4. At what coordinates does the terminal side of a -420° angle intersect the unit circle?

Answer:

-----------------------------------------------

Given polynomial

Factorize it as below:

4ab + 6bn - 2a - 3n​ =    

(4ab - 2a) + (6bn - 3n) =         Regroup        

2a(2b - 1) + 3n(2b - 1) =           Factorize each group using common factors

(2b - 1)(2a + 3n)                       Factorize using common factor

Answer:

[tex](2b-1)(2a+3n)[/tex]

Step-by-step explanation:

Given expression:

[tex]4ab+6bn-2a-3n[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies 2b(2a+3n)-1(2a+3n)[/tex]

Factor out the common term (2a + 3n):

[tex]\implies (2b-1)(2a+3n)[/tex]

Answer:

slide - translate

Step-by-step explanation:

you slided them both as neither of the figures changed

Answer:

value of car depreciate each year = $2000

y + 2000x = 16,500

slope of line = -2000

No, not proportional

Step-by-step explanation:

Value of depreciation of an object is given by :-

Depreciation = [tex]\frac{ total Cost-scrap value}{estimated life}[/tex]

according to question ;

total cost = $16500

scrap value = $500

estimated life = 8 years

therefore,

depreciation = [tex]\frac{16500 - 500}{8}[/tex] = [tex]\frac{16000}{8}[/tex] = $2000

now,

let the value of car after 'x' years be 'y'

therefore linear equation showing the relation of x and y is

y + 2000x = 16500

The graph of a linear equation is a line.

If c = 0 in a linear equation (so y = mx), then the equation is a proportional linear relationship between y and x.

If c ≠ 0, then y = mx + c is a non-proportional linear relationship between y and x.

here equation is of type,

y = mx +c, thus it is not linear.

also in the equation y = mx +c,

'm' is the slope of line

therefore by comparing the equation,

y +2000x = 16500

y = -2000x + 16500

slope is - 2000

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Answer:

A or 19/5

Step-by-step explanation:

To solve first we isolate are variables so we distubte to get -2y-2+21=3y then we add 2y to the opposite side to get -2+21=5y. Then we add -2+21 to get 19 so are equation is 19=5y. Next we just divide 19 by 5 to get y=(19/5) or option A

Answer:

400.9 m

Step-by-step explanation:

Answer:

67.13°

Step-by-step explanation:

First separate triangles then you use Pythagoras theorem to get the third side and then apply the sine rule

Answer:

Another rational number.

Step-by-step explanation:

For example, [tex]\pi[/tex] is incorrect because It is a irrational number

you must add another rational number to 1/2 to make the sum rational.

Rational number are numbers that can be converted into a fraction.

all natural numbers, whole numbers, integers, are rational.

and all rational and irrational numbers are real numbers

According to the function transformations, the value of h is -2

The complete question is in the attachment

The functions are given as:

[tex]f(x) = (2.5)^x[/tex]

[tex]g(x) = (2.5)^{x-h[/tex]

From the question, we understand that the function f(x) is translated to the left to get g(x)

From the attached graph, we can see that the function h(x) is 2 units to the left of f(x).

This transformation is represented by:

(x, y) => (x + 2, y)

So, we have:

x - h = x + 2

Evaluate the like terms

h = -2

Hence, the value of h is -2

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Answer:H=-2

Step-by-step explanation:

Answer:

-1/11

Step-by-step explanation:

A reciprocal means the reverse of a number. So the numerator becomes a one and the number goes in the denominator (for example 2 becomes 1/2). Or vice versa: the one becomes the denominator and the denominator becomes the numerator (for example 1/2 becomes 2/1 which is 2).

The reciprocal of -1/5 is -5.

The reciprocal of -1/6 is -6.

The sum of both reciprocals: -5 + -6 = -11

The reciprocal of the sum -11 is -1/11.

The value of the composite function f(g(x)) is 5x + 2

Composite functions are functions inside another function. Given the following functions:

f(x) = 5√x+1 - 2

g(x) = x² - 1

Determine the composite function f(g(x))

f(g(x)) = f(x² - 1)

f(x² - 1) = 5√x² - 1+1 - 2

f(x² - 1) = 5√x² + 2

f(x² - 1) = 5x + 2

Hence the value of the composite function f(g(x)) is 5x + 2

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Answer:

D

Step-by-step explanation:

Original area = x * x  =  x^2

New area =   x ( x +3.5) = x^2 + 3.5x    <====the underlined is the increase in area

The pair of equations (c) y = (1 / 6) x + 8 and y = 6x + 4 are not parallel

A linear equation is represented as:

y = mx + b

Where m is the slope of the line

Two lines are said to be parallel if their slopes are the same

i.e. y = mx + b and y = mx + c

Using the above as a guide, the option (c) represents lines that are not parallel, because they do not have the same slope

Hence, y = (1 / 6) x + 8 and y = 6x + 4 are not parallel

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Answer: The answer is x < 5/2 and x > -5.

Step-by-step explanation:

First you need to separate the inequality and keep x on one side to maintain consistency. For instance the problem-

[tex]\frac{5-2x}{3} > 0\\\frac{5-2x}{3} < 5\\[/tex]

Now solve as normal.

*Note: When dividing a side or multiplying a side by a negative number, the sign of the inequality switches (this will be shown when I do the equation if it doesn't make since how I word it).

[tex]5-2x > 0*3\\5-2x < 5*3[/tex]

[tex]-2x > 0-5\\-2x < 15-5[/tex]

[tex]x < \frac{-5}{-2} =x < \frac{5}{2} \\x > \frac{10}{-2} =x > -5[/tex]

So, x < 5/2 and x > -5.

If anything is confusing about the procedure just leave a comment, and I'll try to explain further.

Answer:

56cmsquared

Step-by-step explanation:

if you look clearly at that question that diagram which has the coloured part out of that small square comes a quarter circle.

now take that quarter circle and get its area .

then put a dotted line such that they'll be formation of a triangle in that quarter circle.

then get the area of that quarter triangle in minus it from the area of the quarter circle.

and you'll get the area of 1 shaded part because you had subdivided those shaded parts by the dotted line you had kept earlier in order to emerge with a triangles

after that what multiply what you got by two to get the whole shaded part then finalize by multiplying by two because two shapes were shaded.

good day

If a system of linear equations has exactly one solution then the slopes of both the lines should be different.

Given A system of linear equations has exactly one solution.

Linear equation is a type of equation  when when plotted on the graph gives a straight line. The slope is the ratio of the vertical change to the horizontal change between two distinct points on a line.

let two equations be who have one solution

2x+3y=7

5x+6y=1

solving them

x=7-3y/2

put the value of x in second equation

5(7-3y)/2+6y=1

35-15y/2+6y=1

35-15y+12y=2

-3y=-33

y=11

put the value of y in x=7-3y/2

x=7-3*11/2

x=7-33/2

x=-26/2

x=-13.

There is only one solution which is (-13,11)

Taking equations and convert them into standard form

first

y=7/3-2/3x

second

y=1/6-5/6x

The standard form is y=a+bx where b is slope

from the above equations we can find that the slope of first equation is -2/3 and the slope of second equation is -5/6. In this way we are able to conclude that slopes should be different for one solution.

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Answer:

L1 and L2 are parallel

BAC = 58° as it is given in the question that AB bisects DAC

similarly BCE = y°

angle B = 90° ( from figure)

Y + 58° + 90° = 180 ( angle Sum property of a triangle).

Y + 148° = 180°

Y = 180 - 148

Y = 32°

Answer:

Let the cost price be X

A Sells to B

profit = 20%

= cost price + 20%

= X + 20/100 of X

= 6x/ 5

B sells to C

profit = 25%

= Cost price + + 25%

= cost price + 25%

= 6x/5 + 25/100*6x/5

= 6x/5.+ 3x/10.

= 3x/2

3x/2 = 225.

3x = 450

x = 150.

sp = C. p + profit

S. p - profit = C. p

X - X/5

4x/5

4(150)/5.

120

Answer:

Answer:

x = 12

Step-by-step explanation:

m∠S + m∠T = 180

8x + 7x = 180

15x = 180

x = 12

does this help?

Answer:

470.88 N

Step-by-step explanation:

F = ma

  48 ( 9.81) = 470.88 N      ( 105.958 lbs)

Answer: 1

Step-by-step explanation:

[tex]a-bc=7-2(3)=7-6=\boxed{1}[/tex]

Answer:

24 square units

Step-by-step explanation:

1) the area can be calculated using the formula:

A=0.5*a*h, where a- base, h-height;

2) if a=8, h=6, then the required area is:

A=0.5*8*6=24 [units²].

Answer: 24 square units

Step-by-step explanation:

The base: 8

The height: 6

The area: 8 x 6 / 2 = 24

/ stands for divided by

The height of water increases by 2 inches per minute option first "The height of the water increases 2 inches per minute" is correct.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have given a table:

Time     height

2                8

4               12

6                16

8               20

10              24

The slope of the line = (12-8)/(4-2) = 4/2 = 2

The value of the slope is positive we can say,  the height of water increases as time passes.

Thus, the height of water increases by 2 inches per minute option first "The height of the water increases 2 inches per minute" is correct.

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the answer is A: The height of the water increases 2 inches per minute.

hope this helped :)

Answer:

The answer will be D. 181

Step-by-step explanation:

603 - 422 = 181

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