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3 years ago

What is the 52nd term of the sequence (-38,-45,-52,-59...)

Mathematics

1 answer:

bezimeni [28]3 years ago

4 0

Answer: - 395

Step-by-step explanation: The sequence is in form of Arithmetic sequence , if you check properly, the difference between the 2nd number and the 1st number is the same as the difference between the 3 rd and the 2nd ...

This difference is called common difference and it's denote with d.

From the sequence given d = - 7

the 52nd term = a + 51d , where " a" is the first term

= - 38 + 51 ( -7 )

= - 38 - 357

= - 395

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What values could be substituted for x to make a true number sentence in x + 4 = x + 8

choli [55]

The answer is no solution.

Explanation: x+4 = x+8
-x -x
4 cannot equal 8
Answer is No solution

5 0

3 years ago

A line passes through the points (–3, –4) and (6, 2). What number is the x-intercept?

LuckyWell [14K]

Answer:

Step-by-step explanation:

$\bold{METHOD\ 1}$

$\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{x-intercept:}\ (x,\ 0).\\\\\text{Susbtitute the coordinates of the points to the formula of a slope}\\\\(-3,\ -4),\ (6,\ 2),\ (x,\ 0):\\\\m=\dfrac{2-(-4)}{6-(-3)}=\dfrac{2+4}{6+3}=\dfrac{6}{9}=\dfrac{6:3}{9:3}=\dfrac{2}{3}\\\\m=\dfrac{0-2}{x-6}=\dfrac{-2}{x-6}\\\\\text{Therefore we have the equation:}\\\\\dfrac{-2}{x-6}=\dfrac{2}{3}\qquad\text{cross multiply}\\\\2(x-6)=(-2)(3)\\\\2(x-6)=-6\qquad\text{divide both sides by 2}\\\\x-6=-3\qquad\text{add 6 to both sides}\\\\x=3$

$\bold{METHOD\ 2}\\\\\text{Look at the picture.}$

Mark points in the coordinate system.

Lead a line through these points.

Read x-intercept.

5 0

3 years ago

Read 2 more answers

Here is a list of the normal monthly precipitation (in inches) for January for 20 different U.S. cities. 4.0, 1.0, 1.5, 1.6, 2.0

shutvik [7]

Answer:

minimum value = 1.0 , the lower quartile = 2.3, the middle value = 3.5.

the upper quartile = 3.95, the maximum value = 7.3.

Step-by-step explanation:

Five Number Summary of any data consists basically of 5 data sets.

1) The minimum Value

2)The first (lower) quartile

3) The middle value (Median)

4) The third (upper) quartile

5)The maximum value

Now, the given data is 4.0, 1.0, 1.5, 1.6, 2.0, 2.2, 2.4, 2.7, 3.4, 3.4, 3.5, 3.6, 3.6, 3.7, 3.7, 3.9, 4.1, 5.8, 4.1, 7.3

Arrange it in the ascending order,

1.0, 1.5, 1.6, 2.0, 2.2, 2.4, 2.7, 3.4, 3.4, 3.5, 3.6, 3.6, 3.7, 3.7, 3.9, 4.0, 4.1, 4.1, 5.8, 7.3

Here,

1) The minimum Value is 1.0

2)The first (lower) quartile is 2.3.

3) The middle value (Median) is 3.5.

4) The third (upper) quartile is 3.95.

5)The maximum value is 7.3.

7 0

3 years ago

Explain how to write a quadratic equation given the following three points on the graph (5,31) (3,11) (0,11)

masha68 [24]

Given:

The graph of a quadratic function passes through the points (5,31) (3,11) (0,11).

To find:

The equation of the quadratic function.

Solution:

A quadratic function is defined as:

$y=ax^2+bx+c$ ...(i)

It is passes through the point (0,11). So, substitute $x=0,y=11$ in (i).

$11=a(0)^2+b(0)+c$

$11=c$

Putting $c=11$ in (i), we get

$y=ax^2+bx+11$ ...(ii)

The quadratic function passes through the point (5,31). So, substitute $x=5,y=31$ in (ii).

$31=a(5)^2+b(5)+11$

$31-11=a(25)+5b$

$20=25a+5b$

Divide both sides by 5.

$4=5a+b$ ...(iii)

The quadratic function passes through the point (3,11). So, substitute $x=3,y=11$ in (ii).

$11=a(3)^2+b(3)+11$

$11-11=a(9)+3b$

$0=9a+3b$

Divide both sides by 3.

$0=3a+b$ ...(iv)

Subtracting (iv) from (iii), we get

$4-0=5a+b-3a-b$

$4=2a$

$\dfrac{4}{2}=a$

$2=a$

Putting $a=2$ in (iv), we get

$0=3(2)+b$

$0=6+b$

$-6=b$

Putting $a=2,b=-6$ in (ii), we get

$y=(2)x^2+(-6)x+11$

$y=2x^2-6x+11$

Therefore, the required quadratic equation is $y=2x^2-6x+11$ .

7 0

3 years ago

4x -y -16 = 0 in slope intercept form

xxMikexx [17]

Y=-4x+16 is slope intercept form. I hope this helped

4 0

3 years ago