A water tank is filled at a constant rate. After 36 minutes, there are 648 gallons of water in the tank. How many gallons of water flowed into the tank each minute? Use the model.

Answer:

  -60°

Step-by-step explanation:

Your calculator and/or your knowledge of trig function values can find this for you.

The arcsine function has a range of -90° to +90°. Positive angles 240° and 300° will also have the sine value -√3/2.

  arcsin(-√3/2) = -60° = -π/3 radians

Answer: 97%

Step-by-step explanation:

what is 194 out of 200 ? 97%

AND IM SO SORRY ABOUT RED DEV!L

Answer:

0.80

Step-by-step explanation:

its the farthest away from 0.60

Answer:

Molly played 4 games

Answer: I don’t know :(

Step-by-step explanation:

Answer:

8

Have an amazing day!

[tex] \large \bigstar \frak{ } \large\underline{\sf{Solution-}}[/tex]

Consider, LHS

[tex]\begin{gathered}\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } \\ \end{gathered}[/tex]

We know,

[tex]\begin{gathered}\boxed{\sf{  \:\rm \: {sec}^{2}x - {tan}^{2}x = 1 \: \: }} \\ \end{gathered} 

\\ \\ \text{So, using this identity, we get}

\\ \\ \begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - ( {sec}^{2}\theta - {tan}^{2}\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}[/tex]

We know,

[tex]\begin{gathered}\boxed{\sf{  \:\rm \: {x}^{2} - {y}^{2} = (x + y)(x - y) \: \: }} \\ \end{gathered}  \\ [/tex]

So, using this identity, we get

[tex]\begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - (sec\theta + tan\theta )(sec\theta - tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}[/tex]

can be rewritten as

[tex]\begin{gathered}\rm\:=\:\dfrac {(\sec \theta + tan\theta ) - (sec\theta + tan\theta )(sec\theta -tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac {(\sec \theta + tan\theta ) \: \cancel{(1 - sec\theta + tan\theta )}} { \cancel{ \tan \theta - \sec \theta + 1} } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:sec\theta + tan\theta \\\end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1}{cos\theta } + \dfrac{sin\theta }{cos\theta } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1 + sin\theta }{cos\theta } \\ \end{gathered}[/tex]

[tex]\begin{gathered} \\ \rm\implies \:\boxed{\sf{  \:\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } = \:\dfrac{1 + sin\theta }{cos\theta } \: \: }} \\ \\ \end{gathered}[/tex]

[tex]\rule{190pt}{2pt}[/tex]

Answer:

x<-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x + 200)20 = 200(10) + x(40)

20x + 4000 = 2000 + 40x

2000 = 20x

X = 100 mL

Answer:

18-3(n-1)

Step-by-step explanation:

Answer:

333.333333333

Step-by-step explanation:

you have to divide

Answer:

Percent change in the price of gas is [tex]9.85\%[/tex]

Step-by-step explanation:

Percentage change equals the change in value divided by the absolute value of the original value, multiplied by  .

[tex]\text { Percentage Change }=\frac{\Delta V}{\left|V_{1}\right|} \times 100[/tex]

Here

[tex]\Delta V=2.26-2.03\\\\=0.23\$/gallon[/tex]

[tex]V_{1}=2.03\$/gallon[/tex]

The percent change in the price of gas

[tex]=\frac{0.23}{2.03} \times100\\\\=9.85\%[/tex]

Percent change in the price of gas is [tex]9.85\%[/tex]

Answer:

x = 13

Step-by-step explanation:

180-52=10x-2

130=10x

13=x

Answer:

i think factor the expression (r+7)(r+14) is answer

Step-by-step explanation:

Answer:

(r + 14)

Step-by-step explanation:

When factoring a trinomial in the form of:

[tex]ax^2+bx+c[/tex]

you need to find 2 numbers that multiply to make ac and add to make b. Here, we need to find 2 numbers that multiply to 98 and add to 21. First, list the factors of 98:

1, 98

2, 49

7, 14

and the reverse of all of those is also true.

Now find factors that add to 21. In this case, those are 7 and 14. You need to break the middle term in the trinomial into those 2 numbers:

[tex]r^2+21r+98\\r^2+7r+14r+98[/tex]

Finally, you can factor each half of this individually.

[tex](r^2+7r)+(14r+98)\\r(r+7)+14(r+7)\\(r+14)(r+7)[/tex]

We were already given (r + 7), so the answer is (r + 14).

Answer:

1st one:5≥x>-infinity

2nd one :5<x<+infinity

3rd one :5>x>- infinity

Answer:

.

Step-by-step explanation:

Based on the information the amount borrowed at each rate is:

Let x=9.5%  

Let 4x= 8.5%  

Let 7% =$2,000,000 - 5x

Formulate

0.095x + 0.085(4x) + 0.07(2,000,000-5x) = 169,750

Collect like terms

0.095x + 0.34x + 140,000 - 0.35x = 169,750

Divide both side by 0.085x

0.085x = 29,750

x=29,750/0.085

x =$350,000

Amount borrowed at each rate:

Z=9.5% =$350,000

Y= 8.5% =$350,000×4

Y= 8.5% =$1,400,000

X=7% =$2,000,000 - 5($350,000)

X=7%=$2,000,000-$1,750,000

X=7% =$250,000

Matrix form

Z $350,000

Y $1,400,000

X $250,000

Inconclusion the amount borrowed at each rate is: $350,000; $1,400,000; $250,000.

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Answer:   [tex]\boldsymbol{-25+18\sqrt{2}}[/tex]

The expression is in the form [tex]a+b\sqrt{2}[/tex] where a = -25 and b = 18

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

Work Shown:

Let [tex]x = 3\sqrt{2}[/tex] and then square both sides

[tex]x = 3\sqrt{2}\\\\x^2 = \left(3\sqrt{2}\right)^2\\\\x^2 = \left(3\right)^2*\left(\sqrt{2}\right)^2\\\\x^2 = 9*2\\\\x^2 = 18\\\\[/tex]

We'll use both x and x^2 later on.

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

The denominator is in the form 4+x. We'll multiply top and bottom by 4-x to then use the difference of squares rule. This will allow us to eliminate the square root in the denominator.

[tex]\frac{8-3\sqrt{2}}{4+3\sqrt{2}}\\\\\frac{8-x}{4+x}\\\\\frac{(8-x)(4-x)}{(4+x)(4-x)}\\\\\frac{32-8x-4x+x^2}{16-x^2} \ \text{ difference of squares rule}\\\\\frac{32-12x+x^2}{16-x^2}\\\\[/tex]

[tex]\frac{32-12*3\sqrt{2}+18}{16-18} \ \text{ plug in } x = 3\sqrt{2} \text{ and } x^2 = 18\\\\\frac{50-36\sqrt{2}}{-2}\\\\\frac{-2(-25+18\sqrt{2})}{-2}\\\\\boldsymbol{-25+18\sqrt{2}}[/tex]

Therefore,

[tex]\frac{8-3\sqrt{2}}{4+3\sqrt{2}}=\boldsymbol{-25+18\sqrt{2}}[/tex]

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

Checking the answer:

Use a calculator to find that,

[tex]\frac{8-3\sqrt{2}}{4+3\sqrt{2}} \approx 0.45584412271571 \\\\-25+18\sqrt{2} \approx 0.45584412271571[/tex]

We get the same decimal approximation, which helps confirm the correct answer.

Or you could use the idea that if M = N, then M-N = 0 to subtract the original expression M and the final result N. You should get 0 or very close to it.

Answer: I'd say the best answer is b.

Step-by-step explanation:

Answer:

160°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 5 , then

sum = 180° × 3 = 540°

sum the interior angles and equate to 540

x + 10 + 2x + 10 + x + 10 + 2x+ x + 20 = 540 , that is

7x + 50 = 540 ( subtract 50 from both sides )

7x = 490 ( divide both sides by 7 )

x = 70

Then

largest angle = 2x + 10 = 2(70) + 10 = 140 + 10 = 150°

The solution is  : the largest angle is 150°.

A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges.

here, we have,

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 5 , then

sum = 180° × 3 = 540°

sum the interior angles and equate to 540

x + 10 + 2x + 10 + x + 10 + 2x+ x + 20 = 540 , that is

7x + 50 = 540 ( subtract 50 from both sides )

7x = 490 ( divide both sides by 7 )

x = 70

Then

largest angle = 2x + 10

                      = 2(70) + 10

                      = 140 + 10

                      = 150°

Hence, The solution is  : the largest angle is 150°.

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Answer:

0.25

Step-by-step explanation:

1/4 is equal to 1.00 split into 4 equal parts. 0.25*4 = 1.00 , meaning that each 1/4 is equal to 0.25

Answer:

0.25.

Step-by-step explanation:

We divide 1 by 4:

4)  1. 00

    0.25

Answer:

30/18=1 2/3 cups of popcorn in each bag

Hope This Helps!!!

Answer:

x=-5 and y= 4

Step-by-step explanation:

To eliminate x, add up both equations

9y= 36

divide both sides by 9

y=36/9

y= 8

To eliminate y, multiply the first equation by 8

-16x + 8y = 112

2x+ 8y= 22

Subtract equation 2 from equation 1

-18x = 90

Divide both sides by -18

x= 90/-18

x= -5

Answer:

y = 3

x = 2

Step-by-step explanation:

-5x + 4y = 2

9x - 4y = 6

Sum both eq.

-5x + 9x = 4x

+4y - 4y = 0

2 + 6 = 8

then:

4x + 0 = 8

4x = 8

x = 8/4

x = 2

from the first eq.

-5x + 4y = 2

-5*2 + 4y = 2

-10 + 4y = 2

4y = 2 + 10

4y = 12

y = 12/4

y = 3

Check:

from the second eq.

9x - 4y = 6

9*2 - 4*3 = 6

18 - 12 = 6

The completed table showing Bianca Ramos's tax deduction and NET PAY

is presented as follows;

SOCIAL SECURITY SYSTEM = Php 1,147

MEDICARE (PHILHEALTH) = Php 268.25

PAGIBIG (FUND) = Php 370

BIR (WITHHOLDING TAX) = Php 5,509.19

Total deductions = Php 7,294.44

NET PAY = Php 11,205.56

Reasons:

Based on online search, the tax rate for the items on the table are as follows;

SOCIAL SECURITY SYSTEM = 6.20% of earnings

MEDICARE (PHILHEALTH) = 1.45% of earnings

PAGIBID (FUND) = 2% of salary

BIR (WITHOLDING TAX) = P1,342.47 + 32% over P5,479

Bianca Ramos's basic salary = 18,500.00

Which gives the deduction amount as follows;

SOCIAL SECURITY SYSTEM = 0.062 × 18,500.00 = 1,147

MEDICARE (PHILHEALTH) = 0.0145 × 18,500.00 = 268.25

PAGIBIG (FUND) = 0.02 × 18,500.00 = 370

BIR (WITHHOLDING TAX) = 1,342.47 + 0.32×(18,500 - 5,479) = 5,509.19

Total deductions = 1,147 + 268.25 + 370 + 5,509.19 = 7,294.44

NET PAY = 18,500 - 7,294.44 = 11,205.56

Her net pay = Php 11,205.56

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Answer:

find the vertical asymptote of the graph of f(×) = (×+3) +2.

Answer:

70

Step-by-step explanation:

10.5/0.15 = 70

Check:

70 · 0.15 = 10.5

Answer:

the answer is number 1 !!

• correct me if I'm wrong

In attachment I have answered this problem.

The value of x {0 < x < (π/2)} satisfying (cos x / cosec x + 1) + (cos x / cosec x-1) = 2 ​is x = π/4.

Since cos x /(cosec x + 1) + cos x /(cosec x - 1) = 2 ​

Taking the L.C.M (cosecx + 1)(cosecx - 1), we have

[cosx(cosecx - 1) + cosx(cosecx + 1)]/(cosecx + 1)(cosecx - 1) = 2

[cosxcosecx - cosx + cosxcosecx + cosx]/(cosec²x - 1²) = 2

[cosx/sinx - cosx + cosx/sinx + cosx]/(cosec²x - 1²) = 2

[cotx - cosx + cotx + cosx]/(cosec²x - 1) = 2

collecting like terms, we have

[cotx + cotx + cosx - cosx ]/(cosec²x - 1) = 2

[2cotx + 0]/(cosec²x - 1) = 2

2cotx/(cosec²x - 1) = 2

cotx/(cosec²x - 1) = 1

Since cot²x + 1 = cosec²x ⇒ cot²x = cosec²x - 1

So, cotx/(cosec²x - 1) = 1

cotx/cot²x = 1

1/cotx = 1

tanx = 1

Taking inverse tan of both sides, we have

x = tan⁻¹(1)

x = 45°

x = 45 × π/180

x = π/4

So, the value of x {0 < x < (π/2)} satisfying (cos x / cosec x + 1) + (cos x / cosec x-1) = 2 ​is x = π/4.

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