The traight line L ha equation 5x2y=31. The point A ha coordinate (0,1). The traight line M i perpendicular to L and pae through A. Line L croe the y-axi at the point B. Line L and M interect at the point C. Work out the area of the triangle ABC

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx

where

k is the constant of proportionality or slope

In this problem

we have a proportional relationship between the land planted and the wheat produced

Let

l ----> number of acres

w ----> wheat produced

so

w=kl

take the point (1,50)

Find teh value of k

k=w/l

k=50/1=50

therefore the equation is equal to

w=50l

When the bottom of the 6-foot ladder is 2 feet from the wall, the bottom is moving along the ground at 1 foot per second.

To find the rate at which the bottom of the ladder moves along the ground, we can use the Pythagorean theorem and related rates. Let x be the distance from the bottom of the ladder to the wall, and y be the height of the ladder on the wall. The Pythagorean theorem is x² + y² = 36.

Differentiating both sides with respect to time (t) gives 2x(dx/dt) + 2y(dy/dt) = 0. We are given that dy/dt = -2 ft/s, and we need to find dx/dt when x = 2 feet.

To find y, we can use the Pythagorean theorem: 2² + y² = 36, so y² = 32, and y = 4√2. Plugging these values into the differentiated equation, we get 2(2)(dx/dt) + 2(4√2)(-2) = 0. Solving for dx/dt, we find that dx/dt = 1 ft/s.

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Answer:

=2,400,000

Step-by-step explanation:

=30,000 x 80

=2,400,000

Answer:

The equation could be used to determine the total production costs for the company if it produced x widgets last month is

y = $8,906.00 + $2.64x ⇒ B

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

∵ A company has fixed costs of $8,906.00 each month

→ That means it is a fixed value every month

∴ b = 8,906.00

∵ The cost of each widget it produces is $2.64 for

→ That means the value is changing according to the number of widgets

∴ m = 2.64

∵ y represents the total costs of production last month

∵ x represents the number of widgets the factory produced last month

→ Substitute the values of m and b in the form of the equation above

∴ y = 2.64x + 8,906.00

The equation could be used to determine the total production costs for the company if it produced x widgets last month is

y = $8,906.00 + $2.64x

Answer:

-3/4

Step-by-step explanation:

First, let's convert the mixed numbers into improper fractions in an effort to make this problem easier to solve.

-2 1/2 as a mixed number is -5/2 and -1 3/4 as a mixed number is -7/4.

Our problem is now -5/2 - (-7/4).

We still can't solve this because the two fractions do not share a common denominator. 4 can serve as one, so -5/2 with a denominator of 4 would be -10/4.

The problem is now -10/4 - (-7/4).

Two negatives make a positive so the problem can be rewritten as -10/4 + 7/4. The final answer is -3/4.

Answer:

B) 2x^9

Step-by-step explanation:

i hope that helps

Answer:

Step-by-step explanation:

\(\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}\)

The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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One more than two-thirds of a number is no less than 25 is x = -30.

An equation is a mathematical expression that contains two algebraic expressions on either side of the "equals (=)" sign. It shows the equality between the words written to the left and the words written to the right. In all mathematics there is L.H.S = R.H.S (left side = right side). Equations can be solved to find the values ​​of unknown variables that represent unknown quantities or numbers. If there is no "equals" sign in the expression, it means it is not equal. It will be treated as a guide.

let the no. be x

According to the question:-

2/3 × x = 1/2× (x-5)

⇒ 2x/3 = x/2- 5

⇒ 2x/3 - x/2 = -5

⇒ (4x- 3x)/6 = -5

⇒ x/6  = -5

⇒ x = -30.

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the largest mortgage Alicia can get with a monthly payment of $1,

100 is approximately $230,109.

1. Sean and Teresa's 20-year adjustable-rate mortgage (ARM) is for $450,000 with terms of 11/1, and the initial interest rate is 3.2% compounded monthly.

a. To calculate their initial monthly payment, we can use the loan payment formula:

Monthly Payment = P * (r *\((1 + r)^n) / ((1 + r)^n - 1),\)

where P is the principal amount, r is the monthly interest rate, and n is the total number of payments.

P = $450,000

r = 3.2% / 100 / 12 = 0.00267 (monthly interest rate)

n = 20 years * 12 = 240 (total number of payments)

Plugging in these values, we get:

Monthly Payment = $450,000 * (0.00267 *\((1 + 0.00267)^{240}) / ((1 + 0.00267)^{240} - 1)\)

Monthly Payment ≈ $2,000.09

Therefore, their initial monthly payment is approximately $2,000.09.

b. After 11 years, we need to calculate the present value of the mortgage.

Using the present value formula:

Present Value = Future Value / (1 + r)^n,

where Future Value is the remaining mortgage balance, r is the monthly interest rate, and n is the remaining number of payments.

The remaining number of payments is 20 years - 11 years = 9 years * 12 = 108 months.

Plugging in the values, we get:

Present Value = $450,000 / (1 + 0.00267)^108

Present Value ≈ $307,513.92

After 11 years, the present value of the mortgage will be approximately $307,513.92.

c. After 11 years, the interest rate increases to 5.9%. To calculate their new monthly payments, we can use the same loan payment formula but with the new interest rate.

r = 5.9% / 100 / 12

= 0.00492 (new monthly interest rate)

Plugging in the new interest rate and other values, we get:

Monthly Payment = $307,513.92 * (0.00492 *\((1 + 0.00492)^{132)} / ((1 + 0.00492)^{132} - 1)\)

Monthly Payment ≈ $2,188.11

Therefore, their new monthly payments after 11 years, with the interest rate increased to 5.9%, will be approximately $2,188.11.

2. Alicia wants a monthly mortgage payment of up to $1,100 for a 30-year mortgage at 4.4% interest (compounded monthly).

To calculate the largest mortgage Alicia can get, we rearrange the loan payment formula to solve for the principal amount (P):

P = (Monthly Payment * \(((1 + r)^n - 1)) / (r * (1 + r)^n)\),

where Monthly Payment is $1,100, r is the monthly interest rate, and n is the total number of payments.

r = 4.4% / 100 / 12

= 0.00367 (monthly interest rate)

n = 30 years * 12

= 360 (total number of payments)

Plugging in the values, we get:

P = ($1,100 * ((1 + 0.00367)^360 - 1)) / (0.00367 * (1 + 0.00367)^360)

P ≈ $230,109.35

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The inverse of the function is given by:

\(w = \frac{82.9}{\sqrt[3]{d}}\)

In this problem, the function is:

\(w(d) = \left(\frac{82.9}{d}\right)^3\)

The output is w, input d, hence we exchange them, and isolate w.

\(d = \left(\frac{82.9}{w}\right)^3\)

\(dw^3 = 82.9^3\)

\(w^3 = \frac{82.9^3}{d}\)

\(w = \sqrt[3]{\frac{82.9^3}{d}}\)

\(w = \frac{82.9}{\sqrt[3]{d}}\)

Considering a weight of 66 pounds, \(w = 66\), hence the distance is:

\(dw^3 = 82.9^3\)

\(d = \frac{82.9^3}{66^3}\)

\(d = 1.98\)

Considering a weight of 66 pounds, the distance is of 1.98 inches.

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Answer:

an obtuse angle is an angle that is wider than 90⁰, 100⁰ for example is an obtuse angle

Answer:

Sextic or Hexic polynomial

Step-by-step explanation:

Polynomials of degree 6 are called Sextic or Hexic polynomials

Or if the naming is to be done based on the number of terms, it is a binomial

Answer:

3x+2

Step-by-step explanation:

i had a test with the same question, i promise its right :)

The formula for calculating the effective annual rate of interest with quarterly compounding is:

(1 + r/4)^4 - 1 = A/P

where r is the quarterly interest rate, A is the final amount, and P is the principal.

In this case, P = $2,000, A = $3,000, and the time period is 7 years or 28 quarters.

So we have:

(1 + r/4)^4 - 1 = 3000/2000

(1 + r/4)^4 = 1.5

1 + r/4 = (1.5)^(1/4)

r/4 = (1.5)^(1/4) - 1

r = 4[(1.5)^(1/4) - 1]

To get the effective annual rate, we need to convert the quarterly rate to an annual rate by multiplying by 4:

effective annual rate = 4[(1.5)^(1/4) - 1] ≈ 8.84%

Therefore, the effective annual rate of interest at which $2,000 will grow to $3,000 in seven years if compounded quarterly is approximately 8.84%, rounded to 2 decimal places.

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Answer: (not sure)

half of 2/8 is 0.125 and half of 8/16 is 0.25

if you want half of both together it's 0.625

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

Upon examining the graph, you can realize that angle 3x is the same as the angle directly to the left of 9x. Since that makes a straight line, we can realize that that sums up to 180. We call this a linear pair.

so you have:

3x+9x = 12x = 180

x = 15

A important concept to know here is vertical angles. Vertical angles occur when two lines intersect each other. The opposite angles formed at an intersection are congruent, which is why 1 is congruent to 3x.

Therefore, angle 1 is 45 degrees.

Answer:

x=7

Step-by-step explanation:

2(5+2x)=−4+6x

Distribute

10 +4x = -4 +6x

Subtract 4x from each side

10 +4x-4x = -4+6x-4x

10 = -4+2x

Add 4 to each side

10+4 =-4+2x+4

14 =2x

Divide by 2

14/2 =2x/2

7 =x

Answer:

\(4^m\)

Step-by-step explanation:

When you exponent an exponent, you multiply the powers together.

When you divide exponents, you subtract the powers.

Step 1: Convert to same base

log₄64 = 3

Step 2: Rewrite equation

\(\frac{(4^3)^{0.5m}}{4^{0.5m}}\)

Step 3: Simplify

\(\frac{4^{1.5m}}{4^{0.5m}}\)

Step 4: Simplify

\(4^m\)

IM NOT QUIT SO SURE BUT IF MY CALCULATIONS ARE CORRECT ITS C

Answer:

i got u, its A

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

Because the line lies on x =3

Answer:

x=3

Step-by-step explanation:

This is a vertical line ( up and down)

Vertical lines are of the form x=

x=3

0.75 i think

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

x=34x=34

Decimal Form:

0.75

Answer:

b

Step-by-step explanation:

51% of the sodas served at Emilia's Diner last night were regular.

A percentage is a relative value that represents one hundredth of a whole. One percent (symbolised 1%) is one hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice the given amount.

To calculate the percentage of regular sodas, divide the total number of sodas by the number of regular sodas and multiply the result by 100.

As a result, the percentage of regular sodas is:

(51/100) x 100% = 51%

As a result, 51% of the sodas served last night at Emilia's Diner were regular.

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Step-by-step explanation:

6×(2.5)+1.5

15+1.5

16.5

or

f(x)= 6x+1.5

f(2.5)= 6(2.5)+15

f(2.5)=16.5

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The approximate values of the non-integral roots of the polynomial equation are -5.57, -1.95, 0.21, 1.27, and 4.73. These values represent the values at which the polynomial equation evaluates to zero, indicating the roots of the equation.

To find the roots of a polynomial equation, we set the equation equal to zero and solve for the unknown variable. In this case, we have a polynomial equation with non-integral roots.

To obtain the approximate values of these roots, numerical methods such as iterative methods or numerical approximation techniques can be used. These methods involve making educated guesses and refining the guesses until the equation evaluates to zero.

The resulting approximate values for the non-integral roots of the polynomial equation are -5.57, -1.95, 0.21, 1.27, and 4.73. These values are not exact, but they are close approximations to the actual roots of the equation.

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Answer:

3 feet

Step-by-step explanation:

\(\boxed{area \: of \: triangle = \frac{1}{2} \times base \times height}\)

Given that the area is 6 ft² and the height is 4 ft,

6= ½ ×base ×4

Simplify:

2(base)= 6

Length of base

= 6 ÷2 (÷2 on both sides)

= 3 ft

Answer:6.67 for number 1

Step-by-step explanation:

Answer:

Answer 1 is 550

and 2 is also 550

Step-by-step explanation:

\((\dfrac{1}{3})^4=\dfrac{1^4}{3^4}=\dfrac{1\cdot1\cdot1\cdot1}{3\cdot3\cdot3\cdot3}=\boxed{\frac{1}{81}}\)