A 5cm x 11cm rectangle sits inside a circle with radius of 12 cm. What is the area of the shaded region? Round your final answer to the nearest hundredth.

Answer:

The rhombus ABCD has an area of 22 square units.

Step-by-step explanation:

The coordinates of rhombus ABCD are shown in the image attached below. The area of the rhombus can be found in terms of their diagonals, which are now calculated by Pythagorean Theorem:

[tex]AC = \sqrt{[6-(-4)]^{2}+[8-(-4)]^{2}}[/tex]

[tex]AC = 15.620[/tex]

[tex]BD = \sqrt{(4-6)^{2}+[0-(-2)]^{2}}[/tex]

[tex]BD \approx 2.828[/tex]

The area of the rhombus is: ([tex]AC = 15.620[/tex] and [tex]BD \approx 2.828[/tex])

[tex]A = \frac{AC\cdot BD}{2}[/tex]

[tex]A = \frac{(15.620)\cdot (2.828)}{2}[/tex]

[tex]A = 22.087[/tex]

The rhombus ABCD has an area of 22 square units.

Answer:

22 units

Step-by-step explanation:

Answer:

Range of Function :  { - 9, - 5, - 1,  4 }

Step-by-step explanation:

We know that y = 2x - 5 provided the domain ( x - values ) { - 2, 0, 2, 4 }. Let us substitute each element in this set of domain as x in the equation "y = 2x - 5" as to solve for the y - values, otherwise known as the range of the function.

{ - 2, 0, 2, 4 }

y = 2( - 2 ) - 5 = - 9,

y = 2( 0 ) - 5 = - 5,

y = 2( 2 ) - 5 = - 1,

y = 2( 4 ) - 5 = 4

We have the set of y - values as { - 9, - 5, - 1, 4 }. This is the range of our function.

Answer:

arccsc(x)=1/cos(x)

Step-by-step explanation:

Answer:

the answer to your question is D

Step-by-step explanation:

Answer:

1) AD=BC(corresponding parts of congruent triangles)

2)The value of x and y are 65 ° and 77.5° respectively

Step-by-step explanation:

1)

Given : AD||BC

AC bisects BD

So, AE=EC and BE=ED

We need to prove AD = BC

In ΔAED and ΔBEC

AE=EC (Given)

[tex]\angle AED = \angel BEC[/tex] ( Vertically opposite angles)

BE=ED (Given)

So, ΔAED ≅ ΔBEC (By SAS)

So, AD=BC(corresponding parts of congruent triangles)

Hence Proved

2)

Refer the attached figure

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

In ΔDBC

BC=DC (Given)

So,[tex]\angle CDB=\angle DBC[/tex](Opposite angles of equal sides are equal)

So,[tex]\angle CDB=\angle DBC=x[/tex]

So,[tex]\angle CDB+\angle DBC+\angle BCD = 180^{\circ}[/tex] (Angle sum property)

x+x+50=180

2x+50=180

2x=130

x=65

So,[tex]\angle CDB=\angle DBC=x = 65^{\circ}[/tex]

Now,

[tex]\angle ABC = 90^{\circ}\\\angle ABC=\angle ABD+\angle DBC=\angle ABD+x=90[/tex]

So,[tex]\angle ABD=90-x=90-65=25^{\circ}[/tex]

In ΔABD

AB = BD (Given)

So,[tex]\angle BAD=\angle BDA[/tex](Opposite angles of equal sides are equal)

So,[tex]\angle BAD=\angle BDA=y[/tex]

So,[tex]\angle BAD+\angle BDA+\angle ABD = 180^{\circ}[/tex](Angle Sum property)

y+y+25=180

2y=180-25

2y=155

y=77.5

So, The value of x and y are 65 ° and 77.5° respectively

Answer:

0.1 = 1/10

0.64 = 64/ 100 = 16/25

0.7841 = 7841 / 10,000

0.67 = 67/100

0.53 = 53/100

0.26 = 26/100 = 13/50

0.6 = 6/10 = 3/5

0.42 = 42/100 = 21/50

Hope this helps you

Answer:

the answer is just 2

Step-by-step explanation:

start at the -3 and move right 3 and up 6 this is a inclined line so the answer will be positive the fraction put the numbers into a rise over run fraction which will be 6/3 which will reduce to 2/1 which is 2.

Answer: y = -1/2x -1

Step-by-step explanation: since the new line is parallel to the given line the slope of both the lines world be same. Therefore putting the new values in the equation

y-y1=m(x-x1)

y-1=-1/2(x+4)

y-1=-1/2x -2

y=-1/2x-1

Answer:

(-6,6), (0,12), (4,8)

Step-by-step explanation:

To dilate an object, we need to multiply the x and y values by the given scale factor.

In this case the scale factor is 2 --> 2(x, y)

Before-> After dilation

2(-3,3) = (-6,6)

2(0,6) = (0,12)

2(2,4) = (4,8)

Please leave a 'thanks' if this helps!

Answer:

7 < (third side length) < 37

Step-by-step explanation:

Add these two side lengths together.  We get 37.  Unless the 3rd side is LESS than 37, we cannot form a triangle.  

Next, subtract 15 from 22, obtaining 7.  The 3rd side has to be GREATER than 7 in order for the sides 7+, 15 and 22 to form a triangle.

7 < (third side length) < 37

Answer:

26.63 ??

Step-by-step explanation:

I think you use pythagorean theorum to solve.

do 22^2 and 15^2 and get 709.1569

sqrt of that is 26.63

Answer:

3/10

Step-by-step explanation:

1/5 of total income - spent on car

remainder income = 4/5

3/8 of remainder = 3/8 ×4/5 = 3/10(of total income spent on rent)

the word "of" means you can find it by multiplication

e.g. 2 of 1/2 means 2 × 1/2 which is 1

Answer:

hope it helps

this is my best

please tell me if I'm wrong

Answer:

x<-5 is the correct answer

Answer:

x<-5 is the answer

Step-by-step explanation:

Answer:

72cm2 (2 means squared)

Step-by-step explanation:

you add all the sides once you get the are for each side. To do that you multiply l(w)

Answer:

The surface area of the rectangular prism is [tex]136cm^{2}[/tex]

Step-by-step explanation:

What is surface area?

Surface area is the amount of space covering the outside of a three-dimensional shape.

What is rectangular prism?

A rectangular prism can be defined as a 3-dimensional solid shape which has six faces that are rectangles. A rectangular prism is also a cuboid.

Given, length l= 7cm

          breadth b=6cm

          height h=2cm

The surface area of the cuboid is,

=2(lb+bh+lh)

=2(7*6+6*2+2*7)

=2(42+12+14)

=2*68

=136 [tex]cm^{2}[/tex]

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Answer:

  8 servings

Step-by-step explanation:

At the ratio of 15:1, the 75 grams of rice in one serving will require 75/15 = 5 g of spice. David's inventory of 40 g of spice is enough for ...

  40 g/(5 g/serving) = 8 servings

Only 8 servings can be made with the available spice.

Rice to spice ratio = 15 : 1

Number of grams per serving = 75 grams

Grams of spice available = 40 grams

Grams of rice, r required for available spice :

15 grams of rice = 1 gram of spice

r grams of rice = 40 grams of spice

Cross multiply :

r = (40 × 15)

r = 600 grams

The grams of rice which can go with the available spice :

Number of servings = grams of rice / grams per serving

Number of serving = 600 grams / 75 grams

Number of grams per serving = 8

Hence, The number of servings which can be made with the available spice is 8 servings

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Answer:

The answer is option B

Step-by-step explanation:

2ln 2 - 2ln3

= ln ( 2²/3²)

= ln (4/9)

Hope this helps you

Answer:

B) 2ln 2 – 2ln 3

Step-by-step explanation:

All three series converge, so the answer is D.

The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.

Consider a geometric sequence with the first term a and common ratio |r| < 1. Then the n-th partial sum (the sum of the first n terms) of the sequence is

[tex]S_n=a+ar+ar^2+\cdots+ar^{n-2}+ar^{n-1}[/tex]

Multiply both sides by r :

[tex]rS_n=ar+ar^2+ar^3+\cdots+ar^{n-1}+ar^n[/tex]

Subtract the latter sum from the first, which eliminates all but the first and last terms:

[tex]S_n-rS_n=a-ar^n[/tex]

Solve for [tex]S_n[/tex]:

[tex](1-r)S_n=a(1-r^n)\implies S_n=\dfrac a{1-r}-\dfrac{ar^n}{1-r}[/tex]

Then as gets arbitrarily large, the term [tex]r^n[/tex] will converge to 0, leaving us with

[tex]S=\displaystyle\lim_{n\to\infty}S_n=\frac a{1-r}[/tex]

So the given series converge to

(I) -243/(1 + 1/9) = -2187/10

(II) -1.1/(1 + 1/10) = -1

(III) 27/(1 + 1/3) = 18

Answer:

Answer- 3/4 divided by 1/8 = 6/8

Answer:

Hello There. ☆~\《`°---_●£●__---`°》\~☆

An exponential growth function is represented by

f(x)=a(b)^{x},a>0,b>1.

The given functions can be written as,

A)f(x)=.001(1.77)^x,0.001>0,1.77>1

B)f(x)=2(1.5)^{x/2}=2(\sqrt{1.5} )^x,2>0,\sqrt{1.5} >1

C)f(x)=5(0.5)^{-x}=5(2)^x,5>0,2>1

D) f(t)=5e^{-t}=5(\frac{1}{e} )^x,5>0,1/e.

So the function f(t)=5e^{-t}=5(\frac{1}{e} )^x,5>0,1/e violates the conditions for an exponential growth function. It is an exponential decay function.

The correct choices are (A), (B), (C).

Hope It Helps!~ ♡

ItsNobody~ ☆

The functions that represent exponential growth are choices (A), (B), and (C). The correct option is A, B, and C.

Exponential growth is the process of gradual increase of quantity over time.

An exponential growth function is represented by

[tex]\rm f(x)=a(b)^{x}[/tex],  a>0,b>1

The given functions can be written as,

A)[tex]f(x) = .001(1.77)^x[/tex], 0.001>0,1.77>1

B) [tex]f(x) = 2(1.5)^{x/2} = 2(\sqrt{1.5} )^x,[/tex]   2>0,  [tex]\sqrt{1.5}[/tex] >1

C)[tex]f(x) = 5(0.5)^{-x}=5(2)^x[/tex],    5>0, 2>1

D) [tex]f(t) = 5e^{-t}=5(\frac{1}{e} )^x[/tex],        5>0,  1/e.

So, the function [tex]f(t)=5e^{-t}=5(\frac{1}{e} )^x,5 > 0,1/e[/tex] violates the conditions for an exponential growth function. It is an exponential decay function.

The correct choices are (A), (B), and (C).

Learn more about exponential growth;

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Answer:

mark my answer as the brainliest

Step-by-step explanation:

x = 53/4

Answer:

4×+1-9 (2^)+2)=0

4×+1-9 (4+2)=0

4×+1(-36-18)=0

4×+1 (-54)=0

4×-54=0

4×=54

×=54÷4

×=13.5

Answer:

2. x = -16       y = -10.5

3. x = 4

4. x = 3         y = 2/9 or 0.2222222222222...

Step-by-step explanation:

2.

in my stategy, you plus -5x + 8y = -4 with 6x - 8y = -12

+8y and -8y could delete each other, then y will be gone.

-5x + 6y = 1x = x because -5 + 6 = 1

so then you could got x = (-4) + (-12) which means x = -16

if x = -16 that will then means

(-5) x (-16) + 8y = -4

80 + 8y = -4

8y = -4 - 80

8y = -84

y = -10.5

3.

This question has already given you that y = -5

that means,  3x + 6 × (-5) = -18

3x + -30 = -18

3x = -18 - (-30)

3x = 12

x = 4

4.

Like the 2. qestion, you first plus the 2 equation together,

+9y + -9y = 0

-7x + 4x = -3x

-19 + 10 = -9

than means

-3x = -9

x = 3

then put the x = 3 in one of the equation.

4 x 3 - 9y = 10

12 - 9y = 10

-9y = 10 - 12

-9y = -2

-7 x 3 + 9y = -19

-21 + 9y = -19

9y = -19 + 21

9y = 2

y = 2/9 or 0.2222222222...

Wish this could help you!

Answer:

Step-by-step explanation:

FIRST ,

ADD BOTH EQUATIONS

THEREFORE X=-16 , Y =-21/2

SECOND,

SUBSTITUTE Y=-5 IN EQN.1

THEREFORE X= 4 , Y=-5

THIRD ,

ADD BOTH EQUATIONS

THEREFORE X= 3 , Y= 2/9

MARK ME AS BRAINLIEST PLS...........................................

Answer:

2/52 or 1/26 or 0.0385 or 3.85%

Step-by-step explanation:

There are 2 black 10's in a standard 52 card deck.

2/52 or 1/26 or 0.0385 or 3.85% (depending on how your teacher wants it expressed)

Step-by-step explanation:

the inverse of the inverse of a function is the function itself

It's like going and coming back

Answer:

9

Step-by-step explanation:

The inverse of the inverse is the input

f^-1 (f^-1(9))  = 9

As a proof

f(x) = 4x+5

y = 4x+5

Exchange x and y

x = 4y+5

Solve for y

(x+5) = 4y

(x+5)/4 = y

f^-1 (x) =  ( x-5)/4

Then find the inverse of this function

y = ( x-5) /4

Exchange x and y

x = (y-5)/4

4x = y-5

4x+5 = y

Which gives us the original function back

f^-1( input) = 4x+5

Using the value given

f^-1 (9) =  ( 9-5)/4=4/4 =1

Using the 1 from the previous part as the input

f^-1( 1) = 4*1+5  = 4+5 = 9

Answer:

88

Step-by-step explanation:

89+85+95+83= 352,

352/4 = 88

Answer:

[tex]x=\frac{7}{8}[/tex]

Step-by-step explanation:

[tex]10x-3-2x=4[/tex]

First, collect and rearrange the like terms.

[tex]10x-3-2x=4[/tex]

[tex]8x-3=4[/tex]

[tex]8x=4+3[/tex]

Then, solve the equation:

[tex]8x=4+3[/tex]

[tex]8x=7[/tex]

[tex]x=\frac{7}{8}[/tex]

So, the answer is [tex]x=\frac{7}{8}[/tex]. Hope my solution and explanation can help you. Thank you!

If you still cannot get the point, you can ask me anytime.

Answer:

x=7/8

Step-by-step explanation:

10x-3-2x=4

collect like term

8x-3=4

move constant to the right-hand side and change its sign

8x-3=4 into 8x=4+3

add up the number : 8x=4+3

8x=7 divide both sides of the equation by 8

x = 7/8

Answer:

C. X=27

Step-by-step explanation:

-11+1/3x+9=7

1/3x=7+11-9

1/3x=9

x=9x3

x=27

Answer:

1/8

Step-by-step explanation:

ok so before i start i wanna say that this is gonna get confusing.....

Since the pizza is a whole quantity let us take it as 1.

Harry ate half of the pizza therefore the fraction that Harry ate = 1/2 of 1

= 1/2 × 1 = 1/2

Therefore fraction Harry ate = 1/2

Fraction of pizza left = 1 - 1/2 (LCM = 2)

= 1/2

Jacqueline ate 1/2 of what was left.

So, Fraction of pizza Jacqueline ate = 1/2 × 1/2 = 1/4

Therefore fraction of pizza left after both Harry and Jacqueline ate =

1 - (1/2 +1/4) = 1 - 3/4 (LCM = 4) = 1/4

Therfore fraction of pizza left = 1/4

Stanley ate 1/2 of what was left.

So, fraction of pizza Stanley ate = 1/2 × 1/4 = 1/8

Therefore, fraction of pizza left after all three of them ate =

1 - (1/2 + 1/4 + 1/8) = 1 - 7/8 (LCM = 8) = 1/8

I hope this helps .......i know this is rlly confusing but i dont know how else to put it : )

Have a nice day!      

Answer:

for every 3 tomato plants there will be 1 squash plants

Step-by-step explanation:

9 divided by 3 = 3. That will find the tomatoes

then you have to divide all the other plants by 3. Squash will be the only one with 1 plant per 3 tomato plants.

The answer is B

Answer:

B. Squash

Step-by-step explanation:

There are 9 tomato plants and there are 3 squash plants.

9 ÷ 3 = 3

3 tomato plants = 1 squash plants

3 × 3 = 1 × 3

9 = 3

9 tomato plants = 3 squash plants

Answer:

Option A.

Step-by-step explanation:

there were 45 stamps purchased for $18.75. Some stamps were 40 cents, and some stamps were 55 cents.

Let x and y be the number of stamps of 40 cents and 55 cents respectively.

Total number of stamps is 45. So

[tex]x+y=45[/tex]

Total cost of stamps is $18.75. So

[tex]0.40x+0.55y=18.75[/tex]

But Krista wrote the system of equations as

[tex]0.40x+y=45[/tex]

[tex]x+0.55y=18.75[/tex]

Krista put 0.40 in the first equation meant for the number of stamps.

Krista did not write 0.40 in the second equation meant for the value of stamps.

Therefore, the correct option is A.

Answer:

The answer is A

Step-by-step explanation:

TOOK THE TEST!

Answer:

The second choice

Step-by-step explanation:

So first we would plug in the first term which is 2 so we would get [tex]an=2[/tex] times [tex]rn-1[/tex] so next we would see that the common ration is -3 since every time the number is being multiplied by -3. so then our equation would be [tex]an= 2[/tex] times [tex]-3n-1[/tex]. Now we would just find the choice that matches and it would be the second choice.

Answer:

option 2

Step-by-step explanation:

First term [tex]a_{1} = 2\\[/tex]

common ratio = r = second term ÷ first term

                            = -6 ÷2 = -4

Plug in the values of  [tex]a_{1}[/tex] & r in the formula

[tex]a_{n} = a_{1}*r^{n-1}\\\\\\a_{n}=2 * (-3)^{n-1}[/tex]

Part A

House 1: we make exponential can be used to describe the

value of house 1. After 1 year, 253480 = 249000 x 1.02

After 2 years, 259059.6 = 25398×1.02. After 3 years 264240.79 =259059.60x1.02.

House 1: we make linear. 256000=249000 + 1000.263000 = 256000 +7000.270000=263000 + 1000.

Part B.

House 1: f(x)=249000 1.02x [genometic sequence]

House 2: f(X) = 24900 + 1000x [arithmetic progression]

Part C

House 1: f(45)=249000×1.02 45 = 607025.697

House 2: f(45) = 249000 +7000x45 = 564000

"House 1 is an arithmetic sequence that increases in price each year while House 2 is an arithmetic sequence that only increases by 1000 per year.

In computational mathematics, a word problem is a problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well.

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