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The 3 sides to a right triangle are:

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides (called the legs) is equal to the square of the length of the longest side (called the hypotenuse).

So, if we have three sides of a triangle and we want to know if it forms a right triangle, we can use the Pythagorean Theorem in the following three ways:

Check if a² + b² = c², where a and b are the lengths of the two legs and c is the length of the hypotenuse. If this equation is true, then the triangle is a right triangle.

Check if b² + c² = a², where b and c are the lengths of the two legs and a is the length of the hypotenuse. If this equation is true, then the triangle is a right triangle.

Check if a² + c² = b², where a and c are the lengths of the two legs and b is the length of the hypotenuse. If this equation is true, then the triangle is a right triangle.

If none of these equations are true, then the triangle is not a right triangle.

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The Bianca will contribute 14.6 works of art, and Claire will contribute 8.7 works of art.

a. In order to find each person's optimal number of art works, one must solve for the point at which the marginal benefit and the marginal cost intersect. For Alice, that point is when N = 7 and MBA = MCA, resulting in an optimal number of works of art of 7. For Bianca, the intersection point is when N = 14 and MBB = MCB, resulting in an optimal number of works of art of 14. For Claire, the intersection point is when N = 8.3 and MBC = MCC, resulting in an optimal number of works of art of 8.3.

b. Without considering altruism, Alice will contribute 7 works of art, Bianca will contribute 14 works of art, and Claire will contribute 8.3 works of art.

c. With altruism, the optimal number of art works for each individual can be calculated in the same way as without altruism, but with the warm-glow benefit added to their respective total marginal benefits. For Alice, that point is when N = 7.3 and TMBA = MCA, resulting in an optimal number of works of art of 7.3. For Bianca, the intersection point is when N = 14.6 and TMBB = MCB, resulting in an optimal number of works of art of 14.6. For Claire, the intersection point is when N = 8.7 and TMBC = MCC, resulting in an optimal number of works of art of 8.7.

d. With altruism, Alice will contribute 7.3 works of art, Bianca will contribute 14.6 works of art, and Claire will contribute 8.7 works of art.

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Answer:

[tex]\boxed{\textsf{16y + 2 is Equivalent to 8 (2y + 1/4).}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to find an \underline{equivalent expression}.}[/tex]

[tex]\textsf{This expression is set up to allow us to use the \underline{Distributive Property}.}[/tex]

[tex]\Large\textsf{What is the Distributive Property?}[/tex]

[tex]\textsf{The \underline{Distributive Property} is a property that allows us to distribute.}[/tex]

[tex]\large\underline{\textsf{For this problem;}}[/tex]

[tex]\textsf{We can use the Distributive Property to distribute the 8 into values in the Parentheses.}[/tex]

[tex]\large\underline{\textsf{Distribute:}}[/tex]

[tex]\mathtt{8(2y+\frac{1}{4} )}[/tex]

[tex]\mathtt{(8 \times 2y) + (8 \times \frac{1}{4}) .}[/tex]

[tex]\boxed{\textsf{16y + 2 is Equivalent to 8 (2y + 1/4).}}[/tex]

Answer:

16y + 2

Step-by-step explanation:

Now we have to,

→ Find the equivalent expression.

The expression is,

→ 8(2y + (1/4))

Let's simplify the expression,

→ 8(2y + (1/4))

→ 8(2y) + 8(1/4)

→ 16y + (8/4)

→ 16y + 2

Hence, the answer is 16y + 2.

The power consumed by resistor R3 is 0.79 watts.

The rate at which energy is transferred or converted is known as Power. It is a measure of how much work can be done in a given amount of time. Power is typically measured in watts and is a key factor in determining the efficiency of machines and systems.

To determine the power consumed by resistor R3, we need to first find the current flowing through it.

E₁ = I(R₁ + R₂ + R3 + R4)

I = E₁ / (R₁ + R₂ + R3 + R4)

= 30 / (152 + 202 + 252 + 102)

= 0.056 A

Now that we know the current flowing through R3, we can use Ohm's Law again to find the power consumed by it:

P = I²R3

= (0.056)² x 252

= 0.79 W

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Answer:

The answer you're looking for is x = 6, and the missing angle is 30º

Step-by-step explanation:

In order to find the answer we need to find out what the angle amount actually is. We can use the equation 180º = 110+ 40 + (8x-18).

Now there are two ways to solve this equation you could solve it by starting with the equation actually is or you can find out the missing angle using another equation.

First Method:

Using 180º = 110+ 40 + (8x-18), you first need to do is to combine like terms such as combining 110, 40, and -18, giving you 132.

Now you have 180 = 132 + 8x.

Then you will have to make sure that 8x is left by itself so do the opposite operation and to keep the equation balanced you do it on both sides giving you 48 = 8x. The only step left to do is to do the opposite operation on both sides which is dividing by 8, giving you 6 = x

Now with that, you replace x, with 6, and go from there.
(8x-18) = (8×6-18) = (48 - 18) = 30.

With that, we are finished with the equation.

However, the other method you could use, which is easier in my opinion, can be found below.

Second Method:

The first thing we do is find out immediately what the missing angle (m) is using the equation 180 = 110 + 40 + m.

You combine like terms 110 and 40, giving 150 and then get,
180 = 150 + m.

You then do the inverse of operations, which is subtracting 150 from both sides and you get 30 = m.

Now that we complete that we start with our other equation which is:
30 = 8x-18. You then do inverse of -18, which adds 18 to both sides giving: 48 = 8x.

Finally doing the inverse operation of multiplying is dividing 8 by both sides giving 6 = x as the correct answer.

Answer:

9, 20 and 4

Step-by-step explanation:

Swimming only 9

Track only 20

All 3 events

14 did track and field

10 did track and swimming

Those who sis all 14- 10 = 4

The answers are the students do a) swimming only = 9, b)track events only = 20 and c) all three events = 4

A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things.

Given that, a school sports team contains 68 students. 33 do field events, 40 do track events, 23 go swimming, 14 do both field and track events. If 15 students do field events only and 10 do both swimming and track events,

Please refer to picture attached

Therefore,

15+a+c+d = 33.......1

b+c+d+e = 40.........2

a+b+d+f = 23..........3

c+d = 14...............4

a+d = 8.............5

b+d = 10.............6

Now, solving for variables,

From 1 and 4,

a = 4

Therefore, from 5,

d = 4

From 6,

b = 6

Put these in eq 3,

f = 9

c = 10

e = 20

Therefore,

Swimming only = 9

Track events = 20

All three = 4

Hence, the answers are the students do a) swimming only = 9, b)track events only = 20 and c) all three events = 4

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The equation correctly relates the total cost y to rent the washer for x days is option (B) Y = 40 + 20x

The rental fee of $40 is charged regardless of the number of days the power washer is rented. In addition to this fee, there is a daily charge of $20 per day.

Therefore, the total cost of renting the power washer for x days can be calculated by multiplying the daily charge by the number of days rented and adding the rental fee:

Total cost = (daily charge) x (number of days rented) + rental fee

Total cost = $20x + $40

This linear equation can be rearranged to the form:

Y = 40 + 20x

Therefore, the correct option is (B) Y = 40 + 20x

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Cross-sectional area of the dam can be calculated without using calculus as explained below:

Step 1: Draw the cross-section of the dam on a graph paper and divide it into simple shapes like triangles, rectangles, and circles.

Step 2: Calculate the area of each shape separately using the appropriate formulae. For example, the area of a rectangle is length times width, area of a triangle is 1/2 times base times height and the area of a circle is pi times radius squared.

Step 3: Add the areas of all the shapes to find the total cross-sectional area of the dam. This gives an approximate value of the area since the actual shape of the cross-section is not perfectly regular.If we take a concrete example of a dam with a cross-section of a trapezoid,

we can calculate the cross-sectional area using the above steps:

Step 1: Draw the cross-section of the dam on a graph paper as shown below. The cross-section of the dam can be divided into a rectangle and a triangle.

Step 2: Calculate the area of the rectangle and the triangle separately using the formulae for the area of the rectangle and the triangle respectively.Area of the rectangle = base times height = 10 m times[tex]4 m = 40 m²[/tex]Area of the triangle = 1/2 times base times height = 6 m times 4 m = 12 m²

Step 3: Add the areas of the rectangle and the triangle to get the total cross-sectional area of the dam.Area of the cross-section = area of rectangle + area of triangle= [tex]40 m² + 12 m²= 52 m²[/tex]The area found using the above method is not exact since it is an approximation of the actual area of the cross-section of the dam. It can be more accurate by dividing the cross-section into smaller and simpler shapes and calculating their areas individually.

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Step-by-step explanation:

94 - 50% * 94   =

             94 - .50 * 94  =

                              94 - 47 =  47  

Answer:

47

Step-by-step explanation:

50 × 94 ÷ 100 =

47,00 ÷ 100=

47

Answer:

769

764 + 3 + 2 = 769

1. She can do   764 + 3 = 767   767 + 2 = 769

2. OR She can do   2 + 3 = 5   5 + 764 = 769

The area of the sector is evaluated to be equal to 9π square meters

The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.

For the area of circle 72π m²;

πr² = 72π m²

r² = 72 m²

hence the area of the sector is calculated as follows:

area of the sector = (45°/360°) × π × 72 m²

we simplify by multiplication and division

area of the sector = 1/8 × π × 72 m²

area of the sector = π × 9 m²

area of the sector = 9π m².

Therefore, the area of the sector is evaluated to be equal to 9π square meters

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To simplify the given expression, we can first evaluate each term inside the square root, and then add them up. Using basic algebraic operations, we get:

T = √(2023^2)(4046) + (2023^2) + 0

T = √(2023^2)(4046 + 1)

T = √(2023^2)(4047)

T = 2023√4047

Therefore, the simplified expression for T is 2023√4047.

Answer:

DE's length is 1/2 of BC's length, due to it being a mid segment (13)((You can tell it is a mid segment due to the congruency lines)). AD's length is 12, due to there being a midpoint. EC's length is 10, also due to the congruency lines.

Answer:

Ill help you figure out how to graph.

Step-by-step explanation:

The value in front of x (like 2x or 7x) is the slope (rise over run) rise is how much the line goes up, and run is how much it goes to the side. the second number (in the bottom left graph, it is -5) is the y intercept. it is where the line crosses the y axis. (in this case on -5) Here is an example. (of the problem y=x-5)

Answer:

1\2

Step-by-step explanation:

Answer:

1 . x(x+1)
2.(3a-1)(5a+8)
3.(4x + 3y) ( 3x - 3y)
4.(a+b)

Answer: x = π - π/4 = 3π/4

Step-by-step explanation:

If sec(x) = -√2 and x is in the second quadrant (between π/2 and π), we can use the identity:

sec^2(x) - 1 = tan^2(x)

to find the value of tan(x):

sec^2(x) - 1 = tan^2(x)

(-√2)^2 - 1 = tan^2(x)

2 - 1 = tan^2(x)

1 = tan^2(x)

Taking the square root of both sides, we get:

tan(x) = ±1

Since x is in the second quadrant, the angle that satisfies tan(x) = 1 is π/4. Therefore, we have:

x = π - π/4 = 3π/4

Note that the angle that satisfies tan(x) = -1 is in the fourth quadrant, so it is not relevant to this problem.

Answer:

$150

Step-by-step explanation:

Interest = Principal x Rate x Time

where Principal is the amount borrowed, Rate is the interest rate, and Time is the duration of the loan.

In this case, the Principal is $1,000, the Rate is 10%, and the Time is 18 months (which we'll convert to a fraction of a year).

First, we need to convert 18 months to a fraction of a year. Since there are 12 months in a year, 18 months is equal to 18/12 = 1.5 years.

Using the formula:

Interest = Principal x Rate x Time

Interest = $1,000 x 0.10 x 1.5

Interest = $150

So the interest on the $1,000 loan with a 10% simple interest rate for 18 months is $150.

Answer:

The formula for simple interest is I = Prt, where I is the interest, P is the principal or amount borrowed, r is the interest rate, and t is the time in years.

In this case, P = $1,000, r = 10% or 0.10 as a decimal, and t = 1.5 years (since 18 months is equivalent to 1.5 years).

I = Prt

I = $1,000 * 0.10 * 1.5

I = $150

Therefore, the interest on the $1,000 loan with a 10% simple interest rate for 18 months is $150.

Answer:

D.) 3.14/2

Step-by-step explanation:

Using the equation C(x) = 120(0.88)ˣ, we found that after 19.27 hours, the amount of caffeine becomes 10mg.

What is meant by an equation?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

Given,

The initial amount of caffeine in the beverage = 120 mg

The rate at which the caffeine decreases = 12% per hour w

We are asked to find the time taken for the caffeine amount to become 10mg.

Now let the initial amount be 100 per cent.

After one hour, the amount becomes (100-12)  = 88% of 120 = 0.88 * 120

So after every one hour, there is 88% caffeine left.

Now after two hours,

the amount of caffeine = 88% of (0.88*120) = 0.88*0.88*120 = 120(0.88)²

So after x hours, we can write the equation as:

Amount of caffeine left C(x) = 120(0.88)ˣ

Now for 10mg to be left, the time taken is:

10 = 120(0.88)ˣ

1/12 = (0.88)ˣ

log (1/12) = x log(0.88)

-1.079 = x (-0.056)

x = 19.27 hours

Therefore using the equation C(x) = 120(0.88)ˣ, we found that after 19.27 hours, the amount of caffeine becomes 10mg.

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Answer:

The sum of a number and 9 can be written as:

x + 9

where "x" represents the number being referred to.

Alternatively, if we want to use a different variable, we can write it as:

n + 9

where "n" represents the number being referred to.

Hope this helped, if not I'm sorry! If you need more help, feel free to ask! :]

Considering the figure, the missing lengths are

In geometry, the phrase "similar triangles" refers to triangles whose respective sides are proportionate and whose corresponding angles are congruent.

Hence, if the triangle's corresponding angles are congruent, the side should be in proportion.

The proportions are as follows

say the side on top of 10 (in horizontal line) is y

y / (10 + 15 + 12.5) = 10 / (10 + 15)

y / 37.5 = 10 / 25

cross multiplying  

25y = 37.5 * 10

25y = 375

y = 15

say the side below side 10 (in horizontal line) is x

x / 10 = 10 / (10 + 15)

x / 10 = 10 / 25

cross multiplying  

25x = 100

x = 4

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Dot plots are useful for visualizing the distribution of data and identifying patterns, trends, and outliers. They are often used in data analysis, quality control, and scientific research to help draw conclusions and make informed decisions based on data.

A dot plot is a graphical representation of statistics that presents character information factors through the use of dots. From a dot plot, possible decide several conclusions, depending on the data being displayed.

For instance, if the dot plot presents information on the height of a collection of people, you can still determine the range of heights inside the organization, the most common top, and any outliers (i.e., individuals with severe heights).

If the dot plot displays facts at the ratings of a collection of students on a test, you can still determine the range of rankings, the median score, and the distribution of rankings (i.e., whether or not the ratings are evenly distributed or clustered round sure values).

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What conclusion can be determined by the dot plot? Explain in detail about the dot plot.

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The integer that satisfies all of these conditions is -4.

Exponentiating -4 gives 16, which is less than -1.

The y-coordinate of -4 on the coordinate plane is above 2.

The x-coordinate of -4 on the coordinate plane is greater than -3.

And, the sum of the absolute values of the coordinates of -4 is 7, which is equal to five.

Answer:

34m

Step-by-step explanation:

To find:-

Answer:-

We are here given that Elizabeth climbed up the mountain vertically 30m , and the distance between frank and the bottom of the mountain is 30m .

We are interested in finding out the distance between frank and Elizabeth. For that we will have to use Pythagoras theorem , in which;

[tex]\rm\implies a^2+b^2 = h^2 \\[/tex]

Where h is the longest side of the triangle and a and b are two other sides. here we need to find out the longest side ( see attachment) .

So on substituting the respective values, we have;

[tex]\rm\implies h^2 = (16m)^2+(30m)^2 \\[/tex]

[tex]\rm\implies h^2 = 256m^2 + 900m^2 \\[/tex]

[tex]\rm\implies h^2 = 1156m^2\\[/tex]

[tex]\rm\implies h =\sqrt{1156 \ m^2} \\[/tex]

[tex]\rm\implies \red{h = 34 m} \\[/tex]

Hence the distance between Elizabeth and Frank is 34m .

a) Tοtal squares shaded is 4*10+(1*6) + 4*10+(1*6) + (1*8) + 3*10+(1*8)

b) The expressiοn gives the tοtal number οf squares.

Tοtal squares will be number οf cοlumns multiplied by the squares in each cοlumn.  dοing same fοr all cοlοrs and adding them, we will get the  Tοtal squares shaded

c) On simplifying the expressiοn, we get  138  squares

Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne arithmetic οperatiοn, and a cοmplete sentence. Any οne οf the fοllοwing mathematical οperatiοns can be used. A sentence has the fοllοwing structure: Number/variable, Math Operatοr, Number/Variable is an expressiοn.

In each cοlumn, there are 10 squares

The first grid has 4 cοlumns and 6 squares shaded green

=> 4*10+(1*6) = 46  green squares

On the same grid, 6 squares and 4 cοlumns are shaded red.

=> 4*10+(1*6) = 46   red squares

On the same grid, 8 squares are shaded blue. => (1*8) blue squares

On the secοnd 10 by 10 grid, 3 cοlumns and 8 squares are shaded blue.

=> 3*10+(1*8) blue squares

a)Tοtal squares shaded

= shades οn first grid +  shades οn secοnd grid

= ( green squares + red squares +  blue squares ) + ( blue squares )

=  4*10+(1*6) + 4*10+(1*6) + (1*8) + 3*10+(1*8)

b)   The expressiοn gives the tοtal number οf squares.

Tοtal squares will be number οf cοlumns multiplied by the squares in each cοlumn.  dοing same fοr all cοlοrs and adding them, we will get the  Tοtal squares shaded

c)  On simplifying the expressiοn, we get

= 46+46+8+38

= 138  squares

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Answer:

5^x+x

Step-by-step explanation:

5^x+1+5^x-1

First of all 1- 1 = 0

so we are here with 5^x +5^x