In the following table of values, the first differences are

x y First Difference
-2 34
-1 27
0 20
1 13
2 6

Answers

Answer 1

Answer:

-7

Step-by-step explanation:

Given

[tex]\begin{array}{ccc}x & {y} & {First\ difference} & {-2} & {34} & {}&{-1} & {27} & {} &{0} & {20} & {} & {1} & {13} & {} & {2} & {6} &{} \ \end{array}[/tex]

Required

The first difference

To do this, we simply calculate the difference between the consecutive y-values.

i.e.

[tex]d = y_{n+1} - y_n[/tex]

So, we have:

[tex]d = y_2 - y_1 = 27 - 34 = -7[/tex]

[tex]d = y_3 - y_2 = 20 - 27 = -7[/tex]

[tex]d = y_4 - y_3 = 13 - 20 = -7[/tex]

[tex]d = y_5 - y_4 = 6-13 = -7[/tex]

Hence, the first differences are -7 (all through)


Related Questions

लेखकाला शाल देणारे जोडपे​

Answers

होय साहेब!!!!!!!!!!

Find the coordinates of the image of M(−1, 5) after the translation (x, y)→(x+3, y−2).

Answers

M’(2, 3)

Work:
x: -1 + 3 = 2
y: 5 - 2 = 3

-8a-5=-7a+3 help someone

Answers

Answer: a = -8

Step-by-step explanation:

Given

-8a - 5 = -7a + 3

Subtract 3 on both sides

-8a - 5 - 3 = -7a + 3 - 3

-8a - 8 = -7a

Add 8a on both sides

-8a - 8 + 8a = -7a + 8a

a = -8

Hope this helps!! :)

Please let me know if you have any questions

Answer:

a = -8

Step-by-step explanation:

-8a-5=-7a+3                    Add 5 to both sides.

- 8a = - 7a + 3 + 5           Combine

-8a = - 7a + 8                  Add 7a to both sides

-8a + 7a = 8                    Combine

-a = 8                              Multiply by - 1

a = - 8                          

When you get a weird number like this, you should check it.

LHS = -8(-8) - 5

LHS = 64 - 5

LHS = 59

RHS = -(7*-8) + 3

RHS = -(-56) + 3

RHS = 56 + 3

RHS = 59

So a = - 8 must be right.

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!

Answers

Answer:

Option B, $2020.00

Step-by-step explanation:

Volume of the pool,

12×5×14.5+4×5×7

= 1010 ft³

each cubit foot costs $2, so 1010 ft³ will cost,

1010×$2

= $2020

How do I do this I need a little help

Answers

Answer:

B

Step-by-step explanation:

the decay will cause loss so it's the function B

Answer:

B

Step-by-step explanation:

trust

Profit And Loss

1. Find the profit percent when 6 pens are sold at the cost price of 9 pens.
Answer stepwise

Answers

0.7% percent is the answer

Find the measure of a. A. 110 B. 125 C. 55 D. 75

Answers

The answer to your question is c 55

16x^2 - 49 when factored is ?

Answers

Answer:

Step-by-step explanation:

16x^2 = (4x)^2

49 = 7^2

16x^2 - 49 = (4x)^2 - (7)^2

Solve for q.
39 + 4 + 9 = -14
q= [?]

Answers

[tex]\\ \sf \longmapsto 39+4+q=-14[/tex]

Simplify left side

[tex]\\ \sf \longmapsto q+43=-14[/tex]

Change side.

[tex]\\ \sf \longmapsto q=-14-43[/tex]

[tex]\\ \sf \longmapsto q=-57[/tex]

What is the value of x?
Enter your answer in the box.

Answers

Answer:

27

Step-by-step explanation:

Triangle proportionality theorem: when you draw a line parallel to one side of a triangle, it'll intersect the other two sides of the triangle and divide them proportionally

[tex]\frac{26}{39}=\frac{18}{x}[/tex]

Cross multiply and you get 702=26x

x=27

Answer:

x=27

Step-by-step explanation:

-We can use the triangle proportionality theorem: if line parallel to a side of a triangle intersects the other two sides, then it divides those sides proportionally.

-we write the proportion and solve for x

[tex]\frac{39}{26} =\frac{x}{18}[/tex]

[tex]x= \frac{39*18}{26}[/tex]

x= 27

The result of adding 14 to twice a number is the same as subtracting 8 from four times that number. Find that number.

Answers

Answer:

11

Step-by-step explanation:

Let the number be x

2x + 14 = 4x - 8                  Add 8 to both sides

2x + 14 + 8 = 4x                 Combine

2x + 22  = 4x                     Subtract 2x

22 = 2x                              Divide by 2

11 = x

help me with this question​

Answers

Answer:

x=5

y=2

w= -5

Step-by-step explanation:

We have that the two matrix are equal, so all corresponding elements are equal.

X-Y=3

From the second row and second column, we have y=2

so x-2=3

x=5

From the third row and the first column, we have w= - 5

Find the general solution for:-

[tex]sin\:x \:cos\: 3x+cos\:x\: sin\:3x=tan140[/tex]


~Please show your work
~Thank you!

Answers

Answer:

[tex] \rm \displaystyle x \approx \bigg \{ {59.3}^{ \circ} + \frac{n\pi}{2} , - {14.3}^{ \circ} + \frac{n\pi}{2} \bigg \}[/tex]

Step-by-step explanation:

we would like to solve the following trigonometric equation:

[tex] \rm \displaystyle \sin(x) \cos(3x) + \cos(x) \sin(3x) = \tan( {140}^{ \circ} ) [/tex]

the left hand side can be rewritten using angle sum indentity of sin which is given by:

[tex] \rm \displaystyle \sin( \alpha + \beta ) = \sin( \alpha ) \cos( \beta ) + \cos( \alpha ) \sin( \beta ) [/tex]

therefore Let

[tex] \alpha = x[/tex][tex] \beta = 3x[/tex]

Thus substitute:

[tex] \rm \displaystyle \sin(x + 3x) = \tan( {140}^{ \circ} ) [/tex]

simplify addition:

[tex] \rm \displaystyle \sin(4x) = \tan( {140}^{ \circ} ) [/tex]

keep in mind that sin(t)=sin(π-t) saying that there're two equation to solve:

[tex] \begin{cases} \rm \displaystyle \sin(4x) = \tan( {140}^{ \circ} ) \\ \\ \displaystyle \sin(\pi - 4x) = \tan( {140}^{ \circ} ) \end{cases}[/tex]

take inverse trig and that yields:

[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) \\ \\ \displaystyle \pi - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) \end{cases}[/tex]

add π to both sides of the second equation and that yields:

[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) \\ \\ \displaystyle - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi\end{cases}[/tex]

sin function has a period of 2nπ thus add the period:

[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) + 2n\pi\\ \\ \displaystyle - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi + 2n\pi\end{cases}[/tex]

divide I equation by 4 and II by -4 which yields:

[tex] \begin{cases} \rm \displaystyle x= \frac{ { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) }{4} + \frac{n\pi}{2} \\ \\ \displaystyle x = - \frac{{ \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi}{4} - \frac{n\pi}{2} \end{cases}[/tex]

recall that,-½(nπ)=½(nπ) therefore,

[tex] \begin{cases} \rm \displaystyle x= \frac{ { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) }{4} + \frac{n\pi}{2} \\ \\ \displaystyle x = - \frac{{ \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi}{4} + \frac{n\pi}{2} \end{cases}[/tex]

by using a calculator we acquire:

[tex] \begin{cases} \rm \displaystyle x \approx - {14.3}^{ \circ} + \frac{n\pi}{2} \\ \\ \displaystyle x \approx {59.3}^{ \circ} + \frac{n\pi}{2} \end{cases}[/tex]

hence,

the general solution for: for the trig equation are

[tex] \rm \displaystyle x \approx \bigg \{ {59.3}^{ \circ} + \frac{n\pi}{2} , - {14.3}^{ \circ} + \frac{n\pi}{2} \bigg \}[/tex]

What is the maximum degree of a reflex angle​

Answers

Answer:

Less than 360 degree

Step-by-step explanation:

I think so

Find the measure of one exterior angle for the following regular polygon.​

Answers

Answer:

40 degrees

Step-by-step explanation:

The formula for calculating the sum of interior angles is ( n − 2 ) × 180 (n = Number of sides)

in this scenario you have 9 sides so put it in the equation.

(9 - 2) ×180 = 1260

1260 is the sum of all the interior angles so we must divide this number by the number of sides to get the angle of one individual interior angle.

1260/9 = 140

180-140 = 40 degrees

Write an expression for the area of the square below.
4x + 2
A. 8x2 + 16x + 4
B. 16x2 + 16x + 4
C. 8x + 4
D. 16x2 + 6x + 4
Help

Answers

Area = Side^2

Area =( 4x + 2 )^2

Area = (4x)^2 + 2(4x)(2) + (2)^2

Area = 16x^2 + 16x + 4

Thus the correct answer is option B .

(a The Slant height of a right circular Cone with radius 7cm s 15cm . Find its Curved Surface area ​

Answers

Answer:

The curved surface area of the cone is approximately 329.9 cm²

Step-by-step explanation:

The parameters of the right circular cone are;

The radius of the cone, r = 7 cm

The slant height of the one, l = 15 cm

The curved surface area of a cone, CSA = π·r·l

Therefore;

CSA = π × 7 cm × 15 cm = 105·π cm² ≈ 329.9 cm².

Find the value of 4 tenths x hundreds.
4000
400
40
4

Answers

the value of 4 tenths x hundreds.

4000

Answer:

40

Step-by-step explanation:

4/10 x 100 = 40

what is the answer to
x^{2} + 2x + 15 = 0

Answers

From my knowledge:

²−2−15=0

x=5

x=-3

Solve for 2. Round to the nearest tenth of a degree, if necessary.
w
36
V
20
50
X

PLS HELP

Answers

Answer:

Step-by-step explanation:

This is classic right triangle trig. If you're solving for x, which you are, you have to consider how the given sides relate to that angle. The side with a length of 50 is opposite the angle x, while the side of length 36 is adjacent to angle x. The trig ratio that utilizes the sides opposite and adjacent is tangent; HOWEVER, we are looking for a missing angle. Finding missing angles on your calculator requires the 2nd button. To find the missing angle x, you are looking for the angle that has a tangent ratio of 50 over 36 (opposite over adjacent...Toa in SohCahToa). Hit the 2nd button on your calculator and then the tangent button (in degree mode, not radian mode) and you will see this on your screen:

[tex]tan^{-1}([/tex]

After the parenthesis, enter the fraction and then hit the enter button to get the angle measure in degrees:

[tex]tan^{-1}(\frac{50}{36})=54.2[/tex] degrees.

It's very important that you learn how to use your calculator to find the trig identities that give you the ratio in decimal form and how to find the missing angles. Missing angles always use the 2nd button along with whatever trig identity you are using.

Please help me solve these problems guys I’m really struggling

Answers

Answer:

Step-by-step explanation:

Can someone please assist me...thank you​

Answers

Answer:

x=10, y=24

[tex]\left(34-y\right)^2+y^2=676[/tex]

Step-by-step explanation:

Answer:

x = 10 and y = 24

Step-by-step explanation:

Perimeter of triangle = sum of the 3 sides of the triangle

:. x + y + 26 = 60

x + y = 60 - 26

x + y = 34 ---- (1)

From Pythagoras theorem,

x² + y² = 26²

x² + y² = 676 ---- (2)

From equation (1): y = 34 - x

:. x² + (34 - x)² = 676

x² + 1,156 - 68x + x² = 676

x² + x² - 68x + 1,156 - 676 = 0

2x² - 68x + 480 = 0

x² - 34x + 240 = 0

(x² - 24x) - (10x + 240) = 0

x(x - 24) -10(x - 24) = 0

(x - 24)(x - 10) = 0

x = 24 or 10

y = 34 - x

y = 34 - 10 = 24

:. x = 10 and y = 24

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Find the mode of the data set that consists of 8, 18, 4, 2, 3, 7, 11, 13, 5, 1.
A. 6
B. 7.2
C. no mode
D. 17

Answers

Answer:

C. no mode

Step-by-step explanation:

Step 1. Rearrange the numbers in order from least to greatest!

1, 2, 3, 4, 5, 7, 8, 11, 13, 18

Step 2. Find the mode. (Number mostly being occurred)

No numbers are being repeated so therefore, there’s no mode

Line AB is perpendicular to line BC. What is the justification for the following statement?
m ABC = 90°

Definition of angle bisector

Definition of complementary angles

Definition of perpendicular lines

Definition of supplementary angles

Answers

Answer:

definition of perpendicular lines

The area of the shaded sector of circle H is 32.
16
H
What is the area of the unshaded sector?
967
O 2247
32871
O 34571

Answers

Answer:

B

Step-by-step explanation:

Area of shaded region + Area of unshaded region = Area of circle

Area of the unshaded sector=256*pi-32*pi=224*pi

Answer:

radius Is 16

total area becomes pi r ^ 2 = 16^2 pi = 256pi

remaining area becomes

256 pi - 32 pi = 224 pi option b

brainliest pls

What’s the rate of change please help

Answers

Answer:

Rate of change, is also another word for slope.

Slope --> y2 - y1 / (x2-x1)

Assuming the table is already in xy, the cords are in xy form too.

1) (8,8)

2) (11,10)

Plug points into slope eq

--> 10 - 8 = 2

----> 11 - 8 = 3

2/3 Is the slope/rate of change.

evaluate the function
f (x) = -x + 3 when x = 5
pls help :(

Answers

Answer:

f(5) = -2

Step-by-step explanation:

f (x) = -x + 3

Let x = 5

f(5) = -5+3

f(5) = -2

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

[tex]\huge\text{f(x) = -x + 3}\\\huge\boxed{\rightarrow}\huge\text{ f(x) = -5 + 3}\\\huge\boxed{\rightarrow}\huge\text{ y = -5 + 3}\\\huge\boxed{\rightarrow}\text{ y = -2}\\\\\\\boxed{\boxed{\huge\text{Answer: \bf f(x) = -2}}}\huge\checkmark[/tex]

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

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

Find the surface area of the rectangular prism.

Answers

Answer:

SA = 112

Step-by-step explanation:

A = 2wl + 2lh + 2hw

length = 8 km

width = 2 km

height = 4 km

SA = 112 km

Answer:

112

Step-by-step explanation:

SA = 2lh + 2lw + 2hw
where l = length w = width and h = height

Dimensions: l = 8, w = 2 and h = 4.

SA = 2(8)(4) + 2(8)(2) + 2(4)(2)

SA = 2(32) + 2(16) + 2(8)

SA = 64 + 32 + 16

SA = 112 km

The surface area of the rectangular prism is 112 km.

Narasimha, Madhu and Pavan started a business by investing Rs. 120,000, Rs. 135,000 and Rs. 150,000 respectively. Find the share of Pavan, out of an annual profit of Rs. 56,700. ​

Answers

Answer:

1.

= Here,

Narasimha invest = 120,000

Madhu 135,000

pavan =

5. Find the measure of x and and the angle measure.
(3x - 15)
(2x + 7)

Answers

Answer:

here's the answer to your question

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