Solve this system:

2x+5y+z=3
x-3y+2z=2
-x+2y-3z=-7

Equation of a line

The slope-intercept form of the line can be written as follows:

Where m is the slope and b is the y-intercept

We have two points through which the line passes. If we substitute them into the equation, we can find the values of m and b.

Using the point (-4,-6):

Using the point (4,4):

Subtract the second equation from the first equation:

Solve for m:

Substituting into the second equation:

Finally, the equation of the required line is:

Answer:

Please find attached the required new cereal boxes for the Yum Yum Cereal Company created with Microsoft Visio

Step-by-step explanation:

The required volume of the cereal box = 2,400 cm³

The box is to be drawn and labeled as follows using Microsoft Visio

Box #1 Length = 16 cm, Width = 15 cm, Height = 10 cm

The volume = Length × Width × Height = 16 cm × 15 cm × 10 cm = 2,400 cm³

Box #2 Length = 30 cm, Width = 10 cm, Height = 8 cm

The volume = Length × Width × Height = 30 cm × 10 cm × 8 cm = 2,400 cm³

Answer:

v = 10

Step-by-step explanation:

-10 = -2 (v - 5)

-2 distribute by v and 5 becomes

-2v + 10

-10 = -2v + 10

Inverse Operation of +10 is -10

-10 - 10 = -20

-20 = -2v

v = 10

Based on the graph, a possible solution for the system of inequalities is 5 and 4.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of hamburgers purchased and number of tacos purchased respectively, and then translate the word problem into algebraic equation as follows:

Since this restaurant sold hamburgers for $5 each and tacos for $2.50 and Kevin has $35 to spend, a linear inequality to describe this situation is given by:

5a + 2.50y ≤ 35 ⇒ y ≤ 14 - 2a

Additionally, Kevin and his children must buy a minimum of 9 hamburgers and tacos altogether:

a + y ≥ 9 ⇒ y ≥ 9 - a

Read more on inequality here: brainly.com/question/28748540

#SPJ1

Answer:

k = 0.25

Step-by-step explanation:

The standard equation of a proportional relationship is

y = kx ← k is the constant of proportion

y = 0.25x ← is in this form

with k = 0.25

Answer:

add words please

Step-by-step explanation:

i cant understand that ppic

On solving the provided question, we can say that The maximum rank of a matrix is 2 and The maximum rank is min (5,2)=2.

A matrix is a set of numbers arranged in rows and columns. learns about the elements and dimensions of matrices and introduces them for the first time. A rectangular grid of numbers in rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns. Its single row and 1 n row matrix order are the reasons behind its name. A = [1 2 4 5] is a row matrix of order 1 by 4, for instance. P = [-4 -21 -17] of order 1-by-cubic is another illustration of a row matrix.

The maximum rank of a matrix is 2.

The maximum rank is min (5,2)=2.

Option c with the biggest rank is min(m,n).

To know more about matrix visit:

https://brainly.com/question/29995229

#SPJ4

Answer:

103

Step-by-step explanation:

bassically what you do is add 7 dollars to the ninety six that she lost when she bought the pie or you can do this equation 96 + m but m would be the money she lost being 7 dollars so you would replace m with 7 so it would be 96 + 7 = 103

Answer:

B) y+1=3(x-1)

Step-by-step explanation:

One of the points is (1,-1), and the slope is 3.

The point slope equation is \(y-y_{1} = m(x-x_{1} )\) where m is the slope.

It would then be y+1=3(x-1), which is B)

The error involved in approximating the sum of the given series by the sum of the first five terms of the series is `R5 = 1/6³ + 1/7³ + ...`.

To estimate the error that is made by approximating the sum of the given series by the series the first 5 terms 1/k³, we can use the remainder term of a convergent series.

The given series is ∑ 1/k³ from k = 1 to infinity.We have to find the error involved in approximating the sum of the given series by the sum of the first five terms of the series.

That is, we need to find the difference between the actual sum of the series and the sum of the first five terms of the series.

The sum of the series is given by: `S = 1/1³ + 1/2³ + 1/3³ + 1/4³ + ... + 1/n³ + ...` We can use the remainder term of the series to find the error in approximation.

The remainder term `Rn` is given by: `Rn = Sn - S` where `Sn` is the sum of the first `n` terms of the series. Thus, we have to find the remainder term for `n = 5`.

The remainder term `Rn` is given by: `Rn = S - Sn = 1/6³ + 1/7³ + ...` Since the given series is convergent, the remainder term `Rn` tends to zero as `n` tends to infinity.

So, if we take the sum of the first five terms of the series, the error involved in approximation is given by the remainder term `R5`.

The error involved in this approximation is very small and can be neglected.

To learn more about : terms

https://brainly.com/question/30643700

#SPJ8

The missing value if the point is a direct variation is -15

From the question, we have the following ordered pairs

(2, -6) and (5, y)

These ordered pairs are direct variation

A direct variation is represented as

k = y/x

This means that

y/5 = -6/2

Evaluate the quotient

y/5 = -3

Multiply both sides by 5

y = -15

Hence, the value of y is -15

Read more about direct variation at

https://brainly.com/question/6499629

#SPJ1

Answer:

the answer is D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Correct on edge

Claudia contains five 10-cent pieces.

Let Claudia, have 'x' 5-cent coins and (12 - x) 10-cent coins.

It is easily observed that any multiple of 5 between 5 and 5x + 10(12 - x)

= 120 - 5x it can be obtained by a combination of coins.

Thus, 24 - x = 17 combinations can be made, so x = 7.

But the answer is not 7, because we are asked for the number of 10-cent coins, which is 12 - 7 = 5

Therefore, Claudia has 5 10-cent coins.

To learn more about combination click here:

brainly.com/question/28042664

#SPJ4

Step-by-step explanation:

(x² /x² + 7x + 6)÷(9x - 9/x² - 1)

(x²/(x + 1)(x + 6))×((x + 1)(x - 1)/9(x - 1))

(x²/(x + 6))×1/9

x²/9(x + 6)

Answer:

D

Step-by-step explanation:

Simply put 0 in the equations and see if it's true then put -2 instead of x and see if it matches. this is the easiest way.

Answer:

1) 31.41593

2) 26.38938

Step-by-step explanation:

Circumference = 2πr

2 · π · 5 ≈ 31.41593

2 · π · 4.2 ≈ 26.38938

Thank you for posting this question! If you feel it's fit, please mark Brainliest! If you have any other questions, let me know :)

The end behavior of the function f(x) is: continues downward to the left and upward to the right.

Consider the function,

f(x) = (x + 1)(x - 2)(x + 3)

The zeros are when f(x) = 0

f(x) = 0

(x + 1)(x - 2)(x + 3) = 0

Therefore,

(x + 1) = 0

So, x = -1

(x - 2) = 0

So, x = 2

(x + 3) = 0

So, x = -3

Therefore, the zeros are at x = - 1, x = 2 and x = - 3

To expand the function, we multiply the brackets:

f(x) = (x + 1)(x - 2)(x + 3)

f(x) = ( x + 1 )( x² + x - 6 )

f(x) = x³ + 2x² - 5x - 6

As the leading coefficient (the coefficient of x³) is positive, the end behavior of the function is:

f(x ) → + ∞, as x → + ∞

f(x ) → - ∞, as x → - ∞

Therefore, the end behavior is "continues downward to the left and upward to the right".

Learn more about end behavior here:

brainly.com/question/28156509

#SPJ4

Answer: 21.44 miles

Step-by-step explanation:hope it helps!

Answer:

If you're asking how to look for a right triangle, look for a 90° produced by the two legs, facing the hypotenuse.

Answer:

The '=' sign.

Step-by-step explanation:

The equals sign ( = ). for example:

3x + 1 = 8.

The  equals sign was invented by Robert Recorde of Tenby, South Wales, UK in the early part of the 16th century.

Answer:

it is now at 108

Step-by-step explanation:

10% of 120 is 12 120-12=108

True. a continuous random variable x assumes an (infinitely) uncountable number of distinct values.

A continuous random variable is one that can take on any value within a specified range, and it is defined over an interval of real numbers. Since the real numbers are uncountably infinite, a continuous random variable can assume an uncountable number of distinct values. In contrast, a discrete random variable can only take on a countable number of distinct values, since its possible values are restricted to a finite or countably infinite set of numbers.

Learn more about random variable here

https://brainly.com/question/14356285

#SPJ11

Using the Binomial probability distribution,

The probability that exactly two customers in the sample will default on their payments is 0.31..

We have given that,

4% of total customers a mortgage company default on their payments .

The probability of success i.e number of customers default on their payments (p) = 4%

= 0.04

The probability of failure (q) = 1-p = 1-0.04 = 0.06

Total number of customers in sample (n) = 20

we have to find out the probability that exactly two customers in the sample will default on their payments.

Using the Binomial probability distribution,

P(X=x)= ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾

the required probability is P(X= 2 )

Now, P(X= 2) = ²⁰C₂(0.04)²(0.06)¹⁸

=> P(X=2) = 190 × 0.0016 × 1.0155 = 0.31

Hence, the required probability is 0.31

To learn more about Binomial probability distribution, refer:

https://brainly.com/question/24239758

#SPJ4

If 10 donuts are sold. Then the expected value of the number of sprinkles will be 5.

Binomial distributions consist of n independent Bernoulli trials.

The expected value will be given as

E(X) = np

At Everyday Donuts, 3 of the last 6 donuts sold had sprinkles. Considering this data.

If 10 donuts are sold.

Then the number of the sprinkles will be

The probability will be

p = 3/6

p = 0.5

n = 10

Then the expected value of the number of the sprinkles will be

E(x) = 10 x 0.5

E(x) = 5

Learn more about binomial distribution here:

https://brainly.com/question/13609688

#SPJ1

The mathematical phrase "e to the ipi" is composed of the imaginary unit i (the square root of -1 raised to the power of pi), which is symbolized by "pi," and the mathematical constant "e" (Euler's number).

The expression "e to the ipi" may be expressed as follows:

\(e^{(i*pi)}\)

The following formula is known as Euler's formula:

\(e^{(ipi)}\) = cos(pi) + isin(pi)

where "cos" and "sin" are the sine and cosine functions, respectively.

We may reduce this formula to using the cosine and sine trigonometric identities.

\(e^{(i*pi)}\) = -1

"e to the ipi" hence equals a negative one. This startling and outstanding finding ties together various crucial mathematical ideas, including calculus, complex numbers, and trigonometry.

Learn more about Euler's number at

https://brainly.com/question/6459192

#SPJ4

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

The rate of change of the distance below the sea level with respect to time is 11 feet per second.

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

The table has a linear relationship.

We can choose two data from the table.

At time = 15,

Distance below the sea level = 545 feet.

At time = 27,

Distance between the sea level = 677

Now,

The rate of change of the distance below the sea level with respect to time.

Slope:

= (677 - 545) / (27 - 15)

= 132 / 12

= 11 feet per second

Thus,

The rate of change of the distance below the sea level with respect to time is 11 feet per second.

Learn more about speed here:

https://brainly.com/question/7359669

#SPJ1

The rate of change of distance for the submarine is given by 11 feet/sec.

In order to find the slope between two points (x₁, y₁) and (x₂, y₂), take the ratio of the difference of the respective coordinates as (y₂ - y₁)/(x₂ - x₁).

Given that,

The table for distance travelled versus time taken for a submarine.

In order to find the slope, take two values of distance and time from the given table as  380 feet at t = 0 and 545 feet at t = 15.

Now, the slope can be found as,

slope = (545 - 380)/(15 - 0)

         = 165/15

         = 11

Hence, the rate of change of distance below sea level with respect to time is given as 11 feet/sec.

To know more about slope of straight line click on,

https://brainly.com/question/17028638

#SPJ2

The probability that, both tries to own a dog is 0.2500.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

P(A) = f / N determines probability, which quantifies the possibility of an event happening. Probability and odds are related, but probability is necessary for odds to exist. Prior to calculating the likelihood that an event will occur, probability is required.

Here, 50% of people own dog.

P(people own dog) = 50/100

= 0.5

P(both people own dog) = 0.5×0.5 = 0​​​​​​.2500

Learn more about probability Visit : brainly.com/question/13604758

#SPJ4

The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

Learn more about trigonometric identities at: https://brainly.com/question/7331447

#SPJ1

Answer:

b = 12d - 7c /a

Step-by-step explanation:

ab+7c=12d

ab+7c-7c=12d-7c

ab/b = 12d/a - 7c/a , a not equal to 0

b = 12d - 7c /a