Amy is traveling across the USA by train over the summer. She is keeping track of all of the stops on her trip. She has just completed stop 8 and the map shows she is 20% complete. How many total stops are on her trip?

[tex]2 \sec^2 x = 3- \tan x \\\\\implies 2(1 +\tan^2 x) = 3- \tan x \\\\\implies 2 + 2 \tan^2 x +\tan x -3 =0\\\\\implies 2 \tan^2 x + \tan x -1 =0\\\\\implies 2u^2 + u -1 =0~~~ ;[\text{set} \tan x = u]\\\\\implies u = \dfrac{-1\pm \sqrt{1-4\cdot 2 \cdot (-1)}}{2(2)}\\\\\implies u =\dfrac{-1 \pm\sqrt{9}}{4}\\\\\implies u = \dfrac{-1 \pm 3}{4}\\\\\implies u = \dfrac{2}{4}=\dfrac 12~~ \text{or} ~~u =\dfrac{-4}{4} =-1\\\\[/tex]

[tex]\implies \tan x = \dfrac 12 ~~ \text{or} ~~ \tan x =-1~~~ ;[\text{Substitute back u =tan x}]\\\\\text{Now,}~ \\\\\tan x = -1,\\\\\implies x = n\pi - \dfrac{\pi}4\\\\\\\text{For interval,}~ [0,2\pi) \\\\x = \dfrac{3\pi}4, \dfrac{7\pi}4\\\\\text{In degrees,}~ x = 135^{\circ}, x =315^{\circ}\\\\\tan x = \dfrac 12\\\\\implies x = n\pi + \tan^{-1} \left(\dfrac 12 \right)\\\\\text{For interval} ~[0,2\pi),\\\\[/tex]

[tex]x=\tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\text{in degrees,} ~~x=\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\\\\text{Combine all solutions:}\\\\x=\dfrac{3\pi}4, \dfrac{7\pi}4, \tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\[/tex]

[tex]\text{In degrees,}~ x = 135^{\circ},~315^{\circ},~\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right][/tex]

Answer:

30 pancakes/6 pancakes = 5, so Sanjay needs to multiply the recipe by 5 (make batches of 6 pancakes 5 times for 30 pancakes in total)

flour: 135g*5=675g

baking powder: 1 tsp*5=5 teaspoons

sugar: 2 tbsps*5=10 tablespoons

milk: 130ml*5=650ml

eggs: 1 egg*5=5 eggs

oil: 2 tbsps*5=10 tablespoons

[tex]a(n) = {n}^{2} + 3[/tex]

Answer:

nth term is equal to n²+3

Answer:

16 minutes

Step-by-step explanation:

First we are going to want to find the area of the window. We then divide that by the amount of area you can wash per minute ( 6 square feet )

So first lets find the area.

We are told that the window is in a shape of a trapezoid.

The area of a trapezoid can be calculated using the formula A = [tex]\frac{a+b}{2} h[/tex]

Where a and b are the base lengths and h is the height

We are told that the length of the bases are 10 ft and 14ft so a and b = 10 and 14. We are also told that the window has a height of 8 so h = 8 .

We then plug these numbers into the formula to find the area

Recall formula: [tex]A=\frac{a+b}{2} h[/tex]

a = 10 , b = 14 and h = 8

plug in these values into formula

[tex]A=\frac{10+14}{2} 8[/tex]

add 10 and 14 to get 24

[tex]A=\frac{24}{2} 8[/tex]

simplify fraction : 24 / 2 = 12

[tex]A=(12)(8)[/tex]

multiply 12 and 8 to get 96.

A = 96 square feet.

To find how long it would take to wash the window we divide the total area of the window by the amount of area that can be washed per minute

Total area of window = 96

Area that can be washed per minute = 6

Time it would take to wash the whole window = 96 / 6 = 16 minutes

Answer:

The momentum for the truck and cargo is 150000 kg·km/h

Step-by-step explanation:

p = mv

p = (2000 kg + 1000 kg)(50 km/h)

p = (3000 kg)(50 km/h)

p = 150000 kg·km/h

Answer:

Step-by-step explanation:

The amount of the discount is ...

  20% of $70 = 0.20·$70 = $14 . . . discount

The discounted amount is ...

  $70 -14 = $56 . . . discounted price

The scale factor is 1.5 because:

9 x 1.5 = 13.5

5 x 1.5 = 7.5

Answer:

(a): 10 civil servants who were absent.

(b): 15 civil servants are in field only.

Step-by-step explanation:

Let;

[tex]{ \rm{ \sum(n) = 90}} \\ \\ { \rm{n(o) = 65}} \\ \\ { \rm{n(f) = 50}} \\ \\ { \rm{(o \: { \huge{n}} \: f) = 35}}[/tex]

Question (a):

Let the absentees be x

[tex]{ \rm{x + (65 - 35) + (50 - 35) + 35 = 90}} \\ \\ { \rm{x + 80 = 90}} \\ \\ { \rm{x = 10}}[/tex]

There are 10 absentees.

Question (b):

Servants in field only;

[tex]{ \rm{n(f \: only) = 50 - 35}} \\ \\ { \rm{n(f \: only) = 15 \: servants}}[/tex]

Answer:

Simplify x+1-2x+1−2 to x-1x−1.

x-1=4

x−1=4

2 Add 11 to both sides.

x=4+1

x=4+1

3 Simplify 4+14+1 to 55.

x=5

x=5

Add 11 to both sides.

x=2+1

x=2+1

2 Simplify 2+12+1 to 33.

x=3

x=3

Answer:

(16+25)×47

Step-by-step explanation:

..........

Answer:

  C = 18

Step-by-step explanation:

Put the numbers in place of their symbols and do the arithmetic. The diagram is showing you r = 3.

  C = 2πr

  C = 2(3)(3) . . . . . using 3 for π, as directed

  C = 18

[tex]\huge\bf\underline{\underline{\pink{A}\orange{N}\blue{S}\green{W}\red{E}\purple{R:-}}}[/tex]

Here we've been provided with the information given that radius (r) = 3.

And we have to find the circumference (c) of circle. And we have been provided with the formula i.e C = 2πr.

Placing (π = 3) in the above equation,

[tex]:\implies\tt{c = 2\pi r}[/tex]

[tex]:\implies\tt{c = 2 \times 3 \times 3}[/tex]

[tex]:\implies\tt{c = 6 \times 3}[/tex]

[tex]:\implies\tt{c = 18}[/tex]

Answer:

y = [tex]\frac{1}{2}[/tex] x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 2x + 8 ← is in slope- intercept form

with slope m = - 2

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex] , then

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

To find c substitute (6, - 1 ) into the partial equation

- 1 = 3 + c ⇒ c = - 1 - 3 = - 4

y = [tex]\frac{1}{2}[/tex] x - 4 ← equation of perpendicular line

Answer:

x = ±[tex]\sqrt{7}[/tex] - 5

Step-by-step explanation:

x^2 - 10x = -18

x^2 - 10x + 18 = 0

(x + 5)^2 - 5^2 + 18 = 0

(x + 5)^2 - 7 = 0

(x + 5)^2  = 7

[tex]\sqrt{(x + 5)^2}[/tex] [tex]=[/tex] ±[tex]\sqrt{7}[/tex]

x = ±[tex]\sqrt{7}[/tex] - 5

Answer:

The answer is 1

Step-by-step explanation:

p² + p + 1; p = -1

Now, Put p = - 1

p² + p + 1

(-1)² + (-1) + 1

1 - 1 + 1 = 1

Thus, The answer is 1

-TheUnknownScientist 72

Hey there!

p(p^2 + p + 1)

= -1(-1^2 + (-1) + 1)

= -1(-1^2 - 2 + 1)

= -1(-1^2) - 1(-2) - 1(1)

= 1 + 2 - 1

= 3 - 1

= 2

Therefore, your answer should be: 2

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer: 63

Step-by-step explanation:

[tex]a_4=-1+8^8\\a_4=63[/tex]

Answer:

Top right

Step-by-step explanation:

The change in y must be constant. 11-13 = 2, 11-9 = 2, 9-7 = 2

Answer:

69 degrees

Step-by-step explanation:

yeah

Answer:

B

Step-by-step explanation:

3(x +1) =3x +3

Plug it in

3(5+1)=3(5)+3

3(6)=15+3

18=18

Answer:

answer is attached on the photo

Answer:

3 3/4 = 15/4

Step-by-step explanation:

To turn a mixed number into an improper fraction, multiply the whole number with the denominator of the proper fraction. Add the numerator of the proper fraction to this product to obtain the numerator of the improper fraction.

Hoped this helped.

We must see which thing would make the conditional statement a false statement. We will see that the correct option is:

"You go to the gym for an hour a week and lose 7 pounds in a month"

So we start with the conditional statement:

"If you go to the gym for an hour a week, then you will lose at least 10 pounds in a month"

Remember that the general conditional statement is:

Where P is the hypothesis and Q is the conclusion.

The conditional statement is false if:

P is true and Q false.

So the given statement is only false if you meet the hypothesis (you go to the gym for an hour a week) but not the conclusion (you lose less than 10 pounds in a month).

With that in mind, the correct option is the third one, the only one where you lose less than 10 pounds in a month.

"You go to the gym for an hour a week and lose 7 pounds in a month"

If you want to learn more about conditional statements, you can read:

https://brainly.com/question/10714086

[tex]\dfrac{10}{1+2i}\\\\\\=\dfrac{10(1-2i)}{(1+2i)(1-2i)}\\\\\\=\dfrac{10-20i}{1 - (2i)^2}\\\\\\=\dfrac{10-20i}{1+4}~~~~~;[i^2 =-1]\\\\\\=\dfrac{10-20i}5\\\\=\dfrac{10}5 - \dfrac{20i}5\\\\=2-4i[/tex]

m11=54°

m8=117°

m7=63°

Step-by-step explanation:

a) m2=m12 (corresponding angles)

m12=126°

180=m12+m11 (supplementary angles equal 180)

180=126+m11

m11=54°

b) m14=m8. (corresponding angles)

m8=117°

C) m7=180-m8 (supplementary angles equal 180)

m7=180-117

m7=63°

Answer:

0.0005, 1/5/100, 5/1000, 5%, 50/100, 50, 500%

Step-by-step explanation:

You can convert all the percentages and fractions into decimals for better comprehension.

0.0005

1/5/100 = 0.002

5/1000 = 0.005

5% = 0.05

50/100 = 0.5

50

500% = 500

Answer:

0.0005, 1/5/100, 5/1000, 5%, 50/100, 50, 500%

Step-by-step explanation:

Answer:

ok points

Step-by-step explanation:

Answer:

Answer:

i think the answer is 45 mins sorry if im wrong

Answer:

Step-by-step explanation:

Given,

No. of days taken by Jenny to read 7 books

= 8

So,

No. of days taken by her to read 1 book

[tex] = \frac{8}{7} [/tex]

Therefore,

No. of days taken by her to read 20 books

[tex] = \frac{8}{7} × 20 [/tex]

[tex] = \frac{160}{7} [/tex]

= 22.85.....

= 23 days (approx. )

Hence,

Jenny will take 23 days to read 20 books (Ans)

If Jenny can read 7 books in 8 days, exactly how many days would it take her to read 20 books?

22.85714 or 23 days

[tex]GIVEN,[/tex]

Number of books Jenny can read in 8 days = 7

[tex]NOW,[/tex]

Number of days taken by Jenny to read 1 book = [tex] \frac{8}{7} [/tex]

Number of days taken by her to read 20 books =

→ [tex]20 \times \frac{8}{7} [/tex]

→ [tex] \frac{160}{7} [/tex]

→ 22.85714 or 23 days

Answer:

2

Step-by-step explanation:

take the 3 put on the side