All categories

2 years ago

Please help Thanks!!

Mathematics

2 answers:

kherson [118]2 years ago

8 0

Answer: 13

Step-by-step explanation:

erik [133]2 years ago

3 0

Answer:

Step-by-step explanation:

pythagorean theorem

You might be interested in

The coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .

daser333 [38]

Answer: The correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

Explanation:

It is given that coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .

The distance formula for two points is given below,

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$DE=\sqrt{(2+2)^2+(4-5)^2}=\sqrt{17}$

$EF=\sqrt{(0-2)^2+(0-4)^2}=\sqrt{20}$

$FG=\sqrt{(-4-0)^2+(1-0)^2}=\sqrt{17}$

$DG=\sqrt{(-4+2)^2+(1-5)^2}=\sqrt{20}$

Slope formula,

$m=\frac{y_2-y_1}{x_2-x_1}$

Slope of DE,

$m_1=\frac{4-5}{2+2}= \frac{-1}{4}$

Slope of EF,

$m_2=\frac{0-4}{0-2}= 2$

Slope of FG,

$m_3=\frac{1-0}{-4-0}= \frac{-1}{4}$

Slope of DG,

$m_4=\frac{1-5}{-4+2}= 2$

The slope of opposite sides are equal, it means the opposite sides are parallel.

All four sides do not have the same length. It means it is not a rhombus.

From the figure it is noticed that the opposite sides are parallel.

Therefore, the correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

3 0

3 years ago

Read 2 more answers

A giant scoop, operated by a crane, is in the shape of a hemisphere of radius 21 inches. The scoop is used to transfer molten st

eduard

Answer:

31.5 in

Step-by-step explanation:

Volume of a hemisphere = (2/3) $\pi$ r³
(where r is the radius)
Volume of a cylinder = $\pi$ r²h
(where r is the radius and h is the height)
radius r = (1/2) diameter

First, find the volume of the scoop using the volume of a hemisphere formula with r = 21:

Volume = (2/3) $\pi$ x 21³ = 6174 $\pi$ in³

Now equate the found volume of the scoop to the equation of the volume of a cylinder with r = 14, and solve for h:

$\pi$ 14²h = 6174 $\pi$

196 $\pi$ h = 6174 $\pi$

Divide both sides by $\pi$ : 196h = 6174

Divide both sides by 196: h = 31.5

Therefore, the height of the molten steel in the storage tank is 31.5 in

3 0

2 years ago

Solve the Equations

Vikentia [17]

Answer:

1) -2.13

2) 2.57

3) 33

Step-by-step explanation:

3(8 + 5h) = -28 Distribute the 3

24 + 15h = -28 Subtract 24 from both sides of the equation

15h = -32 Divide both sides by 15 and round

h = - 2.13

19 = 7(3n - 5) Distribute the 7

19 = 21n - 35 Add 35 to both sides of the equation

54 = 21n Divide both sides of the equation by 21

2.57 = n

6s - 7s = -33 Combine the s's

-s = -33 Multiply both sides by -1

s = 33

5 0

1 year ago

What is the equation of the axis of symmetry

Marina86 [1]

The line of symmetry is 1

4 0

3 years ago

How can I solve this?<br>Please use the simplest format

IgorLugansk [536]

Answer:

option D is true.

Step-by-step explanation:

The right-angled triangle is shown.

From the right-angled triangle,

The angle Ф = 60°

We know that the trigonometric ratio

tan Ф = opposite / adjacent

opposite = 4

adjacent = n

Thus,

tan 60 = 4 / n

√3 = 4/n

n = 4/√3

Thus,

n = 4/√3

= (4 × √3) / (√3 × √3)

= 4√3 / 3

Thus,

n = 4√3 / 3

Using Pythagorean theorem

m = √n²+4²

$m=\sqrt{\left(4\cdot \frac{\sqrt{3}}{3}\right)^2+4^2}$

$m=\sqrt{\frac{4^2}{3}+4^2}$

$m=\sqrt{\frac{64}{3}}$

$m=\frac{8}{\sqrt{3}}$

$m=\frac{8\sqrt{3}}{3}$

Thus,

$m=\frac{8\sqrt{3}}{3}$

n = 4√3 / 3

Therefore, option D is true.

3 0

2 years ago