3) Where do planes M and NJF intersect?
A. KJH
B. FG
C. JFG
D.GN

Part (i)

Angle ABC is 150 degrees. The angle CBX is supplementary to this, so,

(angleABC)+(angleCBX) = 180

angle CBX = 180-(angleABC)

angle CBX = 180-150

angle CBX = 30 degrees

Because of the right angle marker at point X, we can find that triangle CBX is a 30-60-90 triangle. This special type of right triangle has its hypotenuse twice as long as the short leg, which we'll call y. The long leg is equal to y*sqrt(3) units.

The diagram shows BC = 6 is the hypotenuse, so the short leg is y = 6/2 = 3. The longer leg is y*sqrt(3) = 3*sqrt(3) which is the distance from B to X.

In summary so far,

CX = 3

BX = 3*sqrt(3)

We have enough information to find the tangent of angle CAB, and then find the actual angle itself.

tan(angle CAB) = opposite/adjacent

tan(angle CAB) = (CX)/(AX)

tan(angle CAB) = 3/(4+3*sqrt(3))

angle CAB = arctan(  3/(4+3*sqrt(3))  )

I'm using arctan in place of tan^(-1) which is the same basic function, just different notation.

========================================================

Part (ii)

Focus on triangle AXC. The legs we found were

AX = 4+3*sqrt(3)

CX = 3

Use the Pythagorean theorem to find the hypotenuse AC

a^2 + b^2 = c^2

(AX)^2 + (CX)^2 = (AC)^2

(AC)^2 = (AX)^2 + (CX)^2

(AC)^2 = (4+3*sqrt(3))^2 + (3)^2

(AC)^2 = (4+3*sqrt(3))(4+3*sqrt(3)) + 9

(AC)^2 = 4(4+3*sqrt(3))+3*sqrt(3)(4+3*sqrt(3)) + 9

(AC)^2 = 16+12*sqrt(3)+12*sqrt(3)+27 + 9

(AC)^2 = 52+24*sqrt(3)

AC = sqrt( 52+24*sqrt(3) )

Note that AC is a length so AC is positive. We don't have to worry about the plus minus.

This is known as a nested radical since one square root is buried in another.

We can write that as [tex]AC = \sqrt{52 + 24\sqrt{3}}[/tex] if you're curious as to how that looks on paper.

Using your calculator, you should find that,

[tex]\sqrt{52+24\sqrt{3}} \approx 9.673118[/tex]

Answer:

Step-by-step explanation:

1. F and M are equal angles and sum of internal angles = 180, so

2. Triangle is equilateral as all angles are equal, so all sides are equal:

3. Isosceles triangle with equal angles of R and T:

Angle S is

4. Angle 2 is supplementary with 156 as isosceles triangles and vertical angles are equal, therefore:

Answer:

i think its answer is option A

Answer:

(8, 0), (12, 4), (16, 8)

Step-by-step explanation:

m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]  

(20, 12)

(4, - 4)

m = [tex]\frac{-4-12}{4-20}[/tex] = 1

y - 12 = (1)(x - 20)

y = x - 8

y = 8 - 8 = 0

y = 12 - 8 = 4

y = 16 - 8 = 8

Answer:

B. 32%

Step-by-step explanation:

16/50 = 32% lol

goodluck!

Answer:

6

Step-by-step explanation:

Answer:

10 cm

Step-by-step explanation:

Answer:

The length is 8

Step-by-step explanation:

Answer:

D.7.68

Step-by-step explanation:

100%= 32 ounces

24%= 24% x 32ounces    =   768 ounces

               100%                        100

= 7.68 ounces

Answer:

12,670,000,000-I think if its moving right one

Step-by-step explanation:

Answer:

[tex]\huge\boxed{2x^x-3x^x-x=-x^x-x}[/tex]

Step-by-step explanation:

[tex]2x^x-3x^x-x=(2-3)x^x-x=-x^x-x[/tex]

Answers:

a. f(-4)=2

b. f(0)=0

d. f(-5)=0

e. x when f(x)=-2  answer: 2

f. x when f(x)=0  answer: 0

Sorry, I can’t answer c. f(3)=  because when x is three from the x-axis on the graph, the line that meets 3 from the x-axis doesn’t show a whole number     y-coordinate on the graph :(

But I hope this helps and answers your question :)

Answer:

2.4x10^-2

Step-by-step explanation:

since this number is a decimal you will use a negative number above the 10...

Answer:

D -5 less than or equal to y less than or equal to -1.

Step-by-step explanation:

the rang is the y-axis the equation has ys from -5 to -1 so -5to y to -1.

Answer:

Quadrant 2

Step-by-step explanation:

It goes over the x axis and rotates 180 which is half a a circle.

Haha you don't got to pay someone to help you bro

Answer:

La longitud de los lados congruentes =

B = 8.5cm

C = 8.5 cm

Step-by-step explanation:

El perímetro del triángulo isósceles mide 24 cm.

El lado no congruente mide 7 cm de largo.

Lados congruentes significa lados que son iguales o iguales entre sí.

El perímetro de un triángulo es =

Lado A + Lado B + Lado C

Por lo tanto,

24 = 7 cm + B + C

24 - 7 = B + C

17 cm = B + C

Los dos lados son congruentes,

B = C

Por lo tanto, 17 cm / 2

= 8.5 cm

La longitud de los lados congruentes =

B = 8.5 cm

C = 8.5 cm

Answer:

One basic property of a parallelogram is that opposite angles have the same value. Hence angle B = angle D. (2n+15°) = (3n-5°). Then have one side for the unknown. The equation will be 3n=2n+15°+5°. To get the n, simplify the equation: 3n-2n = 20° or n = 20°. Afterwards substitute the value of n to the angles. Angle B = (2(20)+15), Angle D = (3(20)-5). Lastly, simplify the equations. Angle B = (40+15°) = 55° and Angle D = (60-5°)=55°. Therefore the value of angles B & D are both 55°.

Step-by-step explanation:

Answer:

60°

Step-by-step explanation:

We can get the other two angles in the top triangle because they are alternate interior.  Then we subtract them from 180.

180-82-38=60

Answer:

The image of point (1,-4) after a rotation of 180° counter clockwise about the origin is: (-1,4)

Step-by-step explanation:

Rotation means that a point is being moved in clockwise or counterclockwise direction with some angle.

The rotation can be done in 90, 180, 270 degrees.

Given point is:

(1,-4)

When a point (x,y) is rotated 180° counter clockwise its coordinates become (-x,-y) the negative of original point.

So for the given point the coordinates will become (-1,4)

Hence,

The image of point (1,-4) after a rotation of 180° counter clockwise about the origin is: (-1,4)

Answer:

24 thereabouts

Step-by-step explanation:

Well every two months there are two new rabbits so I multiplied two and twelve. This got me twenty-four. I hope this helps! :) I don't know if this is right or not I attempted this in my head.

Answer:

The answer is D

Step-by-step explanation:

Took the test

answer: none of these

T−7×−5 = Tn

Let T equal the present temperature

7 = the number of days

-5= the drop each day

Let Tn = the new temperature

Answer:

3x+9

Step-by-step explanation:

you are multiplying 3 and x because it says "three times a number x" which means 3x and you are adding it to 9 which is 3x+9.

Answer:

x < -8

General Formulas and Concepts:

Pre-Alg

Step-by-step explanation:

Step 1: Define inequality

12 < -3(x + 4)

Step 2: Solve for x

Here we see that any value x that is smaller than -8 would work.

Answer:

it would be 8 hours.....

Step-by-step explanation:

      im  am a bit confused, why is that not an answer choice

Answer:

what do you need?

Step-by-step explanation:

pictures would be nice

Answer:

yea sure whats the problem

Answer:

yes

Step-by-step explanation:

Each value of x multiplied by 4 gives the corresponding value of y, that is

3 × 4 = 12

5 × 4 = 20

6 × 4 = 24

9 × 4 = 36

Thus x and y are proportional and the constant of proportion is 4

Answer:

honestly i don't think it's either of these

Step-by-step explanation:

a proportional relationship goes through the origin and neither of these do

Answer:

[tex]0.17\ \text{yards}[/tex]

Step-by-step explanation:

Total length of yellow fabric = 3.5 yards

[tex]\dfrac{2}{3}[/tex] of the yellow fabric was made to make a chicken costume.

So, the fraction of the yellow fabric used to make toys for her 7 dogs is

[tex]1-\dfrac{2}{3}=\dfrac{1}{3}[/tex]

The amount of fabric to make the 7 toys is

[tex]\dfrac{1}{3}\times 3.5=1.17\ \text{yards}[/tex]

Assuming that equal amount of fabric was used for 1 toy for 7 of her dogs each.

The amount of fabric used for 1 dog's toy is

[tex]\dfrac{1}{7}\times 1.17=0.17\ \text{yards}[/tex]

The amount of fabric used to make each banana is [tex]0.17\ \text{yards}[/tex].

Answer:

D

Step-by-step explanation:

y-intercept or "b":

the line touches the y-axis at -4

slope:

the line rises 1, runs 1 every time

equation:

the y-intercept of -4 combined with the slope of 1/1 is the equivalent of

y=1x/1-4 OR in a more simplified format: D, y = x - 4