Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength= (λ/2).

This can be expressed mathematically as:
w * sin(θ) = (m + 1/2) * λ, where m = 0 for the first dark fringe, w is the slit width, θ is the angle of the dark fringe from the central maximum, and λ is the wavelength of light.
When light passes through a single slit, it diffracts and creates an interference pattern with alternating bright and dark fringes on a screen. The dark fringes occur when light waves from the edges of the slit interfere destructively, which means their path difference must be an odd multiple of half a wavelength (λ/2).
For the first dark fringe, we set m = 0 in the equation:
w * sin(θ) = (0 + 1/2) * λ
So, the condition for the first dark fringe is:
w * sin(θ) = λ/2

Hence, The condition for the first dark fringe through a single slit of width w is when the path difference between the light waves at the edges of the slit equals a half wavelength (λ/2). This can be represented by the equation w * sin(θ) = λ/2.

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Answer:

view explanation, please

Step-by-step explanation:

If the variable is the same and you are multiplying: add the exponents.

\(Z^8 * Z^6 = Z^8+^6\)

8+6=14

If the variable is the same and you are dividing: subtract the exponents.

\(Z^1^4-^8=Z^6\)

Answer:

The answer is Z⁶

Step-by-step explanation:

Cancel the common factor, Z⁸

Answer:

  13 meters

Step-by-step explanation:

Adjacent sides form half the perimeter, so the sum of the unknown side and the given side is 34/2 = 17 meters.

  4 meters + width = 17 meters

  width = 13 meters . . . . . subtract 4 meters

The dimensions that will result in a solid with maximum volume are approximately x = 12.02 centimeters and h = 5.01 centimeters.

Let the side of the square base be x, and let the height of the rectangular solid be h. Then, the surface area of the solid is given by:

Surface area = area of base + area of front + area of back + area of left + area of right

Surface area = x² + 2xh + 2xh + 2xh + 2xh = x² + 8xh

We are given that the surface area is 433.5 square centimeters, so we can write: x² + 8xh = 433.5

We want to find the dimensions that will result in a solid with maximum volume. The volume of the solid is given by:

Volume = area of base × height = x² × h

We can use the surface area equation to solve for h in terms of x:

x² + 8xh = 433.5

h = (433.5 - x²)/(8x)

Substituting this expression for h into the volume equation, we get:

Volume = x² × (433.5 - x²)/(8x) = (433.5x - x³)/8

To find the maximum volume, we need to find the value of x that maximizes this expression. To do this, we can take the derivative of the expression with respect to x, set it equal to zero, and solve for x:

d(Volume)/dx = (433.5 - 3x²)/8 = 0

433.5 - 3x² = 0

x² = 144.5

x = sqrt(144.5) ≈ 12.02

We can check that this is a maximum by computing the second derivative of the volume expression with respect to x:

d²(Volume)/dx² = -3x/4

At x = sqrt(144.5), this is negative, which means that the volume is maximized at x = sqrt(144.5).

Substituting x = sqrt(144.5) into the expression for h, we get:

h = (433.5 - (sqrt(144.5))²)/(8×sqrt(144.5))

h = 433.5/(8×sqrt(144.5)) - sqrt(144.5)/8

h = 5.01

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The dimensions of the rectangular solid that will result in a maximum volume are approximately.\(6.34 cm \times 9.03 cm \times 9.03 cm.\)

Let's assume that the length, width, and height of the rectangular solid are all equal to x, so the base of the solid is a square.

The surface area of the rectangular solid can be expressed as:

\(SA = 2xy + 2xz + 2yz\)

Substituting x for y and z, we get:

\(SA = 2x^2 + 4xy\)

We are given that the surface area is 433.5 square centimeters, so:

\(2x^2 + 4xy = 433.5\)

Simplifying, we get:

\(x^2 + 2xy - 216.75 = 0\)

Using the quadratic formula to solve for y, we get:

\(y = (-2x\± \sqrt (4x^2 + 4(216.75)))/2\)

\(y = -x \± \sqrt (x^2 + 216.75)\)

Since the base of the rectangular solid is a square, we know that y = z. So:

\(z = -x \± \sqrt(x^2 + 216.75)\)

The volume of the rectangular solid is given by:

\(V = x^2y\)

Substituting y for\(-x + \sqrt (x^2 + 216.75),\) we get:

\(V = x^2(-x + \sqrt(x^2 + 216.75))\)

Expanding and simplifying, we get:

\(V = -x^3 + x^2\sqrt(x^2 + 216.75)\)

The dimensions that will result in a solid with maximum volume, we need to find the value of x that maximizes the volume V.

We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:

\(dV/dx = -3x^2 + 2x\sqrt(x^2 + 216.75) + x^2/(2\sqrt (x^2 + 216.75)) = 0\)

Multiplying both sides by \(2\sqrt (x^2 + 216.75)\) to eliminate the denominator, we get:

\(-6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) + x^3 = 0\)

Simplifying, we get:

\(x^3 - 6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) = 0\)

We can solve this equation numerically using a graphing calculator or computer software.

\(The solution is approximately x = 6.34 centimeters.\)

Substituting x = 6.34 into the expression for y and z, we get:

\(y = z \approx 9.03 centimeters\)

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Answer:

7 Kids like cats

Step-by-step explanation:

You will be able to withdraw approximately $3,076.32 at the end of 5 years.

To calculate the amount you will be able to withdraw at the end of 5 years, we can use the future value formula for compound interest.

The formula for calculating the future value (FV) of a present value (PV) invested at an annual interest rate (r) for a certain number of years (t) is:

\(FV = PV * (1 + r)^t\)

Given:

PV = $2,300

r = 6% = 0.06 (decimal representation)

t = 5 years

Substituting these values into the formula, we get:

FV = $2,300 * \((1 + 0.06)^5\)

Calculating the expression inside the parentheses:

\((1 + 0.06)^5 = 1.338225\)

Multiplying the present value by this factor:

FV = $2,300 * 1.338225

FV ≈ $3,076.32

Therefore, you will be able to withdraw approximately $3,076.32 at the end of 5 years.

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You deposit $2,300 into an account that pays 6% per year. Your plan is to withdraw this amount at the end of 5 years to use for a down payment on a new car. How much will you be able to withdraw at the end of 5 years? Do not round intermediate calculations. Round your answer to the nearest cent

Answer:

3(3 - 4x + 2y).

Step-by-step explanation:

Notice that 3 is a factor of 9, -12 and 6.  

There's no other "common factor."

Therefore, the GCF is 3 and in factored form the given polynomial is

3(3 - 4x + 2y).

Answer: \(3\left(3-4x+2y\right)\)

Step-by-step explanation:

\(3\cdot \:3+4\cdot \:3x+2\cdot \:3y\)

\(3\left(3-4x+2y\right)\)

Answer: It is 160

Step-by-step explanation:

I just completed the test

Therefore , the solution of the given problem of surface area comes out to be the right response is option c 160 in².

Calculating how much space would be needed to fully cover the outside will reveal its overall size. The surroundings are considered when determining the same surface with a rectangular form. The surface area of something determines its overall dimensions. The amount of edges present in the space between a cuboid's four trapezoidal corners determines how much water it can hold inside.

Here,

the base's outermost boundary is:

=> Perimeter = 4s

To locate s,

=> Base  Area = s² = 64 in².

To solve for s, we obtain:

=> √(64 in²) = 8 in

We can now determine the perimeter:

=> perimeter: 4s

=> (4 * 8 inches)/(32 inches)

Finally, we can enter the numbers into the surface area formula as follows:

=>  Base Area + (1/2) x Perimeter x Slant Height

=> Surface Area Surface Area = 64 in² + (1/2) x 32 in x 6 in

=> Surface area = 64 in² + 96 in².

160 in² is the surface area.

Consequently, the cone has a surface area of 160 in².

The right response is (c) 160 in².

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The speed of the moving body that is being referred to here is 80 kilometer per hour.

The given problem is a straightforward one based on the idea of the universal law of motion. According to the universal law of motion, any uniformly traveling body's distance traveled is determined by the product of its speed and the time elapsed. Distance is calculated as speed * time. Therefore the body is going at a speed of 80 kilometers per hour, according to the same relation as above, assuming that it is moving at a constant speed.

                                \(Distance = speed * time\)

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Answer:

Dude... u added them, you need to divide them.

5/6÷1/12

2 · c + 2 · (c - 2) =

= 2c + 2c - 4 = 4c - 4 ← the end

Answer:

The perimeter is 4c - 4

Step-by-step explanation:

We will use the Rectangle Perimeter formula:

P = 2(l + w)

Given:

l = c

w = c - 2

Now, we just plug them into the formula:

P = 2(l + w)

P = 2(c + c - 2)

P = 2(2c - 2)

P = 4c - 4

The team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.

For the team with the homecourt advantage, let \(Wi\) and \(Li\) denote whether the game '\(i\)' was a win or a loss. Because games 1 and 3 are home games and game 2 is an away game.

The probability that the team with the home-court advantage wins is

P [H] = P [\(W1W2\)] + P [\(W1L2W3\)] + P [\(L1W2W3\)]

        = \(p(1-p)\) + \(p3\) + \(p(1-p){2}\)

Note that P[H] ≤ pfor 1/2≤p≤1.

Since the team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.

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For the team with the homecourt advantage, let  and  denote whether the game '' was a win or a loss. Because games 1 and 3 are home games and game 2 is an away game.

The probability that the team with the home-court advantage wins is

P[H] ≤ pfor 1/2≤p≤1.

Since the team with the home-court advantage would win a 1 game playoff with probability (p), the home-court team is less likely to win a three-game series than a 1 game playoff.

Answer: 960 crayons

Step-by-step explanation:

From the question, we are informed that Mr Andrew bought 15 boxes of crayons at the store to share with his students and that each box contains 64 crayons.

The equation that represents ​c​, the total number of crayons that Mr. Andrew bought will be:

C = 15 × 64

= 960 crayons

Answer:

x = -1

Step-by-step explanation:

factor and you get

(x + 1)(x + 1) or (x + 1)^2

now set it equal to zero

x + 1 = 0

subtract one from both sides

x = -1

The number of ways a diner can design her meal by selecting exactly one option from each of the four categories is 2160. There are 2160 different combinations of options that the diner can select to make up her meal.

When a diner is selecting her meal from a restaurant, she needs to choose one option from each of the four categories: appetizers, entrees, desserts, and beverages. The number of options she has in each category determines the number of ways she can design her meal.

In this case, the number of options the diner has in each category are:

Appetizers: 4 options

Entrees: 14 options

Desserts: 6 options

Beverages: 5 options

The number of ways the diner can design her meal is equal to the product of the number of options she has in each category. This is because each category is independent of the other categories, and the order in which she selects the options does not matter.

Therefore, the number of ways the diner can design her meal is 4 * 14 * 6 * 5 = 4 * 14 * 30 = 2160. This means that there are 2160 different combinations of options that the diner can select to make up her meal.

In conclusion, the number of ways a diner can design her meal by selecting exactly one option from each of the four categories is 2160.

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Answer:

B

Step-by-step explanation:

I know it because the screen is black

Answer:

Katrina would need to buy 20 sweatshirts.

Step-by-step explanation:

The number of sweatshirts Katrina would need to order from  each company can be determined by forming the linear equation in two variables.

Given :

Let the number of sweatshirts orders from company MH Designs be 'x' and the number of sweatshirts orders from company Print Rich be 'y'.

So, the cost for ordering the sweatshirt from the company MH Design is:

\(21.50x = c\)

Now, the cost for ordering the sweatshirt from the company Print Rich is:

18y + 70 = c'

Given that the number of sweatshirts Katrina would need to order from  each company for the costs to be the same. So :

21.5x = 18y + 70

Now, put the value of x and y so, that in the above equation, both sides become equal.

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Answer:

h,c

Step-by-step explanation:

Answer:

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

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

Answer: 206

Step-by-step explanation:

a=3/4, b=-8, c=-2, d=3

-b[a+(c-d)^2]=

-(-8)[3/4+(-2-3)^2]=

8[3/4+(-5)^2]=

8[3/4+25]=

8*3/4 + 200=

24/4 + 200=

6+200=206

The x- coordinate of the vertex P is  -4  and the y coordinate is -3. The coordinates of the image of vertex P is thus,  (-4, -3).

Coordinates are numbers describing the position of a point or shape in a line or particular space. We can represent a line or shape in the space between number lines with both positive and negative coordinates.

The vertical axis in the number line is called y-axis and the horizontal axis is called the x- axis. The coordinate of a point is written as (x, y). The x, y represents the numbers on x-axis and y -axis touched at which the point lies in the graph.

For the given vertex P, the vertex lies on the point -4 on x-axis and on -3 in y axis. Hence, the coordinate of P is (-4, -3).

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The rate at which the top of the ladder is slipping down at the instant when the bottom of the ladder is 15 feet from the base of the building is -75/8 feet per second

The length of the ladder = 17

Consider the length of the base as x and the height is h

The rate at which the ladder is sliding = 5 feet per second

dx/dt = 5

Apply the Pythagorean theorem

x^2 + h^2 = 17^2

h^2 = 289 - x^2

h = \(\sqrt{289-x^2}\)

The rate of change of height with respect to x is

dh/dx = - x / (289 - x^2)^(1/2)

dh/dt = dh/dx × dx/dt

Substitute the values in the equation

= - 15 / (289 - 15^2)^(1/2) × 5

= -15/8 × 5

= -75/8 feet per second

Therefore, the rate of change of height when x = 15 is -75/8 feet per second

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The energy dissipated by the resistor is given by the equation E = Sºp(t) dt, where P(t) = (*3*5e Rd)** .P( * R. To find the energy dissipated, we need to evaluate the integral Sºp(t) dt.

The integral Sºp(t) dt can be evaluated using integration by parts. Let u = t and v = (*3*5e Rd)** .P( * R. Then du = dt and v = -(3*5e Rd)** .P( * R) / R. The integral Sºp(t) dt can then be written as follows:

Sºp(t) dt = -(3*5e Rd)** .P( * R) / R + Sºv du

The integral Sºv du can be evaluated using the following formula:

Sºv du = uv - Sºu dv

In this case, u = t and v = -(3*5e Rd)** .P( * R) / R. Therefore, the integral Sºv du is equal to the following:

Sºv du = -(3*5e Rd)** .P( * R) / R * t - Sº(3*5e Rd)** .P( * R) / R dt

Substituting the value of Sºv du into the equation for Sºp(t) dt, we get the following:

Sºp(t) dt = -(3*5e Rd)** .P( * R) / R + (-(3*5e Rd)** .P( * R) / R * t - Sº(3*5e Rd)** .P( * R) / R dt)

Simplifying the equation, we get the following:

Sºp(t) dt = -(3*5e Rd)** .P( * R) / R (1 + t)

The value of the integral Sºp(t) dt is then given by the following:

E = -(3*5e Rd)** .P( * R) / R (1 + t)

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Answer:

Donna traveled for 8 hours at 90 mph

Maple traveled for 4 hours at 50 mph

Step-by-step explanation:

The velocity at which each person traveled is given by the distance traveled divided by the time spent (t). From the information given, the following expressions can be written

\(t_d = 2t_m\\V_d = V_m+40\\V_d = \frac{720}{t_d}\\V_m = \frac{200}{t_m}\\\\V_d = \frac{360}{t_m}\\ \frac{360}{t_m}=\frac{200}{t_m}+40\\t_m = 4\ hours\\t_d=2*4 = 8\ hours\\\\V_d = \frac{720}{8}=90\ mph\\V_m = \frac{200}{4}=50\ mph\\\)

Therefore, Donna traveled for 8 hours at 90 mph and Maple traveled for 4 hours at 50 mph.

The required answer is , the particle's position at time t = 9 seconds is 15 meters along the x-axis.

To find the particle's position at time t = 9 seconds, given the velocity function v(t) = √(9 - t) and the initial position s(0) = 9, we need to integrate the velocity function and then use the initial condition to find the position function s(t).

Step 1: Integrate the velocity function
∫v(t) dt = ∫√(9 - t) dt
We also known the initial position of the particle = 9
Step 2: Use substitution method
Let u = 9 - t, then du = -dt
           So, the integral becomes: -∫√u du
Step 3: Integrate
-∫√u du = -2/3 * u^(3/2) + C = -2/3 (9 - t)^(3/2) + C
Step 4: Find the constant C using the initial condition s(0) = 9
9 = -2/3 (9 - 0)^(3/2) + C
C = 9 + 6 = 15
Step 5: Write the position function s(t)
s(t) = -2/3 (9 - t)^(3/2) + 15
Step 6: Find the position at time t = 9 seconds
s(9) = -2/3 (9 - 9)^(3/2) + 15 = 15

Therefore, the position function of the particle is: s(t) = -2/3(9-t)^(3/2) + 15 Plugging in t = 9, we get: s(9) = -2/3(9-9)^(3/2) + 15 s(9) = 15 So the particle's position at time t = 9 seconds , 15 meters.

So, the particle's position at time t = 9 seconds is 15 meters along the x-axis.

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Answer: 78

Step-by-step explanation:

Given

Mrs. Lee has \(132\) students

On a particular day, one-fourth of her students are sick i.e.

\(\Rightarrow \dfrac{1}{4}\times 132=33\)

and 24 were on a field trip.

The total no of students taught on that day will be the subtraction of the gone students and the addition of three new.

\(\Rightarrow 132-33-24+3\\\Rightarrow 78\)

The volume of the pyramid is 2520cm³. The Option C.

A triangular pyramid refers to the three dimensional object. It is made up of a triangular base and three triangular faces. The three triangular faces are equilateral. A  triangular pyramid is also called a tetrahedron.

The formula for the volume of a pyramid is: 1/3 x (base area x height)

The base area is:

= 1/2 x base x height

= 1/2 x 24 x 18

= 216 cm²

The  volume of a pyramid is:

= 1/3 x (35 x  216 cm²)

= 2520cm³

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The height of the water tank given the volume, length and width is 40 cm

Volume of the water tank= 40 liters

Length of the water tank= 50 cm

Width of the water tank= 20 cm

Height of the water tank= x

convert liters to centimeters

1 liter= 1000 cm

40 liters= 40,000 cm

Volume of the water tank= length × width × height

40,000 = 50 × 20 × x

40,000 = 1000x

divide both sides by 1000

x = 40,000 / 1000

x = 40 cm

Therefore, the height of the water tank is 40 cm

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