Mathematics High School

why is 5 a rational number?

Answers

Answer 1
Every integer is a rational number, since each integer n can be written in the form n/1. For example 5 = 5/1 and thus 5 is a rational number.  i hope this helps you
Answer 2
A rational number is any number that can be written as a ratio of two integers (hence the name!). In other words, a number is rational if we can write it as a fraction where the numerator and denominator are both integers.

5 is a rational number because it can be expressed as the quotient of two integers: 5÷ 1

Hope this helps!! ;))
Have a grat day!! <3

Related Questions

helppppppppppppppppppppp

Answers

Answer:
1.796

Explanation:
log base 6 of 25 can be rewritten as:
log base 6 of (5^2) = 2 * log base 6 of 5 
                               = 2 *0.8982
                               = 1.7965

Hope this helps :)

If the function graphed is f(x), find f(1).
A) -4
B) -1/4

C) 0
D) 4

Answers

Answer: choice A) -4

-----------------------------------------------

Step 1) Draw a vertical line through 1 on the x axis

Step 2) Mark the point where the vertical line and the blue curve intersect (or cross each other)

Step 3) Draw a horizontal line through the point marked in step 2. Note how this horizontal line goes through -4 on the y axis. 

So the point (1,-4) is on the blue curve. This means if x = 1 is the input then y = -4 is the output. Recall that y = f(x). So f(x) = -4 is the output as well when the input is x = 1.

In short, this is why f(1) = -4

please help.
solve the inequality |6 - v| < 9

write the inequality as two inequalities with the absolute value and give a solution set.

Answers

-9 < 6 -v < 9 . . . . two inequalities
-15 < -v < 3 . . . . . subtract 6
-3 < v < 15 . . . . . . multiply by -1

Joes is 10 years older than james. in 8 years joe will be three times older than james. how old are they now

Answers

Joes is 16 and James is 6!!

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Answers

I agree with the 14x all right, but the remainder of the other part is 178. I'm going to recheck my answer. I'm not confident about using synthetic division for this question. It is 57 years since I did something like this. If I was more confident, I would list the results of synthetic division because it is much easier to show than long division. I'm saying the answer should be 14x + 178.

we are given

[tex]\frac{3x^6-19x^4-4x^3-24x^2+2x+178}{-2x^2-6}[/tex]

we can use long division method to divide it

so, we get

[tex]Quotient=-\frac{3x^4}{2}+14x^2+2x-30[/tex]

[tex]Remainder=14x-2[/tex]...........Answer


PLZ HELP ME ON THIS

PLZ EXPLAIN IT TO ME

Answers

I think it might be the first one 400(1.04) it can't be the last cause 80(1.04) + 5 is basically like the third one 85(1.04).
80 * 5 = 400 
Hope it helps

A freight carrier charges $0.57 for a package weighing up to one ounce plus and additional $0.32 for each additional ounce or fraction of an ounce. A company is shipping a package weighing 224 grams. What is the weight of the package in ounces?

Answers

There are approximately 8 ounces (7.901) in 224 grams. 

Answer:

its is 8 oz 224 grams is = to 7.901

Step-by-step explanation:


If the clock has a radius of 15 inches, how many inches of ribbon will terry need to use to surround the clock?

Answers

the circumference is C=2*3.14*r
r=15 inches
C=2*3.14*15=94.20 inches of ribbon 

A large bag of marbles contains an equal amount of red, orange, yellow, blue, and green marbles. Brody randomly selects 1 marble from the bag. Which of the following represents the probability of selecting a red, blue, yellow, or green marble
A) 0.8
B) 0.7
C) 0.9
D) 0.6

Answers

the answer will be
[tex] \frac{4}{5} = 0.8[/tex]
hope this helps

Answer:  The correct option is (A) 0.8.

Step-by-step explanation:  Given that a  large bag of marbles contains an equal amount of red, orange, yellow, blue, and green marbles. Brody randomly selects 1 marble from the bag.

We are to find the probability of selecting a red, blue, yellow or green marble.

Let n be the number of each color of marbles in the bag.

That is, the number of red, orange, yellow, blue, and green marbles, each equals n.

Let S denote the sample space of selecting a marble from the bag and A denote the event of selecting a red, blue, yellow or green marble.

Then, we have

n(S) = n + n + n + n + n = 5n,

n(A) = n + n + n + n = 4n.

Therefore, the probability of event A is given by

[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{4n}{5n}=\dfrac{4}{5}=0.8.[/tex]

Thus the required probability selecting a red, blue, yellow or green marble is 0.8.

Option (A) is CORRECT.

Find the product of (x + 5)(x − 5). (1 point)


x2 − 10x + 25

x2 + 10x + 25

x2 − 25

x2 + 25

Answers

FOIL (first outside inside last)

x^2-5x+5x-25 = x^2-25
The answer is x2- 25 hope this helps!

12 ticket sellers, 25 cleaning persons, and 15 ushers employees will be paid $10, $7.50, 8.50 per hour for 50 hours per month what is the monthly salary

Answers

----------------------------------------------------------
Ticket Sellers
----------------------------------------------------------
1 ticket seller  = $10 x 50
1 ticket seller  = $500

12 ticket sellers = $500 x 12
12 ticket sellers = $6000

----------------------------------------------------------
Cleaning person
----------------------------------------------------------
1 cleaning person = $7.50 x 50 
1 cleaning person = $ 375

25 cleaning person = $375 x 25
25 cleaning person = $9375

----------------------------------------------------------
Ushers
----------------------------------------------------------
1 usher = $8.50 x 50
1 usher = $425

15 ushers = $425 x 15
15 ushers = $6375

----------------------------------------------------------
Total
----------------------------------------------------------
$6000 + $9375 + $6375 = $21750

----------------------------------------------------------
Answer: Total monthly salary per month = $21750
----------------------------------------------------------

Compare and Contrast: Below are two equations. Solve each equation and compare the two solutions. Choose the statement that is true about each solution. Equation #1 Equation #2 |2x - 4| = 5 |3x - 4| = -12 Equation #1 and Equation #2 have the same number of solutions. Equation #1 has more solutions than equation #2. Equation #1 has fewer solutions than equation #2. None of the statements above describe the number of solutions to equations shown.

Answers

Equation 1:

[tex]|2x-4|=5[/tex]

This means:

[tex]2x-4=5[/tex] and [tex]2x-4=-5[/tex]

Simplifying both the equations we get:

x = 4.5 and x = - 0.5

Equation 2:
[tex]|3x-4|=-12[/tex]

There is no solution to this equation, as the modulus or absolute value of any expression can never be negative

Therefore, we can conclude that Equation 1 has more number of solutions that Equation 2.

a building in san francisco is shaped like a square pyramid it has a slant height og 856.1 feet and each side of its base is 145 feel long find the lateral area of the building

Answers

we know that

for a Square Pyramid
[lateral area]=4*[a*s/2]--------> 2aS

where
a  is the length side of the square base
S is the slant height
a=145 ft
S=856.1 ft

[lateral area]=2*145*856.1---------> 248269 ft²

the answer is 248269 ft²

The area of a right triangle with one leg measuring 5ft and hypotenuse measuring 13ft is

A 30ft to the 2
B 37.5 ft to the 2
C 65ft to the 2

Answers

Calculating the other leg:
other leg^2 = 13^2 - 5^2
other leg^2 = 169 -25
other leg^2 = 144
other leg = 12

Area = .5 * 12 *5
Area = 30 sq feet
answer is A


99pts WILL GIVE BRAINLIEST Use the diagram and given information to answer the questions and prove the statement. Given: X Z 
 Prove: [see image] Re-draw the diagram of the overlapping triangles so that the two triangles are separated.


What additional information would be necessary to prove that the two triangles, XBY and ZAY, are congruent?

What congruency theorem would be applied?

Prove using a list/flow chart proof.

Answers

I will base the figure from the one you attached in the other problem you posted. (Also attached here).

Statements [Reasons]
1. Angle X is congruent to Angle Z [Given]
2. Line XY is congruent to Line YZ [Given]
3. Angle Y is congruent to Angle Y [Congruence is reflexive]
4. Triangle XBY is congruent to Triangle ZAY [ASA]

ANSWER: The ASA (Angle Side Angle) Congruency Theorem could be applied.

Can someone please help me solve for x and y? Thank you

Answers

Answer: 
Choice D) x*y = -10

============================================

Explanation:

Multiply both sides of the first equation by 10 to clear out the fractions (10 is the LCD)
3x/5 + y/2 = 13/10
10*(3x/5 + y/2) = 10*(13/10)
6x + 5y = 13

Multiply both sides of the second equation by 100 to get each decimal value to turn into a whole number (move the decimal point over 2 spots to the right)
0.5y + 0.04x = 2.42
50y + 4x = 242
4x + 50y = 242

So we have this new system of equations which is equivalent to the original system
6x + 5y = 13
4x + 50y = 242

Multiply both sides of the top equation by 10 so that the 5y turns into 50y
6x + 5y = 13
10*(6x + 5y) = 10*13
60x + 50y = 130

Now we have this system of equations
60x + 50y = 130
4x + 50y = 242

If we subtract straight down then we have
60x-4x = 56x
50y-50y = 0y = 0 ... notice how the y terms go away effectively
130-242 = -112

The y terms go away leaving us with this simplified equation
56x = -112
Which solves to
x = -2
when we divide both sides by 56

Now use that x value to find y
6x + 5y = 13
6(-2) + 5y = 13 ... replace x with -2
-12 + 5y = 13
-12+5y+12 = 13+12 ... adding 12 to both sides
5y = 25
5y/5 = 25/5 .... dividing both sides by 5
y = 5

In summary we have x = -2 and y = 5. Therefore, x*y = -2*5 = -10 is the answer

6.3% of 41 is?

a. 2.6
b. 6.5
c. 258.3
d. 650.8

Answers

(41/100)6.3= 2.583≈ 2.6
a✓
I think it's A 2.6 hope that helps

Carbon-14 has a half-life of 5,730 years. If the age of an object older than 50,000 years cannot be determined by radiocarbon dating, then

* carbon-14 levels in a sample are undetectable after approximately ten half-lives.
* carbon-14 levels in a sample are undetectable after approximately nine half-lives.
* the half-life of carbon-14 is too long to accurately date the object.
* a radioisotope with a shorter half-life should be used to date the object.

Answers

* carbon-14 levels in a sample are undetectable after approximately nine half-lives.
Nine half-lives pf carbon 14 is 51,570 years.

Source:
https://en.wikipedia.org/wiki/Radiocarbon_dating


C-14 has a half-life of 5730 years. Let's figure out how many half lives would pass in 50,000 years. We take 50,000 and divide it by 5730 = 8.72 half-lives. This is fairly close to 9. The answer is B) C-14 levels in a sample are undetectable after approximately nine half-lives.

Please help.
What are the dimensions of the matrix?
⎡1 0 9⎤
⎢-2 3 5⎢
⎢5 4 -6⎢
⎣11 5 7⎦
Enter your answers in the boxes.
The matrix is a [_] × [_] matrix.

Answers

Matrices always go row x column.

Count the rows: 4

Count the columns: 3

The matrix is a 4 x 3 matrix

The size of a matrix is defined by the number of rows and columns that it contains.

The dimensions of a matrix are the number of rows by the number of columns.

The number of rows and columns of a matrix, written in the form rows×columns.

The given Matrix has four rows and three columns,

The rows go side to side; the columns go up and down. "Row" and "column" are technical terms, and are not interchangeable.

Matrix dimensions are always given with the number of rows first, followed by the number of columns.

The matrix is a [4_] × [3_] matrix.


3. Divers looking for a sunken ship have defined the search area as a triangle with adjacent sides of length 2.75 miles and 1.32 miles. The angle between the sides of the triangle is 35. To the nearest hundredth, find the search area. 2.08 mi²
2.97 mi²
1.49 mi²
1.04 mi²

Answers

Area = (1/2) x 2.75 x 1.32 x sin(35 deg) = 1.815 x (0.573576) = 1.04 sq. miles.

Answer:

2.08 mi²

Step-by-step explanation:

Since, the area of the triangle is,

[tex]A=s_1\times s_2\times sin \theta[/tex]

Where, [tex]s_1[/tex] and [tex]s_2[/tex] are adjacent sides and [tex]\theta[/tex] is the included angle of these sides,

Here, [tex]s_1[/tex] = 2.75 miles,

[tex]s_2[/tex] = 1.32 miles,

And, [tex]\theta[/tex]  = 35°,

hence, the area of the given triangle is,

[tex]A=2.75\times 1.32\times sin 35^{\circ}[/tex]

[tex]= 3.63\times 0.57357643635[/tex]

[tex]= 2.08208246395\approx 2.08\text{ square miles}[/tex]

El lote de la familia lópez tiene un lote de 16m*10m y se desea construir una casa de base rectangular en el centro de el.¿que dimensiones debe tener el rectángulo del piso de la casa si tiene un área de 91m2?

Answers

The dimensions of the house should be 7 m by 13 m.

If the house is to be centered, we will take the same amount from the width as we do from the length of the lot for the dimensions.  This gives us (10-x) and (16-x) as the dimensions.

The area of a rectangle is found by multiplying the length and width:
(10-x)(16-x) = 91

Multiplying the binomials we have:
10*16 - x*10 - x*16 -x*(-x) = 91
160 - 10x - 16x --x² = 91
160-10x-16x+x² =91

Combine like terms:
160-26x+x²=91

Rewrite this in standard form:
x²-26x+160=91

Subtract 91 from both sides:
x²-26x+160-91 = 91-91
x²-26x+69 = 0

Factoring this, we look for factors of 69 that sum to -26.  -23*-3 = 69 and -23+-3 = -26, so:

(x-23)(x-3) = 0

Using the zero product property we know that either x-23=0 or x-3=0, so x=23 or x=3. 

x was the amount we take off of the width and length of the lot; if we took 23m off of it, 10-23 gives us a negative amount, which is not realistic. This means both the width and length are subtracted by 3.

10-3 = 7 and 16-3 = 13.

These are the dimensions of the house.

Please help me answer

Answers

1. given
2. transitive prop of equality 
3. subtraction property of equality

2, 4, 6, 8, 10
I know this diverges but what is the limit?

Also, is there a limit with numbers that repeat? (ie: -1,1,-1,1...(-1)^n)

Answers

1. You are right, this sequence diverges (or converges to infinity) so

[tex]$\lim_{n\to\infty}\,2n=\infty[/tex]

2. In this case limit does not exist.

which are the solutions of the quadratic equation x^2=9x+6

Answers

You can use the quadratic equation to solve this once you have this set equal to zero. The answers would be roughly 9.6 and -0.6. 

The solutions of the quadratic equation [tex]\(x^2 = 9x + 6\)[/tex]are:

[tex]\[x = \frac{9 + \sqrt{105}}{2}\][/tex] and [tex]\[x = \frac{9 - \sqrt{105}}{2}\][/tex]

To find the solutions of the quadratic equation [tex]\(x^2 = 9x + 6\)[/tex], we need to rewrite it in standard quadratic form [tex]\(ax^2 + bx + c = 0\).[/tex]

Given:

[tex]\[x^2 = 9x + 6\][/tex]

Subtract [tex]\(9x\) and \(6\)[/tex] from both sides to get it in standard form:

[tex]\[x^2 - 9x - 6 = 0\][/tex]

Now, to solve this quadratic equation, we can factor it or use the quadratic formula:

The quadratic formula is:

[tex]\[x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\][/tex]

For our equation:

[tex]\[a = 1, b = -9, \text{ and } c = -6\][/tex]

Substituting these values into the quadratic formula:

[tex]\[x = \frac{-(-9) \pm \sqrt{(-9)^2-4(1)(-6)}}{2(1)}\]\[x = \frac{9 \pm \sqrt{81+24}}{2}\]\[x = \frac{9 \pm \sqrt{105}}{2}\][/tex]

So, the solutions of the quadratic equation [tex]\(x^2 = 9x + 6\)[/tex]are:

[tex]\[x = \frac{9 + \sqrt{105}}{2}\][/tex] and [tex]\[x = \frac{9 - \sqrt{105}}{2}\][/tex]

30 POINTS + BRAINLIEST! SHOW YOUR WORK FOR BRAINLIEST PLEASE!

Answers

A four sided figure that figs inside a circle is called a cyclic quadrilateral. One of the properties of such a figure is that the opposite angles add up to 180o

2x + 3 + 4x + 3 = 180o
6x + 6 = 180
6x = 174
x = 174 / 6
x = 29

C = 2x + 1
C = 2*29 + 1
C = 59o

2x+3+4x+3= 180o     6x+6=180    6x=174    174/6   29

2x+1    (2)29+1     59o

Step-by-step explanation:

The sales tax on a $250 computer is 17.50. find the sales tax rate.

Answers

if we take 250 to be the 100%, what is 17.50 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 250&100\\ 17.50&t \end{array}\implies \cfrac{250}{17.50}=\cfrac{100}{t}\implies t=\cfrac{17.50\cdot 100}{250}[/tex]

Abby walked miles on Monday, miles on Tuesday, and miles on Wednesday. What is the total distance Abby walked in the three days?
a. miles
b. miles
c. miles
d. miles

Answers

Answer:WE Cant se the numbers

Step-by-step explanation:the ancwer would be 7 and 7/12

What is the missing value in the following arithmetic sequence?

Answers

3.8 - 2 = 1.8

so
5.6 + 1.8 = 7.4

missing is 7.4

answer is C. 7.4

Answer:

Step-by-step explanation:

Alright, lets get started.

The first term is 2 and the second term is 3.8.

It means the common difference is [tex]3.8-2 = 1.8[/tex]

So, adding common difference :

First term = 2

Second term = 3.8

Third term = [tex]3.8+1.8=5.6[/tex]

Fourth term = [tex]5.6+1.8 = 7.4[/tex]

So the answer is 7.4   :   answer

Hope it will help :)

Use the formula V = s³, where V is the volume and s is the edge length of the cube, to solve this problem.A cube-shaped bin has an edge length of 34 yard.What is the volume of the container? Enter your answer, as a fraction in simplest form, in the box.

Answers

Volume: 39,304 cubic yards

To find the volume, you simply have to use the formula that is given. It is V = s^3.  This means you multiply the side by itself 3 times.

S x S x S = V
34 x 34 x 34 = 39304 cubic yards

Let g(x) = 2x and h(x) = x2 + 4. Evaluate (h ∘ g)(1). 2 8 10 4

Answers

Hello!

You can solve this by plugging 1 into [tex] g(x) [/tex] and plugging the result into [tex] h(x)[/tex].

[tex]g(x) = 2x[/tex]
[tex]g(1) = 2(1)[/tex]
[tex]g(1) = 2[/tex]

[tex]h(x) = 2x + 4[/tex]
[tex]h(g(1)) = 2(2) + 4[/tex]
[tex]h(g(1)) = 4 + 4[/tex]
[tex]h(g(1)) = 8[/tex]

Answer:
(h ∘ g)(1) = 8
Other Questions
Your parents have decided to buy a new Toyota 4Runner for 25,635. According to the dealer, the car will depreciate in value approximately $3,000 per year. Write and solve a linear equation to find how many years it will be until the car is worth $3,135 Trayvon sells candy bars at a price of $3 each. He purchases every order of 200 candy bars for $350. If the cost of shipping is $0.15 per bar, what is Trayvons profit function? What conditions in the nucleus are likely to result in an atom undergoing radioactive decay?a. When the attraction of the strong force is weaker than the repulsion of the electrostatic forceb. When the repulsion of the strong force is weaker than the repulsion of the electrostatic forcec. When the repulsion of the strong force is greater than the attraction of the electrostatic forced. When the attraction of the strong force is greater than the attraction of the electrostatic force, After the sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a white dwarf state. in this state, it would have approximately the same mass as it has now, but its radius would be equal to the radius of the earth. (a) calculate the average density of the white dwarf. Lexi bought 1 2/5 of green grapes and 2 3/10 of red grapes. Grapes are 2.99 a pound.Did lexi spend more or less then $12? The Pythagorean theorem describes the relationship between the lengths of legs a and b and the hypotenuse c of any right triangle. a 2 + b 2 = c 2 Complete the equation below by writing an expression equivalent to the length of a, the leg of a right triangle. While Joey was standing outside on a sunny day, his shadow was 5 feet long. The shadow of a nearby Oak tree was 12 feet long. If Joey is 6 feet tall, how tall is the Oak tree? 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Determine the volume of water that can remain in the cylinder after the ball is inserted so that the water rises to the top edge of the cylinder without spilling What experience do you have caring for children? What ages of child have you worked with? What have you observed about the needs, behaviors, and abilities of children at different ages? How do you nurture different kinds of children at different stages of life? Compare your experiences with the rest of the class. Read the stanza. From The Tyger by William Blake Tyger Tyger, burning bright, In the forests of the night; What immortal hand or eye, Could frame thy fearful symmetry? In The Tyger, to what does the fearful symmetry of the tiger refer? 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