The diagram shows a rectangle ABCE.
D lies on EC.
DAB is a sector of a circle radius 8cm and sector angle 30º.
Calculate the area of the shaded region.​

Answer:

a = 49

b = - 20√2

Step-by-step explanation:

5 - 2√6 / 5 + 2√6

We can rationalise the denominator as follow:

5 - 2√6 / 5 + 2√6

Multiply the numerator and the denominator by the conjugate of

5 + 2√6. The conjugate of 5 + 2√6 is

5 - 2√6

(5 - 2√6 / 5 + 2√6) x (5 - 2√6 / 5 - 2√6)

(5 - 2√6) (5 - 2√6) /(5 + 2√6) (5 - 2√6)

Expand

(25 - 10√6 - 10√6 + 4×6) / (25 - 10√6 + 10√6 + 4×6)

25 - 20√6 + 24 / 25 - 24

25 + 24 - 20√6 / 1

49 - 20√6

Equating 49 - 20√6 with a + b√3, we can obtain the value of a and b as follow:

49 - 20√6 = a + b√3

From the above

a = 49

b√3 = - 20√6

Divide both side by √3

b = - 20√6/√3

Rationalise

b = - 20√6/√3 x √3/√3

b = - 20√(6×3)/ √3×√3

b = - 20√18 / 3

b = - 20√(9×2) / 3

b = - 20 × 3√2 / 3

b = - 20√2

Given info:- Rationalise the denominator and find out the value of "a" and "b"

Given expression: {(5-2√6)/(5+2√6)} = a+b√3

Explanation:-

{(5-2√6)/(5+2√6)} = a+b√3

We know that Rationalising factor of a+b√c is a-b√c.

Therefore, the rationalising factor of 5+2√6 is 5-2√6.

⇛{(5-2√6)/(5+2√6)} × {(5-2√6)/(5-2√6)} = a+b√3

⇛{(5-2√6)(5-2√6)}/{(5+2√6)/(5-2√6)} = a+b√3

⇛{(5-2√6)²}/{5+2√6)(5-2√6)} = a+b√3 [∵(a-b)(a-b)=(a-b)²]

⇛{(5-2√6)²}/{(5)²-(2√6)²} = a+b√3 [∵(a+b)(a-b)=a²-b²]

⇛{(5-2√6)²}/({5*5)-(2*2√6*6)} = a+b√3

⇛{(5-2√6)²}/(25 - 4√6) = a+b√3

⇛{(5-2√6)²}/(25-24) = a+b√3

⇛{(5-2√6)²}/1 = a+b√3

⇛(5-2√6)² = a+b√3

⇛(5)²-(2√6)²+2(5)(2√6) = a+b√3

⇛(5*5) - (2*2√6*6) - 10 - 2√6 = a+b√3

⇛25 - 10 - 4√6 - 2√6 = a+b√3

⇛15 - 4√6 - 2√6 = a+b√3

⇛15 + 6√6 = a+b√3

∴ 15 + 6√6 = a+b√3

On, comparing with both RHS we notice that:

The value of a = 15 and b = 6.

Hope this helps!!

If you have any doubt, then you can ask me in the comments.

Answer:

perimeter = 322.5 ft ( to the nearest tenth of a foot)

Step-by-step explanation:

Length the length of the sides of the square be L

Area of a square = L²

∴ 6,500 = L²

L = √(6,500)

L = 80.6226

Next Let us calculate the perimeter

Perimeter of a square = L + L + L + L = 4L

perimeter = 4 × 80.6226

Perimeter = 322.4904 ft

perimeter = 322.5 ft ( to the nearest tenth of a foot)

N:B rounding to the nearest tenth of a foot is same as rounding to 1 decimal place.

Answer:

21x-7/7x

=7x(3x-1)/7= 3x-1

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

To find the area of a rectangle, you must multiply its length with its width.

We know that either the length or it's width is 7x.

To find the length of the other side, we essentially have to figure out what 7x you to be multiplied by to get 14x (21x-7x can be simplified to that by combining like terms)

To reverse multiplication, we can use division.

Let's set up the following expression:

14x/7x

2x/x

2

The length of its other side is 2.

Answer:

Jake can use 19.70 ccf to not exceed $ 64.00 in water bill.

Step-by-step explanation:

The cost function of water bill is:

[tex]C = C_{f}+C_{v}[/tex]

Where:

[tex]C_{f}[/tex] - Fix costs, measured in USD.

[tex]C_{v}[/tex] - Variable costs, measured in USD.

The fix and variable costs are, respectively:

[tex]C_{f} = 24.60[/tex]

[tex]C_{v} =2\cdot \left(\frac{Q}{100} \right)[/tex]

Where [tex]Q[/tex] is the water capacity consumed within a month, measured in cubic feet. Therefore, first formula is expanded:

[tex]C = 24.60+2\cdot \left(\frac{Q}{100} \right)[/tex]

If [tex]C = 64\,USD[/tex], the maximum water capacity is:

[tex]64 = 24.60+2\cdot \left(\frac{Q}{100} \right)[/tex]

[tex]39.40 = 2\cdot \left(\frac{Q}{100} \right)[/tex]

[tex]Q = 1970\,ft^{3}[/tex]

Which is equivalent to 19.70 ccf.

Answer:

x≤9

Step-by-step explanation:

x−6≤3

Add 6 to both sides.

x≤3+6

Add 3 and 6 to get 9

x≤9

Answer: x ≤ 9

Step-by-step explanation: When solving an inequality, your goal is the same as it would be if you were solving an equation – to get the variable by itself or isolated on one side of the equals sign.

Since 6 is being subtracted from x, add 6 to both sides of the inequality.

On the left, the -6 +6 cancel out and on the right, 3 + 6 is 9.

So we have x ≤ 9.

Answer:

196metres

Step-by-step explanation:

Maria drives 48 mph and Ming drives 50 mph.

We were told to find How far apart will they be in 2 hours which means that what distance have Maria and Ming passed in total.

Let us calculate how far did Maria go for 2 hours.

Which is

Velocity v = distance s/ time t

V= S1/t

48=s/2

S1= 96metres

Then we calculate how far did Ming go for 2 hours

v= S2/t

50=s/2

S2= 100metres

The total distance between them in two hours is (S1+S2)=96+100

=196metres.

Hence,they were 196 metres apart in 2 hours

Answer:

i. 179.775 kg

IIa)the weight=585.225 kg

IIb) percentage=75.6%

3)=30240 kg

Step-by-step explanation:

From the question were given the total area of the land as 1000 sq. meter

Amount of cultivated rice= 765 kg

the percentage of wastage rice =23.5%.

But we can convert the amount of the wastage rice from percentage to kilogram which is

23.5/100=0.235

Then to kilogram 0.235× 765 kg= 179.775 kg

Then amount of wastage rice= 179.775 kg

I)Find the weight of the wastage. ?

The amount of wastage rice is the conversion of it's percentage to kilogram which I did above

Then amount of wastage rice= 179.775 kg

II) Find the weight and percentage of rice cultivated.

Since we know amount of wastage as 179.775 kg, then the amount of cultivated will b difference between the cultivated and wastage=765 - 179. 775 = 585.225 kg

Then it's percentage is the substraction of the percentage of wastage from 100%

= 75.6%

3)If the area has been increased 40 times in size, how much rice will be cultivated (excluding the wastage)

Increase in the land in 40 times= 40×1000= 40,000sm

Then the rice cultivated= 75.6% ×40000

=30240 kg

Answer:

[tex]\Huge \boxed{-x^2+2x}[/tex]

Step-by-step explanation:

2 times x subtracted by x².

[tex]\Rightarrow 2 \cdot x-x^2[/tex]

[tex]\Rightarrow 2x-x^2[/tex]

Rearranging the expression.

[tex]\Rightarrow -x^2+2x[/tex]

Answer:

2x -x^2

Step-by-step explanation:

[tex]2(x) - x^2\\= 2x-x^2[/tex]

Answer:

18 1/5

Step-by-step explanation:

Answer:

x = 5.98

Step-by-step explanation:

Step 1: Use tangent to solve for x

tan50.1 = [tex]\frac{x}{5}[/tex]

x = 5tan50.1

x = 5.98

Therefore x is equal to 5.98

Answer:

Step-by-step explanation:

[tex] \sf{9 - 4x = 17}[/tex]

Move 9 to right hand side and change it's sign

⇒[tex] \sf{ - 4x = 17 - 9}[/tex]

Subtract 9 from 17

⇒[tex] \sf{ - 4x = 8}[/tex]

Divide both sides of the equation by -4

⇒[tex] \sf{ \frac{ - 4x}{ - 4} = \frac{8}{ - 4}} [/tex]

Calculate

⇒[tex] \sf{x = - 2}[/tex]

Hope I helped!

Best regards!!

Answer:

QR=12

ST=18

QS=24

QT=42

Step-by-step explanation:

The question tells us that PR is congruent to RS. But there's no point P in the line. So, I'm going to assume it's a typo and that they meant point Q.

So, we know that QR is congruent so RS. RS is 12 and RT is 30. With that information, we can find the other lengths:

1) QR

Since QR is congruent to RS and RS is 12, this means that QR is also 12.

2) ST

We know that RT is 30. RT is made by adding up RS and ST. In an equation, this is:

[tex]RT=RS+ST[/tex]

We know that RT is 30 and RS is 12. Thus, substitute:

[tex]30=12+ST\\ST=18[/tex]

Thus, ST is 18.

3) QS

QS is the length of QR plus RS. Since QR is 12 and RS is also 12, QS is 12+12 or 24.

4) QT is the length of the entire segment. The entire segment can be written as:

[tex]QT=QR+RT[/tex]

And since we already know that QR is 12 and RT is 30:

[tex]QT=12+30\\QT=42[/tex]

QT is 42.

Answer: 153.94cm

Step-by-step explanation:

Answer:

A  =  49 cm ²

Step-by-step explanation:

A = πr²

   = 22/7 * 7 *7

      = 49 cm²

Answer:

90 degrees

Step-by-step explanation:

I don't really have an explanation but I'm 100% sure that it is

Answer:

90 degrees

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

Answer:

False, if you get a negitive it would be - square root symbol 9

This is just an example

Step-by-step explanation:

Answer:

i)-240*a^4*b^3*c^2

ii)-15*x^2*y^2+3*x^3*y^2

iii)x^4*y^3*z^2-x^2*y^3*z^3+x^3*y^2*z^3

iv)p*q+6*q-7*p-42

v)2*x^3-3*x^2-23*x+42

vii)2*x^2-2*y^2+7*x-12*y-15

Step-by-step explanation:

Answer:

b so  it doesnt tell you how many people come to the hospital a day

Step-by-step explanation:

a--->b--->=c

Answer:

A) A nonresponse occurred

Step-by-step explanation:

We understand that in the span of 10 years, 1000 patients were monitored, and among those were some individuals who had moved. These certain individuals are not responsive anymore, and can not be a source of data, and the poll would be incorrect if the hospital decided to switch out the patients in the midst of the decade. Therefore we are to assume a nonresponse occurred. (To define nonresponse, it is simply a failure to respond, which is indeed what is defined for those who had moved.)

It is not B for the two variables have no correlation, it is not C for all patients were at first patrons and the problem did not explicitly state there was missing info, and D is incorrect for it said the sample group was selected at random. Therefore, with process of elimination, A would still be correct.

Answer:

y = -5, 1

Step-by-step explanation:

2y² - 10y + 44 = (y - 7)²

expand (y - 7)²

(y - 7)² = y² - 14y + 49

move it to the left

(2y² - 10y + 44) - (y² - 14y + 49) = 0

distribute the (-)

2y² - 10 y + 44 - y² + 14y - 49 = 0

combine like terms

y² - 4y -5

factor with factoring X

y² + 5y - y - 5 = 0

factor by grouping ↓

factor out a y from first half of equation

y(y + 5) - y - 5 = 0

factor out a (-) from second half of equation

y(y +5) - (y + 5) = 0

(y +5)(y - 1) = 0

y = -5, 1

Answer:

Area of the triangle = 12 square feet

Step-by-step explanation:

Area of a triangle is calculated by the formula,

Area = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

From the picture attached,

Height of the given triangle = Vertical distance of the top vertex = 4 feet

Base of the triangle = 6 feet

Area of this triangle = [tex]\frac{1}{2}(6)(4)[/tex]

                                 = 12 square feet

Therefore, area of the given triangle will be 12 square feet.

Answer:

0.00432 km = 4320 mm

Step-by-step explanation:

There are 1000000 millimeters in a kilometer. To convert kilometers to millimeters, multiply the kilometer value by 1000000.

Quick check 0.00432 * 1000000 = 4320 mm

Answer:

4320

Step-by-step explanation:

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the question the equation of the line is

y = - 4x + 9

Comparing the equation with the general equation of a line above

Slope / m = - 4

Hope this helps you

Answer:

1.3888888888889 mps

Step-by-step explanation:

1 kph = 0.27777777777778 mps, so just multiply that by 5.

Answer:

rational numbers are the number which can not expressed into simpler fraction

Answer:8640 square inches

Step-by-step explanation:

Answer:

r = (5000 - [(5000 x 0.3) + (4000 x 0.6) + (300 x 0.25)])0.8

Simplified - r = 820

Step-by-step explanation:

I don't know how to explain it exactly, but I know you have to find out how much the carnations, tulips, and irises all cost,subtract that from how much money he has, and divide what left by the cost of the roses (by multiplying the 0.8 cents, because it's a decimal).

r = (5000 - [(5000 x 0.3) + (4000 x 0.6) + (300 x 0.25)])0.8

r = (5000 - [1500 + 2400 + 75])0.8

r = (5000 - 3975)0.8

r = 1025(0.8)

r = 820

Answer:

This will be -8x^3y^9.

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

Explanation:

See the attached image below to see one way you could draw the diagram based on the given info. The drawing is not to scale.

The color coded angles hopefully let you see which angles are congruent to one another

These three pairs of congruences are possible because of the angle bisections that occur.

Since EXB is 20, this means DXE is 20 as well. They combine to 20+20 = 40, which is the measure of angle DXB (angle addition postulate).

Angle DXB is congruent to CXD, so both are 40 and they combine to 40+40 = 80. This is the measure of angle CXB.

Finally, angle CXB = 80 doubles to 160 which is the measure of angle AXB. Or you could say

angle AXB = (angle AXC) + (angle CXB) = 80 + 80 = 160.

Answer:

251

Step-by-step explanation:

Given - Mean length of fish  = μ= 73  cm

SD  σ =8 c m

Number of fish having a length greater than 57 cm out of 480.

Find the value of  z  at  x = 57

[tex]z= \frac{x-\mu}{\sigma} = \frac{57-73}{8}\\=\frac{-16}{8} = -2[/tex]

Area between  z = − 2 and  z =  ∞

= Area between  z = − 1  and  z = 0 +

Area between  z = 0  and  z = ∞

=0.02275+0.5= 0.52275

Therefore number of fish having teeth greater than 57 cm

= 0.52275*480 = 5.2275*48 = 250.92 ≅251

Answer:

Two other exponents that results in 256 are [tex]16^2[/tex] and [tex]4^4[/tex]

Step-by-step explanation:

Given

[tex]2^8 = 256[/tex]

Required

Write two exponential expression that equals 256

[tex]2^8 = 256[/tex]

Expand 8 as 4 * 2

[tex]2^{4*2} = 256[/tex]

Using laws of indices, we have

[tex](2^4)^2 = 256[/tex]

2⁴ = 16; So, we have

[tex]16^2 = 256[/tex] --- This is one

Recall that

[tex]2^{4*2} = 256[/tex]

This can also be rewritten as

[tex]2^{2*4} = 256[/tex]

Using laws of indices, we have

[tex](2^2)^4 = 256[/tex]

2² = 4; So, we have

[tex]4^4 = 256[/tex] --- This is another one

Hence, two other exponents that results in 256 are [tex]16^2[/tex] and [tex]4^4[/tex]

Answer:

D. divide by -8

Step-by-step explanation: