A, B, C, D, E, F, G & H form a cuboid.
AB= 5.4 cm, BC = 3.4 cm & CG = 6.7 cm.
Find HC rounded to 1 DP.

The first four terms of the sequence defined by the rule f(n) = n³-1 are -1, 0, 7 and 26.

According to the question,

We have the following expression:

f(n) = n³-1

Now, in order to find the first four values of the given expression, we will change the values of n from 0 to 3.

So, putting the value of n as 0, we have:

f(0) = 0³-1

0-1 = -1

Now, putting the value of n as 1, we have:

1³-1

1-1

0

Now, putting the value of n as 2, we have:

2³-1

8-1

7

Now, putting the value of n as 3, we have:

3³-1

27-1

26

Hence, the first four terms of the sequence defined by the rule f(n) = n³-1 are -1, 0, 7 and 26.

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Answer:

Yolanda bought 48 yards of ribbon, and spent 7.68 cents on it.

Step-by-step explanation:

First Step: Find out how much Yolanda spent

20.00 -12.32 = 7.68

Second Step: Divide Total Cost by Price of one Yard

7.68/0.16 = 48

Third Step: Double Check

48 x 0.16 = 7.68

I hope my answer helped you, good luck on your homework!

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:

90 m

Step-by-step explanation:

because the helicopter is 60 m up and the submarine is 30 m under so combining the two helps us identify the difference between the two objects

Answer:

[tex]12x -6[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

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

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.

The needed sample size Smaller if the margin of error .

Given,

In the question:

This question in the form of: Fill in the blanks.

So, You want to estimate the proportion of students at your university in favor of a longer spring break. changing the confidence level from 95% to 90% will decrease the needed sample size_____ if the margin of error.

Hence, The answer is smaller the margin of error.

Let's Know:

What is Confidence level?

The confidence level is the percentage of times you expect to get close to the same estimate if you run your experiment again or resample the population in the same way. The confidence interval consists of the upper and lower bounds of the estimate you expect to find at a given level of confidence.

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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: (p/6 + q) + 8

Step-by-step explanation:

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:

1.209  <  1.29  <  1.9  <  3.76

Step-by-step explanation:

Answer:  2/3+ 1/6

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

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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Answer:

No

Step-by-step explanation:

parallel is when 2 lines never touch and move in the same direction and these touch and move in different directions

Hopes this helps please mark brainliest

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:

x=26

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:

16.53

Step-by-step explanation:

Start by finding the length of the line in the center. I will call this line a. Using the Pythagorean Theorem with 12.3 as the hypotenuse:

[tex]c^2=a^2+b^2\\a=\sqrt{c^2-b^2} \\a=\sqrt{12.3^2-5.4^2} \\a=\sqrt{122.13} \\a=11.05[/tex]

Now that this line is known, x can be found. Once again using the Pythagorean Theorem:

[tex]x^2=a^2+b^2\\x=\sqrt{a^2+b^2} \\x=\sqrt{12.3^2+11.05^2} \\x=\sqrt{273.39} \\x=16.53[/tex]

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:

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:

(0,-22)

Step-by-step explanation:

Plug in 0 for x and solve for y

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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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:

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]