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kupik [55]
3 years ago
11

To finish an order in time the company had to produce 40 items daily, but it produced 20 items more daily and finished the order

3 days ahead of time. In how many days was the company supposed to finish the order?
Mathematics
1 answer:
Nimfa-mama [501]3 years ago
8 0

Answer:

9 days.

Step-by-step explanation:

If the company produced 20 more items than 40 items each day, then it must have produced 60 items each day.

Though you're probably expected to write an equation, it's easiest to solve this through educated guess and check.

If there were 120 items to be produced, the company would be required to do it in 3 days (120 items, 40 items/day) but completed it in 2 days (120 items, 60 items/day). In this case, they finished their order 1 day early. But the problem states that they finished 3 days early. So we guess 3 times 120 items, or 360 items. Checking this, they should have finished their order in 9 days (360 items, 40 items/day) but they finished in 6 days (360 items, 60 items/day). 6 is three less than 9, so our guess of 360 items was correct. We have shown that the company should have finished the order in 9 days.

If you had to use an equation:

Let the desired number of days be x. Then, the company finished its order in x - 3 days. Since number of items produced is the number of days times items per day, and it doesn't change:

number of items = 40 items/day * x days = 60 items/day * (x - 3) days

40x = 60(x - 3) = 60x - 180

180 = 20x

x = 9

9 days is the desired answer.

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The function f(x) = –x2 + 20x – 75 models the profit from one customer, in dollars, a shop makes for printing photos, where x is
trasher [3.6K]
The function is graphed as shown below

Part A:

We use the formula - \frac{b}{2a} to find the vertex of the function. A quadratic function of the form of a x^{2} +bx+c and equating this form to the given function - x^{2} +20x-75, we have
b=20 and a=-1.

Substituting a and b into the vertex formula, we have
x=- \frac{20}{2(-1)}=10, as shown in the graph

This calculation means that the highest profit is achieved when the number of photo printed equals to ten photos

Part B:

We can find solution to this equation by factorising

- x^{2} +20x-75=0
-( x^{2} -20x+75)=0
x^{2} -20x+75=0
(x-5)(x-15)=0
x=5 and x=15, as shown in the graph

The two values means that the company makes no profit when they either produce 5 or 15 photos

8 0
3 years ago
MO bisects angle LMN , angle LMO = 6x-22 and angle NMO = 2x +34. Solve for x and find angle LMN.
Mkey [24]

Answer:

  • x=14
  • \angle{LMN}=124\textdegree

Step-by-step explanation:

<u><em>To Determine:</em></u>

Solve for x and find angle LMN.

<u><em>Fetching Information and Solution Steps:</em></u>

Considering the angle \angle{LMN}

As MO bisects the angle \angle{LMN} into two equal angle parts. These equal angles are:

\angle{LMO}=6x-22

\angle{NMO}=2x+34

As these angles are equal. i.e.

\angle{LMO}=\angle{NMO}

6x-22=2x+34

\mathrm{Add\:}22\mathrm{\:to\:both\:sides}

6x-22+22=2x+34+22

6x=2x+56

\mathrm{Subtract\:}2x\mathrm{\:from\:both\:sides}

6x-2x=2x+56-2x

4x=56

\mathrm{Divide\:both\:sides\:by\:}4

\frac{4x}{4}=\frac{56}{4}

\mathrm{Simplify}

x=14

Hence, x=14

As  \angle{LMN} was cut into two equal parts \angle{LMO} and \angle{NMO}

So,

\angle{LMN} = \angle{LMO} + \angle{NMO}

            = 6x-22+2x+34

            = 8x + 12

            = 8(14) + 12     ∵ x=14

            = 124\textdegree

Therefore, \angle{LMN}=124\textdegree

Keywords: angle bisector, congruent angles

Learn more about angle bisector and congruent angles from brainly.com/question/711370

#learnwithBrainly

3 0
3 years ago
Jada is solving the equation shown below. Negative one-half (x + 4) = 6 Which is a possible first step to begin to simplify the
elena-14-01-66 [18.8K]

The two options that are the possible first step to begin to simplify the equation are (c) Multiply both sides of the equation by –2. and (d). Distribute Negative one-half over (x + 4).

<h3>How to determine which two options are the possible first step to begin to simplify the equation?</h3>

The equation is given as:

Negative one-half (x + 4) = 6

Rewrite the above equation properly

So, we have

-1/2(x + 4) = 6

A possible first step is to multiply both sides of the equation -1/2(x + 4) = 6 by -2

So, we have

x + 4 = -12

Another possible first step is to distribute the expression -1/2(x + 4) in the equation

So, we have

-1/2x - 1/2 * 4 = 6

Hence, the two options that are the possible first step to begin to simplify the equation are (c) Multiply both sides of the equation by –2. and (d). Distribute Negative one-half over (x + 4).

Read more about equations at:

brainly.com/question/2972832

#SPJ1

3 0
1 year ago
The coefficient of determination is used to: compute correlations for truncated ranges. compare the relative strength of coeffic
kozerog [31]

Answer: compare the relative strength of coefficients.

Step-by-step explanation: The Coefficient of determination usually denoted as R^2 is obtained by taking the squared value of the correlation Coefficient (R). It's value ranges from 0 to 1 and the value obtained gives the proportion of variation in the dependent variable which could be attributed to it's correlation or relationship to th independent variable. With a R^2 value close to 1, this means a large portion of Variation in a variable A could be explained due to changes in variable B while a low value signifies a low variance between the variables. Hence, the Coefficient of determination is used in comparing the relative strength of the Coefficients in other to establish whether a weak or strong relationship exist.

6 0
3 years ago
Find the midpoint between (4,-1) and (3,2)
zepelin [54]

Midpoint has form of,

M(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})

We can insert the data,

M(\dfrac{4+3}{2},\dfrac{-1+2}{2})

Which simplifies to,

\boxed{M(3.5, 0.5)}

Hope this helps.

r3t40

4 0
3 years ago
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