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3 years ago

9

the width of the rectangle is 5 inches less than it's length, and the area is 84 square inches. what are the length and width of

the rectangle?

1 answer:

inysia [295]3 years ago

7 0

W= l - 5 where w = width and l = length

area = 84 = l*w = l(l-5)

l(l-5) = 84
l^2 - 5l - 84 = 0
(l - 12)(l + 7) = 0
l = 12

length = 12 and width = 7

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The cost of six hens and one duck at the university poultry farm is GH₵40. While four hens and three ducks cost GH₵36. What is t

Anon25 [30]

Answer:

Step-by-step explanation:

Let's call hens h and ducks d. The first algebraic equation says that 6 hens (6h) plus (+) 1 duck (1d) cost (=) 40.

The second algebraic equations says that 4 hens (4h) plus (+) 3 ducks (3d) cost (=) 36.

The system is

6h + 1d = 40

4h + 3d = 36

The best way to go about this is to solve it by substitution since we have a 1d in the first equation. We will solve that equation for d since that makes the most sense algebraically. Doing that,

1d = 40 - 6h.

Now that we know what d equals, we can sub it into the second equation where we see a d. In order,

4h + 3d = 36 becomes

4h + 3(40 - 6h) = 36 and then simplify. By substituting into the second equation we eliminated one of the variables. You can only have 1 unknown in a single equation, and now we do!

4h + 120 - 18h = 36 and

-14h = -84 so

h = 6.

That means that each hen costs $6. Since the cost of a duck is found in the bold print equation above, we will sub in a 6 for h to solve for d:

1d = 40 - 6(6) and

d = 40 - 36 so

d = 4.

That means that each duck costs $4.

3 0

3 years ago

if the store purchased a kitchen appliance for $42 and sold it for $58.80, what was the percent markup?

oksano4ka [1.4K]

Answer:

40%

Step-by-step explanation:

Percent markup = new price - original price/original price

Do the subtraction first.

58.80 - 42.00 = 16.80

Now do the division

16.8/42 = 0.40

Change the decimal to a percent by moving the decimal two place to the right.

0.40 = 40%

6 0

2 years ago

PSEG Long Island charges its residential customers a little monthly service charge plus an energy charge based on the amount of

german

Using linear function concepts, it is found that:

a) It costs $0.1 for each kilowatt hour of electricity used in excess of 250 kWh.
b) f(90) = 46.6, which is the cost of 340 kWh of consumption in a month.

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

A <em>linear function </em>has the format given by:

$y = mx + b$

In which:

m is the slope, which is the rate of change, that is, how much y changes when x changes by 1.
b is the y-intercept, which is the value of y when x = 0.

The equation for the cost of h kilowatt hours (kWh) of electricity used in excess of 250 kWh is of:

$C = f(h) = 37.6 + 0.1h$

Item a:

The slope is of $m = 0.1$ , which means that it costs $0.1 for each kilowatt hour of electricity used in excess of 250 kWh.

Item b:

$f(90) = 37.6 + 0.1(90) = 37.6 + 9 = 46.6$

250 + 90 = 340.

f(90) = 46.6, which is the cost of 340 kWh of consumption in a month.

A similar problem is given at brainly.com/question/24808124

8 0

2 years ago

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If

PSYCHO15rus [73]

The length will be 3 because of the altitude

7 0

2 years ago

Week 1 2 3 4 5 Water Level (inches) − 1 1 4 1 3 8 2 1 2 − 1 5 8 − 1 3 4 Between which two weeks did the water level change the m

suter [353]

Answer:

The water level change the most in week 3 and week 4

The change = -370 inches

Step-by-step explanation:

Given - Week 1 2 3 4 5

Water Level (inches) − 1 1 4 1 3 8 2 1 2 -1 5 8 -1 3 4

To find - Between which two weeks did the water level change the most? Calculate the change .

Proof -

The formula for change in water level with respect to week be-

Rate of Change in Water Level = Difference in water level / Difference in weeks

Now,

For week 1 and week 2

Rate of change in water level = $\frac{138 - 114}{2 - 1}$ = $\frac{24}{1}$ = 24 inches

Now,

For week 1 and week 3

Rate of change in water level = $\frac{212 - 114}{3 - 1}$ = $\frac{98}{2}$ = 49 inches

Now,

For week 1 and week 4

Rate of change in water level = $\frac{-158 - 114}{4 - 1}$ = $-\frac{272}{3}$ = -90.67 inches

Now,

For week 1 and week 5

Rate of change in water level = $\frac{-134 - 114}{5 - 1}$ = $-\frac{248}{4}$ = -62 inches

Now,

For week 2 and week 3

Rate of change in water level = $\frac{212 - 138}{3 - 2}$ = $\frac{74}{1}$ = 74 inches

Now,

For week 2 and week 4

Rate of change in water level = $\frac{-158 - 138}{4 - 2}$ = $-\frac{296}{2}$ = -148 inches

Now,

For week 2 and week 5

Rate of change in water level = $\frac{-134 - 138}{5 - 2}$ = $-\frac{272}{3}$ = -90.67 inches

Now,

For week 3 and week 4

Rate of change in water level = $\frac{-158 - 212}{4 - 3}$ = $-\frac{370}{1}$ = -370 inches

Now,

For week 3 and week 5

Rate of change in water level = $\frac{-134 - 212}{5 - 3}$ = $-\frac{346}{2}$ = 173 inches

Now,

For week 4 and week 5

Rate of change in water level = $\frac{-134 + 158}{5 - 4}$ = $\frac{24}{1}$ = 24 inches

∴ we get

The water level change the most in week 3 and week 4

The change = -370 inches

Note :

The highest change means which temperature goes the most change in water level. It can be negative also.

So, We have to take the modulus and then find the highest number.

Here, 370 > 173

So, Highest change occurs in Week 3 and Week 4 but not in Week 3 and Week 5.

7 0

2 years ago