individual radioactive isotope's half-life is unaffected by environmental factors and is independent of the isotope's starting concentration.

The amount of time needed for half of a radioactive sample's atomic nuclei to decay

Given:

As, The amount of a substance after t days is given by:

p(t)= [tex]p(0)[/tex][tex]e^{-kt[/tex]

Original amount after 300 days.

p(300)= 0.778p(0).

p(t)= [tex]p(0)[/tex][tex]e^{-kt[/tex]

0.778 = p(0)[tex]e^{-300k[/tex]

-300k= log (0.778)

-300k= -0.109020

k = 0.0003634

So, p(t)= [tex]p(0)[/tex][tex]e^{-0.0003634t[/tex]

This is t for which P(t) = 0.5P(0). So

0.5p(0)=  [tex]p(0)[/tex][tex]e^{-0.0003634t[/tex]

[tex]e^{-0.0003634t[/tex] = 0.5

log ( [tex]e^{-0.0003634t[/tex]) = log 0.5

-0.0003634 t = log 0.5

t= -0.30102999566/ -0.0003634

t= 828.37

Hence, the half life of the substance is 828.37

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If a clock shows the hour hand between 6 and 7 and the minute hand at 10. It means : D.50 minutes after 6, E. 6:50

Each of the section time of an analog clock is 5 minutes. Since the hour hand is between 6 and 7 and the minute hand is on 10 ,  it implies that :

5 minutes × 10 minutes

= 50 minutes after 6

Or

6: 50minutes

Therefore the correct option is D and E.

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When the function g(x) = 4 - x and fog (x) = 11 - 2x then the function f(x) is

When a function is expressed in terms of another function it can be called a composite function

if g(x) = 4 - x and fog (x) = 11 - 2x

let f(x) = ax + b

fog = f(g(x))

11 - 2x = f((4 - x) + b)

11 - 2x = a(4 - x) + b

11 - 2x = 4a - ax + b

grouping by coefficients

11 - 2x = (4a + b) - ax

equating the coefficients

11 = 4a + b

-2x = -ax

a = 2

plugging a = 2 into 11 = 4a + b

11 = 4 * 2 + b

11 = 8 + b

b = 3

if a = 2  and b = 3 then f(x) = 2x + 3

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As per the dividing system, If every box gets the same amount, then the mass of fruit in each box is 10 kilograms.

Division

Division refers a process of splitting a specific amount into equal parts.

Given,

Felipe has 8 boxes.

He puts a total of 80 kilograms of fruit into these boxes.

Here we need to find the mass of fruit in each box, if every box gets the same amount.

While we looking into the given question, we have identify the following this,

Number of boxes = 8

Total weight of fruits = 80 kilograms.

And we also know that, each box must has same amount of weight.

Therefore, it can be calculated as, by dividing the total weight by the number of boxes, then we get,

=> 80/8

=> 10

Therefore, each box has 10 kilograms of fruits.

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Using the difference, the difference between the number of heads and half the number of tosses is 1.

In the given question,

The proportion of heads is 0.49 in 100 tosses.

We have to find the difference between the number of heads and half the number of tosses.

The proportion of heads=0.49

Total tosses =100

So the total number of heads

=0.49*100

=49

Since we have to find the difference between the total number of head and half the number of tosses.

So the half on the number of tosses=Total number of tosses/2

The half on the number of tosses=100/2

The half on the number of tosses=50

So, The difference=The half on the number of tosses−Total number of heads

The difference=50−49

The difference=1

Hence, the difference between the number of heads and half the number of tosses is 1.

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The sampling distribution of the sample mean will always have the same Mean as the original distribution.

Sampling distribution:

Sampling distribution means a probability distribution of a statistic that is obtained through repeated sampling of a specific population.

Given,

Here we have the statement "The sampling distribution of the sample mean will always have the same _________ as the original distribution."

Now, we have to find the missing word in the statement.

We know that, the mean of the sampling distribution of the sample mean will always be the same as the mean of the original non-normal distribution. Simply said that the sample mean is equal to the population mean.

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