Find measure of angles B, E, D and C and the length of BC.

Triangle ABC ~ Triangle DEF. Measure of angle A = 30 degrees and measure of angle F = 65 degrees. AB=20, DE = 35, EF= 28.

9514 1404 393

Answer:

  n cm = 3 cm

Step-by-step explanation:

The total surface area is the sum of the base areas and the lateral area. The base areas are the sum of the areas of the rectangle and triangle that define the shape of the base.

The rectangle has dimensions 5 cm by n cm. The triangle is 5-2 = 3 cm high and 4 cm at the base. Then the front face area is ...

  A = lw + 1/2bh

  A = (5 cm)(n cm) +1/2(4 cm)(3 cm) = (6 +5n) cm²

The lateral area is the product of the perimeter of the base and the depth of the prism.

  A = Ph

  A = (5 cm + n cm + 2 cm + 5 cm + 4 cm + n cm)(4 cm) = (64 +8n) cm²

The total surface area is the sum of the areas of the two bases and the lateral area:

  130 cm² = 2(6 +5n) cm² +(64 +8n) cm²

  130 = 76 +18n . . . . . . divide by cm², collect terms

  54 = 18n . . . . . . . . . subtract 76

  3 = n . . . . . . . . . . divide by 3

The value of n in centimeters is 3 cm.

Answer:

With respect to air, the refractive indices of water and benzene are 1.33 and 1.50 respectively

Use the edges of the triangles to determine which ones are closest together for the smallest of furthest apart for the largest.

1. Smallest = b

Largest = c

2. Smallest = f

Largest = g

The solution is Option C.

The graph which represents the inequality equation is

f ( x ) = { 0.50 , if x < 3

             1       , if 3 ≤ x < 6

             1.50  , if 6 ≤ x < 9

             2.00 , if 9 ≤ x < 12 }

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the number of years be = x

Let the increment in wages be = y

Now , the equation will be

For the employees that have been with the company for less than three years can expect to receive an increase of $0.50 per hour

So , the inequality equation is x < 3 , f ( x ) = 0.50

Employees that have been with the company for at least three years, but less than six years can expect an increase of $1.00

So , the inequality equation is 3 ≤ x < 6 , f ( x ) = 1

Employees that have been with the company for at six years, but less than nine years, receive an increase of $1.50 per hour

So , the inequality equation is 6 ≤ x < 9 , f ( x ) = 1.50

Employees of at least nine years, but less than twelve years receive an increase of $2.00

So , the inequality equation is 9 ≤ x < 12 , f ( x ) = 2

Therefore , the graph which represents the solution is Option C.

Hence , the inequality equation is 9 ≤ x < 12 , f ( x ) = 2

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Answer:

C

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to original, so

scale factor = [tex]\frac{EF}{BC}[/tex] = [tex]\frac{11}{66}[/tex] = [tex]\frac{1}{6}[/tex] → C

Answer:

y = 7/2x - 9/2

Step-by-step explanation:

y2 - y1 / x2 - x1

-1 - 6 / 1 - 3

-7 / -2

7/2

y = 7/2x + b

-1 = 7/2(1) + b

-1 = 7/2 + b

-9/2 = b

The Answer: C I did this yesterday

Step-by-step explanation:

Given:

In a right angle triangle,

Hypotenuse = 25 cm

Base = x

Angle between base and hypotenuse = 18 degrees.

To find:

The value of x.

Solution:

In a right angle triangle,

[tex]\cos \theta =\dfrac{Base}{Hypotenuse}[/tex]

In the given right triangle,

[tex]\cos (18^\circ) =\dfrac{x}{25}[/tex]

[tex]\cos (18^\circ) \times 25=x[/tex]

[tex]0.9510565 \times 25=x[/tex]

[tex]23.7764125=x[/tex]

Round the answer to the nearest hundredth (two decimal).

[tex]x=23.78[/tex]

Therefore, the value of x is about 23.78 cm.

15/25= y/30

y= 3/5×30

y= 3×6

y=18

THE ANSWER IS Y=18

Answer:

y = 6

Step-by-step explanation:

One way of doing this problem is to start by reducing the first fraction, 5/25, obtaining 1/5.  Then

 1       y

---- = -----

  5    30

Through cross-multiplication, we get 5y = 30, or y = 6

Answer:

[tex]27a^{3} +27a^{2}b+9ab+b^{3}[/tex]

Step-by-step explanation:

[tex](3a+b)(3a+b) = 9a^{2}+6ab+b^{2}\\(9a^{2}+6ab+b^{2})(3a+b) = 27a^{3} + 27a^{2}b +9ab^{2} +b^{3}[/tex]

Answer:

Step-by-step explanation:

9a^3+18a^2b+9ab^2+b^2

Answer:

16

Step-by-step explanation:

let boys equal to 5x

and girls equal to 4x

so 4x+5x=36

X=4

so boys are 5*4

boys are 20

and girls are 16

so boys are 4 more than girls

Answer:

16 girls

Step-by-step explanation:

boys : girls : total

5          4        5+4 = 9

take the total number of people and divide by 9

36/9 = 4

Each number should be multiplied by 4

boys : girls : total

5*4        4*4     9*4

20          16        36

There are 16 girls

Answer:

y=x +10

Step-by-step explanation:

answer is in photo above

Answer:

y = 1x + 10

Step-by-step explanation:

y2 - y1 / x2 - x1

4 - 6 / -6 - (-4)

-2 / -2

= 1

y = 1x + b

4 = 1(-6) + b

4 = -6 + b

10 = b

Answer Expert Verified

3.1/5

18

Surface of a cube=S(x)

S(x)=6x²

S(2 m)=6(2 m)²=6(4 m²)=24 m²

The surface of this cube is 24 m².

Volume of a cube=V(x)

V(x)=x³

V(2 m)=(2 m)³=8 m³

Answer:

18

Step-by-step explanation:

Answer:

just took the test

1st root= x1 =(17+√65)/16

2nd root =x2 =(17-√65)/16

A quadratic equation is any equation that can be  rearranged in standard form as where x represents an unknown and a, b , and c represent known numbers , where a should not be equal to 0.

D = b^2 - 4 * a *c

D = (-17)^2 - (4)(8)(7)

D= 65 >0

There will be two solutions exist in this condition

1st root :    (-b+√D)/2a

=(-(-17)+√65)/2*8)

1st root=  x1 = (17+√65)/16

2nd root :   (-b-√D)/2a

= (-(-17)-√65)/2*8)

2nd root = x2 = (17-√65)/16

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Answer:

D) the scaled triangles perimeter is 1/3 the size of the original triangles perimeter

Step-by-step explanation:

Given

Original:

[tex]Height = 18, Slant = 30, Length =24[/tex]

Scaled:

[tex]Height =6, Slant=10, Length=8[/tex]

Looking at the dimension of both triangles, The relationship between the original and the scaled copy is:

[tex]Scaled = \frac{1}{3} * Original[/tex]

Hence, the perimeter is:

[tex]Perimeter (Scaled) = \frac{1}{3} * Perimeter (Original)[/tex]

Answer:

Ms. Lesure is going to need to buy 4 pizzas for Mr. Shows Interactions A class. The boys would eat 20 slices and the Girls in total will eat 12 slices. In total you'll need about 32 slices and 32 divided by 8 is 4.

Step-by-step explanation:

X = 21

Y = 30

X:

(3x - 15) + (6x + 6) = 180 -- combine like terms

9x - 9 = 180 -- add 9 to both sides

9x = 189

x = 21

Y:

Plug x into 3x-15

3(21) - 15 = y + 18

63 - 15 = y + 18

48 = y + 18 -- subtract 18 from both sides

y = 30

Answer:

Rotate 90' clockwise Centre (-2, -2)

if you mean A onto B

Answer:

f(- 4) = - 4

Step-by-step explanation:

f(- 4) with x = - 4 gives f(- 4) = - 4

Answer:

Exposed group has 2 times the odds of bladder cancer than not exposed group based on our odds ratio.

The disease is bladder cancer.

Explanation:

Calculate odds for exposed group =

1293 with bladder cancer had used artificial sweeteners in the past/

855 without bladder cancer had used sweeteners= 1.51

Calculate odds for not exposed group=

1707 with bladder cancer had never used artificial sweeteners/ 2145 without bladder cancer had never used artificial sweeteners=0.795

Odds ratio=odds for exposed group/odds for not exposed group

= 1.51/0.795

= 1.899

Therefore exposed group has two times the odds of bladder cancer than not exposed group.

Answer:

c). y = -2x + 9

Step-by-step explanation:

y = -2x + b

1 = -2(4) + b

1 = -8 + b

9 = b

Answer:

y = 5x - 21

Step-by-step explanation:

[tex]y+1=5(x-4)\\y+1=5x-20\\y=5x-21[/tex]

Answer:

x = 4.4

Step-by-step explanation:

cos theta = adjacent side / hypotenuse

cos 24 =  y/x

cos 24  = 4/x

x cos 24 = 4

x = 4/cos 24

x =4.378545114

Rounding to 1 decimal place

x = 4.4

Answer:

x=4.4cm

Step-by-step explanation:

We can use cosine to find x as we're given y (adjacent) and the angle. This is also a right triangle.

cos24=4/x

x=4/cos24

x=4.4

Answer:

Step-by-step explanation:

distance between center and (1,-2) is

[tex]d=\sqrt{(1-(-3))^2+(-2-1)^2} \\=\sqrt{16+9} \\=5>4\\[/tex]

distance of the point from the center>radius of circle.

So it lies outside the circle.

9514 1404 393

Answer:

   (3x +4)(j -f)

Step-by-step explanation:

  3x(j -f) -4(f -j) = 3x(j -f) +4(-f +j) . . . . distribute the minus sign in -4(f-j)

  = 3x(j -f) +4(j -f)

  = (3x +4)(j -f)

Answer:

k = -12

Step-by-step explanation:

When lines are perpendicular, their slopes are the opposite reciprocal of each other.

The opposite reciprocal of [tex]\frac{1}{4}[/tex] is -4

[tex]\frac{k}{3}=-4[/tex]

k = -12

Answer:

35.97

Step-by-step explanation:

113 divided by pie (3.14)

Answer:

1st onne I believe I couldd be wrong but thats what I got

Step-by-step explanation:

Answer:

6 units^2

Step-by-step explanation:

To solve this problem i use the net to find the area. Each square is a unit. there was 4 units and 4 halves. 4 halves combined, would be 2.

2 + 4= 6.