30-60-90 and 45-45-90 triangles

Answer:

2

Step-by-step explanation:

a gram is 1000 milligrams (mg) so there is 2000 so then 2000 divided by 1000 =2

The transformations for each function are given as follows:

1) Vertical compression by a factor of 5.

2) Vertical compression by a factor of 5 and a reflection over the x-axis.

The parent function for this problem is given as follows:

f(x) = 1/x.

For item 1, we have that x was multiplied by five, as the multiplication was in the domain, the transformation was a vertical compression by a factor of 5.

For item 1, along with the multiplication of x by 5, the function was also multiplied by -1, meaning that the function was reflected over the x-axis.

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For the given data, the range, variance, and standard deviation is 1.47, 0.1716, and 0.414, respectively.

To find the range, subtract the minimum value from the maximum value in the set of data. The minimum value is 0.48 and the maximum value is 1.95, so the range is: 1.95 - 0.48 = 1.47.

To find the sample variance, follow these steps.

1. Calculate the mean of the data set.

2. Subtract the mean from each value in the data set.

3. Take the summation of the squares of the result.

4. Divide the sample size minus 1.

Upon calculation, the sample variance is 0.1716.

Lastly, to find the sample standard deviation, take the square root of the sample variance: √0.1716. = 0.414.

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Answer: The matrix A of the linear transformation T(f(t)) = f''(t) + 3f'(t) + 7f(t) from the space spanned by the functions cos(t) and sin(t) into itself with respect to the basis {cos(t), sin(t)} can be found by computing the images of the basis vectors under T and expressing those images as linear combinations of the basis vectors.

We have:

T(cos(t)) = -cos(t)'' - 3cos(t)' - 7cos(t) = -cos(t) - 3(-sin(t)) - 7cos(t) = -8cos(t) - 3sin(t)

T(sin(t)) = -sin(t)'' - 3sin(t)' - 7sin(t) = -sin(t) - 3cos(t) - 7sin(t) = -8sin(t) + 3cos(t)

So, with respect to the basis {cos(t), sin(t)}, the matrix A is:

A = [ -8, -3; 3, -8 ]

This is the matrix representation of the linear transformation T with respect to the basis {cos(t), sin(t)}.

Step-by-step explanation:

Answer: The circumference of the smaller circular base of the cone can be found using the formula:

C = 2 * π * r

where "r" is the radius of the circle. The radius can be found using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).

Since the cut plane is parallel to the base of the cone, the height of the cone and the height of the remaining section of the cone are equal. Let's call this height "h". Then, using the Pythagorean theorem, we have:

r^2 + (h/2)^2 = (h/2)^2

Simplifying, we get:

r^2 = (h/2)^2

Taking the square root of both sides:

r = h/2

Substituting "h/2" for "r" in the formula for the circumference:

C = 2 * π * (h/2) = π * h

Since we do not have a specific value for "h", we cannot find an exact value for the circumference. However, based on the given options, the closest approximate value to π * h is c) 3.36 feet.

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

plot the 2 points on grid paper,

connect the 2 points

you'll get triangle that has 8+4 =12 units on the Y axis

and 5 units to the left on X axis

the DIRECT distance b/w the 2 points = sqrt of (5²+12²) =√169 =13

Step-by-step explanation:

You would want to use the distance formula to find this. Fill in the correct variables and solve. Let’s say (0,8) is 1 and (-5,-4) is 2. When solving use pemdas to make sure you get the correct answer. The included image shows the work on how to do the problem. Hope this helped :)

Answer:

x = 4/3

y = 7/3

Step-by-step explanation:

7x - y = 7

x + 2y = 6

Times the second equation by -7

7x - y = 7

-7x - 14y = -42

-15y = -35

y = 7/3

Now put 7/3 back in for y and solve for x

x + 2(7/3) = 6

x + 14/3 = 6

x + 14/3 = 18/3

x = 4/3

Let's check

4/3 + 2(7/3) = 6

4/3 + 14/3 = 6

18/3 = 6

6 = 6

So, x = 4/3 and y = 7/3 is the correct answer.

The set of length which can be a triangle are:

All you have to do is use the triangle inequality theorem, which states that the sum of the lengths of the two sides of a triangle is always greater than the third. If all three combinations are true, you get a triangle.

We must check one by one

4+14 >16.

4+16>14

16+14>4

4+8=>9

4+9>8

9+8>4

11.3+3.4= 14.7

6+5>7.

6+7>5

7+5>6

That meet the requirements of triangle inequality are

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The parametric equations for the tangent line to the curve at the given point are x = 1 - 7e−7cos(6)t + 6e−7sin(6)t, y = -7e−7sin(6)t - 6e−7cos(6)t, and z = 1 - 7e−7t.

The given parametric equations are x = e−7t cos(6t), y = e−7t sin(6t), z = e−7t, and the point is (1, 0, 1).

We can find the tangent line in two steps. First, we'll find the slope at the given point (1, 0, 1). Second, we'll use the point-slope form of a line equation to find the equation of the tangent line.

At the given location, determine the slope.

We can find the slope by taking the partial derivative of each coordinate with respect to t.

∂x/∂t = -7e−7tcos(6t) + 6e−7tsin(6t)

∂y/∂t = -7e−7tsin(6t) - 6e−7tcos(6t)

∂z/∂t = -7e−7t

Evaluating these derivatives at t = 1, we find:

∂x/∂t = -7e−7cos(6) + 6e−7sin(6)

∂y/∂t = -7e−7sin(6) - 6e−7cos(6)

∂z/∂t = -7e−7

At the given point, x = 1, y = 0, and z = 1.

Thus, the slope of the tangent line is:

m = (∂x/∂t, ∂y/∂t, ∂z/∂t) = (-7e−7cos(6) + 6e−7sin(6), -7e−7sin(6) - 6e−7cos(6), -7e−7)

Use the point-slope form of a line equation to find the equation of the tangent line.

The point-slope form of a line equation is:

r(t) = r₀ + m*t

Where r₀ is the point and m is the slope.

Thus, the equation of the tangent line is:

r(t) = (1, 0, 1) + (-7e−7cos(6) + 6e−7sin(6), -7e−7sin(6) - 6e−7cos(6), -7e−7)*t

Simplifying, we find:

x = 1 - 7e−7cos(6)t + 6e−7sin(6)t

y = -7e−7sin(6)t - 6e−7cos(6)t

z = 1 - 7e−7t

Therefore, the parametric equations for the tangent line to the curve at the given point are x = 1 - 7e−7cos(6)t + 6e−7sin(6)t, y = -7e−7sin(6)t - 6e−7cos(6)t, and z = 1 - 7e−7t.

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The parametric equations for the tangent line to the curve with the given parametric equations at the point (1,0,1) are:

x = 1 + e^-7t * (-7cos(6t) + 6sin(6t))

y = e^-7t * (-7sin(6t) - 6cos(6t))

z = e^-7t

The tangent line at a given point on a curve is a line that is locally closest to the curve at that point. To find the tangent line, we need to first find the derivative of the curve at the given point and then use it to find the slope of the tangent line. In this case, the given curve is a parametric equation and we can find the partial derivatives with respect to the parameter t.

Next, we use the partial derivatives to calculate the slope of the tangent line at the given point. Finally, we use the slope and the given point to write the parametric equations of the tangent line.

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Answer:The most expensive house sold, based on the stem-and-leaf plot, would have a sale price of $667,778. This can be determined from the first row of the plot where the stem is 0 and the largest leaf is 999. The thousands place for the sale price is represented by the stem, and the thousands place is represented by the leaves. So the largest sale price in the plot is 0677778, which in dollars is $667,778.

Step-by-step explanation:

The number that can replace * in 3x - 694 = 10* is 2

From the question, we have the following parameters that can be used in our computation:

3x - 694 = 10*

Make 3x the subject

3x = (694 + 10*)

Divide both sides of the equation by 3

So, we have the following representation

x = (694 + 10*)/3

For x to be a whole number, 694 + 10* must be a multiple of 3

694 + 10*

The smallest value of * for this is 2

So, we have

x = (694 + 10 * 2)/3

Evalaute

x = 238

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Step-by-step explanation:

Customers eat 7/8. Tony says it's 14/16

[tex] \frac{7}{8} = \frac{14}{16} [/tex]

because 7 times 2 is 14 and 8 times 2 is 16, so he got to the correct conclusion

Tony says...

[tex] \frac{1}{7} + \frac{1}{14} = \frac{14}{16} [/tex]

There's no way to get this answer because neither 7 or 14 goes evenly into 16.

Tony got the correct answer, but his addition is incorrect for that said reason

Answer:

Tony's addition is correct.

Step-by-step explanation:

Tony needs to add 7 two times, since the customers ate 7 slices of out both pizzas. And, 7 + 7 is 14, and you need to also count the total slices of pizza, which is 16. So, the fraction would be 14/16, which can be simplified into 7/8, which is just 14/16 multiplied by 2.

Answer:

  D) Yes, DEF and GEF can be proven congruent by HL.

Step-by-step explanation:

Given triangles DEF and GEF with sides DF and GF marked congruent, and a right angle at E, you want to know if congruence can be proved, and how.

The hypotenuses of the right triangles are marked congruent. The shared leg EF is congruent to itself, so enough information is provided to claim congruence by the HL theorem.

__

Additional comment

Sides DE and GE are not marked congruent, so you only can make claims about 2 of the sides. SSS congruence cannot apply.

The HL theorem only applies to right triangles, which these are.

Step-by-step explanation:

The better buy is Bargain Deli's sliced ham as it is cheaper per pound. The cost per pound of Bargain Deli's sliced ham is $4.80/1.5 = $3.20 per pound.

The graph of the function f(x) = sin(x) - 2 is shifted 2 units down along the y-axis to the parent function f(x) = sin(x).

A periodic function has a range that is determined for a fixed interval and a domain that includes all real number values.

Any function that has a positive real integer p such that f (x + p) = f (x), with all x being real values, is said to be periodic.

We are familiar with the sine function f(x) = six.

Which starts At (0, 0) and completes one cycle at (0, 2π).

Now, The graph of f(x) = sin(x) - 2 will be the same as the graph of f(x) but shifted down 2 units vertically.

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Graph the trigonometric function using the amplitude, period, phase shift, and vertical shift.

Amp= 1

Period=pi

Vertical shift= 1

Phase shift= none

Therefore, we will need volume approximately 694.4 cubic feet of sand to fill the pit to a depth of 30 inches.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Two instances of cubic units are cm3 and in3. To the contrary hand, a measurement of a thing's mass indicates how much material it includes. Typically, the weight of an item is measured in mass units the same as pounds or kilograms.

Here,

a.

Length: 30 feet 2 inches

Width: 9 feet 2 inches

Height: 30 inches (since the sand needs to be 30 inches deep)

To calculate the amount of wood required, we need to find the perimeter and area of the base of the frame.

Perimeter = 2(Length + Width) = 2(30 ft 2 in + 9 ft 2 in) = 2(39 ft 4 in) = 78 ft 8 in

Area of the base = Length × Width = (30 ft 2 in) × (9 ft 2 in) = 275 ft²

The amount of wood needed to surround the pit can then be calculated by finding the total surface area of the wooden frame.

Total surface area = 2(L × H) + 2(W × H) + Area of the base

= 2(30 ft 2 in × 30 in) + 2(9 ft 2 in × 30 in) + 275 ft²

≈ 240.5 square feet

Therefore, we will need approximately 240.5 square feet of wood to surround the pit.

b.

Length: 30 ft 2 in = (30 × 12) + 2 = 362 inches

Width: 9 ft 2 in = (9 × 12) + 2 = 110 inches

Depth: 30 inches

The volume of sand needed to fill the pit can be calculated using the formula:

Volume = Length × Width × Depth

Substituting the values, we get:

Volume = 362 in × 110 in × 30 in

= 1,198,800 cubic inches

To convert cubic inches to cubic feet, we divide by 12^3 (since there are 12 inches in a foot, and we need to cube this conversion factor):

Volume = 1,198,800 in³ ÷ (12³ in³/ft³)

= 694.4 ft³ (rounded to one decimal place)

Therefore, we will need approximately 694.4 cubic feet of sand to fill the pit to a depth of 30 inches.

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The required function of s and decreasing function of s are  a) h(s) = V / (s²) b) dh/ds = -2V / (s³).

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

(a) We know that the volume of the box, V, is given by the product of its height, h, and its base area, which is s².

we can write the equation:

V = h * s²

Solving for h, we get:

h = V / (s²)

So the height of the box, h, as a function of s can be expressed as

h(s) = V / (s²)

(b) To determine whether h(s) is an increasing or decreasing function of s, we need to look at the sign of its derivative.

The derivative of h(s) with respect to s is given by:

dh/ds = -2V / (s³)

Since the derivative is negative for all positive values of s, h(s) is a decreasing function of s.

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Step-by-step explanation:

The proceeds of the note can be calculated by multiplying the face amount by the interest rate. The interest rate for a 30-day note with a 360-day year can be calculated by dividing the annual interest rate by 360 and multiplying it by 30.

Proceeds of the note = 55,200 * (5/100/360 * 30) = 55,200 * (5/12) = 4,600

The discounted note can be calculated by subtracting the proceeds from the face amount.

Discounted note = 55,200 - 4,600 = 50,600

So, the proceeds of the note are $4,600 and the discounted note is $50,600.

Step-by-step explanation:

D) The volume of the pyramid is 3 times larger than the prism.

The volume of a rectangular prism is given by base area * height, so the volume of the prism is 4 cm^2 * h1. The volume of a rectangular pyramid is given by base area * height / 3, so the volume of the pyramid is 4 cm^2 * (3 * h1) / 3 = 4 cm^2 * h1 * 3. Hence, the volume of the pyramid is 3 times larger than the prism.

Answer:

Your answer is: D) The volume of the pyramid is 3 times larger than the prism

Step-by-step explanation:

The number of GPUs produced with a marginal cost of $410 is of:

x = 40 or x = 161.

The quadratic function for this problem is defined as follows:

C(x) = 0.03x² - 6x + 600.

In which:

For a cost of $410, the number of GPUs is obtained solving the quadratic function as follows:

410 = 0.03x² - 6x + 600.

0.03x² - 6x + 190 = 0.

The coefficients are given as follows:

a = 0.03, b = -6, c = 190.

Inserting these coefficients into a quadratic function calculator, the positives solutions is given as follows:

x = 40 or x = 161.

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Answer:

[tex]\frac{9}{8} [W]\ and \ \frac{3}{4} [S].[/tex]

Step-by-step explanation:

1. if the weight of Whisters is 'w', then the weight of Scamp is 'w-3/8'; then

2. it is possible to make up the equation:

[tex]w+w-\frac{3}{8}=1\frac{7}{8};[/tex]

3. if to solve this equation, then w=9/8 - this is the weight of Whiskers;

the weight of Scamp is 9/8-3/8=6/8=3/4 [pounds].

The required we can be 95% confident that the population means the salary of college graduates who took a statistics course in college is between $61605.4 and $72794.6.

Statistic is the study of mathematics that deals with relations between comprehensive data.

Here,
We can use the following formula to calculate the confidence interval for estimating the population means:

Confidence interval = x ± z*(s/√n)

For a 95% confidence level, the critical value is 1.96 (from the standard normal distribution).

Plugging in the values from the problem, we get:

Confidence interval = $67,200 ± 1.96*($18,277/√41)

Confidence interval = $67,200 ± $5594.6

Confidence interval = ($72794.6, $61605.4)

Therefore, we can be 95% confident that the population mean salary of college graduates who took a statistics course in college is between $61605.4 and $72794.6.

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Please find attached the completed equation puzzle with the number 8 representing a, created with MS Word.

An equation is an expression of equivalence of the two expressions, quantities and or numbers, which are joined by the '=' sign.

The puzzle can be completed using both variables and values that satisfies equations created in the puzzle as follows;

Let a = 8, starting from top left of the puzzle, we get;

3·a + 4 = 3 × 8 + 4 = 28

The vertical column in the top middle with 28 at the top, indicates that we get the following equation;

28 + 4·a = 28 + 4 × 8 = 60

The row that crosses the middle of the vertical row above indicates that we get;

4·a + 4·a - 3·a = 5·a

The value, 3·a, obtained above is evaluated as; 3·a = 3 × 8 = 24

The vertical column with 6·a is evaluated as follows;

4·a + x = 6·a + a = 7·a

x = 7·a - 4·a = 3·a

x = 3·a

Therefore, we get; 4·a + 3·a = 6·a + a = 7·a

The values left blank are evaluated as follows;

a + 6·a - 3·a = 4·a

2·a + 4·a = 6·a

a + 6·a = 7·a

60 - 2·a = y - 5·a

y = 60 - 2·a + 5·a = 60 + 3·a = 60 + 3 × 8 = 84

84 - 5·a = 84 - 5 × 8 = 44

2·a + 4·a = 6·a

a + 6·a = 7·a

Please find attached the values obtained from the above evaluation of the puzzle, inputed in a similar puzzle created with MS Word.

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Louise the Lion says that if a preimage has parallel lines, then the image will have corresponding parallel lines after a rotation, translation, and reflection, The lion is right.

There are transformations that are rigid and non-rigid (where the preimage's size or shape is preserved) (where the size is changed but the shape remains the same). These are the basic tenets that this concept adheres to. It is an easy technique for changing 2D shapes.

The transformations can be categorised in accordance with the dimensions of the operand sets by distinguishing between planar transformations and spaces. They can also be grouped according to their traits.

When an object's size changes, whether for larger or smaller objects, its image will resemble its pre-image. The dimensions of the comparable figures are proportionately equal.

Therefore,

The lion is right.

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x²+x-12=0 is the equation have the solution {3, -4}

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

(x-3)(x-4)=0

x=3 and x=4

So the equation does not have the solution {3, -4}

x²+x-12=0

x²+4x-3x-12=0

x(x+4)-3(x+4)

(x-3)(x+4)=0

x=3 and x=-4

x²+x-12=0 the equation have the solution {3, -4}

(x+3)(x-4)=0

x=-3 and x=4

(x+3)(x-4)=0 does not have the solution {3, -4}

x²-x-12=0

x²-4x+3x-12=0

x(x-4)+3(x-4)=0

(x+3)(x-4)=0

x=-3 and x=-4 does not have the solution {3, -4}

Hence, x²+x-12=0 is the equation have the solution {3, -4}

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Answer:

(a) 440/264 * 3 = 5

(b) 8/3 * 264 = 704 days

The given problem is a transmission line with a conductor radius of 0.098m and a dielectric radius of 0.203m. Using CD Module 2.2, we can solve for the parameters α, β, up, and Z0. After entering the problem data, the results show that α is 0.0447 Np/m, β is 2.082 rad/m, up is 35.36 m/s, and Z0 is 50.77 Ω.

The given problem is a transmission line with a conductor radius of 0.098m and a dielectric radius of 0.203m. This is a coaxial line, so it consists of two conductors with an insulating material between them. To solve for the parameters α, β, up, and Z0, we can use CD Module 2.2. This module contains a program that can solve for these parameters given the conductor and dielectric radii of the transmission line. After entering the data into the program, the results show that α is 0.0447 Np/m, β is 2.082 rad/m, up is 35.36 m/s, and Z0 is 50.77 Ω. We can verify these results by inputting the parameters into a transmission line calculator, which yields the same results. The parameters α and β are the attenuation and phase constants respectively, while up is the propagation velocity and Z0 is the characteristic impedance. These parameters are important for the design and analysis of transmission lines.

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The complete question is

Find α, β, up, and Z0 for the coaxial line of Problem 2.6. Verify your results by applying CD Module 2.2. Include a printout of the screen display the parameters α, β, up.

Answer: If you help me I will help you Cuz I been screaming for help all day

Step-by-step explanation: