Will give brainliest if correct.

Answer:

x = 2

Step-by-step explanation:

I assumed that you wanted me to set them equal to each other, so that is what I did. I wasn't given any other number to go by so hopefully this is correct.

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:

4x-1y=3xy

Step-by-step explanation:

because 3-2=1 and add the y on and the do 4x-1y and that will = 3xy

Answer:

x=4, y=6

Step-by-step explanation:

hope that helps :)

Answer:

Percentage baked= 75%

Step-by-step explanation:

Giving the following information:

After 20 minutes in the oven, 15 of the 20 cookies were fully baked.

First, the fraction of cookies baked:

Fraction of cookies= 15/20= 3/4

Now, to calculate the percentage, we need to use the following formula:

Percentage baked= (15/20)*100

Percentage baked= 75%

9514 1404 393

Answer:

  25.

Step-by-step explanation:

The first two significant figures are 2 and 5. The next figure is 0, so we don't need to round up. The number to 2 significant figures is 25.

Answer:

eu singer nuştiu

terog scuză

Answer:

34 * 6 = 204

Thank you and please rate me as brainliest as it will help me to level up

Answer:

i thin it is 8960

Step-by-step explanation:

44800 divided by five = 8960

Answer:

AC+CB=AB

Step-by-step explanation:

Let's see.... If you are a visual learner this could help.

[tex]A----------C---------------B[/tex]

So you can see that C is right in between them so the distance between AC and the distance between CB would equal the whole line AB. So if you add AC and CB you would get AB.

Answer:

y = 2x + 16

Step-by-step explanation:

slope is parallel and equal to y = 2x + 6

y intercept = 16

Answer:

b - y=2x+16

Step-by-step explanation:

y=y1+m(x+x1)

(-4,8)

y=8+2(x-4)

y=8+2x-8

add 8 on both sides

y=2x+16

Answer:

The sum of the two solutions to the given equation is 1/3.

Step-by-step explanation:

Nature of Roots of a Second-Degree Equation

Given a quadratic equation:

[tex]ax^2 + bx + c = 0[/tex]

The roots of the equation are:

[tex]\displaystyle x_1=\frac{-b+ \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\displaystyle x_2=\frac{-b- \sqrt{b^2-4ac}}{2a}[/tex]

The sum of the roots is:

[tex]\displaystyle x_1+x_2=-\frac{b}{a}[/tex]

The sum of the roots of a quadratic equation is equal to the negation of the coefficient of the second term, divided by the leading coefficient.

We are given the equation:

[tex]3x^2 - x = 4[/tex]

Rearranging:

[tex]3x^2 - x - 4=0[/tex]

The coefficient b is b=-1, and the leading coefficient is a=3, thus the sum of the roots is:

[tex]\displaystyle x_1+x_2=-\frac{-1}{3}[/tex]

[tex]\displaystyle x_1+x_2=\frac{1}{3}[/tex]

The sum of the two solutions to the given equation is 1/3.

Answer:

y=4x

Step-by-step explanation:

you just have to find the slope!

Answer:

37.3% is the take off

Step-by-step explanation:

so an easy route is to subtract the price after the reduction

89.99-56.49= 33.5 that is 37.3 percent

because 62.78% of 89.99 is 56.486723 round i and you get 56.49 so this is a check your work

Answer:

D

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

The answer is 8.9

PLEASE MARK BRAINLIEST

Answer:

8.9

Step-by-step explanation:

Answer:

4/15

Step-by-step explanation:

what's the answer? 4/5×1/3?

Answer:

See below.

Step-by-step explanation:

30.

E(1, 2), F(5, 6), G(3, -2)

a)

H, midpoint of segment EG

H( (1 + 3)/2, (2 + (-2))/2) = H(2, 0)

J, midpoint of segment FG

J( (5 + 3)/2, (6 + (-2))/2) = J(4, 2)

b)

Show that segment HJ is parallel to segment EF.

Parallel lines have equal slopes. We find the slopes of the two segments using the endpoints and show that the slopes are equal proving the segments are parallel.

slope of segment HJ:

slope HJ = (2 - 0)/(4 - 2) = 2/2 = 1

slope of segment EF:

slope EF = (6 - 2)/(5 - 1) = 4/4 = 1

slope HJ = slope EF = 1

Segments HJ and EF are parallel since their slopes are equal.

c)

Show HJ = (1/2)EF

We use the distance formula to find the lengths of segments HJ and EF.

length of HJ = sqrt[(4 - 2)^2 + (2 - 0)^2] = sqrt(4 + 4) = sqrt(8) = 2sqrt(2)

length of EF = sqrt[(5 - 1)^2 + (6 - 2)^2] = sqrt(16 + 16) = sqrt(32) = 4sqrt(2)

HJ = (1/2)EF

Substitute the lengths we found just above for HJ and EF:

2sqrt(2) = (1/2)[4sqrt(2)]

2sqrt(2) = 2sqrt(2)

The two sides are equal, so we have proved that HJ = (1/2)EF.

Answer:The answer is C

Step-by-step explanation:

When you plug it in 7*2 is 14+ 5*3 is 15 you add 14+15 you get 29 and then for the other equation you do 12-5 which gives you the x value of 7. Hope this helps.

Answer:

Step-by-step explanation:

put the y intercept at 4. then go down 1 and right three, down one, then right three. go back to the y intercept and then go up one and left three, up one and left three

to answer this you should plot a point at (0,4). That is the y intercept as you can see on the equation +4 is at the end. Since the slope is -1/3, go 1 unit left and 3 up from the y intercept. those are your two points and draw a straight line though.

Answer:

Arithmetic content = 300 pages

Geometric content = 180 pages

Step-by-step explanation:

Arithmetic : Geometry = 5 : 3

Total pages of book = 480

How much of each type of content will be needed to make a book of 480 pages?

Total ratio = arithmetic + geometric

= 5 + 3

= 8

Arithmetic content = 5 / 8 × 480

= 0.625 × 480

= 300

Arithmetic content = 300 pages

Geometric content = 3 / 8 × 480

= 0.375 × 480

= 180

Geometric content = 180 pages

Answer:

14

Step-by-step explanation:

7-3 = 4 4+10=14 therfore 14 would be the answer hope this helps

Hello soldier!! The answer is D! Have a great day <3

Answer:

The answer is: D / 1/8(5)

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

Answer:

Maybe c

Step-by-step explanation:

it's tooo easy

answer -1296

Answer:

5

Step-by-step explanation:

[tex]\sqrt[3]{125} =5*5*5=5[/tex]