Mathematics, 18.07.2019 02:00 ayoismeisalex

The sum of two numbers is 18. one number is 2 more that for times the other. find the numbers.

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Answer from: mprjug6

Hi there!

Let the first number be represented by X.
The second number (which is 2 more than four times the other), can be represented by 4X + 2.

We can now find the sum of this expression.
X + 4X + 2

Collect terms
5X + 2

The sum of the numbers is 18. Therefore we can set up the following equation.
5X + 2 = 18

Subtract 2.
5X = 16

Divide both sides by 5.
X = 16/5 = 3 1/5.

Therefore, the first number is 3 1/5. To find the second number we must plug in X = 3 1/5 into the expression 4X + 2

4 * (3 1/5) + 2 = 12 4/5 + 2 = 14 4/5
The two numbers are
$3 \frac{1}{5} \: \: and \: \: 14 \frac{4}{5}$

~ Hope this helps you!

Answer from: Quest

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

= 2×(-2)+(-8)×(6)+(-8)×(-5)

= -4-48+40

= -12

hence, v.w= -12

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

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The sum of two numbers is 18. one number is 2 more that for times the other. find the numbers....