Which of the following is the equation for the line perpendicular to the line y=−x+20 that passes through the point (−4, 2)?

A)Y = -x + 6
B)Y = x - 2
C)Y = x + 6
D)Y = -x - 2

Jara has 2 alternatives: -2 and -1 A number line is a diagram that depicts numbers,

As we walk along the line from left to right, the numbers rise. Positive numbers are often to the right and negative numbers to the left of zero, which is typically in the middle of the line.

Jara wants to choose a negative number that, in this instance, is closer to zero than -3. This suggests that instead of choosing -3, she should choose a negative integer that is situated nearer to zero on the number line.

-2 and -1 are the two negative numbers that are nearer to zero than -3. On the number line, these values are to the right of -3 and are nearer to zero than -3.

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Answer:

well im pretty sure its ( 1,1,3)

Step-by-step explanation:

21-1-2

The equation that quickly reveals the y-intercept is f(x) = 3x²+ 36x + 33 and the y- intercept is 33

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

This shows that the y-intercept is gotten when x is 0

Therefore amongst the equation above equation 1 is the equation that easily shows the y-intercept.

The equation f(x) = 3x²+ 36x + 33 is presented in a standard form of quadratic equation.

when x= 0

f(x) = 3x²+ 36x + 33

f(x) = 3(0)²+ 36(0) + 33

f(x) = 0+ 0+ 33

= 33

therefore the y-intercept is 33

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The most important details are the formulas used to calculate the amount to be invested today, the sales expected to be made after 6 years, the implied rate of interest, and the time taken to save money for a new car. The initial investment is R300,000 and the rate of interest is 11%. The amount needed after t years is R400,000 and the time taken to save money is 4.73 years.

2.1) Calculation of the amount to be invested today: Given, the amount needed for the education of daughter is R170,000 and she will need it after 15 years.The expected rate of return is 8.5% per year.Using the formula:

Future Value = Present Value * [1+rate]^nFuture value = R170,000Present Value = ?Rate = 8.5%Time = 15 years

Future value = Present value * [1 + rate]^n170000

= Present value * [1 + 0.085]^15Present value = R56,453.74

Therefore, the amount that the person needs to invest today is R56,453.742.2)

Calculation of the sales expected to be made after 6 years:Given, the sales of widgets made in 1 year are 2 million.The expected increase in sales is 16% per year for the next 6 years.

Using the formula for the compound amount:

Final amount = P(1 + r/n)^(nt)

P = Principal Amount

r = rate of interest

n = number of times per year compounded

t = time in years2,000,000(1 + 0.16/1)^(6*1) = 7,170,881.942

Therefore, the number of widgets expected to be sold in 6 years is 7,170,881.942.2.3) Calculation of the implied rate of interest:Given, R1,500 will be received in 4 years if R800 is invested today.Using the formula to calculate interest rate:

Simple interest formula :I = PRT/100

I = Interest

P = Principal Amount

R = Rate of Interest

T = TimeI = R * P * T

Given, I = R1,500P = R800T = 4 years R = I/P*T = (1500/800*4) = 0.46875Rate of Interest = 46.875%

Therefore, the implied rate of interest is 46.875%.2.4) Calculation of time taken to save money for a new car:Given, a new car is worth R400,000.The investment at the rate of 11% per year is being made.Initial investment is R300,000Let the time taken to save money for a new car be 't' years.Using the formula:

Amount = Principal Amount * [1 + Rate of Interest]^(Number of years)

New car price = R400,000Principal Amount = R300,000Rate of Interest = 11%Amount needed after t years = R400,000

\(Principal Amount = Amount needed after t years / [1+ Rate of Interest]^tPrincipal Amount\)

\(= 400,000 / [1.11]^t300,000*[1.11]^t\)

\(= 400,000[1.11]^t\)

= 4/3t

= 4.73 years

Therefore, the time taken to save the money for the new car is 4.73 years.

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Answer: True

Step-by-step explanation: Hope this help :D

Answer:

Perimeter = 2*(na) + 2b

                 = 2na + 2*b

The area of the polygon would be equal to the combined area of the cards.

Step-by-step explanation:

To arrange the rectangular cards without overlapping to form one larger polygon with the smallest possible perimeter, Juanita should align the cards in a way that their sides form the perimeter of the polygon.

If each rectangular card has dimensions "a" inches by "b" inches, Juanita can arrange them by aligning the sides of the cards in a continuous manner. Let's assume she arranges "n" cards in a row. The resulting polygon will have a length of n*a inches and a width of b inches.

The perimeter of the polygon can be calculated by adding the lengths of all sides. In this case, since we have n cards aligned horizontally, the perimeter would be the sum of the lengths of the top and bottom sides, as well as the sum of the lengths of the left and right sides.

Perimeter = 2*(na) + 2b

= 2na + 2*b

The area of the resulting polygon can be calculated by multiplying its length by its width.

Area = (na) * b

= na*b

Now, let's compare the area of the polygon to the combined area of the individual cards. Assuming Juanita has "n" cards, the combined area of the cards would be n*(ab), as each card has an area of ab.

The ratio of the area of the polygon to the combined area of the cards can be calculated as:

Area of the polygon / Combined area of the cards

= (nab) / (n*(a*b))

= 1

Therefore, the area of the polygon would be equal to the combined area of the cards.

To summarize, to form the smallest possible perimeter, Juanita should align the rectangular cards in a continuous manner, and the resulting polygon's perimeter would be 2na + 2*b. The area of the polygon would be equal to the combined area of the cards.

Answer:

Step-by-step explanation:

and equals the state of art called minecraft

The linear approximation of f at x = π/4 is  1 + 2(x - π/4), the value tan(π/5) is 1 - 3π/40 ≈ 0.3634.

Linear approximation is a technique used in calculus to approximate the value of a function near a particular point using the tangent line of the function at that point. This approximation is often used to simplify calculations and solve problems in a variety of fields, including physics, engineering, and finance.

The linear approximation of a function f(x) near a point a is given by:

L(x) = f(a) + f'(a)(x-a)

where f'(a) is the derivative of the function f(x) evaluated at a. The linear approximation L(x) is the equation of the tangent line to the function at the point (a, f(a)), and it provides an approximation of the function's behavior near that point.

We have,

f(x) = tan x

f'(x) = sec² x

At x = π/4, we have

f(π/4) = tan(π/4) = 1

f'(π/4) = sec²(π/4) = 2

So the linear approximation of f at x = π/4 is given by

L(x) = f(π/4) + f'(π/4)(x - π/4)

 = 1 + 2(x - π/4)

Now, we can use this to estimate tan(π/5) as follows:

tan(π/5) ~ L(π/5)

      = 1 + 2(π/5 - π/4)

      = 1 + 2π/20 - 2π/16

      = 1 + π/40 - π/8

      = 1 - 3π/40

So the estimated value of tan(pi/5) using the linear approximation of f(x) = tan x at x = π/4 is

tan(π/5) ≈ 1 - 3π/40 ≈ 0.3634 (using π ≈ 3.14159).

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Answer:

8.00am

Step-by-step explanation:

from 12 at night to 12 noon the time notation for 24 hrs and 12 hrs stay the same

Answer:

3

Step-by-step explanation:

y+3=-y+9

Move -y to the left and move +3 to the right and change the + into a -

y+y=-3+9

Calculate

2y=6

Divide both members by 2

y=3

Answer:

The number of children = x = 176

The number of Adults = y = 87

Step-by-step explanation:

Let us represent

The number of children = x

The number of Adults = y

On a certain hot summer's day, 263 people used the public swimming pool.

x + y = 263.... Equation 1

x = 263 - y

The daily prices are $1.25 for children and $2.50 for adults. The receipts for admission totaled $437.50.

$1.25 × x + $2.50 × y = $437.50

1.25x + 2.50y = 437.50.....Equation 2

We substitute 263 - y for x in Equation 2

1.25(263 - y) + 2.50y = 437.50

328.75 - 1.25y + 2.50y = 437.50

- 1.25y + 2.50y = 437.50 - 328.75

1.25y = 108.75

y = 108.75 ÷ 1.25

y = 87

Solving for x

x = 263 - y

x = 263 - 87

x = 176

Therefore:

The number of children = x = 176

The number of Adults = y = 87

A 11.544 acre-feet of this ice field will melt from the beginning of day 1 (t = 0) to the beginning of day 4 (t = 3). So, correct option is C.

To solve the problem, we need to integrate the given rate of melting with respect to time over the interval [0,3] to find the total amount of ice that melts during this time.

First, we can simplify the given rate of melting by using the identity: sin³(t) = (3sin(t) - sin(3t))/4

So, M(t) = 4 - (3sin(t) - sin(3t))/4 = 16/4 - 3sin(t)/4 + sin(3t)/4 = 4 - 0.75sin(t) + 0.25sin(3t)

Integrating this expression with respect to t over the interval [0,3], we get:

\(\int\limits^3_0\) M(t) dt = \(\int\limits^3_0\) (4 - 0.75sin(t) + 0.25sin(3t)) dt

= [4t + 0.75cos(t) - (1/3)cos(3t)]|[0,3]

= (12 + 0.75cos(3) - (1/3)cos(9)) - (0 + 0.75cos(0) - (1/3)cos(0))

= 11.544

Therefore, the answer is (C) 11.544.

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Points M and N will be located on the number line as:

M is at -15

N is at 3.

Here, we have,

to Find the Coordinate of a Point on a Number Line:

The number line gives us an idea of how real numbers are ordered, where we have the negative numbers to the left, and the positive numbers to the right.

The distance between two points on a number line is the number of units between both points.

Given that point L is at -6 on a number line, thus:

Point M is 9 units away from point L = -6 - 9 = -15

Point N is 9 units away from point L = -6 + 9 = 3

Therefore, points M and N will be located on the number line as:

M is at -15

N is at 3.

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Answer:

Estimated=189

Exact=190.026

Step-by-step explanation:

Estimated values

20.7 to nearest whole number= 21

9.18 to nearest whole number= 9

Product means multiplication

Estimated product of 20.7 and 9.18

=21×9

=189

Exact product of 20.7 and 9.18

=20.7 × 9.18

=190.026

It has 3 decimal places

Answer:

The estimated product of 20.7 and 9.18, after rounding both factors to the nearest whole number,

is

✔ 189

.

The exact product of 20.7 and 9.18 has

✔ 3

decimal places.

Step-by-step explanation: Hope this helps(:

Given:

The sequence can be generated by

\(a_n=4a_{(n - 1)}\)

Where \(a_1= 6\) and \(n\) is a whole number greater than 1.

To find:

The first four terms of the given sequence.

Solution:

We have,

\(a_n=4a_{(n - 1)}\)          ...(i)

It is given that \(a_1= 6\). So, for \(n=2\), we get

\(a_2=4a_{(2 - 1)}\)

\(a_2=4a_1\)

\(a_2=4(6)\)

\(a_2=24\)

Putting \(n=3\) in (i), we get

\(a_3=4a_{(3- 1)}\)

\(a_3=4a_2\)

\(a_3=4(24)\)

\(a_3=96\)

Putting \(n=4\) in (i), we get

\(a_4=4a_{(4- 1)}\)

\(a_4=4a_3\)

\(a_4=4(96)\)

\(a_4=384\)

The first four terms of the given sequence are 6, 24, 96,384.

Therefore, the correct option is C.

Answer:

a) the answer is 6 (6 years to get below 50% of original value)

b) the answer is 2.8 (the value of R is 2.8 so interest rate is 2.8%)

Step-by-step explanation:

a) We have to find the number of years n after which his bike's value is less than 50%

Now, Originally, his bike's value was,

£14500

and 50% of that is,

(0.5)(14500) = 7250 = V

Putting this value of V into the given formula and solving for n,

\(7250 = 14500*(0.88)^n\\7250/14500 = 0.88^n\\1/2 = 0.88^n\\Taking \ the \ log \ on \ both\ sides,\\log(1/2) = log(0.88^n)\\log(1/2)=nlog(0.88)\\n = log(1/2)/log(0.88)\\which \ gives,\\n = 5.422\)

Since we only look at the end of years,

so we round up to get,

6 years,

After 6 years, The value becomes less than 50% of the original

b) Work out the value of R

The invested amount = 8500

he invests for n = 1 year.

and pays 30% tax on the amount he gets due to interest.

Now, without tax, the amount he gets is,

A = (8500)(R%)

After paying 30% of A as tax, he gets £166.60

so, 70% of A is £166.60

or,

(0.7)A = 166

A = 238

Using this to find R, since

A = (8500)(R%)

238 = (8500)(R%)

238/8500 = R%

0.028 = R%

Hence multiplying by 100 on both sides to get R,

R = 2.8

The interest rate is 2.8%

The coordinate of the point that represents the number of pens that Keisha buys and the total cost is (2, 4)

The given parameters are

Number of pen = 2

Unit price = $2

This means that the total amount spent is

Total amount = Number of pen * Unit price

Evaluate the product

Total amount = 2 * 2

Evaluate the product

Total amount = 4

So, the coordinate of the point that represents the number of pens that Keisha buys and the total cost is (2, 4)

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Partial product multiplication involves breaking down multiplication problems into smaller, manageable parts. It is taught by demonstrating how to multiply each digit of one number by each digit of the other number and then adding the products.

Start with a simple example. For instance, you could use the problem 23 x 4. Write out the problem horizontally with the larger number on top.

Break down the numbers. Look at each digit in the larger number and multiply it by the entire smaller number. For example, 2 x 4 = 8 and 3 x 4 = 12.

Write out the partial products. Write each partial product below the original problem, aligned by the place value of the digit being multiplied. In this case, the partial products are 8 and 12.

Add up the partial products. Add up the partial products to get the final product. In this case, 8 + 12 = 20. So 23 x 4 = 92.

Practice with more examples. Once students understand the process, you can give them more complex problems to solve using partial product multiplication. Make sure to include problems that require carrying over to the next place value.

Reinforce the concept. To help reinforce the concept, you can have students create their own problems to solve using partial product multiplication.

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Answer:

y = - \(\frac{5}{2}\) x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2, - 6 ) and (x₂, y₂ ) = (- 2, 4 )

m = \(\frac{4-(-6)}{-2-2}\) = \(\frac{4+6}{-4}\) = \(\frac{10}{-4}\) = - \(\frac{5}{2}\) , then

y = - \(\frac{5}{2}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 2, 4 ) , then

4 = 5 + c ⇒ c = 4 - 5 = - 1

y = - \(\frac{5}{2}\) x - 1 ← equation of line

Answer: 132 with a remainder of 5

Step-by-step explanation: 137/6 gives us 22 an multiplying 22x6 gives us 132 leaving us with a remainder of 5.

Answer:

He can sell 22 groups of crickets and have 5 left over

Step-by-step explanation:

Answer:

500 feet

Step-by-step explanation:

\(area \: = s \times s \\ 250000 = {s \\}^{2} \\ \sqrt{250000} = \sqrt{ {s}^{2} } \\ 500 = s\)

The flux of F coming out of the circle C is 126π.

The flux of a vector field, F, out of a surface, S, is given by the formula

Flux = ∮F •  n ds,

where n is a unit normal vector to the surface S.

In this case, the surface S is the circle C with radius 6 centered at the origin and the vector field F is given by F(x, y) = (7x, 11). We can use Green's Theorem to find the flux from the circle C. The equation for the circle is x2 + y2 = 36. Differentiating this equation with respect to x and y gives us the unit normal vector, n = (x/6, y/6).

Plugging these values into the flux formula, we get

Flux = ∮F •  n ds = ∮ (7x, 11) •  (x/6, y/6) ds

= ∮ 7x2/6 + 11y/6 ds

= (7/6) ∮ (x2 + y2) ds

= (7/6) * Area of C

= (7/6) * π * 36

= 126π.

Therefore, the flux of F coming out of the circle C is 126π.

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The variable expression that represents Nora's finishing time, given Maria's time (m) in seconds, can be expressed as (m - 3.8). This expression shows Nora's finishing time by subtracting 3.8 seconds from Maria's time.

To determine Nora's finishing time, we start with the given information that Nora finished the race 3.8 seconds before Maria. This means that Nora's finishing time must be less than Maria's time. By subtracting 3.8 seconds from Maria's time (represented by the variable m), we obtain Nora's finishing time. The expression (m - 3.8) provides the relative time difference between Nora and Maria, where Nora finishes 3.8 seconds earlier than Maria. Therefore, by substituting the value of Maria's time into this expression, we can calculate Nora's finishing time.

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Answer:

More info needed

Step-by-step explanation:

If 13,-6 represents (13,-6), this is a point. The y coordinate is -6, but there would be no y intercept since a single point won't cross the y axis.

Answer:

1/4 chance

Step-by-step explanation:

First you need to find the probability of Tess choosing a red ribbon.

1/2

Then you need to multiply that probability by the reciprocal of 2, which is 1/2

1/2 x 1/2 = 1/4

Answer:

6.244 x 10^-1

Step-by-step explanation:

1. The cheapest meat is Ms barker free Ronge whole chicken in $6 per kilo.

2. The cost of 200 grams of honey leg ham is $3.4.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The cost of all meat is shown in figure.

Now,

By the figure, we get;

The cheapest meat is Ms barker free Ronge whole chicken which is in

$6 per kilo.

And, The cost of honey leg ham = $17 per kilo

Since, 1 kilograms = 1,000 grams

The cost of 1 gram of honey leg ham = $17/1000

So, The cost of 200 grams of honey leg ham = 200 × 17 / 1000

                                                                      = $3.4

Thus,

1. The cheapest meat is Ms barker free Ronge whole chicken in $6 per kilo.

2. The cost of 200 grams of honey leg ham is $3.4.

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1. The total amount (future value) Marcus had at the end of the second year of investing $5,000 at 2.5% compounded annually was $5,253.13.

2. The minimum number of years Marcus must leave the $5,253.13 to be more than $10,000 is 11.3 years.

The future value is the compounded present value at an interest rate.

The future value can be derived from an online finance calculator as follows:

With the future value so determined, we can then compute the minimum time in years required for it to reach more than $10,000 at the simple interest rate.

Initial investment = $5,000

Interest rate = 2.5% compounded annually

Investment period = 2 years

N (# of periods) = 2

I/Y (Interest per year) = 2.5%

PV (Present Value) = $5,000

PMT (Periodic Payment) = $0

Results:

FV = $5,253.13

Total Interest = $253.13

Principal = $5,253.13

Interest rate = 8% per annum

Future amount = $10,000

Time to reach the future amount = (Future Value/Principal - 1) ÷ Interest rate

= ($10,000/$5,253.13 - 1) ÷ 0.08

= 11.3 years

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