Is 6 /1.2 a rational number

Answer:

22b - 15

Step-by-step explanation:

add the dependent variable together

Answer: 23b- 15

Explation:

Answer:

x=7

Step-by-step explanation:

Move all terms containing x to the left side of the equation.

2x+3=17

Move all terms not containing x to the right side of the equation.

2x=14

Divide each term by 2 and simplify.

x=7

Answer:

40 cups of food

Step-by-step explanation:

First, you would multiply 2/3 by 2, which gives you 4/3. That means the beagle will eat 1 and 1/3 of a cup a day. If you multiply that by 30, you get 40.

Henry was 40 feet away from his original starting point. Using Pythagorean's theorem it is calculated.

The theorem says that,

In a right-angled triangle, the sum of squares of the lengths of two arms (opposite and adjacent sides) is equal to the square of the hypotenuse.

I.e, Consider a right-angled triangle ΔABC, where AC is the hypotenuse side of the triangle. So, according to the theory,

AC² = AB² + BC²

It is given that,

Henry walked on a flat field,

9 meters - towards the north

24 feet - towards the east

9 meters + 32 feet - towards the south

This can be shown in the diagram below.

In the diagram, the distance from the starting point is X, and the last point is  S.

To find the distance between these two points, a line is joined as shown in the diagram. Thus, it is formed as a right-angled triangle.

So, according to the Pythagorean theorem,

XS² = (24)² + (32)²

(here 32 feet is the only distance from the assumed point to the endpoint)

⇒ XS² = 1600 = 40²

∴ XS = 40 feet

So, Henry is 40 feet away from the original starting point.

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Answer:

355mg of medication

Step-by-step explanation:

The value of a will be equal to \(\dfrac{1}{4}\) for the given expression.

The process of reducing the complex mathematical expressions into the simplest form is called as the simplification.

here we have two expressions.

\(a^4=3\ \ \ \ a^6=\dfrac{3}{16}\)

We can write the expression as:

\(a^6=\dfrac{3}{16}\\\\\\a^4\times a^2=\dfrac{3}{16}\\\\\\3\times a^2=\dfrac{3}{16}\\\\\\a=\sqrt{\dfrac{1}{16}}\\\\\\a=\dfrac{1}{4}\)

Hence the value of a will be equal to \(\dfrac{1}{4}\) for the given expression.

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1. Sunlight is absorbed by the chloroplasts in the plant cells. 2. Water molecules are split into oxygen and hydrogen ions.  3. The hydrogen ions combine with carbon dioxide to form glucose.  4. Oxygen is released into the atmosphere as a byproduct.

Photosynthesis is the process by which plants, algae, and some bacteria convert light energy into chemical energy in the form of glucose, which can then be used by the organism for energy. The equation for photosynthesis is 6\(CO_{2}\) + 6\(H_{2}\)O → \(C_{6}\)\(H_{12}\)\(O_{6}\) + 6\(O_{2}\). However, the question asks for the sequence of the equation, which is important for understanding the order in which the process occurs.
The process of photosynthesis begins with the absorption of sunlight by the chloroplasts in the plant cells. This light energy is used to split water molecules into oxygen and hydrogen ions. The hydrogen ions combine with carbon dioxide to form glucose, which is stored in the plant as energy. The oxygen is released into the atmosphere as a byproduct.

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a. the value of the amount after one year, if it is compounded monthly, is $26,775.19.

b. the value of the amount after one year, if it is compounded daily, is $26,822.82.

c. the value of the amount after one year, if it is compounded quarterly, is $26,815.11.

Given that amount of money invested = $25,000 and the interest rate offered by the account is 6.30%.

a. To find the value if the money is compounded monthly:

We need to use the formula for compound interest which is given as;

A=\(P(1+r/n)^{nt}\)

Where,

A is the amount

P is the principal

r is the interest rate

t is the time of investment

n is the number of times the interest is compounded per year

We have,

P = $25,000

r = 6.30%/100 = 0.063

n = 12 (as the interest is compounded monthly, the number of periods in a year becomes 12)

and t = 1

We have to find the amount A, so we substitute the given values in the above formula.

A = $25,000\((1+0.063/12)^{(12*1)}\)

= $26,775.19

b. To find the value if the money is compounded daily:

Here, n = 365 as the interest is compounded daily.

A = $25,000\((1+0.063/365)^{(365*1) }\)

= $26,822.82

c. To find the value if the money is compounded quarterly:

Here, n = 4 as the interest is compounded quarterly.

A = $25,000\((1+0.063/4)^{(4*1)}\) = $26,815.11

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To generate the overall equation A → 2C, should be B → 2C added to  

A → B gives the equation A + B → B + 2C.  

In mathematics, an equation is a method that expresses the equality of two expressions, by using connecting them with the equals signal =. The phrase equation and its cognates in other languages may also have subtly exclusive meanings; for example, in French, an equation is described as containing one or more variables, at the same time as in English, any nicely shaped formula together with expressions associated with an equal’s signal is an equation.

Solving an equation containing variables includes determining which values of the variables make the equality actual. The variables for which the equation must be solved are also known as unknowns, and the values of the unknowns that satisfy the equality are referred to as solutions of the equation. Equations come in two varieties: identities and conditional equations. An identification is actual for all values of the variables. A conditional equation is handiest genuine for unique values of the variables.

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the maximum time that he can have in his last race is 23 seconds.

We know that the average can not be greater than 22.8 seconds, then if x represents the time of the last race, the maximum value that x can take is given by the equation:

(23.1 + 23.2 + 22.8 + 21.9 + x)/5 = 22.8

(That is the equation for the mean of the 5 times)

Solving that for x we will get:

(23.1 + 23.2 + 22.8 + 21.9 + x) = 5*22.8

91 + x = 114

x = 114 - 91 = 23

So the maximum time that he can have in his last race is 23 seconds.

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Answer:

Two geometric objects are perpendicular if they intersect at a right angle.

Step-by-step explanation:

How you know:

The condition of perpendicularity may be represented graphically using the perpendicular symbol, ⟂.

Surface area of old cube

Side of new cube

Surface area

Difference

Answer:

A)  6(x + y)² = 6x² + 12xy +6y²

B)  12xy +6y²

Step-by-step explanation:

Surface area of a cube = 6s²  (where s is the side length)

Part A

Given:

⇒ Surface area of the original cube = 6x²

If the side length of the cube is increased by y, then:

⇒ Surface area of the new cube = 6(x + y)²

Expand and simplify:

⇒ 6(x + y)²

⇒ 6(x + y)(x + y)

⇒ 6(x² + xy + xy + y²)

⇒ 6x² + 12xy +6y²

Part B

To find the difference between the surface areas of the new and original cubes, subtract the surface area of the original cube from the surface area of the new cube:

⇒ SA of new cube - SA of original cube

⇒ 6x² + 12xy +6y² - 6x²

⇒ 12xy +6y²

The first step is to subtract $500 from $2000 and then you end up with $1500 which you then divide by 5.

Each payment will have to be $300

Answer:

Step-by-step explanation:

= 1/4 + 2/5

= 5/20 + 8/20

= 13/20

Answer:

-4.75

Step-by-step explanation:

Slope = (y2-y1) / (x2-x1)

So applying the formula

(-29-9)/(15-7)

= -38/8 = -4.75

Answer:

The first answer should be the 3rd one.

The second answer should be the first one.

Step-by-step explanation:

Answer:

first one: C

second one: A

Given the two similar solids A and B are:

a. Volume of Solid B = 480 cm³

b. Surface Area of Solid A = 35 cm²

Volume of a solid:

In geometry, 3D shapes are called three-dimensional or solid shapes. It takes up space and has 3 dimensions. Typically, 3D shapes are obtained from rotations of 2D shapes. The faces of a solid shape are just two-dimensional shapes. Some examples of 3D shapes include cubes, cuboids, cones, cylinders, spheres, prisms, etc. The amount of any substance that can contain these forms is called its volume.

According to the Question:

Given that :

The two solids, A and B, are similar, therefore, assuming they have a pair of corresponding dimension, given as, a and b respectively, thus:

\(\frac{VolumeA}{Volume B}\) = \(\frac{a^3}{b^3}\)  (ratio of their volume to their corresponding sides)

Aₐ/ Ba = a²/ b² (ratio of their surface area to their corresponding sides)

Thus:

a. Volume of Solid A =

a = 3 cm

b = 6 cm

Substitute

    \(\frac{60}{Volume B} = \frac{3^3}{6^3}\)

⇒ \(\frac{60}{Volume B}\) = \(\frac{27}{216}\)

⇒ 27 (Volume B) = 60 × 216

⇒ Volume B = 12960/ 27

⇒ Volume B = 480 cm³

a. Area of Solid B =

a = 3 cm

b = 6 cm

Substitute

    Aₐ/ 140 = 3²/6²

⇒ 36 Aₐ = 9 × 140

⇒ Aₐ = 1260/ 36

⇒ Aₐ = 35 cm²

Therefore, given the two similar solids :

a. Volume of Solid B = 480 cm³

b. Surface Area of Solid A = 35 cm²

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Answer:

6

Step-by-step explanation:

pemdas=parenthesis, exponents, multiplication, division, addition, subtraction. with this, we multiply 2 x the absolute value of -3, which is just 3. therefore, 6. now we see we need to subtract the absolute value of 6 from the absolute value of 8, which gives us 2. and 2+4 is 6.

Answer: 6

Step-by-step explanation:

8-2 x 3+4

2x3=6

8-6+4

2+4

=6

hope this helps

Answer:

(7^2)^2

Step-by-step explanation:

(7^-2)*(7^6)=7^-2+6

......since the base 7 is the same, when u multiply them, you should add the exponents and keep 7 as it is. That will be 7^4, which in equivalent to ans D(7^2)^2

Answer:

Step-by-step explanation:

do it yourself

Step-by-step explanation:

Todd fills 30 paper cups with ketchup and Yuki fills 27 paper cups with ketchup.

Each paper cup holds 1 ounce

Todd = 30 * 1 = 30 ounces

Yuki = 27 * 1 = 27 ounces

Total ounces = 30 + 27

Later, Todd and Yuki learn that two other company employees completed exactly the same task.

Total ounces = 2 (30 + 27)

Answer:2(30+27)

Step-by-step explanation:

the other company is doing the same thing so you multiply by 2  

and we have 30 and 27 so we use those numbers to make

2(30+27)

2x57

114

Answer:

Mention any Two study routes(courses or program) that higher education could offer.

Answer:

the solution points for the system of equations are (3, 25) and (-7/2, -7).

Step-by-step explanation:

We can solve this system of equations using substitution or elimination. Here, we will use the substitution method:

Substitute y = 2x^2 + 5x - 10 into the second equation:

4x - (2x^2 + 5x - 10) = -11

Simplifying the left side of the equation:

4x - 2x^2 - 5x + 10 = -11

Rearranging the terms:

2x^2 - x + 21 = 0

Using the quadratic formula:

x = (-(-1) ± sqrt((-1)^2 - 4(2)(21))) / 2(2)

x = (1 ± sqrt(169)) / 4

x = (1 ± 13) / 4

Simplifying:

x = 3 or x = -7/2

Now, substitute each value of x back into one of the original equations to find the corresponding value(s) of y:

For x = 3:

y = 2(3)^2 + 5(3) - 10 = 25

So one solution point is (3, 25).

For x = -7/2:

y = 4(-7/2) + 11 = -7

So the other solution point is (-7/2, -7).

Therefore, the solution points for the system of equations are (3, 25) and (-7/2, -7).

Answer:

The price fell by 13.5%.

Step-by-step explanation:

Formula: Subtract the lower price from the higher price. Divide that answer by the higher price. Multiply by 100 to get the percent. This is also the formula for percent error.

1: \((\frac{3.7-3.2}{3.7})*100\)

2: \((\frac{0.5}{3.7}) *100\)

3. 0.135*100

4: 13.51%

The final answer is 13.5%.

One strategy that may help Emilio write more fluently is practicing speed writing or shorthand techniques.

Practicing speed writing or shorthand techniques can help Emilio increase his writing speed without sacrificing legibility. Speed writing involves using abbreviations, symbols, and shortcuts to represent words or phrases, allowing for faster transcription of thoughts onto paper.

Shorthand systems, such as Gregg shorthand or Pitman shorthand, provide structured methods for condensing words and phrases into simplified symbols.

By learning and practicing speed writing or shorthand techniques, Emilio can improve his writing efficiency and reduce the time it takes to write a few sentences. This strategy allows him to maintain neatness while increasing his writing speed, enabling him to express his thoughts more fluently.

With regular practice and familiarity, Emilio will become more comfortable with the shorthand system and experience a significant improvement in his writing speed and fluency.

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Answer:

Its a number

Step-by-step explanation

Answer: 1 over 3

Step-by-step explanation:

Hallie: 2

Mattie: 6

2:6 = 2/6 = 1/3 = 1 over 3

The average speed of the first plane is 339.5 mph, and the average speed of the second plane is 97 mph.

To find the average speed of each plane, we can use the formula:

Speed = Distance / Time

Let's assign variables to the speeds of the two planes. Let's say the speed of the second plane is 'x' mph. Since the first plane is traveling 3.5 times as fast, the speed of the first plane would be 3.5x mph.

Now, we know that both planes have traveled for 6 hours and are 1455 miles apart. Since they are traveling in the same direction, the distance between them will be the difference of their distances. Therefore, we have:

Distance of the first plane = 3.5x * 6 = 21x miles
Distance of the second plane = x * 6 = 6x miles

The difference between their distances is 1455 miles, so we can set up the equation:

21x - 6x = 1455

Combining like terms, we get:

15x = 1455

Dividing both sides by 15, we find:

x = 97

So, the speed of the second plane is 97 mph, and the speed of the first plane is 3.5 * 97 = 339.5 mph.

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Answer:

51.048053

Step-by-step explanation: