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1 year ago

Create an equivalent expression for 13 ^−7 x 13 ^5.

Mathematics

2 answers:

Sveta_85 [38]1 year ago

8 0

$13^{-7} \times 13^5=13^{-2}=\boxed{\frac{1}{13^2}}$

Zina [86]1 year ago

3 0

13-7 x 135
= 13-2
1
132

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Determine an equation for the right bisector of the line segment with endpoints J(-5,3) and K(3,-2)

Norma-Jean [14]

Answer:

$y=1.6x+2.1$

Step-by-step explanation:

we know that

The right bisector of the line segment JK is a perpendicular line to the segment JK that pass through the midpoint of segment JK

step 1

Find the midpoint JK

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have

$J(-5,3),K(3,-2)$

substitute the values

$M(\frac{-5+3}{2},\frac{3-2}{2})$

$M(\frac{-2}{2},\frac{1}{2})$

$M(-1,\frac{1}{2})$

step 2

Find the slope JK

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$J(-5,3),K(3,-2)$

substitute

$m=\frac{-2-3}{3+5}$

$m=\frac{-5}{8}$

$m=-\frac{5}{8}$

step 3

Find the slope of the line perpendicular to the segment JK

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)

$m_1*m_2=-1$

we have

$m_1=-\frac{5}{8}$ ----> slope of segment JK

Find m_2

substitute

$(-\frac{5}{8})*m_2=-1$

$m_2=\frac{8}{5}$

step 4

Find the equation for the right bisector of the line segment JK

The equation in point slope form is equal to

$y-y1=m(x-x1)$

we have

$m=\frac{8}{5}$

$point\ M(-1,\frac{1}{2})$

substitute

$y-\frac{1}{2}=\frac{8}{5}(x+1)$

Convert to slope intercept form

isolate the variable y

$y-\frac{1}{2}=\frac{8}{5}x+\frac{8}{5}$

$y=\frac{8}{5}x+\frac{8}{5}+\frac{1}{2}$

$y=\frac{8}{5}x+\frac{21}{10}$

$y=1.6x+2.1$

7 0

3 years ago

The length of the longer leg of a right triangle is

Harman [31]

A and b are legs
a^2+b^2=c^2
lets say
a>b

so
a=13+3b
c=14+3b

a^2+b^2=c^2
(13+3b)^2+b^2=(14+3b)^2
9b^2+78b+169+b^2=9b^2+84b+196
10b^2+78b+169=9b^2+84b+196
minus 9b^2 both sides
b^2+78b+169=84b+196
minus 84b both sides
b^2-6b+169=196
minus 196 both sides
b^2-6b-27=0
factor
(b+3)(b-9)=0
set to zero
b+3=0
b=-3, false, dimentions cannot be negative

b-9=0
b=9

shorter leg is 9

a=13+3b
a=13+3(9)
a=13+27
a=40

c=14+3b
c=14+27
c=41

side legnths are
9in, 40in, 41in

3 0

2 years ago

The following are the temperatures of 10 days in winter in °C.

LUCKY_DIMON [66]

Mean basically means average/ all the numbers added together divided by the amount of numbers given to us

So all the numbers added up will equal to 51 (-5+-3+-1+6+6+9+9+10+10+10) now divide that by the number of of numbers me given to us which is 10 so

51/10= 5.1

Mean=5.1

6 0

2 years ago

Michael goes to the store to buy apples. He buys 3 apples for $3.75. What is the unit rate?

____ [38]

Answer

yes it is 1.25/1

Step-by-step explanation:

divide 3.75 by 3

3 0

2 years ago

Solve for x:<br> 2 - 6 = 0<br> X =<br><br> Help plz

antiseptic1488 [7]

Answer:

because when you subtract 6 from 6 you get 0

6 - 6 = 0

8 0

2 years ago