Find the distance between the points (-4,-5) and (3, -1).
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A right rectangular prism has a base of 20cm² and a height of 9.2cm will have a volume of  184 cm³

The right rectangular prism has four rectangle-shaped lateral faces, each of which is perpendicular to one of its bases, and two parallel end faces.

A non-right rectangular prism (oblique prism) has parallelograms for its faces. The term "cuboid" can also refer to a right rectangular prism.

In the given problem the formula used for volume of prism is

= are of base * height

= 20 * 9.2

= 184 cm³

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The result of the addition operation of 1204.2 + 4.72613 is approximately 1208.93.

An addition operation involves two addends added together to result in a number called the sum.

The addition operation is one of the four basic mathematical operations, including subtraction, division, and multiplication.

Mathematical operations combine numbers, variables, and values with mathematical operands to solve mathematical questions.

1204.2 + 4.72613

= 1208.92613

= 1208.93

Thus, the addition of 1204 and 4.72613 yields a total of 1208.93 approximately.

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Answer:

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Answer:

Step-by-step explanation:

You have omitted relevant parts of the question. What is the question? Are you looking for the area of the yard? The amount of fencing needed?

What units are used? (Feet, yards, meters, etc.)

area of yard = 75×55 = 4125 units²

amount of fencing needed = perimeter of rectangle = 2(75+55) = 260 units.

The total length of the fencing is the perimeter of the rectangular yard which is P = 260 feet

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P = 2 ( Length + Width )

Given data ,

The width of the rectangular yard W = 55 feet

The length of the rectangular yard L = 75 feet

Let the perimeter of the rectangular yard be = P

And , the required fencing = Perimeter of rectangular yard

Perimeter of rectangular yard P = 2 ( L + W )

Substituting the values in the equation , we get;

Perimeter of rectangular yard P = 2 ( 55 + 75 )

Perimeter of rectangular yard P = 2 ( 130 )

Perimeter of rectangular yard P = 260 feet

Therefore , the value of P is 260 feet

Hence , the perimeter of yard is 260 feet

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Mr. Fuller wants to put fencing around his rectangular-shaped yard. the width of the yard is 55 feet and the length is 75 feet. how many feet of fencing does Mr. Fuller

Step-by-step explanation:

x = total area of land

x - 1/6 × x - 5/9 × x = 48.5 | multiply both sides by 6

6x - x - 30/9 × x = 291

5x - 30/9 × x = 291 | multitude both sides by 9

45x - 30x = 2,619

15x = 2,619

x = 174.6 acres

pineapples were planted on 174.6 × 1/6 = 29.1 acres.

durians were planted on 174.6 × 5/9 = 97 acres.

Step-by-step explanation:

Using the following property of logarithms,

\(\ln{\left(\dfrac{a}{b}\right)} = \ln{a} - \ln{b}\)

we can write the given equation as

\(\ln{(x^2 + 1)} - \ln{(x^2 - 1)} = \ln{\left(\dfrac{x^2 + 1}{x^2 - 1}\right)}\)

\(\:\:\:\:\:\:\:\:\:= \ln{\dfrac{x(x + 1)}{x(x - 1)}} = \ln{\left(\dfrac{x + 1}{x - 1}\right)}\)

But recall that \(\ln{e} = 1\) so we can write our original equation as

\(\ln{\left(\dfrac{x + 1}{x - 1}\right)} = \ln{e}\)

or simply

\(\dfrac{x + 1}{x - 1} = e\)

Multiplying both sides by \((x - 1),\) we get

\(x + 1 = e(x - 1)\)

Solving for x, we get

\(x = \dfrac{e + 1}{e - 1}\)

Answer:

We want to find:

\(y'*dx = dy\)

Where:

\(y = x^4*sin(9x)\)

Remember that when we have a function like:

f(x) = g(x)*h(x)

The derivation gives:

f'(x) = g'(x)*h(x) + g(x)*h'(x)

In this case we can define:

f(x) = y

g(x) = x^4

h(x) = sin(9x)

These functions are easy to differentiate:

g'(x) = 4*x^3

h'(x) = 9*cos(9*x)

Then we have:

\(y' = \frac{dy}{dx} = 4x^3*sin(9x) + x^4*9cos(9x)\)

Then we can write:

\(dy = (4x^3*sin(9x) + 9x^4*cos(9x))dx\)

Answer:

where is the pictures??

Answer:

Since 2.1387 is Greater Than 1.645;

we reject null hypothesis; we conclude that, the nickname is justified based on the data.

Step-by-step explanation:

Given the data in the question;

Null hypothesis H₀ : p = 0.262

Alternative Hypothesis H₁ : p > 0.262.

p" = 0.357

q = 1 - p = 1 - 0.262 = 0.738

n = 98

so;

z = (p" - p) / √(pq/n)

we substitute

z = (0.357 - 0.262) / √((0.262×0.738) / 98)

z = 0.095 / 0.04441869

z = 2.1387

at 5% CONFIDENCE INTERVAL

z-critical = 1.645

Since 2.1387 is Greater Than 1.645;

we reject null hypothesis; we conclude that, the nickname is justified based on the data.

Answer:

the area of the shape is 48m

Step-by-step explanation:

10*4=40

2*4=8

40+8=48

brake it up into two triangles. one is a triangle that is 10m tall and 8m wide at the top. you can solve that by doing 4*10=40. the other triangle is 4m wide at the bottom and 2m tall. you can solve that by doing 2*4=8. and 40+8=48.

Levy is painting a miniature model of a World War II tank. His figure uses a 1:72 scale and is 22.5 cm long. The actual tank is 1620 cm long.

To determine the length of the actual tank, we need to scale up the length of the miniature model using the given scale of 1:72.

Let's denote the length of the actual tank as "x".

According to the scale, 1 cm on the miniature model represents 72 cm on the actual tank.

So, we can set up the following proportion:

1 cm (miniature model) / 72 cm (actual tank) = 22.5 cm (miniature model) / x cm (actual tank)

Cross-multiplying and solving for x, we get:

x = (72 cm * 22.5 cm) / 1 cmx = 1620 cm

The actual tank is 1620 cm long.

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Answer:

Length = 16 or -5 feet.

Width = 5 or -16 feet.

Step-by-step explanation:

Let the length of the concrete pad = l

Let the width of the concrete pad = w

Given the following data;

Area of concrete pad, a = 80ft²

Translating the word problem into an algebraic equation, we have;

\( l = 11 + w\)

We know that, the area of rectangle, A = length * width

\( A = l*w\)

Substituting the values into the equation, we have;

\( 80 = (11 + w)w\)

Expanding the bracket, we have;

\( 80 = 11w + w^{2}\)

\( w^{2} + 11w - 80 = 0\)

*Solving the quadratic equation by using factorization method*

\( w^{2} + 16w - 5w - 80 = 0\)

\( w(w + 16) - 5(w + 16) = 0\)

\( (w - 5)(w + 16) = 0 \)

Width, w = 5 feet or w = -16 feet.

Therefore, the width of the concrete pad is 5 feet or -16 feet.

To find its length, l;

\( l = 11 + w\)

When w = 5 feet

\( l = 11 + 5\)

Length, l = 16 feet

When w = - 16 feet

\( l = 11 + (-16)\)

\( l = 11 - 16\)

Length, l = -5 feet.

Hence, the dimensions of the concrete pad is 16 by 5 feet or -5 by -16 feet.

It is just a way of describing a set.

You put the set in braces (sometimes called curly brackets), {}, which is a typical way to show that you are talking about sets.

Here are a few examples:

{x| x > 0} This is read: The set of all x such that x is greater than 0.

Reading it character by character:

{ — shows you that we are talking about a set, and it sort of opens up, or starts the set

x — tells you that we are talking about a set of elements x

| (and a : is also used sometimes) — such that (this is just notation). This says that you are about to be given to rule to see what “rule” or characteristic the x’s will have.

x > 0 — This just says what characteristics x must have to be in this set. So 7, 1/2, .3 and pi are all in this set, while -1, 0, -radical(2) are not.

So this example is just how you would use set builder notation to talk about the set “the positive real numbers”

So why use it? Because it can describe more complicated sets much more succinctly.

2. {3n + 1 | n is an element of the natural numbers} (and this could be written more succinctly if I used certain symbols) would be the set {4, 7, 10, 13, …}

3. {n^2 + n + 1 | n is an element of the natural numbers} would be the set {3, 7, 13, 21, …} and notice here, if you didn’t see the set builder notation, you might have trouble knowing what the next term in the set was.

Answer:

42x + 21y = -2

~theLocoCoco

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

This equation can be factored as:

(2x + 5)(x - 2) = 0

Setting each factor equal to zero, we get:

2x + 5 = 0 => 2x = -5 => x = -5/2

x - 2 = 0 => x = 2

Therefore, the x-intercepts of the graph of f(x) are x = -5/2 and x = 2.

Part B: The vertex of the graph of f(x) can be determined using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c = 0).

In this case, a = 2 and b = -1. Plugging these values into the formula, we have:

x = -(-1) / (2 * 2) = 1/4

To determine if the vertex is a maximum or a minimum, we can examine the coefficient of the x² term. Since the coefficient a is positive (a = 2), the parabola opens upwards, and the vertex represents a minimum point

Therefore, the vertex of the graph of f(x) is (1/4, f(1/4)), where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Part C: To graph f(x), we can follow these steps:

Plot the x-intercepts: Plot the points (-5/2, 0) and (2, 0) on the x-axis.

Plot the vertex: Plot the point (1/4, f(1/4)) as the vertex, where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Determine the direction of the graph: Since the coefficient of the x² term is positive, the graph opens upwards from the vertex.

Determine additional points: Choose a few x-values on either side of the vertex and calculate their corresponding y-values by substituting them into the equation f(x). Plot these points on the graph.

Draw the graph: Connect the plotted points smoothly, following the shape of the parabola. Ensure the graph is symmetrical with respect to the vertex.

The answers obtained in Part A (x-intercepts) and Part B (vertex) provide crucial points to plot on the graph, helping us determine the shape and position of the parabola.

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The x-intercepts from the graph attached are

The vertex  from the graph attached is

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

x = (-b ± √(b² - 4ac)) / (2a)

a = 2, b = -1, c = -10

Plugging these values into the quadratic formula:

x = (-(-1) ± √((-1)² - 4 * 2 * (-10))) / (2 * 2)

x = (1 ± √(1 + 80)) / 4

x = (1 ± √81) / 4

x = (1 ± 9) / 4

x₁ = (1 + 9) / 4 = 10 / 4 = 2.5

x₂ = (1 - 9) / 4 = -8 / 4 = -2

Therefore, the x-intercepts of the graph of f(x) are 2.5 and -2.

Part B

To find the coordinates of the vertex, we can use the formula:

x = -b / (2a)

x = -(-1) / (2 * 2) = 1 / 4 = 0.25

we substitute this value back into the original function:

f(0.25) = 2(0.25)² - 0.25 - 10

f(0.25) = 0.125 - 0.25 - 10

f(0.25) = -10.125

Therefore, the vertex of the graph of f(x) is located at (0.25, -9.125).

Part C: The steps to graph f(x) include:

Plotting the x-intercepts: Based on the results from Part A, we know that the x-intercepts are 2.5 and -2. We mark these points on the x-axis.

Plotting the vertex: Using the coordinates from Part B, we plot the vertex at (0.25, -9.125). This represents the minimum point of the graph.

Drawing the shape of the graph: Since the coefficient of the x² term is positive, the graph opens upward. From the vertex, the graph will curve upward on both sides.

Additional points and smooth curve: To further sketch the graph, we can choose additional x-values and calculate their corresponding y-values using the equation f(x) = 2x² - x - 10. Plotting these points and connecting them smoothly will give us the shape of the graph.

By using the x-intercepts and vertex obtained in Part A and Part B, we have the necessary information to draw the graph accurately and show the key features of the quadratic function f(x)

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Answer:

70.5

Step-by-step explanation:

multiply the denominator 3.5 on both sides.

you get 57.5 + 13 = 70.5

11 by 35

how?

well, i have no idea just found it on internet

Answer:

Step-by-step explanation:

Find the difference:

Answer:

1:10

Step-by-step explanation:

30 boxes = 180 eggs

3 boxes = 18 eggs

18:180 = 1:10

The mean absolute deviation (MAD) for the given data is 1/20. This means that, on average, each data point in the set differs from the mean by 1/20.

To find the mean absolute deviation (MAD) of a set of data, we need to calculate the average difference between each data point and the mean of the data set. Here's how we can calculate it for the given data:

Step 1: Find the mean (average) of the data set.

Mean = (1/4 + 5/8 + 3/8 + 3/4 + 1/2) / 5 = 2/5

Step 2: Calculate the difference between each data point and the mean.

Differences: |1/4 - 2/5|, |5/8 - 2/5|, |3/8 - 2/5|, |3/4 - 2/5|, |1/2 - 2/5|

Step 3: Calculate the absolute value of each difference.

Absolute Differences: 1/20, 1/40, 1/40, 1/20, 1/10

Step 4: Find the average of the absolute differences.

MAD = (1/20 + 1/40 + 1/40 + 1/20 + 1/10) / 5 = 1/20

The MAD provides a measure of the average amount of variation or dispersion in the data set. In this case, a MAD of 1/20 indicates that the data points are relatively close to the mean, with most values falling within 1/20 of the mean value.

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Answer:

5 13/20

Step-by-step explanation:

Answer:

x>-3

Step-by-step explanation:

Answer:

x > 3

Step-by-step explanation:

Step-by-step explanation:

the center of the circle is the midpoint of the diameter.

and the radius is the distance of the midpoint to either endpoint (or simply half of the distance between the diameter endpoints).

the midpoint between points A and B

(xm, ym) = ((xa + xb)/2, (ya + yb)/2)

in our case the midpoint (center of the circle) is

((-6 + 2)/2, (10 + 3)/2) = (-4/2, 13/2) = (-2, 6.5)

about the radius

diameter² = (-6 - 2)² + (10 - 3)² = (-8)² + 7² = 64 + 49 =

= 113

diameter = sqrt(113) = 10.63014581...

radius = diameter / 2 = 5.315072906... ≈ 5.315

ion even know yet

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Answer:

Number of hours worked overtime = 5.5 hours

overtime rate = $17.925 per hour

overtime pay = $98.59

Step-by-step explanation:

a. Her overtime hours are the number of hours worked over 40 hours, and we are told that she worked 45 1/2 hours last week.

Therefore, her overtime hours = 45.5 - 40 = 5.5 hours

b. overtime rate:

for her overtime rate, we are given that she has a time-and-a-half pay for her overtime hours. This means that she is paid 1.5 times the normal rate for working overtime.

∴ overtime rate = 1.5 × normal rate

overtime rate = 1.5 × 11.95/hour

overtime rate = $17.925/hour

c. overtime pay:

overtime pay = overtime rate × overtime hours worked

overtime pay = 17.925 × 5.5

overtime pay = $98.59

Answer:

1/(7^7)

Step-by-step explanation:

Thus, the translation rule which represents the translation of pre-image, ΔABC, into the image, ΔA'B'C is of : (x, y) → (x + 7, y – 6)

In geometry, a function that shifts an object a specific distance is referred to as translation. Nothing else is done to change the object. It is not scaled, reflected, rotated, or refracted.

Every point of such object must be translated by the same amount and in the same direction.

Given data:

coordinates of pre-image ΔABC:

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

coordinates of image ΔABC:

A'(4,-2), B'(3, -5) C'(5,-5)

A(-3 + 7,4 – 6) - > A'(4,-2)

B(-2 + 7, 1 – 6) - > B'(3, -5)

C(-4 + 7,1 – 6) -> C'(5,-5)

Thus, the translation rule which represents the translation of pre-image, ΔABC, into the image, ΔA'B'C is of : (x, y) → (x + 7, y – 6)

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Answer:

f(x)=-8sin(pi/6x)+2

Step-by-step explanation:

The graph of a sinusoidal function intersects its midline at (0,2) and then has a minimum point at (3,-6) So, the function is f(x) = -8sin(pi/6x)+2.

The sinusoidal function has the following form:

\(y = x_0 + A\: sin(w.x+\theta)\)

Where:

A= Amplitude

w = Angular frequency

\(x_0\) = Independent component of the midpoint value

\(\theta\) = Phase angle

Amplitude is the absolute value of the difference between a dependent component of the midline and the absolute minimum

A = |-6 - 2|

A = 8

\(x_0\) = 2

The angular frequency of the function is now determined by substituting all remaining variables and clearing it within the sinusoidal function

\(w.x + \theta = \pi / 6\)

The sinusoidal function

f(x) = -8sin(pi/6x)+2

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2 I believe I’m not 100% sure tho