Mathematics High School

What is A rational number? square root of 15, square root of 16 square root of 17, square root of 18

Answers

Answer 1

Answer:

B. [tex]\sqrt{16}[/tex]

Step-by-step explanation:

We have been given 4 numbers. We are asked to find the rational number from our given choices.

We know that a number is a rational number, when it could be written as a fraction.

Let us check our given choices one by one.

A. [tex]\sqrt{15}[/tex]

[tex]\sqrt{15}=3.8729833462074169[/tex]

Since our given number has non-terminating decimal, therefore, [tex]\sqrt{15}[/tex] is not a rational number.

B. [tex]\sqrt{16}[/tex]

[tex]\sqrt{16}=\sqrt{4^2}=4[/tex]

Since our given number is an integer and we can write it as a fraction [tex]\frac{4}{1}[/tex], therefore, [tex]\sqrt{16}[/tex] is a rational number.

C. [tex]\sqrt{17}[/tex]

[tex]\sqrt{17}=4.1231056256176605[/tex]

Since our given number has non-terminating decimal, therefore, [tex]\sqrt{17}[/tex] is not a rational number.

D. [tex]\sqrt{18}[/tex]

[tex]\sqrt{18}=4.2426406871192851[/tex]

Since our given number has non-terminating decimal, therefore, [tex]\sqrt{18}[/tex] is not a rational number.

Answer 2

It is to be noted that from the options given, the rational number is √16

What is a rational number?

A rational number is any number that can be expressed as a fraction, where the numerator and denominator are integers.

Among the given numbers, the √16 is a rational number.

The √16 equals 4, which can be expressed as the fraction 4/1.

The square roots of 15, 17, and 18 are irrational numbers because they cannot be expressed as fractions or terminate or repeat in decimal form.

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Related Questions

Which is an equivalent equation solved for y ?

Answers

d
divide both sides of the function by πx to get y=a/(πx)

Answer:

4th Option is correct.

Step-by-step explanation:

Given:

x and y are the half length of the largest and smallest diameter of the ellipse.

Area of the Ellipse , a = πxy

To find: Equivalent Equation for y.

Consider,

a = πxy

πxy = a

(πx)y = a

transpose πx to RHS,

[tex]y=\frac{a}{\pi x}[/tex]

y = a ÷ ( πx )

Therefore, 4th Option is correct.

Which of the following statements is true?

All trapezoids are parallelograms.
All parallelograms are trapezoids.
All rectangles are squares.
All rhombuses are rectangles.

Answers

Answer:

The answer is B. All parallelograms are trapezoids.

Step-by-step explanation:

The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. That makes the opposite of facing sides are parallel to each other. The the definition of trapezoid is a convex quadrilateral with at least one pair of parallel sides. Therefore, all parallelograms are trapezoids.

The true statement among the given options is, B. All parallelograms are trapezoids.

A trapezoid is a quadrilateral with at least one pair of parallel sides, but it doesn't require all sides to be parallel. Therefore, not all trapezoids are parallelograms. (Statement A is false)

A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Every trapezoid has at least one pair of parallel sides, so it can be considered a special case of a parallelogram. Therefore, all trapezoids are parallelograms. (Statement B is true)

A rectangle is a quadrilateral with all four angles equal to 90 degrees. It has opposite sides that are parallel and equal in length. A square is a special type of rectangle with all sides of equal length. However, not all rectangles have all sides of equal length, so statement C is false.

A rhombus is a quadrilateral with all four sides of equal length. It has opposite sides that are parallel, making it a parallelogram. Since a rectangle is a parallelogram with right angles, and a rhombus is a parallelogram with equal sides. Therefore, statement D is also false.

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7(2+5v)=3v+14 can anyone help???

Answers

7(2+5v)=3v+14

14 + 35v = 3v + 14

14 (-14) + 35v = 3v + 14 (-14)

35v = 3v

unsolvable

hope this helps

The solution to the equation is v = 0.

We have,

To solve the equation 7(2 + 5v) = 3v + 14, we can simplify and isolate the variable v.

Expanding the left side of the equation:

7(2 + 5v) = 14 + 35v

Now we have:

14 + 35v = 3v + 14

Next, we can combine like terms:

35v - 3v = 14 - 14

32v = 0

To solve for v, we divide both sides of the equation by 32:

v = 0/32

v = 0

Therefore,

The solution to the equation is v = 0.

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Front-row tickets for a concert cost $60. After every 5 rows, the ticket price goes down by $5. What is the total amount of money generated by a full house? Info: There are 20 rows that increase by 3 seats each time starting with 18.

Answers

I think I got it, but just in case...tell me the whole thing again. I wasn't listening.

n a 20 row theater, the number of seats increases by 3 with each successive row.  The first row has 18 seats.

a. Write an arithmetic series in summation notation to represent the number of seats in the theater,∑n=12018+3(n−1)b. What is the total seating capacity of the theater?
930 seats

c. Front row seats cost $60.  After every 5 rows, the price drops $5.  What is the amount generated by a full house?
$46950

2.  An arithmetic series has a first term of 4.  The sum of the first 40 terms is 6080.  Find the value of the 40th term?
use the formula
sum of first n terms = n/2 * (s1 + sn)
6080 = 40/2 * (4 + sn)

Suppose that a circular coin has an area a, a radius of r, and a diameter of
d. write a as a function of
d.

Answers

The area of a circle is A= pi * r^2
The radius is half of the diameter, r = (1/2)d
Replace r in the formula with the expression with d

A = pi * ((1/2)d)^2

A = pi * 1/4 * d^2

A = (pi * d^2)/4

Area of the given Circle as the function of its diameter πd²/4

What is circle?

A Circle is the 2D shape which is measured in the terms of its radius.

Given that Area, radius and diameter of the given Circle is a , r and d respectively.

Area of Circle (A) = π X radius²

radius = diameter/2

Therefore replacing radius by diameter we get,

A = π(d/2)²

A = πd²/4

Hence, Area as a function of d is given by A = πd²/4

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In how many ways can i arrange the 6 letters a, b, c, d, e, f?

Answers

If there are no restrictions, there can be;

6 ways x 6 ways x 6 ways x 6 ways x 6 ways x 6 ways = 6^6 ways for the letters a, b, c, d, e and f to be arranged.

However, if you want to arrange them so that each letter is used only once;

6 ways x 5 ways x 4 ways x 3 ways x 2 ways x 1 way = 6! ways

Hope I helped :)

A street that is 270m long is covered in snow. city workers are using a snowplow to clear the street. a tire on the snowplow has to turn 45 times in traveling the length of the street. what is the diameter of the tire?

Answers

1.9 meters is the diameter of the tire

Solve an equation to answer the question

Jose bought 2 movie tickets and a box of popcorn. The popcorn cost $6, and he spent a total of $24. How much did each ticket cost? Use m to represent the cost of each movie ticket.

A. 6m+2=24 m=3 ; each ticket cost $3.

B. 2m+6=24 m=9 ; each ticket cost $9.

C. 2m+6=24 m=15 ; each ticket cost $15.

D. 6m+2=24 m=4 ; each ticket cost $4.

Answers

2m + 6 = 24

Subtract 6 from both sides.

2m = 18

Divide both sides by 2.

m = 9

Hope this helps!

Answer:

B) 2m+6=24 m=9 ; each ticket cost $9.

Step-by-step explanation:

Given: Jose bought 2 movie tickets and a box of popcorn. The popcorn cost $6, and he spent a total of $24.

Here "m" represents the cost of each movie ticket.

Now let's form an equation.

2m + box of popcorn = $24

Box of popcorn cost $6

So,

2m + 6 = 24

Now, we have to solve for m.

Subtract 6 from both sides, we get

2m + 6 - 6 = 24 - 6

2m = 18

Dividing both sides by 2, we get

2m/2 = 18/2

m = 9

So, the cost of movie ticket is $9 each.

Therefore, the answer is B) 2m+6=24 m=9 ; each ticket cost $9.

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Drag an answer to each box to complete this paragraph proof.

Given: ∠PQR and ∠RQS are supplementary angles and m∠PQR=115°

Prove: ∠RQS is an acute angle.

It is given that ∠PQR and ∠RQS are supplementary angles. So, m∠PQR+m∠RQS=180° using the ________ . It is also given that m∠PQR=115° . Using the substitution property of equality, ________ + m∠RQS=180° . Using the subtraction property of equality, m∠PQR=65° . Therefore, ∠RQS is an acute angle by ________ .

A. definition of complementary angles
B. definition of supplementary angles
C. definition of acute angle
D. definition of obtuse angle
E. 180°
F. 115°

Image uploaded below:
V V V

Answers

definition of acute angle

Answer: The correct options for blank 1,2 and 3 are B, F and C respectively.

Explanation:

It is given that the ∠PQR and ∠RQS are supplementary angles and ∠PQR=115°.

The two angles are called supplementary angles if they are lies on the same arc of a straight line and their sum is 180 degree.

Since it is given that ∠PQR and ∠RQS are supplementary angles, so by the definition of supplementary angles we can say that their sum is 180 degree.

[tex]\angle PQR+\angle RQS=180^{\circ}[/tex] .... (1)

Therefore, the correct option for first blank is option B.

It is given that ∠PQR=115°.

Using the substitution property of equality, the equation (1) can be written as,

[tex]115^{\circ}+\angle RQS=180^{\circ}[/tex]

Therefore, the correct option for second blank is option F.

Using the subtraction property of equality, ∠PQR=65° .

An angle less that 90 degree is called an acute angle and the an angle more than 90 degree but not more that 180 degree is called an obtuse angle.

Since 65 is less than 90, so by the definition of acute angle the ∠RQS is an acute angle.

Therefore, the correct option for third blank is option C.

How many possible outcomes, including both main effects and interaction effects, are possible for a factorial design with three independent variables?

Answers

your answer will be 8

Change each fraction to a decimal. If the division doesn’t end, round your answer to the nearest hundredth. a. 3⁄4 b. 7⁄16 d. 3⁄5 e. 7⁄40 f. 51⁄20

Answers

a. 0.75
b. 0.44
d. 0.6
e. 0.18
f. 2.55

Answer:

the other person forgot to answer c

Step-by-step explanation:

a 0.75

b 0.44

c 0.6

d 0.6

e 0.18

Simplify.

(-5.12) - (-4.7) + (7.021)

6.79
6.601
-2.799

Answers

The answer is 6.601, and therefore, the second option.

The answer is 6.601

(-5.12)-(-4.7)+(7.021)

= -0.42+7.021
= 6.601

Nine friends will equally share 12 glasses of punch how many glasses of punch will each friend get A.3/4 B.1/3 C.4/3 D.3

Answers

9/12

simplify;
3/4

so A is the answer.

God bless!

$8 euros were worth $9 and $24 euros were worth $27 write an equation of the form y=kx to show the relationship between the number of euros and the value in dollars.

Answers

Sent a picture of the solution to the problem (s).

Which ordered pairs are solutions to the inequality 2y−x≤−6 ?

Select each correct answer.

(0, −3)

(2, −2)

(1, −4)

(6, 1)

(−3, 0)

Answers

try plugging them in, might seem tedious, but it's the best way to practice. if you plug in a pair and the left side of the equation is less than or equal to 6, it's the right answer.

we have

[tex]2y-x\leq -6[/tex]

we know that

if a ordered pair is a solution of the inequality

then

the ordered pair must satisfy the inequality

we will proceed to verify each case to determine the solution of the problem

case A) [tex](0,-3)[/tex]