Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points in simplest radical form. (-9, -4) and (-2, 2)

The greatest number of 4 cm cubes that Haley can fit in the box and still be able to close the lid is 6.

First, we need to determine the dimensions of the box in terms of the length of a side of a cube. We can do this by finding the smallest dimension of the box and dividing it by the length of the side of a cube.

The smallest dimension of the box is the height, which is 6 cm. Therefore, the length of the side of a cube must be a factor of 6.

The length and width of the box are both 8 cm, so the length of the side of a cube must be less than or equal to 8 cm.

We can check the factors of 6 to find the largest possible size of the cube that can fit in the box:

A cube with side length 6 cm would fit in the box, but the lid would not be able to close.

A cube with side length 4 cm would fit in the box, and the lid would be able to close, so this is the largest size cube that can fit in the box.

To determine how many 4 cm cubes can fit in the box, we need to find the volume of the box and divide by the volume of a single cube. The volume of the box is:

V_box = length x width x height

V_box = 8 cm x 8 cm x 6 cm

V_box = 384 cm³

The volume of a single 4 cm cube is:

V_cube = side length³

V_cube = 4 cm x 4 cm x 4 cm

V_cube = 64 cm³

Dividing the volume of the box by the volume of a single cube gives us the maximum number of cubes that can fit in the box:

384  / 64  = 6

Therefore, the greatest number of 4 cm cubes that Haley can fit in the box and still be able to close the lid is 6.

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Answer:6

Step-by-step explanation:

dependent is the varible

Answer:

$68000

Step-by-step explanation:

Answer:

$6800

Step-by-step explanation:

30x1600+10x2000

=48000+2000

=68000

The rate of change of a periodic function is itself a periodic function. In the case of a sinusoidal wave, the derivative is also a sinusoidal wave with the same period, but shifted by a phase angle of [tex]π/2.[/tex]

The rate of change of a periodic function at a specific point is equal to the instantaneous slope of the tangent line to the graph of the function at that point.

To calculate the rate of change of a periodic function, you need to take the derivative of the function with respect to the independent variable (usually time). If the function is a sinusoidal wave, you can use trigonometric identities to find the derivative.

For example, let's say we have a function f(t) = sin(t), which represents a sinusoidal wave. To find the rate of change of the function at a particular point t = a, we need to take the derivative of the function with respect to t:

f'(t) = cos(t)

Then we can evaluate this derivative at t = a to find the rate of change at that point:

f'(a) = cos(a)

This tells us the instantaneous rate of change of the function at the point t = a.

Note that the rate of change of a periodic function is itself a periodic function. In the case of a sinusoidal wave, the derivative is also a sinusoidal wave with the same period, but shifted by a phase angle of [tex]π/2.[/tex]

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Answer:

48cm³

Step-by-step explanation:

volume = (7 X 6 X 1) + (3 X 2 X 1)

= (42 + 6)

= 48cm³

The area covered by the lawn sprinkler is approximately 461.63 square feet.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

A = πr²

Where r is radius and π is constant pi ( π = 3.14 )

Given that; the diameter of the circle is 24.25 feet.

The radius of the circle is half of the diameter, so:

Radius r = diameter/2

Radius r = 24.25 / 2

Radius r = 12.125 feet

Next, plug the values into the above formula and solve for area.

Area = πr²

Area = 3.14 × ( 12.125 ft )²

Area = 3.14 × ( 12.125 ft )²

Area = 461.63 ft²

Therefore, the area is 461.63 ft².

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Answer:

L = J + 5

Step-by-step explanation:

Let's use "L" to represent Leanne's age and "J" to represent Jose's age.

From the given information, we know that Leanne is 5 years older than Jose, so we can write:

L = J + 5

This equation states that Leanne's age "L" is equal to Jose's age "J" plus 5 years.

Answer:

The correct answer is 12.6n2 + 7.14n.

Step-by-step explanation:

To find the product of 2.1n(6n + 3.4), we can use the distributive property of multiplication:

2.1n(6n + 3.4) = 2.1n(6n) + 2.1n(3.4)

Simplifying this expression gives:

12.6n^2 + 7.14n

Therefore, the product of 2.1n(6n + 3.4) is 12.6n^2 + 7.14n.

Answer:

12.6n2 + 7.14n.

Step-by-step explanation:

2.1×n×(6n+3.4)

Rewrite the expression

2.1×n(6n+3.4)

Calculate the product

2.1n(6n+3.4)

Apply the distributive property

2.1n×6n+2.1n×3.4

Multiply the terms

12.6n

2

+2.1n×3.4

Solution

12.6n

2

+7.14n

The length of segment BD, which represents the altitude of the triangle, is given as follows:

BD = 6.

The geometric mean theorem states that the length of the altitude of a triangle is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.

The altitude segment for this problem is given as follows:

BD.

The bases for this problem are given as follows:

3 and 12.

Hence the length of segment BD is obtained as follows:

(BD)² = 3 x 12 -> geometric mean formula

(BD)² = 36

(BD)² = 6².

BD = 6.

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Answer: illustrates similarity of figures

Step-by-step explanation: more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal. This common ratio is called the scale factor.

Answer:

11.7b

Step-by-step explanation:

If you do 339.30 divided by 29 it equals 11.7 but the full equation would be c=11.7b

The proportional equation for the total cost 'c' in terms of the number of boxed lunches 'b' is:

c = (339.30 / 29) * b

What is proportion?

The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.

Let's assume that each boxed lunch costs the same amount, denoted by the variable 'x'.

We are given that the company ordered 29 boxed lunches for a total cost of $339.30. Therefore, we can write the equation:

29x = 339.30

To find the cost 'c' for any number 'b' of boxed lunches, we can set up a proportion:

29x / 29 = 339.30 / b

Simplifying this equation, we get:

x = 339.30 / 29

Now, we can substitute this value of 'x' back into the equation:

c = bx = b * (339.30 / 29)

Therefore, the proportional equation for the total cost 'c' in terms of the number of boxed lunches 'b' is:

c = (339.30 / 29) * b

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The seismograph reading of the earthquake is approximately 1.99526.To determine the seismograph reading of the earthquake with a magnitude of 3.3 on the Richter scale, we can use the formula M(I) = log(I/0.001), where M(I) represents the magnitude and I represents the intensity of the earthquake.

In this case, we are given the magnitude of 3.3. Let's substitute this value into the formula and solve for I:

3.3 = log(I/0.001)

To isolate I, we need to convert the equation into exponential form:

10^(3.3) = I/0.001

Simplifying the equation, we have:

I = 10^(3.3) * 0.001

Using a calculator, we find that 10^(3.3) is approximately 1995.26.

So, the seismograph reading of the earthquake is:

I = 1995.26 * 0.001

≈ 1.99526.

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The sector area is 6π square meters.

We can use the formula for the area of a sector of a circle, which is:

A = (θ/2π) × πr²

where θ is the representation of the central angle in radians, and r is the representation of the radius of the circle.

In this case, we are given that 2π/3 is the central angle and r = 6 m. We can simplify 2π/3 as 120 degrees or π/3 radians.

When we enter these values into the formula, we get:

A = (π/3 × 1/2π) × (36)

= (1/6) × 36π

= 6π

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Use  Theoretical probability  there are 220 students in the grade.

We can use the formula for theoretical probability to find the number of students in the grade:

P(event) = number of favorable outcomes / number of total outcomes

In this case, the probability of a student trying out for the school play is 1/10, so we have:

1/10 = number of students who try out / total number of students in the grade

We can simplify this equation by multiplying both sides by the total number of students in the grade:

total number of students in the grade * 1/10 = number of students who try out

Multiplying both sides by 10, we get:

total number of students in the grade = 10 * number of students who try out

Substituting the given value of 22 for the number of students who try out, we get:

total number of students in the grade = 10 * 22

total number of students in the grade = 220

Therefore, there are 220 students in the grade.

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Answer:

Step-by-step explanation:

20 seconds = 8 copies

so every 2.5 seconds, 1 page is made( 20sec/8 page = 2.5 page per second)

2.5 sec = 1 page

48 sec = x page

now you cross multiply, and that goes to: 2.5x = 48

isolate for x

x= 48/2.5

x= 19.2 but it says whole pages so you round down

x = 19 pages in 49 seconds

The quantity 1.0 mg/cm2 is the same as 1.0 x 10-4 kg/m2.

To convert from milligrams per square centimeter (mg/cm2) to kilograms per square meter (kg/m2), we need to use conversion factors to adjust the units. The given options represent different powers of 10 that can be used as conversion factors.

We know that 1 kilogram (kg) is equal to 1,000,000 milligrams (mg), and 1 meter (m) is equal to 100 centimeters (cm). Therefore, we can express the conversion factors as follows:

1 kg = 1,000,000 mg (1)

1 m2 = 10,000 cm2 (2)

To convert from mg/cm2 to kg/m2, we can combine these conversion factors:

1 mg/cm2 = (1 mg / 1 cm2) x (1 kg / 1,000,000 mg) x (10,000 cm2 / 1 m2)

Simplifying the expression, we have:

1 mg/cm2 = (1 / 1,000,000) kg/m2 = 1 x 10-6 kg/m2

Therefore, the quantity 1.0 mg/cm2 is the same as 1.0 x 10-6 kg/m2.

Among the given options, the value that matches the conversion is option A: 10-4

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Answer:

21x+6

Here is the answer

Its a pleasire

Answer:

21x+6

Step-by-step explanation:

first distrbute the 3 on the brackets

and note that in mathematics when there is no sign just like after the 3 it means it's multiplication

3(2x+5)+3(5x-3)

=6x+15+15x-9

now add or subtract

=21x+6

that is the simplest we can get and we can't find the value of x cuz this is not an equation

(there is no equal sign and numbers on both sides )

Answer:

”an event can have a probability of 0”

Step-by-step explanation:

A probability can not be 0 it has to be more then 0

To make 8 small meat loaves, you will need a total of 6 pounds of meat.

This is because each small meat loaf requires three quarters (0.75) of a pound of meat, and 8 loaves multiplied by 0.75 pounds per loaf equals 6 pounds of meat.

When preparing the meat, it's important to measure out each loaf accurately to ensure they are all the same size and cook evenly. You can use a kitchen scale to measure out the appropriate amount of meat for each loaf.

Once the meat is prepared, you can add your desired seasonings and mix-ins to create a flavorful dish. Some popular additions to meatloaf include onions, garlic, Worcestershire sauce, breadcrumbs, and eggs.

When shaping the loaves, you can use a muffin tin or form them by hand. Bake them in the oven at 350°F for 25-30 minutes or until they reach an internal temperature of 160°F.

Overall, making small meat loaves is a delicious and easy way to enjoy a classic comfort food.

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After 4 seconds, both containers will have the same amount of water.

Let's assume that after "t" seconds, both containers will have the same amount of water.

In "t" seconds, the first container will have 56 + t gallons of water.

In "t" seconds, the second container will have 64 - t gallons of water.

To find out when both containers will have the same amount of water, we need to solve the equation:

56 + t = 64 - t

By solving for "t", we get:

2t = 8

t = 4

Therefore, after 4 seconds, both containers will have the same amount of water.

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To find out how much pasta the restaurant needs, we can use the ratio of pasta to cheese given in the recipe: 8 cups of pasta for every 6 cups of cheese.

First, we need to determine the ratio of cheese to pasta. We can do this by taking the reciprocal of the original ratio, which gives us 6 cups of cheese for every 8 cups of pasta.

Next, we can set up a proportion with the known amount of cheese (15 cups) and the unknown amount of pasta (let's call it x cups):

6 cups of cheese / 8 cups of pasta = 15 cups of cheese / x cups of pasta

We can cross-multiply to solve for x:

6 cups of cheese * x cups of pasta = 8 cups of pasta * 15 cups of cheese

Simplifying this equation gives:

x = (8 cups of pasta * 15 cups of cheese) / 6 cups of cheese

x = 20 cups of pasta

Therefore, the restaurant would need 20 cups of pasta to make the large batch of mac and cheese using 15 cups of cheese, according to the recipe.

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The mean of a sampling distribution of mean is equal to the population mean.

The mean of a sampling distribution of the mean is equal to the population mean. This is a fundamental property of sampling distributions. When repeatedly taking random samples from a population and calculating the mean of each sample, the distribution of those sample means will have a mean that is equal to the population mean. This is known as the central limit theorem, which states that as the sample size increases, the sampling distribution of the mean approaches a normal distribution centered around the population mean. Therefore, the mean of the sampling distribution of the mean will be the same as the population mean.

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The length of segment RT is given as follows:

[tex]RT = 36\sqrt{2}[/tex]

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The right angle in this problem is given as follows:

S, as R = T = 45º.

As the other two angles have the same measure, we have that the two sides are RS = ST = 36, hence the hypotenuse RT is given as follows:

h² = 36² + 26²

[tex]h = \sqrt{2 \times 36^2}[/tex]

[tex]RT = 36\sqrt{2}[/tex]

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The area of the flower bed in square yards is 28 Square yards.

The area of the rectangular flower bed in square yards, we need to convert the measurements from feet to yards. There are 3 feet in 1 yard, so:

Length in yards = 21 feet / 3 = 7 yards

Width in yards = 12 feet / 3 = 4 yards

Now we can calculate the area in square yards:

Area = Length × Width

Area = 7 yards × 4 yards

Area = 28 square yards

Therefore, the area of the flower bed in square yards is 28 square yards.

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Therefore, the probability that the average daily revenue of the sample is between $2450 and $2460 is approximately 0.0443 or 4.43%.

The distribution of the sample means of size n = 100 from a population with mean μ = $2500 and standard deviation σ = $300 can be approximated by a normal distribution with mean = μ = $2500 and standard deviation = σ/√n = $300/√100 = $30.

Thus, we need to find the probability that the sample mean falls between $2450 and $2460.

Z-score for $2450:

z = (2450 - 2500) / 30 = -1.67

Z-score for $2460:

z = (2460 - 2500) / 30 = -1.33

Using a standard normal distribution table or calculator, we can find the probabilities associated with these z-scores:

P(z < -1.67) = 0.0475

P(z < -1.33) = 0.0918

Therefore, the probability that the average daily revenue of the sample is between $2450 and $2460 is:

P(-1.67 < z < -1.33) = P(z < -1.33) - P(z < -1.67)

= 0.0918 - 0.0475

= 0.0443

So, the probability is approximately 0.0443 or 4.43%.

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Para calcular la velocidad del joven, Podemos utilizar la fórmula de la velocidad promedio Por lo tanto, la posición del joven a las 9 h es 1100 km.

a) Para calcular la velocidad del joven, podemos utilizar la fórmula de la velocidad promedio:

velocidad = distancia / tiempo

La distancia recorrida por el joven es xf - xo = 500 km - 200 km = 300 km, y el tiempo transcurrido es 11 h - 8 h = 3 h. Entonces, la velocidad del joven es:

velocidad = 300 km / 3 h = 100 km/h

Por lo tanto, el joven se movió a una velocidad constante de 100 km/h.

b) La ecuación que determina la posición del joven en función del tiempo puede ser expresada como:

x = xo + velocidad × tiempo

donde x es la posición del joven en un momento dado, xo es la posición inicial (xo = 200 km), velocidad es la velocidad constante a la que se mueve el joven, y tiempo es el tiempo transcurrido desde la posición inicial.

Sustituyendo los valores conocidos, obtenemos:

x = 200 km + 100 km/h × t

donde t es el tiempo en horas.

c) Para calcular la posición del joven a las 9 h, podemos utilizar la ecuación que determina la posición del joven en función del tiempo:

x = 200 km + 100 km/h × t

Sustituyendo t = 9 h, obtenemos:

x = 200 km + 100 km/h × 9 h = 1100 km

Por lo tanto, la posición del joven a las 9 h es 1100 km.

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To calculate the average rate of ascent we need to use the following formula:

rate = (final depth - initial depth) / time

Plugging in the given values:

rate = (180 ft - (-1,320 ft)) / 60 min = 1,500 ft / 60 min = 25 ft/min

However, since the submarine is currently below the desired depth, the rate needs to be negative (i.e. descending). So, we need to subtract the ascent rate from the descent rate:

ascent rate = (-1,320 ft - (-180 ft)) / 60 min = -1,140 ft / 60 min = -19 ft/min

total rate = 25 ft/min - 19 ft/min = 6 ft/min

Therefore, the average rate of ascent needed would be 17 feet per minute (rounding to the nearest whole number).

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Answer:

y = 4x^2 + 32x + 28

Step-by-step explanation:

Before we can find the standard form of the quadratic function with the given coordinates, we must first start with the intercept form, whose general equation is

y = a(x - p)(x - q), where

Step 1:  We can plug in (-6, -20) for x and y, -7 for p and -1 for q into the intercept form.  This will allows us to solve for a:

-20 = a(-6 - (-7))(-6 - (-1))

-20 = a(-6 + 7)(-6 + 1)

-20 = a(1)(-5)

-20 = -5a

4 = a

Thus, the full equation in vertex form is

y = 4(x + 7)(x + 1).

Step 1:  The general equation for standard form is

y = ax^2 + bx + c.

We can convert from vertex to standard form by simply expanding the expression.  Let's ignore the 4 for a moment simply focus on (x + 7)(x + 1).

We can expand using the FOIL method, where you multiply

We see that the first terms are x and x, the outer terms are x and 1, the inner terms are 7 and x and the last terms are 7 * 1.  Now, we multiply and simplify:

(x * x) + (x * 1) + (7 * x) + (7 * 1)

x^2 + x + 7x + 7

x^2 + 8x + 7

Step 3:  Now, we can distribute the four to each term with multiplication:

4(x^2 + 8x + 7)

4x^2 + 32x + 28

Optional Step 4:  We can check that our quadratic function in standard form, by plugging in -7, -1, and -6 for x and seeing that we get 0 as the y value for both x = -7 and x = -1 and -20 as the y value for x = -6:

Checking that (-7, 0) lies on the parabola of 4x^2 + 32x + 28:

0 = 4(-7)^2 + 32(-7) + 28

0 = 4(49) - 224 + 28

0 = 196 - 196

0 = 0

Checking that (-1, 0) lies on the parabola of 4x^2 + 32x + 28:

0 = 4(-1)^2 + 32(-1) + 28

0 = 4(1) - 32 + 28

0 = 4 - 4

0 = 0

Checking that (-6, -20) lies on the parabola of 4x^2 + 32x + 28:

-20 = 4(-6)^2 + 32(-6) + 28

-20 = 4(36) -192 + 28

-20 = 144 -164

-20 = -20

I attached a graph from Desmos to show how the function y = 4x^2 + 32x + 28 contains the points (-7, 0), (-1, 0), (-6, 20), further proving that we've correctly found the quadratic function in standard form passing through these three points

Let's say the total work to be done is represented by 1.

On the first day, three-fifths of the work is completed. Therefore, the remaining work to be done is 1 - 3/5 = 2/5.

On the second day, three-quarters of the remainder is completed. The remainder after the first day's work is 2/5. So, the work completed on the second day is 3/4 x 2/5 = 3/10. The remaining work to be done is 2/5 - 3/10 = 1/5.

On the third day, seven-eighths of what remained is done. The remaining work to be done after the second day's work is 1/5. So, the work completed on the third day is 7/8 x 1/5 = 7/40.

Therefore, the fraction of work still remaining to be done is 1/5 - 7/40 = 8/40 - 7/40 = 1/40.