Solve the equation for solutions over the interval ​[0​°, 360°​).
[tex]tan^{2}x + 7 tanx +8 =0[/tex]

Answers

Answer 1

Answer:

[tex]x=98.13^\circ,135^\circ,278.13^\circ,315^\circ[/tex]

Step-by-step explanation:

[tex]tan^2x+7tanx+8=0,[0^{\circ},360^\circ)[/tex]

[tex]tan^2x+7tanx+8=0[/tex]

[tex]u=tanx[/tex] <-- U-substitution

[tex]u^2+7u+8=0[/tex]

[tex](u+7)(u+1)=0[/tex]

[tex](tanx+7)(tanx+1)=0[/tex] <-- Replace u with tanx

[tex]tanx+7=0[/tex]

[tex]tanx=-7[/tex]

[tex]x=98.13^\circ,278.13^\circ[/tex]

[tex]tanx+1=0[/tex]

[tex]tanx=-1[/tex]

[tex]x=135^\circ,315^\circ[/tex]

Therefore, [tex]x=98.13^\circ,135^\circ,278.13^\circ,315^\circ[/tex]


Related Questions

find the value of the variable in the isosceles triangle. show your work plz

Answers

Step-by-step explanation:

3x-3 = x+5 add 3 on both sides

3x = x+8 subtract x in both sides

2x = 8 divide both sides by 2

x = 4

helppppppppppppppp me

Answers

Answer:

I think it is A hope this helps

Step-by-step explanation:

X=
Y=
Find the values of X and Y

Answers

Answer:x = 50°y = 65°Step-by-step explanation:

We can clearly see that the triangle is an isosceles triangle. This also means that y must equal to 180 - 115. Let's solve.

=> x + y + 180 - 115 = 180=> x + y + 65 = 180

Since 180 - 115 equals 65, this means that y = 65.

=> x + 65 + 65 = 180=> x + 130 = 180=> x = 180 - 130=> x = 50Conclusion:

Therefore, our answers are:

x = 50°y = 65°

Hoped this helped.

[tex]-BrainiacUser1357-[/tex]

The distance between Mr. Tomback’s hometown and NYC is 36 centimeters on a road map. The map scale indicates that 5cm on the map represents 125 kilometers in real life. If Mr. Tomback drives at an average speed of 80 kilometers per hour, then how many hours will it take him to get home from NYC?

Answers

Answer:

First, we need to figure out the number of kilometers.

if 5 cm is equivalent to 125 kilometers in real life this means

1 cm is equivalent to 25 kilometers making the conversion much easier.

36 centimeters multiplied by 25 is 900,  which means in real life the distance between Mr.Tomback's hometown and NYC is 900 kilometers.

900 km ÷ 80 kmh

= 11.25000000

= 11 hours

0.25000000 × 60

= 15.00000000

= 15 minutes

it will take him 11 hours and 15 minutes to get home to NYC

Given p(x) = x4 – 13x2 – 25x – 12.

A) Use long division to determine the remainder when p(x) is divided by (x2 – 4)? Show all of your work for full credit.

B) Use mathematical methods to prove that your quotient and remainder are correct. Show all of your work for full credit.

Answers

Answer:

Below.

Step-by-step explanation:

p(x) = x^4 - 13x^2 – 25x – 12

Long division:

x^2 - 4)x^4 - 13x^2 – 25x – 12( x^2 - 9  <-------- Quotient

           x^4 -  4x^2

Subtract:       -9x^2 -  25x

                     -9x^2  + 36

                                 -25x - 36 - 12

So the remainder is -25x - 48 (Answer).

B)   If the above are correct then:

(x^2 - 4) * quotient + remainder  = the original form of  p(x).

(x^2 - 4)(x^2 -9)  - 25x - 48 = the original p(x).

p(x) = x^4 - 9x^2 - 4x^2 + 36  - 25x - 48

= x^4 - 13x^2 - 25x -12 = original p(x)

                   

Do these ordered pairs represent a function? {(4,1), (5,2), (8,2), (9,8)} *

Answers

Answer:

Yes

Step-by-step explanation:

A function is a set of ordered pairs in which each x-element has only ONE y-element associated with it, but while it may NOT have two y-values assigned to the same x-value, it may have two x-values assigned to the same y-value.

The points (5,2) and (8,2) have the same y value, but their x values are different.  It is a function (there are no values of x for which we have more than one value of y).

From the graph, which statement is correct if x^2 – 13x + 22 ≤ 0?

A) 2 ≤ x ≤ 11
B) –11 ≤ x ≤ –2
C) x ≤ 2 or x ≥ 11
D) x ≥ 2 or x ≤ 11

please only reply if you know the answer!!

Answers

Answer:

a

Step-by-step explanation:

(x-2)(x-11) less than or equal to 0

which means x is between 2 and 11 when it is less than 0

A colony of bacteria is growing at a rate of 50% per hour. If this rate of growth remains the same and the colony starts with 100 bacteria, approximately how many bacteria will there be after 6 hours

Answers

Answer:

1,139.0625

Step-by-step explanation:)

100 BACTERIA to start

1Hour = 50% of the start (which is 100 so half would be 50) this suggest 100+50= 150

2hour = 50% of 150 which is 75 and this suggest

150+75= 225

3 hour = 50% of 225 which is 112.5 this suggest

225+112.5=337.5

4hours = 50% of 337.5 which is 168.75 this suggest

337.5 + 168.75=506.25

5hours = 50% of 506.25 which is 253.125 this suggest

506.25+253.125=759.375

6hours = 50% of 759.375 which is 379.6875 this suggest

759.375+379.6875=1,139.0625

Answer: 1139 bacteria

Which model shows the greater rate of change​

Answers

Answer:

Model B

Step-by-step explanation:

In Model A as x increases by 2 y decreases by 1. So as x increases by 1 y decreases by 0.5 giving us a rate of change of -0.5

In Model B we have a slope of 2/3 (because as x inreases 2 times y increases 3 times)

-0.5 < 2/3

Challenge: The perimeter of a semicircular patio is 35.98 ft. What is its radius? Use 3. 14 for a.
Please Be accurate and explain

Answers

Answer:

  7 ft

Step-by-step explanation:

The circumference of a circle is given by the formula ...

  C = 2πr

The curved portion of a semicircle will be ...

  C/2 = (2πr)/2 = πr

The straight portion of the semicircular shape will be the diameter, or 2r. That means the total perimeter of a semicircular shape is ...

  P = πr +2r = r(π+2)

Then the radius is ...

  r = P/(π+2) = (35.98 ft)/(3.14+2) = 7 ft

The radius of the patio is 7 ft.

Which that is that could be represented by the plot chart shown below?

Answers

Answer:

24 25 26 27 28 29 30 31 32 33 34

Step-by-step explanation:

Mr. Jay sells a box of 15 seedlings for new trees for $12.84. Mr. Tony sells a box of 18 seedlings for $14.95. What is the cost per seedling for each person? Round your answer to the nearest cent (hundredth). Which is the better buy?

Mr. Jay’s cost $____________ per seed. Mr. Tony’s cost $____________ per seed.

Buying a box of seedlings from _____________________ is the batter buy.

Answers

Answer: Mr. Jay’s cost 85 cents and Mr. Tony’s costs 83 cents.

Step-by-step explanation:

you divide the price by how many seeds they sold.

Mean for population data

Answers

Answer:

I need only 5 brainlisted please give me

Step-by-step explanation:

please understand my situation

The polynomial p(x) = 5x^2 – 9x2 - 6x + 8 has a known factor of (x + 1).
Rewrite p(x) as a product of linear factors.

Answers

First, start of by dividing the polynomial given by the linear factor

This will result in a quadratic factor

Factorise the quadratic factor as shown

LAST ATTEMPT IM MARKING AS BRAINLIEST!! (What is the circumference of the circle?)

Answers

Use the pythagorean theorem [tex]a^2+b^2 = c^2[/tex] to plug in a = 8 and b = 6. You should find that the hypotenuse is c = 10. The diameter of the circle is 10 units, which leads to the circumference of [tex]C = 10\pi[/tex]

Answer:  [tex]\boldsymbol{10\pi}[/tex]

QUESTION 13 PLEASE HELP ME ASAPP

Answers

Answer:

option 1 is the best choice

Step-by-step explanation:

for every 5 minutes, the number of toys increases by 2.

Alec invested $1500 in an account with annually compounded interest. The account earns 4% annual interest. How much will Alec have in his account after 4 years?

Answers

Answer:

He will have $1,754.79 in his account after 4 years

Step-by-step explanation:

We can use the compound interest formula to find how much money he will have after 4 years:

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex] ;

where

A= final amount

P= initial amount

r= interest rate

n= number of times interest applied per time period

t= number of time periods elapsed,

so from the given information, we know that 1500 is our initial amount, so P= 1500.

Annual interest means once a year, so n= 1, and the interest rate is 4%, so r= 4% or 0.04

and we are asked to find the amount in his account after 4 years, so t= 4

Now, all we need to do is plug in these values for each of the variables and solve.

[tex]A= 1500(1+\frac{0.04}{1} )^{(1)(4)}[/tex]

and we get

A= $1,754.79

Find the least common multiple of 8y^2 and 7m

Answers

Answer:   [tex]56y^2m[/tex]

which is the same as writing 56y^2m

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

Explanation:

Let's focus on the coefficients 8 and 7 for now.

To find the LCM of those values, list out the multiples. Circle the smallest number that can be found in both sets at the same time.

multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, ...multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56, 63, ....

We see that 56 is the LCM of 7 and 8.

Or you could use this shortcut

LCM = (x*y)/GCF

where x and y are the two numbers. The mention of "GCF" refers to the GCF of x and y. In this case, the GCF is 1 so,

LCM = (x*y)/GCF = (8*7)/1 = 8*7 = 56.

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

Once we determine that, we look at the variable terms now.

The y^2 and m will be tacked onto the 56 to arrive at the final answer 56y^2m

This is because y and m are the unique variables, and we go for the highest exponent of each. It's similar to the LCM formula used earlier.

Can you please help me I am stuck on a math problem

Question

6/4 x 9/12=

What is the answer

Answers

Answer:

Step-by-step explanation:

Formula

(numerator * numerator ) divided by (denominator * denominator)

Numerator * numerator = 6*9 = 54

Denominator * denominator = 4 * 12 = 48

The answer is 54 / 48 = 9/8 = 1 1/8

Both numerator and denominator can be divided by 6

Using y = 1 − 2x, plot the ordered pairs from the table. Then graph the function represented by the ordered pairs and tell whether the function is linear or nonlinear.
Helppp plzz due in 20 min

Answers

I think therefore its a linear function

Explain how to use the distributive property to find the product (3) (4 1/5) ​

Answers

Answer:

you didn’t answer my question correctly :(

Step-by-step explanation:

Find the 11th term of the arithmetic sequence 10,-40,160,….

Answers

Answer:

10,485,760

Step-by-step explanation:

Multiply -4

why do these sisters have different traits?

Answers

Answer: because dna is  game of chance

Step-by-step explanation: hope it helps

Because there are thousands of different gene codes

I have 100 points
i need some help!!

Answers

Answer:

6c+2(5-7c)=6c+10-14c

=10-8c=-8c+10

A. -8c+10 is correct option.

Thanks :)

1/5 of 400 showing work

Answers

1/5 of 400 = 80
400 x 1/5 = 400/5
400/5 = 80

aproxima a las unidades de mil y obtén los resultados estimados

Answers

Answer:

hi

Step-by-step explanation:

To check out a customer, a grocery store cashier needs 2 seconds to scan each item being purchased, as well as 30 seconds to process payment. If it takes 44 seconds to ring up a particular customer, how many items is the customer purchasing?

Answers

Answer:

7

Step-by-step explanation:

Let's say the customer has x items. For each item, we add 2 seconds. For 3 items, we need 2 + 2 + 2 = 2*3 seconds. For x items, we need 2 * x seconds. Then, we add the processing payment time of 30 seconds, so for x items, the total amount of time = 30 + 2 * x

Here, the total amount of time is 44, so we have

44 = 30 + 2x

subtract 30 from both sides to isolate the variable and its coefficient

14 = 2x

divide both sides by 2 to isolate x

x = 7

Can someone help me find w and X for my parallelogram ?? Will mark brainiest :)

Answers

Answer:

5x+3x=8x, 6w+2w=8w is the answer

Which algebraic expression is equivalent to the expression below?

3/5x-7/5y

Answers

Answer:

455554444444555556555555554444

Captain Brewster captured a pack of aliens. The following data points represent the lengths of each of the aliens' big toes (in centimeters). 18, 16, 17, 17, 16, 15, 16. Using this date, create a dot plot where each dot represents a big toe.

Answers

Answer:

15 ·

16 ···

17 ··

18 ·

19

Step-by-step explanation:

There were 2 aliens that each have big toes measuring 17 cm long. So, the 17 would have 2 dots above it:

17 ··

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