What is cos θ when sin θ = 2/5? Rationalize the denominator if necessary.

Answer:

[tex]m\angle A=\tan^{-1}(\frac{m}{n})[/tex]

[tex]AB=\sqrt{m^2+n^2}[/tex]

Step-by-step explanation:

Given:

In Δ ABC

m∠C= 90°

[tex]BC=m[/tex]

[tex]AC=n[/tex]

For the triangle ABC we can apply trigonometric ratio to find m∠A.

We have:

[tex]\tan\angle A=\frac{BC}{AC}[/tex]

Substituting values of side BC and AC

[tex]\tan \angle A=\frac{m}{n}[/tex]

Taking inverse tan to get m∠A.

∴ [tex]m\angle A=\tan^{-1}(\frac{m}{n})[/tex]

AB can be found out using Pythagorean theorem:

AB being the hypotenuse can be written as

[tex]AB^2=BC^2+AC^2[/tex]

Substituting values of side BC and AC

[tex]AB^2=m^2+n^2[/tex]

Taking square roots both sides:

[tex]\sqrt{AB^2}=\sqrt{m^2+n^2}[/tex]

∴ [tex]AB=\sqrt{m^2+n^2}[/tex]

Answer:

$54

Step-by-step explanation:

let the initial amount of money per person be x

let the total cost of the pizza be y

Before one person left:

10x = y ------------> (eq 1)

After one person left, each of the 9 remaining people had to pay $0.60 extra.

9(x+0.6) = y ----------(eq 2)

equating y from both equations

10x = 9(x+0.6)

10x = 9x+(0.6)(9)

10x = 9x + 5.4     (subtract 9x from both sides)

10x - 9x = 5.4

x = 5.4 (substitute this back into equation 1)

10x = y

y = 10(5.4) = $54

Final answer:

The total bill for the pizza was $54.00. Each of the ten people would have contributed $5.40, but after one person left, the remaining nine paid an additional 60 cents each.

Explanation:

When the tenth person left the group, the nine remaining people each had to pay 60 cents extra for the pizza. This means that the contribution of the tenth person would have been 9 times 60 cents, which is $5.40. To find the total bill, we also need to add the amount that the remaining nine people paid before the extra charge. Since each person originally was going to pay the same amount, this amount is also $5.40. Therefore, each of the 10 people would have paid $5.40 making the total bill 10 times $5.40, which equals $54.00.

The equation of a parabola that opens up and has the following x intercepts (-3,0) and (4,0) is [tex]y=x^{2}-x-12[/tex]

We have to find the equation of a parabola that opens up and has the following x intercepts (-3, 0) and (4, 0)

x-intercepts of the parabola are (−3, 0) and (4, 0)

So, we can form an equation:

Also x = 4

x – 4 = 0

x – 4 = 0 is another factor of quadratic equation.

The quadratic function is:

[tex]\begin{array}{l}{y=(x+3)(x-4)} \\\\ {y=x^{2}-4 x+3 x-12} \\\\ {y=x^{2}-x-12}\end{array}[/tex]

Hence, the equation of the parabola is  [tex]y=x^{2}-x-12[/tex]

To find the equation of a parabola with x-intercepts at (-3,0) and (4,0), we can use the factored form of a quadratic equation. By plugging in the values of the roots and simplifying, we can determine that the equation of the parabola is y = x^2 - x - 12.

To find the equation of a parabola that opens up and has x-intercepts at (-3,0) and (4,0), we can start by recognizing that the x-intercepts are the points where the parabola intersects the x-axis. This means that the parabola has roots of -3 and 4. To find the equation, we can use the factored form of a quadratic equation: (x - root1)(x - root2) = 0. Plugging in the values of the roots, we get (x - (-3))(x - 4) = 0. Simplifying this, we have (x + 3)(x - 4) = 0. Expanding this, we have x^2 - x - 12 = 0. Therefore, the equation of the parabola is y = x^2 - x - 12.

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Answer:

To calculate percentages, start by writing the number you want to turn into a percentage over the total value so you end up with a fraction. Then, turn the fraction into a decimal by dividing the top number by the bottom number. Finally, multiply the decimal by 100 to find the percentage.

Step-by-step explanation

To calculate what percentage one number is of another, divide the 'part' by the 'total' and multiply by 100. This formula is used to convert a ratio into a percentage, which represents a part per hundred of the total.

The method for calculating what percentage a number is of another number involves a straightforward formula: 'part over total, times one hundred, equals percent'. For example, if a class has 35 students and 13 are wearing sandals, you would use the equation 13 divided by 35, multiplied by 100, to find the percentage. The calculation would be 13/35 x 100, which is 0.37 x 100, resulting in 37 percent of the students wearing sandals.

Calculating Percents

To express a fractional amount as a percent, you divide the numerator (the part) by the denominator (the total) and then multiply by 100. The percent symbol, %, is used to indicate that the number is a percentage of the total. For instance, 3 out of 4 can be written as 3/4, which is equal to 0.75, and when multiplied by 100 gives you 75%.

Another example is understanding voter registration percentages. If 10,458 out of 18,145 students registered to vote at a college, the equation to find the percentage would be 10,458/18,145 x 100, equal to 58 percent registration.

Answer:

no becase the x value 2 has two y values 5 and 7. for it to be a function each x value can only have 1 y value

Step-by-step explanation:

Answer:

no it is not

Step-by-step explanation:

Final answer:

The height of the coin when Jake tosses it is 6 feet.

Explanation:

The equation that models the height and time of the parabola is [tex]h(t) = -16t^2 + 24t + 6.[/tex]

To find the height of the coin when Jake tosses it, we need to determine the height at time t = 0.

Plugging in t = 0 into the equation, we have [tex]h(0) = -16(0)^2 + 24(0) + 6[/tex]

= 6 feet.

So the height of the coin when Jake tosses it is 6 feet.

Answer:

20 years apart.

Step-by-step explanation:

Daughter is 10 years old, and mother is 3 times older. This makes mother 30 years old.  There is a 20 year difference between them.

Ten years later, the daughter is 20 years old. Since the mother is 20 years older, she is now 40, which is 2 times older than the daughter.

Answer:

The difference (d) = - 8

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Arithmetic series :  14 + 6 + (–2) + (–10) + (–18) + (–26) + (–34)

2. What is the common difference d of the arithmetic sequence on which the series is based?

1st an 2nd element difference = 14 - 6 = 8

2nd and 3rd element difference = - 6 - 2 = -8

3rd and 4th element difference = - 2 + 10 = 8

4th and 5th element difference = -10 + 18 = 8

The difference (d) is 8 and it's negative because the series is lowering the previous value.

3. Proof of d = - 8

14 - 8 = 6

6 - 8 = - 2

- 2 - 8 = - 10

- 10 - 8 = - 18

- 18 - 8 = - 26

-26 - 8 = -34

Answers:

1st: -8

2nd: 14 + (k-1)(-8)

3rd: x=7 y= 22 z= -8

explanation:

i did it :))

Answer:

89

Step-by-step explanation:

2^3=2*2*2=8

3^4=3*3*3*3=9*9=81

8+81=89

Answer:

[tex]\large\boxed{x^\frac{4}{5}}[/tex]

Step-by-step explanation:

[tex]x^\frac{2}{3}\cdot x^\frac{2}{15}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=x^{\frac{2}{3}+\frac{2}{15}}\qquad\text{LDC = 15}\\\\=x^{\frac{2\cdot5}{3\cdot5}+\frac{2}{15}}=x^{\frac{10}{15}+\frac{2}{15}}=x^{\frac{12}{15}}=x^{\frac{12:3}{15:3}}=x^\frac{4}{5}[/tex]

Answer:

The total minutes Nick volunteer in a year are 5000 minutes.

Step-by-step explanation:

Given:

Nick volunteer Saturday for 60 minutes and each Sunday for 40 minutes. He takes 2 weeks off every year.

Now, how many minutes did he volunteer in one year.

So, in one year there are 52 weeks.

And, total weeks Nick volunteer are 50 in a year as he takes 2 weeks off every year.

And, total minutes in a week nick volunteer = 60+40= 100 minutes.

Now, for getting the total minutes Nick volunteer in a year, we multiply the total weeks he volunteer in a year from total minutes he volunteer in a week :

Total minutes Nick volunteer in a year = total weeks he volunteer in a year × total minutes he volunteer in a week

Total minutes Nick volunteer in a year [tex]=50\times 100\ minutes[/tex]

Total minutes Nick volunteer in a year [tex]=5000\ minutes[/tex]

Therefore, the total minutes Nick volunteer in a year are 5000 minutes.

Answer:

m∠FAD=48°

Step-by-step explanation:

we know that

The Perpendicular Bisector Theorem states that: A radius that bisect a chord is perpendicular to the chord

we have

FD=DE

The radius AC bisect the chord FE

so

AC is perpendicular to FE

The triangle FAD is a right triangle

m∠FAD+m∠AFD=90° ---> by complementary angles in a right triangle

we have

m∠AFD=42°

substitute

m∠FAD+42°=90°

m∠FAD=90°-42°

m∠FAD=48°

Answer:

10 hours

Step-by-step explanation:

Two boats leave a port at the same​ time, one going north and the other traveling south.

Southbound boat rate = 40 mph

The northbound boat travels 18 mph faster than the southbound boat.

Northbound boat rate = 40 + 18 = 58 mph

Two boats rate = 40 + 58 = 98 mph (this means they are apart 98 km after one hour)

Total distance = 980 miles

Total rate = 98 mph

Time [tex]=980:98=10[/tex] hours

Answer: First option.

Step-by-step explanation:

Let be "x" the number of spaghetti dinner tickets sold and "y" the number of barbecue dinner tickets sold.

You know that 1 spaghetti dinner ticket costs $7.25; so the total amount of money earned selling these tickects can be represented with this expression:

[tex]7.25x[/tex]

Since 1 barbecue dinner ticket costs $8.75; the total amount of money earned selling them can be represented with this expression:

[tex]8.75y[/tex]

Knowing that the total amount of money the band raised was $2,790, we can write the following equation to represent this situation:

[tex]7.25x+8.75y=2,790[/tex]

The band sold twice as many spaghetti dinners as barbecue dinners, which means that the amount of spaghetti dinners sold was two times the amount of barbecue dinners sold.

This can be represented with this equation:

[tex]x=2y[/tex]

Therefore, the set of equations that can be used to find "x" and "y", is:

[tex]\left \{ {{x=2y} \atop {7.25x+8.75y=2,790}} \right.[/tex]

Answer:

Step-by-step explanation:

[tex]\text{Distributive property:}\ a(b+c)=ab+ac\\\\27=\boxed{9}\cdot3\\\\36=\boxed{9}\cdot4\\\\GCF(27,\ 36)=\boxed{9}\\\\\\27+36=\boxed{9}\cdot3+\boxed{9}\cdot4=\boxed{9}(3+4)[/tex]

Answer:

Sally had 917 bottles of water \she plans on buying 67 more bottles of water so in all she will have 984 bottles of water.

Step-by-step explanation:

Answer:

3x^4-75

Step-by-step explanation:

3(x^2+5)(x^2-5)

3(x^4+5x^2-5x^2-25)

3(x^4-25)

3x^4-75

Just multiply each term out and combine like terms.

[tex]\bf \textit{zeros at } \begin{cases} x = -3\implies &x+3=0\\ x = -1\implies &x+1=0\\ x = 4\implies &x-4=0 \end{cases}\qquad \implies (x+3)(x+1)(x-4)=\stackrel{y}{0} \\\\\\ (x^2+4x+3)(x-4)=0\implies x^3~~\begin{matrix}+ 4x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+3x~~\begin{matrix} -4x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-16x-12=0 \\\\\\ x^3-13x-12=0[/tex]

we know that f(-2) = 24, namely when x = -2, y = 24, let's see if that's true

[tex]\bf x^3-13x-12=y\implies \stackrel{x = -2}{(-2)^3-13(-2)-12}=y \\\\\\ -8+26-22=y \implies 6=y[/tex]

darn!! no dice.... hmmmm wait a second.... 4 * 6 = 24, if we could just use a common factor of 4 on the function, that common factor times 6 will give us 24, let's check.

[tex]\bf 4(x^3-13x-12)=y\implies \stackrel{x = -2}{4[~~(-2)^3-13(-2)-12~~]}=y \\\\\\ 4[~~-8+26-22~~]=y\implies 4[6]=y\implies 24=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 4x^3-52x-48=y~\hfill[/tex]

Answer:

82%

Step-by-step explanation:

The total number of marbles is 9 + 6 + 7 + 11 = 33.  6 marbles are blue, so 27 are not.  So the probability of selecting a non-blue marble is 27/33 ≈ 82%.

The probability of NOT getting a blue marble is 82%.

Probability denotes the possibility of the outcome of any random event.

Given that, a bag contains 9 red marbles, 6 blue marbles, 7 green marbles, and 11 yellow marbles, one is selected randomly, we need to find the probability that a blue marble will not be selected,

So, the probability of NOT event = 1-P(E)

Therefore,

The probability of getting a blue marble = 6/33 = 2/11

The probability of NOT getting a blue marble = 1-2/11 = 9/11

= 0.81818181 ≈ 82%

Hence, the probability of NOT getting a blue marble is 82%.

Learn more about probability click;

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Answer:

0.02419354838

"The answer to the question 9 divided by 372 is 0.02419.

To calculate [tex]\[ \frac{9}{372}[/tex] , simply divide the numerator (9) by the denominator (372):

[tex]\[ \frac{9}{372} = \frac{9}{372} \][/tex]

[tex]\[ \frac{9}{372}[/tex] = 0.02419

This fraction cannot be simplified any further because 9 and 372 do not have any common factors other than 1. So, [tex]\[ \frac{9}{372}[/tex]  is already in its simplest form and its value in decimal is 0.02419.

Answer:

A) The sum of given digits is 5417.412

B ) The sum of given digits is 401.103  

Step-by-step explanation:

Given sum of numbers as :

A ) 5 × 10³ + 4 × 10² + 1 × [tex]10^{1}[/tex] + 7 × [tex]10^{0}[/tex] + 4 × [tex]\frac{1} {10^{1}}[/tex] + 1 × [tex]\frac{1}{10^{2}}[/tex] + 2 × [tex]\frac{1}{10^{3}}[/tex]

Or , 5000 + 400 + 10 + 7 × 1 + 0.4 + 0.01 + 0.002

or, ( 5400 + 10 + 7 ) + ( 0.4 + 0.01 + 0.002 )

Or, 5417 + 0.412

Or, 5417.412

Hence The sum of given digits is 5417.412

B ) 4 × 10² + 1 × ( 1 [tex]\frac{1} {10^{1}}[/tex] ) + 3 × [tex]\frac{1}{10^{3}}[/tex]

Or, 400 + 1 × ([tex]\frac{10+1}{10}[/tex] ) + 0.003

Or, 400 + [tex]\frac{11}{10}[/tex] + 0.003

Or, 400 + 1.1 + 0.003

Or, 401.103

Hence The sum of given digits is 401.103  

Answer

Answer:

1) 5417.412

2) 401.13

Step-by-step explanation:

1) [tex]$ 5 \times 10^3 + 4 \times 10^2 + 1 \times 10^1 + 7 \times 10^0 + 4 \times \frac{1}{10^1} + 1 \times \frac{1}{10^2} + 2  \times \frac{1}{10^3} $[/tex]

[tex]$ 5 \times 10^3 = 5000 $\\ $  4 \times 10^2 = 400 $ \\ $   1 \times 10^1 = 10 $\\$  7 \times 10^0 = 7 \times 1 = 7 $\\$  4 \times \frac{1}{10^1} = 0.4 $\\$ 1 \times \frac{1}{10^2} = 0.01 $\\ $  2  \times \frac{1}{10^3} = 0.02 $ \\[/tex]

Combining we have: [tex]$ 5000 + 400 + 10 + 7 + 0.4 + 0.01 + 0.002 = $[/tex] 5417.412.

2) [tex]$ 4 \times 10^2 + 1 \times 1\frac{1}{10^1} + 3 \times \frac{1}{10^2} $[/tex]

[tex]$ 4 \times 10^2 = 400 $\\$ 1 \times 1\frac{1}{10^1} = 1 \times \frac{11}{10} = 1 \times 1.1 = 1.1 $\\$ 3 \times \frac{1}{10^2} = 0.03 $[/tex]

Combining we have: 400 + 1.1 + 0.03 = 401.13.

Hence, we have the answers.

Answer:

8:6

Hope it helped. :)

Answer: 6:8

to Find any equivalent ratio, you multiply both numbers (in this example, 6 and 8) by the same number (in this example, 2).

Answer:

n+132

Step-by-step explanation:

Answer:

1) Actual Measurements of Gym = 50 m x 40 m

2)The actual measurements of the closet  =20 m x 10 m

3) if 1 cm  = 12 m the actual dimensions of the gym  are : 60 m x  48 m

4) The area of the gym =  2000 sq m

Step-by-step explanation:

Here, the question is INCOMPLETE.

I am attaching the correct figure for the reference.

Here, The dimensions of Closet are   =   2 cm , 1 cm

The dimensions of gym are = 5 cm , 4 cm

Now as the scale represents 1 cm  = 10 m

So, the ACTUAL dimensions of the closet are :

2 cm  = 2 x  1 cm  = 2 x 10 m   = 20 m

1 cm  = 10 m

And, the ACTUAL dimensions of the gym  are :

5 cm  = 5 x  1 cm  = 5 x 10 m   = 50 m

4 cm  = 4 x  1 cm  = 4 x 10 m   = 40 m

Now, solving the giver parts:

1) Actual Measurements of Gym = 50 m x 40 m

2)The actual measurements of the closet  =20 m x 10 m

3) if 1 cm  = 12 m

the ACTUAL dimensions of the gym  are :

5 cm  = 5 x  1 cm  = 5 x 12 m   = 60 m

4 cm  = 4 x  1 cm  = 4 x 12 m   = 48 m

4) The area of the gym = LENGTH x WIDTH

                                        =  50 m x 40 m   = 2000 sq m.

Answer: $157.50 is the sale price

Step-by-step explanation:

because there is a 25% discount, 75% of the regular price will be the sale price

75% x 210 = $157.50 is the sale price

Answer:

3,330/18=185

so

185 columns*18 rows

3,330/18=185

so

185 columns*18 rows

Answer:

h = 1.41

c = 3.46

Step-by-step explanation:

See the triangles diagram attached.

For the first triangle, Base = h, Hypotenuse = 2 and the angle between base and hypotenuse is 45°.

Therefore, [tex]\cos 45 = \frac{\textrm {Base}}{\textrm {Hypotenuse}} = \frac{h}{2}[/tex]

⇒ [tex]h = 2 \cos 45 = \frac{2}{\sqrt{2} } = \sqrt{2} = 1.414 = 1.41[/tex] (Answer)

{Rounded to the nearest tenth}

Again in the second triangle, Perpendicular = c, Hypotenuse = 4 and the angle between base and hypotenuse is 60°.

Therefore, [tex]\sin 60 = \frac{\textrm {Perpendicular}}{\textrm {Hypotenuse}} = \frac{c}{4}[/tex]

⇒ [tex]c = 4 \sin 60 = \frac{4 \times \sqrt{3} }{2} = 2\sqrt{3} = 3.46[/tex] (Answer)

{Rounded to the nearest tenth}

Answer:

I got youuuu

Step-by-step explanation: what you need?

Answer:

Initial fee: 6 Dollars. Fee per Kilometer: 1.30588235294

Step-by-step explanation:

Divide 222/170=Fee per a Kilo