1
Select the correct answer.
Which expression is equivalent to sec2xcot?x?
O A Sin?x
O B. cScZx
OC. (1)/(cos^2x)
OD. (1)/(tan^2x)

To Find :

The value of side CD.

Solution :

Applying Pythagoras theorem in ΔABC :

[tex]AC^2 + CB^2=AB^2 \\\\AC^2 + CB^2 = 13^2[/tex]     ....1)

Applying Pythagoras theorem in ΔACD and ΔCDB :

[tex]AD^2 + CD^2 = AC^2[/tex]     ....2)

[tex]CD^2 + DB^2 = CB^2[/tex]     ....3)

Adding equation 2 and 3, we get :

[tex]AC^2 + CB^2 =AD^2 + 2CD^2 + DB^2[/tex]   ...4)

Solving equation 1) and 4), we get :

[tex]AD^2 + 2CD^2 + DB^2 = 13^2\\\\9^2 + 2CD^2 + ( 13 - 9 )^2 = 13^2\\\\2CD^2 = 72\\\\CD = 6[/tex]

Therefore, length of CD is 6 .

tan(2A) + sin(2A) = sin(2A)/cos(2A) + sin(2A)

• rewrite tan = sin/cos

… = 1/cos(2A) (sin(2A) + sin(2A) cos(2A))

• expand the functions of 2A using the double angle identities

… = 2/(2 cos²(A) - 1) (sin(A) cos(A) + sin(A) cos(A) (cos²(A) - sin²(A)))

• factor out sin(A) cos(A)

… = 2 sin(A) cos(A)/(2 cos²(A) - 1) (1 + cos²(A) - sin²(A))

• simplify the last factor using the Pythagorean identity, 1 - sin²(A) = cos²(A)

… = 2 sin(A) cos(A)/(2 cos²(A) - 1) (2 cos²(A))

• rearrange terms in the product

… = 2 sin(A) cos(A) (2 cos²(A))/(2 cos²(A) - 1)

• combine the factors of 2 in the numerator to get 4, and divide through the rightmost product by cos²(A)

… = 4 sin(A) cos(A) / (2 - 1/cos²(A))

• rewrite cos = 1/sec, i.e. sec = 1/cos

… = 4 sin(A) cos(A) / (2 - sec²(A))

• divide through again by cos²(A)

… = (4 sin(A)/cos(A)) / (2/cos²(A) - sec²(A)/cos²(A))

• rewrite sin/cos = tan and 1/cos = sec

… = 4 tan(A) / (2 sec²(A) - sec⁴(A))

• factor out sec²(A) in the denominator

… = 4 tan(A) / (sec²(A) (2 - sec²(A)))

• rewrite using the Pythagorean identity, sec²(A) = 1 + tan²(A)

… = 4 tan(A) / ((1 + tan²(A)) (2 - (1 + tan²(A))))

• simplify

… = 4 tan(A) / ((1 + tan²(A)) (1 - tan²(A)))

• condense the denominator as the difference of squares

… = 4 tan(A) / (1 - tan⁴(A))

(Note that some of these steps are optional or can be done simultaneously)

Answer:

1. No solution

2. Infinite many solutions

3. One solution

4. No solution

5. No solution

6. One solution

7. No solution

8. One solution

9. Infinite many solutions

10. Infinite many solutions

Step-by-step explanation:

Answer: 22 mor packages.

Give me brainlyest please.

Step-by-step explanation:

Answer:

a=22.478

Step-by-step explanation:

Answer:

Angle DE = 11

Step-by-step explanation:

DE = DF

8x + 3 = 6x + 5

8x = 6x + 5 - 3

8x - 6x = 2

2x = 2

2x/2 = 2/2

x = 1

DE = 8x + 3

DE = 8(1) + 3

DE = 8 + 3

DE = 11

Hope this helps

Answer:

The answer is 6x -7y = 21

Step-by-step explanation:

Im taking the diagnostic

Answer: I it’s D

Step-by-step explanation:I did the assignment

Hey,

The answer is 55

I wrote the solution, you can look.

Good luck :)

Answer:

26.

Step-by-step explanation:

1 day/24 hours, makes 4 revolutions.

4 x 6 = 24,

1/2 of 4 = 2.

24+2 = 26.

26 revolutions, if my answer is wrong someone please correct me.

Answer:

C

Step-by-step explanation:

The domain of the given function is  {–2, 0, 2} while range is {4, 0} so option (C) will be correct.

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

Given the function,

An arrow goes from negative 2 to 4, 0 to 0, and 2 to 4.

So,

-2 → 4 , 0 → 0 and 2 → 4

Since the domain is a set of input values here input is -2,0 and 2.

So

Domain = {-2,0,2}

And the range is a set of output values here output is 4, 0

So,

Range = {4,0}

Hence "The domain of the given function is  {–2, 0, 2} while range is {4, 0}".

For more details about the range and domain of the function,

brainly.com/question/28135761

#SPJ2

Answer: x₁=7, x₂=-1

Step-by-step explanation:

(x-3)^2= x^2-6x+9

2(x^2-6x+9)=28+4

x^2-6x+9=16

x^2-6x-7=0

you use the quadratic equation will give you 2 roots,

x₁=7, x₂=-1

Answer: Y = e^2

The steps are shown in the picture!

Answer:

Mario brought 5 magazines

Step-by-step explanation:

If you just add $12.60 and $2.25 together then keep adding $2.25 until you get to $23.85, you'll get your answer.

So like,  

(1) 12.60 + 2.25 = 14.85

(2) 14.85 + 2.25 = 17.1

(3) 17.1 + 2.25 = 19.35

(4) 19.35 + 2.25 = 21.6

(5) 21.6 + 2.25 = 23.85  

So the total would be 5. Mario bought 5 magazines.

Answer:

$6.08

Step-by-step explanation:

8% = 0.08

76 × 0.08

= $ 6.08

Answer: 1. 4

2. 12

3. 6

4. 8

Step-by-step explanation:

Answer:

it helps us to add faster bc we can regroup numbers when we add. in the associative property, the order of the numbers don't change, only the grouping does

Step-by-step explanation:

Answer:

Did you know that the associative property can help us solve problems faster? ... According to the associative property, we can regroup the numbers when we add, and we can regroup the numbers when we multiply.

Step-by-step explanation:

There are nine campers in total. There are five boys in the camp. Here are the details:

Ratio: 5:9

Fraction: 5/9

Decimal: 0.5555...........

Percentage: 56%

Hope this helped! Have a wonderful Day! :D

Answer:

[tex]5y=-x+23\\[/tex]

Step-by-step explanation:

Since the equation of the line is perpendicular to the line y = 5x +6

we can use the formula:

[tex]m_1m_2=-1\\[/tex]

where m1 is the slope of the line we have and,

m2 is the slope of the line we need

so here m1 is 5 as we compare it with the slope-intercept form our slope is:

[tex]y=5x+6\\y=mx+b[/tex]

our m1 is 5 but we need m2 so plugging in the value we get m2 to be:

[tex]m_1m_2=-1\\5m_2=-1\\m_2=-1/5\\[/tex]

and now we have our m2, now furthermore since the line passes through the point (-2 , 5) it means the point must lie on the line and satisfy it. We can use this point and the slope m2 and find out the equation by the point-slope form equation:

[tex]y-y_1=m(x-x_1)\\y-5=-\frac{1}{5}(x-(-2))\\\\5(y-5)=(-1)(x+2)\\5y-25=-x-2\\5y=-x-2+25\\5y=-x+23\\[/tex]

Answer:

$75

Step-by-step explanation:

$15 divided by 0.2 = $75

0.2 = 20%

Given:

Blue car travels [tex]44\dfrac{1}{2}[/tex] miles on [tex]1\dfrac{1}{4}[/tex] gallons of gasoline.

Red car travels [tex]20\dfrac{4}{5}[/tex] miles on [tex]\dfrac{4}{5}[/tex] gallons of gasoline.

To find:

The unit rate for miles per gallon for each car and find which car could travel the greatest distance on one gallon of gasoline.

Solution:

We know that,

[tex]\text{Unit rate}=\dfrac{\text{Total distance covered by the car}}{\text{Number of gallons of gasoline}}[/tex]

Using this formula, the unit rate of blue car is

[tex]\text{Unit rate of blue car}=\dfrac{44\dfrac{1}{2}}{1\dfrac{1}{4}}[/tex]

[tex]\text{Unit rate of blue car}=\dfrac{\dfrac{88+1}{2}}{\dfrac{4+1}{4}}[/tex]

[tex]\text{Unit rate of blue car}=\dfrac{89}{2}\times \dfrac{4}{5}[/tex]

[tex]\text{Unit rate of blue car}=\dfrac{178}{5}[/tex]

[tex]\text{Unit rate of blue car}=35.6[/tex]

Unit rate of red car is

[tex]\text{Unit rate of red car}=\dfrac{20\dfrac{4}{5}}{\dfrac{4}{5}}[/tex]

[tex]\text{Unit rate of red car}=\dfrac{\dfrac{100+4}{5}}{\dfrac{4}{5}}[/tex]

[tex]\text{Unit rate of red car}=\dfrac{104}{5}\times \dfrac{5}{4}[/tex]

[tex]\text{Unit rate of red car}=26[/tex]

Therefore, the unit rate of blue car is 35.6 miles per gallon of gasoline and  unit rate of red car is 26 miles per gallon of gasoline.

Since, unit rate of blue car is greater than the red car, therefore blue car travel the greatest distance on one gallon of gasoline.

Given:

A line passes through (-2,-6) and has a slope of [tex]\dfrac{1}{3}[/tex].

To find:

The point slope form of the given line.

Solution:

If a line passes through a point [tex](x_1,y_1)[/tex] with slope m, then the slope intercept form of the line is

[tex]y-y_1=m(x-x_1)[/tex]

The line passes through (-2,-6) and has a slope of [tex]\dfrac{1}{3}[/tex]. So, the point slope form of the line is

[tex]y-(-6)=\dfrac{1}{3}(x-(-2))[/tex]

[tex]y+6=\dfrac{1}{3}(x+2)[/tex]

Therefore, the correct option is A.

Answer:

14

Step-by-step explanation:

When you sqaure a number you multiply it by itself once so it would be (3x3) + 5. Rmemeber PEMDAS, so you multiply 3x3 first to get 9 and then you add 5 to get 14.

Answer:

200

Step-by-step explanation:

because,they said that they

Answer:

a) tan x = 1

b) tany = 4 + tanx /2tanx - 3

Step-by-step explanation:

a) Given the equation

2(sinx + 2cosx) = sinx +5cosx

Open the bracket

2sinx + 4cosx =  sinx +5cosx

Collect like terms

2sinx - sinx = 5cosx - 4cosx

sinx = cos x

Divide both sides by cos x

sinx/cosx = cosx/cosx

tanx = 1

Hence the value of tan x is 1

b) Given the expression

sinxcosy + 3cosxsiny = 2sinxsiny - 4cosxcosy

We are to express tany in terms of tan x

Divide through by cosx cosy

sinxcosy/cosx cosy + 3cosxsiny/cosx cosy = 2sinxsiny/cosx cosy - 4cosxcosy/cosx cosy

sinx/cosx + 3siny/cosy = 2tanxtany - 4

tanx +3tany =  2tanxtany - 4

Collect like terms

tanx - 2tanxtany = -4 - 3tany

- 2tanxtany+3tany = -4 - tanx

tany (-2tanx+3) = -4 - tanx

tan y = -4 - tanx/-2tanx+3

tan y = -(4+tanx)/-(2tanx-3)

tany = 4 + tanx /2tanx - 3

Hence the function of tany in term of tan x is tany = 4 + tanx /2tanx - 3

Answer:

DFBG

Step-by-step explanation:

At any point in time;

slope m = (y2-y1)/(x2-x1)

1. (3,19) and ((-1,-13)

m = (-13-19)/-1-3 = -32/-4 = 8

Letter here is D

2. we pick out two points to use here from the line

These are ((0,1) and (2,5)

Slope is ;

(5-1)/2-0 = 4/2 = 2

Letter here is F

3. We pick any two points

(1,-8) and (4,-32)

slope =

(-32 + 8)/4-1 = -24/3 = -8

Letter here is B

4. Slope = 8 + 10/0-9 = 18/-9 = -2

letter here is G

Answer:

1,6,8

Step-by-step explanation:

Answer:

11 % of 3rds into 8

Step-by-step explanation:

Answer:

8100

Step-by-step explanation:

printed price = $7500

sales tax = 8%

selling price of DVD

= 7500 + 8% of 7500

= 7500 + 600 = $8100

Answer: DVD was sold for $8100

Step-by-step explanation:

hlejsjsisjdjsisjsjsjsjsjsisjsnsjssjjsjsjs as

Answer:

13. The measure of a is 35°

14. The measure of b is 74°

15. The measure of c is 66°

Step-by-step explanation:

In the given figure

13.

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ 33° + 112° + a = 180°

→ Add the like terms in the left side

∴ 145° + a = 180

→ Subtract 145° from both sides

∵ 145° - 145° + a = 180° - 145°

∴ a = 35°

14.

∵ a, 71° and b formed a straight line

∵ The sum of the measures of the linear angles is 180°

∴ a + 71° + b = 180°

→ Substitute the value of a

∴ 35° + 71° + b = 180°

→ Add the like terms in the left side

∴ 106° + b = 180°

→ Subtract 106° from both sides

∵ 106° - 106° + b = 180° - 106°

∴ b = 74°

15.

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ 43° + 71° + c = 180°

→ Add the like terms in the left side

∴ 114° + c = 180°

→ Subtract 114° from both sides

∵ 114° - 114° + c = 180° - 114°

∴ c = 66°