Write an equation of the line in slope-intercept form.

Step-by-step explanation:

sin45 deg = 6/b

Root2/ 2 = 6/b

you will find b value

a = 8 + x

tan45 deg = 6/x

1 = 6/x

x = 6

a = 8+6

= 14

The value of a is 16 units and the value of b is 11.42 units.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the sine rule for triangles a/sinA = b/sinB = c/sinC.

Let, (a - 8) = x and the angle opposite to the side b is 90°.

Therefore,

b/sin90° = 8/sin45° = x/sin45°.

b/sin90° = 8/sin45°

b = 8/0.7.

b = 11.42.

11.42/sin90° = x/sin45°.

11.42 = x/0.7.

x = 8.

So, The value of a is (8 + 8) = 16 units.

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The slope of the line that passes through the graph is -1/3

From the graph, the points are given as

(6, 2) and (-6, 6)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (6, 2) and (-6, 6)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (6, 2) and (-6, 6)

Substitute the known values in the above equation

So, we have the following equation

Slope = (6 - 2)/(-6 - 6)

Evaluate

Slope = -1/3

Hence, the slope of the line is -1/3

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Determine the area of the ceiling whose shape is square with side of 52 feet.

One can paint the area of 208 ft square.

Determine the number of cans required to paint 2704 ft square.

So, 13 cans are required to piant the ceiling of the restaurant.

Answer:

answer is 5.50

Step-by-step explanation:

multiply 2.75 times two because 3 by 5 is half of 9 by 15

Answer:

2.5

Step-by-step explanation:

the other persons answer is wrong

The number after rounding to the one significant figure is 4000.

The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation

Rounding off means a number is made simpler by keeping its value intact but closer to the next number

According to the given question we have an expression.

\(\frac{798}{8} (41)\)

When we evaluate this expression we get

\(\frac{798}{8} (41)\)

\(=99.75(41)\)

\(= 4089.75\)

Here, the first significant figure is 4 and the second one is 0 which is less than 5.

Hence, the number after rounding to the one significant figure is 4000.

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a) Parallelograms are quadrilaterals with parallel opposite sides that have the following properties: They have equal opposite sides. They have equal opposite angles.

Answer: Figure A and Figure B

b) The squares have equal sides.

Answer: Figure A

c) In a rectangle the opposite sides have the same length.

Answer: Figure B

Answer:

225 is the answer

15 times 15

Step-by-step explanation:

Answer:

The calf raiser uses 960 oz of milk replacer for 15 calves, so each calf gets 960 oz / 15 = 64 oz of milk replacer.

To convert this to quarts, we need to divide by 32 (since there are 32 oz in a quart)

64 oz / 32 oz/quart = 2 quarts

Each calf gets 2 quarts of milk replacer and the calf raiser needs to add 34 as much water as milk replacer

So the total amount of water she needs is 2*34 = 68 quarts

To convert the quarts of water to ounces we need to multiply by 32 (since there are 32 oz in a quart)

68 quarts * 32 oz/quart = 2176 oz of water.

So the calf raiser needs 2176 ounces of water to mix with the milk replacer for 15 calves.

A, percentages

You would see percentages on a circle graph, because it's how many parts of the whole that they take up.

Happy to help, have a great day! :)

We can infer that hypertension status and gender are dependent rather than independent because the odds of being hypertensive differ between males and females (0.366 vs 0.266).

It is represented by a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty. P is frequently used to represent the likelihood of an event occurring (event). The probability equation is: P(event) equals the proportion of favourable events to all other possible outcomes. For instance, the likelihood of receiving heads when flipping a fair coin is: P(heads) equals the ratio of positive outcomes (1) to all other potential outcomes (2), or 1/2, to equal 0.5. This indicates that when flipping a fair coin, the chance of receiving heads is 0.5, or 50%. To create predictions and interpret data, probability is utilised in many branches of mathematics, statistics, and science.

given

Let's start by calculating the total population of hypertensives, which is equal to the sum of hypertension males and hypertensive females:

120 is the total number of hypertensive individuals (56 + 64).

Let's now determine the likelihood of males having hypertension:

P(Hypertensive|Male) = Number of hypertensive men / Total men = 56 / 153 = 0.366

Secondly, let's determine the likelihood that women will have hypertension:

P(Hypertensive|Female) = Number of female hypertensives / Total number of females = 64 / 241 = 0.266

We can infer that hypertension status and gender are dependent rather than independent because the odds of being hypertensive differ between males and females (0.366 vs 0.266).

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Answer:

1.5 MPH

Step-by-step explanation:

3/4 = 0.75

3/4 x 2 = 0.75 x 2 = 1.5

Answer:

\(x + y = 150\)

\(2x + y = 250\)

The sale price of the shoe is given as follows:

P3,436.

The sale price of the shoe is obtained applying the proportions in the context of the problem.

The initial price is of:

P 4,295.

The shoe is sold at a discount of 20%, meaning that the sale price is 80% of the initial price, and the value is given as follows:

0.8 x 4295 = P3,436.

The problem asks for the selling price of the shoe.

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Answer:

8/12

Step-by-step explanation:

8 is the number greater than 7

The diagram which best represents the hiking track of the hiker is attached below.

Speed = Distance / Time

As time increases, speed is constant, i.e., 214 miles per hour

So, the distance increases with an increase in time.

Speed = Distance/Time

Let, Distance = D and Time = T,

214 = D / T

D = 214T

Let, D = Y coordinate, Time = X coordinate

y = 214 x→→Equation of the line passing through the origin and slope 214.

For the given situation, the equation is a linear equation and the equation will be on the y-axis.

Hence, a diagram that represents this information is:

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Answer:

2^4   * 9^4

Step-by-step explanation:

(2*9)^4

We can take the power to each term inside the parentheses

2^4   * 9^4

Answer:

Not entirely sure about this because it was grabbed from someone else

There are 210 ways to win 1st place

There are 209 ways to win 2nd place

There are 208 ways to win 3rd place

Every time an award is won, a spot if taken, therefore one person is eliminated from possibly taking that spot.

Hope that makes sense :)

The total number of ways of contestants can win first, second, and third prizes will be 9,129,120.

A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.

The number of contestants is 210.

The number of ways of contestants who won the first prize will be given as,

⇒ ²¹⁰C₁

⇒ 210

The number of ways of contestants who won the second prize will be given as,

⇒ ²⁰⁹C₁

⇒ 209

The number of ways of contestants who won the third prize will be given as,

⇒ ²⁰⁸C₁

⇒ 208

Then the total number of ways of contestants can win first, second, and third prizes will be

⇒ 210 x 209 x 208

⇒ 9,129,120

The total number of ways of contestants can win first, second, and third prizes will be 9,129,120.

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Answer:

  x = 1

Step-by-step explanation:

You want to know the value of x in the trapezoid with adjacent angles (43x+2)° and 135°.

The two marked angles can be considered "consecutive interior angles" where a transversal crosses parallel lines. As such, they are supplementary.

  (43x +2)° +135° = 180°

  43x = 43 . . . . . . . . . . . . . . divide by °, subtract 137

  x = 1 . . . . . . . . . . . . . . . divide by 43

The value of x is 1.

__

Additional comment

Given that the figure is a trapezoid, we have to assume that the top and bottom horizontal lines are the parallel bases.

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Answer:

y = - 2x + 12

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (6, 0 ) and (x₂, y₂ ) = (- 1, 14 )

m = \(\frac{14-0}{-1-6}\) = \(\frac{14}{-7}\) = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (6, 0 )

0 = - 12 + c ⇒ c = 0 + 12 = 12

y = - 2x + 12 ← equation of line

The reasons for the steps are given below.

The value of x is -4.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

-2(4x + 3) = 26

[ The distributive property of multiplication over addition ]

-2(4x) + -2(3) = 26

-8x - 6 = 26

[ Adding 6 on both sides ]

-8x - 6 + 6 = 26 + 6

-8x = 32

[ Divide -8 into both sides ]

-8x/-8 = 32/-8

x = -4

Thus,

The reasons for the steps are given above.

x = -4

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Answer: 120 degrees.

Step-by-step explanation: A 90-degree angle would be a right angle. The segments would be perpendicular. In a 180-degree angle, the line would be flat. This angle is between these two angle measures. It appears quite close to a 120-degree angle such as the one shown below:

Because of this, I would estimate that the angle is around 120 degrees. It may be 130 degrees or 110 degrees but it appears to be approximately 120 degrees.

The impact on Carns Company's income from eliminating the Small Tools Division would be a decrease of $1,209,000.

To determine the impact on Carns Company's income from eliminating the Small Tools Division, we need to consider the avoidable costs associated with the division.

The avoidable costs include all of the variable costs of the division and a portion of the fixed costs that are specifically related to the Small Tools Division. In this case, the variable costs of the division are $1,295,000, and $119,000 of the fixed costs are avoidable.

To calculate the impact on income, we subtract the avoidable costs from the loss reported by the division:

Impact on income = Loss - Avoidable costs

Impact on income = $205,000 - ($1,295,000 + $119,000)

Impact on income = $205,000 - $1,414,000

Impact on income = -$1,209,000

The negative sign indicates a decrease in income.

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a) \(\frac{(x+1)^{2}}{3^{2}}-\frac{(y+2)^{2}}{2^{2}} = 1\).

b) (h, k) = (-1, -2).

c) F₁ (x, y) = (-1 - √13, -2), F₂ (x, y) = (-1 + √13, -2).

d) y = ±2 · (x + 1) / 3 - 2.

e) See the image attached below.

In this question we must analyze the general equation of a hyperbola  and derive all the required information by algebraic and graphic means. All this information is derived from the standard equation of the hyperbola, which is presented below:

\(\frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}} = 1\)   (1)

Where:

The foci are located at the following two points: \(F_{1} (x, y) = (h - c, k)\), \(F_{2} (x,y) = (h + c, k)\).

Where \(c = \sqrt{a^{2}+b^{2}}\).

And the asymptotes of the hyperbola are described by the following formulas:

y₁ = b · (x - h)  / a + k   (2)

y₂ = - b · (x - h) / a + k   (3)

a) We transform the general equation into its standard form:

The standard equation of the hiperbola is \(\frac{(x+1)^{2}}{3^{2}}-\frac{(y+2)^{2}}{2^{2}} = 1\). \(\blacksquare\)

b) From the result found in a) we conclude that the center of the hyperbola is (h, k) = (-1, -2).

c) The foci of the hyperbola are located at the following two points:

\(c = \sqrt{3^{2}+2^{2}}\)  

\(c = \sqrt{13}\)

F₁ (x, y) = (-1 - √13, -2), F₂ (x, y) = (-1 + √13, -2)

The foci of the hyperbola are F₁ (x, y) = (-1 - √13, -2) and F₂ (x, y) = (-1 + √13, -2). \(\blacksquare\)

d) And the asymptotes of the hyperbola are presented below:

y₁ = 2 · x / 3   (2)

y₂ = - 2 · x / 3   (3)

The asymptotes of the hyperbola are y₁ = 2 · (x + 1) / 3 - 2 and y₂ = - 2 · (x + 1) / 3 - 2. \(\blacksquare\)

e) The graph of the hyperbola and all its characteristics are presented by means of graphing tool. The result is presented in the image attached below.

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Answer:

The equation of the hyperbola = (x + 1)^2/3^2 - (y + 2)^2/2^2 = 1

The center of the hyperbola = (-1, -2) (h, k)

The vertices of the hyperbola (my assingment asked me for vertices) = (2, -2) and (-4, 2)

The asymptotes = one at y = (2x+2/3) - 2 and the other is at

y = -((2x+2/3) -2)).

Step-by-step explanation:

For the graphing part plug the equation into desm0s and the asymptote equation. For the guiding box part, you use the B variable. Since b = 2 in this problem, you count up two spaces from the center (-1,-2) and then down two spaces. These will be the top and bottom of your guiding box. Then use your vertices as the sides and make a box that connects.

Good luck!

The value of

a. k = 0.0315

b. m(t) = m(o) e^-kt

c. m(t) = 4.2g

d. t = 60.2 years

The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.

half life = 0.693/k

22 = 0.693 / K

22k = 0.693

K = 0.693/22

K = 0.0315

The mass after time t is given as ;

m(t) =m(o)e^-kt

where m(o) = 20g

after 50 years

m(t) = 20e^-(0.0315)(50)

= 20e^-1.575

m(t) = 20 × 0.21

m(t) = 4.2

3 = 20e^-0.0315t

3/20 = e^-0.0315t

0.15 = e^-0.0315t

ln 0.15 = -0.0315t

- 1.897 = -0.0315t

t = -1.897/-0.0315

t = 60.2 years

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Answer:

The function is neither even nor odd.

Step-by-step explanation:

A function is odd if:

f(x) = - (f-x)

A function is even if:

f(x) = f(-x)

A function is neither odd nor even if neither of the above two equalities are true, that is to say:

f(x) != f(-x) and f(x) != -f(-x)

Which is our case. (because substituting (-x) in place of (x) will not give us either of the equations. So the function is neither odd, nor even.

Answer:

B the mean increases by 6.8

Designing an easy do-it-yourself compost bin:

Drawing and Description:

The compost bin can be a simple structure made of wood or wire mesh. It consists of four sides, a bottom, and a removable lid. The sides and bottom are connected securely to form a rectangular shape, while the lid allows for easy access to the contents inside.

The bin can be placed directly on the ground or on a solid surface, depending on personal preference.

Materials Used:

Wood or wire mesh (depending on preference)

Nails or screws to assemble the structure

Size of the Bin:

The size of the bin can vary based on the available space and the amount of compostable materials you generate. A suitable size for a home compost bin could be approximately 3 feet wide, 3 feet deep, and 3 feet tall.

Substances Used to Fill It:

To fill the compost bin, you would need a mix of "green" and "brown" materials. "Green" materials include fruit and vegetable scraps, coffee grounds, tea leaves, grass clippings, and plant trimmings. "Brown" materials consist of dry leaves, shredded newspaper, cardboard, and small twigs.

Household Items That Can Go in It:

You can add a variety of household items to the compost bin, such as fruit and vegetable peels, eggshells, coffee grounds, tea bags, yard waste (leaves, grass clippings, plant trimmings), shredded paper, cardboard, and natural fibers (like cotton or wool scraps).

Time for Compost to Be Ready:

The time it takes for the compost to be ready varies depending on factors like temperature, moisture, and the type of materials used. Generally, it takes about 2 to 6 months for compost to fully decompose and become ready to use.

Using the Compost:

Once the compost has broken down into a dark, crumbly, and earthy material, it is ready to use. You can spread it in your garden beds or pots as a nutrient-rich soil amendment. It improves soil structure, retains moisture, and provides essential nutrients for plants' growth.

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Answer:

y = \(\frac{16}{3}x-79\)

Step-by-step explanation:

From the given table,

Two points are (1, 15) and (7, 47)

If the two points \((x_1,y_1)\) and \((x_2,y_2)\) are lying on a line then slope 'm' of the line will be,

m = \(\frac{y_2-y_1}{x_2-x_1}\)

   = \(\frac{47-15}{7-1}\)

   = \(\frac{32}{6}\)

   = \(\frac{16}{3}\)

Let the equation of a line passing through (h, k) is,

y - h = m(x - k)

If the line passes through (1, 15)

y - 1 = \(\frac{16}{3}(x-15)\)

y = \(\frac{16}{3}x-\frac{16}{3}(15)+1\)

y = \(\frac{16}{3}x-80+1\)

y = \(\frac{16}{3}x-79\)

Answer:

$12

Step-by-step explanation:

first we multiply the candies by the weight to find out the total weight

60* 25= 1500g

1500g to kg = 1500/1000 = 1.5kg

so its going to be 1.5kg * 8

1.5* 8 = 12