State if triangles HAG and CAB are similar and why.

Answer:

x³ - 6·x² + 6·x + 8 = (x - 4) × (x - (1 + √3)) × (x + 1 + √3)

Step-by-step explanation:

From the given graph of the polynomial, x³ - 6·x² + 6·x + 8, we have that one of the zeros of the polynomial, which is one point the graph cuts the x-axis is given as follows;

At a zero, we have, x = 4

∴ x - 4 = 0 is a factor of the polynomial

Dividing the given polynomial by (x - 4), gives;

x² - 2·x - 2

(x³ - 6·x² + 6·x + 8)÷(x - 4)

x³ -4·x²

-2·x² + 6·x + 8

-2·x² + 8·x

-2·x + 8

-2·x + 8

0

∴ (x³ - 6·x² + 6·x + 8)÷(x - 4) = x² - 2·x - 2

∴ (x - 4) × (x² - 2·x - 2) = x³ - 6·x² + 6·x + 8

Factorizing x² - 2·x - 2, gives;

x = (2 ± √((-2)² - 4×1×(-2)))/(2 × 1) =  (2 ± 2·√(3)/(2) = (1 ± √(3)

Therefore, x = 1 + √3, (x - (1 + √3)) = 0 or x = 1 - √3, (x - (1 - √3)) = 0 which gives the factors, after factorizing completely as follows;

x³ - 6·x² + 6·x + 8 = (x - 4) × (x - (1 + √3)) × (x + 1 + √3)

Slope = change in y / change in x

Slope = (4 - -8) / (-14 - -6)

Slope = 12/-8

Simplify:

Slope = -6/4

Answer:

-3/2

Step-by-step explanation:

To find the slope, use the slope formula

m = (y2-y1)/(x2-x1)

m = (4 - -8)/(-14 - -6)

   = ( 4+8)/(-14+6)

   = 12/-8

-3/2

Answer:

Step-by-step explanation:

They tell you the slope of the line is -63      :/    m= -63

and then they tell you the y-intercept  is 825   b= 825

Why did you even need to ask about this ?

B. x = y

Hope this helps! :)

Answer:

x = y

Step-by-step explanation:

∠x and ∠y are corresponding angles

corresponding angles are congruent ( equal to each other )

Hence x = y

Answer:

x=3 and y=−2

Step-by-step explanation:

Multiply the first equation by 4,and multiply the second equation by 3.

4(2x−3y=12)

3(3x+4y=1)

Becomes:

8x−12y=48

9x+12y=3

Add these equations to eliminate y:

17x=51

Then solve17x=51for x:

17x=51

17x

17

=

51

17

(Divide both sides by 17)

x=3

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

2x−3y=12

Substitute3forxin2x−3y=12:

(2)(3)−3y=12

−3y+6=12(Simplify both sides of the equation)

−3y+6+−6=12+−6(Add -6 to both sides)

−3y=6

−3y

−3

=

6

−3

(Divide both sides by -3)

y=−2

Answer:

[tex](3,-2)[/tex]

Step-by-step explanation:

[tex]2x-3y=12[/tex]

[tex]2(3)-3(-2)=12[/tex]

[tex]6--6=12[/tex]        Two negative signs together makes a addition

[tex]3x+4y=1[/tex]

[tex]3(3)+4(-2)=1[/tex]

[tex]9-8=1[/tex]            

Step-by-step explanation:

> find the angle of center circle:

cos~¹ 5/(5+12) = cos~¹ 5/17 = 72°

so the sector area of the shaded

region =

(360-72)/360 × 3.14 × 5²

= 288/360 × 78.5

= 62.8

> the height of triangle (red Line) =

4×tan 72° = 4× 3.078 = 12.31

the height of pyramid (green

Line) = √12.31²-8.5² =√74.16

= 8.61

so the volume of pyramid =

⅓×(17×8)×8.61 = 390.32

Answer:

120 crackers

Step-by-step explanation:

Given

[tex]Box = 5[/tex]

[tex]Crackers = 24/box[/tex]

Required

The total number of crackers

To do this, we simply multiply the number of box by the crackers per box

[tex]Total = Box * Crackers[/tex]

[tex]Total = 5 * 24[/tex]

[tex]Total = 120[/tex]

Answer:

30cm

Step-by-step explanation:

Vn = Vc

1/3 X Pie x 6^2 x hn = Pie x 6^ x 10

hn = 30cm

Given: Radius=7cm,

Height=10cm

Volume of the cylinder=πr2h

=722×7×6×10=1540cm3

Answer:

area of the circular plate =πr²

50.24 =3.14×r²

r² =50.24/3.14

r² =16

radius =4 inch

Answer:

4 in

Step-by-step explanation:

Answer:5 exponent of 15

Step-by-step explanation:trust

Answer:

A: less that

Step-by-step explanation:

4( 14)+3

36+3= 39

39 (2+9)6-7

(11)6-7

66-7

59

39<59

Answer:

what expression

Step-by-step explanation:

Answer:

The program in Python is as follows:

age = int(input("Age: "))

if age>=13 and age <=19:

   print("Teenager")

else:

   print("Not a teenager")

Step-by-step explanation:

This gets input for age

age = int(input("Age: "))

This checks if age is between 13 and 19 (inclusive)

if age>=13 and age <=19:

If yes, the age is teenage

   print("Teenager")

If otherwise, the age is not teenage

else:

   print("Not a teenager")

Multiply the number of days (x) by the amount per day (80) to get 80x.

She is driving 150 miles at 0.10 per mile so multiply to get the mileage cost: 150 x 0.10 = 15

Add this to the daily amount:

80x+15

She can spend up to 300, so less than or equal to 300:

80x +15 <=300

Answer:

129 = x

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

47+82 = x

129 = x

Answer:

47+82 = x

129 = x

hope it helps

Answer:

1/3 kilograms

Step-by-step explanation:

Answer:

2 1/4

Step-by-step explanation:

amount left of apple pie = 1 - 3/4 = 1/4

amount left of blackberry pie = 1 - 1/2 = 1/2

amount left of blueberry pie = 1 - 1/8 = 7/8

amount left of cherry pie = 1 - 5/8 = 3/8

amount left of peach pie = 1 - 3/4 = 1/4

add this figures together

1/4 + 1/2 + 7/8 + 3/8 + 1/4

2 4 + 7 + 3 + 2

8

Answer:

<2 = 75

Step-by-step explanation:

<1 and <2 form a straight line which means that they add to 180

<1+<2 =180

105+<2 =180

Subtract 105 from each side

<2 =180-105

<2 = 75

Answer:

I think the answer is A. 45m - 30 over 4 ≥ 275

Answer:

49

Step-by-step explanation:

Answer:

49

Step-by-step explanation:

3x² + 4y⁰ - x⁻¹

3(4)² + 4(5)⁰ * (4)⁻¹

3(16) + 4(1) * 1/4

48 + 4 * 1/4

48 + 4/4

48 + 1

49

Answer:

x=56

Step-by-step explanation:

Since the angles are all the same,

D=78

F=46

All you have to do is subtract these numbers from 180, which gives you 56

Answer:

56

Step-by-step explanation:

Answer:

w = 26

Step-by-step explanation:

set up an equation; since this is a right angle, it equals 90 degrees

90 = w + 12 + 2w

90 - 12 = w + 2w

78 = 3w

78/3

w = 26

Answer:

w = 26

Step-by-step explanation:

2w +w + 12 =90

3w +12 = 90

      -12    -12

3w = 78       then 3w/3 = 78/3

w=26

Answer:

8n < 72

n < 9

Step-by-step explanation:

Note that

> means greater than

< means less than

≥ means greater than or equal to  

≤ less than or equal to  

for example : 2 < 3 means 2 is less than 3

3 >2 means 3 is greater than 2

8 times n = 8n

8n is less than 72, this can be represented by the equation : 8n < 72

to determine the value of n, divide both sides of the equation by 8

n < 9  

Answer:

it is too fine i cant really see the work

Answer:

Step-by-step explanation:

If we draw radii from the center of this 18-gon to each vertex, we end up with 18 triangles that are all congruent to each other. If we divide 360 by 18 we get the measure of the vertex angle of each of these 18 triangles. 360/18 = 20. So we take one of these triangles and pull it out and use it as a representative triangle from which we use trig to find its height and its base length.

The formula for the area for a regular polygon is

[tex]A=\frac{1}{2}ap[/tex] where a is the apothem (the height of our triangle) and p is the perimeter (found from the base of our triangle).

If we split this triangle we extracted right down the center vertically, we get 2 right triangles. Pull one of those out and this is the triangle we work with. The vertex angle is split in half and it now measures 10. The one base angle is the right angle and, by the Triangle Angle-Sum Theorem, the other base angle is 80. To find the height (or the apothem) of this right triangle that has a hypotenuse of 1 (the radius of the polygon is the hypotenuse of the right triangle), we use the sin or cos ratio. I used cos:

[tex]cos10=\frac{a}{1}[/tex] so

a = .9848

To find the base of this right triangle, I used the sin ratio:

[tex]sin10=\frac{p}{1}[/tex] so

p = .1736. But this is only half the length of one of the sides of the polygon, so multiply it by 2 to get the length of the whole side.

.1736 * 2 = .3473

Now, in order to find the perimeter, we multiply that one side by 18 to get

p = 6.2514

Now we're ready to find the area:

[tex]A=\frac{1}{2}(.9848)(6.2514)[/tex] so

A = 3.078 square feet

Answer:

-3

Step-by-step explanation:

-2= x+1

-2-1=x

-3=x

Answer:

1302 males & 3038 females

Step-by-step explanation:

3x + 7x = 4340

10x = 4340

x = 434

3(434) = 1302 males

7(434) = 3038 females

Answer:

whats the question

Step-by-step explanation: