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3 years ago

11

37.5 in scientific notation

1 answer:

Rom4ik [11]3 years ago

8 0

I think it would be 3.75 x 10^1.

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Two collinear points on a line are given in the table below:

katrin [286]

Answer:

$(4,3)$ and $(7,2)$ do not lie on the line

Step-by-step explanation:

Given

$(0,0)\ and\ (2,1)$

Required

Determine which points that are not on the line

First, we need to determine the slope (m) of the line:

$m = \frac{y_2 - y_1}{x_2- x_1}$

Where

$(x_1,y_1) = (0,0)$

$(x_2,y_2) = (2,1)$

So;

$m = \frac{y_2 - y_1}{x_2- x_1}$

$m = \frac{1 - 0}{2-0}$

$m = \frac{1}{2}$

Next, we determine the line equation using:

$y - y_1 = m(x -x_1)$

Where

$m = \frac{1}{2}$

$(x_1,y_1) = (0,0)$

$y - y_1 = m(x -x_1)$ becomes

$y - 0 = \frac{1}{2}(x - 0)$

$y = \frac{1}{2}x$

To determine which point is on the line, we simply plug in the values of x to in the equation check.

For $(4,2)$

$x = 4$ and $y =2$

Substitute 4 for x and 2 for y in $y = \frac{1}{2}x$

$2 = \frac{1}{2} * 4$

$2 = \frac{4}{2}$

$2=2$

<em>This point is on the graph</em>

<em></em>

For $(4,3)$

$x = 4$ and $y = 3$

Substitute 4 for x and 3 for y in $y = \frac{1}{2}x$

$3 = \frac{1}{2} * 4$

$3 = \frac{4}{2}$

$3 \neq 2$

<em>This point is not on the graph</em>

<em></em>

For $(7,2)$

$x = 7$ and $y = 2$

Substitute 7 for x and 2 for y in $y = \frac{1}{2}x$

$2 = \frac{1}{2} * 7$

$2 = \frac{7}{2}$

$2 \neq 3.5$

<em></em>

<em>This point is not on the graph</em>

<em></em>

<em></em> $(\frac{4}{8},\frac{2}{8})$ <em></em>

<em></em> $x = \frac{4}{8}$ and<em> </em> $y = \frac{2}{8}$ <em></em>

<em>Substitute </em> $\frac{4}{8}$ <em> for x and </em> $\frac{2}{8}$ <em> for y in </em> $y = \frac{1}{2}x$ <em></em>

<em></em> $\frac{2}{8} = \frac{1}{2} * \frac{4}{8}$ <em></em>

<em></em> $\frac{2}{8} = \frac{1 * 4}{8 * 2}$ <em></em>

<em></em> $\frac{2}{8} = \frac{4}{16}$ <em></em>

<em></em> $\frac{1}{4} = \frac{1}{4}$ <em></em>

<em></em>

<em>This point is on the graph</em>

3 0

3 years ago

Find the sum of the given arithmetic series. 24 + 48 + 72 + 96 +...+ 480

Alja [10]

Answer:

5040

Step-by-step explanation:

The given series is :

24 + 48 + 72 + 96 +...+ 480

The first term, a= 24

Common difference, d = 24

The last term, $a_n=480$

Let there are n terms in the AP.

So,

$a_n=a+(n-1)d\\\\480=24+(n-1)24\\\\480=24+24n-24\\\\n=20$

There are 20 terms in the series. The sum of 20 terms is :

$S_{20}=\dfrac{n}{2}(2a+(n-1)d))\\\\=\dfrac{20}{2}\times (2(24)+19(24))\\\\=5040$

So, the sum of the given arithmetic series is equal to 5040.

8 0

3 years ago

The value of y varies jointly with the values of x and z When x = 4 and z = 10, the value of y is 360.

Igoryamba

Answer:

A

Step-by-step explanation:

Joint variation is given by:

$y=kxz$

Where k is some constant.

We are given that y = 360 when x = 4 and z = 10. Therefore:

$360=k(4)(10)$

Solving for k:

$40k=360\Rightarrow k=9$

Therefore, our equation is:

$y=9xz$

Then when x = 5 and z = 12:

$y=9(5)(12)=540$

The answer is A.

3 0

3 years ago

for the following questions, determine how many solutions each equation has. if one solution, state the value of x. x+6+8=2x-x+1

vichka [17]

Answer:

infinite solutions

Step-by-step explanation:

x+6+8=2x-x+14

x+6+8=x+14

x+14=x+14

14=14

or

x=x

plug in any number

2+6+8=2(2)-2+14

16=16

another example

8+6+8=2(8)-8=14

22=22

5 0

3 years ago

a) The quadratic 3x^2-12x-11 can be written in the form 3(x+a)^2+b. Find the values of a and b. b) Given that the solutions of t

LenKa [72]

Answer:

Step-by-step explanation:

a) 3x^2-12x-11=3*x^2-3*2*2*x+3*4-23=3*(x^2-2*2x+2^2)-23=3*(x-2)^2-23

so a= -2 ,b= -23

b) x1=[12+V(12^2-4*3* -11)]/6=12/6+V(144+132)/6=2+2/6V69=2+1/3V69=

2+V69/9=2+V23/3

c=2, d= 23/3

5 0

3 years ago