Complete the table by dragging the correct sequence or formula to the correct container.
Sequence
Recursive Formula
0, 4.5, 9, 13.5, 18,
[Container 3]
[Container 5]
[Container 1]
anan-1-11; a₁ = 68
[Container 6]
12, 19, 33, 40...
Explicit Formula
[Container 2]
[Container 4]
an=5+7n
68, 57, 46, 35, 24,
an=-4.5+ 4.5n
Container 1 Container 2
Container 3
an = 79-11n
Container 4
anan-1+4.5; a₁ = 0 anan-1
Container 5 Container 6
-1+7; a₁ = 12

Answer:

20km

Step-by-step explanation:

rounding down because it's not over five

Answer:

check below

Step-by-step explanation:

2x + 3y = -21

3y = -21 - 2x

3y = - 2x -21

divide both sides by 3

y = -[tex]\frac{2}{3}[/tex]x - 7

Answer:

6 m/s²

Step-by-step explanation:

[tex]\frac{27 \text{ m/s}}{4.5 \text{ s}}=6 \text{ m/s}^2[/tex]

10 is the correct answer

The expression that represents the perimeter of the triangle in the image is: 7a - 2.

To find the perimeter of a triangle, add the lengths of the three sides of the triangle together. The sum of the three sides of the triangle is the perimeter of the triangle.

The triangle in the image has the following as the lengths of its sides:

Therefore:

The perimeter of the triangle = 2a - 3 + 2a + 3a + 1

Combine like terms

The perimeter of the triangle = (2a + 2a + 3a) + (- 3 + 1)

The perimeter of the triangle = 7a - 2

Therefore, the expression that represents the perimeter of the triangle in the image is: 7a - 2.

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The numbers given illustrates that the nth term will be:

1. n² + 1

2. n²

1. It should be noted that from the information given, the numbers are 2, 5, 10 and 17. It should be noted that the nth term will be:

n² + 1.

Therefore, the 5th term will be:

n² + 1 = 5² + 1 = 26

2. The numbers given are 0, 1, 4, 9. The nth term is n². In this case, the 4th number will be:

n² = 4² = 16

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Answer:

Answer:

17. 9a^2/16

18. 25c^2/9

19. 49m^2/64

20. 16x^4/25

Step-by-step explanation:

:)

Answer:

8/15

Step-by-step explanation:

1/3+1/5

The rainfall rate in inches per hour is 2/3 inches per hour.

A rate is a special ratio in which the two terms are in different units. a fixed ratio between two things2: a number, amount, or degree measured in relation to another quantity; examples include the heartbeat, metabolic rate, pulse, and sedimentation rate.

Given that,

The inches of the rain is 14×1/2is 29/2

The direction of the rain is 21×3/4 is 87/4

Rate is 29/2 /87/4

is29/2×4/87 is 2/3

Therefore, rate of rain is 2/3.

The rainfall rate in inches per hour is 2/3 inches per hour.

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The appropriate choices will be as follows in light of the provided information:

So,

Add equation I to equation II.

Consequently, x=0 and y=11 Each variable's solution is provided by this.

Put equation I into equation II.

This means there is no answer.

Put equation I into equation II.

This implies that there are an infinite number of possible answers.

Therefore, the appropriate choices will be as follows in light of the provided information:

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Answer:

AB and CD are congruent.

Step-by-step explanation:

Given points:

After plotting the given points (see attachment), we can easily determine that AB is 7 units and CD is 7 units.  Therefore, AB and CD are congruent.

Alternatively, as points A and B share the same x-coordinate, the length of AB is the difference between the y-coordinates:

⇒ AB = 8 - 1 = 7 units

Similarly, as points C and D share the same y-coordinate, the length of CD is the difference between the x-coordinates:

⇒ CD = 5 - (-2) = 7 units

Finally, we can prove that AB and CD are congruent by calculating their lengths using the distance formula.

[tex]\boxed{\begin{minipage}{7.8 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two endpoints.\end{minipage}}[/tex]

[tex]\begin{aligned}\implies AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(-4-(-4))^2+(8-1)^2}\\& =\sqrt{(0)^2+(7)^2}\\& =\sqrt{0+49}\\& =\sqrt{49}\\& =7\end{aligned}[/tex]

[tex]\begin{aligned}\implies CD & =\sqrt{(x_D-x_C)^2+(y_D-y_C)^2}\\ & =\sqrt{(5-(-2))^2+(-5-(-5))^2}\\ & =\sqrt{(7)^2+(0)^2}\\ & =\sqrt{49+0}\\ & =\sqrt{49}\\ & =7\end{aligned}[/tex]

Therefore, as AB = CD, this proves that AB and CD are congruent.

By using the concepts of line segment and collinearity of line segments, the numerical length of the line segment JK within the line segment IK is 21 units.

In this problem we find two collinear line segments IJ and JK, two line segments are collinear if they are contained by the same line. The mathematical expression that represents the two collinear line segments are shown below:

IJ + JK = IK

If we know that JK = x + 6, IJ = 9 and IK = 2 · x, then the numerical length of JK is:

9 + (x + 6) = 2 · x

x + 15 = 2 · x

15 = 2 · x - x

15 = x

x = 15

JK = x + 6

JK = 15 + 6

JK = 21

The length of the line segment JK is 21 units.

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Answer: The multiplication of $.79 and 3.7 should be 2.923.

Given that,

The number is 0.79 and 3.7

We have to multiply both the numbers.

Based on the above information

$0.79

× 3.7

--------

5.53

+2.370

---------

2.923

Here the decimal should be moved three times to the left hand side as it tells the number of spaces that should be written in the real equation till the coming decimal.

In this way, the multiplication could be done of these two numbers.

Answer:

50 hrs

Step-by-step explanation:

80=4h (h=hours)

h=20 (1hr=20 bucks)

1000=xh (x=number of hrs.)

1000=20x (h=20 so sub that in)

x=1000 divided by 20

which is 50hrs til johnny gets 1000 bucks

Step-by-step explanation:

the area of any triangle is

baseline × height / 2

so, in our case

12 × height / 2 = 48

6 × height = 48

height = 48/6 = 8 units

m with the height and half of the baseline creates a right-angled triangle. and we can use Pythagoras to get m.

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90° angle), which is m for this right-angled triangle.

a and b are the legs, which are in our case the height of the main triangle and half of the baseline of the main triangle.

so we get

m² = 8² + (12/2)² = 8² + 6² = 64 + 36 = 100

m = 10 units

Ivan and Tanya share £150 in the ratio 4:1 workout. lvan gets more compared to Tanya. = $ 90

Ratio :

A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one. For example, if the number of marks scored in a test is 7 out of 10, then the ratio of marks obtained to the total number of marks is written as 7:10.

Total Ivan and Tanya share = £150

Ivan and Tanya share in the ratio of 4:1 respectively.

Let 4x be the money got by Ivan and x be the money got by Tanya.

Then, according to the question, we have

4x+x= 150

5x = 150

x= 150/5

x= 30

∴ Ivan has Money = 4x

= 4*30

= $ 120

Tanya has Money = x

= $ 30

Difference =   120-30 =  $  90

Hence,  Ivan gets more compared to Tanya. = $ 90

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Tanya and Ivan split £150 in the 4:1 workout. Tanya receives less compared to Ivan. = $ 90

Ratio:

A ratio is the relationship or comparison between two numbers belonging to the same unit in order to determine how much larger one number is than the other. For instance, if a test result is 7 out of 10, the ratio of the number of points earned to the total number of points is 7:10.

Ivan and Tanya's combined portion is £150.

Tanya and Ivan each share in a ratio of 4:1.

Let x and 4x represent Tanya's and Ivan's respective earnings.

Then, according to the question, we have

4x+x= 150

5x = 150

x= 150/5

x= 30

∴ Ivan has Money = 4x

= 4*30

= $ 120

Tanya has Money = x

= $ 30

Difference =   120-30 =  $  90

Hence,  Ivan gets more compared to Tanya. = $ 90

Answer: X = -4, 0, 2

Step-by-step explanation:

Wherever the line touches the x-axis the f(x) or y = 0

The new mean after adding a 6-inch high platform is 73 inches, while the median changes from 66 inches to 72 inches.

The mean refers to the average of a data set and is the result of the sum of the values of the data set divided by the number of items.

The median is the middle value in the data set when arranged in an ascending or descending order.

For instance, the number of the data set is 25.  The median value is the number 13, whose value is 66 inches in the old distribution or 72 inches in the new distribution.

Height (in.)  Number of Students  Cumulative Total

60                       1                                    60 (60 x 1)

61                       0                                    60 (60 + 61 x 0)

62                      2                                   184

63                      4                                  436

64                      2                                  564

65                      1                                  629

66                     3 Median                    827

67                      1                                  894

68                     3                               1,098

69                     2                               1,236

70                     0                               1,236

71                      1                                1,307

72                    2                                1,451

73                    0                                1,451

74                    1                                1,525

75                   2                                1,675

Mean = 67 (1,675/25)

Height (in.)  Number of Students  Cumulative Total

66                       1                                   66 (66 x 1)

67                       0                                  66 (66 + 67 x 0)

68                      2                                 202

69                      4                                 478

70                      2                                 618

71                       1                                 689

72                     3 Median                   905

73                      1                                 978

74                     3                              1,200

75                     2                              1,350

76                     0                              1,350

77                      1                              1,427

78                     2                             1,583

79                     0                             1,583

80                     1                             1,663

81                     2                             1,825

Mean = 73 (1,825/25)

Thus, the new mean is 73 inches and the new median is 72 inches.

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The standard form of  the equation is(x + 2)² +(y - 5)² = 26

The equation of a circle in standard form is

(x - a)² + (y - b)² = r²

where (a , b) are the coordinates of the centre and r the radius

The centre is at the midpoint of the endpoints of the diameter and r is the distance from the centre to either of the 2 endpoints

Find centre using the ' midpoint formula'

(a , b) = [  (3 - 7),  (4 + 6) ] = (-2 , 5)

to find r use the ' distance formula '

with (-2 ,5) and (3 , 4)

r = √(3 + 2)² + (4 - 5)² = √(25 + 1 ) = √26 ⇒ r² = (√26)² = 26

(x + 2)^² + (y - 5)² = 26 it is the equation in standard form'

The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circumference of the circle.  we can find the center point of the circle. Because the two points from the problem are the endpoints of a diameter, the midpoint of the line segment is the center point of the circle.

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The graph of a function f(x) is translated up when a positive number is added to the y-value of the function by 3 units that is the graph g(x) that is g(x) = f(x) + 3.

The correct option that illustrate the transformation that gives g(x) that has a y-intercept at 3, is the option B;

g(x) = f(x) + 3

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

The graph of the function f(x) = x, as an illustration is attached

The transformation of linear functions are:

Horizontal shifts;

f(x + h); A shift of h units left

f(x - h); A shift of h units right

Vertical shifts;

f(x) + m; A shift of m units up

f(x) - m; A shift of m units down

Whereby the y-intercept of f(x) is 0, we have;

Let f(x) = x, therefore;

g(x) = f(x) + 3

      = x + 3

The graph has to be shifted 3 places up to get g(x), therefore;

The function that gives g(x) from f(x) is the option;

B. g(x) = f(x) + 3

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Answer:

Step-by-step explanation:

let weight of DVD & packing material=x lb

8.50x+1.10=2.50x+2.25

8.50 x-2.50 x=2.25-1.10

6 x=1.15

x=1.15/6=0.19166... lb

The correct option is (B) That'is

[tex] \bf \implies{{3x}^{3} - {2x}^{2} + 10x - 12}[/tex]

Step 1) : Operations of functions

[tex] \bf \longrightarrow{f(x) + g(x)} \\ \bf \longrightarrow( {3x}^{3} - {2x}^{2} + 4x - 5) + (6x - 7)[/tex]

Step 2) : Simplify or expand

[tex]\bf \longrightarrow( {3x}^{3} - {2x}^{2} + 4x - 5) + (6x - 7)[/tex]

[tex]\bf \longrightarrow {3x}^{3} - {2x}^{2} + 4x - 5 + 6x - 7[/tex]

[tex]\bf \longrightarrow {3x}^{3} - {2x}^{2} +( 4x + 6x) + (- 5 - 7)[/tex]

[tex]\bf \longrightarrow {3x}^{3} - {2x}^{2} +( 4 + 6) \times x+ (- 5 - 7)[/tex]

[tex]\bf \longrightarrow {3x}^{3} - {2x}^{2} +10x - 12[/tex]

The total of yes voter present in the election are 3048.

Now, for the given question;

Let the number of yes voters be 'x'.

Let the number of no voters  be 'y'.

The ratio of yes to no voters is 4:3.

Thus,

x/y = 4/3

or x = 4y/3

Now there are total 5334 voters;

Thus,

x + y = 5334

Put the value of x.

4y/3 + y = 5334

On simplification;

7y = 16002

y = 2286 (no voters)

Now, calculate 'x'.

x = 5334 - 2286

x = 3048 (yes voters)

Thus, the number of yes voters are 3048.

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The correct option regarding what is required to disprove a conditional statement is given by:

A single counterexample that shows the statement is not always true.

A conditional statement has the following format:

If Clause 1 then Clause 2...

In which:

The statement is disproved when there is even one single case in which Clause 1 is true and Clause 2 is false, that is, a counter example showing that the statement is not always true, hence the third option in this problem is correct.

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The number of dollars Laura should pay at the dinner party is $84.

Given that, the last time Laura hosted a fancy dinner party for her friends, she spent $108 to feed 9 people. This time, there will be only 7 people at the dinner party.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. The proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Let the number of dollars paid by Laura for 7 people be x.

Now, 9:108::7:x

⇒9x=108×7

⇒x=12×7

⇒x=84

Therefore, the number of dollars Laura should pay at the dinner party is $84.

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The range of the exponential function y based on its equation and the context of the problem is; 0 < y ≤ 45529

The range of a function is the set that contains all possible output values for the function.

In this question, the function is given as: y = 45,529(0.78)^x.

It is an exponential function with initial value 45,529 and rate of change  of 0.78.

Now, it should be noted that exponential functions that are not shifted down, such as this one, are never negative nor zero. Thus, the range also has the restriction y > 0, and is given by:

D. 0 < y ≤ 45529

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The measure of the angle of the straight line is equal to 180 degrees. the measure of the ∠HLI and ∠ILM is equal to the which is 30 degrees. Thus option 4 is the correct option.

An endlessly long row of evenly spaced dots that spans in both directions makes up a line. Its length is the only dimension it has. A geometry called an angle is created when two line segments, lines, or rays intersect.

Given information-

The measure of the angle KLH is 120 degrees.

The image is attached below for the given problem.

The angle of the straight line

The measure of the angle of the straight line is equal to 180 degrees.

The line KLM is a straight line thus the angle of the line KLM is equal to 180 degrees.

The value of the angle ILH is 30 degrees given in the figure.

The value of the angle KLH is given in the question which is equal to 120 degrees. Thus,

∠KLM = ∠ILM + ∠KLH + ∠ILH

Take the angle KLH and the angle ILH on the other side,

∠ILM = ∠KLM - ∠KLH - ∠ILH

∠ILM = 180 - 120 - 30

∠ILM = 30

Thus the measure of the is 30 degrees.

As the measure of the is equal to the which is 30 degrees. Thus option 4 is the correct option.

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Answer:

d. mAngleHLI = mAngleILM

Step-by-step explanation:

trust