Stop light A changes color every 45 seconds and Stop light B changes color every 80 seconds. Both Stop lights just changed. After how many seconds will the stoplights change color at the same time?

The threes solutions to the given equation sec²x - secx = 2 are:

To solve: sec²x - secx = 2 on interval [0,2[tex]\pi[/tex])

When we set t = sec x, we get the quadratic equation:

As a result, we must seek solutions to the equations:

[tex][1] \sec x=2: \quad \cos x=\frac{1}{2} \rightarrow x_1=\frac{\pi}{3} ; \quad x_2=\frac{5 \pi}{3} ;$\\\text { [2] } \sec x=-1: \quad \cos x=-1 \rightarrow x_3=\pi ;[/tex]

Therefore, the three solutions are:

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The correct question is given below:
solve the equation sec²x - secx = 2 on interval [0,2[tex]\pi[/tex])

Answer:

Step-by-step explanation:

Compute the midpoint of the line segment with endpoints:

p_1 = (-4, 4) and p_2 = (5, -1)

The midpoint between (x_1, y_1) and (x_2, y_2) is their componentwise average:

((x_1 + x_2)/2, (y_1 + y_2)/2)

Substitute (x_1, y_1) = (-4, 4) and (x_2, y_2) = (5, -1):

= ((-4 + 5)/2, (4 - 1)/2)

-4 + 5 = 1:

= (1/2, (4 - 1)/2)

4 - 1 = 3:

Answer:  = (1/2, 3/2)

The sum to infinity of the sequence is 96/13

Given the nth term of a geometric sequence expressed as:

Tn = Σ12(-5/8)^n

The sum to infinity of the sequence is expressed as;

S∞ = a/1-r

where

a is the first term = 12

r is the common ratio = -5/8

Substitute

S∞ =  12/1-(-5/8)

S∞ = 12/1+5/8

S∞ = 12/(13/8)

S∞ =12 *8/13

S∞ = 96/13

Hence the sum to infinity of the sequence is 96/13

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Answer:

Choice a) 3700 €

Step-by-step explanation:

Total salary among 12 workers = Avg Salary x 12 = 3500 x 12 = 42,000 €

Total salary of 2 part-timers = part-time avg x 2 = 2500 x 2 = 5000

Total salary without part-timers salary= 42,000 - 5000 = 37,000 €

If we exclude the 2 part-timers, there are 10 full-timers who earn 37,000 €

So new Average Salary = 37000/10 = 3,700 €

answer: Choice a) 3700 €

The population variance ad standard deviation are 64 and 8 respectively.

The variance for a population is calculated by the below steps :

1) First find the mean (the average).

2) Subtracting the mean from each number in the data set and then    squaring the result. The results are squared to make the negatives value positive

3) Averaging the squared differences.

Here, the data set of population is given as :

population difference difference²

6                  -12                   144

12                 -6                     36

20                 2                       4

24                 6                     36

28                 10                  100

₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋₋

∑ 90                                  ∑ 320

Now, the average population will be :

∑ 90/5 = 18

Now finding the variance σ² using the formula :

σ² = ∑(x- x')²/N

σ² = 320/5

σ² = 64

Now, the standard deviation σ will be :

standard deviation = √σ²

standard deviation = √64

standard deviation = 8

Therefore, the population variance ad standard deviation are 64 and 8 respectively.

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1) When k = 1.5 and x = 50, the value of y is; y = 75

2) When k = 14 and y = 334, the value of x is; x = 23.84

3) When k = 12 and x = 245, the value of y is; y = 2940

4) When k = 16 and y = 38, the value of x is; x = 2.375

We are given the equation for the constant of proportionality, as y/x = k

1) When k = 1.5 and x = 50, we want to find the value of y = ?

y/50 = 1.5

y = 50 * 1.5

y = 75

2) k = 14 and y = 334, x = ?. We want to find the value of x. Thus;

334/x = 14

x = 334/14

x = 23.84

3) k = 12 and x = 245, y = ?

y/245 = 12

y = 245 * 12

y = 2940

4) k = 16 and y = 38; x = ?

38/x = 16

x = 38/16

x = 2.375

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Complete question is;

Solve for the unknown value using the equation for the constant of proportionality, y/x = k .Known Values​ Unknown Value​

k = 1.5 and x = 50

y = ?

k = 14 and y = 334, x = ?

k=12 and x=245, y = ?

k = 16 and y = 38; x = ?

p = (n - 30)/ 6 as a function of n.

Here we need to find the value of p in terms of n.

From the question, we have two equation

The first equation is:

   m = 1/6n .......(1)

The second equation is:

    p = m - 5.......(2)

From equations 1 and 2 we have to find the value of p in term of n.

So by putting the value of m in the second equation we have:

p = 1/6n - 5

  = (n - 30)/6

Therefore we get the value of p as (n -30)/6 in terms of n.

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adding a negative is the same as subtracting a positive

the expression -6+ (-2) is the same as -6-2 which is -8

Answer: Slope = 7/6

Step-by-step explanation:

The slope of the line -1/6.

The value of m = -1.

The slope of a line is a measure of its steepness. slope is calculated as "rise over run" (change in y divided by change in x).

given:

f(x) = √10-x

let f(x)=y

y = √10-x

Now,

dy/dx = -1/2(√10-x)

at x=1

dy/dx =  -1/2(√10-1)

dy/dx = -1/2(3)

dy/dx = -1/6

equation of line is

y= mx + b

y= (-1/6)x + b

6y = -x + b

So, m= -1

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Step-by-step explanation:

|2|=2

Hope this helps !!!!

Answer:

The absolute value is 2

Step-by-step explanation:

The absolute value is defined by how far a value is from zero and it is represented by a / /

/2/ = 2

Answer:

the answer is B

Step-by-step explanation:

x = y - 9

y - 4 = 10

x = ?

y = 10 + 4

° y = 14

x = y - 9

= 14 - 9

✔️ x = +5

ANSWERS

y-4=10

y=10+4

y=14

sub y equ 1

x=14-9

x=+5

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

Value of g (x) is -2, when :

[tex]\qquad \sf  \dashrightarrow \: - 2.5 < x \leqslant - 1.5[/tex]

And since -2 lies in this range of x,

[tex]\qquad \sf  \dashrightarrow \:g( - 2) = - 2[/tex]

Value of x is -1, when :

[tex]\qquad \sf  \dashrightarrow \: - 1.5 < x \leqslant - 0.5[/tex]

And -0.5 falls in this range, hence

[tex]\qquad \sf  \dashrightarrow \:g( - 0.5 ) = - 1[/tex]

Next, The value of x is 0 when :

[tex]\qquad \sf  \dashrightarrow \: - 0.5 < x < 0.5 [/tex]

But, it isnt equal to 0.5, since there is open interval at both extremes.

Next, Value of x is 1, when :

[tex]\qquad \sf  \dashrightarrow \:0.5 \leqslant x < 1.5[/tex]

And since it also has the value 0.5 included in it,

[tex]\qquad \sf  \dashrightarrow \:g(0.5) = 1[/tex]

Answer:

653209

Step-by-step explanation:

Because i did this already

The correct option is M(2) = 39; If Hazel mows a yard for 2 hours, she will earn $39 . Option C

A function can be defined as an expression that shows the relationship between an independent variable and a dependent variable.

Given the function;

M(t) = 7t + 25

Where;

For M(2), we substitute the value of t as 2 in the function

M(2) = 7(2) + 25

M(2) = 14 + 25

M(2) = $39

This explains that the she mows the yard for t = 2 hours, she would earn $39

Thus, the correct option is M(2) = 39; If Hazel mows a yard for 2 hours, she will earn $39. Option C

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Answer:

x=142°

Step-by-step explanation:

hope it helps ⁄(⁄ ⁄•⁄ω⁄•⁄ ⁄)⁄

Answer:

E

Step-by-step explanation:

2018 :   75 000 pines

2019 :     2000 pines / km^2  *  30 km^2 = 60 000 pines

(75 000 - 60 000) / 75 000 = .2        or 20 %  

Answer:

Both factors are negative,so that the product will be positive

Step-by-step explanation:

Hope it helps you

From the given examples 5z - 3x = -3x + 5z  and 5(xy) = 5(xy) are following the commutative property.

According to the given question.

We have some equations

2x + 3x = 5x

5xy = 5(xy)

5z - 3x = -3x + 5z

3(a + b) = 3a + 3b

Here, we have to find which equation is following the commutative property.

As we know that, the commutative property is a math rule that says that the order in which we multiply numbers does not change the product.

For, example 4 + 5 gives 9, and 5 + 4 also gives 9.

From the given example the equation

5z - 3x = -3x + 5z is following the commutaive property of addition.

And, 5(xy) = 5(xy) is following the commutative property of multiplication.

Hence, from the given examples 5z - 3x = -3x + 5z  and 5(xy) = 5(xy) are following the commutative property.

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A point that is part of the intersection of planes ACD and MHG is: Point B.

A plane has at least three points that lie on it. When two planes intersect, they do so at some certain points. This means that two intersecting planes share some points in common alone the line of their intersection.

In the diagram given, plane ACD and plane MHG intersect along line BA. This means that both planes share points A and B in common.

Therefore, we can state that a point that is part of the intersection of planes ACD and MHG is: Point B.

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Answer: 1680ml

Step-by-step explanation:

1000 mL are in 1 L, so with that logic

1=1000

.68=680

1000+680=1680

Answer:

it d

Step-by-step explanation:

Answer:  [tex](5.6)^3[/tex]

This is the same as saying (5.6)^3

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

Explanation:

The base is 5.6 and it is multiplied a total of 3 times. We use an exponent of 3 to condense things down. So [tex]5.6 * 5.6 * 5.6 = (5.6)^3[/tex]

Another example: [tex]2^4 = 2*2*2*2 = \text{four copies of '2' multiplied}[/tex]

Answer:

Step-by-step explanation:

annie runs in park = every 3 days

ron runs in park = every 5 days

lets find LCM of 3 and 5 = 3*5 = 15

if they ran on 1st of January then they will meet again on on 15th January , will again meet on 30th of January and will again meet on 14 February . if is was a leap year they would again meet at 29th February .

Answer:

D. ∠1 and ∠3

Hope this helps!

Answer:

1 and 3 or also known as D

Step-by-step explanation:

i took the test and got it right

Using the it's formula, the total opportunity cost of three unit(s) of tanks is of 350 autos.

The opportunity cost formula is given by:

C = F - A.

In which:

For this problem, we have that:

Thus:

F = 1000 - 650 = 350.

The total opportunity cost of three unit(s) of tanks is of 350 autos.

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Step-by-step explanation:

A=Xb c

2+4=6

5+5=10

9+20=75

Answer:

ab=20 bc=16+4=20 ac=40