Fractions and Decimals
Write each fraction as a decimal.
4. //
2/5

For the given triangle, its greatest possible perimeter is 45 cm.

The term perimeter has to do with the distance round on object. In this case we do have a triangle and the triangle has three sides. The perimeter of the triangle would be the distance round the triangle.

From the statements we have;

Third side = 15

second side = x

first side = 3x

Then;

x + 15 > 3x

15 > 3x - x

15> 2x

x < 7.5

Thus;

For the first side; 3 * 7.5 = 22.5

For the second side = 7.5

Third side = 15

Greatest possible perimeter of the triangle = 22.5 + 7.5  + 15

= 45 cm

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The line equation passing through the given points and parallel to the given lines are:

Line 1: y=-4x+13...(i)

Line 2: y=2x-12...(ii)

Line 1

The first line is passing through point (1,9) and parallel to the y=4x+2 line.

Since line 1 would be parallel to line y=4x+2, hence both lines would have the same value of slope (m).

Using the standard formula of line equation, we could identify that line y=4x+2 has:

ay = bx + c, m= -b/a

y=4x+2, m=-4

We could use the line equation formula, where:

y-y1 = m (x-x1)

we use the given point (1,9) and the slope value (m=-4) to get the line equation passing through the point:

y-9 = -4(x-1)

y-9=-4x+4

y=-4x+13...(i)

Line 2

The first line is passing through point (5,2) and parallel to the y=-2x+7 line.

Since line 2 would be parallel to line y=-2x+7, hence both lines would have the same value of slope (m).

Using the standard formula of line equation, we could identify that line y=-2x+7 has:

ay = bx + c, m= -b/a

y=-2x+7, m=-2

We could use the line equation formula, where:

y-y2 = m (x-x2)

we use the given point (5,2) and the slope value (m=2) to get the line equation passing through the point:

y-2 = 2(x-5)

y-2 = 2x-10

y=2x-12...(ii)

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The correct option for the method and additional information that would prove triangle ONP and triangle MNL similar by AA similarity postulate is

option B.

B. Use rigid transformation to prove that angle NPO is congruent to angle NLM.

Angle Angle AA similarity postulate states that two triangles are similar if : two angles in one of the triangles are congruent (equal) to two angles in the other triangle.

The reason for arriving at the above selection is as follows:

According to vertically opposite angles theorem ∠ONP and ∠LNM, which are vertically opposite angles are congruent, and we can write.

                        ∠ONP ≅ ∠LNM

The required parameters are:

To find the additional information that would prove ΔONP and ΔMNL by

AA (Angle-Angle) similarity postulate.

Given from the drawing,

One (vertex) angle in one triangle is congruent to one (vertex) angle in the other triangle, that is ∠ONP ≅ ∠LNM, it is required to prove that one other angle in triangle ΔONP is congruent to a corresponding angle in triangle ΔMNL.

Prove that:

either ∠NPO or ∠NOP in ΔONP are congruent to ∠NLM or ∠NML respectively in ΔMNL by performing rigid transformations (transformations that does not change shape) on either ΔONP or ΔMNL including:

Rotating triangle ΔONP by 180° with origin at point N, to form the image ΔO'N'P'.

Translating the vertex point P' in the image ΔO'N'P', to the location of the point L in ΔMNL, and verify that the segments LN and LM in ΔMNL coincide with the segments P'N' and P'O' respectively of triangle ΔO'N'P'.

Therefore, the correct option is option B. Use rigid transformation to prove that angle NPO is congruent to angle NLM.

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Answer:

b

Step-by-step explanation:

Point A, C and F lies on the given line y = [tex](\frac{1}{4} )^{x}[/tex] .

Given in question,

y = [tex](\frac{1}{4} )^{x}[/tex]

y = [tex]4^{-x}[/tex]

Points A(-2,16),  B(2,8),  C(-1,4), D(0,4), E(1,4), F(0,1) and G(-2,0)

We will points in the equation.

For point A(-2,16)

[tex]16 = 4^{-(-2)}[/tex]

    [tex]= 4^{2}[/tex]

    [tex]16=16[/tex]       True

For point B(2,8)

[tex]8= 4^{-2}[/tex]

  [tex]=\frac{1}{4^{2} }[/tex]

  [tex]=\frac{1}{16}[/tex]

[tex]8=\frac{1}{16}[/tex]            False

For point C(-1,4)

[tex]4=4^{-(-1)}[/tex]

  [tex]=4^{1}[/tex]

[tex]4=4[/tex]             True

For point D(0,4)

[tex]4=4^{-0}[/tex]

[tex]4= 1[/tex]            False

For point E(1,4)

[tex]4=4^{-1}[/tex]

[tex]4=\frac{1}{4}[/tex]           False

For point F(0,1)

[tex]1=4^{-0}[/tex]

[tex]1=1[/tex]            True

For point G(-2,0)

[tex]0=4^{-(-2)}[/tex]

  [tex]= 4^{2}[/tex]

[tex]0=16[/tex]          False

Hence, only point A,C and F satisfies the equation.

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A situation which could be represented by this graph is: A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 40 minutes.

In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively such as time (min) and distance (km).

In this scenario, the time (in minutes) was plotted on the x-axis of the graph while the distance covered (in kilometers) was plotted on the y-axis of the graph.

By critically observing the graph (see attachment), we can reasonably and logically deduce that the first student walked a distance of 1.5 kilometer to his or her friend’s house in 20 minutes, then, they both walked at a constant speed for 5 seconds before increasing their speed, covering another distance of 1.5 kilometer to their school within 40 minutes (60 - 20 minutes).

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Complete Question:

The graph below shows distance over time. Which of these situations could be represented by this graph?

answer choices

A student walks 1.5 km to a friend’s house in 40 minutes. The two students then walk another 1.5 km to school in 20 minutes.

A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 40 minutes.

A student walks 1.5 km to a friend’s house in 30 minutes. The two students then walk another 1.5 km to school in 30 minutes.

A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 60 minutes.

Answer: (p/6 + q) + 8

Step-by-step explanation:

The function f (x) has steeper slope.

So, The Paige is correct.

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The input output pairs of f (x) are (- 6, 5/2) and (- 1, 17/2)

And, The input output pairs of g (x) are (2, 13/3) and (6, - 1)

Now,

Find the slope for f (x) as;

m₁ = (17/2 - 5/2) / (- 1 - (-6))

m₁ = (15/2) / 5

m₁ = 15/10

m₁ = 3/2

And, Slope for g (x) is;

m₂ = (- 1 - 13/3) / (6 - 2)

m₂ = (- 16/3) / 4

m₂ = - 16 / 12

m₂ = - 4 / 3

Thus, The function f (x) has steeper slope.

So, The Paige is correct.

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Answer:

125 in simplest form is 1/8.

Step-by-step explanation:

Answer:

43446

Step-by-step explanation:

52 weeks in an year

835.5 × 52 = 43446

Andre used 2983 gallons of liquid all through this month.

Given;

Andre used 785 gallons of water at his house in a single month. In a gallon, there are roughly 3.8 liters.

To get the measurement that is closest to the number of liters Andre used during this month;

The total gallons of water used in a month = 785 gallons

The quantity of water in a single gallon = 3.8 liters

Therefore, the number of liters Andre used during this month;

U = total gallons of water used in a month * quantity of water in a single gallon

U = 785 * 3.8

U = 2983

Hence, the number of liters Andre used during this month is 2983 gallons.

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Answer:

Step-by-step explanation:

105 min

60 min in a hour and then 3/4 of a hour is 45 min.

Total: 105 minutes

Answer:

As a fraction in simplest form it SHOULD be 24 over 25.

Step-by-step explanation:

"0.96 as a fraction (simplified form)" MagnetsAndMotors (Dr. B's Other Channel)

Answer:

24/25

Step-by-step explanation:

0.96

By counting the numbers after the decimal point which is two.

so we will write: 96/100, since hundred has to two zero.

Then we will divide 96/100 to it simplest form which is 24/25

Answer: C

Step-by-step explanation:

Answer:

10 + 5i

Step-by-step explanation:

[tex] \rm \implies \sqrt{25} + \sqrt{ - 81} + \sqrt{25} - \sqrt{ - 16} \\ \\ \rm \implies 5 + 9i + 5 - 4i \\ \\ \rm \implies 10 + 5i[/tex]

The simplest form of the given expression is -19x + 10.

The process or product of making something less complicated and thus easier to do or understand is called simplification. Replace 'of' with 'Multiplication' and '/' with 'Division.' Always perform operations in the order specified by 'BODMAS.' Division and multiplication are both given equal weight (Starting from left) Subtraction and addition have the same.

Given that

(-10x+2) + (-9x+8)

We have to simplify the given expression

= -10x + 2 - 9x + 8

= (-10x - 9x) + (2 + 8)

= -19x + 10

Therefore the simplest form of the given expression is -19x + 10

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Answer:

Step-by-step explanation:

18 Vans. That will hold 162 Students if 9 student per Van

19 Vans since we need 163.

Answer: 19 Vans, and All but one will be full the one that isn't full holds one Student.

Answer:

Step-by-step explanation:

Given isosceles triangle DOG with DO≅GO, DO = (n²+1), GO = (4n-2) and DG = (2n -3), you want the value of n and the lengths of the sides.

The expressions for the congruent sides will have the same value, so ...

  DG -GO = 0

  (n² +1) -(4n -2) = 0

  n² -4n +3 = 0 . . . . . . . . simplify

  (n -3)(n -1) = 0 . . . . . . factor

  n = 1 or 3 . . . . . . . . values of n that make the factors zero

The length of leg DG is ...

  2n -3 = 2{1, 3} -3 = {2, 6} -3 = {-1, 3}

Side DG cannot be negative, so the "solution" n = 1 is extraneous.

  GO = 4n -2 = 4(3) -2 = 10

The number is 3, the leg lengths are DO = OG = 10, and the base length is DG = 3.

Answer:

(0,-22)

Step-by-step explanation:

Plug in 0 for x and solve for y

Answer:

[tex]12x -6[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Answer:

Step-by-step explanation:

x=26

The value of the exponent 3.6 x 10^7 + 2.1 x 10.^7 is D. None of the above.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this case, the value of 3.6 x 10^7 + 2.1 x 10^7 will be:

= 3.6 x 10^7 + 2.1 x 10.^7

= 5.7 × 10^7

Therefore, the correct option is D.

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Answer:

64000

Step-by-step explanation:

When you are rounder you must look at the last number to determine if you are rounding up or down.

Answer:

perimeter = 22 km and area = 18 km^2

Step-by-step explanation:

First I found and labeled the missing lengths. For the one at the top of the shape, I added 1 + 2 + 3 to get the length, since those are what make up the length.

Afterwards I just added up all the side lengths to get the perimeter. 2+6+2+3+2+3+1=22, so the perimeter is 22 km.

To find the area, I split the shape into two, labeled 1 and 2. (Check the image attached) To find the area you multiply length by width, so i did that for shapes 1 and 2. For shape 1, I did 2 x 6 and got 12, and for shape 2 I did 3 x 2 to get 6. To get the total area of the entire shape, add these two areas. 12 + 6 = 18, so the total area is 18 km^2. (km squared)

let me know if anything is confusing :-))

Answer:

1.209  <  1.29  <  1.9  <  3.76

Step-by-step explanation:

From the calculation, the original number is obtained as 84.

We know that we are told in the question that in the question, we are required to obtain the number and that is what we are going to do below.

Let the tens digit be T and let the units digit be U

We can then write

10U+T = 10T+U-36

Since the reversed number is 36 less than the original number.

Then;

9U = 9T -36

Dividing both sides of the equation by  9

U = T -4

U=2U-4

U=4

T = 8

It then follows that the original number is 84.

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Answer:

y = - x

Step-by-step explanation:

-y = -x is the same as y=x and to get an equation that is perpendicular to another one you just have to find the reciprocal (opposite) number of the SLOPE. The reciprocal of 1 is -1, therefore the perpendicular equation to -y=-x is y=-1

2944 distinct 5-letter strings can be created using the letters a, b, c, d, and e if repetition is allowed but the letter a appears at most twice

Given that

form 5-letter distinct strings can be created using the letters a,b,c,d, and e, and repetitions are allowed but the letter a appears at most twice

let's consider that letter a is not there in the string

each letter is repetitive then it is [tex]4^{5}[/tex]

now letter a is considered once

5c1 ×[tex]4^{4}[/tex]

now letter a is repetitive twice

5c2 × [tex]4^{3}[/tex]

[tex]4^{5}[/tex] + 5c1 × [tex]4^{4}[/tex] + 5c2 × [tex]4^{3}[/tex]

1024+ 1280 + 640 = 2944

2944 distinct 5-letter strings can be created using the letters a, b, c, d, and e if repetition is allowed but the letter a appears at most twice

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Answer:  2/3+ 1/6

Step-by-step explanation: 2/3= 4/6   4/6 + 1/6 = 5/6