Can the sum of two irrational numbers ever be a rational number?

Answers

Answer 1

Irrational numbers are numbers that can not be written as a ratio of two integers. (example: square root of 2). Rational numbers on the other hand can be written as a ratio, as decimal or percentage.
If X is a irrational number, than the number Y=1-X is also irrational and the sum of these two irrational numbers is: X+Y=X+1-X=1 is rational number.
So, the sum of two irrational numbers can be a rational number.

Related Questions

A jacket is on sale for $15 off. As part of a one-day sale, a 20% discount is applied to all purchases. If x represents the original price of the jacket, which expression represents the final price of the jacket during this sale? 0.2x – 3 0.8x – 12 0.8x – 15 0.2x – 15

Answers

Answer:

0.8x – 12

Explanation:

The sale price is (x-15). After the 20% discount, the final price is 0.80 times the sale price, so is ...

... final price = 0.80×(x -15) = 0.80x -12

Answer:

The correct option is B.

Step-by-step explanation:

Let the original price of the jacket be x.

A jacket is on sale for $15 off. As part of a one-day sale, a 20% discount is applied to all purchases.

The price of jacket after $15 off is [tex]x-15[/tex].

Then 20% discount is applied, so the final price of the jacket is

[tex]P=(x-15)(1-\frac{20}{100})[/tex]

[tex]P=(x-15)(1-0.2)[/tex]

[tex]P=(x-15)(0.8)[/tex]

[tex]P=0.8x-12[/tex]

The final price of the jacket during this sale is 0.8x-12. Therefore the correct option is B.

A flagpole cast a shadow 16 feet long at the same time a pole 9 feet high casts a shadow 6feet long what is the height in feet of the flagpole

Answers

The pole would be 24 feet high.
X/16=9/6
X=24

Consider a line l with positive x- and y- intercepts. Suppose l makes an angle of with the positive x- axis. What is the slope of l in terms of theta?

Answers

check the picture.

line l is the orange line, intersecting the positive x-axis and the positive y axis.

The angle with measure ∅ is the angle made by the line and the positive x-axis. It is the obtuse (>90° angle) shown in the picture.

the slope of the line l is tan∅

Tank 1 initially contains 50 gals of water with 10 oz of salt in it, while tank 2 initially contains 20 gals of water with 15 oz of salt in it. water containing 2 oz/gal of salt flows into tank 1 at a rate of 5 gal/min and the well-stirred mixture flows from tank 1 into tank 2 at the same rate of 5 gal/min. the solution in tank 2 flows out to the ground at a rate of 5 gal/min. if x1(t) and x2(t) represent the number of ounces of salt in tank 1 and tank 2, respectively, set up but do not solve an initial value problem describing this system.

Answers

[tex]\dfrac{\mathrm dx_1}{\mathrm dt}=\dfrac{2\text{ oz}}{1\text{ gal}}\dfrac{5\text{ gal}}{1\text{ min}}-\dfrac{x_1(t)\text{ oz}}{50\text{ gal}}\dfrac{5\text{ gal}}{1\text{ min}}[/tex]
[tex]\dfrac{\mathrm dx_2}{\mathrm dt}=\dfrac{x_1(t)\text{ oz}}{50\text{ gal}}\dfrac{5\text{ gal}}{1\text{ min}}-\dfrac{x_2(t)\text{ oz}}{20\text{ gal}}\dfrac{5\text{ gal}}{1\text{ min}}[/tex]

[tex]\implies\begin{cases}\dfrac{\mathrm dx_1}{\mathrm dt}=10-\dfrac1{10}x_1\\\\\dfrac{\mathrm dx_2}{\mathrm dt}=\dfrac1{10}x_1-\dfrac14x_2\\\\x_1(0)=10\\\\x_2(0)=15\end{cases}[/tex]

let A and B be nxn matrices such that AB is singular prove that either A or Bis singular

Answers

[tex]\det(\mathbf{AB})=\det\mathbf A\times\det\mathbf B[/tex]

Because [tex]\mathbf{AB}[/tex] is singular, we have

[tex]\det(\mathbf{AB})=0[/tex]

from which it follows that either [tex]\det\mathbf A=0[/tex] or [tex]\det\mathbf B=0[/tex].

the formula I=square root w/r gives the electric current I amperes that flows through an appliance, where W is the power in watts and R is the resistance in ohms. which set of numbers best describes the value of I for the given values of W and R? ( 42.) W=100,R=25 ( 43.)W=100,R=50

Answers

Final answer:

The value of I for the given values of W and R can be calculated using the formula I = [tex]\sqrt{(W/R)[/tex]. For W = 100 and R = 25, the value of I is 2 amperes. For W = 100 and R = 50, the value of I is approximately 1.41 amperes.

Explanation:

The formula I = [tex]\sqrt{(W/R)[/tex] gives the electric current in amperes that flows through an appliance, where W is the power in watts and R is the resistance in ohms.

To determine the value of I for the given values of W and R, we can simply substitute the values into the formula. For the first set of numbers, W = 100 and R = 25:

[tex]I = \sqrt{(100/25)} = \sqrt{(4)} = 2[/tex] amperes.

For the second set of numbers, W = 100 and R = 50:

[tex]I = \sqrt{(100/50)} = \sqrt{(2) }[/tex]≈ 1.41 amperes.

Therefore, the value of I for the first set of numbers (W = 100, R = 25) is 2 amperes, and the value of I for the second set of numbers (W = 100, R = 50) is approximately 1.41 amperes.

Suppose there is a test for esophageal cancer that is 95% accurate both on those that do and those that do not have esophageal cancer. if 0.7 percent of the population has esophageal cancer, compute the probability that a person has this cancer, given that his or her test results indicates so.

Answers

It was already stated that the probability that the population may have esophageal cancer is 0.7 percent. However, the additional statement that the accuracy is 95% will affect the probability as follows:

Probability = (0.007)(0.95) = 0.00665 or 0.665%

So instead of 0.7%, the probability will decreased to 0.665% because of the accuracy.

What if the atom has no charge

Answers

The answer to this question is:

What if the atom has no charge
"Then its called "Not Yet Charge" or "Neutral" because the atom has no Protons, Neutrons or Electrons. And here is one that loses some of it electrons to this is called an Ion"

Hoped This Helped, Mikggc
Your Welcome :)

Each canvas bag will hold exactly 5 pounds of kings tomatoes. How many bags will be necessary to hold 5 kg worth of these same tomatoes? (1 kg = 2.25 pounds)

Answers

1 kg = 2.25 pounds

5*2.25 = 11.25 pounds

11.25/5 = 2.25 bags

so you would need 3 bags

1 kg = 2.25 lbs....so 5 kg = (5 * 2.25) = 11.25 lbs

at 5 lbs per bag.....2 full bags + 1.25 lbs in the other bag...so it would be 3 bags with 1 bag partially full or 2 bags, leaving out 1.25 lbs

what is the value of x in the equation 5(4x-10)+10x=4(2x-3)+2(x-4) ?

-7/4
-1/4
3/20
3/2

Answers

5(4x - 10) + 10x = 4(2x - 3) + 2(x - 4)
20x - 50 + 10x = 8x - 12 + 2x - 8
30x - 50 = 10x - 20
30x - 10x = -20 + 50
20x = 30
x = 3/2 <==

Answer:

[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Here, the given expression is,

[tex]5(4x-10)+10x=4(2x-3)+2(x-4)[/tex]

By distributive property,

[tex]20x - 50 + 10x = 8x - 12 + 2x - 8[/tex]

By combining like terms,

[tex]30x -50=10x-20[/tex]

Adding 50 on both sides,

[tex]30x=10x-20+50[/tex]

[tex]30x = 10x + 30[/tex]

Subtracting 10x on both sides,

[tex]20x = 30[/tex]

Divide both sides by 20,.

[tex]x=\frac{3}{2}[/tex]

Hence, LAST option is correct.

A motorboat takes 3 hours to travel 108 km going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Answers

recall your d = rt, distance = rate * time.

let's say the boat has a still water rate of "b", and the current has a a rate of "c", ok.... when the boat is going upstream, is not really going "b" fast, is going slower at "b - c", due to the current going in the opposite direction.

when the boat is coming downstream, is not going "b" fast either, is going faster, is going "b + c", due to the current adding speed to it.

we know the trip up was 108 kms, thus the return trip is also 108 kms.

[tex]\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ Upstream&108&b-c&3\\ Downstream&108&b+c&2 \end{array} \\\\\\ \begin{cases} 108=3(b-c)\implies \cfrac{108}{3}=b-c\implies 36+c=\boxed{b}\\\\ 108=2(b+c)\\ --------------------\\ 108=2\left(\boxed{36+c} +c \right) \end{cases} \\\\\\ \cfrac{108}{2}=36+2c\implies 54=36-2c\implies \cfrac{54-36}{2}=c[/tex]

and surely you know how much that is.

what's the boat's speed? well, 36 + c = b.

Curt is installing a picket fence around his garden which is 45.45 ft by 14.63 ft. When he gets to the hardware store he finds that each picket fence slat is two feet wide. If Curt does not want any spaces between each slat, use estimation to determine how many slats of fencing he should buy.

Answers

The perimeter of the garden is given

P = 45.45 + 45.45 + 14.63 + 14.63 = 120.16 feet

One picket fence slat is 2 feet wide, so the number of fence Curt should buy is

120.16÷2 = 60.08 rounded to 61 fences

The equation of the line of best fit of a scatter plot is y = −4x − 6. What is the slope of the equation?

−6
−4
4
6

Answers

The slope-intercept form of a line is:

y=mx+b, where m=slope and b=y-intecept

So if y=-4x-6 the slope is -4.

y = -4x -6

the equation is written in slope intercept form ( y = mx +b ) where b is the y intercept
therefore the y intercept is -6

53 ℃ below zero degrees

Answers

your answer is -53 degrees celsius

hope this helps

Hello, I'm working on a project and I've been stumped.

How would I find the central ark of a ferris wheel? I'm using the London Eye ferris wheel for my project, and so far I know it has a diameter of 120 meters and 32 cars. It has a circumference of 377m and an area of 11,310m.

How can that information help me? Please include all steps and a clear explanation, and give the answer in degrees. Thank you.

Answers

a circle has 360 degrees

the ferris wheel has 32 cars so the circle is broken up into 32 sections

the central angle would be the angle between 2 of the cars

so divide 360 by 32

360/32 = 11.25 degrees

Lena bought 10 pounds of potatoes for $5.50 write the cost as cents per pound

Answers

10 pounds of potatoes for $5.50
one pound = $5.50 / 10 = $0.55

answer

it cost 55 cents per pound

Just set the proportional problem up with the total cost over the total pound

Convert the measurement as indicated.

26ft= _ yd _ ft

Answers

26ft(yd/3ft)

8yd+2yd/3

8yd+(2yd/3)(3ft/yd)

8yd+2ft

8yd 2ft

1 yard is 3 feet, and 26÷3 is 8, and we have 2 left over (3×8=24)

So the correct answer would be 26 ft=8 yd and 2 ft.

What is after 100,99,07,94,90

Answers

100,99,07,94,91. The ones has to go up one.

please vote my answer brainliest. thanks!

If 12 bumper stickers cost $8.64, then how much do 18 cost

Answers

In order to solve this problem, we must first find the GCF of 12 and 18. This would be six. Next, we would need to find out the value of six stickers. This can be done by halving the value of 12, as 6 is one-half of 12. 8.64/2 = $4.32, which is the cost of 6 stickers. Next, we need to multiply the cost of six stickers by 3 in order to get the cost of 18 stickers, because 18 is three times 6. 4.32 x 3 = $12.96. Therefore, the cost of 18 stickers is $12.96.

Hope this helps!

The proportion is solved and the cost of 18 bumper stickers is $ 12.96.

Given data:

To find out how much 18 bumper stickers cost, use a proportion since the cost of bumper stickers is directly proportional to the number of stickers.

Cost of 12 bumper stickers / Number of 12 bumper stickers = Cost of 18 bumper stickers / Number of 18 bumper stickers

On simplifying the proportion:

$8.64 / 12 = x / 18

Now, solve for x (the cost of 18 bumper stickers):

x = ($8.64 / 12) * 18

x = $12.96

Hence, 18 bumper stickers cost $12.96.

To learn more about proportion, refer:

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The Greasy Grab Bag claims that customers can make 20 different meal combinations from the menu items. If the Greasy Grab Bag has 4 sandwiches, 3 sides, and 2 drinks, which of the following is correct?

Answers

The answer is A. The Greasy Grab Bag is understating the number of meal combinations.
4 * 3 * 2 = 24
and 24 > 20

The correct number of different meal combinations that customers can make from the menu items at the Greasy Grab Bag is 24.

To determine the number of different meal combinations, we need to consider that each meal consists of one sandwich, one side, and one drink. Given that there are 4 sandwiches, 3 sides, and 2 drinks to choose from, we can calculate the total number of combinations by multiplying the number of choices for each category together.

The number of sandwich choices is 4, the number of side choices is 3, and the number of drink choices is 2. Therefore, the total number of meal combinations is calculated as follows:

Total combinations = Number of sandwich choices — Number of side choices — Number of drink choices

Total combinations = [tex]$4 \times 3 \times 2$[/tex]

Now, let's calculate the total number of combinations:

Total combinations =[tex]$4 \times 3 \times 2 = 12 \times 2 = 24$[/tex]

Thus, there are 24 different meal combinations that customers can make, which means the Greasy Grab Bag's claim of 20 different meal combinations is incorrect. The correct number is 24.

Write an equation of a line that is perpendicular to the given line and that passes through the given point.
-x + 5y= 14; (-5, -2)

A. Y=-5x-27
B.y=-1/5x-27
C. Y=-1/5x-15
D. Y=5x-27

Answers

To determine the equation that would be perpendicular with a certain line, we must first know the characteristics of a perpendicular line. This line would have a 90 degrees angle with another line so that the slope of this line would be the negative reciprocal of the slope of the other line. To write the equation, given a certain point we use the point-slope form of a line, y -y1 = m(x - x1).

Original line: -x + 5y= 14
y = x/5 + 14/5
slope = 1/5

Perpendicular line's slope = -5
y - y1 = m (x - x1)
y - (-2) = -5 (x - (-5))
y = -5x - 25 -2
y = -5x -27

Susan invests
2
times as much money at
8%
as she does at
4%
. If her total interest after
1
year is
$800
, how much does she have invested at each rate?

Answers

Let f=amount invested at 4% and e=amount invested at 8%

0.04f+.08e=800

However, e=2f so the above equation becomes:

0.04f+0.08(2f)=800

0.04f+0.16f=800

0.2f=800

f=$4000, since e=2f

e=$8000

So Susan invested $4000 at 4% and $8000 at 8%.

Final answer:

To find how much Susan has invested at each rate when she invests 2 times as much money at 8% as she does at 4%, create and solve an equation based on the total interest earned.

Explanation:

Susan has invested $x at 4% interest rate and $2x at 8% interest rate.

Given that the total interest after 1 year is $800, we can create the equation: $x(0.04) + $2x(0.08) = $800.

Solving the equation, we find that Susan has $3,000 invested at 4% and $6,000 invested at 8%.

If m and n are positive integers such that the greatest common factor of [tex] m^{2} n^{2}[/tex] and [tex] m n^{3}[/tex] is 45, then which of the following could n equal?
(A) 3
(B) 5
(C) 9
(D) 15
(E) 45

Answers

the greatest common factor of [tex] m^{2} n^{2} [/tex] and [tex]m n^{3} [/tex]

is

gcd(m*m*n*n, m*n*n*n) =m*n*n=[tex]m n^{2} [/tex]

what we did, was to see how many m's and how many n's, each expression have, and then pick the smallest of each letter (factor).

the reason is that the common factor, must have enough m's and n's to divide the m's and n's of both expressions

so
[tex]45=m n^{2} [/tex]
also
[tex]45=5*9=5*3^{2}[/tex]

thus, n is equal to 3

Answer: A)3

Angle BCA is congruent to angle DAC, and angle BAC is congruent to angle DCA by:

the vertical angle theorem.
the alternate interior angles theorem.
the reflexive property.
None of the choices are correct.

Answers

Answer is the alternate interior angles theorem

Angle BAC is congruent to angle DCA by the alternate interior angles theorem. Option B is correct.

What is the angle?

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

here,
The pro[perty of parallel lines states that when two parallel lines intersect by the same transversal line the alternate interior angle will be equal as also the alternate exterior angles.

So,
Line BC and AB are parallel lines and AC is a transversal line,
So,

Angle BAC = angle DCA

Thus, angle BAC is congruent to angle DCA by the alternate interior angles theorem. Option B is correct.

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for f(x) = x^3-7X^2+8x+16 find f(10) using synthetic division

Answers

[tex]\bf x^3-7x^2+8x+16\qquad f(10)\\\\ -------------------------------\\\\ f(10)=r\implies \begin{cases} x=10\\ remainder=r \end{cases}\\\\ -------------------------------\\\\ \textit{so, let's do the division} \\\\\\ \begin{array}{r|rrrrrrrllll} 10&&1&-7&8&16\\ &&&10&30&380\\ -&&-&--&--&--\\ &&1&3&38&\boxed{396}&\leftarrow remainder \end{array}[/tex]

Linear regression describes the extent to which _______ predicts ________.

Answers

Linear regression describes the extent to which the known variable predicts the to-be-predicted variable.

Final answer:

Linear regression describes the extent to which an independent variable predicts a dependent variable through a linear relationship.

Explanation:

Linear regression describes the extent to which an independent variable (x) predicts a dependent variable (y) through a linear relationship.

For example, if we have data that shows the number of hours studied (x) and the test score (y) of students, linear regression can help us determine how well the number of hours studied predicts the test score.

The regression line is used to model the linear relationship between the independent and dependent variables in the population.

Learn more about Linear regression here:

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What is 4.76 hours converted to min and sec

Answers

4hr +(.76hr(60min/hr))

4hr + 45.6 min

4hr+45min+(.6min(60sec/min))

4hr+45min+36sec

4:45:36

Oh, if you really only wanted min and sec without hours...

4hr(60min/hr)+45min+36sec

240min+45min+36sec

285min+36sec

4.76 hours times 60 minutes gives 285.6 minutes. We already have 285 minutes. 60% of 1 minute is 36 seconds, so the answer is 285 minutes and 36 seconds. :D

Compare the value of the
4 in 40 and 400

Answers

The 4 in 40 is in the tens place and the 4 in 400 is in the hundreds place so 40 will be less than 400.

What is the integral of 1/x?

Answers

The indefinite integral is usually written as ln(x) if x>0, as u can see it's undefined for x = 0.

Final answer:

The integral of 1/x is the natural logarithm of the absolute value of x, plus an integration constant C. This expression is central to calculations in many areas of science and mathematics.

Explanation:

The integral of 1/x is known as the natural logarithm of the absolute value of x, plus a constant of integration, commonly referred to as C. In mathematical terms, this is expressed as:

[tex]$ \int \frac{1}{x} dx = \ln(|x|) + C $[/tex]

The natural logarithm arises due to the fundamental properties of the integral, and it's significant as it appears frequently across various fields of science and mathematics. While the basic form of integration of 1/x involves the natural logarithm, in applied examples like the cases mentioned above, where one works with additional functions or domain restrictions, the integral may lead to more complex expressions or even vanish under certain symmetry conditions.

If f(x)=2x^2sqrt(x-2), complete the following statement f(6)

Answers

f(x) = 2x^2 + 5sqrt (x - 2)....when x = 6
f(6) = 2(6^2) + 5 sqrt (6 - 2)
f(6) = 2(36) + 5 sqrt 4
f(6) = 72 + 5 * 2
f(6) = 72 + 10
f(6) = 82

The value of f(6) in the function [tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex] is 82

How to determine the function value?

The function is given as:

[tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex]

Substitute 6 for x

[tex]f(6)=2 * 6^2 + 5\sqrt{6-2}[/tex]

Evaluate the difference

[tex]f(6)=2 * 6^2 + 5\sqrt{4}[/tex]

Evaluate the exponents

f(6)=2 * 36 + 5 * 2

Evaluate the sum of products

f(6) = 82

Hence, the value of f(6) in the function [tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex] is 82