b. Without calculating, use the pattern to predict the sum of the squares of the first ten terms of the Fibonacci sequence.

Answer:

the answer would be 20.

Step-by-step explanation:

-

Answer:

[tex](((-2)^{4} )/(-4))-(2*(-3)*(8-4))\\[/tex] = 20

Step-by-step explanation:

breaking into 2 parts:

calculate within parenthesis: [tex](((-2)^{4} )/(-4))[/tex] = 16/(-4) = -4

calculate within parenthesis: (2*(-3)*(8-4)) = (2*(-3)*(4)) = -24

add and subtract (left to right): -4-(-24)=20

Answer:

Answers on attached image

Step-by-step explanation:

Answer:

The answer is in the attached screenshot!!! :)

Step-by-step explanation:

Please let me know if you have any questions!!! :)

Answer:

x = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\frac{2}{3}[/tex] + [tex]\frac{1}{3}[/tex] = 2x ( combine fractions on left side )

1 = 2x ( divide both sides by 2 )

[tex]\frac{1}{2}[/tex] = x

A triangle's centroid is the point through which all of the mass of a triangular plate appears to act.

The centroid of a triangle is the point through which all of the mass of a triangular plate appears to act. Also known as the "center of gravity," "center of mass," or "barycenter." A fascinating fact is that the centroid is the point at which the triangle's medians intersect.

The triangle's centroid is defined as the point of convergence. Three triangle medians intersect at the figure's centroid "G." The center of gravity is another name for a centroid.

The triangle is divided into two equal-area triangles by each median. The centroid is the intersection of the three medians The centroid is the intersection of the three medians. The three medians divide the triangle into six triangles, each with the same area.

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Answer: y=4x/3 + 1/3

Step-by-step explanation:

y=mx+c

**Substitute already known variables**

3=2m+1/3=

(3=2m+1/3)*3=      ==> Multiply the equation by 3 to get rid of fractions

9=6m+1

6m=8

m=8/6

m=4/3

y=4x/3 + 1/3

Answer: y=-4x/9 + 1/3

Step-by-step explanation:

y=mx + c

**Substitute known variables into the equation**

-1=3m + 1/3

(-1=3m + 1/3)*3      ==> Multiply equation by 3 to get rid of fractions

-3=9m+1

9m=-4

m=-4/9

y=-4x/9 + 1/3

Answer:

18 + 2y + 6 = 36

2y = 12

y = 6
step explanation:

Since RS bisects AB,

25 - 3x = 2y + 5

25 - 3x = 2(6) + 5 = 12 + 5 = 17

3x = 25 - 17 = 8

x = 8/3

By substitution, the solution of the system of equations, y = 2x - 1 and 3x - y = -1, is (-2 , -5).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

y = 2x - 1     (equation 1)

3x - y = -1     (equation 2)

Since the first equation is already expressed in y in terms of x, substitute the value of y to the second equation.

3x - y = -1     (equation 2)

3x - (2x - 1) = -1

3x - 2x + 1 = -1

Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solving for x.

3x - 2x + 1 = -1

3x - 2x = -1 - 1

x = -2

Substitute the value of x in the first equation.

y = 2x - 1     (equation 1)

y = 2(-2) - 1

y = -4 - 1

y = -5

Hence, the solution of the given system of equations is (-2 , -5).

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Answer:

X=least=30

Y=greatest=40

Given statement 'The sum of two vectors is the resultant.' is True.

We know that in mathematics, a vector is a quantity that has both magnitude and direction but no position.

Examples : velocity, force and acceleration.

Also, the resultant vector is the vector sum of two or more vectors. We find the resultant vectors by  adding two or more vectors together. Any two vectors can be added if and only if they are the same vector quantity.

For vector P = [tex]a\vec i+b\vec j[/tex] and vector Q = [tex]m\vec i+n\vec j[/tex]

The resultant vector R would be,

R = P + Q

R = [tex](a+m)\vec i+(b+n)\vec j[/tex]

Therefore, given  statement 'The sum of two vectors is the resultant.' is True.

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The total number of registered voters is 3700.

Percentage can be described as the fraction of a number expressed as an amount out of 100. Percentage is a measure of frequency. The sign that is used to represent percentages is %.

The first step is to determine the percentage of independent voters.

Percentage of independent voters : 100 - (percent of democrats + percent of republicans)

100 - (34% + 25%)

100- 59% = 41%

Total number of voters = number of independent voters / percentage of independent voters

1517 / 41%

1517 / 0.41 = 3,700

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Answer:

https://www.calculator.net/volume-calculator.html

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

[tex](x)(x+4) = 32\\x^2 + 4x - 32 = 0\\(x - 8)(x + 4)\\\\x - 8 = 0\\x = 8 \\\\x + 4 = 0\\x = -4\\\\x = 8 \\x = -4[/tex]

8 is the answer as in a measurement there is no negative number.

Answer: y = 3x/2 + 5/2

Step-by-step explanation:

Write the slope formula m = y2 - y1                                                  

                                                x2 - X1                                                                    

 Substiue { x1 = 2

                 { x2 = -4      Into m =3 -  (-1)

                 {  y1 = -1                      -4 - 2

                { y2 = - 3                                                                                                                            

Calculate and you get m = -2/3

Slope of  the line that is perpendicular to m = -2/3 is m = 3/2

Substitute it: ( 2 - 4 -1 + 3 )

                            2          2

Calculate it 2 - 4

                       2

Simplify -2/2 and you get -1

Calculate -1 + 3

                    2

Simplify it 2/2 and you get 1

Rewrite solutions as coordinates: (-1 , 1)

Substitute     { m = 3/2

                      { x = -1

                      {y = 1

y = mx + b

Calculate 1 = 3/2 x (-1)= b and you get b = 5/2

Lastly Substitute { m = 3/2 into y = mx + b

                             { b = 5/2

Answer: y +3x/2 + 5/2

Answer:

9

Step-by-step explanation:

- 7 (4 - r) = 35

First you need to do the parentheses

-7 times 4 is -28

-7 times -r is 7r

-28+7r=35

add 28 to both sides

7r=63

r=9

Answer:

r=9

Step-by-step explanation:

-28+7r=35, rearrange to put like terms together

7r=35+28, 7r=63, divide both sides by 7 to get r

r=63/7, r=9

mark me brainliest if it helped

Answer:

x = 56

Step-by-step explanation:

assuming you require to find the value of x

the sum of the exterior angles of a polygon = 360°

sum the 6 exterior angles and equate to 360

x + x + x + 67 + 50 + 75 = 360

3x + 192 = 360 ( subtract 192 from both sides )

3x = 168 ( divide both sides by 3 )

x = 56

32(-5) + 0 + 160 = 0 is the line in the general form of the line the passing through (−5,0) with the slope 32.

A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics. There is no obvious reason why the letter m is used to represent slope, although it first appears in English in O'Brien (1844), who wrote the equation for a straight line as "y = mx + b," and it may also be found in Todhunter (1888), who wrote it as "y = mx + c."

Let us write the given data in slope-intercept form that is

y = m(x) + b

where m = slope of the line

b = y-intercept

So substituting the values we get

0 = 32(-5) + b

-b = -160

b = 160

so we have the slope intercept form

0 = 32(-5) + 160

Converting this to General form

ax + by + c = 0

32(-5) + 0 + 160 = 0

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Translated question

Given the following conditions, determine the equation of the line in its general form Ax+By+C=0.

It passes through (−5,0) and has slope m=32.

The simplified expression is -3/5.

To simplify the given expression in question, we will solve it step wise. Firstly we will simplify the numerator by performing operation according to the sign. Similar approach will be repeated for the denominator. Then we will write it in fraction form to find the simplified form of expression.

Numerator -

Numerator = 8 - 17

Here subtraction of large number is required form small number, so the result will be subtracted value with negative sign

Numerator = -9

Denominator -

Denominator = 12 - (-3)

Here two negative signs are present, so, we will perform addition and the result will be with positive sign

Denominator = 12 + 3

Denominator = 15

Writing the fraction form -

Expression = -9/15

Dividing the expression by 3

Expression = -3/5

Hence, the simplified expression is -3/5.

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The sequence 3/32, 3/16, 3/8, 3/4, 3/2, 3,6, ... is a geometric sequence with common ratio 2.

To determine whether the sequence is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.

If it is an arithmetic sequence, then:

  a(n) = a(n-1) + d

where d is the common difference.

If it is a geometric sequence, then:

  a(n) = a(n-1) . r

where r is the common ratio.

The given sequence is:

     3/32, 3/16, 3/8, 3/4, 3/2, 3,6, . . . .

Notice that

a(2) : a(1) = 3/16 : 3/32 = 2

a(3) : a(2) = 3/8 : 3/16 = 2

and so on

Since the ratio of consecutive terms are constant, then the given sequence is a geometric sequence. Furthermore, its ratio, r = 2

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The function which represents the frog population after x years will be F(x) = [tex]1200 * (0.97)^{x}[/tex]

The population is decreasing at an average rate of 3% per year.

For decrease in population, if the rate is decreasing per year is r%, the initial population is P, after time x the equation to use would be:

net decrease = [tex]P * (\frac{100 - r}{100})^{x}[/tex]

r = Reduction

x = time duration

P = 1200

Reduction rate = 100 - 3 = 97%

Reduction rate will be 97% i.e. 0.97

Reduction after one year = 1200 * 0.97

Reduction after two years = 1200 * 0.97 *0.97

                                            = 1200 * (0.97)²

Reduction rate after three years = 1200 * 0.97 * 0.97 * 0.97

                                                      = 1200 * (0.97)³

therefore,

Reduction rate after x years =  [tex]1200 * (0.97)^{x}[/tex]

The function representing the frog population after x years is F(x) =    [tex]1200 * (0.97)^{x}[/tex]

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The given expression written in standard form is 4.076008 × 10³

From the question, we are to simplify the given expression in standard form

The given expression is

(4 × 1000) + (7 × 10) + (6 × 1) + (8 × 0.001)

Simplifying

(4 × 1000) + (7 × 10) + (6 × 1) + (8 × 0.001)

(4000) + (70) + (6) + (0.008)

= 4000 + 70 + 6 + 0.008

= 4076.008

In standard form, we get

4.076008 × 10³

Hence, the given expression written in standard form is 4.076008 × 10³

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The equation that can be used to represent the cost of oranges and cookies is; 6.58 + 3x = 22.39. Thus, the cost of each bag of orange is x = $5.27

We are given;

Total Amount paid by Mila = $22.39.

Amount Mila paid for cookies = $6.58

Now, we are told that she also buys three bags of oranges. Now, if we denote the cost of each bag of orange to be x, then it means that;

Cost of 3 bags of oranges = $3x

Thus, we can write the equation to represent the cost of oranges and cookies as;

6.58 + 3x = 22.39

Subtract 6.58 from both sides to get;

3x = 22.39 - 6.58

3x = 15.81

x = 15.81/3

x = 5.27

Thus, the cost of each bag of orange is x = $5.27

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Answer:

10

Step-by-step explanation:

:D

False , Combining a coin toss and a roll of a die makes a simple event.

In statistics, what does a probability mean?

False , Combining a coin toss and a roll of a die makes a simple event.

A true statement is​ "For data at the interval​ level, you CAN calculate meaningful differences between data​ entries."

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Answer:

2 days: 1 week

Step-by-step explanation:

4 days : 2 weeks

2 2

2:1

Answer:

Step-by-step explanation:

So we Have 4 days to 2 weeks

In order to simplify this, we need to turn weeks into days

2 x 7 = 14

so 4 days to 14 days

Now we divide and fnd a common multiple

4/2 = 2

and 14/2 = 7

so, 2 days to 7 days, or 2/7

We can leave it at that, or turn it into a decimal

4/14 =0.2857

Hope this helps!^^

Answer:

12,000 for college 7.5,000 in car whe he pays around 20k for that

Step-by-step explanation:

Given that

          -8 ≥ -5x + 2 > -38

To find

So, according to the question

we have,

          -8 ≥ -5x + 2 > -38

For finding the solution of this function let's solve it on two part,

First part

          -8 ≥ -5x + 2,    and

Second part

          -5x + 2 > -38

For solution of first part ,

          -8 ≥ -5x + 2,

Add (-2) both side

We will get,

          -8 +(-2)  ≥ -5x + 2 +(-2)

          -8 -2  ≥ -5x + 2 -2

            -10  ≥ -5x

            10  ≥ 5x

Divide 5 both side,

We will get,

            [tex]\frac{5x}{5} \ge \frac{10}{5}[/tex]

             x ≥ 2

Now, for solution of second part,

          -5x + 2 > -38

Add (-2) both side

We will get,

          -5x + 2 +(-2) > -38+(-2)

          -5x + 2 -2 > -38 -2

                   -5x  > -40

                   40  > 5x

Divide 5 both side,

               5x/5  < 40/5

               x  < 8

So, the solution of given function,

            2 ≤ x < 8

Answer:

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Answer:

................................

Answer:

X = √2 R , where X is the length of the legs as R is the length of the radius .

Step-by-step explanation:

The opposite sides of two same angled triangle is also same . So in this case we can say two legs are in same length as their opposite angles are same (45°)

Now , suppose the given radius is R (look at the diagram) then total diameter  is 2R ( DIAMETER = 2 × RADIUS )

Now , we will consider the length of the legs are X ( as the are same ).

Now, we will apply Pythagoras theorem ( The squares on the legs of a right triangle is equal to the square on the hypotenuse . )

∵  X² + X² = (2R)²

or , 2X² = 4R²

or, X² = 2R²

We will root both side

X = √2R

So , X is the length of the legs as R is the length of the radius .

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