A certain alloy contains 14% tin and 32% copper. (The percentages are by weight.) How many pounds of tin and how many pounds of copper must be melted with 1750 lb of the given alloy to yield a new alloy containing 20% tin and 35% copper? Hint: Introduce variables for the weights of tin and copper to be added to the given alloy. Express the total weight of the new alloy in terms of these variables. The total weight of tin in the new alloy can be computed two ways, giving one equation. Computing the total weight of copper similarly gives a second equation.

Answer:

6n+2

Step-by-step explanation:

The the length of each side of the triangle are: 5 units, 8.7 units and 10 units respective

A triangle is a polygon with three sides, three angles, three vertices and sum of angles equal to 180 degrees

From the triangle, Using the trigonometric ratio of sine

Sin C = opposite/Hypothenuse

Sin30 = 5/H

Making h the subject of the relation we have

h= 5/sin30

h=5/0.5

Therefore the value of h=10 units

To find the third side use Pythagoras theorem

10² = 5²+p²

100-25 = p²

75 = p²

Taking the square of both sides

p=√75

p=8.7 units

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Answer:

The answer is \(12\log{(x(x-2))}\)

Step-by-step explanation:

Exponential property of logarithm:

We have that:

\(a \log{x} = \log{x^{a}}\)

Sum of logarithms:

We have that:

\(\log{a} + \log{b} = \log{ab}\)

Applying the exponential property:

\(3\log{x} = \log{x^3}\)

\(4\log{(x-2)} = \log{(x-2)^4}\)

So

\(3\log{x} + 4\log{x-2} = \log{x^3} + \log{(x-2)^4}\)

Additive property

\(\log{x^3} + \log{(x-2)^4} = \log{x^3(x-2)^4} = \log{(x(x-2))^12}\)

Exponential property:

\(\log{(x(x-2))^12} = 12\log{(x(x-2))}\)

The answer is \(12\log{(x(x-2))}\)

Answer:

b

Step-by-step explanation:

positive linear means more of this = more of the other.

and that's what it looks like it's doing. bigger screen = more hours

Answer: y + 7x = -6

Step-by-step explanation:

Standard form: Ax + By = c, where a, b, and c are constants.

Distribute

y - 8 = -7x - 14

Add 8 and 7x to both sides:

y + 7x = -6

Hope it helps :)

The standard form of the equation is y = -7x-14

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given an equation, y-8 = -7(x+2)

We know that standard form of an equation of a line is y = mx+c

Converting into standard form,

y-8 = -7(x+2)

y-8 = -7x-14

y = -7x-14+8

y = -7x-6

Hence, The standard form of the equation is y = -7x-14

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Answer:

d 1-12-3-5 is the answer

Answer:

B

Step-by-step explanation:

The general form is y=mx + b where m is the slope and b is the intercept.

The y intercept is 1. So eliminate choice C.

The line is going down, meaning as x increases, y decreases, so the slope is negative. Eliminate choice D.

Now calc the slope. slope = rise/run = (y2-y1)/(x2-x1). Pick any 2 points. I am going to use (0,1) and (5,0). Honestly it doesn't matter which 2 points you use.

slope = (1-0)/(0-5)

slope = 1/-5 = -1/5

So the equation would be y=-(1/5)x + 1, which is option B.

Area of sector = θ/360 × πr²

θ = m∠ACB = 120°

radius = r = 6

Answer:

math is hard

Step-by-step explanation:

The equation of the line in slope-point form is:

y - 7 = -4/5(x + 6)

The equation of a line in slope-point form is given by:

y - y₁ = m(x - x₁)

where:

(x₁, y₁) represents the coordinates of a point on the line.

m represents the slope of the line.

m = (y₂ - y₁)/(x₂ - x₁)

(x₁, y₁) represents the coordinates of the 1st point on the line

where (x₂, y₂) represents the coordinates of the 2nd point on the line

We have

(x₁, y₁) = (-6, 7)

(x₂, y₂) = (4, -1)

m = (y₂ - y₁)/(x₂ - x₁)

m = (-1 - 7) / (4 - (-6))

m = -8/10

m = -4/5

Using y - y₁ = m(x - x₁):

y - 7 = -4/5(x - (-6))

y - 7 = -4/5(x + 6)

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Answer:

$17,184.80.

Step-by-step explanation:

Jessica's loan for home renovations is for $17,100 for 54 days. The bank charges simple interest at an annual rate of 9.65%. To calculate the interest charged, first, we need to find the daily interest rate, which is 9.65% divided by 365, resulting in 0.0264%. The total interest charged on the loan is $84.80, which is calculated by multiplying the daily interest rate by the loan amount and the number of days (0.000264 x $17,100 x 54). Therefore, Jessica's total amount owed to the bank at the end of the loan term is $17,184.80.

Collin's gross salary, after the 7% raise, for each 2-week pay period, will be approximately $1,159.17.

To calculate Collin's gross salary after the 7% raise for each 2-week pay period, we need to find the raise amount and add it to his current gross salary.

Collin's current gross salary is $1,083.34.

To find the raise amount, we multiply his current gross salary by 7% (or 0.07):

Raise amount = $1,083.34 \(\times\) 0.07

= $75.8338 (rounded to two decimal places)

Now, we add the raise amount to his current gross salary to find the new gross salary:

New gross salary = $1,083.34 + $75.8338 = $1,159.1738 (rounded to two decimal places)

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Step-by-step explanation:

this is a relatively easy function. Just plug in the value for x

Answer:

10.3

Step-by-step explanation:

(7 + 8 + 10 + 10 + 12 + 15) / 6 = 10.333

Answer: Solve for the specified variables

Step-by-step explanation:

1. w= A/l

2. d=C/pi

3. s=v-gt

4. y= 5/2x-11/2

5. P^2= P^1V^1 / P^2 Put ^ as lowercase as shown, can't find symbol on my keboard T.T

6. W= Ke2g / V^2

7. h= V / 2/3 pi r^2

8. n=2S/a+k

9. S=A/pi r - r (not 100% sure on that one)

10. r= E/I-R

11. h= E-1/2mv^2/mg

12. a=K+5b/b+3

13. c=ab/b+a

Wooh, finally finished all that. Hope I didn't make any mistakes. Have a great day!

Answer:

6 by 8 or ( -4. 4)

Step-by-step explanation:

because that the answer

Answer:

4-2(16x+8)^1/3=-8

-2(16x+8)^1/3=-12

(16x+8)^1/3=6

16x+8=216

16x=208

x=13

Checking if x=13 is an extraneous solution:

4-2[16(13)+8]^1/3=-8
4-2(208+8]^1/3=-8

4-2(216)^1/3=-8

4-2(6)=-8

4-12=-8

-8=-8

Not an extraneous solution.

Answer:

option d.opposite / adjacent

Step-by-step explanation:

opposite /adjacent ratio represents the tangent of an angle .

hope it is helpful to you ☺️

Answer:

D.

Step-by-step explanation:

From the trigonometry shortcuts we can use the acronyms:

SOH  CAH  TOA

for an arbitrary angle Ф, plug in the length of the sides:

sin(Ф) = opposite/hypotenuse

cos(Ф) = adjacent/hypotenuse

tan(Ф) = opposite/adjacent

Answer: Divide the volume of the bath tub by the rate at which the hose folks the bath tub

Time = 251/ 4.86

= 51.64 hours

Step-by-step explanation:

Justin's average speed from Boston to Hyannis is 40 miles per hour.

We define the average speed as the quotient between the total distance traveled and the total time in which that distance was traveled.

Here we know that Justin travels 70 miles from Boston to Hyannis, and he travels that distance in 1 hour and 45 minutes.

First notice that:

1 hour = 60 min

45 min = 45/60 hours = 0.75 hours.

Then:

1 hour and 45 min = 1.75 hours.

Then the average speed will be:

S = 70mi/1.75h = 40 miles per hour.

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The number of jerseys that the senior class at Legion Academy can purchase for $430, using quadratic equation, is 190.

Quadratic equation is an algebraic equation of the second degree in x, represented in the form of ax²+bx+c=0.

In the quadratic equation, a, b, and c are known values but a ≠ 0 and x is unknown.

x = [-b ± √b² - 4ac]/2a

when ax^2 + bx + c = 0

C = 0 .1x² + 2.4x + 25, where C is the amount, it costs to buy x jerseys.

Simplifying the equation, we get:

x = 0.2 − 2.4 ± 40.4​

The two possible values of x are:

1) x = 0.2 − 2.4 + 40.4​ = 190

or

2) x = 0.2 − 2.4 − 40.4 ​= −214

The value of x cannot be negative, therefore, the class bought 190 jerseys for $430.

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Answer:

Teachers are the one that teach the doctors how to do their profession. They are both critical parts of society and should both be respected. Though doctors work with patients and determine what problems they have and how to help solve them. They work on treatments and can reassure patients in tough situations. They only goal is to help others and keep everyone has happy and healthy as possible.

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer: $3.65

Step-by-step explanation:

By subtracting the money he has by the controller cost, you'll get the remaining balance he has left.

23.50 - 19.85 = 3.65

Answer:

$3.65

Step-by-step explanation:

$23.50 - $19.85 = $3.65

Since Boris use m minutes

Since he pays a monthly fee of 22 dollars (fixed amount)

Since the cost of each minute