Prove the following.
If VZ ≅ VY and WY ≅ XZ , then VW ≅ VX .

Answer:

3

Step-by-step explanation:

if m is the number of months

Beckett: 90 + 25m

Lakota Hills 45 + 40m

so 90 + 25m = 45 + 40m

40m - 25 = 90 - 45

15m = 45

m = 45/15 = 3

1) The mathematical expression that represents this scenario is T = 40/5.

2) The value of T in the equation is $8.

A mathematical expression is a mathematical statement that has two different numbers (known or unknown) and at least one operation.

For instance, an equation is a mathematical equation showing that two variables are equal.

The payment for a subway pass = $55

The number of subway rides = 5

The total amount deducted from the value of the pass = $40

This implies that each subway ride costs = $8 ($40/5)

If T is the cost of a ticket and the total cost incurred for 5 subway rides is $40, therefore T = 40/5.

Thus, the mathematical expression that represents this scenario is T = 40/5.

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Answer:

3[tex]x^{2}[/tex] + 4x + xy

Step-by-step explanation:

Basically just combining like terms

[tex] \large \bf \implies{ {3x}^{2} + xy + 4x} \\ [/tex]

Step 1) Combine the like terms

Step 2) Add/Subtract the terms

Step 3) We have got the answer

Answer: give me the context please

Step-by-step explanation:

The distance between pair of parallel lines with the given equations

x=-2 x=5 is 7 units

Parallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.

The fundamental characteristics listed below make it simple to recognize parallel lines.

The distance between parallel lines on a graph can be given as x1 - x2 as both are equidistance from y for which y has been cancelled.

here x1 =5 and x2 = -2

So, x1 - x2 = 5 -(-2)

                 = 5 + 2

                 = 7

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Answer:

-7

Assuming that "It can be any"

The eighth term of the given geometric sequence is 256/6561.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: 2/3, 4/9, 8/27...

As we can observe, each successive term of the geometric sequence is 2/3 of the previous one.

Thus, r = 2/3  and a₁ = 2/3.

The formula used to find the nth term of a geometric sequence is given by: [tex]a_n=a_1(r^{n-1})[/tex]

For n = 8, [tex]a_8=\frac{2}{3}(\frac{2}{3})^7=\frac{2}{3}^8=\frac{256}{6561}[/tex]

Thus, the eighth term of the given geometric sequence is 256/6561.

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The following set of numbers, 8, 15, and 17, can be the measures of the sides of a triangle, specifically a right triangle.

To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 8, b = 15, and c = 17

a + b > c     8 + 15 > 17     23 > 17     True

a + c > b     8 + 17 > 15      25 > 15     True

b + c > a     15 + 17 > 8     32 > 8     True

To know what type of triangle based on the length of its side:

1. Take the sum of the squares of the two smaller sides.

8^2 + 15^2 = 289

2. Compare it to the square of the largest side.

17^2 = 289

289 = 289

If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.

if they are equal, it is a right triangle

if they are smaller, then it is an obtuse triangle.

Hence, 8, 15, and 17 can be the measure of the sides of a right triangle.

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The solutions of the given polynomial equation p⁴+32=12 p² is p = {-2√2, 2√2, -2, 2}.

The given polynomial equation is:

p⁴+32=12 p²

Subtract both sides by 12 p²

p⁴ + 32 -12 p² = 12 p² 12 p²

p⁴ -12 p² + 32 = 0     ...... (1)

Let x = p², then equation (1) becomes

x² -12x + 32 = 0  

This is a quadratic equation.

Factorize:

   x² -12x + 32 = 0  

⇔ (x - 8 ) (x - 4) = 0

Take:

x - 8 = 0

x = 8

p² = 8

p = ±√8 = ±2√2

Take:

x - 4 = 0

x = 4

p² = 4

p = ±√4 = ±2

Hence the solution is p = {-2√2, 2√2, -2, 2}

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Answer: c=-0.01

Step-by-step explanation:

Inequality is [tex]p + 31 \ge 85[/tex]

Solution is [tex]p \ge 54[/tex]

===============================================

Explanation:

p = number of pages left to read

31 = number of pages already read

p+31 = total number of pages (unread + read)

This total must be 85 or larger, so that's how we end up with [tex]p+31 \ge 85[/tex]

To solve this inequality, we subtract 31 from both sides to end up with [tex]p \ge 54[/tex] which means Jen still needs to read at least 54 pages.

Answer:

875

Step-by-step explanation:

215+200+185+170+155+140+125+110+95+80+65+50+35+20+5+(-10)+(-25)+(-40)+(-55)+(-70)+(-85)+(-100)+(-115)+(-130)+(-145) =875

I'm sure there's an easier way to do this, but if you want a correct answer, here you go. Have a good day!

Answer:

875

Step-by-step explanation:

I think hope it right

The simplified form of the expression is -29y - 8

Linear equations are equations that has a linear degree of 1. For instance the expression y =mx + b has a linear degree of 1.

Given the linear equation below:
-7 (3y)+2(-4y+-4)

When solving linear equation, first we will need to expand the expression first.

-7 (3y)+2(-4y+-4)

-21y + 2(-4y) + 2(-4)

Simplify the resulting expression

-21y -8y. - 8

-29y - 8

Hence the simplified form of the expression is -29y - 8

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Answer:

?

Step-by-step explanation:

The range of each amazon box is 1.6035m

According to the question we have been given that

        height of the conveyer belt = 1.4m

        Speed of the belt = 3m/s

We need to find the range of the amazon box, that is we have to find the distance.

Formula for distance is ,  d = speed * time

We have been given the value of speed we need to find the value of time. For that we will use the formula,

                                     h = [tex]\frac{1}{2} g t^{2}[/tex]

where,         h = height

                   g = acceleration due to gravity = 9.8m/s²

                    t = time

Putting the required value for t we get,

        t = [tex]\sqrt{\frac{2h}{g} } \\[/tex]

          = [tex]\sqrt{\frac{2(1.4)}{9.8} } \\[/tex]

          = √0.286

          = 0.5435 s

Putting the value of time in distance formula we get,

                d = 3 * 0.5435 m

                   = 1.6035 m

Hence the range of each amazon box is 1.6035m

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The base and height of triangle are 25 and 22 feet.

We are given the relation between base and height of triangle. Let us represent height with h and base with b. The equation relating the two quantities is as follows -

h = b - 3

Now, the area of triangle is given  by the formula -

Area = 1/2 × base × height

Keep the values in formula to find the base of triangle

275 = 1/2 × b × (b-3)

550 = b × (b-3)

b² - 3b - 550 = 0

b² + 22b - 25b - 550 = 0

b (b + 22) -25 (b + 22) = 0

(b + 22) (b - 25) = 0

b = -22 and 25

As the value of base can not be negative, so, the base of triangle is 25 feet.

Calculating height of triangle-

Height = Base - 3

Height = 25 - 3

Height = 22 feet

Hence, the base and height of triangle are 25 and 22 feet.

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Step-by-step explanation:

Lets understand the situation,

This means Each team can have 3, 4 or 5 people.And 21 people take part.

we have to find How many different possible arrangements of teams are there.

Situation 1.

situation 2.

Situation 3.

situation 4.

Answer:

The large box weighs 18.75 and the small box weights 15.75

Step-by-step explanation:

We are looking to find 2 variables so we will need two equations.

Let l = the large box weight

Let s = the small box weight

7l + 9s + 273                   5l +3s = 141

I want to add these two equations together and have one of the variables be eliminated.  The way both equations are written now, neither variable will drop out.  I see that 9 is a multiple of 3.  If I multiply the second equation all the way through by - 3, the s variable will be eliminated.

-3(5l +3s) -3(141)  Multiple everything by -3

-15l -9s = -423  Now I will add this to the original equation 7l + 9s = 273

7l + 9s = 273

-8l = -150  Divide both sides by -8

l = 18.75  This is the weight of the large box.

Plug in 18.75 to either of the ordinal equations to find the weight of the small box.

5l + 3s = 141

5(18.75) + 3s = 141  Distribute the 5

93.75 + 3s = 141  Subtract 93.75 from both sides

3s = 47.25  Divide both sides by 3

s = 15.75

Check:

Plug in 15.75 for s and 18.75 for l into both of the original equation to see if they equal.

7l + 9s = 273

7(18.75) + 9(15.75) =273

131.25 + 141.75 = 273  Checks

5l + 3s = 141

5(18.75) + 3(15.75) = 141

93.75 + 47.25 = 141

141 = 141 Checks

==================================================

Work Shown:

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

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

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

x+2 = 0 or C-x+2 = 0

x = -2 or x = C+2

If we want one solution only, then we must make C+2 = -2 which solves to C = -4

If C = -4, then x = C+2 = -4+2 = -2 which matches with the first solution mentioned. If C is anything else but -4, then we'd have two different solutions (eg: C = 10 leads to x = C+2 = 12 as the other solution)

Answer:

Step-by-step explanation:

triangles are similar so:

[tex]\frac{10}{10+14} = \frac{x}{36}[/tex]

24x=360

x=15

The best friend is the faster runner as his speed is 51.28 m/s while my speed is 48.78 m/s.

Speed is defined as the distance travelled by someone or something in unit time. The SI unit of speed is meters per second. The speed is calculated by dividing the distance travelled by the total time taken to travel said distance.  

Given the distance travelled by both of the friends is 400 meters.

Now The first friend travels this distance in 8.2 seconds:

Therefore speed is calculated by distance ÷ time

or, speed = 400 ÷ 8.2

or , speed = 48.7804... m/s

or, speed ≈ 48.78 meters per second

And the best friend travels this distance in 7.8 seconds:

Therefore speed is calculated by distance ÷ time

or, speed = 400 ÷ 7.8

or , speed =51.2820... m/s

or, speed ≈ 51.28 meters per second

Therefore by comparing both the speeds we can conclude that the best friend is the faster runner.

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Answer: x<1

Step-by-step explanation:

add 12 to both sides, divide by 2 on both sides.

Answer:

1 is 6 pages, 7 minutes is 24 pages, 14 minutes is 45 pages

Step-by-step explanation:

the unite rate is 3

The arithmetic series 1+5+9+. . . . . +41+45 can be expressed in summation notation as [tex]\sum\limits^{12}_{n=1} {(4n-3)}[/tex]

The given arithmetic series:

    1+5+9+. . . . . +41+45

To write the series in summation notation:

Find the common difference (d) of the series.

d = 5 - 1 = 4

Recall the formula for the nth term in an arithmetic sequence:

a(n) = a(1) + (n-1) . d

Substitute a(1) = 1 and d = 4:

a(n) = 1 + (n-1) . 4

a(n) = 4n - 3

Find n that leads to a(n) = 45

a(n) = 4n - 3

45 = 4n - 3

4n = 48

n = 12

Thus, the lower limit of the summation is n =1, and the upper limit is n = 12

Now write in summation notation as:

[tex]\sum\limits^{12}_{n=1} {a(n)}= \sum\limits^{12}_{n=1} {(4n-3)}[/tex]

This summation notation can be further simplified using the properties of summation operator:

[tex]\sum\limits^{12}_{n=1} {(4n-3)}=\sum\limits^{12}_{n=1} {4n}-\sum\limits^{12}_{n=1} {3}[/tex]

[tex]=\sum\limits^{12}_{n=1} {4n}-12\times3[/tex]

[tex]=\sum\limits^{12}_{n=1} {4n}-36[/tex]

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The equation is 24.36 = 5.31 + 5 * x  and the cost of each bag of lemon is $3.81

The given parameters are:

The above means that

Total = Cheese + Bags of lemon * 5

This gives

24.36 = 5.31 + 5 * x

Collect the like terms

So, we have

24.36  - 5.31 = 5 * x

Evaluate the like terms

So, we have

19.05 = 5 * x

Divide through by 5

So, we have

x = 3.81

Hence, the equation is 24.36 = 5.31 + 5 * x  and the cost of each bag of lemon is $3.81

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The correct option is F. 25.

The total number of gallons of gas Amanda will use to travel all the distances is 25.

The amount of between two things, or the state of being far apart, is defined as distance. A five-foot distance between two tables is an example of distance. The difference of the two sides of an issue is an example of distance.

Now, as per the given question;

Amanda plans to drive 160 miles, 235 miles, 185 miles, and 220 miles.

Thus, the total distance ravelled by Amanada is;

= 160 miles + 235 miles + 185 miles + 220 miles

= 800 miles

Amanada's car has the average of 32 miles per gallon of gas.

Thus, the car will cover a total of 32 miles for each gallon of gas.

Thus,

The number of gallon of gas requires = Total distance/(distance travelled for one gallon of gas)

The number of gallon of gas requires = 800/32

The number of gallon of gas requires = 25

Therefore, the gas required to travel a total distance of 800 miles is 25 gallons.

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The common difference d is 6 and the first term a1 is 20.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same value.

The formula of Arithmetic progression is

a(n) = a1 + (n - 1)d

given that the two terms of arithmetic sequence,

a3 = 32 and a7 = -8.

now, find the common difference d.

a(n) = a1 + (n - 1)d

Let take a(n) = a7 and a1 = a3.

a7 = a3 + (7 - 3)d

a7 = a3 + 4d

now substitute the values of a6 and a4

-8 = 32 + 4d

-8 + 32 = 4d

d = 24/4

d = 6

so, the common difference d is 6.

then, find the term a1.

take the formula

a(n) = a1 + (n - 1)d

now, substitute a(n) = a3 and d = 6.

32 = a1 + (3-1)d

32 = a1 + 2d

32 = a1 + 2(6)

32 = a1 + 12

a1 = -12+32

a1 = 20.

so, the first term a1 is 20.

Hence, the common difference d is 6 and the first term a1 is 20.

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Answer:

y = -1/4 -x/2

Step-by-step explanation:

The solution is attached.