Arrange in order from least to greatest 150% 1.75, 5/4​

The equivalent equation to the (x² - 5)² - 3x² + 15 = -2 in form of 'm' is given by option c.  m² -3m + 2 = 0.

The equation is equal to,

(x² - 5)² - 3x² + 15 = -2

let the value of m be equals to x² - 5.

Simplify the equation we have,

⇒ ( x² - 5 )² - 3x² + 15 = -2

Take '3' common factor from the 3x² + 15 so that it get convert into x² - 5 we get,

⇒ ( x² - 5 )² - 3 (x² - 5 )  = -2

Now replace x² - 5 by m to get the equivalent equation,

⇒ ( m )² - 3 (m ) = -2

⇒ m² -3m + 2 = 0

Therefore, the equivalent equation to the given equation is written as option c.  m² -3m + 2 = 0.

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5754 62

6543213

6514654

2

5416543196

4165461674

Answer:

(-7, 3)

Step-by-step explanation:

-6-1=-7  2+1=3

The Reagan doctrine of American activism in the Third World was most particularly exercised in Nicaragua and Grenada. These countries became focal points of U.S. involvement and intervention.

The Reagan doctrine, implemented during the presidency of Ronald Reagan in the 1980s, aimed to counter Soviet influence and promote American interests in the Third World. This doctrine was characterized by a strong anti-communist stance and support for anti-communist governments and movements. Among the various countries where the Reagan doctrine was applied, Nicaragua and Grenada stand out as prime examples.

In Nicaragua, the Reagan administration actively supported the Contras, a rebel group fighting against the Sandinista government. The Contras were seen as a counterforce to the left-wing Sandinistas, who were aligned with the Soviet Union and Cuba. The United States provided financial and military assistance to the Contras, including covert operations, in an effort to undermine the Sandinista regime.

Grenada, a small island nation in the Caribbean, also witnessed American intervention under the Reagan doctrine. The United States launched Operation Urgent Fury, invading Grenada and overthrowing the government, with the stated objective of protecting American citizens and restoring democracy.

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y₂(x) = x¹/2 In(x) [ (C1/6)I-1(x) - (2/3) ln|x| ]. Given function y₁(x) is a solution of differential equation 6y" + y' - y = 0 and y₁(x) = Y₁ ex/3.

Reduction of order: First, we will find the first derivative and second derivative of y₁(x).y₁(x)

= Y₁ ex/3y₁'(x)

= Y₁/3 ex/3y₁''(x)

= Y₁/9 ex/3

As we have y₂(x) = v(x) y₁(x) and we will substitute it in differential equation 6y" + y' - y

= 0. 6(v''(x) y₁(x) + 2v'(x) y₁'(x) + v(x) y₁''(x)) + v'(x) y₁(x) - v(x) y₁(x)

= 0

Putting the values of y₁(x), y₁'(x), and y₁''(x),

we get 6v''(x) Y₁ ex/3 + 4v'(x) Y₁ ex/3 + v(x) Y₁ ex/3 = 0

Now, dividing both sides by Y₁ ex/3,

we get6v''(x) + 4v'(x) + v(x) = 0

We can find the integrating factor by multiplying both sides by integrating factor

I(x). I(x) (6v''(x) + 4v'(x) + v(x)) = 0

Multiplying the integrating factor I(x) to the left-hand side,

we get d/dx [ I(x) (4v'(x) + 6v''(x))] = 0

Applying integration on both sides,

we get I(x) (4v'(x) + 6v''(x)) = C₁  

Where C₁  is an arbitrary constant.

Solving the above equation for v(x),

we get v(x) = (C₁ /6)I-1(x) - (2/3) ∫ I-1(x) dx

This is the general form of the second solution y₂(x).

Here, Y₁ = x¹/2 In(x)

So, we will put this value in the above formula and find the second solution.

∫ I-1(x) dx= ∫ (e-SP(x))/x dx

= ∫ e-∫ P(x) dx /x dx

= ∫ e-∫ 0 dx /x dx

= ∫ e-x dx /x

= ln|x|

Now, v(x) = (C₁/6)I-1(x) - (2/3) ln|x| y₂(x)

= v(x) y₁(x)

Therefore, y₂(x) = x/2 In(x) [ (C₁/6)I-1(x) - (2/3) ln|x| ]

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Answer:

brand b

Step-by-step explanation:

to find the unit price you have to divid the # of items but the price

so for brand a you would do

1.54/36 which equals 0.04

and for brand b you would do

1.66/48 which equals 0.03

brand b is cheaper by 0.01

Answer:

C ( third one )

Step-by-step explanation:

Answer:

The answer is C.

Step-by-step explanation:

To start off 250g is $1.85 and we want to get to 500g so if we add $1.85 with $1.85 we will get $3.70.  This amount is more than the number if we bought just 500g once than if we bought 250g twice, because if we did, we would be paying more.  But that's not all, if we add 500g with 500g we will get $6.20.  That's more than the original price for 1 kg and if we multiply 250g 4 times than we get 7.4.  So in all we would buy 1 kg.

Answer: D. The two rotations map the same image since 350° is a full rotation and 180° + 360° = 540°.

Answer:

System of Equations

c + r = 32 ..... Equation 1

2c + 4r = 72......... Equation 2

We have 28 chickens and 4 rabbits

Step-by-step explanation:

Let the number of chickens be represented by c

The number of rabbits be represented by r

From the question, John counts:a total of 32 heads

32 heads = a total of 32 animals

Hence:

c + r = 32....... Equation 1

c = 32 - r

Also, John counts:

A total of 72 legs in his backyard.

Chickens have: 2 legs

Rabbits have: 4 legs

Hence:

2c + 4r = 72......... Equation 2

System of Equations is:

c + r = 32 ..... Equation 1

2c + 4r = 72......... Equation 2

Lets us substitute 32 - r for c in Equation 2

2(32 - r) + 4r = 72

64 - 2r + 4r = 72

Collect like terms

- 2r + 4r = 72 - 64

2r = 8

r = 8/2

r = 4

This means we have 4 rabbits

Note:

c = 32 - r

r = 4

c = 32 - 4

c = 28

Hence, we have 28 chickens

The four basic measurements that serve as the foundation for other units of measure are length, mass, time, and temperature.

Length is a measure of distance between two points, typically measured in meters (m) within the International System of Units (SI). Mass is the amount of matter in an object, measured in kilograms (kg) in the SI system. Time refers to the duration or interval between events and is measured in seconds (s) within the SI system.

Lastly, temperature is a measure of the average kinetic energy of particles in a substance, represented in degrees Celsius (°C) or Kelvin (K) in the SI system.

All other units of measure are defined and compared to these four basic measurements. For instance, speed is derived from the combination of length and time (e.g., meters per second). Similarly, force is derived from mass and acceleration, which itself is derived from the change in velocity over time (e.g., newtons).

The combination and comparison of these fundamental measurements enable scientists, engineers, and other professionals to quantify and analyze various phenomena in the physical world.

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Answer:

Not sure but i think 183.333333333

Answer:

670.21 inches^3

Step-by-step explanation:

To find the volume of the spheres, all you need to know is the formula for the volume of a sphere, which you've included in your problem. From the problem, you also know that r = 2. From here, you calculate the volume of 1 of the spheres, which turns out to be:

V = 33.51032

Since there are 20 spheres in this box, you multiple the volume of a single sphere by 20 to get the total volume occupied by the spheres.

V = 20 * 33.51032

V = 670.2064

If you round to 2 decimal places, this becomes 670.21.

Answer:

just do it by Pythagoras theoram

Step-by-step explanation:

because it is a right angle

Answer:

32.7

Step-by-step explanation:

Using the Pythagorean theorem, we can set an equation to 5^2+c^2=14^2,

which is equal to 196-25 = c^2, which is equal to c^2=171, therefore, c=\(\sqrt{171}\)

5*\(\sqrt{171}\)/2=32.69, rounded will equal to 32.7

The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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This simplifies to:
a² = 12x + 144

This is the equation that results from applying the Secant-Tangent Segment Theorem to the given figure.

Let's first define the terms and state the Secant-Tangent Segment Theorem.

1. Equation: A mathematical statement that shows the equality of two expressions.

2. Secant: A line that intersects a circle at two points.

3. Tangent: A line that touches a circle at only one point, without crossing it.

Secant-Tangent Segment Theorem: If a secant and a tangent are drawn from a point outside a circle, the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.

Let's represent the given lengths as follows:
- Length of tangent segment = a
- Length of secant segment (inside the circle) = 12
- Length of the external part of the secant segment (outside the circle) = x

According to the Secant-Tangent Segment Theorem, the equation is:
(a)(a) = (12)(x + 12)

This simplifies to:
a² = 12x + 144

This is the equation that results from applying the Secant-Tangent Segment Theorem to the given figure.

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Answer:

83 and 99 The sequence is going in +16 so the answer is 83 and 99 sorry if I am a bad explainer I’m new to this app :(

Step-by-step explanation:

Answer:

a) 44g
b)4620g

Step-by-step explanation:

a)
25 chocolates = 1100g
1 chocolate = 1100/25
answer: 44g

b)
25 chocolates = 1100g
1 chocolate = 1100/25
100 chocolates = 1100/25×105
answer: 4620g

The model y = β0 + β1x + ε tells us about the linear relationship between the variables x and y.

In this model:

- y represents the dependent variable that we want to explain or predict
- x represents the independent variable that we use to explain or predict y
- β0 (beta0) is the intercept, which is the value of y when x is zero
- β1 (beta1) is the slope, representing the change in y for a one-unit change in x
- ε (epsilon) is the error term, accounting for the unexplained variation in y that is not captured by the model

The model helps us understand the association between x and y, with β1 indicating the strength and direction of the relationship. A positive β1 indicates a direct relationship (as x increases, y increases), while a negative β1 indicates an inverse relationship (as x increases, y decreases).

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Answer: 1 <= 9

Step-by-step explanation:

Do math

Answer:

≈ 22 cm

Step-by-step explanation:

the circumference (C) of a circle ( the perimeter ) is calculated as

C = 2πr ( r is the radius )

   = 2π × 7 = 14π

since divided into 2 equal parts then

\(\frac{1}{2}\) C = 14π ÷ 2 = 7π ≈ 22 cm ( to the nearest whole number )

In order to find the perimeter of the polygon we need to find the measure of each side

We have the next sides

s1=18.4

s2=21.9

s3=20.5

s4=?

we need to find s4 with the fact that two tangents from the same vertex have equal measurements

then we sum all the sides in order to find the perimeter

The perimeter is P=77.8

The Maclaurin series for f(x) converges absolutely for x within the interval (-2/3, 2/3).

To find the Maclaurin series for the function f(x) = (3cos(x))ln(1+x), we can use the standard formulas for the Maclaurin series expansion of elementary functions.

First, let's find the derivatives of f(x) up to the third order:

f(x) = (3cos(x))ln(1+x)

f'(x) = -3sin(x)ln(1+x) + (3cos(x))/(1+x)

f''(x) = -3cos(x)ln(1+x) - (6sin(x))/(1+x) + (3sin(x))/(1+x)² - (3cos(x))/(1+x)²

f'''(x) = 3sin(x)ln(1+x) - (9cos(x))/(1+x) + (18sin(x))/(1+x)² - (12sin(x))/(1+x)³ + (12cos(x))/(1+x)² - (3cos(x))/(1+x)³

Next, we evaluate these derivatives at x = 0 to find the coefficients of the Maclaurin series:

f(0) = (3cos(0))ln(1+0) = 0

f'(0) = -3sin(0)ln(1+0) + (3cos(0))/(1+0) = 3

f''(0) = -3cos(0)ln(1+0) - (6sin(0))/(1+0) + (3sin(0))/(1+0)² - (3cos(0))/(1+0)² = -3

f'''(0) = 3sin(0)ln(1+0) - (9cos(0))/(1+0) + (18sin(0))/(1+0)² - (12sin(0))/(1+0)³ + (12cos(0))/(1+0)² - (3cos(0))/(1+0)³ = -9

Now we can write the first three nonzero terms of the Maclaurin series:

f(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + ...

f(x) = 0 + 3x - (3/2)x² - (9/6)x³ + ...

Simplifying, we have:

f(x) = 3x - (3/2)x² - (3/2)x³ + ...

To determine the values of x for which the series converges absolutely, we need to find the interval of convergence. In this case, we can use the ratio test:

Let aₙ be the nth term of the series.

|r| = lim(n->infinity) |a_(n+1)/aₙ|

= lim(n->infinity) |(3/2)(xⁿ+1)/(xⁿ)|

= lim(n->infinity) |(3/2)x|

For the series to converge absolutely, we need |r| < 1:

|(3/2)x| < 1

|x| < 2/3

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The value of the profitability index of the project is 2.381.

We know that the growth rate is 4% and the cash flow is $3.7 million, so we can calculate the present value of all future cash flows as follows;

PV of all subsequent cash flows = 3.7 million * (1 + 0.04) / (0.11 - 0.04) = $68.1333 million

Total PV = PV of first-year cash flow + PV of all subsequent cash flows = $3.3154 million + $68.1333 million = $71.4487 million

Finally, we can calculate the profitability index as;

Profitability index = PV of future cash flows / Initial investment = $71.4487 million / $30 million = 2.381

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"100 raised to the sixth power" can be written in an algebraic expression as follows:

Meaning that we have to multiply 100 six times:

We can simplify by multiplying each 100 (adding the 0 of the next one hundred to the previous one) as follows:

0. Adding the 0 of the second 100 to the first

2. Adding the 0 of the third (now second from the previous operation) 100 to the first:

3. Adding the 0 of the fourth (now second from the previous operation) 100 to the first:

4. Adding the 0 of the fifth (now second from the previous operation) 100 to the first:

5. Adding the 0 of the sixth (now second from the previous operation) 100 to the first:

Answer:

The inequality that shows the number of travel hours, t, before which Jonas should call his friend is t ≥ 5050 hours, which can also be written as t ≥ 300300300 miles / 454545 miles per hour.

The inequality that shows the number of travel hours, t, before which Jonas should call his friend is t ≥ 300300300 miles / 454545 miles per hour.

Explanation:
To find the number of travel hours, we divide the distance traveled (300300300 miles) by the speed of the bus (454545 miles per hour). This gives us t = 300300300 miles / 454545 miles per hour.

Since Jonas needs to call his friend at least 303030 minutes before arriving, we need to convert this to hours by dividing 303030 minutes by 60 (since there are 60 minutes in an hour). This gives us t ≥ 303030 / 60 = 5050 hours.

Therefore, the inequality that shows the number of travel hours, t, before which Jonas should call his friend is t ≥ 5050 hours, which can also be written as t ≥ 300300300 miles / 454545 miles per hour.

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