An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a cylinder, as shown below:

Hourglass with sand measuring 47 millimeters high

© 2011 Jupiterimages Corporation

Each cone of the hourglass has a height of 12 millimeters. The total height of the sand within the top portion of the hourglass is 47 millimeters. The radius of both the cylinder and cone is 4 millimeters. Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second. How many seconds will it take until all of the sand has dripped to the bottom of the hourglass?
A(6.4)
B(62.4)
C(8.5)
D(56.0)

Answers

Answer 1
The volume of a cylinder is given by the formula Vr²h². In this instance, r is 4 and the height is 47-12 (the height of the cone at the bottom is 12 mm and the sand goes up to 47 mm on the top portion of the hourglass, including both the cone and cylinder) or 35 mm.
V=π(4²)(35)=560π mm³.
The volume of a cone is given by the formula V=1/3πr²h².  In this instance, r is 4 and the height is 12 mm.
V=1/3π(4²)(12)=π(1/3)(12)(4²)=π(4)(4²)=64π mm³.  
This gives a total volume of 560π+64π=624π mm³ of sand.
Since the sand goes down to the bottom at a rate of 10π mm³/second, it will take 624π/10π=62.4 seconds for the sand to all drain out.
Answer 2

Answer:

62.4

Step-by-step explanation:


Related Questions

WILL GIVE BRAINLIEST ANSWER TO THE FIRST PERSON TO ANSWER CORRECTLY!
Draw any two convex pentagons. For each of them measure the sum of its interior angles using a protractor. Explain the result of the measuring.

Answers

In a convex polygon, all interior angles are less than or equal to 180. So pentagons are polygons of five sides. We need to draw two different pentagons with the previous characteristics and measures of the internal angles. Therefore, we will choose to type of pentagons.

Every pentagon can be divided up into three triangles, either a regular or irregular one and each triangle adds up to 180 degrees. Therefore, the angles in every pentagon must add up to 540 degrees.

1. Drawing of the first convex pentagon (Regular Pentagon).

A polygon is regular when all angles are equal and all sides are equal. The regular pentagon is a 5-sided polygon. This is shown in Figure 1. Note that all angles are equal to 108°.

1.1. Sum of the interior angles of the first convex pentagon.

According to Figure 1, the sum of its interior angles is as follows:

[tex]\alpha=5 \times 108^{\circ}=540^{\circ}[/tex]

As we said, the angles in every pentagon must add up to 540 degrees. If the pentagon is regular each internal angle measures 108°. In fact, in a Regular Polygon with N sides, each angle is:

[tex]\frac{(N-2)180{^\circ}}{N} \\ \\ Since \ N=5 \\ \\ \\ \frac{(5-2)180{^\circ}}{5}= 108^{\circ}[/tex]

2. Drawing of the second convex pentagon (Irregular Pentagon)

This is a type of polygon that does not have all sides equal and all angles equal. In Figure 2 is shown this pentagon. Note that there are five sides and all angles are not equal.

2.1 Sum of the interior angles of the second convex pentagon.

According to Figure 2, the sum of its interior angles is given by:

 [tex]\beta=81^{\circ}+139^{\circ}+139^{\circ}+94^{\circ}+87^{\circ}=540^{\circ}[/tex]

As we said, no matter if the pentagon is irregular, the angles in every pentagon must add up to 540 degrees.

Answer with explanation:

A Polygon is said to be convex, if all the diagonals of the polygon lies in the interior of the polygon.

→Sum of interior angle of polygon =(n-2)×180°, where n is the number of sides of the polygon.-----(1)

→A pentagon is said to be convex, if it has 5 sides and all the Diagonals of pentagon lies in the interior.

Sum of interior Angles of Triangle =(3-2)×180°=180°

Sum of interior angles of Quadrilateral = (4-2)×180°=2×180°=360°

Sum of Interior angles of Polygon =(5-2)×180°=3×180°=540°

Used the formula (1) in all the three cases.

True or false. This transformation is a dilation

Answers

true transformation is a dilation


Yes it is true!! Dilation is a transformation because each point of the object is moved- like tracing- a perfectly strait line! The strait line is drawn from a point called the center of dilation!


Have a great day! :)

Given: MQ = NQ; Q is the midpoint of LP; LM ≅ PN Which congruence theorem can be used to prove △MLQ ≅ △NPQ?

Answers

Since Q is the midpoint of LP, that means that LQ is congruent to QP.  We are given that MQ is congruent to NQ and LM is congruent to PN.  We therefore have all 3 sides of one triangle congruent with all 3 sides of the other, so the triangles are congruent by the Side Side Side (SSS) theorem.
Final answer:

The congruence theorem that can be used to prove △MLQ ≅ △NPQ is the SAS (Side-Angle-Side) congruence theorem.

Explanation:

To prove that triangles MLQ and NPQ are congruent, we can use the SAS (Side-Angle-Side) congruence theorem. The given information MQ = NQ indicates that the sides MQ and NQ are congruent. Since Q is the midpoint of LP, we can conclude that the side LQ is congruent to side PQ. Lastly, the fact that LM ≅ PN means that the side LM is congruent to side PN. Therefore, we have congruent corresponding sides and an included congruent angle, allowing us to use the SAS congruence theorem. So, △MLQ ≅ △NPQ.

Learn more about Congruent Triangles here:

https://brainly.com/question/22062407

#SPJ11

What is the area of this polygon?



Enter your answer in the box.


Answers

Hey there! :D

Find the length and width of the rectangle. 

Length= 7 Width= 5 

5*7= 35

Triangle= 1/2*b*h

base= 7 height= 2 (if you were to draw a line from the vertex to the base of the triangle, it would be 2 units)

1/2*7*2

1/2*14

7

35+7= 42

The area equals 42. 

I hope this helps!
~kaikers
35 plus 2= 45 is the area of this polygon

If f(x)=4^x-1+6 and g(x)=2x-5, what is (f-g)(x)?

A. (f-g)(x)=4^x-1-2x-1
B. (f-g)(x)=4^x-1-2x+11
C. (f-g)(x)=4^x-1-2x-11
D. (f-g)(x)=4^x-1-2x+1

Answers

I believe the answer is
B. (f-g)(x)=4^x-1-2x+11
(f-g)(x) = (4^x-1+6) - (2x-5) 
apply like terms while retaining order of operations
6 - (-5) = 11
4^x - 1 - 2x + 11
I'm fairly certain, I just did this section, but just in case, sorry!

Answer:

B is correct.

Step-by-step explanation:

Juanita is making bread.She needs 3 1/2 cups of flour.Juanita only has a 1/4-measuring cup.How many 1/4 cups of flour will Juanita use to prepare he bread?

Answers

she will need to use 14 1/4 cups of flour
Juanita will need 14 1/4 cups of flour in order to make the bread

Isaac made all these rectangles with 24cm lengths of string. This implies that the perimeter of all these rectangles are equal

Answers

the correct question is 
Isaac made all these rectangles with 24cm lengths of string. This implies that the perimeter of all these rectangles are equal. What do we observe about the sum of the length and the width?

Let
x-----------> the length of rectangle
y-----------> the width of rectangle

we know that
[perimeter of rectangle]=2x+2y
24=2x+2y------------> 12=x+y

the answer is

it is observed that in all the rectangles the sum of its length and its width will be equal to 12




Final answer:

When Isaac uses 24cm of string to make rectangles, no matter the individual dimensions, the sum of the length and width of these rectangles must always be 12 cm. This is a direct result of the fixed perimeter, which requires that the combined measurements of length and width halves the total perimeter to maintain the consistent total string usage.

Explanation:

Isaac made all these rectangles with 24cm lengths of string, which implies that the perimeter of all these rectangles is equal. The observation about the sum of the length and the width of these rectangles is that regardless of the individual measurements of the length and width, their sum must always be half the total perimeter of the rectangle. Given a fixed perimeter of 24cm, the formula for the perimeter of a rectangle (P) is

P = 2(l + w),

where l is the length and w is the width. Since the perimeter is given as 24cm, this simplifies to

24 = 2(l + w), or 12 = l + w.

This equation means that the sum of the length and width of the rectangles must always equal 12 cm. This is because the total loop made by the string when forming the rectangle has to be divided into four edges, two lengths, and two widths, which totals the provided 24cm of string. Therefore, if we adjust either the length or the width, the other measurement must adjust in such a way that their sum remains constant at 12 cm to maintain the total perimeter as 24cm.

Which equation is in point-slope form and is depicted by the line in this graph?


a) (y - 3 ) = 3/5 ( x - 2 )
b) (y - 3 ) = - 3/5 ( x + 2 )
c) (y - 3 ) + 5/3 ( x - 2 )
d) (y + 3 ) - 5/3 ( x + 2)

Answers

The correct answer would be B.i hope that helped!! if you have any questions or concerns about the answer i gave you please feel free to let me know!!
The first thing you should do in this case is to write the equation in its generic form.
 We have then:
 y-yo = m (x-xo)
 We look for the slope:
 m = (y2-y1) / (x2-x1)
 m = (0-3) / (3 - (- 2))
 m = -3 / 5
 We choose any point of the line:
 (xo, yo) = (- 2, 3)
 We substitute the values in the generic equation:
 y-3 = -3 / 5 (x - (- 2))
 We rewrite:
 y-3 = -3 / 5 (x + 2)
 Answer: 
 b) (y - 3) = - 3/5 (x + 2)

what is straight continues in both direction and does not stop



Answers

Hmm...lemme guess...a line?

what is y−2=−3(x−7) written in standard form?

Answers

we know that

standard form is--------------------> ax+by=c
then
y−2=−3(x−7)---------> y-2=-3x+21--------------> y+3x=21+2----------> 3x+y=23

the answer is 
3x+y=23

WZ←→ is tangent to circle O at point B.

What is the measure of ∠OBZ?


80º

90º

160º

180º

Answers

Answer:

The correct option is 2.

Step-by-step explanation:

Given information: WZ is tangent to circle O at point B.

According to the tangent of circle theorem: The tangent line is perpendicular to the radius at the point of tangency. It means the angle formed on the point of tangency by tangent and radius is a right angle.

Since WZ is tangent to circle O at point B and OB is radius, therefore

[tex]\angle OBZ=90^{\circ}[/tex]

Therefore correct option is 2.

Final answer:

The measure of angle ∠OBZ is 90°, as the tangent line to a circle at a point is perpendicular to the radius at that point.

Explanation:

The question regards the measure of angle OBZ where WZ↔ is tangent to circle O at point B. By a well-known theorem in geometry, a line tangent to a circle is perpendicular to the radius drawn to the point of tangency. Therefore, the measure of angle ∠OBZ, which is formed by the radius OB and the tangent line at B, must be 90°.

Find the circumference

Answers

circumference = 2 X PI X r

orange circle r = 5cm 
circumference = 2 x 3.14 x 5 = 31.4 cm

blue circle r = 5+5 = 10
circumference = 2 x 3.14 x 10 = 62.8 cm
Hey there!

We'll start with the outer circle.

Circumference is defined as 2πr, which is 2π times the radius. If the outer circle has a radius of 5, we plug in:

2π(5) = 10π

For the outer circle, we have a radius of 5 as well, therefore we also get:


2π(5) = 10π


For our total circumference, we get 20π

Hope this helps!

For which intervals is the function increasing?



Select each correct answer.




(0, 1)

(2, ∞)

(1, 2)

(−∞, 0)
 
Note: Multiple choice question

Answers

Answer:

The intervals where the function is increasing are [tex](-\infty,0)[/tex] and [tex](1,2)[/tex]

Step-by-step explanation:

We are required to find the intervals in which the function is increasing.

From the figure, we see that,

The graph is going up towards the origin to reach the point (0,0).

Then, it is going down in the interval (0,1).

Then, it is again going up to reach the point (2,0).

Finally, it is going downwards towards infinity.

Thus, we see that,

The intervals where the function is increasing are [tex](-\infty,0)[/tex] and [tex](1,2)[/tex]

Answer:(−∞, 0) and(1,2)

Step-by-step explanation:

The amount of trout y (in tons) caught in a lake from 1995 to 2014 can be modeled by the equation y = -0.08x2 + 1.6x + 10, where x is the number of years since 1995. When were about 15 tons of trout caught in the lake? The year and the year .

Answers

For this case, the first thing we want to do is substitute the value of y = 15 in the equation.
 We have then:
 15 = -0.08x ^ 2 + 1.6x + 10
 Rewriting we have:
 0 = -0.08x ^ 2 + 1.6x + 10 - 15
 0 = -0.08x ^ 2 + 1.6x - 5
 The solutions are:
 x1 = 3.876275643042054
 x2 = 16.123724356957947
 Nearest whole number:
 x1 = 4
 x2 = 16
 were about 15 tons of trout caught in the lake in the years:
 1995 + 4 = 1999
 1995 + 16 = 2011
 Answer:
 The year 1999 and the year 2011

About 15 tons of trout were caught in the lake in the years 1999 and 2011.

To determine the years when about 15 tons of trout were caught in the lake, we need to solve the equation [tex]\( y = -0.08x^2 + 1.6x + 10 \) for \( y = 15 \).[/tex]

The equation becomes:

[tex]\[ 15 = -0.08x^2 + 1.6x + 10 \][/tex]

Subtract 15 from both sides to set the equation to zero:

[tex]\[ 0 = -0.08x^2 + 1.6x - 5 \][/tex]

This is a quadratic equation in the form of [tex]\( ax^2 + bx + c = 0 \)[/tex], where:

- ( a = -0.08 )

- ( b = 1.6 )

- ( c = -5 )

We solve this quadratic equation using the quadratic formula [tex]\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \):[/tex]

First, calculate the discriminant [tex]\( \Delta = b^2 - 4ac \):[/tex]

[tex]\[ \Delta = (1.6)^2 - 4(-0.08)(-5) \][/tex]

[tex]\[ \Delta = 2.56 - 1.6 \][/tex]

[tex]\[ \Delta = 0.96 \][/tex]

Now, calculate the two possible values of ( x ):

[tex]\[ x = \frac{-1.6 \pm \sqrt{0.96}}{2(-0.08)} \][/tex]

Calculate [tex]\( \sqrt{0.96} \):[/tex]

[tex]\[ \sqrt{0.96} \approx 0.9798 \][/tex]

Now solve for ( x ):

[tex]\[ x_1 = \frac{-1.6 + 0.9798}{-0.16} \][/tex]

[tex]\[ x_1 = \frac{-0.6202}{-0.16} \][/tex]

[tex]\[ x_1 \approx 3.88 \][/tex]

[tex]\[ x_2 = \frac{-1.6 - 0.9798}{-0.16} \][/tex]

[tex]\[ x_2 = \frac{-2.5798}{-0.16} \][/tex]

[tex]\[ x_2 \approx 16.12 \][/tex]

Since ( x ) is the number of years since 1995:

For [tex]\( x_1 \approx 3.88 \):[/tex]

[tex]\[ \text{Year} = 1995 + 4 = 1999 \][/tex]

For [tex]\( x_2 \approx 16.12 \):[/tex]

[tex]\[ \text{Year} = 1995 + 16 = 2011 \][/tex]

Therefore, about 15 tons of trout were caught in the lake in the years 1999 and 2011.

lease help...

Tyler has $1000 that he wants to put in a savings account. He wants to save the money for 6 years. After 6 years he plans to take the money out and spend it on college. He looks at two different banks, and they offer him different interest options.

Bank A offers Tyler 4% simple interest. How much would Tyler’s investment be worth after 6 years in this account? Show your calculations below.

Bank B offers Tyler 3% interest compounded annually. How much would Tyler’s investment be worth after 6 years in this account? Show your calculations below.


In which bank should Tyler place the $1000 he is saving for college

Answers

Bank A = 1000 x  (1 + (0.04*6)) = $1,240

Bank B = 1000 x (1+0.03)^6 = $1,194.05

Bank A would be worth more

Answer:

He should place it in Bank A

For bank A Total amount = $1240

For bank bA= $1196.68

Step-by-step explanation:

For bank A with simple interest rate of 4%

Interest = PRT/100

Interest =( 1000*4*6)/100

Interest=$240

Total amount = principal + interest

Total amount = $1000+$240

Total amount = $1240

For Bank B with compound interest rate of 3%

A = p(1+r/n)^(nt)

A = 1000(1+(0.03/6))^(6*6)

A = 1000*1.19668

A= $1196.68

Please help me with this math problem.

Answers

Hello!

Tangent lines have only one point on the circle, meaning they form straight angles with the edge of the circle. The radius goes from the center of the circle to the point where the tangent line is on circle, creating a right angle.

Answer:
90°

Triangle GHI is similar to triangle JKL. If JP = 26, MH = 36 and PK = 16 then GM =


A.
44.3
B.
58.5
C.
86
D.
117

Answers

Since the two triangles are similar, then the ratio of the corresponding sides is equal. Therefore;
JP/GM=PK/MH
26/GM = 16/36
   GM=  (26×36)/16
         =  58.5

Solve 3x+11= k for x.
A. x=3k-11
B. x=k-11
C. k+11
x=———
3

D. k-11
x= ———
3

Answers

 x =k − 11divided by 3
This is the answer to your problem 

Answer:  the correct option is (D) [tex]x=\dfrac{k-11}{3}.[/tex]

Step-by-step explanation:  We are given to solve the following equation for the value of x :

[tex]3x+11=k~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To solve the given equation for x, we need to take x on one side and all other terms on the other side of the equality.

The solution of equation (i) is as follows :

[tex]3x+11=k\\\\\Rightarrow 3x=k-11\\\\\Rightarrow x=\dfrac{k-11}{3}.[/tex]

Thus, the required value of x is [tex]x=\dfrac{k-11}{3}.[/tex]

Option (D) is CORRECT.

Leonardo da Vinci drew a portrait of a young woman. The portrait is shaped like a rectangle. It is 13.5 inches long and 10 inches wide. What is the length of a diagonal that connects one corner of the portrait to the other? Round the answer to the nearest tenth of an inch.

Answers

Let
x---------------> long side rectangle------------> 13.5 in
y---------------> wide side rectangle------------> 10 in
d--------------> length of a diagonal

we know applying the Pythagorean theorem
d²=x²+y²-----------> d²=13.5²+10²-> d²=282.25
d=√282.25=16.80 in

the answer is 16.8 in

Find the value of x. Round the length to the nearest tenth. Diagram is not drawn to scale.
A.7.2ft
B.6.9ft
C.13.9ft
D.9.7ft

Answers

Answer:

(A) [tex]x=7.2 ft[/tex]

Step-by-step explanation:

Given: A triangle whose base angle is 44° and hypotenuse is 10ft.

To find: The value of x.

solution: Using the trigonometry, we have

[tex]\frac{x}{10}=cos44^{{\circ}}[/tex]

⇒[tex]x=10{\times}cos44^{{\circ}}[/tex]

⇒[tex]x=10{\times}0.72[/tex]

⇒[tex]x=7.2 ft[/tex]

Thus,the value of [tex]x=7.2 ft[/tex]

Answer: A. 7.2 ft

Step-by-step explanation:

Given: A right triangle with hypotenuse 10 ft and base angle [tex]44^{\circ}[/tex]

By using Trigonometry, we have

[tex]\cos (44^{\circ})=\frac{\text{side adjacent to }44^{\circ}}{\text{hypotenuse}}\\\\\Rightarrow \cos (44^{\circ})=\frac{x}{10}\\\\\Rightarrow0.71933980033=\frac{x}{10}\\\\\Rightarrow\ x=10\times0.71933980033=7.1933980033\approx7.2\ ft.[/tex]

Hence, the value of x = 7.2 ft.

If the sum of interior angles is 180 then what is the sum?

Answers

If there were an angle of 180, and then, we would then want to find the sum, we would then would understand that there would have to be either two or more angles that would then resolve to be 180 degrees.

Answer:

Sum = (n -2) * 180

Step-by-step explanation:

Step 1 : The formula for calculating the sum of the interior angles = (n - 2) × 180, where "n" is the number of sides of a regular polygon.

Step 2: Here we are given the sum of the interior angles is 180 degrees. Therefore, the given figure must be triangle.

Help Needed
Let ​f(x)=x2+12x+32.​ What are the zeros of the function? Enter your answers in the boxes.

Answers

The zeros of this function is -4 and -8

Answer:

Step-by-step explanation:

The given equation is:

[tex]f(x)=x^2+12x+32[/tex]

Simplifying the above expression, we have

[tex]f(x)=x^2+4x+8x+32[/tex]

[tex]f(x)=x(x+4)+8(x+4)[/tex]

[tex]f(x)=(x+4)(x+8)[/tex]

Thus, zeroes of the given function will be:

[tex]f(x)=0[/tex]

[tex](x+4)(x+8)=0[/tex]

[tex]x=-4 and x=-8[/tex]

Therefore the zeroes of the given function are [tex]x=-4 and x=-8[/tex].

PLEASE FULL ANSWERS! need all the help I can get

Answers

A
This is one of those questions that is hard to explain, because I don't know what you know. I'll start with the most obvious reason I know. At x = -1 the top and bottom of the function is 0/0. zero/zero can give indeterminate results and you must look for other ways of explaining what is going on. Here's another thought which is less reliable.

The fraction factors.
(x + 1)*(x - 1)
============
    (x + 1)
The two common factors cancel and you are left with f(x) = x - 1

If you have a graphing calculation you can put this in as y = x - 1 and you see that it is a straight line.

Question B is much nicer
when you put x = 1 into the fraction, you get 0 /2 which gives you 0. That's much easier to handle because the answer is 0.
you are still graphing y = x - 1, but this time the graph is much more well behaved.
a. f(-1) = (1-1)/(-1+1) = 0
This is still continuous I believe as the whole y equals 0, though I am not sure about this.

b. f(1) = (1-1)/(1+1)= 0
This is definitely continuous as the denominator did not equal 0. 


a sperm whale can stay underwater 7 times longer than a sea cow can.how long can a sperm whale stay underwater?

Answers

The sperm whale's underwater duration is seven times that of the sea cow, showcasing remarkable breath-holding abilities, likely adapted for deep-sea foraging and hunting.

The relationship between the underwater durations of a sperm whale and a sea cow suggests that the sperm whale's capability is sevenfold that of the sea cow. Let's denote the sea cow's duration as "x." Accordingly, the sperm whale's underwater duration would be 7 times x.

In practical terms, if we assume the sea cow can stay submerged for 10 minutes (x = 10), then the sperm whale, being seven times more proficient, can stay underwater for 7 times 10, which is 70 minutes (7x = 7 * 10 = 70). This sevenfold difference implies a significant contrast in their breath-holding abilities.

The numerical representation extends universally; if the sea cow can endure underwater for "x" units of time, the sperm whale can endure for 7 times "x" units of time. This relationship showcases the remarkable adaptation of the sperm whale to extended submersion, likely linked to its deep-sea foraging behavior and hunting strategies.

In essence, the sperm whale can stay underwater for a duration that is seven times longer than that of the sea cow, highlighting its remarkable breath-holding capacity.

A sperm whale can stay underwater for 7 times longer than a sea cow, so it can stay underwater for 7 times the duration of a sea cow.

If a sperm whale can stay underwater 7 times longer than a sea cow, we can express this relationship as:

Time a sperm whale can stay underwater = 7 * Time a sea cow can stay underwater

So, if we let the time a sea cow can stay underwater be represented by 'x', then the time a sperm whale can stay underwater is:

7 * x

Therefore, a sperm whale can stay underwater for 7 times longer than a sea cow, which means it can stay underwater for 7x.

A store has a 25% off sale on coats.With this discount,the price of one coat is $34.50.What is the original price of the coat?

Answers

price after discount: $34.5
x - 0.25x = 34.5
0.75x = 34.5
x = 46
The original price is $46

Which professional needs the knowledge of statistics and geometry in order to comprehend maps, graphs and charts? Pilot, banker, fashion designer, or an architect?

Answers

the answer is an architect. Architecture is the art and technique of projecting, designing, building and modifying the human habitat through buildings, architectural and urban structures and public spaces of all kinds, for this the architect must master the field of geometry and interpretation of plans, to carry out their work in a responsible and professional manner.

Answer:

The correct answer is pilot. I took the test

Step-by-step explanation:

what is the exponent of 9x9x9x9x7x7

Answers

9 to the 4th and 7 squared
It’s is 321489, it depends what exponents we’re used in the problem but this is what I got

Mitsu borrowed $1,250. She made 36 payments of $45.15 each. How
much did she pay in interest?
a. $375.40
b. $162.54
c. $1,625.40
d. $37.54

Answers

C. 1,625.40 is how much she payed in interest

Batman is 4 times robins age. The sum has f their ages is equal to 45. How old is Batman and robin?

Answers

Hey there! :D

f= 4x+x 

Where f is their total ages, and x is Robin's age. Batman's age is 4 times Robin's. 

Plug in what you know. 

45=4x+x

45=5x

x=9 

Robin is 9. 

9*4= 36

Batman is 36.

I hope this helps!
~kaikers

Answer:

Robin is 9 years old and Batman is 36 years old

Step-by-step explanation:

Batman: 4x

Robin: x

4x + x = 45

5x = 45

x= 9

A piece of wire 32cm Long is cut into two parts. Each part is bent to form a square. Given that the total area of the two squares is 34cm square, find the perimeter of each square

Answers

The possible perimeters for the squares are 20 cm and 12 cm, depending on how the wire is cut.

Let's denote the length of one part of the wire as x and the length of the other part as 32−x. Each part is bent to form a square.

The perimeter (P) of a square is given by 4 × side length.

The side length of the first square ([tex]S_1[/tex] ) is x/4, and the side length of the second square ([tex]S_2[/tex] ) is (32−x)/4.

The total area of the two squares is given as [tex]34cm^2[/tex] , so we can write the equation:

[tex]S^2_1 + S^2_2 = 34[/tex]

Substitute the expressions for [tex]S_1 and S_2[/tex] :

[tex](\frac{x}{4})^2 + (\frac{(32-x)}{4})^2 =34[/tex]

Now, solve for x:

[tex]\frac{x^2}{16} + \frac{(32-x)^2}{4} =34[/tex]

Multiply both sides by 16 to get rid of the denominators:

[tex]x^2 +(32-x)^2=544[/tex]

Expand and simplify:

[tex]x^2+1024-64x+x^2 =544[/tex]

Combine like terms:

−64x+480=0

Divide the entire equation by 2 to simplify:

−32x+240=0

Now, factor the quadratic equation:

(x−20)(x−12)=0

So, x=20 or x=12.

If x=20, the lengths of the two parts are 20 cm and

32−20=12 cm.

If x=12, the lengths of the two parts are 12 cm and

32−12=20 cm.

Now, we can find the perimeter of each square by multiplying the side length by 4:

For x=20, the perimeter is [tex]4 \times \frac{20}{4} = 20 cm[/tex]

For x=12, the perimeter is [tex]4 \times \frac{12}{4} = 12 cm[/tex]

So, the possible perimeters for the squares are 20 cm and 12 cm, depending on how the wire is cut.

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