3. Let Angle ABC be an isosceles triangle with AB = AC. Which of the following describes

How do I find the value of x?

svetoff [14.1K]

Answer:

x = 2

Step-by-step explanation:

If ΔABC~ΔAED then:

$\dfrac{AC}{AD}=\dfrac{BC}{ED}\\\\\\\dfrac{x+4}{4}=\dfrac{3}{2}\\\\\dfrac{x+4}{4}=\dfrac64\\\\x+4=6\\\\x=2$

4 0

3 years ago

Q2.What is the ratio of volumes of the two cylinders formed by rolling a sheet of dimensions lxb in two different ways? Q3.What

Kobotan [32]

Answer:

2. b : l

3. 20cm

4. 49 $cm^{2}$

5. $(2\pi+1):2\pi$

Step-by-step explanation:

<u>Solution 2:</u>

Let cylinder is rolled along 'l':

Height of cylinder , h = length of rectangle = l

Perimeter of base = b

Let 'r' be the radius of cylinder's base:

$2\pi r = b\\\Rightarrow r = \dfrac{b}{2\pi}$

Volume of a cylinder is given as:

$V = \pi r^{2} h$

Putting the values:

$V_1 = \pi (\dfrac{b}{2\pi})^2 l\\\Rightarrow V_1 = (\dfrac{b^2}{4\pi}) l$

Let cylinder is rolled along 'b':

Height of cylinder , h = length of rectangle = b

Perimeter of base = l

Let 'r' be the radius of cylinder's base:

$2\pi r = l\\\Rightarrow r = \dfrac{l}{2\pi}$

Volume of a cylinder is given as:

$V = \pi r^{2} h$

Putting the values:

$V_2 = \pi (\dfrac{l}{2\pi})^2 b\\\Rightarrow V_2 = (\dfrac{l^2}{4\pi}) b$

Taking ratio:

$V_1:V_2 = \dfrac{(\dfrac{b^2}{4\pi}) l}{(\dfrac{l^2}{4\pi}) b} = b:l$

Solution 3:

Rectangle is rolled along its length to make a cylinder, so height will be equal to its length.

$\therefore$ height of cylinder = 20 cm

Solution 4:

Side of square = 7 cm

Height of cylinder =Side of square = 7 cm

7 cm will be the circumference of the circle.

i.e. $2\pi r$ = 7 cm

Curved surface area of a cylinder:

$CSA = 2\pi rh$

Putting the above values:

CSA = 7 $\times$ 7 = 49 $cm^{2}$

Solution 5:

As calculated in above step:

CSA = $2\pi rh =$ 7 $\times$ 7 = 49 $cm^{2}$

Total surface area = $2\pi r^{2} + 2\pi r h$

Calculating value of r:

$2\pi r$ = 7 cm

$\Rightarrow 2 \pi r = 7\\\Rightarrow r = \dfrac{7}{2\pi}$

Total surface area =

$2\pi (\dfrac{7}{2\pi})^{2} + 49\\\Rightarrow \dfrac{49}{2\pi}+49\\\Rightarrow 49(\dfrac{1}{2\pi}+1) cm^2$

Ratio of TSA: CSA is

$49(\dfrac{1}{2\pi}+1) cm^2 : 49 cm^2\\\Rightarrow (\dfrac{1}{2\pi}+1):1\\\Rightarrow (2\pi+1): 2\pi$

5 0

3 years ago

In a random sample of 500 handwritten zip code digits, 464 were read correctly by an optical character recognition (OCR) system

In-s [12.5K]

Answer:

z= 2.38

P = 0.008656

Step-by-step explanation:

Here n= 500 and p~= 464/500= 0.928 and q`= 1- 0.928 = 0.072

We formulate our null and alternate hypothesis as

H0 = 0.9 ; H0 > 0.9

The degree of confidence = 90%

z₀.₀₅ = 1.645 for α= 0.05

We use the test statistic

z= x- np/√npq

z= 466-500 *0.9/ √500 * 0.9(1-0.9)

z= 466- 450/ √45

z= 16/6.7082

z= 2.38

As the calculated value of z= 2.38 is greater than α =1.645 so we reject H0.

If H0 is true the P value is calculated as

P = 1- Ф( 2.38)

P = 1-0.991344=0.008656

7 0

3 years ago

Line segment XY has endpoints X(5,7) and Y(-3,3)

dem82 [27]

y=-2x+7

Step-by-step explanation:

line segment xy has endpoints x(5 7) and y(-3 3)

for the equation of the perpendicular bisector of line segment xy

slope of line segment xy = 7-3 / 5+3

= 4/8

=1/2

so slope of perpendicular bisector is -2

as m1m2= -1 or m1= -1/m2

As perpendicular bisector goes through midpoint of xy , let's find midpoint of xy

midpoint(x,y) = (5-3 / 2 , 7+3 / 2)

=(2/2, 10/2)

=(1,5)

find the equation of line(perpendicular bisector) passing through (1,5) and the slope -2

y-5 = -2(x-1)

y-5 =-2x+2

y=-2x+7

6 0

3 years ago

Write the range of <br><img src="https://tex.z-dn.net/?f=y%20%3D%20%28x%20-%202%20%29%7B%7D%5E%7B2%7D%20%20%2B%204" id="TexFormu

8090 [49]

Answer:

Range: y ≥ 4

Step-by-step explanation:

Range is the y value

y = (x-2)^2 +4

The smallest the squared term can be is zero

y = 0 +4

The smallest y can be is 4

y ≥ 4

6 0

3 years ago