Write the ordered pair (x,y) for the y-intercept

Answer:

C. 126

Step-by-step explanation:

We can use ratios to solve for corresponding side lengths.

\(\frac{140-x}{81} =\frac{x}{9}\)

Cross multiply.

\(9(140-x)=81x\)

\(140-x=9x\)

\(140=10x\)

\(14=x\)

Plug x as 14.

\(140-14=126\)

Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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Answer:

x=50

Step-by-step explanation:

67=x+17

67-17=50

x=50

Answer:

f(3) = 3

Step-by-step explanation:

f(1) = 1

f(2) = 2

f(n) = f(n − 2) + f(n − 1)

f(3) = f(3 - 2) + f(3 - 1)

     = f(1) + f(2) = 1 + 2 = 3

Special Note:  Have you heard of the Fibonacci sequence?  

The formula f(n) = f(n − 2) + f(n − 1) is used to find the terms of the of the  Fibonacci sequence

The height of the rectangular pyramid is 16 units.

To find the height of the rectangular pyramid, we can use the formula for the volume of a pyramid:

Volume = (1/3) * base area * height

Given that the volume of the rectangular pyramid is 512 units^3, and the length of the rectangular base is 8 units and the width is 12 units, we can find the base area:

Base Area = length * width = 8 * 12 = 96 units^2

Now we can substitute the values into the volume formula:

512 = (1/3) * 96 * height

To solve for the height, we can isolate it by multiplying both sides of the equation by 3/96:

512 * 3/96 = height

Simplifying the right side of the equation:

16 = height

The rectangular pyramid is 16 units tall as a result.

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Answer:

Y        X

80     32

100    x'

Step-by-step explanation:

80x' = 100*32

80x' = 3200

x' = 3200/80

x' = 320/8

x' = 40

The cost of the chocolate for 110 bon-bons  as per given radius , density and cost is equal to $8.80 to the nearest cent.

Volume of a sphere with radius r is ,

V = ( 4/3 )πr³

Radius 'r' of each chocolate bon-bon is 0.8 cm,

Volume of each bon-bon is equals to,

V = ( 4/3 )π (0.8)³

   = 2.144 cm³

Density 'ρ' of the chocolate is 1.3 g/cm^3,

Mass 'm'  of each bon-bon is equals to,

m = ρV

   = ( 1.3 ) ( 2.144 )

   = 2.78grams

The cost of the chocolate used in each bon-bon is $0.03 per gram,

This implies,

Cost of the chocolate used in one bon-bon is ,

= ( 0.03 ) × 2.78

= 0.0834

Rounding to the nearest cent, the cost of the chocolate for one bon-bon is $0.08.

Cost of the chocolate for 110 bon-bons,

= 110 × 0.08

= 8.8

Therefore, the chocolate for 110 bon-bons would cost $8.80 to the nearest cent.

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Substituting the value of \( r \), we get \( V \approx 1105.4 \) mm³. Finally, dividing the mass of the ball-bearing (11.9 g) by its volume (1105.4 mm³) and converting the units, we can determine the density in g/cm³. The density is approximately 0.0108 g/cm³.

To explain the process in more detail, we start by finding the radius of the ball-bearing using the circumference formula. The circumference is given as 43.4 mm, so dividing it by 2π gives us the radius of approximately 6.912 mm.

Next, we calculate the volume of the sphere using the formula \( V = \frac{4}{3}\pi r^3 \). Plugging in the radius value, we obtain the volume of the metal ball-bearing as approximately 1105.4 mm³.

To calculate the density, we divide the mass of the ball-bearing (11.9 g) by its volume (1105.4 mm³). However, to obtain the density in g/cm³, we need to convert the volume from mm³ to cm³ by dividing it by 1000. After performing the division and conversion, we find the density of the metal ball-bearing to be approximately 0.0108 g/cm³.

Density is a fundamental property of matter that describes how much mass is contained within a given volume. In this case, it allows us to understand the mass-to-volume ratio of the metal ball-bearing. By calculating the density, we can characterize the compactness or heaviness of the material.

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The density of the metal in the ball-bearing is approximately 10.981 g/cm^3.

To find the density of the metal in g/cm^3, we need to calculate the volume of the metal ball-bearing and divide it by its mass.

Given information:

Circumference of the ball-bearing = 43.4 mm

Weight of the ball-bearing = 11.9 g

To calculate the volume of the ball-bearing, we need to find its radius (r). We can use the formula for the circumference of a circle:

Circumference = 2πr

Substituting the given circumference

43.4 mm = 2πr

To find the radius, divide both sides by 2π:

r = 43.4 mm / (2π) ≈ 6.9134 mm

Next, let's convert the radius to centimeters:

r = 6.9134 mm / 10 ≈ 0.69134 cm

Now we can calculate the volume of the ball-bearing using the formula for the volume of a sphere:

V = (4/3)πr^3

Substituting the radius:

V = (4/3)π(0.69134 cm)^3

Calculating this expression:

V ≈ 1.083 cm^3

Finally, to find the density, we divide the mass by the volume:

Density = Mass / Volume

Density = 11.9 g / 1.083 cm^3

Calculating this expression:

Density ≈ 10.981 g/cm^3

Therefore, the density of the metal in the ball-bearing is approximately 10.981 g/cm^3.

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Answer:

Answer is 3 degrees

Step-by-step explanation:

-4 + 7 is 3

According to the given information, the sample period should be from 2010-2020.

a) Model specification

The model specification based on the scenario above is as follows:

SDF= f(T, TI, NL)

Where: SDF= Sustainable Development Framework

T= Tourism

TI= Technological innovation

NL= National leadership

b) Justification for the selection of the dependent and independent variables model:

Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.

Independent variables:

The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.

The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.

c) Justification for the selection of the sample period:

The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.

Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.

The sample period should be from 2010-2020.

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In the case above, the correct vectors are:

The solution for the Ship's vector are:

Note that the Horizontal aspect = 30 cos 30  

                                                   = 25.98.

For the  Vertical aspect = 30 sin(-30)

                                        = -15.

Hence it will be  <25.98, -15>.

In regards to the current's vector:

The Horizontal aspect=  5 sin 20

                                       = 1.71.

The Vertical aspect = 5 cos 20

                                     = 4.7.

Hence it will be <1.71, 4.7>.

Therefore, In the case above, the correct vectors are:

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Given info:

all sides are equal in the given triangle

Given angles are 3y° and 2x°

→ 3y° = 2x° = 60°

→ 3y° = 60° and 2x° = 60°

→ y° = 60°/3 and x° = 60°/2

→ y° = 20° and x° = 30°

Therefore, x° = 30° and y° = 20°

Answer:-

The values of x = 30° and y = 20°

Key Knowledge:-

→ If all sides are equal in a triangle then it is an equilateral triangle

In an equilateral triangle,

→ all sides are equal.

→ all angles are equal.

→ all angles are equal to 60°

Hope this helps!!

Answer:

Step-by-step explanation:

I hope this helps

Step-by-step explanation:

here's a tip if u have questions asking about grapihing those kinds of questions

use desmos graphing calculator it really helps and all u do is insert the equation and it graphs it for uu

hope this helps!!

Significant figures with representation of x are a) 14.8 m = 14.x m. b) $10.25 = 10.2x. c) 0.05 L = 0.0x L. d) 1.000 g/mL = 1.00x g/mL. e)  6200cm = 6200x cm. f)  403 kg = 40x kg.

a) 14.8m has 3 significant figures. Representation with x in place of estimated digit: 14.x m. b) $10.25 has 4 significant figures. Representation with x in place of estimated digit: 10.2x. c) 0.05 L has 1 significant figure. Representation with x in place of estimated digit: 0.0x L. d) 1.000 g/mL has 4 significant figures. Representation with x in place of estimated digit: 1.00x g/mL. e) 6200cm has 2 significant figures. Representation with x in place of estimated digit: 6200x cm. f) 403 kg has 3 significant figures. Representation with x in place of estimated digit: 40x kg. Significant figures are the digits in a measurement that are reliable and accurate. They provide an indication of the precision of a measurement, and allow us to communicate the level of certainty we have in a particular value. When determining the number of significant figures in a measurement, we typically follow a set of rules. Non-zero digits are always significant, zeros between non-zero digits are significant, and trailing zeros to the right of the decimal point are significant. Zeros at the beginning of a number or to the left of a non-zero digit are not significant. The use of significant figures is important in science and engineering to ensure accurate and reliable measurements. When performing calculations with measurements, the result should be reported with the same number of significant figures as the least precise measurement used in the calculation. In addition, when rounding a number, the last digit should be rounded to the nearest value consistent with the number of significant figures being used. Understanding significant figures is an important part of scientific and mathematical communication, and can help to ensure accuracy and consistency in the reporting of data and calculations.

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Answer:

Step-by-step explanation:

Please refer to the attachement. I defined the height (H), width (W), and length (L) and set:

H = 4m and W = (1/3)L. The total cost of 640 Rs/m^2 is divided by the rate cost of Rs 5/m^2 to give 128 m^2 that was plastered. The total area of the walls must be 128 m^2, so then calculate the total wall area: The walls for the length are 2*LH and for the width are 2*WH. Substituting, we have a total of 8*L + (4/3)L = 128 m^2. Solve for L to obtain L = 12m. W is 1/3L, or 4m. The room is (W,L,H) 4, 12, and 4 meters. The floor is W*L, or 48m^2. At Rs 250/m^2, the rug will cost Rs 12000. Ouch.

The differential equation (dy/dx) + y² = xy² with the initial condition y(0) = 1 does not have an elementary closed-form solution.

To solve the differential equation (dy/dx) + y² = xy² with the initial condition y(0) = 1, we can use the method of separable variables. Rearranging the equation, we have,

(dy/dx) = xy² - y²

Next, we separate the variables by dividing both sides by (xy² - y²),

1/(xy² - y²) dy = dx

Now, we integrate both sides,

∫1/(xy² - y²) dy = ∫dx

To integrate the left side, we can use partial fraction decomposition,

∫[1/((y-1)(y+1))] dy = ∫dx

The partial fraction decomposition gives,

(1/2)∫[1/(y-1) - 1/(y+1)] dy = ∫dx

Now we can integrate,

(1/2)ln|y-1| - (1/2)ln|y+1| = x + C

Applying the initial condition y(0) = 1, we substitute x = 0 and y = 1 into the equation,

(1/2)ln|1-1| - (1/2)ln|1+1| = 0 + C

(1/2)ln|0| - (1/2)ln|2| = C

Since ln|0| is undefined, we can see that the term (1/2)ln|y-1| is not defined for y = 1. Therefore, we need to consider a different approach.

The differential equation (dy/dx) + y² = xy² is a first-order nonlinear ordinary differential equation. It does not have an elementary closed-form solution, and the initial condition y(0) = 1 does not provide a unique solution. Instead, we can solve the equation numerically or use approximation methods to find an approximate solution.

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1.You can recognize exponential and linear function by their graph.Linear functions are straights while exponential functions are curved lines.You can also recognize them by the change in your.If the same number is being added to y,then the function has a constant change and is linear.3:-An example of a exponential function is the growth of bacteria and A common equation,y=mx+b y=mx+b,(namely the slope-intercept form,which we will learn more about later)is a example of a linear function.2:-For constant increments in x,a linear growth would increase by a constant difference,and an experimental growth would increase by a constant ratio.

Answer:

168 ft²

Step-by-step explanation:

The equation for the lateral area of a square pyramid is LA = (Pl/2)

Plug in the values LA = (24(14)) / 2

LA = 336/2

LA = 168 ft²

The lateral surface area of the given pyramid whose base is an equilateral triangle is 126 square feet.

The lateral surface area of a triangular pyramid is 1⁄2(perimeter of the base × slant height) which further becomes 3⁄2(side × slant height).

Given that, slant height is 14 ft and the length of each side of the triangular base is 6 ft.

The equation for the lateral area of a square pyramid is 3/2 (6×14)

= 3×3×14

= 126 square feet

Therefore, the lateral surface area of the given pyramid whose base is an equilateral triangle is 126 square feet.

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The fraction that represents the point M is 2 3/10

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

The number line

Such that

M is between 2 1/5 and 2 1/2

This means that

M is between 2.2 and 2.5

By the positiining of the points, we have

M = 2.2 + 0.1

Evaluate

M = 2.3

As a fraction, we have

M = 2 3/10

Hence, the fraction is 2 3/10

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The probability of adding either ground beef or onion as the first ingredient  0.25 or 25%.

If there are a total of 8 ingredients and 2 of them are either ground beef or onion, then the probability would be:

Probability = (Number of desired outcomes) / (Total number of possible outcomes)

           = 2 / 8

           = 1 / 4

           = 0.25

So, the probability of adding either ground beef or onion as the first ingredient is 0.25 or 25%.

In this case, we have a total of 8 ingredients, out of which 2 are either ground beef or onion. When selecting the first ingredient, there are 8 possible outcomes. Since we want to calculate the probability of adding either ground beef or onion as the first ingredient, we count the number of desired outcomes, which is 2 (either ground beef or onion). Dividing the number of desired outcomes by the total number of possible outcomes gives us the probability.

The probability of adding either ground beef or onion as the first ingredient is 0.25 or 25%. This means that there is a 25% chance that either ground beef or onion will be the first ingredient added, assuming the ingredients are added randomly without any specific order.

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To find a recurrence relation for the number of n-letter sequences using the letters a, b, c such that any a not in the last position of the sequence is always followed by a b, we can use the following approach.

Let's consider the last two letters of the sequence. There are three possible cases:

1. The last letter is not "a": In this case, we can append any of the three letters (a, b, or c) to the end of an (n-1)-letter sequence that satisfies the given condition. This gives us a total of 3 times the number of (n-1)-letter sequences that satisfy the condition.

2. The last letter is "a" and the second to last letter is "b": In this case, we can append any of the two letters (a or c) to the end of an (n-2)-letter sequence that satisfies the given condition. This gives us a total of 2 times the number of (n-2)-letter sequences that satisfy the condition.

3. The last letter is "a" and the second to last letter is not "b": In this case, we cannot append any letter to the end of the sequence that satisfies the condition. Therefore, there are no such sequences of length n in this case.

Putting all these cases together, we get the following recurrence relation:

f(n) = 3f(n-1) + 2f(n-2), where f(1) = 3 and f(2) = 9.

Here, f(n) denotes the number of n-letter sequences using the letters a, b, c such that any a not in the last position of the sequence is always followed by a b.

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a. To calculate the Euclidean distances between the three pairs of facilities, we use the formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2) where (x1, y1) and (x2, y2) are the coordinates of the two points.

Calculating the Euclidean distances:

dAB = sqrt((51 - 27)^2 + (59 - 17)^2) ≈ 45.28 miles

dBC = sqrt((61 - 51)^2 + (66 - 59)^2) ≈ 10.82 miles

dAC = sqrt((61 - 27)^2 + (66 - 17)^2) ≈ 51.23 miles

b. To calculate the rectilinear distances, we use the formula:

d = |x2 - x1| + |y2 - y1|

Calculating the rectilinear distances:

dAB = |51 - 27| + |59 - 17| = 27 + 42 = 69 miles

dBC = |61 - 51| + |66 - 59| = 10 + 7 = 17 miles

dAC = |61 - 27| + |66 - 17| = 34 + 49 = 83 miles

Therefore, the Euclidean distances are approximately dAB = 45.28 miles, dBC = 10.82 miles, and dAC = 51.23 miles. The rectilinear distances are dAB = 69 miles, dBC = 17 miles, and dAC = 83 miles.

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The values of c for which the vectors v(-1, 2, c) and w(-7, 8, 9) are orthogonal are c = -1 and c = 17.

In order for two vectors to be orthogonal, their dot product must be zero. The dot product of two vectors v = (v1, v2, v3) and w = (w1, w2, w3) is given by v · w = v1w1 + v2w2 + v3w3.

Let's calculate the dot product of v(-1, 2, c) and w(-7, 8, 9):

v · w = (-1)(-7) + (2)(8) + (c)(9)

= 7 + 16 + 9c

= 23 + 9c

For the vectors to be orthogonal, the dot product must be zero, so we have:

23 + 9c = 0

Solving this equation for c, we get:

9c = -23

c = -23/9

Therefore, the vectors v(-1, 2, c) and w(-7, 8, 9) are orthogonal when c = -23/9.

However, we need to find all the values of c for which the vectors are orthogonal. Since the equation 9c = -23 only gives us one solution, we need to explore further. Let's substitute c = -23/9 back into the dot product equation:

v · w = 23 + 9(-23/9)

= 23 - 23

= 0

The dot product is zero, which means that the vectors v(-1, 2, c) and w(-7, 8, 9) are orthogonal when c = -23/9.

So, the only values of c for which the vectors v and w are orthogonal are c = -23/9 and c=17.

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Answer:

Coordinates:

(-1,2)

(2,2)

(2,3)

(1,3)

(1,4)

(-1,4)

Step-by-step explanation:

The line y=-x is basically a diagonal going from top left to bottom right.

Answer:

20 points

Step-by-step explanation:

Points:

Average:

They must score 20 points

Answer:

57 miles per hour

Step-by-step explanation:

Find his average speed by dividing the total of miles he traveled by the number of hours:

456/8

= 57

So, this means he traveled 57 miles in one hour.

His average speed was 57 miles per hour

Answer:

\(y=-1 \frac{2}{3}x+5\)  

Step-by-step explanation:

y=mx+b is slope-intercept form

m= slope

b= y-intercept (where the line on the graph touches the y=axis aka the line that goes vertically or up and down).

The photo you have attached is very blurry but i will do my best to read the numbers on the graph.

the y-intercept looks to be at 5

so we plug that in

y=mx+5

now let's get the slope.

pick two points you can easily see,

slope is change in y over the change in x --- which is simplified below

rise over run

y2-y1 divided by x2-x1

we can see the point (0,5) and the point (3,0)

(3,0) is going to be the x2 and y2 and the other point is the x and y 1s

0-5= -5

3-0= 3

-5/3

let's simplify that

we know three goes into five once, so that gives us one whole but it's still negative because our slope is negative.

-1 2/3

that is our slope

let's plug it in:

\(y=-1 \frac{2}{3}x+5\)

that is our answer!

Answer: x =-2/9

Explanation:

The expression we have is:

Step 1. Multiply both sides by 5/2

this is so that in the left side 5/2 x 2/5 would cancel each other:

Step 2: Solve the multiplication in the right side

As we can see we are left with an expression that can be solved for x.

Step 3: Move all of the terms that contain x to the left side, and all of the numbers to the right side:

Step 4: Combine like terms

Step 5: Divide both sides by -9:

Answer: x =-2/9