Find two integers whose sum is 5 and product is -66 TWO INTEGRES
NOT 1 TWO

Answer:

12

Step-by-step explanation:

LCM of 12 and 4 is 12.

Answer:

13

Step-by-step explanation:

radius of the circle​ (r) = √12²+5² = √169 = 13

It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

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To use Newton's method to estimate the solutions of equation x^3 + 2x + 3 = 0, you first need to find the derivative of the function. In this case, the function is f(x) = x^3 + 2x + 3, and its derivative is f'(x) = 3x^2 + 2.
Newton's method formula is as follows: x_n+1 = x_n - f(x_n) / f'(x_n).
You are given the starting point x0 = 0. Let's find x1 and x2 using the formula:
x1 = x0 - f(x0) / f'(x0) = 0 - (0^3 + 2*0 + 3) / (3*0^2 + 2) = 0 - 3 / 2 = -1.5

Now, find x2:
x2 = x1 - f(x1) / f'(x1) = -1.5 - ((-1.5)^3 + 2*(-1.5) + 3) / (3*(-1.5)^2 + 2)
x2 ≈ -1.5 - (-4.875 / 11.25) = -1.5 + 0.4333 = -1.0667

Therefore, the estimated solution x2 for the equation x^3 + 2x + 3 = 0 using Newton's method is approximately -1.0667, rounded to four decimal places.

Newton's method is a numerical method used to find the roots of a function. The general idea is to start with an initial guess (in this case, x0 = 0) and use the derivative of the function to iteratively refine the guess until it converges to a solution.
To apply Newton's method to the equation x3 + 2x + 3 = 0, we need to first find its derivative:
f'(x) = 3x^2 + 2
Then, the iterative formula for Newton's method is:
xn+1 = xn - f(xn)/f'(xn)

Starting with x0 = 0, we have:
x1 = x0 - f(x0)/f'(x0) = 0 - (0^3 + 2(0) + 3)/(3(0)^2 + 2) = -1
x2 = x1 - f(x1)/f'(x1) = -1 - (-1^3 + 2(-1) + 3)/(3(-1)^2 + 2) = -1.6667
So the solution using Newton's method is x2 = -1.6667 (rounded to four decimal places).

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Answer:\(m\leq 2\)

Step-by-step explanation:

6≥5m−4

Swap sides so that all variable terms are on the left-hand side. This changes the sign direction.

5m−4≤6

Add 4 to both sides

5m≤6+4

add 6+4 to get 10

5m≤10

next Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

m ≤ 10/5

now Divide 10 by 5 to get 2.

and your answer is m ≤ 2 Hopes this helps :)

a supply function and a demand function are given- Supply: p = 1/3q2 + 8, Demand: p = 65 − 12q − 2q2. Then,  the market equilibrium point is approximately (q, p) = (3, 11).

To determine the market equilibrium point, we need to find the point where the supply function and demand function intersect, i.e., where supply equals demand. We will do this by setting the two functions equal to each other and solving for q.

Supply function: p = 1/3q^2 + 8
Demand function: p = 65 - 12q - 2q^2

Set the supply function equal to the demand function:

1/3q^2 + 8 = 65 - 12q - 2q^2

Now, let's solve for q. First, rearrange the equation:

(1/3q^2 + 2q^2) + 12q + (8 - 65) = 0

(7/3q^2) + 12q - 57 = 0

Now, use any algebraic method (such as factoring, completing the square, or the quadratic formula) to solve for q. In this case, we will use the quadratic formula:

q = (-b ± √(b^2 - 4ac)) / 2a

where a = 7/3, b = 12, and c = -57.

q = (-12 ± √(12^2 - 4(7/3)(-57))) / 2(7/3)

q ≈ 3 or q ≈ -8.143

Since we cannot have a negative quantity, the equilibrium quantity (q) is approximately 3. Now, let's find the equilibrium price (p) by plugging q back into either the supply or demand function. We will use the supply function:

p = 1/3(3^2) + 8
p = 1/3(9) + 8
p ≈ 11

So, the market equilibrium point is approximately (q, p) = (3, 11).

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Answer:

10^2*3^6

Step-by-step explanation:

there are 2 tens and 6 threes

The possible number of nickels that Alison would have had is given as  [14, 15, 16, 17]

We would first have to define the variables x and y. We have x as the number of pennies that she has while y is the number of nickels that she has.

We would have the inequality equation as

x + y ≤ 23

Let us define an equation

0.01x + 0.05y ≥ 0.75   ------ 1

Given that she is said to have 6 pennies then x would be = 6

6 + y ≤ 23

we would have to solve the equation above

y ≤ 23 - 6

y ≤ 17

put the value of 6 as x in the equation 1 above

0.01(6) + 0.05y ≥ 0.75

simplify the equation

0.05y ≥ 0.69

divide through by 0.05

y ≥ 13.8

y ~ 14

Hence we would have the range of values to be between  14 ≤ y ≤ 17.

This would be listed as y = [14, 15, 16, 17]

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The solution to the given inequalities will be x≤2 and x≤4.

The relation between two expressions that are not equal employs a sign such as ≠ ‘not equal to, > ‘greater than, or < ‘less than. The greater than and less than sign is used to represent inequalities.

Given inequalities are x-0.8>0 and -5x<10. The inequalities will be solved as:-

(I) 2 - x ≤ 0

Take negative -x to the right.

x ≤ 2

(II) x -4 ≤ 0

Solve the inequality x - 4 ≤ 0.

x ≤ 4

Therefore, the solution to the given inequalities will be x≤2 and x≤4.

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The value of side length x in the right triangle is 12.1 units.

The figure in the image is a right triangle meaning one angle of the triangle is 90 degrees.

The side x is not a missing angle, instead it is a missing side length

To solve for the missing side length x, we use the trigonometric ratio.

Note that:

Tangent = opposite / adjacent

Hence:

tan(θ) = opposite / adjacent

Plug in the given values and solve for x:

tan(34) = x/18

Cross multiply the values

x = tan(34) × 18

Evaluate

x = 12.1 units.

Therefore, side x has a value of 12.1.

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Answer:

It is given that,

x²+y² = 34 ----(1)

xy = 10½ = 21/2 ---(2)

Value of 2(x+y)²+(x-y)²

= (x+y)² + [(x+y)²+(x-y)²]

= x²+y²+2xy + 2(x²+y²)

= 34 + 2×(21/2)+2×34

= 34 + 21 + 68

= 123

The solution of the piecewise function at the given values of the independent variable g(0) is 5, g(-7) is 12 and g(2) is 7.

This is an example of a piecewise function, which is a function composed of two or more parts, each part being defined by a separate equation.

In this function, the first part is defined as g(x) = x+5 if x >= -5, and the second part is defined as g(x) = -(x+5) if x < -5.

To evaluate the function at the given values of the independent variable, we can simply substitute the values into the appropriate equation.

At x = 0,

=> g(0) = 0+5 = 5.

At x = -7,

=> g(-7) = -(-7+5) = 12.

And at x = 2,

=> g(2) = 2+5 = 7.

Therefore, the values of the function are 5, 12, and 7 respectively

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To determine the greatest number of books and magazines Julie can put on each shelf without mixing them, we need to find the highest common factor (HCF) of the given numbers.

The prime factorization of 36 is 2^2 * 3^2.

The prime factorization of 54 is 2 * 3^3.

To find the HCF, we take the highest power of each common prime factor. In this case, the HCF would be 2^2 * 3^2, which is 4 * 9 = 36.

Therefore, Julie can put a maximum of 36 books and 36 magazines on each shelf without mixing them.

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♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

18

Step-by-step explanation:

in this case, we need to find the HCF of 36 and 54 which is 18

this means that she can put 18 on 1 shelf

Answer:

Step-by-step explanation:

11 ÷ 4 = 2 + 2 = 4

1 + 4 + 4 = 9

19 ÷ 4 = 4

Answer:

1

Key:

Step-by-step explanation:

\(2^0=1\)

Answer:

w: number of weeks

Step-by-step explanation:

Because it mentions she starts with $400 and spends $40 a week. That's like saying every week she'll spend $40.  

Just because I feel like it, I'll give you the equation.

40w = 400

400/40 = w

Hope that helps and have a great day!

Answer:

Answer: 27:8

Step-by-step explanation:

There are 24 + 16 + 14 = 24+16+14= 54

54 marbles in total.

The ratio of total marbles to red marbles is 54 : 16, which simplifies to 27 : 8.

Answer: 27:8

Answer:

(28-16)

Step-by-step explanation:

x=7

4x-16

If x is 7

then it is 4x7 = 28

Therefore we can say 28-16 is our final answer.

Thank you.

Answer:

the blue one

Step-by-step explanation:

Answer: b

Step-by-step explanation:

On solving the provided question, we can say that integral  =  \(\int\limits^a_b \,\)t√9 + 16t² dt  =   \(\int\limits^a_b \,\)√9 + 16t² d (9 + 16t²)

In mathematics, integrals translate integers into functions that express concepts like displacement, area, and volume that result from the combination of little facts. Integral discovery is a process that is referred to as integration. Integrals are mathematical constructs that, in calculus, have the same meaning as areas or generalized versions of areas. The main goal of calculus is to work with derivatives and integrals. Primitives and inverse derivatives are other terms for integral. Integration is essentially utilized to determine the area of 2D space and determine the volume of 3D objects. As a result, calculating an integral of a function with respect to x entails calculating the area between the curve and the x-axis.

integral

Curves, x = t³ or,

 = 3t²

y = t⁴ or,

  = 4t³  

Now, the line integral along C will be:

→  =  \(\int\limits^a_b \,\)√(3t²)² + (4t³)² dt

            =  \(\int\limits^a_b \,\)√9t⁴ + 16t⁶ dt

            =  \(\int\limits^a_b \,\)√9 + 16t² dt

           =  \(\int\limits^a_b \,\)√9 + 16t² dt

            =  \(\int\limits^a_b \,\)t√9 + 16t² dt

            =   \(\int\limits^a_b \,\)√9 + 16t² d (9 + 16t²)

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ANSWER:

The figures are not similar.

STEP-BY-STEP EXPLANATION:

We have to be similar the angles must be equal and the sides must have a constant scale factor.

The angles are not the same.

And we calculate the scale factor for each corresponding side like this

The scale factor is not constant, therefore we can say that the figures are not similar.

Answer:

Why do you need to set up a graph for this equation?

Step-by-step explanation:

A
____
M = 10
5x10 = 50

Answer:

The average rate of change of the function over the given interval is -6

Step-by-step explanation:

The function we want to find its average rate of change is;

F(x) = 17 - x^2

Mathematically, the average rate of change of a function F(x) over an interval (a,b) can be calculated as;

{F(b) - F(a)}/(b-a)

According to this question, a = 1 and b = 5

F(a) = F(1) = 17 -(1)^2 = 17 -1 = 16

F(b) = F(5) = 17 - 5^2 = 17-25 = -8

So making the substitution; we have

(-8)-16/(5-1) = -24/4 = -6

Answer:

A: -6

Step-by-step explanation:

The margin of error for the percentage of Britons who think the monarchy should be more democratic when constructing a 95% confidence interval is approximately 0.018.

Option e is correct.

This range is defined by the confidence interval. For the 95% confidence interval, the standard error is calculated as follows:Standard error = square root of [(proportion of successes x proportion of failures) / n]Where:

Proportion of successes = 0.53 (given in the problem)

Proportion of failures = 1 - proportion of successes = 1 - 0.53 = 0.47

n = 3000 (given in the problem)Now we can plug in the values and solve:

Standard error = square root of [(0.53 x 0.47) / 3000] ≈ 0.0125

The margin of error is then calculated as follows:Margin of error = critical value x standard error.

The critical value for a 95% confidence interval is 1.96 (this value can be found using a standard normal distribution table or calculator).So:Margin of error = 1.96 x 0.0125 ≈ 0.0245To find the margin of error for the percentage of Britons who think the monarchy should be more democratic, we need to divide the margin of error by the total number of participants in the survey:

Margin of error for percentage = margin of error / nMargin of error for percentage = 0.0245 / 3000 ≈ 0.000818

So the margin of error for the percentage of Britons who think the monarchy should be more democratic when constructing a 95% confidence interval is approximately 0.000818. This is the same as 0.0818% or 0.018 rounded to three decimal places.

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Answer:

see explanation

Step-by-step explanation:

(a)

calculate the lengths using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = J (- 3, - 7 ) and (x₂, y₂ ) = K (3, - 8 )

JK = \(\sqrt{(3-(-3))^2+(-8-(-7))^2}\)

    = \(\sqrt{(3+3)^2+(-8+7)^2}\)

    = \(\sqrt{6^2+(-1)^2}\)

    = \(\sqrt{36+1}\)

    = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = M (8, 3 ) and (x₂, y₂ ) = N (7, - 3 )

MN = \(\sqrt{(7-8)^2+(-3-3)^2}\)

      = \(\sqrt{(-1)^2+(-6)^2}\)

     = \(\sqrt{1+36}\)

     = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = P (- 8, 1 ) and (x₂, y₂ ) = Q (- 2, 2 )

PQ = \(\sqrt{-2-(-8))^2+(2-1)^2}\)

      = \(\sqrt{(-2+8)^2+1^2}\)

      = \(\sqrt{6^2+1}\)

      = \(\sqrt{36+1}\)

      = \(\sqrt{37}\)

(b)

JK ≅ MN ← true

JK ≅ PQ ← true

MN ≅ PQ ← true