Convert the following system of equations into an augmented matrix: (1) 2x + 2y + 2z = 4(2) -x − 3y = 2 + 8z − 3y(3) -z = 2x + y

Answer:

A'(-6,4) B'(2,2) C'(-2,-2)

Step-by-step explanation:

The dilation is by 2. This just means you multiply each number by two. FOr example, for point a, multiply -3 by 2 and 2 by 2 to get (-6, 4).

Answer:

Step-by-step explanation:

Me personally, I think buffets are the best because you can take as music food as you much, without being charged for much! But thats only for some buffets. If you go to a chinese buffet, they might lower the price allowing you to get as much food as you please!

The length of the side opposite to the reference angle is 7.77 units.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

If we take the reference angle 45°, The side 'x' is opposite and the side having a length of 11 units is the hypotenuse.

We know, sin = opposite/hypotenuse.

Therefore,

sin45° = x/11.

1/√2 = x/11.

x = 11/√2.

x = 7.77 units.

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Answer:

19/20 , 1 1/4 , 1 4/5

Step-by-step explanation:

1.8 = 1 4/5 (fraction)

1.8 converts to 18/10. This can be simplified twice, firstly by making it 9/5 since both 18 and 10 are divisible by two, but can be simplified further to 1 4/5

1.25 = 1 1/4 (fraction)

1.25 converts to 125/100. This can be simplified to 5/4 or 1 1/4

0.95 = 19/20 (fraction)

0.95 converts to 95/100. This can be simplified to 19/20

Ascending Order (smallest to largest)

smallest - 19/20

middle - 1 1/4

largest - 1 4/5

I believe this is the right answer, but haven't done fractions in a while so may want to double check to make sure

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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Answer:

(a) Yes, E and F are independent events.

(b) P(E and F) = P(E)P(F) = (1/2)(1/2) = 1/4

Answer:

30

Explanation:

We will call the missing value a, so we can write the expression as:

6(3x + 5) = 15x + a + 3x

Applying the distributive property on the left side we get:

Then, adding like terms in the right side, we get:

Therefore, the expressions are equivalent if a is equal to 30.

So, the answer is 30

The equation of the curve that intersects at right angles to every curve of the family y=(1/x)+k is y=lnx

y=-x+k is the equation of a curve that meets at right angles every curve in the family y=(1/x)+k (where k can take any real value). This is known as the 'orthogonal curve' of the y=(1/x)+k family. It is calculated by obtaining the reciprocal of the original equation and then removing k from the y-axis.

A straight line with a negative slope is given by the equation y=-x+k. Every point on the line has an x-value that is the inverse of its y-value. At the point where x=1/k and y=k, the equation will always meet the curve of the family y=(1/x)+k at a right angle. This point is the same for all values of k and is known as the 'origin' of the function.

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The equation in the form y = mx + b for this situation is y = 35 + 70x

The cost of the plan for 6 months is $455.00.

The cost of a 2-yr contract for the cell phone package is $1715.00

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

y = 35 + 70 * x

So, we have

y = 35 + 70x

Here, we have

x = 6

So, we have

y = 35 + 70 * 6

Evaluate

y = 455

So, we have

(6, 455)

This means that the total cost for x = 6 is $455

Here, we have

x = 2 * 12 = 24

So, we have

y = 35 + 70 * 24

Evaluate

y = 1715

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Answer:

The slope will be 25

Step-by-step explanation:

slope is change in y over change in x

so..the change in Y is 25, and in X is 1 so..

25/1 = 25

Answer:

12755 base-8

Step-by-step explanation:

You’re welcome :) please brainliest me btw.

Answer:

Step-by-step explanation:

11/20 = 55/100 = 55%

may be the answer is :4g-2=8 ^-^

but donot depend in this answer it's not sure okay

The rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

From the question, we have the following parameters that can be used in our computation:

John drove from here to San Antonio which is 180 miles away in 3 hours.

This means that

Distance = 180 miles

Time = 3 hours

Using the above as a guide, we have the following:

Speed = Distance/Time

Substitute the known values in the above equation, so, we have the following representation

Speed = 180/3

Evaluate

Speed = 60

Hence. the rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

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(-3, 2)

Step-by-step explanation:

when the point is rotated through 90∘ about the origin in the counterclockwise direction then the point M(h,k) takes the image M′(−k,h)

so the point (2,3) will be (-3 ,2 )

Answer:

\(\frac{2}{25}\)

Step-by-step explanation:

All percents can be written as a fraction with their denominator as 100.

So, first we can write the fraction as 8/100 and start making it smaller and simplifying it.

\(\frac{8}{100}\) can be divided by 4 since that is the GCF ( Greatest common factor)

Now, the numerator would be 2 and the denominator would be 25 as shown below ...

\(\frac{2}{25}\)

This is the simplest form of 8% as a fraction

Hope this Helps!!! :)

Let me know in the comments if the answer was perfect or if I should change anything!!!

The simplest form of the 8% as a fraction is 2 / 25.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %.

All percentages can be written as a fraction with their denominator as 100. First, write the fraction as 8/100 and start making it smaller and simplifying it.

Fraction = 8 /100

Fraction = ( 4 x 2) / ( 4 x 25)

Fraction  = 2 / 25

Thus, the 8% in the fraction is 2 / 25.

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Answer:

The answer is 50x + 70

Step-by-step explanation:

I am happy to help. An expression has no equal sign. We don't know how much the electrician will charge Laura. But we do know how much hours the job is. Laura also has to pay for the electrical parts that are 20 dollars and 50 dollars for a new ceiling fan. This is an additional cost. In all, the expression would be 50x + 70, if it is simplified. You would add like terms, such as 20 and 50 to get 70.

we have the equation

y=2x-7

The equation of the line in slope-intercept form is

y=mx+b

where

m is the slope

b is the y-intercept

so

In this problem

m=2

b=-7

the slope is 2 and the y-intercept is -7

see the attached figure below

Hello!

This is an equilateral triangle. In this triangle, the angles are congruent, respectively, the sides. Here, the mediator corresponds to the bisector, the median. So this line will form two  right triangles.

Th 30-60-90

I used the 30-60-90 theorem, which says that the opposing the angle of 30 degrees has the length equal to half the hypotenuse.

Th Pitagora's

Which states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

Good luck:)

Answer:

id ont givea

efijhaoieuvbhzoiubhoewivbawzoufhbealivjhbr

Step-by-step explanation:

idsifui piuh vSeth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?

Answer:

10miles I think

Step-by-step explanation:

The required distance between, Nate's house and the restaurant is 7.5 miles.

From the graph,

Consider point C on the graph, which is 6  and 8 units apart from A and B respectively.

The distance between, Nate's house and the restaurant is given as,
AB = √[AC² + BC²]
AB = √[6² + 8²]
AB = 10 units

Now 1 unit = 3/4 miles
AB = 10 * 3/4
AB = 7.5 miles

Thus, the required distance between, Nate's house and the restaurant is 7.5 miles.

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Answer: shehshywhwyw

Step-by-step explanation:

After solving the equations, we know that a total of 25 ladies attended the party.

A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.

As in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, and others.

So, take dudes as x and ladies as y.

Now, form the required 2 equations as follows:
2x + y = 45 ...(1)

x + y = 35 ...(2)

Work on equation (2):

x + y = 35

x = 35 - y

Now, substitute x = 35 - y in equation (1):

2x + y = 45

2(35-y) + y = 45

70 - 2y + y = 45

-y = -25

y = 25

Since ladies were charged $1 for each ticket, then 25 ladies attended the party.

Therefore, after solving the equations, we know that a total of 25 ladies attended the party.

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Answer:

Step-by-step explanation:

Line B passes through (3.75, 0) and (0, negative 5) represents the line -3y = 15 – 4x. the slope of the line is = 4/3 and the y-intercept is -5.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.

A line can be defined by the shortest distance between two points is called as a line.

Given the expression of the line,
–3y = 15 – 4x

Now by putting every given point of the lines given with their passing points in –3y = 15 – 4x , it is found that point (3.75, 0) and (0, -5) lies on the line.

Hence, the expression –3y = 15 – 4x represents line B.

Now, the slope and y-intercept of the equation.
Rearrange the equation into standard form,
y = 4/3 x - 5
Now compare the above equation with the standard form line
y = mx +c

m = 4/3 and c = -5

Thus, line B passes through (3.75, 0) and (0, negative 5) represents the line -3y = 15 – 4x. the slope of the line is = 4/3 and the y-intercept is -5.

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Answer:

im pretty sure the answer is (-5,-7)?

Answer:

1x0.8=0.8 ,10x0.08=0.8 and 100x0.008=0.8

Step-by-step explanation:

Answer:

It would take 74.5 minutes for the element to decay 17 grams.

Step-by-step explanation:

The amount of element X after t minutes is given by the follwoing equation:

\(X(t) = X(0)e^{rt}\)

In which X(0) is the initial amount of the substance and r is the decay rate.

Half life of 14 minutes.

This means that \(X(14) = 0.5X(0)\)

So

\(X(t) = X(0)e^{rt}\)

\(0.5X(0) = X(0)e^{14r}\)

\(e^{14r} = 0.5\)

\(\ln{e^{14r}} = \ln{0.5}\)

\(14r = \ln{0.5}\)

\(r = \frac{\ln{0.5}}{14}\)

\(r = -0.0495\)

So

\(X(t) = X(0)e^{-0.0495t}\)

There are 680 grams of element X

This means that \(X(0) = 680\)

\(X(t) = X(0)e^{-0.0495t}\)

\(X(t) = 680e^{-0.0495t}\)

How long would it take the element to decay 17 grams

This is t for which X(t) = 17. So

\(X(t) = 680e^{-0.0495t}\)

\(17 = 680e^{-0.0495t}\)

\(e^{-0.0495t} = \frac{17}{680}\)

\(e^{-0.0495t} = 0.025\)

\(\ln{e^{-0.0495t}} = \ln{0.025}\)

\(-0.0495t = \ln{0.025}\)

\(0.0495t = -\ln{0.025}\)

\(t = -\frac{\ln{0.025}}{0.0495}\)

\(t = 74.5\)

It would take 74.5 minutes for the element to decay 17 grams.

Answer:

Step-by-step explanation:

Answer:

3

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8

Step-by-step explanation:

the ratio of cakes to pies will be 3:8 if pies to cakes is 8:3

the fraction is 3/8

Answer: 1, 2, and 4.

Step-by-step explanation: Each must be wider than the angle than a "L" has.