hey I need help with a problem 3/k = 5/15

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$. Therefore $x=y=12\sqrt{3}$, which is our answer

In a 30-60-90 triangle, the sides have the ratio of $1: \sqrt{3}: 2$. Let's apply this to solve for the variables in the given problem.

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x=y=Let's first find the ratio of the sides in a 30-60-90 triangle.

Since the hypotenuse is always twice as long as the shorter leg, we can let $x$ be the shorter leg and $2x$ be the hypotenuse.

Thus, we have: Shorter leg: $x$Opposite the $60^{\circ}$ angle: $x\sqrt{3}$ Hypotenuse: $2x$

Now, let's apply this ratio to solve for the variables in the given problem. We know that $x = y$ since they are equal in the problem.

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$

Therefore, $x=y=12\sqrt{3}$, which is our answer.

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Answer:

It is a function!

Step-by-step explanation:

It wouldnt be a funtion if the arrows pointed to the same number hope this helps!:)

Answer:

x = 31 degrees

Step-by-step explanation:

This is a triangle because there are 3 angles so they all add up to 180 degrees.

116 + 33 + x + 180   Add 116 and 33

149 + x = 180    subtract both sides by 149

x = 31

The possible perimeters are 140 feet, 148 feet and 160 feet.

In order to determine the width that would be used to determine the possible perimeters, the formula for the area would have to be rewritten.

A rectangle is a 2-dimensional quadrilateral with four right angles and two diagonals that bisect each other at right angles.

Area of a rectangle = length x width

Width = area / length

1200 / 40 = 30 feet

1200 / 50 = 24 feet

1200 / 60 = 20 feet

Perimeter of a rectangle = 2 x (length + width)

Perimeter when width is 30 feet : 2(40 + 30) = 140 feet

Perimeter when width is 24 feet : 2(24 + 50) = 148 feet

Perimeter when width is 20 feet : 2 (20 + 60) = 160 feet

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Answer: 523.8 cubic inches

Step-by-step explanation:

Volume of the sphere, V = (4/3) * π * r^3

where r is the radius of the sphere.

Given, the diameter of the sphere (d) = 10 inches

Therefore, the radius of the sphere, r = d/2 =10/2 = 5 inches

Now, substituting the value of the radius to the volume formula,

V = (4/3) * π * (5^3)

= (4/3) * (22/7) * 125

≈ 523.8 cubic inches

Answer:

Both A and B

Step-by-step explanation:

Both a and b. A three-way intersection can be referred to as a T-intersection or a Y-intersection, depending on the shape of the intersection. In a T-intersection, one road intersects another road perpendicularly, forming a T-shape. In a Y-intersection, one road splits into two branches, forming a Y-shape.

Answer:

What we suppose to be answering?

Step-by-step explanation:

The formula to find the slope of a line is:

So, in this case, you have

Therefore, the slope of this line is 6.

ANSWER:

Difference of squares

STEP-BY-STEP EXPLANATION:

We have the following quotient:

We factor, knowing that the numerator is a difference of squares, therefore:

to find the inverse of any expression, we start off by doing a quick variables switcheroo and then solve for "y", so let's do so

\(\stackrel{P(x)}{y}~~=~~3\sqrt[3]{x}-1\implies \stackrel{\textit{quick switcheroo}}{x~~ =~~3\sqrt[3]{y}-1}\implies x+1 = 3\sqrt[3]{y}\\\\\\\cfrac{x + 1}{3}=\sqrt[3]{y}\implies \left( \cfrac{x + 1}{3} \right)^3 =y\implies \cfrac{(x+1)^3}{3^3}=y\implies \cfrac{(x+1)^3}{27}=\stackrel{\stackrel{y}{\downarrow }}{P^{-1}(x)}\)

Answer:

The surface area is 46 square inches

Step-by-step explanation:

The question is roughly formatted.

From the complete question, we have the following parameters.\

Plan A:

Shape: Rectangular Prism

\(Height = 3in\)

\(Length = 1\ in\)

\(Width = 5in\)

Plan B:

Shape: Triangular Prism

\(Base: 2.8\ in\ by\ 2\ in\)

\(Height = 2\ in\)

\(Slant\ height =5\)

Required

Determine the total surface area of A

Plan A is a rectangular prism

The surface area is calculated as:

\(Area = 2 *[Length * Width + Height * Width + Length * Height]\)

So, we have:

\(Area = 2 *[1in * 5in + 3in * 5in+ 1in* 3in]\)

\(Area = 2 *[5in^2 + 15in^2+ 3in^2]\)

\(Area = 2 *[23in^2]\)

\(Area = 46in^2\)

The perimeter and area of a rectangle are (5,6) and (6,5).

The perimeter method for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width. when you are given the size of a square form, you may simply plug within the values of L and W into the formula that allows you to clear up for the fringe.

A perimeter is a closed course that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional period. The perimeter of a circle or an ellipse is known as its circumference. Calculating the perimeter has several practical programs.

The perimeter P of a rectangle is given by means of the method, P=2l+2w, in which l is the period and w is the width of the rectangle. The place A of a rectangle is given with the aid of the components, A=lw, wherein l is the length and w is the width.

The perimeter of the rectangle:

P=2l+2w=22

divide 2 into both sides

l+w=11 -------------> (1)

w=11-l

Area of the rectangle:

l*w=30

l(11-l)=30

11l-l^2-30=0

l^2-11l+30=0

By factor method,

(l-5)(l-6)=0

l=5,6.

Substitute this value in w,

l=5 implies w=6

l=6 implies w=5

There we have two solutions.

The length and breadth of the rectangle is

(5,6) and (6,5).

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Answer/Step-by-step explanation:

Starting with:

8r + 5p + 7



There are three terms. 8r is a term; 5p is a term; 7 is a term. See how the terms are separated by + or -

r and p are variables. Most often the variable is a letter, that way it can stand for an unknown value. It can vary.

5 is the coefficient of p. Its the number right next to the p. (They are multiplied together)

7 is the constant. Constant means unchanging, right? So 7 is a plain old number, it doesn't change like a variable can. A plain number with no variable is a constant.

The maximum profit that the considered company can get is 142,400 bucks. That profit is earned when input x  (the number of items produced) is 380

To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.

Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.

The missing part of question is:

" \(C(x)=2000+70x\), \(R(x)=830x-x^2\)

A. Determine the maximum profit of the company.

B. Determine the number of items that must be produced and sold to obtain the maximum profit"

The profit is the difference between the revenue and the cost, so we get:

\(P(x) = R(x) - C(x) = 760x - x^2 - 2000\)

Finding its first and second rate with respect to x:

\(P'(x) = 760 -2x\\P''(x) = -2\)

Equating first rate to 0 to get the critical values:

\(P'(x) = 0 \implies 760 = 2x \implies x = 380\)

The second rate is < 0 for any x, x = 380 is minima, and x = 380 being only critical value, it is global maximum.

At x = 380, the profit evaluates to:

\(P(x) = 760x - x^2 - 2000\\P(380) = 760(380) - (380)^2 - 2000 = (380)^2 - 2000\\P(380) = 142400\)

Thus, the maximum profit that the considered company can get is 142,400 bucks. That profit is earned when input x  (the number of items produced) is 380

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The statement that a clock that is set fifteen minutes fast is less precise than an identical clock that keeps correct time is false

When a time is set away from the correct time, the time on the clock would be incorrect.

However, this has nothing to do with the precision of the clock.

This is so because precision deals with closeness of the time measurement to the original time

Since the time is ten minutes fast, it would not be less precise

Hence, the statement is false

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Answer:

38 plain chocolate bars and 17 king-size chocolate bars.

Step-by-step explanation:

Let's define the variables:

P = number of plain chocolate bars sold

K = number of king chocolate bars sold

We know that each plain one costs $1.50, and each king one costs $2.25, then the total revenue is:

P*$1.50 + K*$2.25

Now we know that Jim sells a total of 55 candy bars, then:

P + K = 55

And we know that the total revenue is $95.25, then:

P*$1.50 + K*$2.25 = $95.25

Then we have the system of equations:

P + K = 55

P*$1.50 + K*$2.25 = $95.25

To solve this we need to isolate one of the variables in one of the equations, I will isolate P in the first equation to get:

P = 55 - K

Now we can replace is on the second one to get:

(55 - K)*$1.50 + K*$2.25 = $95.25

Now we can solve this for K

$82.50 - K*$1.50 + K*$2.25 = $95.25

K*($2.25 - $1.50) = $95.25 - $82.50 = $12.75

K*$0.75 = $12.75

K = $12.75/$0.75 = 17

This means that Jim sold 17 king-size chocolate bars.

Now we can replace this in the equation:

P + K = 55

P + 17 = 55

P = 55 - 17  =38

P = 38

Jim sold 38 plain chocolate bars.

Answer:

y = (-3/4)x + 7/4

Step-by-step explanation:

Step 1: Define general form of equation of line

An equation of a straight line on two-dimensional plane could be represented in form of: y = Mx + b, with M is slope and b is y-intercept

Step 2: Set up the system to solve for parameters of equation of line

(solve for M and b)

That equation passes 2 points, which are represented in form of (x, y), (5, -2) and (-3, 4).

Substitute these values of x and y into the original equation in step 1:

-2 = 5M + b

4 = -3M + b

Step 3: Solve the system of equations in step 2 for M and b

Subtract 1st equation from 2nd equation:

     6 = -8M

=> M = -6/8 = -3/4

Substitute M back into 1st equation:

=> -2 = 5*(-3/4) + b

=>  b = -2 + 15/4

=>  b = 7/4

=>  The equation of the line that passes through (5, -2) and (-3, 4):

      y = (-3/4)x + 7/4

Hope this helps!

:)

Answer:

Y= -4/3(x-7/2)

Step-by-step explanation:

So first calculate the difference between them,

changes by 8 x units, and -6 y units.

Then substitute them into y/x to find gradient

-6/8 = -4/3

so now we have a part of the equation:

Y= -4/3(x-a)

substitute Y= -2 and x=5 (from (5,-2))

-2= -4/3(5-a)

-2= -20/3+4a/3

Multiply by 3 on both sides

-6= -20+4a

add 20 on both sides

14=4a

a=7/2

use this as the value of a

Y= -4/3(x-7/2)

XY = 30, XZ = 24, JQ = 8

From the given diagram we can see that;

XJ = JY

So,

XJ = JY = XY/2

XJ = JY = 30/2 = 15

Here, Point Q is the centroid of the ∆XYZ, which means that XQ = QZ = QY will be the radius of the circumscribed circle.

Since,

We know JQ and XJ, let us consider triangle XJQ.

By Using Pythagoras Theorem;

(XQ)² = (XJ)² + (JQ)²

(XQ)² = (15)² + (8)²

(XQ)² = 225 + 64

(XQ)² = 289 +

XQ = √289

XQ = 17

Thus, The radius of the circumscribed circle of ∆XYZ is 17

-TheUnknownScientist 72

Answer:

1/4

Step-by-step explanation:

The rocket is 64 feet high at 3±√5 seconds.

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Answer:

x+100

Step-by-step explanation:

x^2-10,000/x-100

x^2-10000 is a difference in squares and can be factored.

x^2-10000 = (x+100)(×-100).

(x+100)(x-100)/(x-100)

(x-100) cancel each other.

x+100 remains.

The equation of the line with coordinates (-7,3), (8,3) is y-3=0 as the slope of line is 0 because x-ordinate is same in both the points.

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

The two point form of equation,

y-y1=m(x-x1)

m=(y2-y1)/(x2-x1)

m=(3-3)/(8--7)

m=0

y-3=0(x+7)

y-3=0

Because the x-ordinate is the same at both points, the equation for the line with coordinates (-7,3) and (8,3) is y-3=0.

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The surface area of the composite figure is 2005 in².

To find the surface area of the composite figure, we need to calculate the sum of the areas of its individual components.

Let's break down the figure into its different parts and calculate the surface area step by step:

Rectangular Prism: The rectangular prism has dimensions of 20 in, 11 in, and 5 in. The surface area of a rectangular prism can be found by adding the areas of its six faces. The total surface area of the rectangular prism is given by:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(20)(11) + 2(20)(5) + 2(11)(5) = 440 + 200 + 110 = 750 in²

Rectangular Prism: Another rectangular prism has dimensions of 19 in, 12 in, and 12 in. Following the same process as above, we can calculate the surface area of this rectangular prism:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(19)(12) + 2(19)(12) + 2(12)(12) = 456 + 456 + 288 = 1200 in²

Base: The base is a rectangle with dimensions 11 in and 5 in. The surface area of a rectangle is given by the formula:

Surface Area of Rectangle = lw

Plugging in the values, we have:

Surface Area of Rectangle = (11)(5) = 55 in²

Finally, to find the total surface area of the composite figure, we add the surface areas of the individual components:

Total Surface Area = Surface Area of Rectangular Prism + Surface Area of Rectangular Prism + Surface Area of Rectangle

Total Surface Area = 750 in² + 1200 in² + 55 in² = 2005 in²

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Answer:

j - 14 = 22

Step-by-step explanation:

Step-by-step explanation:

yes, the step is correct.

a² = cx | multiply by c

ca² = c²x

I am just not sure how that simplified the equation.

what do you want to achieve ? what's the goal here ?

to solve the equation for x it would be to divide both sides by c, which gives

a²/c = x

Answer:

Remember length times width times height when finding volume.

In non-terms of pi, the answer would be \(2\) \(ft^2\)

Answer:

Volume is 2ft

Step-by-step explanation:

Multiply the length x width once you find the answer for lengthxwidth.

Multiply the answer you got by height

Using the Pythagoras theorem, the longest leg has the length of 24 feet.

Given that,

A ladder of length (2x+6) feet is positioned x feet from a wall.

Height of the ladder = (2x + 6) feet

Distance of ladder from the wall = x feet

Height of the wall that the ladder is placed = (2x + 4) feet

These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.

Longest leg is (2x + 4) feet

Using the Pythagoras theorem,

(2x + 6)² = (2x + 4)² + x²

4x² + 24x + 36 = 4x² + 16x + 16 + x²

4x² + 24x + 36 = 5x² + 16x + 16

x² - 8x - 20 = 0

(x - 10) (x + 2) = 0

x = 10 or x = -2

x = 2 is not possible.

So x = 10

Longest leg = 2x + 4 = 20 + 4 = 24 feet

Hence the length of the longest leg is 24 feet.

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Answer: 64,000} lbs

Step-by-step explanation: hope it helps ! <3!

The inequality that represents the value of x is (b)  x > 80

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

The figure

The general rule is that

The larger the side length, the larger the angle opposite it

using the above as a guide, we have the following:

1/8x > 10

So, we have

x > 80

Hence, the inequality is x > 80

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