use the graph and the translation (x,y) = (x+3, y+1)

Answer:

a₁ = - 11 and d = 3

Step-by-step explanation:

the sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

given S₄₀ = 1900 , then

S₄₀ = [tex]\frac{40}{2}[/tex] [ 2a₁ + 39d ] = 1900 , that is

20(2a₁ + 39d) = 1900 ( divide both sides by 20 )

2a₁ + 39d = 95 → (1)

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

given a₄₀ = 106 , then

a₁ + 39d = 106 → (2)

subtract (2) from (1) term by term to eliminate d

a₁ + 0 = - 11 , so

a₁ = - 11

substitute a₁ = - 11 into (2) and solve for d

- 11 + 39d = 106 ( add 11 to both sides )

39d = 117 ( divide both sides by 39 )

d = 3

A Scatter plot is used for examining data with more than two variables, and it includes a different vertical axis for each variable.

The variables in the scatter plot made from the data are described by the independent variable, time, which is graphed along the horizontal axis. The independent variable will be time, and the dependent variable will be the number of calories provided.

When analyzing data with more than two variables, a scatter plot is used, which has a separate vertical axis for each variable.

Therefore, a scatter plot is used for examining data with more than two variables, and it includes a different vertical axis for each variable.

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Answer:

judging from the list of numbers i would pick a

Hence the required expression is Proved.

Given the expression is 2 1/4 ₋ 6/7 = 39/28

Consider L.H.S 2 1/4 ₋ 6/7

Convert improper fraction to proper fraction.

2 1/4 = 9/4

take LCM of the denominators.

The LCM is 28.

9×7/28 ₋ 6×4/28

63/28 ₋ 24/28

Now subtract.

63 ₋ 24/28

39/28

Hence proved.

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Your question is incomplete. Please find the missing content here.

Show that 2 1/4 ₋ 6/7 = 39/28

Answer:

2c+2

The number that will go in the green box is 2.

Step-by-step explanation:

3c-1-c+3

Combine the like terms.

3c-1-c+3=2c+2

Hope this helps!

Please mark as brainliest if correct!

Answer:

You would start at 3 and then go backwords till the end.

So you'd choose the 3 option. <-o

Only use the filled in o if the equation is <_ with the line underneath, if its like < then its o

Hope this helps! <3

Answer:

c

Step-by-step explanation:

because 7 of the 12 sections are shaded in blue.

Answer:

I think it is none of the choices.

Step-by-step explanation:

Answer:

type 1 in a1 type 2 in a2, (or whatever ur preferred no.s are),then heighlight both cells, then go to the bottom right corner of a2 and drag down or double click

Step-by-step explanation:

Drag down or double-click the bottom right corner of a2 to begin with a 1 in a1 and a 2 in a2 and complete the sequence.

Excel is a software in which we can process large amount of data and data handling easily and effectively, Excel can be used in Data analysis.

in a1 type 1 Type 2 in cell a2 (or whatever your chosen numbers are), highlight both cells, and then drag down or double-click the bottom right corner of a2.

Thus, drag down or double-click the bottom right corner of a2 to begin with a 1 in a1 and a 2 in a2 and complete the sequence.

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Answer:

No.

Step-by-step explanation:

The order of operations in both problems are different, giving two very different results. Therefore, they are unequal.

Considering that the transformation is a dilation, the correct statement is given by:

The angles of Quadrilateral ABCD and A'B'C'D' are the same.

There are three statements:

A figure is said to go through a dilation is when it's side lengths are changed, either enlarged or diminished, but the angles remain constant.

For this problem, the scale factor is of 2, meaning that the side lengths are doubled, while the angles remain constant and the correct statement is:

The angles of Quadrilateral ABCD and A'B'C'D' are the same.

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Answer:

Price: $178.57

30% off: -$53.57

Sale Price: $125.00

Step-by-step explanation:

She buys each shirt for $100.

She wants to make a profit of 25%.

25% of $100 = 0.25 × $100 = $125

She must sell the shirt at $125.

She wants to mark the shirt at a higher price than $125, so that after the 30% discount, she will still sell it for $125.

Call the higher price x.

x - 30% of x = 125

x - 0.3x = 125

0.7x = 125

x = 125/0.7

x = 178.57

The sale tag can read:

Price: $178.57

30% off: -$53.57

Sale Price: $125.00

Answer: p - 1 > 6, or p > 7

Step-by-step explanation:

   We will write an expression from the sentence given.

difference of a number (p) and 1 ➜ p - 1

is greater than ➜ >

    The difference of a number p and 1 is greater than 6​ ➜ p - 1 > 6

   To solve for the possible values of p, we will add 1 to both sides of the equation;

p > 7

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The unknown number is 8.

Let the unknown number be x.

According to the given question.

We have a phrase "Triple a number decreased by 25 is equivalent to five less than half the same number".

Therefore, the equation for the phrase "Triple a number decreased by 25 is equivalent to five less than half the same number" is given by

3x - 25 = x/2 - 5

To find the unknown number we have to solve the above equation for x.

Therefore,

3x - 25 = x - 10/2

⇒ 6x - 50 = x - 10

⇒ 6x - x = -10 + 50

⇒ 5x = 40

⇒ x = 40/5

⇒ x = 8

Hence, the unknown number is 8.

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The equation of the line is y = -7.5x - 2.5

The given parameters are

y-intercept = -5/2

x-intercept = -1/3

A linear equation is represented s

y = mx + c

Where

c = y-intercept = -5/2

So, we have:

y = mx - 5/2

The equation x-intercept = -1/3 means that

y = 0 and x = -1/3

So, we have

0 = -1/3m - 5/2

This gives

1/3m = -5/2

Evaluate

m = -15/2

Substitute m = -15/2 in y = mx - 5/2

y = -15/2x - 5/2

Rewrite as

y = -7.5x - 2.5

Hence, the equation of the line is y = -7.5x - 2.5

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There are four levels of measurements in statistics, namely nominal, ordinal, interval, ratio. These levels are important when it comes to analyzing data, since it helps us determine the technique that we can use to support or refute our study.

In the nominal level, we can categorize data but they cannot be ranked. An example would be hair color. In an ordinal data, the data can be both categorize and ranked, but doing mathematical calculation may not make sense. Also, the intervals between rankings doesn't necessarily dictate how close or far apart the data are.

A good example is level of education. In an interval level, the data can be categorized, ranked, and measured but they do not have a true zero. An example could be a range of values that does not include zero. Lastly, in the Ratio level the data can be categorized, rank, and measured, and it has a true zero.

So ratio level is most appropriate for ages of children. Note that ages can be categorized, rank, and measured .Moreover, an age equal to zero means that there is no age or the absence of age.  

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Answer:

27

Step-by-step explanation:

4.5*3*2 = 27

hi,

You just have to multiply the three measures.  

So :  

2*3*4.5 =  27 cm³

Easy, is it not ?  

Answer: c=6, d=-6

Step-by-step explanation:

c+12d=-66

-4c+3d=-42

(-4c+3d=-42)*4

-16c+12d=-168      ==> subtract this

c+12d=-66           ==> by this

-17c=-168-(-66)       ==> subtract the top two equations

-17c=-168+66

-17c=-102

c=6

c+12d=-66

6+12d=-66

12d=-72

d=-6

The relation 1 is not a function, while the relation 2 is a function

For a relation to be a function, the following must be true:

Each y value in the function must have a unique x value

i.e. Each y value must have exactly one x value

Using the above as a guide, we have

Relation 1: This relation is not a function, because the x value 5 has two y values 2 and 4

Relation 2: This relation is a function, because each y value must have exactly one x value

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Amount after 10 years at 3%, 4% and 5.5% interest with principal $20000 is $26878.32, $29604.88 & $34162.88 respectively.

Although a part of your question is missing, you might be referring to this full question: Suppose that P dollars in principal are invested for years at the given interest rates with continuous compounding. Determine the amount that the investment is worth at the end of the given time period. p=$20000, t=10yr

a. 3% interest

b. 4% interest

c. 5.5% interest

P = $2000

T = 10 years

Formula to be used:

A = P(1+r/100)^n

A = total amount after n years

P = principal amount invested

r  = rate of interest

n = number of years the money is invested

Solving for part a:

A = 20000(1+3/100)^10

= 20000*1.34

A = 26878.32

Solving for part b:

A = 20000(1+4/100)^10

= 20000*1.48

A = 29604.88

Solving for part c:

A = 20000(1+5.5/100)^10

= 20000*1.70

A = 34162.88  

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Answer:

x = 10

Step-by-step explanation:

the angle is equally bisected from the middle so

3x - 3 = 4x - 13

13 - 3 = 4x - 3x

x = 10

<FGH = 3(10) - 3 = 27

< HGI = 4(10) - 13 = 27

<FGI = <FGH + <HGI = 27 + 27 = 54

Answer:

your answer is 21

Step-by-step explanation:

The gap between 3 and 6 is 3 the gap between 6 and 10 is 4 the gap between 10 and 15 is 5 so your answer will be 6 more than 15 which is 21

your welcome

Answer:

[tex]\textsf{A)} \quad x=-2, \:\:x=\dfrac{5}{2}[/tex]

[tex]\textsf{B)} \quad \left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)[/tex]

C)  See attachment.

Step-by-step explanation:

Given function:

[tex]f(x)=2x^2-x-10[/tex]

To factor a quadratic in the form  [tex]ax^2+bx+c[/tex] , find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex] :

[tex]\implies ac=2 \cdot -10=-20[/tex]

[tex]\implies b=-1[/tex]

Therefore, the two numbers are -5 and 4.

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies f(x)=2x^2-5x+4x-10[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies f(x)=x(2x-5)+2(2x-5)[/tex]

Factor out the common term  (2x - 5):

[tex]\implies f(x)=(x+2)(2x-5)[/tex]

The x-intercepts are when the curve crosses the x-axis, so when y = 0:

[tex]\implies (x+2)(2x-5)=0[/tex]

Therefore:

[tex]\implies (x+2)=0 \implies x=-2[/tex]

[tex]\implies (2x-5)=0 \implies x=\dfrac{5}{2}[/tex]

So the x-intercepts are:

[tex]x=-2, \:\:x=\dfrac{5}{2}[/tex]

The x-value of the vertex is:

[tex]\implies x=\dfrac{-b}{2a}[/tex]

Therefore, the x-value of the vertex of the given function is:

[tex]\implies x=\dfrac{-(-1)}{2(2)}=\dfrac{1}{4}[/tex]

To find the y-value of the vertex, substitute the found value of x into the function:

[tex]\implies f\left(\dfrac{1}{4}\right)=2\left(\dfrac{1}{4}\right)^2-\left(\dfrac{1}{4}\right)-10=-\dfrac{81}{8}[/tex]

Therefore, the vertex of the function is:

[tex]\left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)[/tex]

Plot the x-intercepts found in Part A.

Plot the vertex found in Part B.

As the leading coefficient of the function is positive, the parabola will open upwards.  This is confirmed as the vertex is a minimum point.

The axis of symmetry is the x-value of the vertex.  Draw a line at x = ¹/₄ and use this to ensure the drawing of the parabola is symmetrical.

Draw a upwards opening parabola that has a minimum point at the vertex and that passes through the x-intercepts (see attachment).

Answer:

2,3,4,6,8

Step-by-step explanation:

prime factorization: 2^3×3×7 which has: 2, 3, 4, 6, 8

Answer:

It is divisible by 1, 2, 3, 4, 6, 7, 8

Step-by-step explanation:

Everything is divisible by one, so this is obvious.

168 is an even number, therefore being able to be divided by 2

1+6+8=15 which is in the 3 times tables (3x5=15)

If the last two digits are divisible by 4 (which 68 is) then you can divide it by 4.

168 doesn't end in 5 or 0 so it can't be divided by 5

This number can be divisible by 2 and 3 so it can be divided by 6

160 is divisible by 8 so if you add 8 it is divisible.

1+6+8=15 again which is not divisible by 9

It doesn't end in 0 meaning it cannot be divisible by 10

Hope this helped! <3

The change of Mandy's score is 600 points.

Here,

Mandy is playing a game.

Early in the game she had - 250 points.

Now, Mandy has 350 points.

We have to find the change of Mandy's score.

What is difference of two number?

To find the difference between two numbers, subtract the number with the smallest value from the number with the largest value.

Now,

Early in the game she had - 250 points.

And, now Mandy has 350 points.

So, The change of Mandy's score = 350 - (-250) = 350 + 250 = 600

Hence, The change of Mandy's score is 600 points.

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