A fruit company delivers its fruit in 2 types of boxes: large and small. A delivery of 3 large boxes and 5 small boxes has a total weight of 79 kilograms. A delivery of 12 large boxes and 2 small boxes has a total weight of 199 kilograms. How much does each type of box weight

Start by writing the system down, I will use [tex]y[/tex] to represent [tex]f(x)[/tex]

[tex]y=x^2-5x+3\wedge y=-3[/tex]

Substitute the fact that [tex]y=-3[/tex] into the first equation to get,

[tex]-3=x^2-5x+3[/tex]

Simplify into a quadratic form ([tex]ax^2+bx+c=0[/tex]),

[tex]x^2-5x+6=0[/tex]

Now you can use Vieta's rule which states that any quadratic equation can be written in the following form,

[tex]x^2+x(m+n)+mn=0[/tex]

which then must factor into

[tex](x+m)(x+n)=0[/tex]

And the solutions will be [tex]m,n[/tex].

Clearly for small coefficients like ours [tex]5,6[/tex], this is very easy to figure out. To get 5 and 6 we simply say that [tex]m=3, n=2[/tex].

This fits the definition as [tex]5=3+2[/tex] and [tex]6=2\cdot3[/tex].

So as mentioned, solutions will equal to [tex]m=3, n=2[/tex] but these are just x-values in the solution pairs of a form [tex](x,y)[/tex].

To get y-values we must substitute 3 for x in the original equation and then also 2 for x in the original equation. Luckily we already know that substituting either of the two numbers yields a zero.

So the solution pairs are [tex](2,0)[/tex] and [tex](3,0)[/tex].

Hope this helps :)

Answer:

It would be the second red dot to the right of 9.85.

After the total distance on the first, second and third days, Patrick had walked 3.45miles

 Patrick walked altogether 3 miles.

What are fractions?

A fraction is referred to as the portion of a whole in mathematics. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers.

Solution:

First day patrick walked = 3/5 miles

Second day patrick walked = 5/7 miles

Third day he walked = half of first day

                                 = 1/2 ×3/5

                                 = 3/10 miles

fourth day he walked = first two days distances

                                 = 3/5 ₊ 5/7

                                 = 46/35 miles

Total distance he walked = 3/5 ₊ 5/7 ₊ 3/10 ₊ 46/35

                                       = 3 miles

Hence total distance he walked is 3 miles.

Learn more about "fractions" here-

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Answer:

Step-by-step explanation:

Try and draw it on a grid and just rotate your book up to 180

Answer:

Hence there are 6 different ways can the representatives be chosen if the president must be a woman and the secretary and treasurer must be men.

Step-by-step explanation:

We know that,

Total males = 3,

Total Females = 2,

Now we want 2 males and a female.

Then the choices are,

           [tex]= ^{3} C_{2} \times ( ^{2} C_{1} )\\\\= 3 \times 2\\\\=6[/tex]

Answer:

It is a mathematical method and with it gives a fitted trend line for the set of data in such a manner that the following tow conditions are satisfied. The sum of the deviation of the actual values of Y and the computed values of Y is zero.

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{6!}\\\large\textsf{= 6}\times\large\textsf{5}\times\large\textsf{4}\times\large\textsf{3}\times\large\textsf{2}\times\large\textsf{1}\\\large\textsf{6(5) = \bf 30}\\\large\textsf{= 30}\times\large\textsf{4}\times\large\textsf{3}\times\large\textsf{2}\times\large\textsf{1}\\\large\textsf{30(4) = \bf 120}\\\large\textsf{= 120}\times\large\textsf{3}\times\large\textsf{2}\times\textsf{1}\\\large\textsf{120(3) = \bf 360}\\\large\textsf{= 360}\times\large\textsf{2}\times\large\textsf{1}[/tex]

[tex]\large\textsf{360(2) = \bf 720}\\\large\textsf{720}\times\large\textsf{1}\\\large\textsf{= \bf 720}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Therefore, your answer is: \bf 720}\huge\textsf{ (option B)}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

a^2 + b^2 = c^2

Step-by-step explanation:

usually used on right triangles.

Answer:

acute

Step-by-step explanation:

beccccccsssdsss

Answer:

m<ABD = 56 degrees

Step-by-step explanation:

If a segment/ray/line bisects an angle, it divides it into 2 equal parts

Since BE bisects ABD, it will divide it into 2 equal parts, one of which is 28 degrees (given)

Now we can find the measure of ABD by doing 28*2=56

Answer:

the slope-intercept form for any line is y = mx + b, where m is the slope and b is the y-intercept.

now, let's calculate the slope:

=  

here is the equation we currently have solved: y = x + b

now we have to solve for the y-intercept. to do this, we substitute one of the given points into the equation, and solve for b.

let's use (8, 2). in this ordered pair, the 8 is the x, and the 2 is the y.

2 = 8 + b

2 - 8 = b

b = -6

and now we have our final equation!  

y = x - 6

hope this helped! please let me know if you are confused about anything i did smiley

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find the slope first:

Use point-slope form and the coordinates of one of the points:

Answer:

B) 13+14 (n - 1)

Step-by-step explanation:

this is an arithmetic sequence

13 represent the first term

14 is a constant difference

Answer:

The answer is B

Step-by-step explanation:

substitute the value of n in the equation.

Answer:

-5

Step-by-step explanation:

We need to find a number less than -3

-1 is greater than -3

0 is greater than -3

2 is greater than -3

-5 is less than -3

Answer:

option A

Step-by-step explanation:

Because its colder than negative 3 degrees F.

Answer:

here's the answer to your question

Answer:

One angle is 70 degrees and the other one is 20 degrees

Step-by-step explanation:

If two angles are complementary, that means that they both add up to 90 degrees.

You have to use algebra to solve this bc you don't have the actual numbers.

So you can use the equation...

7f + 2f = 90

Solve for f, and then substitute the f back into the equation to find the measure of each angle.

7f + 2f = 90

9f = 90

f = 10

Substituting the 10 back in

7f = 7(10) = 70

2f = 2(10) = 20

9514 1404 393

Answer:

  x ∈ {-35, 0, 35}

Step-by-step explanation:

We can solve for x and equate those values to find corresponding y-values. Substituting into the original expressions for x gives the possible x-values.

  [tex]x+xy^2=250y\ \Rightarrow\ x=\dfrac{250y}{1+y^2}\\\\x-xy^2=-240y\ \Rightarrow\ x=\dfrac{-240y}{1-y^2}\\\\\dfrac{250y}{1+y^2}+\dfrac{240y}{1-y^2}=0\\\\\dfrac{25y(1-y^2)+24y(1+y^2)}{(1+y^2)(1-y^2)}=0\\\\y(-y^2+49)=0=y(7-y)(7+y)\ \Rightarrow\ y\in\{-7,0,7\}\\\\x=\dfrac{250(\pm 7)}{1+(\pm7)^2}=\pm35,\quad=\dfrac{250(0)}{1+0^2}=0\\\\\boxed{x\in\{-35,0,35\}}[/tex]

Answer:

i dont know

Step-by-step explanation:

hmmm

Answer:

0.6826 = 68.26% probability Z will be within one standard deviation of average.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

What is the probability Z will be within one standard deviation of average?

This is the p-value of Z = 1 subtracted by the p-value of Z = -1.

Z = 1 has a p-value of 0.8413.

Z = -1 has a p-value of 0.1587.

0.8413 - 0.1587 = 0.6826

0.6826 = 68.26% probability Z will be within one standard deviation of average.

Answer:

The choose (2)

y=x²+5x+6

Step-by-step explanation:

y=x²+5x+6 —> (–5/2 , –1/4)

y=-3x² + 5 X + 6 —> (5/6, 97/12)

y=-x² + 5x + 6 —> (5/2,49/4)

y = -4 x² + 5x + 6 —> (5/8 , 121/16)

Answer:

20%

Step-by-step explanation:

if zero toppings is an option, then there would be 5 possibilities for toppings

0,1,2,3,or 4

the server randomly chose 3 toppings so that would be one out of 5 or 20%.

(If the server did not have the option to put zero toppings on then there would be only 4 options 1,2,3, or 4 toppings and the correct answer would be one out of 4 or 25%.)

Answer:

The graph should look like the one below/above.

OAmalOHopeO

Answer:

$10390.817

Step-by-step explanation:

Given that :

Sculpture is made in Shape of a cone with :

Height, h = 70 inches

Radius, r = 9 inches

Volume of a cone = 1/3πr²h

Volume = 1/3 * π * 9² * 70

Volume of sculpture = 5937.6101 in³

Cost per in³ = $1.75

Cost of tin for the sculpture :

Cost per in³ * volume of sculpture

$1.75 * 5937.6101 = $10390.817

Answer:

mana saya tau iwnisbagcayabaonsoanuwvsybwiwnusvwuagwyvwkwnwibsyafa

Answer:

4

Step-by-step explanation:

The first value (10) is the x value. 10 is positive so the point is on your right. The second value (-1) goes down below the x axis. because it is minus. right and down means you are in the 4th quadrant.

Answer:

IV

Step-by-step explanation:

In the picture below, it shows the model of all quadrants. Since the point (10, -1) has a positive as the x, you can eliminate quadrant II and III. The ones left are I and IV. Since y is a negative, you eliminate I because it is only positives while IV has a negative as it's y.

Hope this helps.

Answer:

40/8= 5

Step-by-step explanation:

5/1

Your selected answer is correct.

5/1

Answer:

7/0

Step-by-step explanation:

This is because if a number is divided by 0 then there is no answer or it is undefined

Think of it like this,

You have 7 apples and wanted to give it to zero friends, is it possible?

Hope this helped :)

Answer:

Second option (7÷0)

Explanation:

Dividing by zero is considered undefined since you can't divide something by nothing. It's like saying you have a pizza and you want to divide it between 7 people but since you're dividing by zero, you're not splitting the pizza between anyone.

Answer:

c I think

Step-by-step explanation:

just cuz I did the math but I don't wanna type rn

Answer: 3628800

Step-by-step explanation: there are 10 letters so we multiply each with the other 1x2x3x4x5x6x7x8x9x10 or 10! to know all possible combinations so the answer will be 3628800.

Hope it helped!

Answer:

[tex]1,814,400[/tex]

Step-by-step explanation:

The number of ways to arrange a word with [tex]d[/tex] distinct digits is each to [tex]d![/tex]. Since there are 10 letters, there are [tex]10![/tex] permutations initially formed.

However, there is one letter that is repeated, S. We need to account for that fact that switching the placement of the S's does not change the word, as they still appear the same. Therefore, divide [tex]10![/tex] by the number of ways you can arrange the 2 S's, which is simply [tex]2![/tex]. Therefore, our answer is:

[tex]\frac{10!}{2!}=10 \cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3=\boxed{1,814,000}[/tex]

Answer:

26,733

Step-by-step explanation:

39,900 - Percentage decrease =

39,900 - (33% × 39,900) =

39,900 - 33% × 39,900 =

(1 - 33%) × 39,900 =

(100% - 33%) × 39,900 =

67% × 39,900 =

67 ÷ 100 × 39,900 =

67 × 39,900 ÷ 100 =

2,673,300 ÷ 100 =

26,733

Hope this helps :)

Answer:

[tex]\angle B = 60^o[/tex]

[tex]b =17.3[/tex]

[tex]c = 20[/tex]

Step-by-step explanation:

Given

[tex]a= 15[/tex]

[tex]\angle A = 30^o[/tex]

[tex]\angle C = 90^o[/tex]

See attachment for illustration

Required

Solve the triangle

First, we calculate the measure of B

[tex]\angle A + \angle B + \angle C = 180^o[/tex] --- angles in a triangle

[tex]30^o + \angle B + 90^o = 180^o[/tex]

Collect like terms

[tex]\angle B = 180^o-90^o-30^o[/tex]

[tex]\angle B = 60^o[/tex]

Solve for (c) using sine function

[tex]\sin(30) = \frac{a}{c}[/tex]

Make c the subject

[tex]c = \frac{a}{\sin(30)}[/tex]

Substitute known values

[tex]c = \frac{10}{0.5}[/tex]

[tex]c = 20[/tex]

Solve for (b) using Pythagoras

[tex]c^2 = a^2 + b^2[/tex]

This gives:

[tex]20^2 = 10^2 + b^2[/tex]

[tex]400 = 100 + b^2[/tex]

Collect like terms

[tex]b^2 =400 - 100[/tex]

[tex]b^2 =300[/tex]

Take square roots

[tex]b =17.3[/tex]