Calculate the value of 4x2 + xy when x = 3 and y=-2.

Answer:

The series has 7 terms

[tex]\displaystyle S_7=\frac{4372}{243}[/tex]

Step-by-step explanation:

Geometric Series

In the geometric series, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.

We are given the series:

-12, -4, -4/3, ..., -4/243

We can find the common ratio by dividing one term by the previous term:

[tex]\displaystyle r=\frac{-4}{-12}[/tex]

Simplifying:

[tex]\displaystyle r=\frac{1}{3}[/tex]

Sum of terms: Given a geometric series with first term a1 and common ratio r, the sum of n terms is:

[tex]\displaystyle S_n=a_1\frac{1-r^n}{1-r}[/tex]

We need to find how many terms the series has. Using the explicit formula of a geometric series:

[tex]a_n=a_1\cdot r^{n-1}[/tex]

The last term is an=-4/243 and the first term is a1=-12. Solving for n:

[tex]\displaystyle n= \frac{\log(a_n/a_1)}{\log r}+1[/tex]

[tex]\displaystyle \frac{\log(-4/243/-12)}{\log 1/3}+1[/tex]

[tex]\displaystyle \frac{\log(1/729)}{\log 1/3}+1[/tex]

n=7

The series has 7 terms

Thus, the sum of the 7 terms of the series is:

[tex]\displaystyle S_7=-12\frac{1-(1/3)^7}{1-(1/3)}[/tex]

[tex]\mathbf{\displaystyle S_7=\frac{4372}{243}}[/tex]

From the given question, the required answer is option D. It can be deduced that: Reflect ΔECD over segment AC. This establishes that ∠ACB ≅ ∠E'C'D'. Then, (translate point E' to point A). This establishes that (∠D'E'C' ≅ ∠BAC). Therefore, ΔACB ~ ΔECD by the AA similarity postulate.

Rigid transformation is a process of resizing a given shape or figure. This can be done by either increasing or decreasing its dimensions (size) or changing its orientation. Some of the methods required in rigid transformation are: reflection, translation, rotation etc.

From the given question,

if ΔECD is first reflected over (turned about) segment AC, it would be deduced that m∠ACB ≅ m∠E'C'D' = [tex]90^{o}[/tex](right angle principle).

Then, the next process is to translate (extend) point E' to point A, so that m∠D'E'C' ≅ m∠BAC.

This would also ensure that m∠E'D'C' ≅ m∠ABC due to the translation.

This implies that ΔACB ~ ΔECD by the AA similarity postulate.

Therefore, performing reflection and translation operations on ΔECD step-wisely can be used to prove that ΔACB ~ ΔECD by the AA similarity postulate.

A sketch for more clarifications is herewith attached to this answer.

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Answer:

its d, i took the test

(at the bottom of the photo it says earned 1 point meaning it right)

Answer:

133.3333333333333333%

Step-by-step explanation:

never ending 3

Answer:133.3%

Step-by-step explanation:

Answer:

RS 146189.8

Step-by-step explanation:

let the price before tax be p

hence the final amount paid (i.e the actual bill)

= price before tax + tax

= p + (0.13% of p)   (convert percentage into fraction)

= p + [ (0.13/100) x  p] ---------------(eq 1)

we are given that the tax (i.e VAT) = 189.80

hence,

[ (0.13/100) x  p] = 189.8

0.13p = (100)(189.8)

p = (100)(189.8) / 0.13

p = 146000

hence our eq 1 above becomes:

p + [ (0.13/100) x  p]

= 146000 + 189.8

= 146189.8

Answer:

Step-by-step explanation:

A. y= -x+2.   The -x makes the line go from left to right. The points are (0,2)(2,0)

B. 3y=2x-1 points are (2,1)

Step-by-step explanation:

find angle c: 180-116= 64

solve for x:

(2x+4)+(3x-13)+64=180

5x+55=180

5x=125

5x/5 = 125/5

x=25

plug in x: 3(25)-13= 62

Answer: See explanation

Step-by-step explanation:

25% + 25% + 25%

= 75%

10% + 25%

= 35%

50% + 10%

= 60%

10% + 10%

= 20%

Answer:

90

Step-by-step explanation:

circumference of total circle = 16 pi

16 pi / 4 pi = 4

1 / 4 =25%

1/4 * 360 = 90

Answer:

n = -3

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define equation

3(-2 - n) = -9 - 4n

Step 2: Solve for n

Step 3: Check

Plug in n to verify it's a solution.

Answer:

the slope is 2

Step-by-step explanation:

y2-y1

divided by

x2-x1

equals

4-0

divided by

0- (-2)

equals

4/2 which is 2

Answer:

2/5

Step-by-step explanation:

The answer is common sense.

The probability that no two consecutive flips have the same result is [tex]\frac{1}{16}[/tex].

If a coin is flipped then there are two possible outcomes Head(H) and Tail (T).

So each flip can have 2 possible outcomes. It means 5 flips have [tex]2^5=32[/tex] possible outcomes.

Among these 32 outcomes only 2 outcomes : HTHTH and THTHT have "no two consecutive flips have the same result".

So the probability that no two consecutive flips have the same result is = [tex]\frac{2}{32} =\frac{1}{16}[/tex].

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Answer:

d

Step-by-step explanation:

I'll edit my response to tell you why later. it seems like you need this answer now.

Answer:

A?

Step-by-step explanation:

I'm pretty sure thats the answer! I,m currently learning that in class so I might be wrong!

Answer:

C

Step-by-step explanation:

We are given that:

[tex]a(x+b)<c[/tex]

Where a < 0.

To solve for x, we can divide both sides by a.

Since a < 0, a is negative. Hence, we must flip the inequality sign. This yields:

[tex]\displaystyle x + b > \frac{c}{a}[/tex]

Subtract b from both sides. Hence:

[tex]\displaystyle x>\frac{c}{a}-b[/tex]

In conclusion, our answer is C.

Answer:

Third choice.

Step-by-step explanation:

y = 15x + 5.

Answer:

Step-by-step explanation:

{4, 5}

{ - 1, - 7 }

{ 0, 5/7 }

{ - 1/3 , 2/5 }  

john: 56

Mary: 24

(Tbh I'm probably really wrong, I'm so sorry )

Answer: john is 20 and mary is 12

Step-by-step explanation:

J + M = 32

J - 4 = 2(M-4)

solve

Answer:

Liquid nitrogen is 1. Liquid and 2. 90°C and dry ice is, well, ice. So dry ice is obviously colder.

Step-by-step explanation:

Answer:

-6,-4

Step-by-step explanation:

Multiple each point by 2

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The image of point D under a dilation about the origin (0,0) with a scale factor of 2 is at (-6, -4)

The graph is given below.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

Point D coordinates = (-3, -2)

The point is dilated with a scale factor of 2.

This means,

Multiply the coordinate with 2.

(-3, -2) becomes (-6, -4)

Thus,

The image of point D under a dilation about the origin (0,0) with a scale factor of 2 is at (-6, -4)

The graph is given below.

Learn more about coordinates here:

https://brainly.com/question/13118993

#SPJ2

Answer:

Explanation:

1.) 3.2 - 5.7 = -2.5

2.) 4.25 - (-2.3) = *double negative = positive* = +6.55

3.) -0.18-2 = -2.18 *2 negatives will add numbers, but the sign remains negative*

4.) -9 + 2.5 = -6.5 *since 9 is greater, we will use its sign, then subtract the two*

5.) (-9 + 5) +4 = -4 +4 = 0

3.2-5.7=C

4.25-(-2.3)=C

-0.18-2=C

-9+2.5=C

-9+5=4=B

Answer:

[tex]\theta=251.6^\circ[/tex]

Step-by-step explanation:

Complex Numbers

They are expressed as the sum of a real part and an imaginary part:

[tex]Z = a+b\mathbf{ i}[/tex]

Complex numbers can also be expressed in polar form:

[tex]Z = r(\cos\theta+\sin\theta \mathbf{ i}) = r. cis(\theta)[/tex]

Where r is the modulus of the complex number and θ is the argument.

The argument can be calculated by:

[tex]\displaystyle \tan\theta=\frac{b}{a}[/tex]

The angle θ must be calculated in the appropriate quadrant depending on the signs of the real and imaginary parts.

The complex number is given as:

[tex]Z = -3 -9\mathbf{ i}[/tex]

Here: a=-3, b=-9

Since both components are negative, the argument lies in the third quadrant (180° < θ < 270°).

[tex]\displaystyle \tan\theta=\frac{-9}{-3}[/tex]

[tex]\displaystyle \tan\theta=3[/tex]

[tex]\theta=\arctan(3)[/tex]

The calculator gives the answer 71.6°, we need to adjust the angle to the third quadrant by adding 180°, thus

[tex]\mathbf{\theta=251.6^\circ}[/tex]

Answer:

y+3 = [tex]\frac{-1}{2}[/tex] (x-10)

Step-by-step explanation:

Answer:

Step-by-step explanation:

8 1/4%

8.25%

0.0825

Answer:

no

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

2(3x+5)=6x+5

6x+10=6x+5

not equal

Answer:

We conclude that the relation is a function but it is not a linear function.

Step-by-step explanation:

The given table represents a function because each input or x-value is related to exactly one output or y-value.

In other words, there is no repetition of 'x' values. This indicates that the given relation in the table represents a function.

In order to check whether the function is linear or not linear​, we need to check how x and y values change.

The table indicated that x increases by 2, now we need to determine whether the y-values increases at a constant rate or not. For this, we need to find the first difference between y-values.

-3 - (-8) = 5

3 - (-3) = 6

7 - 3 = 4

As the first difference between the consecutive y-values is not constant, meaning that y-values do not increase at a constant rate as x-values increase by 2.

Thus, it is not a linear function,

Therefore, we conclude that the relation is a function but it is not a linear function.

Answer:

4 strips

Step-by-step explanation:

There are one hundred centimeters in one meter, so you multiply 2 and 100.

2*100=200

And then you divide by 50, since the strips are 50cm long

200/50=4

4 fifty cm strips

Answer:

Substitute the given value into the function and evaluate.

2 x 3 + 7 x 2 − 4 x − 15

Step-by-Step Process

Answer:

$13,400

Step-by-step explanation:

We will first have to take account of the commuting cost, years at school, and total cost of tuition and books

It would cost $5,500 per year, she is studying at the school for 2 years, we will multiply 5,500 by 2

$5,500 * 2

= $11,000

The cost of commuting per month will be multiplied by 12 to represent a year and another 2 for two years

$100 * 12 * 2

= $2400

We all these together for the total cost of her education

$11,000 + $2,400

= $13,400

Answer:

I put it in a calculator and got 51.5

Step-by-step explanation:

Answer:

If I'm understanding the question right it's -.05

Step-by-step explanation:

(2x - 3) = 2

There is no more simplifying to be done in the parentheses.

2x - 3 = 2

Subtract 3 on each side to get the x value by itself.

2x = -1

Divide each side by 2 so the x is by itself.

x = -.05

And that's it, hope I helped :)

Answer:

result(s) found

x8y18

See steps

Step by Step Solution:



Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "y3"   was replaced by   "y^3".  1 more similar replacement(s).

Simplify :sqrt(x16y36)

Simplify the Variable part of the SQRT

Rules for simplifing variables which may be raised to a power:

   (1) variables with no exponent stay inside the radical

   (2) variables raised to power 1 or (-1) stay inside the radical

   (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

      (3.1) sqrt(x8)=x4

     (3.2) sqrt(x-6)=x-3

    (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

      (4.1) sqrt(x5)=x2•sqrt(x)

     (4.2) sqrt(x-7)=x-3•sqrt(x-1)

 Applying these rules to our case we find out that

      SQRT(x16y36) = x8y18

Simplified Root :

 x8y18 

Step-by-step explanation:

please mark me as the brainliest thank you