A square with an area of A2 is enlarged to a square with an area of 25A2. How was the side of the smaller square changed?

The side length was increased by 5.
The side length was multiplied by 5.
The side length was increased by 10.
The side length was multiplied by 10.

Answers

Answer 1

Answer:

second option : the side length was multiplied by 5.

Step-by-step explanation:

a = side length of the original square

A² = a×a

(a+5)×(a+5) = a² + 10a + 25

and that should be equal to a²×25

a² + 10a + 25 = 25a² ?

10a + 25 = 24a²

no, that is not true for all a

a×5 × a×5 = a²×25 = 25A²

this is the correct solution, as it is true for all a.

Answer 2

For the area to be  25a², the side length was increased by 5.

How to calculate the area of a square

Let a be the side length of the original square, hence:

A = a²

Increasing the length by 5 will give:

(a+5)×(a+5) = a² + 10a + 25

Factorizing the result

a² + 10a + 25 = (a+5)²

a² + 10a + 25 = 25a²

This shows that for the area to be  25a², the side length was increased by 5.

Learn more on area of square here: https://brainly.com/question/25092270


Related Questions

Solve the following system by graphing and identify the point of intersection -2x - y=-12 2x-3y=4

Answers

Answer:

{x,y} ={10,-8}

Step-by-step explanation:

hope it help please mark me as brinnelist

if the angle of elevation of the sun is 40 degrees, and is decreasing 1/3 radians/hour how fast is the shadow of a 35m tall pole lengthening?

Answers

[tex] \frac{dx}{dt} = 28.2 \: \frac{m}{hr}[/tex]

Step-by-step explanation:

Let y = height of the pole = 35 m (constant)

x = length of the shadow

They are related as

[tex] \tan \theta = \frac{y}{x} [/tex]

or

[tex]x = \frac{y}{ \tan\theta } = y \cot \theta[/tex]

Taking the time derivative of the above expression and keeping in mind that y is constant, we get

[tex] \frac{dx}{dt} = y( - \csc^{2} \theta) \frac{d \theta}{dt} [/tex]

Before we plug in the numbers, let's convert the degree unit into radians:

[tex]40° \times ( \frac{\pi \: rad}{180°}) = \frac{2\pi}{9} \: radians[/tex]

Since the angle is decreasing, then d(theta)/dt is negative. Therefore, the rate at which the shadow is lengthening is

[tex] \frac{dx}{dt} = (35 \: m)( - \csc^{2} \frac{2\pi}{9} )( - \frac{1}{3} \frac{rad}{hr} )[/tex]

or

[tex] \frac{dx}{dt} = 28.2 \: \frac{m}{hr} [/tex]

83 in scientific notation​

Answers

Answer:

8.3 x 10^1

hope this helps

have a good day :)

Step-by-step explanation:


A regular polygon of (2A+ 1) sides has 140°
as the size of each
interior angle. Find A​

Answers

Answer:

Ext angles = 40 degs 360/40 = 9 sides

Step-by-step explanation:

The following expressions are factorizations of 60. Which is the prime factorization?

Answers

Answer:

d

Step-by-step explanation:

press 60 on your casio calculator then the equal sign then shift and then 3rd row this button ".,,," which means factorise

(Trigonometry) Find the values of x and y. Round your answers to the nearest tenth.

Answers

Answer:

[tex]x = 38.1[/tex]

[tex]y = 23.4[/tex]

Step-by-step explanation:

The given triangle is a right triangle. This is indicated by the box around one of the angles, signifying that the angle measure is (9) degrees. By its definition, a right triangle is a triangle with a (90) degree angle, thus the given triangle is a right triangle. In this situation, one can use right-angle trigonometry to find the value of the unknown side. In essence, right triangle trigonometry provides one with a series of ratios to describe the relationship between the sides and angles of the right trinagle. These ratios are the following,

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]

Keep in mind that the way a side is named is relative to the angle it is being described from. Thus, the (opposite) and (adjacent) sides acquire different names based on the angle relative to them. However, the (hypotenuse) is the hypotenuse no matter the angle, as the hypotenuse is the side opposite the right angle.

Solve for (y) first. One is given the angle measure and the measure of the side opposite the angle measure. One is asked to find the measure of the side adjacent to the angle. Use the ratio of tangent (tan) to achieve this.

[tex]tan(\theta)=\frac{opposite}{adajcent}\\[/tex]

Substitute,

[tex]tan(52)=\frac{30}{y}[/tex]

Inverse operations,

[tex]y=\frac{30}{tan(52)}[/tex]

Simplify,

[tex]y = 23.4386[/tex]

Now solve for the hypotenuse (x). One could use the Pythagorean theorem to do this, but since this is trigonometry, one might as well use the trigonometric ratios. One is given an angle, as well as the side opposite the angle, one is asked to find the hypotenuse. To do this, one can use the trigonometric ratio of sine (sin).

[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]

Substitute,

[tex]sin(52)=\frac{30}{x}[/tex]

Inverse operations,

[tex]x=\frac{30}{sin(52)}[/tex]

Simplify,

[tex]x = 38.0705[/tex]

quadrilateral BANK is a parallelogram. if AB= 10cm and AN= 6cm, what is the length of NK?

guys patulong, thanks!

Answers

Answer:

The length of NK is 10 cm.

Answer:

10 cm

Step-by-step explanation:

In parallelogram, opposite sides are parallel and equal.

AB and NK are opposite sides

So, NK = AB = 10cm

Evaluate the following expression at x = -5
-2x-3

Answers

Answer:

7.

Step-by-step explanation:

-5 x -2 = 10 (2 negatives being multiplies = positive)

Then, 10 - 3 = 7.

between which 2 square roots does 7 lie
6,7
23,30
32,43
45,60

Answers

Answer:

32, 43

Step-by-step explanation:

Your welcome! :)

Answer:

The answer is 45,60.

Step-by-step explanation:

We can use a square chart to answer this question.

I will zoom in to the particular ones we need.

[tex] {6}^{2} = 36[/tex]

[tex]{7}^{2} = 49[/tex]

[tex] {8}^{2} = 64[/tex]

7 is the square root of 49.

45 lies in between 36 and 49 so its square root is more than 6 but less than 7. It is around 6.708 to the nearest thousandth.

Meanwhile, 60 lies in between 49 and 64 so its square root is more than 7 but less than 8. It is around 7.746 to the nearest thousandth.

Hence, we can say that 7 lies in between the square root of 45 and the square root of 60.

When factored completely, which is a factor of 6x^3-12x^2-48x?

Answers

Answer: C

Step-by-step explanation:

The solution is Option A.

The value of the equation is 6x³ - 12x² - 48x is A = 6x ( x + 2 ) ( x - 4 )

What is an Equation?

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

A = 6x³ - 12x² - 48x   be equation (1)

On simplifying the equation , we get

Taking 6x as the common factor , we get

A = 6x ( x² - 2x - 8 )

On simplifying the equation , we get

A = 6x ( x + 2 ) ( x - 4 )

Therefore , the value of A is 6x ( x + 2 ) ( x - 4 )

Hence , the equation is 6x ( x + 2 ) ( x - 4 )

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

Which one of the following represents exponential growth?

A: y = (48000)(.05)^x
B: y = (48000)(.95)^x
C: y = 2400(.05)^x
D: y = (48000)(1.05)^x

Answers

I believe D !!!!!! Hopefully that helps

Choose the number sentence that illustrates the distributive property of multiplication over addition.
a.) 3 × (4 + 6) = (3 × 4) + (3 × 6)
b.) 3 × (4 + 6) = (3 + 4) × (3 + 6)
c.) 3 × (4 + 6) = (3 × 4) + 6

Answers

Answer:

A. LHS,

3×(4+6)

3×10

30

NOW,

RHS,

(3×4)+(3×6)

12+18

30

Therefore, A is ans

what does the scale 1:500 000 mean​

Answers

A scale of 1:5000000 means that:

This is mainly used in map or shadow etc. things.

For example in map it is given that the scale is 1mm:5000000mm, then it means that 1mm on the map is equal to 5000000mm in real life. So, you can be asked what does 5mm on map means in real life. So, you have to solve like this:

5 × 5000000 = real life size

25000000mm = real life size

In shadow like question, it can be asked that if 5000000 m of building casts a shadow of 1 m, then how much will be the shadow of a 10000000 m building. So, you have to solve it like this:

(10000000/5000000) × 1 = shadow size

=> 2 × 1 = shadow size

=> 2m = shadow size

You can tell me the specific questions so that I can help.

The scale 1:500 000 mean​s 1 unit on a map represents 500000 in real life

What are scales?

Scales are used to represent big or small measurements on a map or graph

How to interpret the scale?

The scale is given as:

1:500 000

The above means that:

1 unit on a map represents 500000 in real life

Read more about scale at:

https://brainly.com/question/3457976

#SPJ6

data distribution lol

Answers

Answer:

The range of the value of numbers is 8

Step-by-step explanation:

Mathematically, the range refers to the difference between the biggest and the smallest number

From the diagram, the biggest number is 13and the smallest is 5

The difference between this two is the range

we have this as 13 -5 = 8

A school has 833 students. Of those students, 463 play a sport (A), 52 are in the band (B), and 21 do both(AB). (C) represents neither.

Answers

Answer:

Im sorry but it is kind of confusing

Step-by-step explanation:

What is the solution to the system of equations

Answers

Step-by-step explanation:

[tex]5x + 3y = 13 \\ 7x + 8y = - 16 \\ 5x = 13 - 3y \\ x = \frac{13 - 3y}{5} \\ 7( \frac{13 - 3y}{5} ) + 8y = - 16 \\ 18.2 - 4.2y + 8y = - 16 \\ 3.8y = - 34.2 \\ y = - 9 \\[/tex]

[tex] x = \frac{13 - 3( - 9)}{5} = \frac{13 + 27}{5} = \frac{40}{5} = 8 \\ x = 8 \\ y = - 9[/tex]

39.76÷7.94
use compatible numbers and estimate

Answers

Answer:

5

Step-by-step explanation:

As for estimation, you may round 39.76 to the whole number, resulting in 40.

7.94 to 8

40 / 8 = 5

5 is your answer for the result of estimation

The answer to the question you asked is 5

Can someone help please ?!

Answers

Step-by-step explanation:

53 is the correct answer

The answer for this is 53 that’s a prime number

HELP! Which of the following statements would prove line l is parallel to line m?

Answers

Answer:

Non of these.

Step-by-step explanation:

Because each of the options before have ≈ instead of =, however, to prove 2 lines are parallel, some angles must be equal. Corresponding angles and alternate angles should be equal. exactly equal.

PLEASE PLEASE I RLY NEED HELP ...... ....... . .. . . . . . . . . .... . . . Pick three Enlightenment thinkers and explain how they inspired America’s founders.

Answers

Answer:

Enlightenment philosophers John Locke, Charles Montesquieu, and Jean-Jacques Rousseau all developed theories of government in which some or even all the people would govern. These thinkers had a profound effect on the American and French revolutions and the democratic governments that they produced.

I am guessing your in the same situation as me sweeping across the internet for help in our summer school history classes well I found this hope it helps

QUESTION 2
Simplify the following
a5×a7​

Answers

Answer:

[tex]a^{12}[/tex]

Step-by-step explanation:

Identity Used :   [tex]a^x \times a^y = a^{x+ y}[/tex]

   

       [tex]a^5 \times a^7 = a^{5 + 7} = a^{12}[/tex]

The point-slope form of the equation of the line that passes through (-9,-2) and (1,3) is y-3=1/2(x-1) what is the slope-intercept form of the equation for this line

Answers

Answer:

y = (1/2)x + 2 1/2

Step-by-step explanation:

y - 3 = (1/2)(x - 1)

Distribute the 1/2

y - 3 = (1/2)x - 1/2

Add 3 to both sides

y = (1/2)x + 2 1/2

Simplify each of the following by rationalizing the denominator.
please do answer my doubt

Answers

Answer:

(47+21√5)/2

Step-by-step explanation:

Given the expression

7+3√5/7-3√5

= 7+3√5/7-3√5 * (7+3√5)/(7+3√5)

= 49+21√5+21√5+9(5)/[7(7)-9(5)]

= 49+42√5+45/49-45

= 94+42√5/4

= 2(47+21√5)/4

=(47+21√5)/2

Hence the required expression is (47+21√5)/2

5 people are going to a dinner party. Each person at the party will eat 23 pounds of turkey. If you can only buy whole pounds of turkey, how many pounds should you buy?

Answers

Answer is B. Hope it helps

michelle has three textbooks each way 5/8 pounds what is the total weight of her textbook

Answers

Answer:

1 and 7/8 pounds

Step-by-step explanation:

There are 3 textbooks that each weigh 5/8 of a pound

3*5/8=15/8

1 and 7/8

Two positive numbers have a difference of 21. The larger number is five more than twice the smaller. Find the two numbers.

Answers

Let n = the smaller of the two numbers, and since the other number is 5 more than twice the smaller number n, then ...

Let 2n + 5 = the second and larger number.

Since the sum of the two unknown numbers is 26, then we can write the following equation to be solved for n as follows:
n + (2n + 5) = 26

n + 2n + 5 = 26

Collecting like-terms on the left, we get:
3n + 5 = 26

3n + 5 - 5 = 26 - 5

3n + 0 = 21

3n = 21

(3n)/3 = 21/3

(3/3)n = 21/3

(1)n = 7

n = 7

Therefore, ...
2n + 5 = 2(7) + 5
= 14 + 5
= 19

CHECK:
n + (2n + 5) = 26
7 + (19) = 26
7 + 19 = 26
26 = 26

Therefore, the two desired numbers whose sum is 26 are indeed 7 and 19.

Hope this helps :)

1. Suly watched a film that was 90 minutes long. 1/6 of the way through the film, the
doorbell rang. The pizza man had arrived with the order.
How many minutes of the film had she watched before the pizza man arrived?
(3 marks)
a.​

Answers

Answer:

15 minutes

Step-by-step explanation:

Suly watched a film that was 90 minutes long. Then, she stopped at the [tex]\frac{1}{6}[/tex]mark. This means that we have to find [tex]\frac{1}{6}[/tex] of 90 minutes to find the amount of time Suly watched before the pizza man arrived. So therefore, the answer is 15 minutes.

Have a nice day. : )

Answer:

15 minutes

Step-by-step explanation:

Given:

The film Suly is watching is 90 minutes longSuly watched 1/6 of the film before the pizza man arrived

Steps:

90/6=15

Subtract the given polynomials using the vertical format.

Answers

Answer:    10c^3 - 7c^2 + 4c

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

Explanation:

The negative out front of the parenthesis will swap the sign of each term. That means -3c^3 becomes +3c^3, or simply 3c^3. The other terms in the parenthesis are handled the same way.

After distributing the negative through, we add straight down.

The 7c^3+3c^3 becomes 10c^3

Then we have -5c^2+(-2c^2) become -7c^2

Finally, 2c+2c simplifies to 4c

Answer:

10C³-7C²+4C

7c³-(-3c³) -5c²-(+2c²) +2c-(-2c)

help me solve this with explanation

Answers

Answer:

x = 19

<6 =  109

<7 = 109

Step-by-step explanation:

Angles 6 and 7 are vertical angles so they are equal

7x -24 = 5x+14

Subtract 5x from each side

7x-5x -24 = 5x-5x+14

2x-24 = 14

Add 24 to each side

2x-24 +24 = 14+24

2x = 38

Divide by 2

2x/2 = 38/2

x = 19

<6 = 7x -24 = 7*19 -24 = 109

<7 = 5(19)+14 = 109

Leon verified that the side lengths 21, 28, 35 form a Pythagorean triple using this procedure. Step 1: Find the greatest common factor of the given lengths: 7 Step 2: Divide the given lengths by the greatest common factor: 3, 4, 5 Step 3: Verify that the lengths found in step 2 form a Pythagorean triple: 3 squared + 4 squared = 9 + 16 = 25 = 5 squared Leon states that 21, 28, 35 is a Pythagorean triple because the lengths found in step 2 form a Pythagorean triple. Which explains whether or not Leon is correct? Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple. Yes, any set of lengths with a common factor is a Pythagorean triple. No, the lengths of Pythagorean triples cannot have any common factors. No, the given side lengths can form a Pythagorean triple even if the lengths found in step 2 do not.

Answers

Answer:

Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple

Step-by-step explanation:

The given side lengths are;

21, 28, and 35

From the given side lengths, the greatest common factor = 7

Therefore, we have;

3 × 7, 4 × 7, and 5 × 7

A Pythagorean triple is formed by three numbers, 'a', 'b', and, 'c', which are both positive and integers, that are related as follows;

c² = a² + b²

Therefore, for the three numbers, we get;

3, 4, and 5 is a Pythagorean triple

5² = 3² + 4²

Multiplying both sides by 7² gives;

(5)² × (7)² = (3)² × (7)² + (4)² × (7)²

By the laws of indices, (a·b)ⁿ = aⁿ × bⁿ

Therefore;

(5 × 7)² = (3 × 7)² + (4 × 7)²

Therefore, multiplying every length of the Pythagorean triple by the same whole number results in a Pythagorean triple.

(The relationship can also be shown using similar triangles, as multiplying the side lengths of a triangle by the same whole number, gives a similar triangle, having the same relationship between its sides)

Other Questions
Ravelo Corporation has provided the following data from its activity-based costing system: Activity Cost Pools Estimated Overhead Cost Expected Activity Assembly $ 498,520 44,000 machine-hours Processing orders $ 54,263 1,100 orders Inspection $ 77,589 1,110 inspection-hours Data concerning the company's product L19B appear below: Annual unit production and sales 430 Annual machine-hours 990 Annual number of orders 70 Annual inspection hours 20 Direct materials cost $ 37.74 per unit Direct labor cost $ 10.45 per unit According to the activity-based costing system, the unit product cost of product L19B is closest to:_________ (Round your intermediate calculations to 2 decimal places.) find out the speed of the car from home to school in meters per second.Time - 15 minsDistance - 8 km Which of the following is an example of a periodical?A. Horse and Hound MagazineB. Milwaukee Morning NewsC. Atlanta Daily NewsD. The New York TimesThe answer is not all of above since I cant click all of them. write an email to your friend to suggest them what unique pet that she can adopt. About 80 wordsPls help me thx :) Read this excerpt from a poem.Sighing sadly, hanging her headRegrets resoundApologies abound.Forgiveness granted is like wings,And she will soar.Which line contains a simile?Sighing sadly, hanging her headRegrets resoundForgiveness granted is like wings,And she will soar. What is the length of leg s of the triangle below?45310729045$ What text helps Douglass solidify his argument for the abolition of slavery? Explain its influence. On a coordinate plane, 3 lines are shown. Line m has points (negative 4, 3) and (0, negative 4). Line n has points (1, 2) and (3, negative 2). Line k has points (negative 3, negative 3) and (4, 1).Use the diagram to answer the questions.Is line m parallel to line n? Explain.Is line m perpendicular to line k? Explain. A household aquarium tank in the shape of a rectangular prism has a base length of 242424 inches (\text{in})(in)(, start text, i, n, end text, )and a base width of 15\,\text{in}15in15, start text, i, n, end text. The height of the water is 12\,\text{in}12in12, start text, i, n, end text above the base. During cleaning, 900900900 cubic inches of water is removed. What is the absolute value of the change in the height of the water in inches A bag contains 4 red marbles, 8 blue marbles and 2 green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be red? Please help me ASAP tysm Help pleaseee (pre algebra) which is considered a chemical mutagen Read the excerpt from "The Adventure of the Mysterious Picture." "And now for the haunted chamber," said the Irish captain, taking his candle. "Aye, whos to be the hero of the night?" said the gentleman with the ruined head. "That we shall see in the morning," said the old gentleman with the nose: "whoever looks pale and grizzly will have seen the ghost." "Well, gentlemen," said the Baronet, "theres many a true thing said in jest." how to get the interval? On George's block, the ratio of cars to houses is 8 to 5. There are 32 cars, how many houses are there? PLEASE HELP THIS IS TIMEDWhich of the following is a physical change?CsF(s) + XeFo(s) CsXeF;(s)CO2 (s) + CO2(g)O N2 (g) + 3H2 (g) 2NH3 (g)2H2 (g) + O2 (g) 2H20 (1)Zn(s) + 2 MnO2(s) + H20(1) Zn(OH)2(s) + Mn2O3(s) A man deposits $ 14,850 into a bank, which pays 4% interest that is compoundedsemiannually. What will he have in his account at the end of three years? The plantation system in the southern colonies led to? 7X^2+20x=24X=?Please answer to 2 d.p