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2 years ago

PLEASE HELP ASAP!!!!!!

Mathematics

1 answer:

pav-90 [236]2 years ago

3 0

Answer:

360 rooms

Step-by-step explanation:

6/432 = 1/x

= (432 *1)/6 = 72 unoccupied rooms.

432 + 72 = 504 (total rooms)

Ratio on Saturday: 2:5 (2+5=7)

504/7 = 72

72 x 5 = 360 unoccupied rooms on Saturday.

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In isosceles triangle △ABC,

Minchanka [31]

Answer:

Isosceles triangle:

* two sides are equal.

* the base angle are always equal and

* the altitude is a perpendicular distance from the vertex to the base.

Since, the triangle ABC is an isosceles and AC is the base

⇒ AB=BC and $\angle A = \angle C$

Also, AD is the angle bisector of $\angle A$ , which implies that it cuts the angle at A in two equal halves,

let $\angle A= x^{\circ}$ , then the bisectors cuts it in $(x/2)^{\circ}$ .

As per the given information, we know $\angle ADB$ is 110°, therefore, the line BDC forms a supplementary angle;

⇒ $\angle CDA = 180-110 =70^{\circ}$

As shown in picture given below:

By sum of all interior angles in a triangle is 180 degree, thus

$x+\frac{x}{2} +70^{\circ} =180^{\circ}$ or

$\frac{3x}{2} = 180-70 = 110^{\circ}$

Simplify:

$x=\frac{220}{3} = 73\frac{1}{3}^{\circ}$

Therefore, the $\angle A =\angle C = 73\frac{1}{3}^{\circ}$ .

Now, to find the angle B, we have;

$\angle A+ \angle B +\angle C = 180^{\circ}$ [Sum of the measure of the angles in a triangle is 180 degree]

$2\angle A+\angle B = 180^{\circ}$ or

$\angle B = 180^{\circ}- 2\cdot \frac{220}{3} =180^{\circ}-\frac{440}{3}$

Simplify:

$\angle B = \frac{100}{3}= 33 \frac{1}{3}^{\circ}$ .

4 0

3 years ago

Write each of the following numerals in base 10. For base twelve, T and E represent the face values ten and eleven, respectively

uysha [10]

(a)

421₅ = 4×5² + 2×5¹ + 1×5⁰

… = 100 + 10 + 1

… = 111

(b)

11101₂ = 1×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰

… = 16 + 8 + 4 + 0 + 1

… = 29

(c)

13T₁₂ = 1×12² + 3×12¹ + 10×12⁰

… = 144 + 36 + 10

… = 190

7 0

1 year ago

The point (-3,1) is moved 3 places in the negative y direction and 2 places in the positive x direction.

luda_lava [24]

Answer:

(-6, 4)

Step-by-step explanation:

Given the coordinate points (-3,1). If The point (-3,1) is moved 3 places in the negative y direction and 2 places in the positive x direction the required coordinate will be expressed ss;

X' = (-3-3, 1+3)

X = (-6, 4)

Hence the resulting coordinate will be at:(-6, 4)

6 0

2 years ago

A cylinder and a cone have the same volume. The cylinder has a radius of 2 inches and a hieght of 3 inches. The cone has a radiu

arlik [135]

The height of the cone is inches, if the cylinder and cone have the same volume.The cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches.

Step-by-step explanation:

The given is,

A cylinder and a cone have the same volume

Cylinder has a radius 2 inches and height of 3 inches.

Cone has a radius of 3 inches

Step:1

For Cylinder'

Formula to calculate the volume of cylinder is,

$V = \pi r^{2} h$ ..................................................(1)

where,

r - 2 inches

h - 3 inches

From the equation (1)

= $\pi$ × $2^{2}$ × 3

= 37.70

V = 37.70 cubic inches

Step:2

For cone,

Formula to calculate the volume of cone is,

$V = \pi r^{2} \frac{h}{3}$ ..................................................(2)

From the statement,

cylinder and a cone have the same volume

$V_{cylinder}$ = $V_{cone}$

37.70 = $\pi$ × $3^{2}$ × $\frac{h}{3}$

37.70 = 9.42478 × h

Height of the cone, h = 4 inches

Result:

Thus the height of the cone is 4 inches, if a cylinder and cone have the same volume.The cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches.

4 0

2 years ago

Whats the answer to c/3+3=5

Svet_ta [14]

Answer:

c=6

Step-by-step explanation:

6 0

3 years ago

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