Find the distance between the points (5, 2) and (1, -3). Round to the nearest tenth if necessary.
a. 3.0
b. 9.0
c. 5.2
d. 6.4 ​

Answer:

A,B,D,

Step-by-step explanation:

My knowledge. Hope it's correct!

Answer: -3

Step-by-step explanation: to solve this, we simply put -1 into the equation in place of x. That can be written like this: p(-1) = -5(-1) -8. The answer to that is -3, which is the answer

Answer: √60

Step-by-step explanation:

Answer:

divide 7/100 which is 0.07

multiply that by 13.75, and you get 0.96

13.75+0.96= $13.20

(this is including sales tax)

Answer:

$12.78

Step-by-step explanation:

I THINK you are supposed to multiply the original price (13.75) by the sales tax as a decimal (0.07) and then subtract that answer from, the original, amount.

The square of the length of the chord that is a common external tangent of the other two circles with radii of 3 and 6 is 45.

Given that circles of radii 3 and 6 are externally tangent to each other and internally tangent to a circle of radius 9. The circle of radius 9 has a chord that serves as a common external tangent for the other two circles. The task is to find the square of the length of this chord.

The distance between the centers of the circles of radii 3 and 6 can be found by adding their radii: d1 = 3 + 6 = 9 units.

Since the circles are internally tangent to the circle of radius 9, the distance between their centers can be found by subtracting their radii from the radius of the larger circle: d2 = 9 - 3 - 6 = 0 units.

The chord is a common external tangent of the circles, and its length can be found by doubling the distance between the center of the circle of radius 9 and the chord: Chord length = 2 × h.

To find the height (h) of the triangle formed by the chord and the center of the circle of radius 9, we can use the formula h = (r1 + r2 - R) / 2, where r1 and r2 are the radii of the smaller circles, and R is the radius of the larger circle. In this case, h = (3 + 6 - 9) / 2 = 0.
Since h is zero, it means that the chord passes through the center of the circle of radius 9. Therefore, its length will be the diameter of the circle of radius 9.

The square of the length of the chord can be found using the Pythagorean theorem. Let's denote the length of the chord as d.

- We know that r1 + h = R, so h = R - r1 = 9 - 3 = 6.

- Using the Pythagorean theorem: d = sqrt(R² - h²) = √(9² - 6²) = √(81 - 36) = √(45).

Therefore, the square of the length of the chord is d^2 = 45.

In summary, the square of the length of the chord that serves as a common external tangent for the circles of radii 3 and 6, and is internally tangent to a circle of radius 9, is 45.

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Answer:

2/3 cup

Step-by-step explanation:

1/2 of 1 1/3

1/2 of 4/3 = 4/6 or 2/3

1 and 1 / 3 = 4 / 3

4 / 3 divided by 2 is 2 / 3

please give brainliest

The number line which represents the solution bro the inequality 2x + 5 < 11 is:

First, we must solve the inequality so that it looks it's simplest form in order to be represented on a number line.

Solving the inequality is as follows:

In essence, representation of the inequality, y < 3 on the number line is as follows:

An open circle is at positive 3. Everything to the left of the circle is shaded.

PS: It is only a closed circle if the inequality includes an equal to sign.

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Answer:

∠

A

=

x

=

32

∘

∠

B

=

3

x

=

3

⋅

32

=

96

∘

∠

C

=

x

+

20

=

32

+

20

=

52

∘

Step-by-step explanation: Every triangle adds up to 180.

Answer:

Step-by-step explanation:

The height of the Eiffel Tower was halved repeatedly to make a model around 30 cm. We know that 30 cm = 0.3 meters.

We can set up an equation:

324m / 2^n = 0.3m

We can solve for n by logarithm base 2:

n = log(324/0.3) / log(2)

n = log(1080) / log(2)

n ≈ 10.6

The height of the Eiffel Tower was divided by 2^10.6, which is not a whole number.

It means that the height of Eiffel Tower was divided by a number that is between 10 and 11 times by 2.

When the area in square units of an expanding circle is increasing twice as fast as its radius in linear units, the radius is E. Pi.

The area of a circle is given by the formula A = π\(r^2\), where A is the area and r is the radius. If the area of the circle is increasing twice as fast as its radius, we can express this relationship as:

dA/dt = 2(dr/dt)

Here, dA/dt represents the rate of change of the area with respect to time, and dr/dt represents the rate of change of the radius with respect to time.

Since we are considering an expanding circle, both dA/dt and dr/dt are positive.

Now, let's solve for the relationship between dA/dt and dr/dt:

dA/dt = 2(dr/dt)

π\(r^2\) = 2(dr/dt)

Dividing both sides by \(r^2\):

π = 2(dr/dt) / \(r^2\)

Simplifying further:

π = 2(dr/dt) / \(r^2\)

π = 2/r

Therefore, the relationship between the rate of change of the area and the rate of change of the radius is π = 2/r.

To find the value of r, we rearrange the equation:

r = 2/π

Thus, the radius is 2/π, which is approximately 0.6366.

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Answer:

This is what I got

Step-by-step explanation:

1. Is decreasing so therefore is negative

2. Is undefined, Changed but is neither negative or positive

3. Is zero because it just stays the same

4. Is increasing therefore is positive

The actual measurement of that side of the courtyard = 165 inches

In this question, we have been given Andre drew a plan of a courtyard at a scale of 1 to 60. in his drawing, one side of the courtyard is 2.75 inches.

We need to find the actual measurement of that side of the courtyard.

In order to calculate the real length,

real length = scale length / scale ratio

here, scale length = 2.75 inches

scale ratio = (1/60)

so, the real length would be,

real length = 2.75/ (1/60)

real length = 2.75 * 60

real length = 165 inches

Therefore, the actual measurement of that side of the courtyard = 165 inches

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Answer:

Step-by-step explanation:

Answer:

q1: no, she does not have enough money to return the bike at 8:15

   equation: (50-40)-(4×5)

                   =10-20

                   = -10

(this means she needs 50+10, 60 dollers to return the bike at 8:15)

q2: 7:30

Step-by-step explanation:

q1: first the q says that she has 50 and she needs to pay 40 to ride the bike from 9 am to 7 pm,

so now she has already used 40 from the 50 she already had, there fore she is left with 10.

the q also tells us the she has to pay 4 per quarter hour, which means 15 min

75÷15=5                                                                                                              (cuz 1 hour = 60 min, 60+15=75)

5×4(cuz she has to pay 4 per 15 min)

=20

but she does not have 20, she only has 10

so... she wont be able to pay that much..

Q2:

she would have to return it after 30 min after 7pm

cuz

4×4=16, 16>10

3×4=12, 12>10

2×4=8, 8<10

so 2×15min= 30

so she would have to return the bike at 7:30 pm

Answer:

degree 3

Step-by-step explanation:

The degree of a polynomial is determined by the largest exponent of the term within the polynomial.

4x²y = 4x²\(y^{1}\) ← with exponent 2 + 1 = 3

x² ← exponent 2

- 2y² ← exponent 2

The term with the largest exponent is 4x²y with exponent 3

Then the polynomial is of degree 3

Answer:

No

Step-by-step explanation:

x=(b-5)/c≠(5-b)/c

supposedly

b=6

c=1

x=6-5/1=1

x=5-6/1= -1

1≠ -1

Answer:

No

Step-by-step explanation:

x = b - 5 / L equal to - (5 - b) / L

The converted to product four times as much in the CSTR than it was in the PFR that is 400%.

Conversion is a term used to describe the process of transferring a reactant into a product.

In this case, the reactant is being transferred from a 72 l plug flow reactor (PFR) to a 24 l continuous stirred tank reactor (CSTR). The conversion achieved by this process can be determined by calculating the ratio of product to reactant in the CSTR.

Specifically, if the PFR has a conversion of x%, then the conversion achieved in the CSTR will be x/(1-x), where x is the conversion in the PFR.

Therefore, if the PFR has a conversion of 80%, then the CSTR will have a conversion of 80/(1-80) = 400%.

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Answer:

A=$12451.67474

Step-by-step explanation:

A=$12000{(1+3/100)^¼)}^4

A=$12451.67474

Answer:

B

Step-by-step explanation:

The dilation of 2.5 about the origin is C.) F'(-5,-2.5), G'(-2.5,5), H'(5,-5).

What is dilation?

Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.

Now from the given graph coordinates of F,G and H are,

F(-2,-1)

G(-1,2)

H(2,-2)

The coordinate points F(-2,-1), G(-1,2) and H(2,-2) it dilated by a factor of 2.5, we will multiply the coordinates by 2.5 to have:

F'(-5,-2.5), G'(-2.5,5), H'(5,-5).

Thus, the dilation of 2.5 about the origin is C.) F'(-5,-2.5), G'(-2.5,5), H'(5,-5).

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The decay factοr fοr the given expressiοn is 0.75.

The cοnstant multiplier οf the expοnential decay functiοn is smaller than 1 when a quantity declines by the same amοunt thrοughοut equal intervals οf time. This quantity, alsο referred tο as the decay factοr, can be written as (1-r).

The given expressiοn can be simplified as:

\(300(1-0.25)^t = 300(0.75)^t\)

The decay factοr in an expοnential decay functiοn is the base οf the expοnent, which is equal tο the fractiοn by which the quantity is decreasing per unit time.

In this case, the decay factοr is 0.75, since the quantity is decreasing by a factοr οf 0.75 per unit time (as the quantity in the parentheses is the fractiοn οf the οriginal quantity that remains after οne unit οf time).

Therefore, the decay factor for the given expression is 0.75.

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Answer:

30%

Step-by-step explanation:

100-70=30

Answer:

i dunno 30%?

Step-by-step explanation:

The measure of each interior angle of the regular polygon is equal to 150°.

In Euclidean geometry, a regular polygon simply refers to a form of polygon which has all of its sides and interior angles being equal.

In Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:

Sum of interior angles = 180 × (n - 2)

Where:

n represents the number of sides of a regular polygon.

Similarly, the measure of each interior angle of a regular polygon can be calculated by using this mathematical expression:

Interior angles = [180 × (n - 2)]/n

Interior angles = [180 × (12 - 2)]/12

Interior angles = 180 × (10)/12

Interior angles = 1800/12

Interior angles = 150°

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Answer:

x = 60

Step-by-step explanation:

The question is asking

$14,700 * (1 - 8%)^x = $100

$14,700 * (1 - 0.08)^x = $100

$14,700 * (0.92)^x = $100

(0.92)^x = $100/$14,700

log(0.92^x) = log($100/$14,700)

x * log(0.92) = log(0.0068027)

x = log(0.0068027)/log(0.92)

x = 59.85

Since this question is asking in terms of years, we always round up (in this case to 60), as it won't fully be worth $100 by the beginning of the 59th year.

Answer:

The roots of the equation
\(x^{3}-10x^{2}+31 x-30 = 0\)

correspond to the x-intercepts of the function graph

Step-by-step explanation:

The roots of the equation
\(x^{3}-10x^{2}+31 x-30 = 0\)

are x = 2, x = 3, x = 5

which are located at points (2, 0), (3, 0), (5,0)

These points are the x-intercepts of the graph of the equation
So the x-intercepts of the equation are the roots of the equation

I have graphed this using Geogebra which I am familiar with. You should probably use Desmos as per the instructions

a.we get, `A = √(2α³/π)`.

b.`⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

c.we can say that the variational principle is valid in this case.

(a) Let's find the normalization constant A.

We know that the integral over all space of the absolute square of the wave function is equal to 1, which is the requirement for normalization.  `∫⟨ψ|ψ⟩dx= 1`

Hence, using the given trial wavefunction, we get, `∫⟨ψ|ψ⟩dx = ∫ |A/(x^2+α²)|²dx= A² ∫ dx / (x²+α²)²`

Using a substitution `x = α tan θ`, we get, `dx = α sec² θ dθ`

Substituting these in the above integral, we get, `A² ∫ dθ/α² sec^4 θ = A²/(α³) ∫ cos^4 θ dθ`

Using the identity, `cos² θ = (1 + cos2θ)/2`twice, we can write,

`A²/(α³) ∫ (1 + cos2θ)²/16 d(2θ) = A²/(α³) [θ/8 + sin 2θ/32 + (1/4)sin4θ/16]`

We need to evaluate this between `0` and `π/2`. Hence, `θ = 0` and `θ = π/2` limits.

Using these limits, we get,`⟨ψ|ψ⟩ = A²/(α³) [π/16 + (1/8)] = 1`

Therefore, we get, `A = √(2α³/π)`.

Hence, we can now write the wavefunction as `ψ(x) = √(2α³/π)/(x²+α²)`.  

(b) Using the wave function found in part (a), we can now determine the expectation value of energy using the time-independent Schrödinger equation, `Hψ = Eψ`. We can write, `H = (p²/2m) + (1/2)mω²x²`.

The first term represents the kinetic energy of the particle and the second term represents the potential energy.

We can write the first term in terms of the momentum operator `p`.We know that `p = -ih(∂/∂x)`Hence, we get, `p² = -h²(∂²/∂x²)`Using this, we can now write, `H = -(h²/2m) (∂²/∂x²) + (1/2)mω²x²`

The expectation value of energy can be obtained by taking the integral, `⟨H⟩ = ⟨ψ|H|ψ⟩ = ∫ψ* H ψ dx`Plugging in the expressions for `H` and `ψ`, we get, `⟨H⟩ = - (h²/2m) ∫ψ*(∂²/∂x²)ψ dx + (1/2)mω² ∫ ψ* x² ψ dx`Evaluating these two integrals, we get, `⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

(c) Since we have an approximate ground state wavefunction, we can expect that the expectation value of energy ⟨H⟩ should be greater than the true ground state energy.

Hence, the value obtained in part (b) should be greater than the true ground state energy obtained by solving the Schrödinger equation exactly.

Therefore, we can say that the variational principle is valid in this case.

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Hey there! :)

Answer:

A. \(f(x) = (x - 2)^{4}\)

Step-by-step explanation:

Recall that the transformation form of a polynomial with degree four is:

\(f(x) =\) ±\(a(b(x-h))^{4} +k\)

In this instance, we will need to use the h value, or the horizontal shift.

It is given that there is only a horizontal shift of 2 units to the right, or h = 2. Plug this into the equation:

\(f(x) = (x - 2)^{4}\)

Answer:

Range of function y=

1+x

2

x

Range is given by 'R'

Say f(x) = y

y=

1+x

2

x

y(1+x

2

)=x

y+yx

2

−x=0

yx

2

−x+y=0

x=

2a

−b±

b

2

−4ac

[∵ quadratic formula

and the sol

n

of x are real when

b

2

−4ac⩾0

so like wire

(

−1)−4(y)(y)⩾0

we solve the inequality for the values set of value of y.

1−4y

2

⩾0

1−4y

2

⩾0

1

2

−(2y)

2

⩾0

(1−2y)(1+2y)⩾0

(2y+1)(2y−1)⩽0 [Taking negative common]

(2y+1)⩾0 & (2y−1)⩽0

y⩾−1/2y⩽1/2

−1/2⩽y⩽1/2

The scale factors of the shapes are 1.25, 1.25. 5 and 2, respectively

To do this, we divide the side length of the larger shape with the corresponding side of the small shape

using the above as a guide, we have the following scale factors calculations

figure 7 = 15/12 = 1.25

figure 8 = 25/20 = 1.25

figure 9 = 40/8 = 5

figure 10 = 10/5 = 2

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Step-by-step explanation:

Just put in n = 1, 2,3,4   into the formula to get

7   10    13    and  16  

Answer:

290

Step-by-step explanation:

Formula :

Number of action figures on wall = Total number of figures × % of figures on wall

=============================================================

Given :

⇒ Total number of action figures = 500

⇒ % of action figures on wall = 58%

=============================================================

Solving :

⇒ Action figures on wall = 500 × 58%

⇒ Action figures on wall = 500 × 58/100 (all % are ratios of 100%)

⇒ Action figures on wall = 5 × 58

⇒ Action figures on wall = 290

Total action figures

Done!