Solve the system of equations



4x + 2y + 1 = 1
2x − y = 1
x + 3y + z = 1

Answer:

1 1/6

Step-by-step explanation:

5/6 + 3/9

Simplify 3/9 by dividing the top and bottom by 3

5/6 + 1/3

Get a common denominator of 6

5/6 + 1/3 *2/2

5/6 + 2/6

7/6

Rewriting

6/6 +1/6

1 1/6

Answer:

√53

Step-by-step explanation:

Distance between two points =  

√(4−6)^2+(−2−5)^2

√(−2)^2+(−7)^2  

= √4+49

=√53

= 7.2801

Hope this helps uwu

9514 1404 393

Answer:

  option 2: √53

Step-by-step explanation:

The distance formula is useful for this:

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((4-6)² +(-2-5)²) = √((-2)² +(-7)²) = √(4+49)

  d = √53

The distance between the given points is √53.

Answer:

A; 120 cubic inches

Step-by-step explanation:

Let us start with the formula of the volume of a rectangular prism,[tex]V=l*w*h[/tex], where l represents the length of the prism, w represents the width of the prism, and h represents the height of the prism. It is given to us that h =5 inches, w =3 inches, and l =8 inches. Let's plug the values in:

[tex]V= 8*3*5\\V=120[/tex]

A. The volume of the rectangular prism is 120 cubic inches.

I hope this helps! Let me know if you have any questions :)

Answer:

The maximum volume of the box is:

[tex]V =\frac{5}{3}\sqrt{\frac{5}{3}}[/tex]

Step-by-step explanation:

Given

[tex]Surface\ Area = 10m^2[/tex]

Required

The maximum volume of the box

Let

[tex]a \to base\ dimension[/tex]

[tex]b \to height[/tex]

The surface area of the box is:

[tex]Surface\ Area = 2(a*a + a*b + a*b)[/tex]

[tex]Surface\ Area = 2(a^2 + ab + ab)[/tex]

[tex]Surface\ Area = 2(a^2 + 2ab)[/tex]

So, we have:

[tex]2(a^2 + 2ab) = 10[/tex]

Divide both sides by 2

[tex]a^2 + 2ab = 5[/tex]

Make b the subject

[tex]2ab = 5 -a^2[/tex]

[tex]b = \frac{5 -a^2}{2a}[/tex]

The volume of the box is:

[tex]V = a*a*b[/tex]

[tex]V = a^2b[/tex]

Substitute: [tex]b = \frac{5 -a^2}{2a}[/tex]

[tex]V = a^2*\frac{5 - a^2}{2a}[/tex]

[tex]V = a*\frac{5 - a^2}{2}[/tex]

[tex]V = \frac{5a - a^3}{2}[/tex]

Spit

[tex]V = \frac{5a}{2} - \frac{a^3}{2}[/tex]

Differentiate V with respect to a

[tex]V' = \frac{5}{2} -3 * \frac{a^2}{2}[/tex]

[tex]V' = \frac{5}{2} -\frac{3a^2}{2}[/tex]

Set [tex]V' =0[/tex] to calculate a

[tex]0 = \frac{5}{2} -\frac{3a^2}{2}[/tex]

Collect like terms

[tex]\frac{3a^2}{2} = \frac{5}{2}[/tex]

Multiply both sides by 2

[tex]3a^2= 5[/tex]

Solve for a

[tex]a^2= \frac{5}{3}[/tex]

[tex]a= \sqrt{\frac{5}{3}}[/tex]

Recall that:

[tex]b = \frac{5 -a^2}{2a}[/tex]

[tex]b = \frac{5 -(\sqrt{\frac{5}{3}})^2}{2*\sqrt{\frac{5}{3}}}[/tex]

[tex]b = \frac{5 -\frac{5}{3}}{2*\sqrt{\frac{5}{3}}}[/tex]

[tex]b = \frac{\frac{15 - 5}{3}}{2*\sqrt{\frac{5}{3}}}[/tex]

[tex]b = \frac{\frac{10}{3}}{2*\sqrt{\frac{5}{3}}}[/tex]

[tex]b = \frac{\frac{5}{3}}{\sqrt{\frac{5}{3}}}[/tex]

Apply law of indices

[tex]b = (\frac{5}{3})^{1 - \frac{1}{2}}[/tex]

[tex]b = (\frac{5}{3})^{\frac{1}{2}}[/tex]

[tex]b = \sqrt{\frac{5}{3}}[/tex]

So:

[tex]V = a^2b[/tex]

[tex]V =\sqrt{(\frac{5}{3})^2} * \sqrt{\frac{5}{3}}[/tex]

[tex]V =\frac{5}{3} * \sqrt{\frac{5}{3}}[/tex]

[tex]V =\frac{5}{3}\sqrt{\frac{5}{3}}[/tex]

The maximum volume of the box which has a 10 m² surface area is given below.

[tex]\rm V_{max} = \dfrac{5}{3} *\sqrt{\dfrac{5}{2}}[/tex]

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

We want to construct a box with a square base and we currently only have 10 m² of material to use in the construction of the box.

The surface area = 10 m²

Let a be the base length and b be the height of the box.

Surface area = 2(a² + 2ab)

  2(a² + 2ab) = 10

      a² + 2ab = 5

Then the value of b will be

[tex]\rm b = \dfrac{5-a^2}{2a}[/tex]

The volume of the box is given as

V = a²b

Then we have

[tex]\rm V = \dfrac{5-a^2 }{2a}* a^2\\\\V = \dfrac{5a - a^3}{2}\\\\V = \dfrac{5a}{2} - \dfrac{a^3}{2}[/tex]

Differentiate the equation with respect to a, and put it equal to zero for the volume to be maximum.

[tex]\begin{aligned} \dfrac{dV}{da} &= \dfrac{d}{da} ( \dfrac{5a}{2} - \dfrac{a^3}{2} ) \\\\\dfrac{dV}{da} &= 0 \\\\\dfrac{5}{2} - \dfrac{3a^2 }{2} &= 0\\\\a &= \sqrt{\dfrac{5}{2}} \end{aligned}[/tex]

Then the value of b will be

[tex]b = \dfrac{5-\sqrt{\dfrac{5}{2}} }{2*\sqrt{\dfrac{5}{2}} }\\\\\\b = \sqrt{\dfrac{5}{2}}[/tex]

Then the volume will be

[tex]\rm V = (\sqrt{\dfrac{5}{2}} )^2*\sqrt{\dfrac{5}{2}} \\\\V = \dfrac{5}{3} *\sqrt{\dfrac{5}{2}}[/tex]

More about the differentiation link is given below.

https://brainly.com/question/24062595

Answer:

Step-by-step explanation:

Given the data :

Using 6 classes :

Class interval ____ Frequency

21 - 30 _________ 6

31 - 40 _________ 10

41 - 50 _________ 5

51 - 60 _________ 0

61 - 70 _________ 1

71 - 80 _________ 2

Answer:

B

Step-by-step explanation:

Have a nice day :)

Answer:

In simple terms, a bar chart is used in summarizing categorical data, where a histogram uses a bar of different heights, it is similar to the bar chart in many terms but the histogram groups the numbers into the ranges while representing the data.

bar chart is a graph in the form of boxes of different heights, with each box representing a different value or category of data, and the heights representing frequencies.

but,

Histogram is graphical display of numerical data in the form of upright bars, with the area of each bar representing frequency.

Answer:

prational number between root2

Answer:

[tex]P(B|A)[/tex]

Step-by-step explanation:

Probability notation:

Suppose that we have two events, event A and event B. The probability of event B occuring, considering that event A has occurred, is given by:

[tex]P(B|A)[/tex], which is the answer to this question.

Answer:

[tex]471\:\mathrm{ft}[/tex]

Step-by-step explanation:

In one full rotation around the roundabout, the car is travelling a distance equal to the circumference, or the perimeter, of the circle. The circumference of a circle with radius [tex]r[/tex] is given by [tex]C=2r\pi[/tex]. In the diagram, the diameter is labelled 150 feet. By definition, the radius of a circle is exactly half of the diameter of the circle. Therefore, the radius must be [tex]\frac{150}{2}=75[/tex] feet. Thus, the car would travel [tex]2\cdot 75\cdot \pi=471.238898038=\boxed{471\:\mathrm{ft}}[/tex]

Answer:

5/12 is already in simplest form

Step-by-step explanation:

12m =  5r + 3y + 4b

red is chosen = 5r / 12 = 5/12

Step-by-step explanation:

the answer is 5/12. It's quite simple

Answer:

A. The slope of Function A is greater than the slope of Function B.

Step-by-step explanation:

The slope of a function can be defined as rise/run. In Function A, the rise/run is 4. The slope in Function B is much easier to see: it is 2. Because 4 is greater than 2, Function A has a greater slope than Function B.

Answer:

-9

Step-by-step explanation:

Two-thirds of a number is negative six. The number is -9. Let the number is x, 2/3x =-6, x=-6x3/2=-9.

This question is incomplete, the complete question is;

If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple are written in increasing order but are not necessarily distinct.

In other words, how many 5-tuples of integers  ( h, i , j , m ), are there with  n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1 ?

Answer:

the number of 5-tuples of integers from 1 through n that can be formed is [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120

Step-by-step explanation:

Given the data in the question;

Any quintuple ( h, i , j , m ), with n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1

this can be represented as a string of ( n-1 ) vertical bars and 5 crosses.

So the positions of the crosses will indicate which 5 integers from 1 to n are indicated in the n-tuple'

Hence, the number of such quintuple is the same as the number of strings of ( n-1 ) vertical bars and 5 crosses such as;

[tex]\left[\begin{array}{ccccc}5&+&n&-&1\\&&5\\\end{array}\right] = \left[\begin{array}{ccc}n&+&4\\&5&\\\end{array}\right][/tex]

= [( n + 4 )! ] / [ 5!( n + 4 - 5 )! ]

= [( n + 4 )!] / [ 5!( n-1 )! ]

= [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120

Therefore, the number of 5-tuples of integers from 1 through n that can be formed is [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120

Answer:

21 cookies

Step-by-step explanation:

First we know that Chris was given a third of 84 cookies so we can start working on this problem by figuring out what a third of 84 is. We can do this by multiplying 84 by 1/3 or just dividing by 3, which gives us: 84/3 = 28

So now we know that Chris was given 28 cookies, we can figure out what 3/4 of that is to work out how many cookies he ate. 28 x (3/4) = 21 cookies.

Chris ate 21 cookies.

Hope this helped!

Answer:

21 cookies

Step-by-step explanation:

1/3 × 84 = 28

3/4 × 28 = 21

Answer:

a= 250

b= 50

250 + 50 = 300

Step-by-step explanation:

There's many solutions but this was the first one I could come up with.

Answer:

my opinion is seince a+b=300 then the sqaure of 300= 17.3?

Step-by-step explanation:

Answer:

The equation of the parabola is y = x²/4

Step-by-step explanation:

The given focus of the parabola = (0, 1)

The directrix of the parabola is y = -1

A form of the equation of a parabola is presented as follows;

(x - h)² = 4·p·(y - k)

We note that the equation of the directrix is y = k - p

The focus = (h, k + p)

Therefore, by comparison, we have;

k + p = 1...(1)

k - p = -1...(2)

h = 0...(3)

Adding equation (1) to equation (2) gives;

On the left hand side of the addition, we have;

k + p + (k - p) = k + k + p - p = 2·k

On the right hand side of the addition, we have;

1 + -1 = 0

Equating both sides, gives;

2·k = 0

∴ k = 0/2 = 0

From equation (1)

k + p = 0 + 1 = 1

∴ p = 1

Plugging in the values of the variables, 'h', 'k', and 'p' into the equation of the parabola, (x - h)² = 4·p·(y - k), gives;

(x - 0)² = 4 × 1 × (y - 0)

∴ x² = 4·y

The general form of the equation of the parabola, y = a·x² + b·x + c, is therefore;

y = x²/4.

Answer:

z = 1.77.

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, which is also the area of the normal curve to the left of Z. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Find z such that 3.8% of the standard normal curve lies to the left of z

Thus, z with a z-score of 0.038. Looking at the z-table, this is z = 1.77.

Answer:

1. Term.

2. Common difference.

3. Arithmetic sequence.

4. Sequence.

Step-by-step explanation:

1. Term: an individual quantity or number in a sequence. For example, 1, 2, 3, 5, 6. The first term is 1 while 5 is the fourth term.

2. Common difference: the fixed amount added on to get to the next term in an arithmetic sequence. For example, 2, 4, 6, 8 have a common difference of 2 i.e (6 - 4 = 2).

3. Arithmetic sequence: a sequence in which a fixed amount such as two (2) is added on to get the next term. For example, 0, 2, 4, 6, 8, 10, 12.... is an arithmetic sequence.

4. Sequence: a set of numbers that follow a pattern, with a specific first number. For example, 1, 2, 3, 4, 5, 6 is a sequence.

Answer:

The plumber worked 50 hours, and his assistant worked 25 hours.

Step-by-step explanation:

Since a plumber and his assistant work together to replace the pipes in an old house, and the plumber charges $ 30 an hour for his own labor and $ 20 an hour for his assistant's labor, and the plumber works twice as long as his assistant on this job, and the labor charge on the final bill is $ 2000, to determine how long did the plumber and his assistant work on this job the following calculation must be performed:

40 x 30 + 20 x 20 = 1200 + 400 = 1600

50 x 30 + 25 x 20 = 1500 + 500 = 2000

Therefore, the plumber worked 50 hours, and his assistant worked 25 hours.

Answer:

A)$60

B)$9

Step-by-step explanation:

THIS IS THE COMPLETE QUESTION BELOW

Three friends, Cleopatra, Dalila, and ebony fo shopping. The money they have each is in the ratio

Cleopatra : Dalila : Ebony =

5 : 7 : 8

Cleopatra has $15.

A) How many dollars do they have in total?

B) Dalila spends 12$ on a hat, how many dollars does she have left?

A)

Total ratio=(5 +7 +8)= 20

Cleopatra has $15.

Let X = total money

Ratio of Cleopatra= 5/20 ×X=15

5X /20 = 15

5X= (15×20)

X= $60

They have $60 in total

B) ratio of Dalila= 7/20 × 60 = $21

But 12$ was spent by Dalila on a hat

Then Dalila will have ($21 - 12$) Left

= $9

Answer:

Thus the function g is the function f stretched vertically by a factor 5.

Step-by-step explanation:

Multiplication of a function by a constant:

When a function is multiplied by a constant a > 1, the function is stretched vertically by a factor of 5.

In this question:

f(x) = x^2

g(x) = 5x^2

Thus the function g is the function f stretched vertically by a factor 5.

Answer:

15π in

Step-by-step explanation:

In order to solve this, we need to know that the circumference of a circle can be found by using the following formula...

Circumference = dπ   (where d is the diameter of the circle)

Therefore the circumference equals...

Circumference = dπ = 15π in

[tex]\boxed{Given:}[/tex]

Diameter of the circle "[tex]d[/tex]" = 15 in.

[tex]\boxed{To\:find:}[/tex]

The circumference of the circle (in terms of π).

[tex]\boxed{Solution:}[/tex]

[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:15\:π\:in.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

We know that,

[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:πd }[/tex]

[tex] = \pi \times 15 \: in \\ \\ = 15 \: \pi \: in[/tex]

Therefore, the circumference of the circle is 15 π in.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]

Answer:

3/10

Step-by-step explanation:

1/10 + 1/5 =          need to get common denominators to add.

1/10 + 2/10 = 3/10

Answer:

25

Step-by-step explanation:

From the given information;

Numbers of posters that can be printed in an hour = no of impression/hour × no of plate utilized in each impression.

= 1000x

Thus, the required number of hours it will take can be computed as:

[tex]\implies \dfrac{100000}{1000x} \\ \\ =\dfrac{100}{x}[/tex]

cost per hour = 125

If each plate costs $20 to make, then the total number of plate will equal to 40x

∴

The total cost can be computed as:

[tex]C(x) = (\dfrac{100}{x}) \times 125 + 20 x --- (1)[/tex]

[tex]C'(x) = (-\dfrac{12500}{x^2}) + 20 --- (2)[/tex]

At C'(x) = 0

[tex]\dfrac{12500}{x^2} = 20[/tex]

[tex]\dfrac{12500}{20} = x^2[/tex]

[tex]x^2= 625[/tex]

[tex]x = \sqrt{625}[/tex]

x = 25

[tex]C'' (x) = -12500 \times \dfrac{-2}{x^3} +0[/tex]

[tex]C'' (x) = \dfrac{25000}{x^3}[/tex]

where; x = 25

[tex]C'' (x) = \dfrac{25000}{25^3}[/tex]

C''(x) = 1.6

Thus, at x = 25, C'' > 0

As such, to minimize the cost, the printer needs to make 25 metal plates.