which choices are equivalent to the expression below. check all apply sqrt 2 x sqrt 5 x sqrt 10A. 10B. 15C. 10 over sqrt 10D. 100C. 2 over sqrt 25F. SQRT 100

Answer:

\(y = 4*5^x\)

Step-by-step explanation:

Given

\((x_1,y_1) = (-3,\frac{4}{125})\)

\((x_2,y_2) = (1,20)\)

Required

Determine the exponential equation

An exponential equation is of the form: \(y = ab^x\)

In: \((x_2,y_2) = (1,20)\)

\(20 = ab^1\)

\(20 = ab\) ---- (1)

In: \((x_1,y_1) = (-3,\frac{4}{125})\)

\(\frac{4}{125} = ab^{-3}\) --- (2)

Divide (1) by (2)

\(20/\frac{4}{125} = \frac{ab}{ab^{-3}}\)

\(20/\frac{4}{125} = b^4\)

\(20*\frac{125}{4} = b^4\)

\(5*125 = b^4\)

\(625 = b^4\)

Take 4th roots of both sides

\(\sqrt[4]{625} = b\)

\(5 = b\)

\(b = 5\)

Substitute \(b = 5\) in \(20 = ab\)

\(20 = a * 5\)

Solve for a

\(a = 20/5\)

\(a = 4\)

Hence, the equation is:

\(y = 4*5^x\)

Answer:6/5 or 1.2

Step-by-step explanation:

4/5 divided by 2/3

=4/5 *3/2

=12/10

=6/5

=1.2

Answer:

$971(nine hundreds and seventy one dollars

Answer:

He would get there at 1:15 (I did this in my head, may be wrong)

Step by step solution:

We know the motorist left home at 10. We can divide the 260/80 and we get 3 hrs, we still have 20 km left over, keep on dividing and you get 1:15 p.m.

Answer:

There is no question given here.

Answer:

Step-by-step explanation:

Given

\(x=1-sin(a)\\y=1+cos(a)\)

Solve for \(a\) in the second equation.

\(y=1+cos(a)\)

\(y-1=cos(a)\)

\(a=cos^{-1}( y-1)\)

Insert our answer for \(a\) into the first equation.

\(x=1-sin(a)\)

\(x=1-sin(cos^{-1}( y-1))\)

\(cos^{-1}=arccos\)

\(x=1-sin(arccos( y-1))\)

Lets simplify \(1-sin(arccos( y-1))\)

A piece of graph paper would be helpful in my opinion.

Here is how I would go about doing so

Draw a triangle in the plane with vertices \((y-1,\sqrt{1^2-(y-1)^2}),(y-1,0)\) and the origin.

\(arccos(y-1)\) is is the angle between the positive x-axis and the ray beginning at the origin and passing through \((y-1,\sqrt{1^2-(y-1)^2})\). Therefore \(sin(arccos(y-1))\) is \(\sqrt{1-(y-1)^2}\)

Now we have

\(x-1-\sqrt{1-(y-1)^2}\\a=arccos(y-1)\)

We can write \(1\) as \(1^2\). Since both terms are now perfect squares, we can factor using the difference of squares formula.

\(a^2-b^2=(a+b)(a-b)\) where \(a=1\) and \(b=y-1\)

\(x=1-\sqrt{(1+y-1)(1-(y-1))}\)

After simplifying we get

\(x=-\sqrt{y(-y+2)}+1\)

\(x=-\sqrt{y(-y+2)}+1\)

\(a=arccos(y-1)\)

I think this is what your question was. If not let me know.

Answer:

864

Step-by-step explanation:

80/100 simplified is 4/5

so you do 4/5 of 1080

which is 1080 divided by 5 that is 216

and then 216 x 4 which is 864

Answer:

\(408cmx^{2}\)

Step-by-step explanation:

A=2(wl+hl+hw)=2·(2·6+24·6+24·2)= 408cm²

length= 6

width= 2

height= 24

the area if the box.

\(a = lwh\)

\(a = 2(wl + hl + hw)\)

\(a = 2 \times (2.6 + 24.6 \times + 24.2)\)

\(a = 408 {cm}^{2} \)

therefore, the area of the box is 408 square centimeters.

Answer:

If the length is 50 yd, the width is  60 yd.

If the length is 40 yd, the width is  75 yd.

If the length is 48 yd, the width is  62.5 yd.

If the length is 36 yd, the width is 83.33 yd.

The length and the width vary inversely because when the length decreased the width increased

Step-by-step explanation:

The area of any rectangle A = L × W, where

The relation is direct proportion if the quotient of two quantity equals constant  (y/x = k, when y and x increased) and inverse if the product of the two quantity equals constant (yx = k, when x increased y decreased and vice versa)  

∵ The area of the rectangular plot of land = 3000 yards²

∴ A = 3000

∵ Its length = 50 yards

∴ L = 50

→ Substitute them in the rule above to find W

∵ 3000 = 50 × W

→ Divide both sides by 50 to find W

∴ 60 = W

∴ The width of the plot is 60 yards

∵ Its length = 40 yards

∴ L = 40

→ Substitute them in the rule above to find W

∵ 3000 = 40 × W

→ Divide both sides by 40 to find W

∴ 75 = W

∴ The width of the plot is 75 yards

∵ Its length = 48 yards

∴ L = 48

→ Substitute them in the rule above to find W

∵ 3000 = 48 × W

→ Divide both sides by 48 to find W

∴ 62.5 = W

∴ The width of the plot is 62.5 yards

∵ Its length = 36 yards

∴ L = 36

→ Substitute them in the rule above to find W

∵ 3000 = 36 × W

→ Divide both sides by 36 to find W

∴ 83. 33 = W

∴ The width of the plot is  83.33 yards

∵ The area is a constant value

∵ A = LW

→ The product of L and W equals the constant value, can you discover

   that from the values of L and W

∴  The length and the width of the rectangular plot vary inversely

The length and the width of the rectangular plot vary  inversely when the same area is needed.

Area of rectangular plot \(=length *width\)

Given that, Area of plot is 3000 square yards.

             \(width=\frac{3000}{50} =60yd\)

            \(width=\frac{3000}{40}=75yd\)

            \(width=\frac{3000}{48}=62.5yd\)

           \(width=\frac{3000}{36}=83.34yd\)

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Answer:   19/17

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

Work Shown:

19cos(x) - 17sin(x) = 0

19cos(x) = 17sin(x)

17sin(x) = 19cos(x)

sin(x) = 19cos(x)/17

sin(x)/cos(x) = 19/17

tan(x) = 19/17

Answer:

see explanation

Step-by-step explanation:

y = - x² + 4

can be expressed in functional notation as

f(x) = - x² + 4

to find the range value, substitute the domain value into f(x) , that is

f(3) = - 3² + 4 = - 9 + 4 = - 5

range value is then - 5

The number is 48.

Let's represent the two-digit number as 10x + y, where x is the tens digit and y is the units digit.

According to the given information, the units digit is twice the tens digit. So we have the equation:

y = 2x

If the number is doubled, it will be 12 more than the number reversed. When we double the number, we get 2(10x + y), and the number reversed is 10y + x.

Therefore, we can write the equation as:

2(10x + y) = 10y + x + 12

Simplifying this equation, we get:

20x + 2y = 10y + x + 12

19x = 8y + 12

19x - 8y = 12

We have two equations now:

y = 2x

19x - 8y = 12

Substituting the value of y from the first equation into the second equation, we get:

19x - 8(2x) = 12

19x - 16x = 12

3x = 12

x = 4

Now we can substitute the value of x back into the first equation to find y:

y = 2x

y = 2(4)

y = 8

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Answer: $4,998

Step-by-step explanation:

34000*1.147

38998-34000=4998

Answer:

Okay so the square root of 6 would be either 3 or 2 because 3×2=6

And the square root of 15 would either be 3 or 5

because 3×5=15

And I don't understand when it says simplify the square root 3 times.

Hey!  The answer is 5

I use OW

have a good day ;)

Answer:

486 square inches

Step-by-step explanation:

Answer:

(a)\(g(n)=0.05\cdot 2^n\)

(b)\(g^{-1}(n)=\log_{2}20g(n)\)

(c)43 times

Step-by-step explanation:

Part A

The paper's thickness = 0.05mm

When the paper is folded, its width doubles (increases by 100%).

The thickness of the paper grows exponentially and can be modeled by the function:

\(g(n)=0.05(1+100\%)^n\\\\g(n)=0.05\cdot 2^n\)

Part B

\(g(n)=0.05\cdot 2^n\\2^n=\dfrac{g(n)}{0.05}\\ 2^n=20g(n)\\$Changing to logarithm form, we have:\\\log_{2}20g(n)=n\\$Therefore:\\g^{-1}(n)=\log_{2}20g(n)\)

Part C

If the thickness of the paper, g(n)=384,472,300,000 mm

Then:

\(g^{-1}(n)=\log_{2}20g(n)\\g^{-1}(n)=\log_{2}20\times 384,472,300,000\\=\dfrac{\log 20\times 384,472,300,000}{\log 2} \\g^{-1}(n)=42.8 \approx 43\\n=43\)

You must fold the paper 43 times to make the folded paper have a thickness that is the same as the distance from the earth to the moon.

\(6\frac{2}{3}\implies 6+\frac{2}{3}\implies \stackrel{\textit{three times that much}}{3\left( 6+\frac{2}{3} \right)\implies} (3\cdot 6)+3\left( \frac{2}{3} \right)\implies 18+2\implies \underset{meters}{20}\)

The number that can complete the equation 5y + 2(3y − 1) = ⬜y − (y + 2) is

5y + 2(3y − 1) = 12 y − (y + 2)

The number that can complete the equation is computed by simplifying the equation at the left hand side of the equality sign and comparing with the right side of the equality side

The comparison will show the number that can fit in the blank

Simplifying the equation at the left hand side of the equation

= 5y + 2(3y − 1)

= 5y + 6y − 2

= 11y - 2

Simplifying the equation at the right hand side of the equation

=  ⬜y − (y + 2)

let x represent the missing number

=  xy − (y + 2)

=  xy − y - 2

comparing both equations

11y - 2 =  xy − y - 2

11y =  xy − y

11y + y =  xy

12y = xy

x = 12

The missing value = 12

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if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

Calculating the loan amount for each brand by subtracting the down payment from the cash price:

Loan amount for Daewoo = RM1,899 - RM300 = RM1,599

Loan amount for Daikin = RM1,699 - RM300 = RM1,399

Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699

Calculating the interest charge for each brand:

Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96

Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96

Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96

To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:

Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22

Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89

Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72

Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

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Answer:

144

Step-by-step explanation:

i just took the test

Answer:

Therefore, the correct statements are A, B, and E.

Explanation:

Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.

To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀

.

- The component form of −4⇀

is obtained by multiplying each component of ⇀

by –4. Therefore, −4⇀

= ⟨–8, –12⟩. This means that statement A is true.

- The magnitude of −4⇀

is obtained by multiplying the magnitude of ⇀

by 4. The magnitude of ⇀

is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀

is 4√13. This means that statement B is true.

- The direction of −4⇀

is opposite to the direction of ⇀

because the scalar –4 is negative. This means that statement C is false.

- The vector −4⇀

is in the third quadrant because its components are both negative. This means that statement D is false.

- The direction of −4⇀

is 180° greater than the inverse tangent of its components because it is opposite to ⇀

. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀

is 180° + tan^(-1)(3/2). This means that statement E is true.

Therefore, the correct statements are A, B, and E.

Answer:

x=12

y = 4

Step-by-step explanation:

3x + y = 4x - 2y

x = 3y

y= 1/3x

3x + y = 40             3x + y = 40

3(3y) + y = 40         3x + (1/3x) = 40

9y + y =40              10/3x = 40

10y = 40                  x = 12

y= 4

Answer:

We know that all sides of the equilateral triangle is equal.

Given :---

An equilateral triangle has a side length of 40.

Another side of the same triangle measures

3x + y.

The third side of the same triangle measures

4x - 2y.

According to the above problem, the equation are

3x+y=40........(i) and 4x-2y=40.........(ii)

Divide the equation (ii) by 2, we get

2x-y=20..........(iii)

Now solving for x and y we get,

3x+y=40.......(i)

2x-y=20........(iii)

5x =60

x=60/5

x=12

Putting the value of x in equation in equation (iii) we get

24-y=20

y=24-20

y=4

The values of x and y that would keep the triangle equilateral are 12 and 4 respectively.

Answer:

D. 0

Step-by-step explanation:

I calculated logically

Answer:

D

Step-by-step explanation:

He already has 150 cards and he is buying 15 cards EACH WEEK. W represents the amount of weeks and since 15W +150 needs to be greater than 500 we need to use this lil guy (>)

140.55 pounds will be sold approximately each week at the optimal price of $0.67/lb.

To find the price elasticity of demand for bananas at $0.20/lb, we need to use the formula:

According to the given data:

E(p) = -p(q'/q(p))

where q' is the derivative of q(p) with respect to p.

First, we need to find q'(p):

\(q'(p) = -225e^(1.5(5-p))\)

Then, we can plug in the values:

E(0.20) = -0.20(q'(0.20)/q(0.20))

= \(-0.20(-225e^(1.5(5-0.20)) / 100e^(1.5(5-0.20)))\)

= 2.70

Therefore, the price elasticity of demand for bananas at $0.20/lb is 2.70.

To find the price elasticity of demand for bananas at $1/lb, we can use the same formula:

E(p) = -p(q'/q(p))

First, we need to find q'(p):

\(q'(p) = -225e^(1.5(5-p))\)

Then, we can plug in the values:

E(1) = -1(q'(1)/q(1))

= \(-1(-225e^(1.5(5-1)) / 100e^(1.5(5-1)))\)

= 0.68

Therefore, the price elasticity of demand for bananas at $1/lb is 0.68.

To find the price that maximizes revenue, we need to find the value of p that makes revenue, R(p), maximum.

Revenue is given by:

R(p) = pq(p)

= \(p100e^(1.5(5-p))\)

To maximize revenue, we need to find the critical point of R(p) by taking its derivative and setting it equal to zero:

\(R'(p) = 100e^(1.5(5-p)) - 150pe^(1.5(5-p)) = 0\)

Simplifying this expression, we get:

\(2e^(1.5(5-p)) - 3pe^(1.5(5-p)) = 0\)

2 = 3p

p = 2/3

Therefore, the price that maximizes revenue is $0.67/lb.

To find the maximum revenue per week, we can plug this price back into the revenue equation:

\(R(2/3) = (2/3)*100e^(1.5(5-2/3))\)

= $167.56

Therefore, the maximum revenue per week is $167.56.

To find how many pounds will be sold each week at the optimal price of $0.67/lb, we can plug this price back into the demand equation:

\(q(2/3) = 100e^(1.5(5-2/3))\)

= 140.55

Therefore, approximately 140.55 pounds will be sold each week at the optimal price of $0.67/lb.

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9514 1404 393

Answer:

  1. 9/20 hours doing math for 1 hour reading

  2. 3 1/3 cups water to 1 cup concentrate

Step-by-step explanation:

1. You have done the math. Copy your answer into the blanks that are waiting for it.

  9/20 hours on math for 1 hour reading

__

2. 1 2/3 ÷ 1/2 = 5/3 × 2/1 = 10/3 = 3 1/3

  3 1/3 cups of water to 1 cup of juice concentrate

Answer:

16.9

Step-by-step explanation:

We can use a proportion also in this case

51.6 : 23 = 38 : NO

NO = (38 x 23)/51.6 = 16.9

Step-by-step explanation:

absolutely. there is no mathematical problem to solve.

just do what the instructions tell you.

that is an exercise for you to get a feeling what is what.

Answer:

x = 50

Step-by-step explanation:

In a polygon, the angles add up to 360°:

x + 10 + 2x + 3x + x = 360

7x + 10 = 360

7x = 350

x = 50

Answer:

x = 50

Step-by-step explanation:

There are 4 angles, making it a Quadrilateral. A Quadrilateral has a ∑m∠ of 360°.

Set each angle equal to 360°:

2x + 3x + x + x + 10 = 360

Simplify. Combine like terms:

(2x + 3x + x + x) + 10 = 360

7x + 10 = 360

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS =

Parenthesis

Exponents

Roots

Multiplication

Division

Addition

Subtraction

First, subtract 10 from both sides:

7x + 10 (-10) = 360 (-10)

7x = 360 - 10

7x = 350

Next, divide 7 from both sides:

(7x)/7 = (350)/7

x = 350/7

x = 50

50 is your value for x.

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