7(1 - x) = 10 – 6(x + 2)

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)

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:

what do you need?

Step-by-step explanation:

pictures would be nice

Answer:

yea sure whats the problem

Answer:

91

Step-by-step explanation:

Sum of the middle two numbers is ''182'' for 4 consecutive even number.

The process of combining or adding two or more numbers is called the Addition.

We have to given that;

Sum of 4 consecutive even numbers = 364

Let 4 consecutive even numbers are,

⇒ (x - 2), x, (x + 2), (x + 4)

So, We can formulate;

⇒ (x - 2) + x + (x + 2) + (x + 4) = 364

Solve for x;

⇒ 4x + 4 = 364

⇒ 4x = 364 - 4

⇒ 4x = 360

⇒ x = 90

Hence, The two middle numbers are,

⇒ (x) = 90

⇒ (x + 2) = 90 + 2

              = 92

So, Sum of two middle numbers = 90 + 92

                                                  = 182

Learn more about the addition visit:

https://brainly.com/question/5454147

#SPJ2

The complete question is this,

The sum of 4 consecutive even numbers is 364. What is the sum of the middle two numbers?

Answer:

Step-by-step explanation:

D = 3,1

E = 1,-2

F= -4,2

Answer:

x = -65

Step-by-step explanation:

To start off, we can create our equation. We know that "of" is just another word for multiply. We will then end up with [tex]\frac{2}{5}[/tex] * x = -26. To solve this equation, we will find [tex]\frac{2}{5}[/tex] of -26. To make things less confusing, lets take away the negative for now. 26 x 5 = 130 and 130 ÷ 2  is 65. We then add our negative back on and x = -65.

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:

it would be 8 hours.....

Step-by-step explanation:

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

Answer:

The length is 8

Step-by-step explanation:

Answer: Each girl will receive $18.75.

Step-by-step explanation:

Given: Two girls babysat three children for five hours.

Hourly pay for each child = $2.50

Payment for 5 hours per child = [tex]5\times\$2.50=\$12.5[/tex]

Payment to 3 children for 5 hours = [tex]3\times \$12.5=\$37.5[/tex]

So, the amount received by each girl  = [tex]\dfrac{\text{Payment to 3 children for 5 hours}}{2}[/tex]

[tex]=\dfrac{37.5}{2}=\$18.75[/tex]

Hence, each girl will receive $18.75.

Answer:

10/10 =1 / 1 =1

m = ^^

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer:

10 cm

Step-by-step explanation:

Answer:

Step-by-step explanation:

What i would do is multiply both sides by 2z + 1

so you get z-6=20z+10

-19z=16

z=-16/19

Answer:

z is every integer and the study of z and its properties is a general understanding save the satisfying of your rate of change

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:

SAS

Step-by-step explanation:

We have 2 sides that are congruent and the angle between them

We can use SAS ( side angle side) to prove congruency

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 height of the kite is approximately 278.6 feet

Step-by-step explanation:

The length of Jason's Kite string, l = 325 feet

The angle of elevation of the kite string, θ = 58°

The height of Jason's hand, h = 3 feet above the ground

Therefore, we have;

The height of the kite = The vertical component of the length of the kite string + The height of Jason's hand above the ground

The height of the kite = l × sin(θ) + h

Substituting the values, we get

The height of the kite = 325 × sin(58°) + 3 ≈ 278.6 (which is obtained by rounding the answer to the nearest tenth)

The height of the kite ≈ 278.6 feet.

Answer:

2.4x10^-2

Step-by-step explanation:

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

Answer:

I think the answer is is X-15

Answer:

Y= -1/3x + 8/3

Step-by-step explanation:

Answer:

i think its answer is option A

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:

B. 32%

Step-by-step explanation:

16/50 = 32% lol

goodluck!

Answer:

79 degrees

Step-by-step explanation:

Quadrilaterals have a total of 360 degrees. They already gave you three of them so you just have to add all the given degrees and subtract it by 360. 101+124+56=281 ; 360-281=79

Answer:

7:12 a.m

Step-by-step explanation:

Given that:

Train to New York city leaves station every 7 minutes

Train to Boston leaves station every 6 minutes

Current time = 6:30 a.m

Time both will leave station together is obtained by finding the least common multiple of 6 and 7

Multiples of ;

6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60,...

7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70,...

The least common multiple of 6 and 7 is 42.

Hence, both trains will leave the station together after 42 minutes ;

Current time + 42 minutes

6:30 a.m+ 42 minutes = 7:12 a.m

Answer:

x = 2,-8

Step-by-step explanation:

Answer:

The answer is "63%"

Step-by-step explanation:

please find the complete question in the attached file.

Time= 10 year =38.0%

let,  

x=rate

[tex]\to 38 = \frac{(36.2 + 29.0 + 46.2 + 37.5 + 40.9 + 40.0 + 32.6 + 40.5 + 40.1 + x)}{10}[/tex]

[tex]\to 38 = \frac{(343 + x )}{10}\\\\\to 380 = (343 + x )\\\\\to 380 - 343 = x \\\\\to x= 37\%[/tex]

The rate of survival differs from the rate of loss, meaning the rate of survival were:

[tex]= 1 - loss\ rate \\\\= 1 - 37\% \\\\= 1 - \frac{37}{100} \\\\= \frac{100-37}{100} \\\\= \frac{63}{100} \\\\=63 \%[/tex]

Answer:

300:500

Step-by-step explanation:

If there are 200 left handed gloves, then there are 300 right handed gloves.

The total amount of gloves is 500, so its 300:500.

Answer:

D.7.68

Step-by-step explanation:

100%= 32 ounces

24%= 24% x 32ounces    =   768 ounces

               100%                        100

= 7.68 ounces