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2 years ago

What is the value of a?

Mathematics

2 answers:

Elenna [48]2 years ago

8 0

I know that c is 68 because 180°=triangle by doing 50+62=112 then 180-112=68 then the base of the triangle is the same as the 31 cm so 31+31=62 that can give u a head start but i am not a high schooler but anyway HOPE IT HELPS!!!:)

Elan Coil [88]2 years ago

6 0

Note that the interior angles must add up to 180 degrees: 50+62+m<C = 180.
Then 112 + m<C = 180, so that m<C =68 degrees.

Use the Law of Sines to find the value of a, as follows:

sin 50 deg sin 62 deg
-------------- = ----------------
a 31 cm
31sin 50 31(0.766)
Then 31sin 50 = a*sin 62, and a = --------------- = ---------------- = 26.9 cm
sin 62 0.883

a =

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The equation 4x2 – 24x + 4y2 + 72y = 76 is equivalent to

DerKrebs [107]

Answer:

Option 4 is correct.

The equation $4x^2 -24x + 4y^2 + 72y = 76$ is equivalent to $4(x-3)^2 + 4(y+9)^2 =436$

Step-by-step explanation:'

Given equation: $4x^2 -24x + 4y^2 + 72y = 76$

First group the terms with x and those with y;

$(4x^2-24x)+(4y^2+72y) = 76$

Next, we complete the squares.

We can do this by adding a third term such that the x terms and the y terms are perfect squares.

For this we must either add the same value on the other side of the equation or subtract the same value on the same side so that the equality is maintained.

⇒ $4(x^2-6x) +4(y+18y) = 76$

$4(x^2 -6x +3^2 -3^2) + 4(y^2 +18y +9^2 -9^2) = 76$

$4(x^2-6x + 3^2) - 36 + 4(y^2+18y +9^2) - 324 = 76$

$4(x-3)^2 + 4(y+9)^2 - 360 =76$

Add 360 on both sides we get;

$4(x-3)^2 + 4(y+9)^2 =360 +76$

Simplify:

$4(x-3)^2 + 4(y+9)^2 =436$

Therefore, the given equation is equivalent to $4(x-3)^2 + 4(y+9)^2 =436$

5 0

2 years ago

if 1000 spherical of radius 1 cm are melted to form a bigger bulb. Then find the radius of bigger bulb

never [62]

Answer:

10 cm

Step-by-step explanation:

Given:

No. of small spherical bulb = 1,000

radius (r) of smaller bulbs = 1 cm

Required:

radius of the bigger bulb

SOLUTION:

The following equation represents the relationship of the volume of the smaller and bigger bulb,

$\frac{V_2}{V_1} = 1,000$

Where,

$V_2$ = volume of bigger bulb

$V_1$ = volume of smaller bulb

1,000 is the number of smaller bulbs melted to form the bigger bulb.

Volume of a sphere is given as, ⁴/3πr³

Therefore:

$V_2$ = ⁴/3*π*r³ = 4πr³/3

$V_1$ = ⁴/3*πr³ = ⁴/3*π*(1)³ = ⁴/3π*1 = 4π/3

Plug the above values into the equation below:

$\frac{V_2}{V_1} = 1,000$

$\frac{\frac{4*pie*r^3}{3}}{\frac{4*pie}{3}} = 1,000$

$\frac{4*pie*r^3}{3}*{\frac{3}{4*pie} = 1,000$

$\frac{4*pie*r^3*3}{3*4*pie} = 1,000$

$\frac{12*pie*r^3}{12*pie} = 1,000$

$r^3 = 1,000$ (12pie cancels 12 pie)

$r = 10$ (taking the cube root of each side)

Radius of the bigger bulb = 10 cm

3 0

2 years ago

The desired percentage of sio2 in a certain type of aluminous cement is 5.5. to test whether the true average percentage is 5.5

k0ka [10]

Wait...what??

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8 0

2 years ago

A theater company is considering raising the price of its tickets. It currently charges $8.50 for each ticket and sells an avera

Licemer1 [7]

Answer:

The answer is c.

Step-by-step explanation:

6 0

2 years ago

Antoine stands on a balcony and throws a ball to his dog, who is at ground level.

sdas [7]

Answer: The ball will hit the ground 4 seconds after being thrown.

Step-by-step explanation:

By definition, the ball hits the grounds when the height is zero.

Then, knowing that the Quadratic function that models that situation is:

$h(x)=-2x^2+4x+16$

You can make it equal to zero:

$0=-2x^2+4x+16$

Now you can use the Quadratic formula:

$x=\frac{-b\±\sqrt{b^2-4ac} }{2a}$

In this case you can identify that:

$a=-2\\b=4\\c=16$

Therefore, knowing these values, you can substitute them into the Quadratic formula and then evaluate, in order to find the solution:

$x=\frac{-4\±\sqrt{4^2-4(-2)(16)} }{2(-2)}\\\\x_1=4\\x_2=-2$

Choose the positive solution.

Then, the ball will hit the ground 4 seconds after being thrown.

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2 years ago