1. Given: AB = 64; M lies on the line AB

Mathematics

1 answer:

Gnom [1K]4 years ago

6 0

Answer:

Step-by-step explanation:

Given the following lengths AB = 64, AM = 4x + 4 and BM= 6x-10, If M lies on the line AB then AM+MB = AB (addition property)

Substituting the given parameters into the addition property above;

AM+MB = AB

4x + 4 + 6x - 10 = 64

combine like terms

4x+6x = 64+10-4

10x = 74-4

10x = 70

Divide both sides by 10

x = 70/10

x = 7

Note that for M to be the midpoint of AB then AM must be equal to BM i.e AM = BM

To get AM ;

Since AM = 4x+4

substitute x = 7 into the function

AM = 4(7)+4

AM = 28+4

AM = 32

Similarly, BM = 6x-10

BM = 6(7)-10

BM = 42-10

BM = 32

Since AM = BM = 32,. then M is the midpoint of AB

You might be interested in

Sec^4x-tan^4x=sec^2x+tan^2x

tino4ka555 [31]

$\sec^4x-\tan^4x=(\sec^2x-\tan^2)(\sec^2x+\tan^2x)=\sec^2x+\tan^2x$

since $\tan^2x+1=\sec^2x$ .

5 0

3 years ago

Cost of a CD: $23.50 Markup: 63% Discount: 50%

Vedmedyk [2.9K]

Alright this equation has two big steps. First we need to find the price after it was marked up, then we need to take that number and find the discounted price.
To find the cost after a percent of it was added, we just need to multiply the two together and add.
=
$
23.50
+
(
$
23.50
⋅
(
63
%
100
)
)
(we divide by 100 to get the number out of a percent)
=
$
23.50
+
(
$
23.50
⋅
0.63
)
=
$
23.50
+
$
14.81
=
$
38.31
Ok now that we have the number after the price increase, we now need to find the final answer after a discount of
50
%
(do the exact same idea as above but switch the sign)
=
$
38.31
−
(
$
38.31
⋅
(
50
%
100
)
)
=
$
38.31
−
(
$
38.31
⋅
0.5
)
=
$
38.31
−
$
19.16
=
$
19.15

7 0

3 years ago

On his last credit card bill, Frank paid a variable finance rate of 1.5 percent on the first $500, and 1 percent

Nady [450]

Answer: