The side of one square is 2 centimeters longer than the side of the second square. If the sum of their
areas is 100cm?, find the length of the side of each square.

*DUE TOMORROW* please help

Answers

Answer 1

Answer:

Side length of first square is 10 cm

Side length of second square is 8 cm

Step-by-step explanation:

Let (x + 2) = side length of first square

Let x = side length of second square

Area of a square = (side length)²

⇒ area of first square = (x + 2)²

⇒ area of second square = x²

If the sum of their areas is 100 cm² then:

⇒ (x + 2)² + x² = 100

Expand the brackets:

⇒ x² + 4x + 4 + x² = 100

Collect and combine like terms:

⇒ 2x² + 4x + 4 = 100

Subtract 100 from both sides:

⇒ 2x² + 4x - 96 = 0

Divide both sides by 2:

⇒ x² + 2x - 48 = 0

Factor:

⇒ (x - 6)(x + 8) = 0

Therefore,

⇒ x = 6, x = -8

As distance is positive, x = 8 only.

Therefore, side length of first square is 10 cm

Side length of second square is 8 cm


Related Questions

Can you please help me???

Answers

Answer:

Your answer of coplanar is correct

Step-by-step explanation:

A skew line are 2 lines that aren't parallel and do not intersect.

Since there are arrows on either end of AC and RS , it mean those lines continue, and they will eventually intersect.

It is also not the other 2 clearly, since they do intersect and they don't make a 90° angle

So yes,

The answer is Coplanar

Hope this helps.

I need help please :)

Answers

Answer:

[        [tex]10000(2)^{-n}[/tex]       ]    where n is the number of hours.

Because the beginning will 10000/2 = 50000, then it keeps double the dividing the time.

The answer is
10000/2
I think it’s right :/

f(x)=x²-1, g(x)=2x+1 ??
1. FoG
2.GoF​

Answers

Answer:

1) 4x² + 4x

2) 2x² - 1

Explanation:

     in these type of questions, we go right to left serially in function

given:

f(x)=x²-1g(x)=2x+1

1)

fg(x)

f(2x+1)

(2x+1)²-1

4x² + 4x + 1 -1

4x² + 4x

2)

gf(x)

g(x²-1)

2(x²-1) + 1

2x² - 2 + 1

2x² - 1

I hope this helps you :)

Name the property shown 4 (x+6) = 4(x) + 4(6)

Answers

Answer:

Distributive property

Step-by-step explanation:

Shows the breakdown of distributing the 4

4(x+6)

4x + 4(6)

Note: Figure is not drawn to scale.

If h = 7 units and r = 3 units, then what is the volume of the cone shown above?

Answers

Given:-

Height of cone = 7 unitsRadius of cone = 3 units

To find:

Volume of Cone

We know:-

[tex] \bigstar \boxed{ \rm Volume \: of \: Cone = \frac{1}{3} \pi {r}^{2} h}[/tex]

[tex] \\ \\ [/tex]

So:-

[tex] \leadsto\sf Volume \: of \: Cone = \dfrac{1}{3} \pi {r}^{2} h[/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto\sf Volume \: of \: Cone = \dfrac{1}{3} \times \pi \times {3}^{2} \times 7 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto\sf Volume \: of \: Cone = \dfrac{1}{3} \times \pi \times 3 \times 3 \times 7 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto\sf Volume \: of \: Cone = \dfrac{1}{\cancel3} \times \pi \times \cancel3 \times 3 \times 7 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto\sf Volume \: of \: Cone =\pi \times 3 \times 7 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto\sf Volume \: of \: Cone =\pi \times 21\\ [/tex]

[tex] \\ \\ [/tex]

[tex] \leadsto\bf Volume \: of \: Cone = 21\pi[/tex]

[tex] \\ \\ [/tex]

Therefore option C is correct.

The Volume of the cone is 21π cubic units

The volume of a cone

The formula for calculating the volume of a cone is expressed as:

V = 1/3πr²h

where:

r is the radius = 3 units

h is the height = 7units

The volume of the cone = 1/3π(3)²*7
Volume of the cone = 3π * 7

Volume of the cone = 21π cubic units

Hence the Volume of the cone is 21π cubic units

Learn more on volume of a cone here: https://brainly.com/question/1082469

PLS ANSWER AS SOON AS POSSIBLE

Answers

Answer:

-(x+8) (x-2) I think this is the answer

PLEEEASEE HELP ASSAAAPP!!!!

Answers

That is so hard I can’t sorry

A parachutist’s speed during a free fall reaches 165 feet per second. What is this speed in meters per second? At this speed, how many meters will the parachutist fall during 10 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answer.

Answers

Answer:

[tex]x=750m[/tex]

Step-by-step explanation:

[tex]Assuming[/tex] [tex]That[/tex]:

[tex]1m=3.3ft[/tex]

We can make the conversion from feet per second to meters per second with this procedure:

[tex](165 \frac{ft}{s} ) (\frac{1m}{3.3ft} )=50\frac{m}{s}[/tex]

Let [tex]x[/tex] be the amount of meters the parachutist will fall during 15 seconds of free fall

Having that in 1 second the parachutist falls 50 meters, we can calculate [tex]x[/tex] :

[tex]x=(50\frac{m}{s} )(15s)[/tex]

[tex]x = 750 m[/tex]

Brainliest?!

help me please!!!!!!!​

Answers

1) no, it’s an exponential equation because it increases exponentially
2) A

what is 29.1 + 78.9+ 41.5

Answers

Answer:

149.5

Step-by-step explanation

Answer:

149.50

Step-by-step explanation:

i did 29.1+78.8 = 107.90+ 41.5 and that's how i got 41.5

-3 1/2 divided by 1 1/4

Answers

-2 and 4/5 ..............................

Simplifying, we get

-3 1/2 is -3.5

1 1/4 is 1.25

so, -3.5/1.25=

-2.8

please help me with this question

Answers

Answer:

x = 14

Step-by-step explanation:

Think:

What subtracts 10 can get you 4?

Or you can add 10 on both sides.

PLEASE HELP ASAP I WILL GIVE BRAINSLET TO THE CORRECT ANSWER!!!!!!!!!!

Answers

Answer:

Therefore has one solution.

explanation:

Given equations:

6x + y = -7

-24x -7y = 25

Make y the subject:

6x + y = -7

y = -7 - 6x ..............equation 1

-24x -7y = 25

-7y = 25 + 24x

y = (25 + 24x)/-7 ..........equation 2

Solve them simultaneously:

(25 + 24x)/-7 = -7 - 6x

25 + 24x = -7 (-7 - 6x)

25 + 24x = 49 + 42x

42x - 24x = 25- 42

18x = -24

x = [tex]-\frac{4}{3}[/tex]

Then y is:

y = -7 - 6x

y = -7 - 6( [tex]-\frac{4}{3}[/tex])

y = 1

Has one separate value of x and y: (  [tex]-\frac{4}{3}[/tex] , 1 ); so it has one solution.

I need the answer in the next 6 hours

Answers

Answer:

180m

Step-by-step explanation:

The figure shown in the picture is a right triangle.

We have two of it's sides and need to find the hypotenuse (the side in front of the right angle).

To find that we must use the Pythagorean theorem:

[tex]c^{2} = {a}^{2} + {b}^{2} [/tex]

Side a is 400m and side b is 300m.

Therefore:

[tex]c^{2} = {300}^{2} + {400}^{2} [/tex]

[tex]c = \sqrt{300 \times 300 + 400 \times 400} = 500[/tex]

Now that we know that side c is 500m we must just substract the distance between Marla and the dock with the lenght of the side to find the answer

500 - 320 = 180m

Answer:

She is 180m from the information Center

She walked 240m from the parking lot to the lake.

Step-by-step explanation:

I searched your question and found the key answers. below is my backup explanation, hope this helps! brainliest, please!

Which of the following is not directly related to the sample size calculations in the case of one sample z testing?

Answers

Answer:

here's your answer hope it helps you

Step-by-step explanation:

the upper bound of an interval uses the number of samples to get its value. same is said for the population standard deviation.

On a piece of paper, sketch or use a protractor to construct right triangle ABC with AB=3 in., m∠A=90°, and m∠B=45°.

What statement is true about the triangle?

A. BC=3 in

B. AC=3 in.

C. AC=6 in.

D. BC=6 in

Answers

B. AC = 3 in.

because when there is a right triangle with an angle that equals 45 degrees, all sides, not including the hypotenuse, are automatically congruent. This triangle is like that. So if one side, that is not the hypotenuse, equals 3 then the other aide equals 3.

the hypotonuse of a right triangle measures 15cm and one of its legs meauseres 8cm find the measure of the other leg

Answers

Answer:

7cm

Step-by-step explanation:

15 - 8

Hypotenuse is the longest side

Hello everyone, I'm just having trouble on two questions for my Calculus work. I need to solve them using trig substitution to eliminate the root. Does anyone know where to start with this problem? Any help would be greatly appreciated!

Answers

The main idea is to exploit the trigonometric identity,

sin²(θ) + cos²(θ) = 1

2. For an integral containing 16 - 81x², you might substitute x = 4/9 sin(θ) (with differential dx = 4/9 cos(θ) dθ, but without an actual integral to work with this isn't really important). Then

16 - 81x² = 16 - 81 (4/9 sin(θ))²

… = 16 - 81 (16/81 sin²(θ))

… = 16 - 16 sin²(θ)

… = 16 (1 - sin²(θ))

… = 16 cos²(θ)

so that in the root expression, we would end up with

[tex]\left(16 - 81x^2\right)^{7/2} = \left(16\cos^2(\theta)\right)^{7/2} = 2^{14} |\cos(\theta)|^7[/tex]

since [tex](ab)^c=a^cb^c[/tex] for all real a, b, and c; [tex]16^{7/2}=\left(2^4\right)^{7/2}=2^{14}[/tex]; and [tex]\sqrt{x^2}=|x|[/tex] for all real x.

The goal is to replace x with some multiple of sin(θ) that makes the coefficients factor out like they did here, which then lets you reduce 1 - sin²(θ) to cos²(θ).

And don't be discouraged by the absolute values; in the context of a definite integral, there are things that can be done to remove them or otherwise simplify absolute value expressions.

3. Substitute z = 1/√8 sin(θ) (so that dz = 1/√8 cos(θ) dθ). Then

1 - 8z² = 1 - 8 (1/√8 sin(θ))²

… = 1 - 8 (1/8 sin²(θ))

… = 1 - sin²(θ)

… = cos²(θ)

so that

[tex]\left(1-8z^2\right)^{3/2} = \left(\cos^2(\theta)\right)^{3/2} = |\cos(\theta)|^3[/tex]

A line which passes through the point (0,4) has gradient 5.
Write down the equation of the line.​

Answers

A(0;4); x=0, y=4; m=5

General equation of linear function is [tex]y=mx+b[/tex] ⇒

[tex]4=0\times x+b\\b=4[/tex]

Answer: [tex]y=5x+4[/tex]

In Chelsea's group, there are three boys and six girls. Write a fraction, in simplest form, to represent the amount of boys in the group.

Answers

Answer: 3/9 should be the answer :)

Step-by-step explanation:

Please help simplify the second question

Answers

Answer:

[tex]\frac{3x}{(x-3)(x+1)}[/tex]

Step-by-step explanation:

[tex]\frac{2x-1}{x^2-2x-3}[/tex] + [tex]\frac{1}{x-3}[/tex]

= [tex]\frac{2x-1}{(x-3)(x+1)}[/tex] + [tex]\frac{1}{x-3}[/tex]

multiply the numerator/ denominator of 2nd fraction by (x + 1)

= [tex]\frac{2x-1}{(x-3)(x+1)}[/tex] + [tex]\frac{x+1}{(x-3)(x+1)}[/tex]

add the numerators , leaving the common denominator

= [tex]\frac{2x-1+x+1}{(x-3)(x+1)}[/tex]

= [tex]\frac{3x}{(x-3)(x+1)}[/tex]

Answer:

A) (x+1)(x-3)

B) 3x / x^2 - 2x - 3

or (3x ÷ x^2 - 2x - 3)

Hope this helps!

Linda, Frank, and Alan served a total of 78 orders Monday at the school cafeteria. Linda served 6 more orders than Alan. Frank served 2 times as many orde as Alan. How many orders did they each serve? Number of orders Linda served:
frank served
Alan served​

Answers

Answer:

Frank served 32

Alan served 18

Linda served 24

Step-by-step explanation:

78-6=72

72 divided by 4 = 18

Next time if you need help on these kind of questions, try drawing a bar diagram, it really helps

I’m so lost, please help!

Answers

Answer:

a = 156°

b = 132°

c = 108°

Step-by-step explanation:

The sum of the exterior angles of a polygon equals 360°. The sum of an interior and exterior angle equals 180°. There are two missing exterior angles that you need to find the measure of so we can find the value of x.

First exterior angle is with the 82° interior angle. Subtract from 180 to find the exterior angle.

180 - 82 = 98°

The second exterior angle is with the 134° interior angle. Subtract from 180 to find the exterior angle.

180 - 134 = 46°

Now add all the exterior angles together and set them equal to 360.

x + 2x + 3x +72 + 98 + 46 = 360

6x + 216 = 360

6x + 216 -216 = 360 -216

6x = 144

6x/6 = 144/6

x = 24

No find the exterior angles then subtract each one from 180°.

To find a.

a + x = 180

a + 24 = 180

a + 24 - 24 = 180 - 24

a = 156°

To find b.

b + 2x = 180

b + 2(24) = 180

b + 48 = 180

b + 48 - 48 = 180 - 48

b = 132°

To find c.

c + 3x = 180

c + 3(24) = 180

c + 72 = 180

c + 72 - 72 = 180 -72

c = 108°

6.What is of 40%of40%? a.12. b.14 .c.15.d.16​

Answers

Percentage

0.4 x 0.4 = 0.16 =16% (d)

The flight from Perth to London is 16 hours and 35 minutes. The time in Perth is 7 hours ahead of London. A flight leaves Perth at 8am on Wednesday. What is the time in London when the flight arrives?​

Answers

Answer:

Flight arrived in london on 5 : 35 pm Wednesday

Step-by-step explanation:

Time = 16 h 35 min

Time difference = 7 h

Flight time  =  8am

So

     According to perth time flight reached in london is

         8 am + 16 h 35 m =  8 am + ( 12 h + 4h + 35 m) =

         8pm + 4h +35 =  12am + 35m   = 12 : 35 am

The time difference is 7 h ,so minus this from  perth time

      12 : 35 am -  7h  =   5 : 35 pm

Mark brainliest if you understand

Absolute minimum and maximum values of [tex]f(x)=2x^{3}-3x^{2} -12x+1[/tex] on the interval [-2,3]

Answers

Step-by-step explanation:

[tex]f'(x)=6x^{2}-6x-12[/tex]

So f'(x)=0:

x^2 - x - 2 = 0

(x-2)(x+1)=0

x=-1, 2

So we need to find the value of f at those critical points and also at the endpoints of the interval

f(-1)=-2-3+12+1=8

f(2)=16-12-24+1=-19

f(-2)=-16-12+24+1=-3

f(3)=54-27-36+1=-8

so the max is 8 and the min is -19

Solve the following inequality algebraically:
1 less-than 3 x minus 2 less-than 4
a.
1 less-than x less-than 2
b.
0 less-than x less-than 3
c.
1 greater-than x greater-than 2
d.
0 greater-than x greater-than 3

Answers

Answer:

1 less-than x less-than 2

b.

0 less-than x less-than 3

c.

1 greater-than x greater-than 2

d.

0 greater-than x greater-than 3

Answer:

The Answer is A.  1 < x < 2

Step-by-step explanation:

Calculator
A net of a cylinder with radius 4 inches and height 8 inches is
given
What is the surface area of this cylinder?
8 in.
Use 3.14 for TT
Enter your answer in the box.
4 in.
in?

Answers

Answer:

200.96 in²

Step-by-step explanation:

Surface area:

S = 2πrhS = 2*3.14*4*8 = 200.96 in²

Help with this geometry problem

Answers

Answer:

∠DCA ≅ 56°

Reason: vertical angles theorem

∠DCF ≅ 144°

Reason: Angles on a straight line (DE) add up to 180°

∠ECB ≅ = 37°

Reason: Angles on a straight line (FA) add up to 180°

∠CAB ≅ ∠DCA ≅ 56°

Reason: Alternate interior angles theorem

∠CBA ≅ ∠ECB ≅ 37°

Reason: Alternate interior angles theorem

Step-by-step explanation:

∠DCA ≅ ∠ECF ≅ 56°

Reason: vertical angles theorem

∠DCF ≅ 180 - 56 = 144°

Reason: Angles on a straight line (DE) add up to 180°

∠ECB ≅ 180 - 56 - 87 = 37°

Reason: Angles on a straight line (FA) add up to 180°

∠CAB ≅ ∠DCA ≅ 56°

Reason: Alternate interior angles theorem

∠CBA ≅ ∠ECB ≅ 37°

Reason: Alternate interior angles theorem

An animal is running at a rate of 50 ft per sec.
(a) If the animal runs for 7 sec,
(b) If the animal travels d ft, what is its time

Answers

Answer:

49

Step-by-step explanation:

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