QUESTION 2 2.1 Given the quadratic sequence: 20; 12; 10; 14;. 2.1.1 Determine an expression for the nth term of the pattern in the form T₁ = an² + bn+c. 2.1.2 The FIRST differences form an arithmetic sequence. Determine between which successive terms in the quadratic sequence, the FIRST difference will be 148. 2.1.3 Determine the smallest value of n for which S,> 10140 in the arithmetic sequence. 2.2. If Σ(r+b) = 10a, determine b in terms of a.​

By SAS property, ABC ≅  DCB.

In this question we have to proof ABCD has congruent diagonal. By SAS property and reflexive property it can be proved as follows:

Given:

ABCD is a rectangle.

Prove:

Diagonal AC ≅ Diagonal BD

From the question,

As we can see that, ABCD is a rectangle, it is also a parallelogram.

Thus, ABCD is a parallelogram, opposite sides of a parallelogram are congruent.

⇒ AB ≅  DC  

⇒ BC ≅ BC (Reflexive Property of Congruence)

Hence, ∠ABC and ∠DCB are right angles by the definition of rectangle.

∠ABC ≅ ∠DCB (all right angles are congruent)

Therefore, by SAS property,  ABC ≅  DCB.

⇒ segment AC ≅ segment BD

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Answer:

♣ = parallelogram side theorem

♦ = SAS

♠ = CPCTC

(Correct On Edgen)

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What are we solving for?}[/tex]

[tex]\mathsf{56 = w(w + 10) }[/tex]

[tex]\huge\textbf{How are we going to solve for the}\\\\\huge\textbf{equation?}[/tex]

[tex]\mathsf{56 = w(w + 10)}[/tex]

[tex]\mathsf{w(w + 10) = 56}[/tex]

[tex]\mathsf{w(w) + w(10) = 56}[/tex]

[tex]\mathsf{w(w) + 10(w) = 56}[/tex]

[tex]\mathsf{w^2 + 10w = 56}[/tex]

[tex]\huge\textbf{Subtract \boxed{\bf 56} to both sides:}[/tex]

[tex]\mathsf{w^2 + 10w - 56 = 56 - 56}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{w^2 + 10w - 56 = 0}[/tex]

[tex]\huge\textbf{Factor the left side of the equation:}[/tex]

[tex]\mathsf{(w - 4)(w + 14) = 0}[/tex]

[tex]\mathsf{(w - 4)\times(w + 14) = 0}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{w - 4 = 0\ or\ w + 14 = 0}[/tex]

[tex]\mathsf{w = 4\ or \ w = -14}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{\mathsf w = 4\ or \ \mathsf w = -14}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

b

Step-by-step explanation:

I'm quite positive its b hopefully:)!

Answer:

B.b if you follow the formula and chances are very high for it to be b

A pole vaulter have to run at 18m/s speed.

According to the statement

The typical pole for pole vaulting is 17 feet long

we use the formula

1/2 m(v)^2 = mgh

Now rearrange the terms

(v)^2 = 2gh

here g = 10 and h = 15 then

substitute the values

(v)^2 = 2*10*15

v = 17.32

So, A pole vaulter have to run at 18m/s speed.

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There is a crossword that has three squares that need to be filled, how many possible three letter arrangements is 26!/23.

To find the number of possible three letter arrangements.

An arrangement of things in a certain sequence is what we refer to as a permutation. The constituents or components of sets are presented in this section in a sequential or chronological fashion. A coming together or merging of several parts or characteristics in which each of the constituent parts or traits retains its unique identity.

Given that:

26 possible letters

assuming you can repeat them

26*26*26

no listed

ok, lets assume that you can't repeat them

that is 26 times 25 times 24 (because you used 1 each time)

that is 26!/23 (because 26*25*24*23!=26!)

Hence, the number of possible three letter arrangements is 26!/23.

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Option is missing

A.26!

B.26!/3!

C.23!

D.26!/23

Answer:

240 yards lost, if I understand the question correctly.

Step-by-step explanation:

If I read this correctly the team lost 85 yards lost in 8 plays.  Then they tripled their loss on the next 17.  3 x 85 = 255 yards lost in the last 17 plays.

Total yards lost was (85 + 255) = 240 yards in 22 plays.

The Canadian goose flew for 4 hours and the Great blue heron flew for 10 hours

An equation is an expression that shows the relationship between two or more variables and numbers.

Let a represent the time flown by the goose and b represent the time flown by the heron. Hence:

a + b = 14    (1)

Also:

20a + 10b = 180   (2)

From equation 1 and 2:

a = 4, b = 10

The Canadian goose flew for 4 hours and the Great blue heron flew for 10 hours

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ANSWER :          -7x + 14

EXPLANATION, to reverse division multiply

Answer: No solutions

Step-by-step explanation: there would be no solutions, because these equations have the same slope and different y-intercepts, so they would end up being parallel from each other, and would never intersect or be equivalent.

Answer:

No solution.

Explanation:

Given equations:

(1) y - 4x = -3

(2) y = 4x + 7

Substitute equation 2 into 1

y - 4x = -3

4x + 7 - 4x = -3

7 = -3

As L.H.S ≠ R.H.S, There are no solution.

The lines are parallel and do not intersect each other. Their slope is same.

The bottom edge of the window is 8 inches above the ground, computed using the Pythagoras Theorem.

According to the Pythagoras Theorem, in a right triangle, the square of the hypotenuse, that is, the side opposite to the right angle is equal to the sum of the square of the legs, that is, the two other sides.

If in a right triangle, c is the hypotenuse, and a and b are the two legs, then by the Pythagoras Theorem, we can write:

a² + b² = c².

In the question, we are informed that a building meets the ground at a right angle. The top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground.

We are asked to draw a diagram that represents the situation and find the height of the bottom edge of the window from the ground.

We assume the building to be DB, meeting the ground BC at a right angle. At point C, the ladder meets the ground and meets the bottom edge of the window at point A.

The diagram is attached.

Now, we get a right triangle ABC, right-angled at B.

By Pythagoras' Theorem, we know that:

AB² + BC² = AC²,

or, AB² + 6² = 10²,

or, AB² = 10² - 6² sq. inches,

or, AB² = 100 - 36 sq. inches,

or, AB = √64 inches,

or, AB = 8 inches.

Thus, the bottom edge of the window is 8 inches above the ground, computed using the Pythagoras Theorem.

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The provided question is incomplete. The complete question is:

"A building meets the ground at a right angle. The top of a 10-foot ladder is placed against the bottom edge of a window in the building, and the base of the ladder is placed 6 feet from where the building meets the ground. Draw a diagram that represents this situation. How far up from the ground is the bottom edge of the window?"

Using the dimensions of a reduced rectangle and one given measurement of an original rectangle:

Reduction is a type of dilation that reduces the size of an original figure to form a new figure that is similar to the original. The corresponding lengths of both figures are therefore proportional.

Assuming the dimensions of the reduced rectangle are 10 cm by 4 cm, and the length of the original rectangle is given as 8 cm, to find the missing measure (x), do the following:

Set up a proportion using the corresponding parts

10/8 = 4/x

Solve the proportion using cross products to find x:

10x = (8)(4)

10x = 32

x = 32/10

x = 3.2 cm

The missing length is 3.2 cm.

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Answer:

Using the given measurements of both figures, set up a proportion that has the corresponding parts in the same position. Then solve the proportion using cross products to find the value for the unknown.

Step-by-step explanation:

Answer: 17/y-5

Step-by-step explanation:

Answer:

yxthgggggyhfffghgggggvggvvggvv

Option 2. The equation of the parabola is given as y = one eighthx² + 5

We have the coordinate plane to be passing through the graph at point C on the y axis. This is used to represent the slope.

Hence the slope is 5

The equation of the line is given as  y=x²+C

Hence we can see that there is a rising slope. So the answer is Option 2.

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The quotient of the synthetic division is x^3 + 3x^2 + 4

The bottom row of synthetic division given as:

1 3 0 4 0

The last digit represents the remainder, while the other represents the quotient.

So, we have:

Quotient = 1 3 0 4

Introduce the variables

Quotient = 1x^3 + 3x^2 + 0x + 4

Evaluate

Quotient = x^3 + 3x^2 + 4

Hence, the quotient of the synthetic division is x^3 + 3x^2 + 4

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Answer:

Step-by-step explanation:

The displacement is 90.7 meter from initial point.

According to the statement

Aster first walks 70m in the direction of 37 degree north of east

Aster walks 82m 20 degree south of east

Aster finally walks 28m in the direction of 30 degree west of north

We use

β= 37 degree +(30 degree −20 degree) = 47 degree

We can use cosine law to solve for R.

R = ((A)^2 + (B)^2 + 2ABcosβ)^1/2

R = ((70)^2 + (28)^2 + 2*70*28cos47)^1/2

R = (4900 + 784 + 3920*0.682)^1/2

R = (4900 + 784 + 2673.5)^1/2

R = (8357.5)^1/2

R = 90.7 m

So, The displacement is 90.7 meter from initial point.

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The value of  [tex]k = 2P/x^2[/tex]

We are aware that an object's location might cause it to store energy. When a bow and arrow are used, the energy that is stored when the bow is pulled is what gives the arrow its kinetic energy when it is released.

when a spring is moved away from its equilibrium position, it gains some energy, which we can notice by the tension our hands experience as we stretch it. Potential energy is a type of energy that arises from a change in its position or condition, according to our definition

We know that P=1/2kx^2

Now solving for k

2P = kx^2

Therefore

k = 2P/x^2

Hence the value of k is 2P/kx^2

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Answer: D

Step-by-step explanation:

Where the x-intercept is 0.25.

Answer:

5/9

Step-by-step explanation:

4+5=9 and there are 5 boys

The value of n is 99

Integers are the set of numbers including all natural numbers and 0. They are part of the real numbers that do not include fractions, decimals, or negative numbers. Counting numbers are also considered whole numbers.

Natural numbers together with zero (0) are referred to as whole numbers. We know that natural numbers refer to the set of counting numbers starting from 1, 2, 3, 4 and so on. Simply put, integers are a set of numbers without fractions, decimals, or even negative integers. It is a collection of positive integers and zero. Or we can say that integers are the set of non-negative integers.

Integers are the set of natural numbers togethe with the number 0. In mathematics, the set of integers is given as {0, 1, 2, 3, ...}, denoted by the symbol W.

W = {0, 1, 2, 3, 4, …}

All natural numbers are integers.

All integers are real numbers.

It is given that If n a whole number, and 0.01 is between 1/n and 1/n+2, then we need to find the value of n.

1/n+2 < 0.01 < 1/n

1/n+2 < 1/100 < 1/n

n< 100 < n +2

Put n = 99, then we get

99 < 100 < 101

Hence the value of n is 99.

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Step-by-step explanation:

x=8-y

2x-y=7

2(8-y)-y=7

16-2y-y=7

-3y=-9

y=3

x=8-y

x=8-3=5

Answer:

Hello

Step-by-step explanation:

Méthode par combinaisons linéaires:

[tex]\left\{ \begin{array}{ccc|c|c}x+y&=&8&1&-2\\2x-y&=&7&1&1\\\end {array} \right.\\\\\\\left\{ \begin{array}{ccc}3x&=&15\\-3y&=&-9\\\end {array} \right.\\\\\\\boxed{\left\{ \begin{array}{ccc}x&=&5\\y&=&3\\\end {array} \right. }\\[/tex]

Proof:

5+3=8 and 2*5-3=7

The population for this study is all registered voters from New York City.

What  is the population for a study?

it is given that the poll has been carried out among 1000 registered voters from New York City. These 1000 people have been selected randomly from the population of the study.

The available study subset of the target population for a study, for instance, schizophrenics in the researcher's hometown, is known as the study population or population of the study. The sample chosen for the study is known as the study sample.

Study Population In This Case

In this case, out of all the New Yorkers, only the registered voters of the city are eligible for making the target subset. Hence, the registered voters of the New York city make the study population. Furthermore, since 1000 random registered voters are chosen for the poll, those 1000 registered voters make the study sample.

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The object represented by h(t) = -4.9t² + 40t + 20 would take 4.082 seconds to reach it's maximum height.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

The height (h) is represented by:

h(t) = -4.9t² + 40t + 20

The maximum height is at h'(t) = 0, hence:

h'(t) = -9,8t + 40

-9.8t + 40 = 0

t =  4.082

The object represented by h(t) = -4.9t² + 40t + 20 would take 4.082 seconds to reach it's maximum height.

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The ratio of the tapestries' height to breadth is 3:2 when using full integers.

The ratio of two numbers is used to indicate proportions.

A/b, for example, is the ratio of a to b.

Given the subsequent sides, it is a tapestry.

Height = 1.5 m

Width = 1 m

So, height : width= 1.5:1

or, the fraction = 1.5/1=15/10= 3/2

or, it can be said 3:2

Since entire numbers are used, the ratio of the tapestries' height to breadth is 3:2.

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The predicted value of the car in the year 2007 is 13310

Given the purchased value of new car in 1998 is  $ 32,900

The value of car was $ 19,900 in the year 2003

We need to find the value of the car in the year 2007

Let the predicted value be x

The exponentially constant rate in 2003

32900*x^5 = $19900 (∵ x^5 = 5 years difference that is 1998 to 2003 )

Now In year 2007

2007 = 32900*x^9

x = 0.9043

The predicted value of the car is 0.09043

But we want the predicted value in 2007

Therefore ,

In 2007 ≈ x = 13310.02

Rounding off to the nearest dollar is $13310

Therefore the predicted value of the car in 2007 is $13310

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: \sqrt[4]{x - 4} = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: x - 4 = (3) {}^{4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x - 4 = 81[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 81 + 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 85[/tex]

So, the correct choice is 85

Answer:

Step-by-step explanation:

4√(x-4) = 3

√(x-4) = 3/4

Square both sides:

x - 4  = 9/16

x = 4 + 9/16

x = 4 9/16.

Answer:

Either 9.71 (adjacent to 36°) or 7.05 (opposite 36°)

Step-by-step explanation:

The question doesn't specify which leg is under question.  Is it the adacent leg or the opposite leg?  I'll assume adjacent.

We can use the acronym

SOHCAHTOA which is a helpful mnemonic for remembering the definitions of the trigonometric functions.  For an angle other than the right angle, the following relationships are defined.

SOH:  S is sine = Opposite/Hypotenuse

CAH:  C is cosine = Adjacent/Hypotenuse

TOA:  T is tangent = Opposite/Adjacent

For a side adjacent (A) to the 36° angle, we can use

Cosine = Adjacent/Hypotenuse

Since we know the hypotenuse (12) we can find A:

Cosine(36) = A/12

A = Cosine(36)*12

A = (0.809)*12

Adjacent = 9.71

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

If the opposite leg is calculated, we would use

Sine= Opposite/Hypotenuse

Sine(36) = Opposite/12

O = (0.5877)*12

Opposite = 7.053

128000.

Let the three frithe ends x, y, z x is the first friend y is secmy ond friend

z is third friend

X+y+z=128000  

x=4z    

z=3y    

x=4(3y)=12y   put values of x and z in the first equation we got

12y+y+3y=128000

16y=128000

= 128000 - = 8000 16

Put the y value in equation 3 wee got

z=3*8000=24000

Put the z value in equation 2 we got

x=4*24000=96000

8000+24000+96000=128000.

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The item which yield the greatest level of accuracy to the true weight of rock with the least error is bricks.

A rock refers to a solid substance formed from the fusion of organic minerals.

Therefore, bricks is the item which yield the greatest level of accuracy to the true weight of rock with the least error.

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