find the value of 4x-6y when x=3 and y=-5

(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

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Answer:

7.1 x 10³

Step-by-step explanation:

Move your decimal so that it follows your first whole number greater than zero. The number of places you moved the decimal is the same as the exponent. Since the number 7.1 needs to INCREASE to be 7,100, then the exponent is positive.

Answer:

7.1 x 10\(^{3}\) (note the 3 is an exponent)

Step-by-step explanation:

1. Count how many places there are to the right of 7

2. There are 3

3. Apply the formula of scientific notation a x 10\(^{b}\)

4. 7.1 x 10\(^{3}\)  (remove all digits after 7.1  

Hope this helps :)

Person 3's payment exceeded person 2's payment by $20.

To find out how much more person 3 paid than person 2, we need to calculate the amounts each person paid based on the given ratio and then compare their payments.

The ratio given is 1:2:3, which means that person 1 gets 1 part, person 2 gets 2 parts, and person 3 gets 3 parts of the total amount.

Step 1: Calculate the total number of parts in the ratio.

1 + 2 + 3 = 6

Step 2: Determine the value of one part.

$120 (total amount) divided by 6 (total number of parts) = $20

Step 3: Calculate the payments for each person based on the ratio.

Person 1: 1 part * $20 = $20

Person 2: 2 parts * $20 = $40

Person 3: 3 parts * $20 = $60

Therefore, person 3 paid $60, while person 2 paid $40. To find out how much more person 3 paid than person 2, we subtract the amount person 2 paid from the amount person 3 paid:

$60 - $40 = $20

Hence, person 3 paid $20 more than person 2.

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The time he start shopping is 2 : 00 PM

From the question, we have the following parameters that can be used in our computation:

Time spent = 25 minutes

Time he left the store = 2 : 25PM

Using the above as a guide, we have the following:

Time he started = Time he left the store - Time spent

substitute the known values in the above equation, so, we have the following representation

Time he started = 2 : 25PM - 25 minutes

Evaluate

Time he started = 2 : 00 PM

Hence, the time he start shopping is 2 : 00 PM

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Answer:

340

Step-by-step explanation:

Answer:

33.3

Step-by-step explanation:

You need to divide 200  and 150 to get you 4/3. Then you will have to _____________________________

Answer:

Both ate the same amount of cake, there will be 6/8 or 3/4ths of the cake left.

Step-by-step explanation:

2/16 is equivalent to 1/8. Therefore they ate the same amount of cake.

Answer:

they ate the same amount 1/8 and 2/16 are the same thing.3/4

Step-by-step explanation:

they both ate 1/8  so 8/8-2/8=6/8=3/4 of the cake left

Answer:

16 for both

Step-by-step explanation:

Therefore, we can see that 10 kilometers is greater than 9 miles (10 km > 14.48 km), and so the comparison "10 kilometers < 9 miles" is false.

A kilometer (km) is a unit of measurement for length, commonly used in the metric system. It is equal to 1000 meters or approximately 0.62 miles. Kilometers are often used to measure longer distances, such as the distance between two cities or countries.

by the question.

To explain this, we can convert kilometers to miles or miles to kilometers to compare them in the same unit.

1 mile is approximately equal to 1.61 kilometers. So, 9 miles would be approximately equal to 14.48 kilometers.

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It is important to note that this equation assumes a constant density of seawater, which is not always the case in the deep ocean. In addition, the pressure at a given depth can vary depending on factors such as temperature and salinity. This equation should be used with caution and in conjunction with other measurements and data analysis techniques.

The given equation for pressure in pounds per square foot at a depth of d feet is P = 14 + 4d/9. We are given that the pressure measured by the scientific team is 306 pounds per square foot. To find the depth at which this pressure is measured, we need to solve the equation for d.

Substituting P = 306 in the equation, we get:

306 = 14 + 4d/9

Multiplying both sides by 9, we get:

2754 = 126 + 4d

Subtracting 126 from both sides, we get:

2628 = 4d

Dividing both sides by 4, we get:

d = 657 feet

The scientific team is measuring the pressure at a depth of 657 feet below the surface of the ocean.

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Let's take a look through each of the potential options and see whether they meet our requirements:A. g(7) = -1We're told at the beginning of the problem that our domain is restricted to the range [-20, 5]. Our input here, x = 7, is out of that range, which means it's not in the domain and can't be true for the function g.B. g(-13) = 20Unlike 7, -13 is in the domain of g since it's between -20 and 5. 20 is also in g's range, since it's between -5 and 45. B could be true for g. We have our answer at this point, but I'll point out why the other two are false, too.C. g(0) = 2We know from the question that g(0) = -2, so this is clearly false.D. g(-4) = -11-11 is less that -5, which means it lies outside the range of g.

Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

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Answer:2300

Step-by-step explanation:

Answer:

2300

Step-by-step explanation:

we can set up a proportion:

n = not teens

.10/230 = .90/n

cross-multiply:

.10n = 207

n = 2070

now we can add the number of teenagers to get the total number of people:

2070+230 = 2300

All the solutions are,

⇒ x = 1/2 (w- v)

⇒ x = (b - 9)/(a - 2)

⇒ x = (4 + w) / (7 - v)

⇒ x = 2 / (v + w)

⇒ x = 7v/(3w - 4)

Given that;

Expressions are,

⇒ 6x + v = 4x + w

⇒ ax + 9 = 2x + b

⇒ 7x - w = vx+4

⇒ 6 - wx = vx + 4

⇒ 3(wx - v) = 4(x + v)

We can simplify as;

⇒ 6x + v = 4x + w

⇒ 6x - 4x = w - v

⇒ 2x = w - v

⇒ x = 1/2 (w- v)

⇒ ax + 9 = 2x + b

⇒ ax - 2x = b - 9

⇒ (a - 2)x = b - 9

⇒ x = (b - 9)/(a - 2)

⇒ 7x - w = vx+4

⇒ 7x - vx = 4 + w

⇒ (7 - v) x = 4 + w

⇒ x = (4 + w) / (7 - v)

⇒ 6 - wx = vx + 4

⇒ vx + wx = 6 - 4

⇒ (v + w)x = 2

⇒ x = 2 / (v + w)

⇒ 3(wx - v) = 4(x + v)

⇒ 3wx - 3v = 4x + 4v

⇒ 3wx - 4x = 7v

⇒ (3w - 4)x = 7v

⇒ x = 7v/(3w - 4)

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Answer:

Use the "Brainly" App

Step-by-step explanation:

Download the "Brainly" app, then log into your account, and enable your camera to have your questions searched into their system.

Answer:

f(x)=x/2

Step-by-step explanation:

let f(x)=ax

f(-4)=-4a=-2

-4a=-2

a=-2/-4=1/2

f(-2)=-2a=-1

-2a=-1

a=-1/-2

a=1/2

f(x)=x/2

Answer:

J.10

Step-by-step explanation:

You just have to add the numbers:

3 + 2 + (-4) + 3 + 7 + (-1) = 10

hope u like it, bye

Step-by-step explanation:

tan0=opp/adj

where opposite =3,adjacent =x,=70

tan 70=3/x

2.7474=3/x

2.7474x=3

divide both sides by 2.7474

x=3/2.7474

x=1.0919

x=1.10 to 1 d.p

Mason can iron 9/2 shirts in one hour

Mason irons 3/4 of a shirt in 1/6 of an hour

At this rate, the number of shirts ironed in one hour can be calculated as follows

3/4 ÷ 1/6 = x/1

3/4 × 6/1= x/1

18/4= x/1

cross multiply both sides

4x= 18

x= 18/4

x= 9/2

Hence Mason can iron 9/2 shirts on 1 hour

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Answer:

I think its C

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to know the intervals on which f(x) = sin(x)/(2+cos(x)²) is increasing and decreasing, and the relative extremes.

The quotient rule can be used to find the derivative of f(x). Where the derivative is positive, the function is increasing.

  f'(x) = ((2+cos(x)²)cos(x) +sin(x)(2cos(x)sin(x)))/(2+cos(x)²)²

  f'(x) = (cos(x)(2 +cos(x)² +2sin(x)²)/(2+cos(x)²)²

  f'(x) = cos(x)(3+sin(x)²)/(2+cos(x)²)²

We observe that the factors (3+sin(x)²) and (2+cos(x)²) are both positive for all x. This means the sign of the derivative will match the sign of cos(x).

The function is increasing where cos(x) > 0, on the intervals ...

  (0, π/2) ∪ (3π/2, 2π)

The function is decreasing where cos(x) < 0, on the interval ...

  (π/2, 3π/2)

The first derivative test tells us the function will have a relative maximum where the function goes from increasing to decreasing, at x = π/2. The function value at that point is ...

  f(π/2) = sin(π/2)/(2 +cos(π/2)²) = 1/2

The relative maximum is at (π/2, 1/2).

The first derivative test tells us the function will have a relative minimum where the function goes from decreasing to increasing, at x = 3π/2. The function value at that point is ...

  f(3π/2) = sin(3π/2)/(2 +cos(3π/2)²) = -1/2

The relative minimum is at (3π/2, -1/2).

Answer:

It is a right angle(info below may be useless or false)

Step-by-step explanation:

ninety, 90, XC(adj) the cardinal number that is the product of ten and nine. ninety, 90, xc(adj) being ten more than eighty.

It will take approximately 7.12 days for a culture with a doubling time of 934 minutes to grow from 15 cells/mL to 86,059 cells/mL. This is calculated using the exponential growth equation and logarithms.

If the doubling time is 934 minutes, it means that the number of cells in the culture doubles every 934 minutes. Let t be the time in minutes required to grow from 15 cells/mL to 86,059 cells/mL. We can set up the following equation:

86,059/15 = 2^(t/934)

Taking the logarithm of both sides, we get:

log(86,059/15) = (t/934) log(2)

Solving for t, we get:

t = (log(86,059/15)/log(2)) * 934 ≈ 10,288 minutes ≈ 7.12 days

Therefore, it will take approximately 7.12 days for the culture to grow from 15 cells/mL to 86,059 cells/mL under the given conditions.

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Answer:

Given the information you provided, we can model cellular phone usage over time with an exponential growth model. An exponential growth model follows the equation:

`y = a * b^(x - h) + k`

where:

- `y` is the quantity you're interested in (cell phone usage),

- `a` is the initial quantity (34 million in 1995),

- `b` is the growth factor (1.22, representing 22% growth per year),

- `x` is the time (the year),

- `h` is the time at which the initial quantity `a` is given (1995), and

- `k` is the vertical shift of the graph (0 in this case, as we're assuming growth starts from the initial quantity).

So, our specific model becomes:

`y = 34 * 1.22^(x - 1995)`

To find the cellular usage in 2003, we plug 2003 in for x:

`y = 34 * 1.22^(2003 - 1995)`

Calculating this out will give us the cellular usage in 2003.

Let's calculate this:

`y = 34 * 1.22^(2003 - 1995)`

So,

`y = 34 * 1.22^8`

Calculating the above expression gives us:

`y ≈ 97.97` million.

So, the cellular phone usage in 2003, according to this model, is approximately 98 million.

Answer:

23

Step-by-step explanation:

An integer is a whole number that can be positive, negative, or zero, without any fractional or decimal parts.

The given expressions for three consecutive integers are:

Give that twice the first number is 20 more than the second:

\(2x = (x + 1) + 20\)

Solve this equation for x:

\(\begin{aligned}2x &= (x + 1) + 20\\2x&=x+1+20\\2x&=x+21\\2x-x&=x+21-x\\x&=21\end{aligned}\)

The expression for the largest integer is (x + 2).

Therefore, to find the largest number, substitute the found value of x into this expression:

\(\begin{aligned}\sf Largest\;number&=(x+2)\\&=21+2\\&=23\end{aligned}\)

Therefore, the largest number is 23.

Answer: 0.04

Step-by-step explanation:

The area \(A_1\) of the square target with side length \(s_1=20 cm\) is:

\(A_1=s_1^{2}=20^{2}=400\)

The area \(A_2\) of the shaded square with side length \(s_2=4cm\) is:

\(A_2=s_2^{2}=4^{2}=16\)

So, the probability that the dart will land in the shaded square on the target is:

\(\frac{A_{2}}{A_{1}}=\frac{16}{400}=0.04\)

Answer:

yes ur friend is correct

Step-by-step explanation:

because the value of x .

The diagram only shows that angles M and B are supplementary ( add up to 180 degrees) and that angel 4x is adjacent to angel M.However, there is no information about the measure of angle B or angel M, so we cannot determine the value of x