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2 years ago

A right triangle has a 30o angle. the leg adjacent to the 30o angle measures 25 inches. what is the length of the other leg

1 answer:

5 0

Since the triangle has a 30° angle and a right angle which is 90°, this triangle must be a 30 - 60 - 90 triangle, which is a triangle with special properties. The length of the leg adjacent to the 30° angle is equal to the √3 times x where x is the length of the angle adjacent to the 60<span>° angle. Here is a visual representation:

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Two cylindrical containers, C and D, with different capacities are shown below. What is the total volume of liquid held in these

Zielflug [23.3K]

Answer:

Option D. (x + 4)(x + 1)

Step-by-step explanation:

From the question given above, the following data were obtained:

C = (6x + 2) L

D = (3x² + 6x + 9) L

Also, we were told that half of container C is full and one third of container D is full. Thus the volume of liquid in each container can be obtained as follow:

Volume in C = ½C

Volume in C = ½(6x + 2)

Volume in C = (3x + 1) L

Volume in D = ⅓D

Volume in D = ⅓(3x² + 6x + 9)

Volume in D = (x² + 2x + 3) L

Finally, we shall determine the total volume of liquid in the two containers. This can be obtained as follow:

Volume in C = (3x + 1) L

Volume in D = (x² + 2x + 3) L

Total volume =?

Total volume = Volume in C + Volume in D

Total volume = (3x + 1) + (x² + 2x + 3)

= 3x + 1 + x² + 2x + 3

= x² + 5x + 4

Factorise

x² + 5x + 4

x² + x + 4x + 4

x(x + 1) + 4(x + 1)

(x + 4)(x + 1)

Thus, the total volume of liquid in the two containers is (x + 4)(x + 1) L.

6 0

3 years ago

If Mary has 12 more mangoes than Jason and Jason has y mangoes how many has Mary?

xeze [42]

Answer:

y+12=m

Step-by-step explanation:

m (marys mangos)

3 0

2 years ago

-4x to the power of 2 y × -3xy to the power of 3

denis23 [38]

- 4x^2y * 3xy^3

multiply the numbers : 4*3 = 12

-12x^2xy^3y

apply exponent rule : x^2x = x^2+1 = x^3

-12x^3y^3y

apply exponent rule again : y^3y = y^1+3 = y^4

answer : -12x^3y^4

5 0

3 years ago

Suppose f⃗ (x,y,z)=⟨x,y,4z⟩f→(x,y,z)=⟨x,y,4z⟩. let w be the solid bounded by the paraboloid z=x2+y 2 z=x2+y2 and the plane z=9.z

Aleonysh [2.5K]

$\mathbf F(x,y,z)=\langle x,y,4z\rangle$

By the divergence theorem, the surface integral taken over $S$ ,

$\displaystyle\iint_S\mathbf F\,\mathrm dS$

is equivalent to the triple integral of the divergence of $\mathbf F$ over $W$ , the space bounded $S$ ,

$\displaystyle\iiint_W(\nabla\cdot\mathbf F)\,\mathrm dV$

We have

$\nabla\cdot\mathbf F=\dfrac{\partial x}{\partial x}+\dfrac{\partial y}{\partial y}+\dfrac{\partial(4z)}{\partial z}=1+1+4=6$

The latter integral is then given by

$\displaystyle6\iiint_W\mathrm dV=6\int_{|x|\le3}\int_{|y|\le3}\int_{x^2+y^2\le z\le9}\mathrm dz\,\mathrm dy\,\mathrm dx=648$

5 0

3 years ago

Identify and calculate the area and perimeter for each quadrilateral I=76cm w=41cm

deff fn [24]

Answer:

A= l x w

= 76 x 41

=3116cm^2

Perimeter

(76+41) x 2 =234cm

4 0

2 years ago