MATHEMATICS HIGH SCHOOL

If y varies directly as x, and y is 6 when x is 72, which is the value of y when x is 8 ?

Answers

Answer 1

Answer:

$(y)/(x) = k$

$(6)/(72) = k$

$(1)/(12) = k$

********************************

$(y)/(x) = k$

$(y)/(8) = (1)/(12)$

12y = 8

$y = (8)/(12)$

$y = (2)/(3)$

Answer 2

Answer:

y = $(2)/(3)$

given y ∝ x

To convert to an equation multiply by k the constant of variation

y = kx

to find k use the given condition y = 6 when x = 72

y = kx ⇒ k = $(y)/(x)$ = $(6)/(72)$ = $(1)/(12)$

equation is → y = $(1)/(12)$ x

when x = 8 then

y = $(1)/(12)$ × 8 = $(8)/(12)$ = $(2)/(3)$

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the length of a rectangle is 8cm more than the width and its area is 172cm2 .find the width of the rectabgle

Answers

$l-the\ length\nl+8-the\ width\nA=172\ cm^2\n\nA=lengtf\cdot width\n\nsubtitute\n\nl(l+8)=172\n\nl^2+8l=172\ \ \ |subtract\ 172\ from\ both\ sides\n\nl^2+8l-172=0\na=1;\ b=8;\ c=-172\n\n\Delta=b^2-4ac\n\n\Delta=8^2-4\cdot1\cdot(-172)=64+688=752 > 0\n\nl_1=(-b-\sqrt\Delta)/(2a)\ and\ l_2=(-b+\sqrt\Delta)/(2a)\n\n\sqrt\Delta=√(752)=√(16\cdot47)=4√(47)\n\nl_1=(-8-4√(47))/(2\cdot1)=-4-2√(47) < 0\n\nl_2=(-8+4√(47))/(2\cdot1)=-4+2√(47) > 0\n\nThe\ width:l+8=-4+2√(47)+8=4+2√(47)\n\nAnswer:\boxed{length=(2√(47)-4)cm;\ width=(4+2√(47))cm}$
$length\approx9.71cm;\ width\approx17.71cm$

Solve the equation s + 2.8 = 6.59

Answers

s + 2.8 = 6.59
s = ?

To solve for s use the inverse operation of addition, which is subtraction.

s + 2.8 = 6.59
6.59 - 2.8 = s
6.59 - 2.8 = 3.79
s = 3.79

Check:

s + 2.8 = 6.59
s = 3.79
3.79 + 2.8 = ?
3.79 + 2.8 = 6.59
Correct!

This proves: s = 3.79 ;)

In order to solve for the variable, isolate the variable.

s + 2.8 = 6.59
- 2.8 -2.80 ( 2.8 is the same as 2.80 )

s = 3.79

Double check by plugging in the variable.

s + 2.8 = 6.59
3.79 + 2.8 = 6.59
6.59 = 6.59

Yes, it's correct!

Hope I helped!

Danae is choosing between two jobs. One job pays an annual bonus of $1,500 plus $120 per day workec second job pays an annual bonus of $2,500 plus $110 per day worked. Which equation can be solved to after how many days, d, Danae would make the same amount of money regardless of the job she choose

Answers

Answer: 120d + 1,500 = 110d + 2,500

Step-by-step explanation:

Answer:

$1,500 + 120d = $2,500 + 110d

Step-by-step explanation:

Just in case you want the solution as well:

10d = 1000

d = 100

Mrs. Daniel pays $324 for a handbag and 3 pairs of shoes. The handbag costs half as much as the 3 pairs of shoes combined. Find the cost of the handbag.

Answers

$h-the\ handbag\ns-shoes\n\n \left\{\begin{array}{ccc}h+3s=324\nh=(1)/(2)\cdot3s\end{array}\right\n\left\{\begin{array}{ccc}h+3s=324\nh=(3)/(2)s&/\cdot(2)/(3)\end{array}\right\n\left\{\begin{array}{ccc}h+3s=324\ns=(2)/(3)h\end{array}\right\n\nsubstitute:\n\nh+3\cdot(2)/(3)h=324\nh+2h=324\n3h=324\ \ \ \ /:3\nh=108\n\nAnswer:Cost\ of\ the\ handbag\ is\ \$108.$

I need help again and can smb help me with the whole study guide pls !

Answers

Answer:

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