find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical (-7,-9) and (-5,-8)

Answers

Answer 1

Answer: easy peasy
slope=(change in rise)/(change in run)
aka
slope between points (x1,y1) and (x2,y2) is
slope=(y2-y1)/(x2-x1) since y is rise/up and x is run/leftright

points

(-7,-9) and (-5,-8)
x1=-7
y1=-9
x2=-5
y2=-8
remember minusing a negative means addin a positive
slope=(-8-(-9))/(-5-(-7))=
(-8+9)/(-5+7)=1/2

slope=1/2

positive slopes go from bottom left to top right

since it is less than 1
it is more horizonal than vertical

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Help me this please..A shopkeeper sold his entire stock of shirts and ties in a sale for $10000. The shirt were priced at 3 for $100 and the ties $20 each. If he had sold only half the shirts and two-thirds of the ties hw would have received $6000. How many did he sell in the sale?

Answers

He sells 300 shirts and 120 ties in the sale.

Given that,

A shopkeeper sold his entire stock of shirts and ties in a sale for $10000.

The shirt was priced at 3 for $100 and the ties $20 each.

If he had sold only half the shirts and two-thirds of the ties he would have received $6000.

We have to determine,

How many did he sell in the sale?

According to the question,

Let the number of shirts be x.

And the number of ties be y.

The shirt was priced at 3 for $100 = $\rm (100x)/(3)$

The ties are $20 each = 20y

A shopkeeper sold his entire stock of shirts and ties in a sale for $10000.

The shirt was priced at 3 for $100 and the ties $20 each.

$\rm (Price \ of \ each \ set \ of \ shirt)/(Number \ of \ sets \ of \ shirts ) + Price \ of \ each\ ties = Total \ sale \ of \ shirt \ and \ ties \n\n(100x)/(3) + 20y = 10000\n\n33.33 x+ 20y = 10000$

And he had sold only half the shirts and two-thirds of the ties he would have received $6000.

$\rm = (Price \ of \ each \ set \ of \ shirt * he \ had \ sold \ half \ shirts)/(Number \ of \ sets \ of \ shirts )\n\n= (100x * (1)/(2))/(3)\n\n= (50x)/(3)$

$= \rm Two \ third * Price \ of \ each\ ties = (2)/(3) * 20y = (40y)/(3)$

Then,

The required equation is,

$\rm(50x )/(3) + (40y )/(3) = 6000$

Multiply equation (ii) by 2,

$\rm 2* [(50x )/(3) ] + (40y )/(3) = 2* 6000\n\n(100x )/( 3 ) + (80y )/(3) = 12000$

Subtract equation (i) from (ii) in order to eliminate x.

$\rm (100x )/( 3 )- (100x )/( 3 ) + 20y - (80y )/(3 )= 10000 - 12000\n\n ( 60y -80y )/(3 ) = - 2000\n\n ( -20y )/(3 ) = - 2000\n\n y = (3 *2000 )/(20)\n\n y=(6000)/(20)\n\n y = 300.$

Substitute the value of y in equation 1,

$(100x )/(3) + 20y = 10000\n\n (100x )/(3) + 20*300 = 10000\n\n(100x )/(3) + 6000 = 10000 \n\n (100x )/(3) = 10000 - 6000\n\n (100x )/(3) = 4000\n\n x =( 4000 * 3 )/( 100)\n\nx =(12000)/(10) \n\nx = 120$

Hence, He sells 300 shirts and 120 ties in the sale.

For more details refer to the link given below.

brainly.com/question/15894203

He sold his entire stock for $10000.

Let the number of shirts be x.
Let the number of ties be    y.

The shirt is at 3 for $100. Therefore, a shirt would cost   $(100/3)
The tie cost $20 each.

Therefore, Multiplying by the number of shirts and ties:

100x / 3 + 20y = 10000 .............(i).

If he had sold half the shirts and two-thirds the ties, the equation becomes:
100/3 * (x/2) + 20 * (2y / 3) = 6000
50x / 3 + 40y / 3 = 6000 ..............(ii)

Multiply equation (ii) by 2.

2*(50x / 3 + 40y / 3 ) = 2* 6000
100x / 3 + 80y / 3 = 12000 .........(iii).

Equation (i) Minus (iii) . Inorder to eliminate x.

100x / 3 - 100x / 3 + 20y - 80y / 3 = 10000 - 12000
      -20y / 3 = - 2000.
         y = 3 * 2000 / 20
   y = 300.
Substituting into equation (i).
100x / 3 + 20y = 10000
100x / 3 + 20*300 = 10000
100x / 3 + 6000 = 10000
100x / 3     = 10000 - 6000
100x / 3     = 4000
x = 4000 * 3 / 100
x = 120.

So he actually sold 120 shirts and 300 ties. Cheers.

What is the second step when evaluating the expression 18 = (24 - 18) + 3-1?18 = 6
O 24 - 18
-18 + 3
3-1

Answers

I believe you meant the equal signs to be division symbols haha. The next step would be 18/6.

Answer:

8/16

Step-by-step explanation:

A bus goes from town A to B in an exact time. If the bus goes at the rate of 50km/h, then it will arrive B 42min later than it had to and if it increases its speed 5.5/9 m/sec., it will arrive B 30min earlier. Find:A) The distance between the two towns;
B) The exact time that it takes to arrive town B
C) The speed of the bus(by schedule) for the exact time.

Answers

Let the speed of bus for the exact time = x km/h
the distance between the cities = y km
then the exact time would be, t hours = (y/x) hours

If the bus goes at the rate of 50km/h, then it will arrive B 42min later,
speed = 50 km/h
42 minutes = 42/60 hours = 7/10 hours = 0.7 hours
time taken = t+0.7
distance = speed×time
⇒ y = 50×(t+0.7)
⇒ y = 50t + 35 ---------------------(1)

it increases its speed 5.5/9 m/sec, it will arrive B 30min earlier.
5.5/9 m/s = (5.5/9)×(18/5) km/h = 2.2 km/h
30 minutes = 30/60 = 0.5 hour
speed = (x+2.2) km/h
time = (t - 0.5) hours

distance = speed×time
⇒ y = (x+2.2)×(t-0.5)
⇒ y = ((y/t) +2.2)×(t-0.5) (t = y/x)
⇒ y = y - 0.5 (y/t) + 2.2t - 1.1
⇒ 0.5 (y/t) - 2.2t + 1.1 = 0   (subtracting y from both sides)
⇒ (y/t) - 4.4t - 2.2 = 0    (dividing both sides by 0.5)
⇒ y - 4.4t² - 2.2t = 0    (multiplying both sides by t)
⇒ 50t + 35 - 4.4t² - 2.2 t = 0 (from equation 1)
⇒ -4.4t² + 35 + 47.8t = 0
⇒ 4.4t² - 47.8t - 35 = 0

solving the quadratic equation, we get t = 11.55 hours
y = 50t + 35 = 612.5 km
x = 612.5/11.55 = 53 km/h

A) 612.5 km
B) 11.55 hours
C) 53 km/h

The Logic Defined:

1 Minute=t, (a unit of time)

Time (By schedule)=nt, (n>0), nt=number of minutes

Metre(s)=m

Speed=s (in metres per minute), s=[distance in metres]/[time in minutes]

Distance=d (in metres), d=[speed in metres per minute]*[time in minutes]

---------------------------------------------

Statement (1):

"If the bus goes at the rate of 50km/h, then it will arrive B 42min later than it had to."

Conclusion 1:

$\frac { 50km }{ h } =\frac { 50,000m }{ 60t } =\frac { 2,500m }{ 3t } \n \n \therefore \quad \frac { 2,500m }{ 3t } =nt+42t\n \n \frac { 2,500m }{ 3t } =t\left( n+42 \right)$

$\n \n 2,500m=3{ t }^( 2 )\left( n+42 \right) \n \n m=\frac { 3{ t }^( 2 )\left( n+42 \right) }{ 2,500 }$

Statement (2):

"if it increases its speed 5.5/9 m/sec., it will arrive B 30min earlier."

Conclusion 2:

$\frac { 5.5m }{ 9\quad seconds } =\frac { 5.5m }{ \frac { 9 }{ 60 } t } =\frac { 110m }{ 3t }$

$\n \n \therefore \quad \frac { 110m }{ 3t } =nt-30t\n \n \frac { 110m }{ 3t } =t\left( n-30 \right) \n \n 110m=3{ t }^( 2 )\left( n-30 \right)$

$\n \n m=\frac { 3{ t }^( 2 )\left( n-30 \right) }{ 110 }$

Conclusion 3, because of conclusion 1 and 2:

$\frac { 3{ t }^( 2 )\left( n-30 \right) }{ 110 } =\frac { 3{ t }^( 2 )\left( n+42 \right) }{ 2,500 } \n \n 7,500{ t }^( 2 )\left( n-30 \right) =330{ t }^( 2 )\left( n+42 \right) \n \n 7,500\left( n-30 \right) =330\left( n+42 \right)$

$\n \n 7,500n-225,000=330n+13,860\n \n 7,500n-330n=13,860+225,000\n \n 7,170n=238,860\n \n n=\frac { 238,860 }{ 7,170 } \n \n \therefore \quad n=\frac { 7962 }{ 239 }$

Therefore,

$Time\quad by\quad schedule=\frac { 7962 }{ 239 } t\n \n Approx:\quad 33.3\quad mins$

Now we want to find the distance between the two towns, so we say that:

$d=\frac { 2,500m }{ 3t } \cdot \left( \frac { 7962 }{ 239 } t+42t \right) \n \n =\frac { 2,500m }{ 3t } \cdot \frac { 18,000 }{ 239 } t$

$\n \n =\frac { 45,000,000 }{ 717 } m\n \n Approx:\quad 62,761.5\quad metres\n \n In\quad km\quad (approx):\quad 62.761\quad km$

So now you want to know how fast the bus has to travel to get to its destination on time...

Use the formula: s=d/t

Therefore:

$s=\frac { \frac { 45,000,000 }{ 717 } m }{ \frac { 7962 }{ 239 } t } \n \n Approx:\quad 1,883.9\quad metres\quad per\quad minute$

Mark earns $135 for selling a $1,500 refrigerator. Which sale listed has the same commission rate? A) $36 commission on a $400 dryer sale B) $40 commission on a $500 dryer sale Eliminate C) $210 commission on a $1,400 oven sale D) $30 commission on a $600 freezer sale

Answers

$36 commission on a $400 dryer sale. Then the commission rate will be 0.09. Then the correct option is A.

What are ratio and proportion?

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

Mark procures $135 for selling a $1,500 fridge.

The commission rate remains constant. Then the commission rate is given as,

Commission rate = 135 / 1500

Commission rate = 0.09

Let's check all the options, then we have

A) $36 commission on a $400 dryer sale. Then the commission rate is given as,

Commission rate = 36 / 400

Commission rate = 0.09

$36 commission on a $400 dryer sale. Then the commission rate will be 0.09. Then the correct option is A.

More about the ratio and the proportion link is given below.

brainly.com/question/14335762

#SPJ5

It’s A

$36 commission on a $400 dryer sale is at the same rate. Both have commission rates of 9%.

135

1500

= 0.09

400

= 0.09

What is the average rate of change of f(x)=1/4x^2-4 over the interval from 0 to 3?

Answers

Answer:

1/4

Step-by-step explanation:

To find the average rate of change we find

f(3) -f(0)

----------

3-0

We need to find f(3) = 1/4 (3)^2 -4 = 1/4 (9) -4 = 9/4 -4 = -7/4

f(0) = 1/4 (0)^2 - 4 = -4

f(3) -f(0)

----------

3-0

-7/4 - (-4)

---------------

3-0

-7/4 +4

-----------

3-0

-7/4 +4

-----------

3-0

-7/4 +16/4

----------------

9/4

---------

9/12

1/4

Answer:

3/4

Step-by-step explanation:

The x values are 0 and 3. Use the formula y2-y1/x2-x1

Plug in the x factors into the orginal equation. Should look like the equations below:

f(x)=1/4(0)^2-4 -------> -4

f(x)=1/4(3)^2-4 --------> -7/4Now plug it in to the formula we saved earlier.

-7/4-(-4)/3-0= -7/4+4/3= -7/4+16/4/3

Then simplify it.

9/4/3, and in this case we have a fraction in a fraction and when this happens just multiply the equation by the x variables reciprical which in this case the x is 3 so the equation is multiplied by 1/3 and you would get 9/12. Now simplify that and you get 3/4.

5/8 as a decimal and as a percent

Answers

It is 0.625 as a decimal and also 62.5%

.625=decimal form

62.5% in percentage form

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