A semicircle is drawn onto one of the shorter sides of a rectangle. The shorter side of the rectangle measures 4 centimeters. The area of the figure is 41.4 square centimeters.

What is the length of the longer side of the rectangle?

Use 3.14 for π.

Enter your answer as decimal in the box.

Answers

Answer 1
Answer:

8.78 cmSolution:

We are given that :

A semicircle is drawn onto the shorter side of rectangle.Shorter side of rectangle measures 4cm. i.e; the diameter of the circle is 4cmArea of the figure is 41.4 cm²

Using Formulas:

Area of rectangle:

[tex] \quad\hookrightarrow\quad{\pmb{ \mathfrak {length\times breadth }}}[/tex]

Area of semicircle:

[tex] \quad\hookrightarrow\quad{\pmb{ \mathfrak{ \dfrac{\pi r^2 }{2}}}}[/tex]

We have to find the length of longer side of rectangle!

Here, we can know that the figure is composed of one rectangle and one semicircle. Therefore by combining the areas of rectangle and circle and taking the length of rectangle as a variable , we will finds its value ;

[tex] \quad\dashrightarrow\quad \sf {Area_{\tiny { total}} = Area_{\tiny {rectangle}}+ Area_{\tiny {semicircle}}}[/tex]

[tex] \quad\dashrightarrow\quad \sf {A = ( l \times b ) + \dfrac{\pi r^2 }{2} }[/tex]

[tex] \quad\dashrightarrow\quad \sf {41.4 = ( l \times 4 ) +\dfrac{3.14\times 2^2}{2} }[/tex]

[tex] \quad\dashrightarrow\quad \sf { 41.4= ( l \times 4 )+ \dfrac{ 3.14\times 4}{2}}[/tex]

[tex] \quad\dashrightarrow\quad \sf { 41.4=( l \times 4 )+ \dfrac{12.56}{2}}[/tex]

[tex] \quad\dashrightarrow\quad \sf { 41.4= (l \times 4 )+ 6.28}[/tex]

[tex] \quad\dashrightarrow\quad \sf {l \times 4 = 41.4-6.28 }[/tex]

[tex] \quad\dashrightarrow\quad \sf { l\times 4 = 35.12}[/tex]

[tex] \quad\dashrightarrow\quad \sf { l =\dfrac{35.12}{4}}[/tex]

[tex] \quad\dashrightarrow\quad \underline{\underline{\pmb{\sf {l = 8.78\:cm}}} }[/tex]

Answer 2

The length of the longer side of the rectangle will be 8.78 cm.

What is the area?

The area of a two - dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

On one of a rectangle's shorter sides, a semicircle is drawn. The rectangle's shorter side is 4 cm long. The figure has a surface area of 41.4 square centimeters.

Then the length of the rectangle is calculated as,

A = πr² / 2 + l × b

41.4 = (3.14 / 2) × (4/2)² + 4l

41.4 = 6.28 + 4

l = 8.78 cm

The length of the longer side of the rectangle will be 8.78 cm.

More about the area link is given below.

https://brainly.com/question/27683633

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Related Questions

If a 5 kg ball is accelerating 1.2 m/s squared, what is the force on it? plss do it now

Answers

Answer:

The answer is 6 N

Step-by-step explanation:

Consider quadrilateral MATH with vertices (0,0), (s,O). (s,t) and (O,t). Sarah used the distance formula to prove that MT=AH. What conclusion can be made from Sarah's calculations?

Answers

Step-by-step explanation:

You could say that the diagonals are congruent.

Below are the demand and supply equations for overhead projectors in a certain market. In these equations, p represents price, D represents demand, and S represents supply. S = three-fourths p minus 28 D = negative 2 p 131 What is S at the point of equilibrium, to the nearest whole number? a. 12 b. 15 c. 58 d. 67.

Answers

For the equilibrium, the value of supply and the value of demand will be equal. Then the value of price (p) is 58.

What is the linear system?

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

The demand and supply equations for overhead projectors in a certain market.

In these equations, p represents price, D represents demand, and S represents supply.

[tex]\rm S = \dfrac{3}{4}p - 28 \\\\D = -2 p + 131[/tex]

For the equilibrium, the value of supply and the value of demand will be equal. Then we have

[tex]\begin{aligned} \dfrac{3}{4}p - 28 &= -2 p + 131\\\\3p- 112 &= -8p + 524\\\\11p &= 636\\\\p &= 57.81818 \approx 58 \end{aligned}[/tex]

More about the linear system link is given below.

https://brainly.com/question/20379472

Answer: B. 15

Step-by-step explanation: edge 2022 i got it right

If a van traveled 240 miles in 4 hours, how far could the van travel in 5 hours?

Answers

Answer: i think 300

Step-by-step explanation: i divided 240 by 4 and got 60 then multiplied 60X5=300

Answer:

300 miles in five hours.

Step-by-step explanation:

speed = distance/time

distance = speed*time

240/4=60

d= 60*5

d=300 miles in five hours.

Word explanation:

You can use the formula, speed=distance/time to find the speed which is 60 mph. Now use the formula for distance which is distance= speed*time. The answer would be 300 miles in five hours.

Jasleen has 6 packs of 8 colored markers to put into party gift bags. She spilts the markers equally among 9 gift bags. What is the minimum amount of markers she can put in each bag?

Answers

Your answer is 252.

I hope this helps.

It takes 33 minutes to walk to the pool from her house. If she rides her bike it takes her 1/3 of that time. Natasha leaves her house for the pool at 3:12. If she is riding her bike, what time will she arrive? _:_

Answers

Answer:

Natasha will arrive at 3:23

Step-by-step explanation:

(1/3)*33= 11

3:12+11= 3:23

10th grade Geo | What does JK equal?

Answers

Answer:

16

Step-by-step explanation:

6x-7=2x+3 Cause point M is the midpoint, so JM and MK have to be equal.

4x=10

x=2.5

JM=15-7=8 and MK=5+3=8

8+8=16

1 by 8 + 3 by 4
I have a photo of you don’t know what I mean:)
And could u explain it too if you can<33
Thank you so much :>

Answers

Answer: 7/8

Step-by-step explanation:

First, we can start by finding a common denominator.

The least common denominator of 8 and 4 is 8.

We can multiply the numerator and denominator of 3/4 by 2:

= 6/8

So, we are esssentially calculating 1/8 + 6/8. We can add the numerators:

= 7/8.

1. Find a number multiplied by 4 that is eight, It would be 2 because two times 4 is eight.

2. Multiply the right side by 2

3. You now have 1 6
— + —
8 8

4. Now you just have to add the numbers , do not add the denominators ( in this case 8)

5. You would get 7

8

Somebody please help with these multi-step equation(s)

Answers

Answer:

h = -1

Step-by-step explanation:

-( 4+h) = 3h

Distribute the minus sign

-4 -h = 3h

Add 4 to each side

-4-h+h = 3h+h

-4 = 4h

Divide each side by 4

-4/4 = 4h/4

-1 = h

2t - 15t is equal to
2t-15t is equal to

Answers

Answer:

2 result(s) found

t=2

t=

2

11

=5.500

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    2*t^2-(15*t-22)=0

Step by step solution :

STEP

1

:

Equation at the end of step 1

 2t2 -  (15t - 22)  = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1     Factoring  2t2-15t+22

The first term is,  2t2  its coefficient is  2 .

The middle term is,  -15t  its coefficient is  -15 .

The last term, "the constant", is  +22

Step-1 : Multiply the coefficient of the first term by the constant   2 • 22 = 44

Step-2 : Find two factors of  44  whose sum equals the coefficient of the middle term, which is   -15 .

     -44    +    -1    =    -45

     -22    +    -2    =    -24

     -11    +    -4    =    -15    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -11  and  -4

                    2t2 - 11t - 4t - 22

Step-4 : Add up the first 2 terms, pulling out like factors :

                   t • (2t-11)

             Add up the last 2 terms, pulling out common factors :

                   2 • (2t-11)

Step-5 : Add up the four terms of step 4 :

                   (t-2)  •  (2t-11)

            Which is the desired factorization

Equation at the end of step

2

:

 (2t - 11) • (t - 2)  = 0

STEP

3

:

Theory - Roots of a product

3.1    A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

3.2      Solve  :    2t-11 = 0

Add  11  to both sides of the equation :

                     2t = 11

Divide both sides of the equation by 2:

                    t = 11/2 = 5.500

Solving a Single Variable Equation:

3.3      Solve  :    t-2 = 0

Add  2  to both sides of the equation :

                     t = 2

Supplement : Solving Quadratic Equation Directly

Solving    2t2-15t+22  = 0   directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

4.1      Find the Vertex of   y = 2t2-15t+22

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 2 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,At2+Bt+C,the  t -coordinate of the vertex is given by  -B/(2A) . In our case the  t  coordinate is   3.7500  

Plugging into the parabola formula   3.7500  for  t  we can calculate the  y -coordinate :

 y = 2.0 * 3.75 * 3.75 - 15.0 * 3.75 + 22.0

or   y = -6.125-0

(-3, 4) and (-1, 10).

What is the slope
Helpasap

Answers

Answer:

6/2

Step-by-step explanation:

10-4=6

-1-(-3)

-1+3=2

6/2

Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.

Answers

Answer: 64.0

Step-by-step explanation:

find the number of bounded and unbounded regions that 4 lines in general position divide a plane into. then find the number of regions for 5 through 10 lines. organize the information in a chart. (ALL THE BLANK SPOTS IN THE ATTACHMENT ARE WHAT I AM CONFUSED ON) please help I have till friday to finish!

Answers

Answer:

10, 15, 21, 28, and 36

Step-by-step explanation:

The rule is the number of line which is n. (n-2)*(n-1) divided by 2

The slope of that line through the origin that divides the region bounded is 1.0315

What is slope?

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

given that,

y = 5x - 3x2

5x - 3x2 = 0

x(5 - 3x) = 0

x = 0 , x = 5/3

Area under y = 5x - 3x2 is A = [0 to 5/3] 5x - 3x2 dx

A = [0 to 5/3] 5x2/2 - 3x3/3

A = [0 to 5/3] 5x2/2 - x3

A = 5(5/3)2/2 - (5/3)3 = 125/54

line passing through origin is in the form of y = mx

==> mx = 5x - 3x2

==> 3x2 + mx - 5x = 0

==> 3x2 + x(m -5) = 0

=> x(3x + (m -5)) = 0

==> x = 0 , x = (5 -m)/3

Area under y = 5x - 3x2 and y = mx is (125/54)/2 = 125/108

==> ?[0 to (5 -m)/3] 5x - 3x2 -mx dx = 125/108

==> ?[0 to (5 -m)/3] (5 - m)x - 3x2 dx = 125/108

==> [0 to (5 -m)/3] (5 - m)x2/2 - x3 = 125/108

==> (5 - m)[(5 -m)/3]2/2 - ((5 -m)/3)3 = 125/108

==> (5 -m)3/18 - (5 -m)3/27 = 125/108

==> (5 -m)3/54 = 125/108

==> (5 -m)3 = 125/2

==> (5 -m) = 3.9685

==> m = 5 - 3.9685

==> m = 1.0315

Hence slope of line = 1.0315

To learn more about slope

brainly.com/question/3605446

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The complete question is given below

There is a line through the origin that divides the region bounded by the parabola y=5x−3x^2 and the x-axis into two regions with equal area. What is the slope of that line?

Determine the slope from the following order pairs:
(5, 7) (6,3)

Answers

Answer:

Step-by-step explanation:

(3-7)/(6-5)= -4/1= -4

PLS HELP ME


Aisha divides 15 meter of ribbon into 2 equal pieces.

What is the length of each piece of ribbon?

Enter your answer as a fraction in simplest form by filling in the boxes.

⊆⊇ m
⊂⊃

Answers

Answer:

7.5 meters

Step-by-step explanation:

14/2=7 16/2=8 so you go halfway for 15

Divide the total length by 2

Length of ribbon=15m

Half:-

15/27.5m

If a car travels 400 miles in 4 hours how fast is it going?

Answers

Answer:

100 miles per hour

Step-by-step explanation:

Answer:

100 miles in 1 hour

Step-by-step explanation:

all you have to do is divied 400 and 4

This nonparametric test requires at least ordinal level data. Its purpose is to find out if there is any difference between two sets of related observations and it is used if the assumptions required for the paired t-test cannot be met. Which test is it?
a. ANOVA
b. Rank correlation
c. Kruskal-Wallis
d. None of the above

Answers

Answer:  Rank correlation

Step-by-step explanation:

hope it helps

is number 1 a function??

Answers

Answer:

yes

Step-by-step explanation:

Help asap I’ll give branniest to the best answer

The diameter of a cylinder is 1 yd. The height is 4 yd find the volume of the cylinder type answer with pie symbol

Answers

Answer:

3.14 cube .yd

Step-by-step explanation:

Volume of cylinder= πr^2h

3.14 × 0.5 × 0.5 × 43.14 cube.yd

How does DNA replication differ in prokaryotic and eukaryotic cells?
a. DNA is single stranded in prokaryotic cells
b. prokaryotic cells do not keep their DNA in a membrane bound nucleus
c. prokaryotic DNA uses uracil as a nitrogenous base instead of thymine
d. prokaryotic cells use a different amino acid code

Answers

the answer you are looking for is A

PLEASE HELP
an artist is constructing a piece of art in the shape of rectangle. The artist wants to use string to tightly tie each vertex of rectangle to the other three vertices. The rectangle is 12.0 feet wide and 7.0 feet long. how much string should the artist use? round your answer to the nearest tenth of a foot


feet of string:

Answers

Answer:

An artist use 51.9 feet of string for constructing a piece of art in the shape of rectangle

Step-by-step explanation:

Here an artist is constructing a piece of art in the shape of rectangle having length 12 feet & width of 7 feet

Since the artist wants to use string to tightly tie each vertex of rectangle to the other three vertices. Hence one string will tie in a diagonal way

Hence total length of string will be

Total length = Perimeter of rectangle  +  length of diagonal

Perimeter of rectangle  = 2( length + width ) = 2 ( 12 + 7 ) = 2 x 19 = 38 feet

Length of diagonal given by Pythagoras theorem

[tex]\mathrm{Length = { \left( { a }^{ 2 } + { b }^{ 2 } \right) }^{ 0.5 } = { \left( { 12 }^{ 2 } + { 7 }^{ 2 } \right) }^{ 0.5 } = 13.89244\:\:feet}[/tex]

Hence

Total length = Perimeter of rectangle  + length of diagonal

Total length = 38 feet + 13.89244 feet = 51.9 feet

Hence an artist use 51.9 feet of string for constructing a piece of art in the shape of rectangle

Large cheese pizzas cost $5 each and large pepperoni pizzas cost $6 each. The expression 5c+6p models the total cost of large cheese pizzas (c) and large pepperoni pizzas (p). What does each part of the expression represent in the context of the situation? Drag the correct description to each part of the expression.

Answers

Answer: 5c represents the cost of 'c' large cheese pizzas and 6p represents the cost of 'p' large pepperoni pizzas.

Step-by-step explanation:

Given: Large cheese pizzas cost $5 each and large pepperoni pizzas cost $6 each.

The expression 5c+6p models the total cost of large cheese pizzas.

here c represents Number of large cheese pizzas and p represents number of  large pepperoni pizzas such that

5c represents the cost of 'c' large cheese pizzas and 6p represents the cost of 'p' large pepperoni pizzas.

[Total cost = Cost of each item x Number of items ]

Some satellites are called 'geo-stationary' - they seem to hover above the earth, as they remain 36,000 km above a single point on the earth's surface and spin with the earth as it rotates. How much time would such a satellite take to complete one revolution of the earth?

Answers

Answer:

24 hours

Step-by-step explanation:

This is because they seem to be stationary about one point on the surface of earth. This is possible when the satellite has the same angular speed as the earth.

This means that it takes the same amount of time to the satellite to take one revolution around the earth as it takes the earth to take one revolution about its axis.

[tex]w=\frac{revolutions}{time}[/tex]

[tex]w_{satellite}=w_{earth}[/tex]

[tex]\frac{N_{satellite}}{t_{satellite}}=\frac{N_{earth}}{t_{earth}}[/tex]

since [tex]N_{satellite}=N_{earth}[/tex]

then, when solving for t we get that:

[tex]t_{satellite}=t_{earth}[/tex]

could someone please help draw this math problem for me ?? i need help!

Answers

Answer:
new angles are both 50 degrees
drawing in picture

Explanation:
an angle bisector is a line or line segment that divides the angle into two equal parts.
I didn’t use a protractor while drawing, but 100 degrees is just a little more than 90 degrees (right angle), so I estimated.

Point hh is located at (4,-2)(4,−2) on the coordinate plane. point hh is reflected over the yy-axis to create point h'h ′ . point h'h ′ is then reflected over the xx-axis to create point h''h ′′ . what ordered pair describes the location of h''?h ′′ ?

Answers

Answer:

(-4,2)

Step-by-step explanation:

Notice that the xx-coordinate and the yy-coordinatechange sign when HH is reflected over the yy-axis and then reflected over the xx-axis.

Answer:

The correct ans is (4,-2)

Step-by-step explanation:

a toy store sells assorted bags of marbles sold in small or large bags the table show the number of each color of marble in the small bag the manager of the store wants to mantain the same ratio of each color of the marble in the large bag as in the small bag
if each marble cost 20 green marble how much does the large bag cost

Answers

10$

Hope this helped!

The population density of Peru one year was approximately 23 people per square kilometer. Brazil has a land area of approximately 8.5 million square kilometers.

If Brazil had the same population density as Peru that year, approximately how many people were living in Brazil?

370,000 people
2,700,000 people
31,500,000 people
195,500,000 people

Answers

Answer:

D (195,500,000)

Step-by-step explanation:

8.5 mil times 23 equals D

The number of people living in Brazil that year was approximately  195,500,000 people. The answer is the last option 195,500,000 people

What is Population density?

From the question, we are to determine the number of people living in Brazil in that year

From the given information,

Brazil land area = 8.5 million square kilometers = 8500000 km²

Brazil population density = Peru population density = 23 people /km²

From population density formula,

[tex]Population\ density = \frac{Number \ of \ people}{Land\ area}[/tex]

Then,

Number of people = Population density × Land area

Therefore,

Number of people living in Brazil = 8500000 × 23

Number of people living in Brazil = 195,500,000 people

Hence, the number of people living in Brazil that year was approximately  195,500,000 people. The answer is the last option 195,500,000 people

Learn more on Population density here: https://brainly.com/question/26910545

solve for x 5x= -20

Answers

Answer:

Today: Monday, 12 October 2020

Hour: 09.13 WIB (in Indonesian)

_________________________

5x = -20

x = -20/5

× = -4

Answer:

x = -4

Step-by-step explanation:

5x = -20

x = -20/5

x = -4

I hope this helped!

Solve the absolute value equation.
(7n+9)+11=3
The solution set is

Answers

17/7 should be the answer

Find the area for this square

Answers

Answer:

361

Step-by-step explanation:

Multiply length x width to find area. 19 x 19 = 361

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