Four students tried to determine the area of a triangle. A sketch of the triangle and the beginning part of their work is shown. Ben 1/2(7ft.) Alex 1/2(ft+7ft)(5ft) Dena 1/2 (7ft)(4ft) Ron 1/2 (3ft)(4ft)

The answer is -4 3/8

Fraction is the parts of a whole or collection of objects represented by a numerator and a denominator.

How to determine this

-1 1/2 - (3 1/2) -(-5/8)

i.e -1 1/2 -3 1/2 + 5/8

3/2 - 7/2 + 5/8

By finding the LCM

= 4(-3) - 4(7) + 1(5)/8

= -12 - 28 + 5/8

= -35/8

= -4 3/8

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Yes, the given function f(x) = -10x is a polynomial function. The degree of a polynomial function is the highest exponent of the variable. In this case, the highest exponent of x is 1, so the degree of f(x) is 1.

The leading coefficient of a polynomial function is the coefficient of the term with the highest exponent. In this case, the coefficient of the x term is -10, so the leading coefficient of f(x) is -10.

Based on the degree, we can classify the type of function. A polynomial function with degree 1 is called a linear function. Therefore, f(x) = -10x is a linear function.

To summarize, the given function f(x) = -10x is a polynomial function with a degree of 1. The leading coefficient is -10, and it is classified as a linear function.

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Answer:

Step-by-step explanation:

0.01199040767

this is the answer I don't know if this helps

Answer:

33 miles

Step-by-step explanation:

The illustration forms a right angled triangle. The opposite side of the triangle is where we are looking for . The adjacent side is the radius 4000 miles.

5280 ft = 1 mile

735 ft = ? miles

cross multiply

735/5280

miles = 0.13920454545  miles

The hypotenuse side is the height of the building + 4000 miles = 0.140 + 4000 = 4000.14  miles

using Pythagoras theorem

c² = a² + b²

c = 4000.14

a = 4000

4000.14² = 4000² + b²

b² = 4000.14² - 4000²

b² = 16001120.0196  - 16000000

b² = 1120.0196

b = √1120.0196

b = 33.4666938911

b = 33 miles

Hello!

V = 2m * 1m * 1m = 2m³

18 * 2m³ = 36m³

Answer:  \(36^{3}\)m

Step-by-step explanation:

First, find the volume of the 18 rectangular-prism-shaped toy chests.

\(2*1*1=2\)

\(18*2=36\)

So I believe the answer is \(36^{3}\) m

Answer:

s=12.7

c=18.5

hope this helps :)

Answer:

(x - 5)² + (y - 3)² = 9

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k ) = (5, 3 ) and r = 3 , then

(x - 5)² + (y - 3)² = 3² , that is

(x - 5)² + (y - 3)² = 9 ← equation of circle

The general solution to the differential equation is y(x) = c1e^(r1x) + c2e^(r2x) + ... + ck e^(rkx) + yp(x). The uniqueness of the solution is guaranteed by the condition that an(x) ≠ 0 on I.

The given differential equation is a linear nth order differential equation with constant coefficients. The general form of such an equation is:

anD^n y + an-1D^(n-1) y + ... + a1Dy + a0y = g(x)

where a0, a1, ..., an are constants.

To solve this equation, we first find the characteristic equation by assuming a solution of the form y = e^(rx) and substituting it into the differential equation:

an(r^n)e^(rx) + an-1(r^(n-1))e^(rx) + ... + a1re^(rx) + a0e^(rx) = g(x)e^(rx)

Dividing both sides by e^(rx) and simplifying gives:

an(r^n) + an-1(r^(n-1)) + ... + a1r + a0 = g(x)

This equation is called the characteristic equation of the differential equation.

The roots of the characteristic equation are called characteristic roots or eigenvalues. Let the roots be r1, r2, ..., rk. Then the general solution to the differential equation is given by:

y(x) = c1e^(r1x) + c2e^(r2x) + ... + ck e^(rkx) + yp(x)

where c1, c2, ..., ck are constants, and yp(x) is a particular solution to the non-homogeneous differential equation.

If the initial conditions are given as y(x0) = y0, y'(x0) = y1, ..., y^(n-1)(x0) = yn-1, then we can determine the values of the constants c1, c2, ..., ck by solving a system of linear equations formed by substituting the initial conditions into the general solution.

The uniqueness of the solution is guaranteed by the condition that an(x) ≠ 0 on I. This condition ensures that the differential equation is not singular, which means that the coefficients do not simultaneously vanish at any point in I. If the equation is singular, then the solution may not be unique.

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(a) The change is -5.403 million enplaned passengers.

The number of enplaned passengers on the given airline decreased from 98.175 million in 2007 to 92.772 million in 2008, resulting in a decrease of 5.403 million enplaned passengers.

(b) The percentage change is -5.51%.

The percentage change is calculated using the formula: ((new value - old value) / old value) x 100%. In this case, the percentage change is ((92.772 - 98.175) / 98.175) x 100% = -5.51%. This indicates a 5.51% decrease in the number of paying passengers on the given airline between 2007 and 2008.

(c) The average rate of change is -2.702 million enplaned passengers per year.

The average rate of change is calculated by dividing the total change in the number of enplaned passengers by the number of years between 2007 and 2008. In this case, the average rate of change is (-5.403 / 2) = -2.702 million enplaned passengers per year.

This means that the number of paying passengers on the given airline decreased by an average of 2.702 million per year between 2007 and 2008.

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Answer:

d = 7.5

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to - 3

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

with (x₁, y₁ ) = (- 3, - 6) and (x₂, y₂ ) = (d, - 5d)

m = \(\frac{-5d+6}{d+3}\) = - 3 ( multiply both sides by (d + 3) )

- 5d + 6 = - 3(d + 3)

- 5d + 6 = - 3d - 9 ( add 3d to both sides )

- 2d + 6 = - 9 ( subtract 6 from both sides )

- 2d = - 15 ( divide both sides by - 2 )

d = 7.5

To find the dimensions of the rectangle that would maximize the enclosed area, we can use the concept of optimization.

Let's assume the length of the rectangle is x cm. Since we have a piece of wire 60 cm long, the remaining length of the wire will be used for the width of the rectangle, which we can denote as (60 - 2x) cm.

The formula for the area of a rectangle is given by A = length × width. In this case, the area is given by A = x × (60 - 2x).

To maximize the area, we need to find the value of x that maximizes the function A.

Taking the derivative of A with respect to x and setting it equal to zero, we can find the critical point. Differentiating A = x(60 - 2x) with respect to x yields dA/dx = 60 - 4x.

Setting dA/dx = 0, we have 60 - 4x = 0. Solving for x gives x = 15.

So, the length of the rectangle should be 15 cm, and the width will be (60 - 2(15)) = 30 cm.

Therefore, the dimensions of the rectangle that would maximize the enclosed area are 15 cm by 30 cm.

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Answer:

I don't see the equation for the line, but I describe the process.

Step-by-step explanation:

Let's look for a line that has the form y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).

The slope of a perpendicular line is the negative inverse of the slope of the reference line.  In this case the equation for the reference line is missing.  If it is in the form y=mx+b, take the m value, invert it, and then give it a "-" sign.  For example, if the line is y = 2x +1, the negative inverse of the slope of 2 would be -(1/2).

The new line will have this new slope [-(1/m)] to make it y = -(1/m)x + b.

To find b, use the given point of (3,-2) in the equation and solve for b:

y = -(1/m)x + b

-2 = -(1/m)*(3) + b

Then solve for b and you'll have the equation for the solution to the problem.

The number square root of 87 which is √87 lies between the two consecutive integers are 9 and 10.

Given that,

The number is square root of 87 which is√87.

We have to find the two consecutive whole numbers does √87 lies.

We know that,

In the category of numbers known as "whole numbers," all natural numbers and 0 are included. They are a subset of "real numbers," which are those that don't contain fractions, decimals, or negative numbers.

The √87 lies between √81 and √100

Which we can write as

√81<√87<√100

9<√87<10

Therefore, The number square root of 87 which is √87 lies between the two consecutive integers are 9 and 10.

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Answer:

  1260 W

Step-by-step explanation:

You want the power supplied by a 300 V source at a current of 4.2 amperes.

The source power being supplied is the product of its voltage and current:

  P = VI

  P = (300 V)(4.2 A) = 1260 W

The circuit is consuming 1260 watts.

Answer:

\(\frac{14}{19}\)

First:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

\(\frac{7}{4} \div \frac{19}{8}\)

Applying the fractions formula for division:

\(= \frac{7 \times 8}{4 \times 19}\)

\(= \frac{56}{76}\)

Simplifying 56/76, the answer is:

\(\frac{14}{19}\)

I hope this helps! :)

Answer:

the answer is 14/19

change the mixed numbers to improper fractions then that becomes 7/4 and 19/8 then multiply across 7x8=56 and 19x4=76 that gives you 56/76

Simplifying 56/76,=  14/19  

Answer:

Step-by-step explanation:

Given points

Midpoint M is

Answer:

  162

Step-by-step explanation:

You want the sum of the first 9 terms described by ...

  a[n] = 7n -17

There are several ways the sum can be found. Most straightforward is simply adding up the terms:

  For n=1, 7n-17 = -10

  For n=2, 7n -17 = -3

The remaining 7 terms are 4, 11, 18, 25, 32, 39, 46.

The sum is ...

  -10 -3 +4 +11 +18 +25 +32 +39 +46 = 162

The terms form an arithmetic sequence with first term -10 and last term 46. The sum will be the average term multiplied by the number of terms:

  ((-10 +46)/2)(9) = 18(9) = 162

The sum can be decomposed into the sums whose formulas we know:

  \(\displaystyle \sum_{n=1}^9(7n-17)=7\sum_{n=1}^9{n}-17\sum_{n=1}^9{1} =7\cdot\left.\dfrac{n(n+1)}{2}-17n\right|_{n=9}\\\\= 7\cdot\dfrac{9\cdot10}{2}-17(9)=315-153=\boxed{162}\)

The addition equation to represent Jackson's net change in money is x + (-y) = 4.63

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Jackson receives 4.63 as his change at the grocery store. He places it into a charity donation jar at the register.

WE need to Write an addition equation to represent Jackson's net change in money.

Given that :

The change received = 4.63

The Net change in money :

Let initial amount before purchase is represented by  x

The Cost of item purchased = y (negative as it is incurred)

The Net change in money:

Initial amount + cost of item purchased = change received

x + (-y) = 4.63

Therefore, an addition equation to represent Jackson's net change in money is x + (-y) = 4.63

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Answer:

3 by 1

Step-by-step explanation:

3 row and 1 column

Answer:

2 by 1.

Step-by-step explanation:

Hi.  I just took this quiz, chose 3 by 1 (per the answer above) and got it wrong.  So, my score was an 83.3%.  To save you from earning the same grade, this answer was the correct one.

Hope it helps.

The ship is approximately 27.97 km from its starting point.

Among the options provided, the closest answer is 28 km (option b).

To find the distance of the ship from its starting point, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the ship has traveled a distance of 25 km at 35° N of E, and then a distance of 15 km at 50° N of W. Let's break down the distances into their north and east components.

For the first leg:

North component = 25 km * sin(35°)

East component = 25 km * cos(35°)

For the second leg:

North component = 15 km * sin(50°)

East component = -15 km * cos(50°)  [Note the negative sign since it's N of W]

Now, let's calculate the north and east components:

For the first leg:

North component = 25 km * sin(35°) ≈ 14.3 km

East component = 25 km * cos(35°) ≈ 20.4 km

For the second leg:

North component = 15 km * sin(50°) ≈ 11.5 km

East component = -15 km * cos(50°) ≈ -9.63 km

To find the total north and east components, we add the corresponding components together:

Total North component = 14.3 km + 11.5 km ≈ 25.8 km

Total East component = 20.4 km + (-9.63 km) ≈ 10.8 km

Now, we can use the Pythagorean theorem to find the distance from the starting point:

Distance = √((Total North component)² + (Total East component)²)

        ≈ √((25.8 km)² + (10.8 km)²)

        ≈ √(665.64 km² + 116.64 km²)

        ≈ √(782.28 km²)

        ≈ 27.97 km

Therefore, the ship is approximately 27.97 km from its starting point.

Among the options provided, the closest answer is 28 km (option b).

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Answer:

$1,645

Step-by-step explanation:

235 * 7 = (total boxes) * (unit price)

235 * 7 = $1,645 (total amount)

The set of numbers {6, 8, 14} and the set {11, 14, 22} could represent the three sides of a triangle.

To determine whether a set of numbers could represent the sides of a triangle, we need to check if it satisfies the triangle inequality theorem. According to the theorem, the sum of any two sides of a triangle must be greater than the length of the third side.

Let's evaluate each set of numbers:

1. {6, 8, 14}

  The sum of the two smaller sides is 6 + 8 = 14, which is greater than the third side 14. Therefore, this set could represent the sides of a triangle.

2. {13, 20, 34}

  The sum of the two smaller sides is 13 + 20 = 33, which is less than the third side 34. Hence, this set cannot represent the sides of a triangle.

3. {11, 14, 22}

  The sum of the two smaller sides is 11 + 14 = 25, which is greater than the third side 22. Therefore, this set could represent the sides of a triangle.

4. {13, 20, 35}

  The sum of the two smaller sides is 13 + 20 = 33, which is less than the third side 35. Hence, this set cannot represent the sides of a triangle.

In summary, the sets {6, 8, 14} and {11, 14, 22} could represent the three sides of a triangle.

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Answer:24

Step-by-step explanation:

Sum of their ages is 60 yr. As such

7x + 3x = 60

10x = 60

x = 60 / 10

x = 6

The rationale is 6, therefore

Father's age is 7x = 7 × 6= 42 years

Son's age is 3x = 3 × 6 = 18 years

Difference in their ages

42 - 18 = 24 years

The largest prime factor that always divides the sum of the terms in the sequence is 37.

The sequence is finite and consists of three-digit integers.

The tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units digits of the last term are, respectively, the hundreds and tens digits of the first term.

From the above property of the sequence, we can see that each digit at the units, tens as well as hundreds place will appear the same number of times in the sequence.

Let "x" be the sum of the digits at unit place in all the terms.

The sum of all the terms is "S".

S = 111*x

S = 3*37*x

We can clearly see that the sum "S" is divisible by 37.

Hence, the largest prime factor that always divides the sum of the terms in the sequence is 37.

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The probability of getting heads at least twice is 0.5

Since we are given two-sided coin, where the probability of getting heads is equal to the probability of getting tails.NO of outcomes in this case is 2,The probability of getting a head = 1/2, similarly probability of getting a  tail is =1/2 .So when a coin is flipped three times, the sample space for the event will be (HHH, HHT, HTH, HTT, THH, THT, TTH, TTT),  H stands for head and T stands for tails, here for tossing the coin the number of outcomes is 8  .So the probability of getting at least two heads is:  4/8= 1/2 =0.5

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1/2 + 2/2 = 3/2

............................

Answer:

sorry I don't know now how to read

Answer:

x=5, y=3

Step-by-step explanation:

y=x−2;4x+y=23

Step: Solve y=x−2 for y:

Step: Substitute x−2 for y in 4x+y=23:

4x+y=23

4x+x−2=23

5x−2=23(Simplify both sides of the equation)

5x−2+2=23+2(Add 2 to both sides)

5x=25

5x/5 = 25/5(Divide both sides by 5)

x=5

Step: Substitute 5 for x in y=x−2:

y=x−2

y=5−2

y=3(Simplify both sides of the equation)

Answer:

10x+2x-1 i guess ??

Step-by-step explanation: