Mathematics High School

Show that √5×√20 is an integer?

Answers

Answer 1

Answer:

See below.

Step-by-step explanation:

1) Simplify √20 to 2√5.

√5 × 2√5

2) Simplify.

2√5×5

3) Simplify 5 × 5 to 25.

2√25

4) Since 5 × 5 = 25, the square root of 25 is 5.

2 × 5

5) Simplify.

When evaluated, this expression equals a positive whole number, therefore showing it is a integer.

Related Questions

A farmer has 45 horses and 20 cows.
(i) Write this as a ratio horses : cows.
Give your answer in its simplest form.

Answers

Answer: 9 : 4

Step-by-step explanation:

45 : 20

simplify

9 : 4

5 quick algebra 1 questions for 50 points!

Only answer if you know the answer, shout-out to subtomex0, tysm for the help!

Answers

Q 3 - c -

[tex]x {}^{2} - 8x - 9 = 0 \\ x + y = 8 \\ xy = - 9[/tex]

Two numbers who sum up to 8 and multiply to -9 are: 9 and -1

Q 4 - d -

[tex]g(x) = x {}^{2} - 7x + 12 \\ g(6) = 36 - 42 + 12 = 6 \\ g( - 7) = 49 + 49 + 12 = 110 \\ g( - 3) = 9 + 21 + 12 = 42 \\ g(4) = 16 - 28 + 12 = 0[/tex]

x=4 is a root

These problems can be approached in many ways: completing the square/factoring/using the quadratic formula...

Q 1 - c -h(x)= -2x+10h(0)=10 ( 0 , 10 )h(x)=0x=5 ( 5 , 0 )

Q 5 - True -f(x) = 2x²+3x-2f(x)=02x²+3x+2=0x=-2 x=1/2

Q 4 - 3 is the zero -

Answer:

Question 1:The correct answer is C. -1 and 9

Question 2: The correct answer is D.4

Question 3: The correct answer is C. The x-intercept of (5,0) and y-intercept of (0,10)

Question 4: The correct answer is B. True

Question 5: The correct answer is b.

Fill the empty slots by dragging tiles from the left to show the next step for solving the equation. Solve the two-step equation. -9x + 0.4 = 4
Which operation must be performed to move all the constants to the right side of the equation?

Answers

In order to move a the constant terms to the right hand side, we need to subtract 0.4 from both sides of the equation.

What are the constant terms?

In an equation, the constant terms are those terms that do not have any alphabet attached to them. In this case, 4 and 0.4 are constant terms.

In order to move a the constant terms to the right hand side, we need to subtract 0.4 from both sides of the equation thus;

-9x + 0.4 - 0.4 = 4 - 0.4

-9x = 3.6

Learn more about constant terms:https://brainly.com/question/14368568

#SPJ1

what is n divided by 2 plus five minus n

Answers

The Simplified algebraic expression for the statement "n divided by 2 plus five minus n" is given by 5-(n/2).

Algebraic Expression is a mathematical expression involving variables, Numbers, other mathematical quantities, and mathematical operations and combinations of them.

Here given statement is "n divided by 2 plus five minus n"

Now we have to write the above given statement as simplified algebraic expression.

"n divided by 2" is given by = n/2

then "n divided by 2 plus five" is given by = (n/2)+5

there after "n divided by 2 plus five minus n" is given by = (n/2)+5-n

Simplifying the total algebraic expression we get,

(n/2)+5-n = 5-{n-(n/2)} = 5-((2n-n)/2) = 5-(n/2)

Hence the suitable Simplified algebraic expression for the given statement is given by = 5-(n/2)

Learn more about Algebraic Expression here-

https://brainly.com/question/2164351

#SPJ10

A company earns a profit of $100 the first month it is in business. Every month after that, the company earns a profit that is 1.5 times the previous month's profit. What will the company's profit be in the fith month?

Answers

The company's profit in fifth month will be $506.25

Profit : The gain in an expenditure, that is when the return is higher than the original amount, then the gained extra amount is called profit.

Example : If someone sell a toy of $10 in $15, then he gained profit & his profit is $(15-10) = $5.

A company earns a profit of $100 the first month it is in business.

Every month after that, the company earns a profit that is 1.5 times the previous month's profit.

In 1st Month,

Profit = $100

In 2nd Month,

Profit = 1.5 times of profit of 1st month

= 1.5 × $100

= $150

In 3rd Month,

Profit = 1.5 times of the profit of 2nd month

= 1.5 × $150

= $225

In 4th Month,

Profit = 1.5 times of the profit of 3rd month

= 1.5 × $225

= $337.5

In 5th Month,

Profit = 1.5 times of the profit of 4th month

= 1.5 × $337.5

= $506.25

So, the profit of 5th month = $506.25

Learn more about profit here :

https://brainly.com/question/19865598

#SPJ10

John lives in Vermont and Julie lives in Florida. One January day, it was 52°F in Florida and 9°F in Vermont. What was the difference in temperature.

Answers

Answer:

Step-by-step explanation:

52-9=43

A tire on a car has an outside diameter of 36.30 in. Through what angle (in radians) does the tire turn while traveling 1 mile?

Answers

Answer: 3491.91 radians

Step-by-step explanation:

The total distance in inches traveled by car = 63,360 inches (1 mile)

Total Revolution made by tire through traveling =

[tex]=\frac{63360}{\pi *36.30}[/tex]

We know 1 revolution angle made by tire = 2π radian (360 degrees/1 revolution of unit circle)

In [tex]\frac{63360}{\pi *36.30}[/tex] ,

the revolution angle made by the tire =

[tex]=2\pi * \frac{63360}{\pi 36.60}[/tex]

[tex]=2 * \frac{63360}{ 36.60}[/tex]

[tex]= 3491.91[/tex] radian

Eight years ago, Marilyn invested $1000 in a stock. The table shows the
value of the stock over time.
Year
0
1
2
3
4
5
6
7
8
Value
$1000
$1095
$1200
$1314
$1440
$1580
$1730
$1890
$2070
Which is closest to the rate of change modeled by the function?
Leaming Inc.
Helo 13

Answers

Answer: 1.095

Step-by-step explanation:

The function is increasing, so the rate of change must be greater than 1.

If x is inversely proportional to y, then as x decreases, y decreases.

Answers

Answer:

Yes

Step-by-step explanation:

Let's assume that x=1/y.

For y=1, x=1

For y=2, x=0.5

For y=4, x=0.25

And so on

Riddle-if you solve it i will delete your answer and you have to post the riddle. Riddle-you enter a room. 2 dogs, 4 horses, 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground?.

Answers

Answer:

Step-by-step explanation:

2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.

The answer will be either 8 or 4 or 0.

What is a riddle?

A riddle is an intentionally framed ambiguous question or statement that requires ingenuity and critical thinking to solve or understand.

In the given riddle, all the two dogs, four horses, one giraffe and a duck are lying on the bed. Three chickens are flying over a chair.

Assumptions:

1) Bed is placed on the ground.

2) Bed and chair considered are of standard type.

case1:

If we consider the legs of only living organisms, the number of legs on the ground at the given instant will be 0.

case2:

If that's not the case, then a typical chair will have four legs, and a standard bed will also have four legs. So a total of 8 legs will be on the ground or floor of the room.

case3:

And if we consider the possibility of the chair being placed on the bed, then the legs of the chair will not touch the ground. So a total of 4 legs will be on the ground or floor of the room.

∴ From different perspectives, the number of legs on the ground will be either 8 or 4 or 0.

Find more riddles here:

https://brainly.com/question/20140875

#SPJ2

ABC is an equilateral triangle whose vertex A has the co-ordinates (0, √3). Find the co- ordinates of B and C.

Answers

Answer:

B = (-1, 0)

C = (1, 0)

Step-by-step explanation:

Properties of an Equilateral Triangle

Three sides of equal lengthAll interior angles are 60°

Given:

ΔABC is an equilateral triangleVertex A is at (0, √3)

Drawing an altitude from vertex A divides the triangle into two 30-60-90 triangles.

A 30-60-90 triangle is special right-angled triangle where:

Angles are in the ratio 1 : 2 : 3Sides are in the ratio 1 : √3 : 2

Therefore, the formula for the sides is: b : b√3 : 2b, where:

b = shortest side opposite the 30° angleb√3 = side opposite the 60° angle2b = longest side (hypotenuse) is opposite the right angle

As Vertex A has the co-ordinates (0, √3), the side opposite the 60° angle is √3 units.

Using the ratios to find b (shortest side length):

b√3 = √3 ⇒ b = 1

As the altitude divides BC into two equal line segments, and the length of the shortest side of the right triangles is 1 unit, the coordinates of B are C are:

B = (-1, 0)C = (1, 0)

Learn more about the 30-60-90 triangle here:

https://brainly.com/question/27942542

https://brainly.com/question/27976403

Express a) 36 b) 80 as sum of two prime numbers

Answers

⊱________________________________________________________⊰

Answer:

See below.

Step-by-step explanation:

[tex]\large\begin{gathered} \sf{36=19+17. 19 \ and \ 17 \ are}\\ \sf{\ both \ primes, \ because \ they're \ only \ divisible \ by \ 1 \ and \ themselves} \\ \sf{ 80=73+7. \ Again, \ 73 \ and \ 7 \ \underline{ARE} \ prime. \end{gathered}}[/tex].

Done!!

⊰________________________________________________________⊱

Cαlligrαphy

The weight of an apple is 150g, rounded to the nearest 5g. what is the lower bound and upper bound?

Answers

The lower bound is 147.5 and the upper bound is 152.5.

Given the weight of an apple 150 g rounded to the nearest 5g.

We have to find lower bound and upper bound.

Lower bound is an element less than or equal to all the elements in a given set.

Upper bound is an element greater than all the elements in a given set.

Lower bound= Number 1- (Number nearest to which number 1 is rounded)/2

Upper bound=Number 1+(number nearest to which number 1 is rounded)/2

Weight of an apple =150 g

Lower bound=150-5/2

=150-2.5

=147.5

Upper bound=150+5/2

=150+2.5

=152.5

Hence the lower bound is 147.5 and upper bound is 152.5.

Learn more about lower and upper bounds at https://brainly.com/question/15408313

#SPJ4

If 3x + 7 =22, what is the value of x

Answers

Answer:

x=5

Step-by-step explanation:

solution,

3x+7=22

or,3x=22-7

or,3x=15

or,x=15/3

:×=5

The value of x in the equation 3x + 7 = 22 is x = 5.

To find the value of x in the equation 3x + 7 = 22, we can solve for x as follows:

Subtract 7 from both sides of the equation:

3x + 7 - 7 = 22 - 7

3x = 15

Divide both sides of the equation by 3 to isolate x:

(3x)/3 = 15/3

x = 5

Therefore, the value of x in the equation 3x + 7 = 22 is x = 5.

Learn more about equations here:

https://brainly.com/question/10413253?

#SPJ2

Triangles F G H and F J H share common side F H. Sides F G and G H are congruent. Sides F J and J H are congruent.
Which explains whether ΔFGH is congruent to ΔFJH?

They are congruent because GH ≅ GF, JF ≅ JH, and FH ≅ FH.
They are congruent because opposite sides of a parallelogram are congruent.
They are not congruent because only one pair of corresponding sides is congruent.
They are not congruent because only two pairs of corresponding sides are congruent.

Answers

Answer:

They are congruent because GH ≅ GF, JF ≅ JH, and FH ≅ FH.

Step-by-step explanation:

Casey was at the surface of a swimming pool and recorded the following two measurements, in feet, on a number line:

−8, which represents the depth of water in the swimming pool
+7, which represents the height of the slide at the pool

Part A: What does 0 represent in this situation? (3 points)

Part B: Describe the height of the slide in relation to 0 in the situation. (3 points)

Part C: Casey held a pole in the swimming pool. The bottom of the pole was at a depth of 2 feet. How should Casey mark the level of the bottom of the pole on the number line? Explain how you determined this. (4 points)

Answers

The point 0 represents the surface of the water. The height of the slide is 7 feet above the surface of the water. The bottom of the pole can be represented by -2 on the number line.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that −8 represents the depth of water in the swimming pool. Hence:

The point 0 represents the surface of the water. The height of the slide is 7 feet above the surface of the water. The bottom of the pole can be represented by -2 on the number line.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Which of the following could be rewritten as an addition problem of two integers with the same sign?

8 - 10
-8 - 10
-8 + 10
-8 - (-8)

Answers

-8-10
because it can also be written as -8 + -10 instead of -8 - 10

A suitcase measures 24 inches long and the diagonal is 30 inches long. What is the area of material that is needed to cover one side of the suitcase

Answers

Answer:

706.858347

Step-by-step explanation:

I need help with this math question

Answers

Answer:

D = 12

Step-by-step explanation:

Side ST is corresponding to side QT. 9" / 3" = 3

3 is the proportion between the two triangles.

Side PT is the corresponding side to side RT.

PT = 4" x 3 = 12"

An architect's sketch of plans for the front of a garage in the shape of pentagon is shown below. What is the approximate perimeter of the
front of the garage?
-8
-6 -4 -2
A. about 36 ft
B. about 21 ft
C. about 10 ft
D. about 77 ft

Answers

Using it's concept, it is found that the approximate perimeter of the front of the garage is:

A. about 36 ft.

What is the perimeter of a figure?

The perimeter of a figure is given by the total length of it's boundary.

In this problem, we have that:

The bottom boundary has length of 10 units.The two lateral boundaries have lengths of 7 units.There are two top boundaries, which are the hypotenuses of a right triangle with legs 3 and 5, hence:

[tex]t = \sqrt{3^2 + 5^2} = 5.83[/tex]

Hence the perimeter of the figure is:

P = 10 + 2 x 7 + 2 x 5.83 = 35.66.

Rounding, it is of about 36 ft, hence option A is correct.

More can be learned about the perimeter of a figure at brainly.com/question/26134384

#SPJ1

Find the midpoint of points A(10,-7) and B(6, 1) graphically.

Answers

Answer:

(8,-3)

Step-by-step explanation:

Midpoint Formula: [tex](\frac{x^{1}+x^{2} }{2}, \frac{y^{1} +y^{2} }{{2} } )[/tex]

Plug in your numbers from the coordinates:

(10+6/2, -7+1/2)

(16/2, -6/2)

(8,-3)

A shopkeeper had 3sacks of sugar each weighing a mass of 90kg.he repacked the sugar in 0.00025tonnes packets.how many packets did he obtain?

Answers

Answer:

1080.

Step-by-step explanation:

0.00025 tonnes = 0.00025 * 1000 = 0.25 kg.

Total number of packets

(3 *90) / 0.25

= 12*90

= 1080.

The mean annual income of certified welders is normally distributed with a mean of $50,000 and a population standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $50,000 annually. The alternate hypothesis is that the mean is not $50,000. If the level of significance is 0.10, what is the decision rule

Answers

Using the p-value method, the decision rule is:

|z| < 1.645: do not reject the null hypothesis.|z| > 1.645: reject the null hypothesis.

What is the relation between the p-value and the test hypothesis?

Depends on if the p-value is less or more than the significance level:

If it is more, the null hypothesis is not rejected.If it is less, it is rejected.

In this problem, we have a two-tailed test, as we are testing if the mean is different of a value. For a significance level of 0.1, the critical value of z(when a p-value of 0.1 is obtained) is of |z| = 1.645, hence the decision rule is:

|z| < 1.645: do not reject the null hypothesis.|z| > 1.645: reject the null hypothesis.

More can be learned about p-values at https://brainly.com/question/13873630

#SPJ1

The surface area of a rectangular prism is increased by a factor of 16.
By what factor is the volume of the figure increased?
04
08
O 32
O 64

Answers

Answer:

The volume of the prism increased by a factor of 64.

Step-by-step explanation:

Given that the original prism and the increased prism are similar, we have that the scale factor is:

Area ∝ (length of side) x (length of side)

If the area increases by a factor of 16, each side increases by a scale factor of √16 = 4. Regarding the volume:

Volume ∝ (length of side) x (length of side) x (length of side)

Thus the increase factor for the volume, in this case, is 4 x 4 x 4 = 64.

What is the length of the hypotenuse of right ΔDEF shown? A) √5041 B) √2545 C) √497 D) √1063

Answers

The length of the hypotenuse of right triangle ΔDEF is 50.44 units

How to find hypotenuse of a right triangle?

The hypotenuse side can be found using Pythagoras theorem,

Therefore,

c² = a² + b²

where

c = hypotenusea and b are the other legs.

Therefore,

x² = 39² + 32²

x² = 1521 + 1024

x = √2545

x = 50.4479930225

x = 50.44

learn more on right triangle here: https://brainly.com/question/12353375

#SPJ1

At a meeting attended by 23 people, the females exceeds the males by 7. how many males were there?

Answers

Number of males in the meet were 8.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

Let the number of males be x.

∴ Number of females = x + 7

Total number of people attending meet = Number of male +

Number of females

23 = x + x + 7

23 = 2x + 7

16 = 2x

x = 8.

Thus number of males in the meet were 8.

Learn more about Linear equations here :

https://brainly.com/question/2263981

#SPJ4

Classify the polynomial by its degree and number of terms. Select all choices that apply for each polynomial.
(which is correct ??)

Answers

Step-by-step explanation:

The polynomial highest degree is 2 so the degree is 2.

The binomial have three terms so it is a trinomial.

A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week. (2 points)

No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100

Answers

Considering the definition of an inequality and system of inequalities, the correct option is: "No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100."

Definition of inequality

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.

An inequality contains one or more unknown values called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.

System of inequalities

A system of inequalities is made up of two or more inequalities.

The solution will be formed by the intersection of the half-planes of each of the inequalities, that is, it will be the enclosure that all the inequalities have in common. That is, the solution of the system is given by the region of the common plane of the half-planes that define each one of the inequalities.

System of inequality in this case

In this case:

c represents child bikes.a represents adult bikes.Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. The company is able to have up to 120 hours of building time and 100 hours of testing time for a week.

Then, the system of inequality is:

[tex]\left \{ {{4c+6a\leq 120} \atop {4c+4a\leq 100}} \right.[/tex]

On the other hand, the company can build 20 child bikes and 6 adult bikes in the week. So, checking the equations, for given c=20 and a=6:

4×20 + 6×6= 116 < 120

4×20 + 4×6= 104 >100

Finally, the correct option is: "No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100."

Learn more about system of inequalities:

https://brainly.com/question/1518009

https://brainly.com/question/9774970

https://brainly.in/question/35046171

#SPJ1

Determine whether the stated conclusion is valid based on the given information. If not,
write invalid. In either case, explain your reasoning.
A. Given: If a point is the midpoint of a segment, then it divides the segment into two
congruent segments. R is the midpoint of QS
Conclusion: QR = RS.

Answers

Both the given statements are true. The figure is given below.

We need to determine whether the stated conclusion is valid based on the given information.

What is the midpoint of the line segment?

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.

Given: If a point is the midpoint of a segment, then it divides the segment into two congruent segments. R is the midpoint of QS.

Conclusion: QR=RS.

Given: If a point is the midpoint of a segment, then it divides the segment into two congruent segments. AB=BC

Conclusion: B divides AC into two congruent segments

Both the given statements are true. The figure is given below.

To learn more about the midpoint of the line segment visit:

https://brainly.com/question/13792156.

#SPJ1

The area and one side of a rectangle are given. Determine the missing dimension

Answers

The missing dimension is x + 4

How to determine the missing dimension?

The given parameters are:

Area = 4x^2 + 13x - 12

Length = 4x - 3

The width is calculated using:

Width = Area/Length

This gives

Width = (4x^2 + 13x - 12)/(4x - 3)

Expand

Width = (4x^2 + 16x - 3x - 12)/(4x - 3)

Factorize

Width = (4x(x + 4) - 3(x + 4)/(4x - 3)

Factor out x + 4

Width = (4x - 3)(x + 4)/(4x - 3)

Cancel out the common factor

Width = x + 4

Hence, the missing dimension is x + 4