Operations on Rational and Irrational Numbers

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Answer:

[tex]\huge\boxed{x = (\frac{b}{a})(P+c)}[/tex]

[tex]\frac{a}{b}x - c = P[/tex]

Solve for x:

Begin isolating the variable by adding "c" to both sides:

[tex]\frac{a}{b}x - c + c= P + c[/tex]

[tex]\frac{a}{b}x = P+ c[/tex]

Divide both sides by a/b, or multiply by the reciprocal (b/a)

[tex](\frac{b}{a}) \frac{a}{b}x = (\frac{b}{a})(P + c)[/tex]

Therefore:

[tex]x = (\frac{b}{a})(P + c)[/tex]

Answer:

2 eurocent per kilo

Step-by-step explanation:

Since we are already given the conversion units, we only simply need to divide/multiply and cancel out units.

Dollars and dollars cancel out.

We are left with eurocent.

Pounds and pounds cancel out.

We are left with kilograms.

We do want eurocent over kilograms.

0.89(0.93) = 0.8277/0.4536 = 1.82474

Since we want to round it to the nearest cent, we round up because 8 ≥ 5:

1.82474 ≈ 2

Answer:  1/4

Step-by-step explanation:

If there are  6 black markers and they are a total combination of 24 difference colored markers.  

The  the fraction will be 6/24  which reduces to 1/4

Answer:

GDE = 63

EDH = 63

GDH = 126

FDG = 74

FDH = 200

FDE = 137

Step-by-step explanation:

It is stated that DE bisects <GDH. Since bisecting means halving into equal parts, <GDE = <EDH

from the question,

<GDE = (8x-1)

<EDH = (6x+15)

Since <GDE = <EDH,

(8x-1) = (6x+15), if we collect like terms

8x - 6x = 15 + 1

2x = 16

x = 8°

Again, from the diagram, we see that

<GDH = <GDE + <EDH, thus

<GDH = (8x-1) + (6x+15)

<GDH = 8x -1 + 6x + 15

<GDH = 14x + 14, substitute for x

<GDH = 14*7 + 14

<GDH = 112 + 14

<GDH = 126°

<FDG = 180 - <CDF - <GDE

<FDG = 180 - 43 - 63

<FDG = 74°

<FDH = <FDG + <GDE + <EDH

<FDH = <FDG + <GDH

<FDH = 74 + 126

<FDH = 200°

<FDE = <FDG + <GDE

<FDE = 74 + 63

<FDE = 137°

The measure of angle m∠GDE is 71.4° and the measure of angle m∠EDH is 65.6° on straight angle ∠CDE.

The straight angle ∠CDE, DE bisects GDH, m∠GDE=(8x-1)°, m∠EDH=(6x+15)° and m∠CDF=43°.

Here, m∠GDE+m∠EDH+m∠CDF = 180°

So, (8x-1)°+(6x+15)°+43°=180°

14x+57°=180°

14x=180°-57°

14x=123

x=123/14

x=8.8°

m∠GDE=8x-1

= 71.4°

m∠EDH= 65.6°

Hence, the measure of angle m∠GDE is 71.4° and the measure of angle m∠EDH is 65.6° on straight angle ∠CDE.

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Answer:

8n - 7 = 5

Step-by-step explanation:

number  -  n

product of 8 and a number    -    8n

Seven less than the product of 8 and a number  -    8n - 7.

Seven less than the product of 8 and a number is equal to 5.

8n - 7 = 5

Answer:

8n-7=5

you can do this

i cand do explaination

Answer:

[tex] \boxed{ \bold{ \sf{x = 25°}}}[/tex]

[tex] \boxed{ \bold{ \sf{(x + 5) = 30°}}}[/tex]

[tex] \boxed{ \bold{ \sf{5x = 125°}}}[/tex]

Step-by-step explanation:

We know that sum of angle of triangle adds up to 180°

Finding the value of x

[tex] \sf{5x + x + x + 5 = 180°}[/tex]

Collect like terms

⇒[tex] \sf{7x + 5 = 180}[/tex]

Move 5 to right hand side and change its sign

⇒[tex] \sf{7x = 180 - 5}[/tex]

Subtract 5 from 180

⇒[tex] \sf{7x = 175}[/tex]

Divide both sides of the equation by 7

⇒[tex] \sf{ \frac{7x}{7} = \frac{175}{7} }[/tex]

Calculate

⇒[tex] \sf{x = 25°}[/tex]

Finding the value of ( x + 5 )°

[tex] \sf{x + 5}[/tex]

plug the value of x

⇒[tex] \sf{25 + 5}[/tex]

Add the numbers

⇒[tex] \sf{30°}[/tex]

Finding the value of 5x

[tex] \sf{5 \times 25}[/tex]

Multiply the numbers

⇒[tex] \sf{125°}[/tex]

Hope I helped!

Best regards!!

Answer:

x° = 25°

(x + 5)° = 30°

5x° = 125°

Step-by-step explanation:

total angle inside the triangle = 180 = x + (x+5) + 5x

180 = x + x + 5 + 5x

group like terms

7x + 5 = 180

subtract 5 each sides

7x = 175

x = 175/7

x = 25°

solve for : (x + 5)°

(x + 5)° = 25 + 5

(x + 5)° = 30°

solve for 5x°

5x° = 5 * 25

5x° = 125

check

180 = x + (x+5) + 5x

180 = 25 + (25+5) + (5*25)

180 = 25 + 30 + 125

180 = 180

Answer:

0.75

Step-by-step explanation:

Answer:

$1.33 per ticket cost

Step-by-step explanation:

5 / $3.75 = $1.33 per 1 ticket cost

It is proven that "the sum of the squares of four consecutive integers is an even integer" is the solution part.

To prove that the sum of the squares of four consecutive integers is an even integer, we need to show that it can be expressed as twice another integer.

Let's assume the four consecutive integers are n, n+1, n+2, and n+3.

The sum of their squares can be expressed as:

[tex]n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2[/tex]

Expanding the squares, we have:

[tex]n^2 + (n^2 + 2n + 1) + (n^2 + 4n + 4) + (n^2 + 6n + 9)[/tex]

Combining like terms, we simplify this expression to:

[tex]4n^2 + 12n + 14[/tex]

Now, let's consider this expression [tex]4n^2 + 12n + 14[/tex].

We can factor out 2 from each term, resulting in:

[tex]2(2n^2 + 6n + 7)[/tex]

Since [tex]2n^2 + 6n + 7[/tex] is an integer, let's denote it as k, where k is an integer.

Therefore, the expression becomes:

2k.

We have successfully expressed the sum of the squares of four consecutive integers as twice another integer (2k), which proves that it is an even integer.

Hence, the sum of the squares of four consecutive integers is an even integer.

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Answer:

hey!

Your answer is ...

-48 , -26 , -5 , 4 , `12

Step-by-step explanation:

HOPE THIS HELPED!

:)

Answer:

The question is not complete, below is the complete question:

Suppose that a factory worker turns 62 years old and retires from her job. Which statistic is not affected? A. number of unemployed B. unemployment rate C. labor force D. labor-force participation rate

Answer:

The correct andwer is:

number of unemployed (A.)

Step-by-step explanation:

The terms highlighted in the options of the question refer to terms associated with the labour force of an economy. Let us take a look at each of them and justify why we chose the option A

1. Number of unemployed: The number of unemployed in an economy refers to the number of people who are without employement, while actively searching for employment, willing to work and have actively sought for employment in the past four weeks. In this example, a factory worker retiring at 62 is not actively looking for work anymore, hence this transition does not affect the number of unemployed individuals in an economy

2. unemployment rate: The unemployment rate refers to the percentage of labor force that is jobless. Mathematically, it is represented as:

[tex]Unemployment\ rate\ =\ \frac{umemployed}{Labour\ force} \times\ 100[/tex]

In this example, a factory worker retiring at 62, reduces the labor force (number fit to work) in a population, and since the unemployment rate is in turn affected by the labour force (inversely), the unemployment rte is affected by the retiring of the factory worker

3. Labor force: The labor force in an economy are all the individuals who are fit and able to work. It inclues all those who are actively employed and those who are unemployed. A retired factory worker is not part of the labor force, because retirement age disqualifies him/her from being fit to work, hence the retirement reduces the labor force.

4. Labor-force participation rate: This is the coolective numbere of civilians or non-institutional people 16 years or older, who are working or actively looking for work. Retirement reduces the labor-force participation rate

Answer:

Step-by-step explanation:

Given,

Rate ( R ) = 4.75 %

Time ( T ) = 25 years

Simple Interest ( I ) = $ 4,750

Principal ( P ) = ?

Finding the principal

We know that,

[tex] \boxed{ \sf{principal = \frac{interest \: \times 100}{ \: time \: \times \: rate} }}[/tex]

plug the values

⇒[tex] \sf{ \frac{4750 \times 100}{4.75 \times 25} }[/tex]

Calculate

⇒[tex] \sf{\frac{475000}{118.75} }[/tex]

⇒$ [tex] \sf{4000}[/tex]

Hope I helped!

Best regards!!

Answer:

2000

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

The given statement is false because behavioral field study deals with the cognitive processes during field study or task.

In the given statement only the physical strength of the students is measured while behavioral field study measures or explores human behavior and how or what techniques are students using to perform the field task.

Hence, the correct option is "False".

Answer:

y = -5x - 29

Step-by-step explanation:

y-intercept form is y = mx +b,

m is slope, for parallel line slope is the same, so m= -5

y = -5x + b

To find b, we need to use the point (-5, - 4).

- 4 = -5*(-5) + b

- 4 = 25 + b

b = - 29

y = -5x - 29

Answer:

1/9

Step-by-step explanation:

Answer:

∠ OLM = 47°

Step-by-step explanation:

Given:

∠ NLO = 41°

∠ NLM = 88°

Find:

∠ OLM

Computation:

⇒ ∠ NLM = ∠ NLO + ∠ OLM

⇒ 88° = 41° + ∠ OLM

⇒ ∠ OLM = 88° - 41°

⇒ ∠ OLM = 47°

Answer:

47

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

Answer:

The range of the function is -10, 10.

 The period of the function is 1.2 seconds.

The maximum of the function is 10 centimeters.

Step-by-step explanation:

The range of a cosine function is the set of output values. In this situation, the range is the distance the pendulum covers, which is represented on the D(t) axis. The graph shows that the range of the function D(t) is [-10, 10].

The period is the length of a cycle. The graph shows that the cycle repeats every 1.2 seconds.

The maximum is the y-value of the highest point on the graph. The graph shows the maximum of the function is 10 centimeters.

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{m = 9}}}}}[/tex]

Option A is the correct option

Step-by-step explanation:

[tex] \sf{5m + 3m - 8 = 64}[/tex]

Collect like terms

⇒[tex] \sf{8m - 8 = 64}[/tex]

Move 8 to right hand side and change it's sign

⇒[tex] \sf{8m = 64 + 8}[/tex]

Add the numbers

⇒[tex] \sf{8m = 72}[/tex]

Divide both sides of the equation by 8

⇒[tex] \sf{ \frac{8m}{8} = \frac{72}{8} }[/tex]

Calculate

⇒[tex] \sf{m = 9}[/tex]

Hope I helped!

Best regards!!

Answer:

[tex]\Huge \boxed{m=9}[/tex]

Step-by-step explanation:

[tex]5m + 3m - 8 = 64[/tex]

Combining like terms.

[tex]8m - 8 = 64[/tex]

Adding 8 to both sides.

[tex]8m=72[/tex]

Dividing both sides by 8.

[tex]m=9[/tex]

Answer:

x is the variable

Step-by-step explanation:

The variable is the letter in the expression

x is the variable

5 is the coefficient of the variable

7 is the constant

Answer:

  107° 30'

Step-by-step explanation:

As in part (a), the hour hand moves 30° per hour, so at 1:25, it has moved ...

  (1 25/60)(30°) = 42.5°

from the vertical at noon.

Similarly, the minute hand moves 6° per minute, so at 1:25, it has moved ...

  (25)(6°) = 150° from the vertical at 1 o'clock.

The exact angle difference is ...

  150° -42.5° = 107.5° = 107° 30'

Answer:

A= Area

B= Base of the figure

H= Height of the figure

B and H are multiplied together to find the area

Step-by-step explanation:

Answer:

Last one - CD with a line over it with arrowheads.

Step-by-step explanation:

Last one - CD with a line over it with arrowheads.

Answer:

12.2

Step-by-step explanation:

By Pythagoras theorem:

[tex] {x}^{2} = {10}^{2} + {7}^{2} \\ {x}^{2} = 100 + 49 \\ {x}^{2} = 149 \\ x = \sqrt{149} \\ x = 12.2065556 \\ x \approx \: 12.2[/tex]

Answer:

4+2/5+3=3/4 slope

Step-by-step explanation:

sssllllooooppppeeee

Answer:

0.3 or 30%

Step-by-step explanation:

Blue = 1/10

Red = 2 white

**************

White + red = 1 - 1/10

White +2white= 9/10

White = 3/10

Red = 6/10

So probability of white ball is 3/10 or 30%

Answer:

Step-by-step explanation:

Given the limit of a function expressed as [tex]\lim_{x \to 1} (\dfrac{3x}{x-1} - \dfrac{3}{lnx})[/tex], we are to evaluate it. To evaluate it, we will simply substitute x = 1 into the function since the variable x tends to 1.

[tex]\lim_{x \to 1} (\dfrac{3x}{x-1} - \dfrac{3}{lnx})\\\\= (\dfrac{3(1)}{1-1} - \dfrac{3}{ln1})\\\\= \dfrac{3}{0} - \dfrac{3}{0}\\\\= \infty - \infty (ind)[/tex]

Since we got an indeterminate function, we will find the LCM of the function and solve again.

[tex]= \lim_{x \to 1} (\dfrac{3x}{x-1} - \dfrac{3}{lnx})\\\\= \lim_{x \to 1} \dfrac{3xlnx-3(x-1)}{(x-1)lnx}\\\\\\= \dfrac{3(1)ln(1)-3(1-1)}{(1-1)ln1}\\\\= \frac{3(0)-3(0)}{0(0)} \\\\= \frac{0}{0} (ind)[/tex]

Applying L'hospital rule;

[tex]\frac{x}{y} = \lim_{x \to 1} \dfrac{d/dx(3xlnx-3(x-1))}{d/dx((x-1)lnx)}\\\\= \lim_{x \to 1} \dfrac{3x(\frac{1}{x})+ 3lnx-3)}{(x-1)\frac{1}{x} +lnx}\\\\= \lim_{x \to 1} \dfrac{3 + 3lnx-3}{(x-1)\frac{1}{x} +lnx}\\\\= \frac{3ln1}{(1-1)\frac{1}{1} +ln1}\\\\= \frac{0}{0} (ind)[/tex]

Applying L'hospital rule again;

[tex]= \lim_{x \to 1} \dfrac{\frac{d}{dx} (3lnx)}{\frac{d}{dx} ((x-1)\frac{1}{x} +lnx)}\\\\= \lim_{x \to 1} \dfrac{\frac{3}{x} }{(x-1)\frac{-1}{x^2} + \frac{1}{x} +\frac{1}{x} }\\\\= \dfrac{\frac{3}{1} }{(1-1)\frac{-1}{1^2} + \frac{1}{1} +\frac{1}{1} }\\\\= \frac{3}{0(-1)+2}\\ \\= \frac{3}{2-0}\\ \\= 3/2[/tex]

Hence the limit of the function is 3/2.

Answer:

It's equal =3

ne s o

Step-by-step explanation:

Answer:

6x^2

Step-by-step explanation:

Because we are multiplying 6 and a number x squared, we know that x will have an exponent of 2. Then, multiplying that by 6 and using conventional algebraic techniques, we can combine the two terms together.

6 * x^2

6x^2

Answer:

[tex]\displaystyle \rm \longmapsto 6 \times x {}^{2} [/tex]

[tex]\displaystyle \rm \longmapsto {6x}^{2} [/tex]