is 7m-2=8m+4-m an identity?

Answer:

its the second one

Step-by-step explanation:

a. The recursive formula for the number of tulips Marko has is: \(Tn = Tn-1 + 5\), where Tn is the number of tulips in year n and Tn-1 is the number of tulips in year n-1.

b. The explicit formula for the number of tulips Marko has is: Tn = 20 + 5n, where Tn is the number of tulips in year n and n is the number of years since Marko started planting.

c. If this trend continues, there will be 90 tulips in 10 years.

d. If this trend continues, it will take Marko 40 years to have 200 tulips.

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Answer:

Option B. ( x + 2, y - 1 ) is the correct answer.

Step-by-step explanation:

First of all, we have to write the coordinates of vertices of both triangles and then compare the respective vertices to find the rule,

So the vertices are:

A(-4,2) , B(-3,4) and C(-1,1)

A'(-2,1), B'(-1,3) and C'(1,0)

By comparing respective vertices we can observe that

A(-4,2) => (x+2,y-1) => A'(-2,1)

B(-3,4) => (x+2,y-1) => B'(-1,3)

C(-1,1) => (x+2,y-1) => C'(1,0)

Hence,

Option B. ( x + 2, y - 1 ) is the correct answer.

Answer:

Diameter, D = 2.65 cm

Step-by-step explanation:

Given the following data;

Circumference of circle = 8.34 cm

To find the length of its diameter;

Mathematically, circumference of a circle is equal to;

C = πD

Where;

Substituting into the formula, we have;

8.34 = 3.142 * D

\( D = \frac {8.34}{3.142} \)

Diameter, D = 2.65 cm

Answer: -10x^2 - 33x + 1

Step-by-step explanation:

Not sure if it’s correct but that’s what I got.

Answer:

Step-by-step explanation:

\(\tt 6x\left(x-4\right)-16x^2-\left(9x-1\right)\)

Apply the distributive property :-

\(\tt 6x^2-24x-16x^2-9x+1\)

Combine like terms:-

\(\tt 6x^2-16x^2=\bf -10x^2\)

\(\tt -24x-9x=\bf -33x\)

\(\tt 10x^2-33x+1\)

---------------------------------------

Hope this helps!

The probability that x is greater than 77. 5 is 0.039828

Given,

Mean, μ = 80

Standard deviation, σ = 25

We have to find z score corresponding to 77.5

z = (x-μ) / σ

   \(=\frac{77.5-80}{25} \\= 0.1\)

Now we have to find P value from Z table:

P(x<77.5) = 0.46017

P(x>77.5) = 1 - P(x<77.5) = 0.53983

P(77.5<x<80) = 0.5 - P(x<77.5) = 0.039828

The probability of x greater than 77.5 is 0.039828

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Answer:

I think B

Step-by-step explanation:

because their age group is 20-25 more of a constant age group

compared to 20-30

The height of the highest point of the trajectory and the horizontal distance the golf ball travels before hitting the ground will be 360 .6 meters

Apparently, x is the distance from the place where the ball is impacted on the ground.

The ball's horizontal speed, given by s, can be calculated using the equation cos(50) = s/60, where s = 38.5 mps.

Size is represented by f(x). The highest point of the parabola would be at -b/2a = -1.19/-.0066 = 180.3 metres, meaning the ball has moved 180.3 metres.

Input 107.28 metres into the formula to find the height.

In order to calculate the distance travelled, the ball must be on the ground, hence f(x) = 0.

-.0033x^2 + 1.19x = 0

x*(-.0033x + 1.19) = 0

x= 1.19/.0033 = 360 .6 meters

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The tip of the woman's shadow is moving away from the pole when she is 22 ft from the base of the pole is 105/11 feet per second.

Given that :

A street light is at the top of a pole that has a height of 15 ft.

Height of the pole = 15 feet

Height of the woman = 4 feet

The speed at that the woman walks = 7 feet per second.

Let x be the distance of the woman from the pole and y be the distance from the shadow tip of the woman to the pole.

We get two similar triangles.

Using the similarity rule :

(y - x) / y = 4 / 15

15(y - x) = 4y

15y- 15x = 4y

11y = 15x

y = 15/11 x

Differentiating on both sides :

dy/dt = 15/11 dx/dt

          = (15/11) (7)

          = 105/11 feet per second.

Hence the shadow is moving at a rate of 105/11 feet per second.

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The equation, in standard form, of the parabola that models the values in the table is \(y = 6x^2 + 5x - 4\).

The given table of values represents the relationship between x and y in a parabolic function. To determine the equation of the parabola, we look for a quadratic expression of the form y = ax² + bx + c, where a, b, and c are constants.

By examining the table and matching the values, we find that the equation y = 6x²+ 5x - 4 best represents the given data. This equation is in standard form, with the highest power of x being 2. It describes a U-shaped curve, known as a parabola, which is concave upward.

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Answer:

10yd x 14 yd x 3yd = 420yd ^3

Step-by-step explanation:

When calculating for the volume you multiply all three numbers. That’s why when you write your answer you cube it.

Answer:

$1,830.6

Step-by-step explanation:

$1,830.6 is your answer!This is because; 30 × 9 ≈ 270 + 1,560.60≈1,830.6

Answer:

If both numbers have to stay equivalent, then y equals 30 if x = 12. My reasoning is 12/4 = 3. 3 times 10 = 30.

Answer:

x=14

Step-by-step explanation:

3x-15=27 (add 15 to both sides)

3x=42 (divide both sides by three)

x=14

The required number is -4.

A linear equation only has one or two variables. No variables in a linear equation is raised to power greater than 1 or used as denominator of a fraction.

Now it is given that, 15 is subtracted from three times a certain number,

the result is 27.

Now let x be the number.

Three times the number = 3x

Therefore, 15 is subtracted from three times a certain number = 15 - 3x

Therefore, the equation for 15 is subtracted from three times a certain number, the result is 27 is,

15 - 3x = 27

Subtracting 15 both the side we get,

15 - 3x - 15 = 27 - 15

⇒ -3x = 12

or, x = -12/3

⇒ x = -4

which is the required number.

Thus, the required number is -4.

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Answer:

196 science books

Step-by-step explanation:

Check the attachment.

The total number of sicience books were 196.

Ratio is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division.

Let the total numbers of science books be x and maths books be y.

According to the given question.

The intial ratio of maths books to the science books is 3:7.

⇒ \(\frac{y}{x} = \frac{3}{7}\) ...(i)

But, after the addition of 84 maths books the ratio gets changed to 6:7.

\(\implies \frac{y +84}{x} = \frac{6}{7}\) ...(ii)

Solving the equations i and ii.

From equation i.

\(7y = 3x\)

And from equation ii

\(7y + 7(84) = 6x\)

Substitute the value of 7y = 3x in the above equation.

\(3x + 588 = 6x\)

\(\implies 588 = 6x -3x\)

\(\implies 3x = 588\)

\(\implies x = \frac{588}{3}\)

\(\implies x = 196\)

Hence, the total number of sicience books were 196.

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Answer:

x < -7/2

Step-by-step explanation:

First, perform the indicated multiplication:

4(1-2x)>32 becomes 4 - 8x > 32.  

Next, isolate the -8x term by subtracting 4 from both sides of this inequality:

-8x > 28

Finally, solve for x by dividing both sides by -8.  This requires that we reverse the direction of the inequality sign:

x < -28/8, or, after reduction, x < -7/2

Answer:

- (27n^3 - 12n - 1) over 3n

Step-by-step explanation:

The equation of motion for an instant t is given as:

m * (d²x/dt²) + β * dx/dt + k * x = 0

The damping constant must meet a condition β > 12, to obtain an over-cushioned mass-spring system.

We use the basic principles of damping in mass-spring systems, and their equations to arrive at answers.

To give an equation of motion to a mass-spring system, which has no external force, we can create a second-order differential equation, which looks like the following:

m * (d²x/dt²) + β * dx/dt + k * x = 0

where,

m = mass of the object (4 kg in this case)

x = displacement from the equilibrium position

t = time

k = spring constant (9 N/m)

β = damping constant

For a particular solution with the given initial conditions, we solve the above given differential equation.

With x(0) = 3 and v(0) = 5,

m * (d²x/dt²) + β * dx/dt + k * x = 0

4 * (d²x/dt²) + 12 * dx/dt + 9 * x = 0

Now, we can use the general ways of solving differential equations.

We first write the characteristic equation, which is:

4r² + 12r + 9 = 0

Solving this,

4r² + 6r + 6r + 9 = 0

2r(2r + 3) + 3(2r + 3) = 0

(2r + 3)(2r + 3) = 0

2r + 3 = 0

2r = -3

r = -3/2 is a solution, obtained twice, as the equation has equal roots.

We substitute this in the general solution for x(t), which can be written as:

x(t) = c₁ * e^(r*t) + c₂ * e^(r*t)

c₁ and c₂ are constants.

For x(0),

x(0) = c₁ * e^(r*0) + c₂ * e^(r*0)

      = c₁ e⁰ + c₂ e⁰

      = c₁ + c₂

c₁ + c₂ = 3            ---------------> (1)        (x(0) = 3, given)

For v(0) = 5, which is dx/dt (0) = 5,

dx/dt(0) = r₁*c₁ * e^(r₁ * 0) + r₂*c₂ * e^(r₂ * 0)

5  = r₁*c₁ + r₂*c₂  -->  (2)

Solving the equations, we end up with values for c₁ and c₂

c₁ = 4/3

c₂ = 5/3.

So, the particular solution equation can be finally written as:

x(t) = (4/3) * e^(-3t/2) + (5/3) * e^(-3t/2)

Finally, we have to find the condition for the damping constant in the special case:

For an over-cushioned mss-spring, it must satisfy the condition,

β² - 4mk > 0

On substituting, we get

β² - 4*4*9 > 0

β² - 144 > 0

β² > 144

β > 12                       (Only take Positive values)

So, the damping constant must be greater than 12 for an over-cushioned system.

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The intersection of given set a and b is a∩b = {5}.

According to the given question.

We have two sets a and b.

a = {2, 5, 8, 11, 14}

And, b = {1, 3, 5, 7}

As, we know that "the intersection of two sets A and B is the set of all those elements which are common to both A and B. Symbolically, we can represent the intersection of A and B as A ∩ B".

Since, only the element which is common to set a and set b is 5.

Thereofore, the intersection of given set a and b is given by

a∩b = {5}

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The table with a constant of proportionality of –3 are

A. 'x' is 1 2 3. 'y' is -3,-6,-9

A. 'x' is 1 2 3. 'y' is -3,-6,-9 C. 'x' is 1, 2, 3. 'y' is -3, -3, -3

A. 'x' is 1 2 3. 'y' is -3,-6,-9 C. 'x' is 1, 2, 3. 'y' is -3, -3, -3D. 'x' is 1, 2, 3. 'y' is -3, -3/2, -1

y = k × x

where,

k = constant of proportionality

A. 'x' is 1 2 3. 'y' is -3,-6,-9

y = k × x

-3 = k × 1

- 3 = k

k = -3

B. 'x' is 1, 2, 3. 'y' is -1, -2, 0

y = k × x

-1 = k × 1

-1 = k

k = -1

C. 'x' is 1, 2, 3. 'y' is -3, -3, -3

y = k × x

-3 = k × 1

-3 = k

k = -3

D. 'x' is 1, 2, 3. 'y' is -3, -3/2, -1

y = k × x

-3 = k × 1

-3 = k

k = -3

or

y = k × x

-3/2 = k × 2

-3/ 2 = 2k

k = -3/2 ÷ 2

k = -3/2 × 1/2

k = -3

Therefore, the table with a constant of proportionality of –3 are

A. 'x' is 1 2 3. 'y' is -3,-6,-9

A. 'x' is 1 2 3. 'y' is -3,-6,-9 C. 'x' is 1, 2, 3. 'y' is -3, -3, -3

A. 'x' is 1 2 3. 'y' is -3,-6,-9 C. 'x' is 1, 2, 3. 'y' is -3, -3, -3D. 'x' is 1, 2, 3. 'y' is -3, -3/2, -1

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The correct option is (E) 2 for the given differential equation.

The given differential equation is (2x + 3) + (2y - 2)y' = 0.Solution:Given differential equation is (2x + 3) + (2y - 2)y' = 0.Rewrite the differential equation in the form of y' as follows.

A differential equation is a type of mathematical equation that connects the derivatives of an unknown function. The function itself, as well as the variables and their rates of change, may be involved. These equations are employed to model a variety of phenomena in the domains of engineering, physics, and other sciences. Depending on whether the function and its derivatives are with regard to one variable or several variables, respectively, differential equations can be categorised as ordinary or partial. Finding a function that solves the equation is the first step in solving a differential equation, which is sometimes done with initial or boundary conditions. There are numerous approaches for resolving these equations, including numerical methods, integrating factors, and variable separation.

(2y - 2)y' = - (2x + 3)y'Taking antiderivative of both sides with respect to x, we get\(\[ \int (2y-2) dy = - \int \frac{2x+3}{y} dx + c_1\]\)

Integrating, we have\(\[y^2 - 2y = - (2x+3) \ln |y| + c_1\]\)

Substitute the initial condition y(0) = 1, we get \(t\[c_1 = 1\]\)

Thus, we have\[y^2 - 2y = - (2x+3) \ln |y| + 1\]Again, taking the derivative of both sides with respect to x, we get\(\[2y \frac{dy}{dx} - 2 \frac{dy}{dx} = - \frac{2x+3}{y} + \frac{d}{dx} (1)\]\)

Simplifying, we get\(\[y' = \frac{-2x - 3 + y}{2y-2}\]\)

Comparing this with the given differential equation, we have m = 2x + 3, n = 2y - 2.Substituting these values in the given options, we have\(\[Mx = Ny = Exact\]\) is correct.

Therefore, the correct option is (E) 2.

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Answer: "x" is 4.5

Step-by-step explanation:

first lets find the leg of the first right triangle using the given leg of 6 and the hypoteneuse of 9 using Pythagorean theorem a^2 + b^2 = c^2.

6^2 + b^2 = 9^2

36 + b^2 = 81

subtract 36 from both sides to isolate b

36 - 36 + b^2 = 81 - 36

simplify

b^2 = 45

take square root of both sides

\(\sqrt{b^{2} }\) = \(\sqrt{45}\)

b = 6.7

Now we can find x of the 2nd right triangle using the know hypoteneuse of 6.7 and the known leg of 5

a^2 + b^2 = c^2

5^2 = b^2 = 6.7^2

25 + b^2 = 44.9

subtract 25 from both sides to isolate b

25 - 25 + b^2 = 44.9 - 25

b^2 = 19.9

take square root of both sides

\(\sqrt{b^2}\) = \(\sqrt{19.9}\)

b= 4.5

so your answer to what is "x" is 4.5

Answer:

3500cal/min

Step-by-step explanation:

You have 210kcal/h. There are 1000cal in 1kcal, and 60 minutes in 1 hour:

\( \frac{210}{1} \frac{kcal}{hour} \times \frac{1000}{1} \frac{cal}{kcal} \times \frac{1}{60} \frac{hour}{minutes} \)

The units kcal cancel and hours cancel, leaving cal per min:

\( \frac{210 \times 1000}{60} \frac{cal}{minute} = 3500 \frac{cal}{min} \)

Answer:

B

Step-by-step explanation:

We know that 3² = 9, so for g(x) to pass through (3,3), we need to multiply x² by 1/3, giving option B.

Answer:

10x + 1

Step-by-step explanation:

First, combine any like terms. Then make sure to rewrite in descending order.

3x + 7x + 1 <== combine any like terms

10x + 1 <== arrange in descending order

Hope this helps!

Answer:

The length of the diagonal from P to Q is

\( \sqrt{ {9}^{2} + {12}^{2} + {8}^{2} } = \sqrt{289} = 17\)

Answer:

A. \(38\ \text{grados}\)

Step-by-step explanation:

La temperatura en Moscú es de 13 grados bajo cero. Entonces, la temperatura es de -13 grados.

La temperatura en Buenos Aires es de 25 grados bajo cero. Entonces, la temperatura es de 25 grados.

La diferencia de temperatura entre las dos ciudades es

\(25-(-13)=38\ \text{grados}\)

La diferencia de temperatura entre las dos ciudades en un momento dado es  \(38\ \text{grados}\).

If you draw a tiny circle with a 90-degree sector, it is not a dilation of the original circle because a dilation is a transformation that changes the size of an object while preserving its shape.

In a dilation, all corresponding points in the original and the transformed shapes lie on a line passing through the center of dilation, and the scale factor of the dilation determines the ratio of the corresponding lengths of any two segments that join corresponding points.

In the case of the tiny circle with a 90-degree sector, the sector has a different shape than the original circle, and the sector has a larger perimeter than the corresponding arc of the original circle. Therefore, the sector is not a dilation of the original circle.

Furthermore, a 90-degree sector of a circle can be obtained by cutting a part of the original circle and thus cannot be obtained by dilation alone.

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Answer:

prime numbers are the natural numbers greater than one that are not products of two smaller natural numbers

Step-by-step explanation:

Answer:

A prime number is a number that is divisible by itself and cannot be divided by any other number only by itself.

For example, 5 is a prime number because nothing can divide into 5 except for itself.