Is the following number rational or irrational?
pi-1
​

Answer:

  4b + 5

Step-by-step explanation:

Equation C tells us ...

  a = 4b + 5

so, the value "4b +5" can be substituted for "a" in Equation D.

_____

In algebra, things that are equal are interchangeable. One can always be substituted for the other.

the value of 'a' that can be substituted into Equation D to solve the system of equations is 19.

To solve the system of equations given by Equation C: a = 4b + 5 and Equation D: a = 6b \\- 2, we are looking for a value of a which satisfies both equations simultaneously. Since equations C and D both define 'a' in terms of 'b', we can set them equal to each other to find the value of 'b', and then use that value to find 'a'.

Step 1: Set Equation C equal to Equation D, since they both equal 'a'.
4b + 5 = 6b - 2.

Step 2: Solve for 'b'.
Subtract '4b' from both sides: 5 = 2b \\- 2.
Add 2 to both sides: 7 = 2b.
Divide both sides by 2: b = 7/2 or 3.5.

Step 3: Substitute the value of 'b' into either Equation C or D to find 'a'.
Using Equation C: a = 4(3.5) + 5 = 14 + 5 = 19.

Therefore, the value of 'a' that can be substituted into Equation D to solve the system of equations is 19.

Answer:

x+y=45, (5,40) and ( 25,20)

Step-by-step explanation:

Here we are given the information that Gian was given 45 mins to spend on computer after dinner. Out of those 45 mins , he can either play games of watch videos.

Therefore If the time for which he watches videos is x and that of the time he spend playing game is y , there sum must be equal to 45 mins.

Hence our equation in terms of x andy will be

[tex]x+y=45[/tex]

Now let us see the graph part.

Here we see that the graph is plot on xy plane where x is taken as time taken in watching videos and y as playing games

i) on Monday , he watch 5 minutes in watching videos

Hence x=5 , we put x=5 in x+y=45 and solve it for y

5+y=45

subtracting 5 from both sides

5+y-5=45-5

y=40

Hence he spend 40 mins on playing games.

So we plot Point (5,40) for monday.

i) on Tuesday , he watch 25 minutes in watching videos

Hence x=25 , we put x=25 in x+y=45 and solve it for y

25+y=45

subtracting 25 from both sides

25+y-25=45-25

y=20

Hence he spend 20 mins on playing games.

So we plot Point (25,20) for Tuesday.

Answer:

p ≥ 5.5 hrs

Step-by-step explanation:

Let p represent the number of hours Brandon spends practicing per week.

So he practices for atleast 5.5 hrs.

i.e p ≥ 5.5 hrs

The inequality to represent the number of hours Brandon will spend practicing this week is p ≥ 5.5 hrs.

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We have,

Brandon wants to practice his trombone for at least 5.5 hours this week.

Let p represent the number of hours Brandon spends practicing per week.

We know the sign for at least is "≥".

So, the inequality is p ≥ 5.5 hrs.

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Answer:

18.1 cm

Step-by-step explanation:

Work out CD

[tex]\sqrt{16^{2}-7^{2}  } = 14.38749457[/tex] ⇒ Pythagoras Theorem

Use CD and AD to work out AC

[tex]\sqrt{14.38749457^{2}+11^{2}  } = 18.11077028[/tex] ⇒ Pythagoras Theorem

Answer:

The equation can be used to find the amount of time Hiroshi spends on his math homework is 1/4 (30 + 60 + x) = x ⇒ answer a

Step-by-step explanation:

* Lets read the problem and take the information to solve the problem

- Hiroshi spends 30 minutes on history homework

- Hiroshi spends 60 minutes on English homework

- Hiroshi spends  x minutes on math homework

* From these information

- The total homework time is (30 + 60 + x) minutes

- Hiroshi spends one fourth of his total homework time on math

- The time of math homework is 1/4 the total homework time

∵ The total homework time = (30 + 60 + x)

∵ The time of math homework is 1/4 the total homework time

∴ The time of math homework = 1/4 (30 + 60 + x)

- Then equate the times of math homework

∵ Hiroshi spends  x minutes on math homework

∵ The time of math homework = 1/4 (30 + 60 + x)

∴ 1/4 (30 + 60 + x) = x

* The equation can be used to find the amount of time Hiroshi

  spends on his math homework is 1/4 (30 + 60 + x) = x

Answer:7/36

Step-by-step explanation:

Firstly, I would draw a table to visually see what the outcomes are. There are many methods but this is what i find to be the easiest so here it goes!!!

I hope the pic helps! If you have any questions feel free to ask!

For this case we have that the fractions have the same denominator, then we can rewrite as:

[tex]\frac {3x + 2 + (2x -5)} {x-1} =[/tex]

We eliminate the parenthesis:

[tex]+*+=+[/tex]

[tex]+*-=-[/tex]

[tex]\frac {3x + 2 + 2x - 5} {x-1} =[/tex]

We add common terms of the numerator:

[tex]\frac {5x-3} {x-1}[/tex]

Thus, the correct expression is option B.

Answer:

Option B

Answer: OPTION B.

Step-by-step explanation:

Given the rational expressions [tex]\frac{3x+2}{x-1}[/tex] and [tex]\frac{2x-5}{x-1}[/tex], we can observe that both have the same denominator, then we can add them.

We must rewrite the denominator [tex]x-1[/tex] and add the numerators. Then:

[tex]=\frac{(3x+2)+(2x-5)}{x-1}[/tex]

Therefore, adding the like terms on the numerator, we get the following sum:

[tex]=\frac{5x-3}{x-1}[/tex]

We can observe that this sum matches with the sum shown in the option B.

C and F are the answers, im pretty sure

i got you

The set of rays form the sides of angle IHG include the following;

C. ray IH

F. ray HG.

In Mathematics and Euclidean Geometry, a line segment is the part of a line in a geometric figure that is bounded by two distinct end points. This ultimately implies that, a line segment typically has a fixed length.

In Mathematics and Euclidean geometry, a ray is composed of two points that are joined by a straight line such as ray IH and ray HG.

By critically observing the figure showing angle IHG, we can reasonably infer and logically deduce that both ray IH and ray HG form it sides.

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Answer:

  C.  13.78 ≤ x ≤ 18.98

Step-by-step explanation:

The rate for Company B is show as 17.4 cents per kWh. That for Company D is shown as 14.8 cents per kWh. The savings obtained by using Company D is ...

  17.4 - 14.8 = 2.6 . . . . cents per kWh

Then to find the savings a household would experience, we multiply this savings rate by the monthly usage rate of the household.

  530 kWh × $0.026/kWh = $13.78

  730 kWh × $0.026/kWh = $18.98

So for household usage between these energy values, the savings (x) using Company D will satisfy ...

  13.78 ≤ x ≤ 18.98

Check the picture below.

Answer:

7.0711

= 7.1 (rounded to nearest tenth)

Step-by-step explanation:

see attached.

For this case we have by definition, that the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]

According to the given data, we have the following points:[tex](x_ {1}, y_ {1}) = (6, -5)\\(x_ {2}, y_ {2}) = (- 1, -4)[/tex]

Substituting the points in the formula we have:

[tex]d = \sqrt {(- 1-6) ^ 2 + (- 4 - (- 5)) ^ 2}\\d = \sqrt {(- 7) ^ 2 + (- 4 + 5) ^ 2}\\d = \sqrt {(- 7) ^ 2 + (1) ^ 2}\\d = \sqrt {49 + 1}\\d = \sqrt {50}\\d = 7.0711[/tex]

Rounding off we have to:

[tex]d = 7.1[/tex]

ANswer:

[tex]d = 7.1[/tex]

Answer:

67.5

Step-by-step explanation:

Used a calculator

Answer:

67.5 sq. ft

Step-by-step explanation:

15 ft is the base, and 9 is the length of one side, if you multiply the two together, you get 135 sq. ft; however, this is just the length of a rectangle twice the size of the triangle, to get the area of the triangle you'll need to divide 135 by 2 which is 67.5 sq. ft.

Answer:

  soccer

Step-by-step explanation:

Neither the 5th-floor nor 6-floor girl likes soccer, so that must be the sport of choice on the 7th floor.

Answer: 1 minute 37 seconds (97 secs)

Step-by-step explanation:

31 x 60 = 1860

1860 + 24 = 1884

29 x 60 = 1740

1740 + 47 = 1787

1884 - 1787 = 97

Answer:

[tex]\dfrac{20}{7}\ \text{units}[/tex]

Step-by-step explanation:

Put the side length where x is, then do the arithmetic.

  P = 4x

  P = 4(5/7) = 20/7

The perimeter is 20/7 units.

First you must distribute the 2x to the numbers inside the parentheses

(2x * x) + (2x * -1) = 3

[tex]2x^{2}[/tex] - 2x = 3

To make this a quadratic equation you can solve bring the 3 over to the left side of the equation by subtracting it to both sides

[tex]2x^{2}[/tex] - 2x - 3 = 0

Use the quadratic equation to solve this (image of the quadratic equation is below)

Remember that quadratic functions are set up like so:

[tex]ax^{2} +bx +c = 0[/tex]

That means that in this equation...

a = 2

b = -2

c = -3

^^^Plug these numbers into the quadratic equation and solve...

[tex]\frac{2+/-\sqrt{(-2)^{2}-4(2)(-3)}}{2(2)}[/tex]

[tex]\frac{2 +/-\sqrt{4+24}}{4}[/tex]

[tex]\frac{2+/-\sqrt{28} }{4}[/tex]

[tex]\frac{2+/-2\sqrt{7} }{4}[/tex]

[tex]\frac{1+/-\sqrt{7} }{2}[/tex]

Keep in mind that +/- is ±

[tex]\frac{1+\sqrt{7} }{2}[/tex]

[tex]\frac{1-\sqrt{7} }{2}[/tex]

^^^Exact answers

Approximations:

1.823

-0.823

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

(2,  6) .

Step-by-step explanation:

The point A has coordinates (5, 9) and B  has coordinates (-1, 3).

The midpoint is (5 + -1)/2 ,  (9 + 3)/2.

= (2,  6) Answer.

Answer:

Step-by-step explanation:

1. Starting with the equation ...

  1 in = 11 ft

You can multiply both sides by 32 to get the answer to your question:

  32 in = 352 ft

The actual length of the steamboat was 352 feet.

__

2. There are 16 ounces in a pound, so the cost is ...

  $0.21/oz × 16 oz/lb × 2.25 lb = $(0.21×16×2.25) = $7.56

A 2.25 lb bag of peanuts will cost $7.56.

__

3. Using the given conversion factors, we have ...

  (20 in) × (2.54 cm/in) × (10 mm/cm) = (20×2.54×10) mm = 508 mm

There are 508 mm present in 20.0 inches.

Answer:

352 ft

$7.56

508 mm

Step-by-step explanation:

1. Starting with the equation ...

 1 in = 11 ft

You can multiply both sides by 32 to get the answer to your question:

 32 in = 352 ft

The actual length of the steamboat was 352 feet.

__

2. There are 16 ounces in a pound, so the cost is ...

 $0.21/oz × 16 oz/lb × 2.25 lb = $(0.21×16×2.25) = $7.56

A 2.25 lb bag of peanuts will cost $7.56.

__

3. Using the given conversion factors, we have ...

 (20 in) × (2.54 cm/in) × (10 mm/cm) = (20×2.54×10) mm = 508 mm

There are 508 mm present in 20.0 inches.

Answer: A

Step-by-step explanation:

S=10r

Answer:

Step-by-step explanation:

that's right on plato

[tex]

\sqrt{4x+15}-3\sqrt{x}=0 \\

\sqrt{4x+15}=3\sqrt{x} \\

4x+15=9x \\

-5x=-15 \\

x=\boxed{3}

[/tex]

Hope this helps.

r3t40

Answer:

  35 miles

Step-by-step explanation:

The segment addition theorem tells you ...

  DE + EF = DF

  125 + EF = 160

  EF = 35 . . . . . . . subtract 125

The distance from E to F is about 35 miles.

Answer:

B

Step-by-step explanation:

h(t)=-4.9t^2+ v_0t+h_0

v_0 represents initial velocity

h_0 represents initial height

we use -4.9 for the coefficient of t^2 because we dealing with meters and seconds

(If it was feet and seconds it would have been -16 instead of -4.9)

Anyways v_0 is 15m/s (We will just put 15 to make it look less complicated)

and from the ground means the initial height was h_0=0

So the answer is B.

Answer:

Step-by-step explanation:

Ratios of perimeters is a one-to-one measure.  From the figure on the left to the one on the right the ratio of the one-to-one measure is 45/25 which reduces to 9/5.

Area is a squared measure.  Once we have the perimeter reduced (we do), we square those perimeter measures to find the area ratio.

[tex](\frac{9}{5})^2=\frac{81}{25}[/tex]

[tex]\bf \stackrel{\textit{rate}}{\cfrac{~~\frac{2}{3}~~}{\frac{1}{2}}\cfrac{ft^2}{hr}}\implies \cfrac{2}{3}\cdot \cfrac{2}{1}\implies \cfrac{4}{3}\implies 1\frac{1}{3}\frac{ft^2}{hr}[/tex]

Answer:

Step-by-step explanation:

In order to answer all of these questions we need the position function and the acceleration function.  We will discuss why when we get there.

The velocity function is given; in order to find the position function we have to take the antiderivative of the velocity function.  So in order are the position, velocity, and acceleration functions below:

[tex]s(t)=\frac{1}{3}t^3-\frac{9}{2}t^2+18t+1[/tex]

[tex]v(t)=t^2-9t+18[/tex]

[tex]a(t)=2t-9[/tex]

I know the constant on the position function is 1 because the info given tells me that s(0) = 1.

For the first question, the formula to find the average velocity is as follows:

[tex]v_{avg} =\frac{s(t_{2})-s(t_{1})  }{t_{2}-t_{1}  }[/tex]

To find s(t2) and s(t1) we sub in 8 for t2 and 0 for t1 to get the following:

[tex]v_{avg}=\frac{\frac{83}{3}-1 }{8-0}[/tex]

That simplifies to

[tex]v_{avg}=\frac{10}{3}m/sec[/tex]

The second question wants the instantaneous velocity at t = 5.  We get this by subbing in a 5 for t in the velocity function:

[tex]v(5)=(5)^2-9(5)+18[/tex] and

v(5) = -2.  This means that the velocity of the particle is 2 m/sec, but it is now going in the opposite (or negative) direction.

The third question is asking for the time interval when the particle is moving to the right.  On a velocity/time graph, the x's represent the time and the y's represent the velocity.  If the "y" values are positive, then the velocity is positive and that means the object is moving to the right.  Where the "y" values are negative, that means that the velocity is negative and the object is moving to the left.  To find the answer to this problem we think about the positive and negative y values.  Because this is a parabola, I know that the places where the graph goes through the x-axis is where the velocity changes from positive to negative and back to positive.  In order to find those places where the graph goes through the x-axis I have to factor the velocity function.  When I throw that into the quadratic formula on my calculator I get that x = 3 and x = 6.  Completing the square on the velocity function gives me a vertex of [tex](\frac{9}{2},-\frac{9}{4})[/tex]

Because the y value of the vertex is negative, that means that the values of x from negative infinity to x = 3 give positive velocity values, between x = 3 and x = 6 the values of the velocity are negative, and from x = 6 to x = positive infinity the velocity is positive again.  

So to sum up question 3, the particle is moving to the right on the intervals

(-∞, 3] and [6, ∞)

The fourth question is really tricky.  It requires you to remember some of your Physics and how velocity and acceleration vectors are related.  If the acceleration and the velocity both have the same sign, whether it be positive or negative, the object is speeding up.  If the acceleration and velocity vectors have opposite signs, one positive and one negative, then the object is slowing down.  We already know that from negative infinity to 3 the velocity is positive, so let's check the acceleration values in that interval.  I only need to test one number, so let's test a(2).  

a(2) = 2(2) - 9 and a(2) = -5

-5 means the object is slowing down here since the velocity is positive and the acceleration is negative.  

Let's test the interval between 3 and 6.  Let's test a(4).

a(4) = -1

Between the interval of 3 and 6 seconds, the velocity is negative.  Since the acceleration is also negative, the object is speeding up between the time interval [3, 6].

We already found that from the left of t = 3, the object was slowing down; so it would also be slowing down to the right of t = 6.

Phew!  That's it!  We're done!

Answer:

  ASA

Step-by-step explanation:

Angles E/R and O and the sides EO/RO between them are indicated as congruent. Hence the Angle-Side-Angle (ASA) postulate will be the one that is applicable.

Answer:

  A.  $4200

Step-by-step explanation:

A "point" is 1% of the loan value, so the cost of 3 points is ...

  0.03 × $140,000 = $4,200

Hilary must bring an additional $4200 to closing.

The additional money Hilary needs to bring to closing the mortgage is given by A = $ 4,200

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Typically, one point is equal to 1% of the total loan amount. Therefore, if Hilary is purchasing 3 points to lower her interest rate, she will need to pay an amount equivalent to 3% of her $140,000 mortgage, which is:

On simplifying the equation , we get

3% x $140,000 = $4,200

Hence , the money is $ 4,200

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Final answer:

To cover a 81 meter by 117 meter field with pallets of grass, we calculate the area in square yards and then the number of pallets needed. Each pallet covers 90 square yards and costs $210. The total cost is $27,300.

Explanation:

The question involves calculating the cost to cover a rectangular field with pallets of grass. The field measures 81 meters by 117 meters. We will first need to calculate the area of the field in square meters and then convert it to square yards since the pallets cover an area in square yards. Then, we'll find out how many pallets are needed and multiply by the cost per pallet to get the total cost.

First, let's find the area of the field in square meters:

Area = length × width = 81 m × 117 m = 9,477 m²

Now, convert square meters to square yards, using the hint that 1 yard ≈ 0.9 meters. Since the area is given in meters and we have that 1 m² = (1/0.9)² yd², we can use:

Area in yd² = 9,477 m² × (1/0.9)² = 9,477 m² × 1.23456790123 yd²/m² ≈ 11,700 yd²

Each pallet of grass covers 90 square yards, so we divide the total area by the coverage per pallet:

Number of pallets = Area in yd² / Coverage per pallet = 11,700 yd² / 90 yd²/pallet ≈ 130 pallets

Finally, we multiply the number of pallets needed by the cost per pallet to get the total cost:

Total cost = Number of pallets × Cost per pallet = 130 × $210 = $27,300

The total cost to cover the field with pallets of grass will be $27,300.

Final answer:

To cover a 81m by 117m field with pallets of grass, you need approximately 130 pallets, resulting in a total cost of $27,300.

Explanation:

The question asks us to calculate the cost to cover a rectangular field with grass pallets. The field's dimensions are 81 meters by 117 meters. First, we need to calculate the field's area in square meters and then convert that area to square yards as the pallet covers a certain number of square yards. Lastly, we will determine the total cost by multiplying the number of pallets needed by the cost per pallet.

To convert the field area from square meters to square yards, we use the approximation given that 1 yard is almost equal to 0.9 meters. So, we have:

To find out how many pallets we need:

The cost to cover the entire field is therefore:

Answer:

x-1 = 0  or x-7 =0

x=1                      or x=7

Step-by-step explanation:

(x-1) (x-7) =0

Using the zero product property

x-1 = 0  or x-7 =0

x-1+1 =0 +1    or x-7+7 =0+7

x=1                      or x=7

Answer:

Step-by-step explanation:

-8 - 7 - 16 - 14 + 2 = -43