Drag each tile to the correct box. a с C b A David proved the Law of Cosines with reference to AABC using a different method. Arrange the steps of his proof in the correct sequence. k² = c² - (b − x)² In AABD, (Pythagorean Theorem) In ABCD, k² = a² - 1² (Pythagorean Theorem) c² (6²-26x + x²) = a² — 1² (on simplification) Similarly, prove that a2b² + c² - 2bccos A and 82 6² = a² + c²2accos B B​

Answer:

[tex] \boxed{\rm \: Volume_{(Drum)} = 5024 \: in {}^{3} }[/tex]

Step-by-step explanation:

Given :

To Find:

The volume of the drum.

Solution:

We all know that drum is cylindrical.So we'll use the formulae of the volume of cylinder,to find its volume.

[tex] \boxed{\rm \: Volume_{(Cylinder)} = \pi{r} {}^{2} h}[/tex]

Where,

The value of radius ain't given,but the diameter is given.We can use the formulae of radius.

[tex] \rm \: Radius = D/2[/tex]

Substitute the value of diameter:

[tex] \rm \: Radius = \cfrac{20}{2} = 10[/tex]

Hence,the radius is 10.

So we could now use the formulae of the volume of cylinder:

[tex] \rm \: Volume_{(Cylinder)} = \pi{r} {}^{2} h[/tex]

[Firstly bring the answer in terms of π then plug π = 3.14 and then simplify.]

[tex] \rm \: Volume_{(Drum)} = \pi(10) {}^{2} (16)[/tex]

[tex] \rm \: Volume_{(Drum)} =\pi100(16)[/tex]

[tex] \rm \: Volume_{(Drum)} = 1600\pi[/tex]

[tex] \rm \: Volume_{(Drum)} = 1600 \times 3.14[/tex]

[tex] \boxed{\rm \: Volume_{(Cylinder)} = 5024 \: in {}^{3}} [/tex]

Hence, we can conclude that:

The volume of this drum is 5024 in^3.

Answer:

18ft

Step-by-step explanation:

i can't lay out the formula

An equation is formed of two equal expressions. The correct option is A.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Ms. Banerjee bought a car for $22,500. The amount she paid for her new car was twice the amount she paid for her previous car, which she bought 8 years ago. Therefore, the equation shows p, the price in dollars that she paid for her previous car,

Price of new car = 2 (Price of the previous car)

22,500 = 2p

Hence, the correct option is A.

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Answer: a

Step-by-step explanation:

Since 0.3 is divided by 100, we will shift the decimal point backward in 2 places to have 0.003

Decimal numbers are numbers that includes the dot in between. Given the percentage value expressed as:
0.3%

This can be expressed as;

0.3% = 0.3/100

Since 0.3 is divided by 100, we will shift the decimal point backward in 2 places to have 0.003

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To expand an expression, use FOIL method.

-7y and y are the first terms in each expression.

(-7y)(y) = -7y²

-7y is the first term in the first expression

-4 is the last term of the second expression

(-7y)(-4) = 28y

-8 is the last term in the first expression

y is the first term in the second expression

(-8)(y) = -8y

-8 is the last term of the first expression

-4 is the last term of the second expression

(-8)(-4) = 32

Combine all simplified terms.

Answer:

Wxndy~~

The term used to describe the equidistance from a given directrix and focus is: C. a locus of points called a parabola.

A parabola can be defined as a curve on a plane where any given point is at equal distance from the focus (fixed point), and from a directrix (fixed straight line).

Thus, we can conclude that what is a locus of points called a parabola is equidistant from a given directrix and focus.

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Answer:

see the attachment photo!

Answer:

A reflection of a point over the y -axis is shown. The rule for a reflection over the y -axis is (x,y)→(−x,y) .

Step-by-step explanation:

[tex]\sqrt x > \sqrt{25} \qquad( x\geq 0)\\\sqrt x > 5\\x > 25[/tex]

When [tex]x > 25[/tex].

The domain of the function is x > 0.

The correct option is (B)

Domain of a function is defined by the set of x-values of the graph of a function.

as, domain of a function is defined by the set of x-values of the graph of a function.

From the graph we can see that,

x-values are starts from x > 0 [Since x ≠ 0]

Also, moves towards infinity,

Hence, domain of the function be, (0, ∞) or x > 0

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Answer:

B

Step-by-step explanation:

Answer:

D, E, and A

Step-by-step explanation:

Because 4 is also equivelent to square root of 16 and square root of 16 times square root of 3 is equal to square root of 48 which is D, and E is also correct because square root 24 x square root 2 is also square root 48 and same concept with A.

The changes in Z would be = 6.1× 10^-4.

Z = Sin (x³ +y³)

Where X = 0.3

y = 0.2

Z= Sin ( 0.3³ + 0.2³)

Z= Sin ( 0.027 + 0.008)

Z= Sin ( 0.035)

Z= 6.1× 10^-4

Therefore, the changes in Z would be = 6.1× 10^-4.

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Answer:

x^2+2x+y^2−2y−7=0

Step-by-step explanation:

The method from converting to standard to general is very simple

this equation in standard form would be

(x+1)^2+(y-1)^2=9

This is because whatever the center of the circle is, you take the negative/positive version of that number

The center is at -1, 1.  So it would flip to be put into the equation as 1, -1.

9 is the radius^2.

The radius is 3.

To convert to general form you just simplify

x^2+1+2x = (x+1)^2

y^2 + 1 -2y = (y-1)^2

x^2 - 2x + y^2 - 2y + 2 = 9

get the nine on the left side

x^2 -2x +y^2 - 2y 2 - 9 = 0

x^2+2x+y^2−2y−7=0

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Hope this helps :)

Answer:

8weeks

Step-by-step explanation:

$16÷(25/100×$8)=8

The quantity of sugar required for 2/4 of the recipe is 1/3 cups

let

Ratio of sugar to recipe

2/3 : 1 = x : 2/4

2/3 ÷ 1 = x ÷ 2/4

2/3 × 1/1 = x × 4/2

2/3 = x × 2

2/3 = 2x

x = 2/3 ÷ 2

x = 2/3 × 1/2

= 2/6

x = 1/3 cups

Therefore, the quantity of sugar required for 2/4 of the recipe is 1/3 cups

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Answer:

3660

Explain

3660ml×1L/100ml

= 3.66L

Answer:

20 miles

Step-by-step explanation:

We are finding the difference.  Take the larger number and subtract the smaller number

40-20 = 20

The difference is 20 miles

The other factor for the given equation will be ( x - 4 ). The correct option is D.

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

The solution of the given quadratic equation will be:-

x² + 2x - 24 = ( x² + 6x -4x -24 )

                   = [ x( x + 6) - 4 ( x + 6 ) ]

                   = ( x + 6 ) ( x - 4 )

Therefore another factor for the given equation will be ( x - 4 ). The correct option is D.

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The statement which is true about the thrown ball is that A. The ball attains a maximum height of 70 meters at 4 seconds

This refers to the highest vertical projectile that an object can attain when acted upon by an external force.

Given the attached diagram that shows the graph of the projectile of the ball, we can observe that its maximum height before it began to fall is 70 meters at 4 seconds based on the values on the x and y-axis.

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Given the following parameters DB = 18 ft, AB = 3 ft, and CB = 10 ft. Therefore, The length of the CE is 4.6 ft.

The secant-secant rule states that if two secants are drawn from an external point to a circle, then the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant.

Mathematically:

(BA + AD)BA = (BE + EC)BE

Given the following parameters

DB = 18 ft, AB = 3 ft, and CB = 10 ft.

Substitute to check if we can find CE

(BA + AD)BA = (BE + CE)BE

(3+ 15) x 3 = (10 + CE ) x 10

18 x 3 = 100 + 10CE

54 = 100 + 10CE

CE = 4.6

Therefore, The length of the CE is 4.6 ft.

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Answer: medians in a triangle.

Answer:

Peter spent 14 dollars on movie tickets. Henry spent 10 dollars on popcorn.

Step-by-step explanation:

I hope this helps! :)

Answer:

c

Step-by-step explanation:

its just the dilate of the triangle which both add up to 180

The statement "151.8​​ is what percent of 69​​ is expressed as 0.69p =  151.8

Equations are expressions separated by an equal sign. Words can be translated to equations.

Let the unknown variable be "p". If p percent of 69is 151.8, this is expressed as;

p% of 69 = 151.8

Convert to decimals

p/100 * 69 = 151.8

0.01p * 69 = 151.8
0.69p =  151.8

Hence the statement "151.8​​ is what percent of 69​​ is expressed as 0.69p =  151.8

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The car would travel a distance of 400 km using 20 litres of petrol

The given parameters can be represented using the following scale ratio :

Scale = 340 km : 17 litres

For 20 litres of petrol, we have:

Distance : 20 = 340 km : 17

Express as fraction

Distance/20 = 340 km/17

Multiply both sides by 20

Distance = 400 km

Hence, the car would travel a distance of 400 km using 20 litres of petrol

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Answer:

d

Step-by-step explanation:

Step-by-step explanation:

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For a quadrilateral to be a square, the diagonals must be congruent and must be perpendicular.

#1

Find y intercept

#2

Y intercept

Both graphs attached

An point should be (1,6)

Answer:

< or > = dashed line

≤ or ≥ = solid line

< or ≤ = shade below the line

> or ≥ = shade above the line

To draw:

[tex]y < \dfrac{2}{3}x+6[/tex]

Treat as a linear equation.

Find 2 points:

[tex]x=0 \implies y=\dfrac{2}{3}(0)+6=6 \implies (0,6)[/tex]

[tex]x=3 \implies y=\dfrac{2}{3}(3)+6=8 \implies (3,8)[/tex]

Plot the 2 points and draw a dashed straight line through them.

To draw:

[tex]y > 1.5^x+4[/tex]

Treat as an exponential equation.

Find y-intercept:

[tex]x=0\implies y=1.5^0+4=5\implies (0,5)[/tex]

End behaviors:

[tex]\textsf{As } x \rightarrow \infty, f(x) \rightarrow \infty[/tex]

[tex]\textsf{As } x \rightarrow - \infty, f(x) \rightarrow 4[/tex]

Draw the curve as a dashed line.

Once both lines are drawn, shade the overlapping region below the linear inequality and above the exponential inequality.  

A point that belongs to the solution is any point in the shaded area,
e.g. (1, 6)