Solve the following system of equations using either Gaussian elimination or a matrix. Write your answer as a point and explain how you would check your work:
2x-y+4z=33
x+2y-3z=-26
-5x-3y+5z=23

The vertex (the common end point for the two rays) in the angle SRQ is the point R as it is in the middle and common.

The angle is SRQ with sides SR and RQ. The common point is R.

A vertex of an angle is the endpoint where two line or rays come together. The vertex of an angle is the point where two rays begin or meet, where two line segments join or meet, where two lines intersect (cross), or any appropriate combination of rays, segments and lines that result in two straight "sides" meeting at one place.

Here two sides are SR and RQ the end point to both the sides is common which is R. So the vertex to the angle SRQ is R.

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The value of logarithmic equation log₂ (x+3) + lox₂ (3) = log₂(27) which is taken as an example is x = 6.

Step 1: Isolate a logarithmic expression (with the same base) on both sides of the equation using exponentiation rules.

Step 2: equalize the arguments.

Step 3: Solve the resultant equation.

Step 4: Verify your responses.

Let us consider an example -

log₂ (x+3) + lox₂ (3) = log₂(27)

using logₐ(m.n) = logₐ(m) + logₐ(n)

log₂(3(x+3)) = log₂(27)

log₂(3x + 9) = log₂(27)

3x+9 = 27

x = 27 - 9 / 3

x = 6

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Solution of logarithmic eq. log (3 - 2x) = -1 is , [tex]x = \frac{29}{20}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .

where, a is the base of function or equation

           x is expression equation

Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as  [tex]log_aN = x[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms :

According to given statement,

log (3 - 2 x)= -1

now convert this equation to exponential form

=> 3 - 2x = 10^-1

=> 3 - 2x = 1/ 10

=> x = 29 / 10

Thus solution for this equation is x =29/20.

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Answer: $96.27

Step-by-step explanation: 15x5=75, 75+21.27=96.27

Answer: $96.27

Step-by-step explanation:

If five of Carries' family members donated $15 we would have 15x5.

15+15+15+15+15=$75.

Carrie, herself, donated $21.27.

$75+$21.27

75+21=96

Add the .27 to 96.

Answer= $96.27 in total

The guarantee period of the electronic components by Accrotime manufactures is 38 months.

mean = μ = 24 months

standard deviation = σ = 5 months

2 years = 24 months

a) P(x < 24)

= P[(x - μ ) / σ < (24 - 28) / 5]

= P[(x - μ ) / σ < -0.8

= P(z < -0.8 )

Using z table,

= 0.212

Percentage = 21.2%

b) Use standard normal table,

Refund percentage = 12%

P(Z > z) = 12%

= 1 - P(Z < z) = 0.12

= P(Z < z) = 1 - 0.12

= P(Z < z ) = 0.88

= P(Z < 0.174 ) = 0.94  

z = 0.174

Using z-score formula,

x = z ×σ  + μ

x = 1.74 × 5 + 28

x = 36.7

The guarantee period = 38 month

Thus, the guarantee period of the electronic components by Accrotime manufactures is 38 months.

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Answer:

A) "If q, then p."

B) "If not p, then (not) q."

C) "If (not) q, then not p."

The height of the street light is approx. 3.5m.

Angle of depression is defined as the angle formed between the horizontal line and the line of sight when the observer looks down .

In the given question  

let h be the height of the street light

let d be the distance from the base of building to the street light .

form the figure given below.

In ΔADE

[tex]tan(57.8)=\frac{AD}{DE}[/tex]

Substituting the value of AD and DE from the figure

[tex]tan (57.8)=\frac{35}{d} \\ \\ d=\frac{35}{tan(57.8)} \\ \\ d=\frac{35}{1.5879}[/tex]....substituting the value of tan (57.8)

d=22.04 m      ...(i)

In ΔABC

[tex]tan(55)=\frac{AB}{BC}[/tex]

Substituting the value of AB and BC from the figure

since AD=AB+BD

35=AB+h

AB=35-h

[tex]tan (55)=\frac{35-h}{d}[/tex]

Substituting the value of d from (i)

[tex]tan (55)=\frac{35-h}{22.04}\\ \\ 35-h=tan(55)*22.04\\ \\ 35-h=1.428*22.04[/tex]( substituting the value of tan(55)  )

[tex]35-h=31.47[/tex]

[tex]h=35-31.47\\h=3.53\\[/tex]

h≅3.5

Therefore , the height of the streetlight is approx. 3.5m  .

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Answer:

[tex] \dfrac{x^{5}}{y^{8}} [/tex]

Step-by-step explanation:

[tex] \dfrac{y^{-8}}{x^{-5}} = [/tex]

[tex] = \dfrac{x^{5}}{y^{8}} [/tex]

The expression is simplified to give y⁻⁸x⁵

First, it is important to note that index forms are described as mathematical forms that are used to represent numbers of variables that are too large or that are too small in more convenient forms.

These index forms are also known as scientific notations or standard forms

From the information given, we have that;

y to the negative eighth power over x to the negative fifth power

This is represented as;

y⁻⁸/x⁻⁵

Since the forms are not of the same bases, we cannot add the exponents

y⁻⁸x⁵

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The school that Ming goes to sell their tickets as follows: price of a senior citizen ticket is $6 and the price of a student ticket is $9

Given data

first day 8 senior citizen tickets and 4 student tickets for a total of $84

second dat 8 senior citizen tickets and 2 student tickets for a total of $66

let the price of a senior citizen ticket be x and the price of a student ticket be y. The equation is written as:

8x + 4y = $84    equation 1

8x + 2y = $66    equation 2

subtracting equation 2 from equation 1

( 8x - 8x ) + 4y - 2y = 84 - 66

0 + 2y = 18

2y = 18

y = 9

substituting y = 9 into equation 1

8x + 4y = 84

8x + 4 * 9 = 84

8x + 36 = 84

8x = 84 - 36

8x = 48

x = 6

Hence the price of a senior citizen ticket is $6 and the price of a student ticket is $9

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Answer:  4 players can play and still have 8 cards each.

39÷8=4.875

Answer:

4 people

Step-by-step explanation:

39 cards / 8 cards = 4.87500

each person must have 8 cards, so only 4 people can play

The total number of cupcakes sold by the bakery on that day were 200.

Here, we are given that a bakery sold 26 vanilla cupcakes in a day.

This was 13% of the total number of cupcakes sold that day.

Let the total number of cupcakes sold that day be x

Then 13% of x is given to be 26. Mathematically this can be represented as-

(13/100)x = 26

solving the equation to find the value of x, we get-

x = 26 × 100/ 13

x = 26/13 × 100

x = 2 × 100

x = 200

Thus, the total number of cupcakes sold by the bakery on that day were 200.

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Answer:

64

Step-by-step explanation:

Angles DBF and EBF form a linear pair, so:

[tex]5x+6+3x-2=180 \\ \\ 8x+4=180 \\ \\ 8x=176 \\ \\ x=22 \\ \\ \implies m\angle DBF=116^{\circ}[/tex]

Similarly, because angles DBF and DBC form a linear pair, the answer is 64°.

Answer: i feel like all of them but dont go by my word

Step-by-step explanation:

Answer:

[tex]x\leq 25[/tex]

Step-by-step explanation:

Since x can equal anything 25 and lower, here are some of the possibilities x can be.

x = 25, 24, 23, 22, 21, 20, etc.

X could also be a decimal and doesn't have to be an integer.

x = 24.7, -20.4, 24 5/7

So to put these numbers in one equation, we can use the [tex]\leq[/tex] symbol.

Therefore, [tex]x\leq 25[/tex].

Hope this helped! Have a great day!

Answer:

The symbol should be equal to.

They are the same when the first expression is multiplied.

Answer:

=

Step-by-step explanation:

6.738 × 10^-11 = 0.00000000006.738

0.00000000006738 = 0.00000000006738

The solutions of the expression are;

a. - 5 - 2 = -7

b. 6 - (-5) = 11

What is Addition?

A process of combining two or more numbers are called Addition.

The given expression are;

a. -5 - 2

b. 6 - (-5)

Now, Solve the expression as;

-5 - 2 = - 7

And, 6 - (-5) = 6 + 5 = 11

So, The solutions of the expression are;

- 5 - 2 = -7

6 - (-5) = 11

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Answer:

6

Step-by-step explanation:

Terms are what is separated by addition and subtraction.

Answer:

I'm not completely sure, but it does look similar to a Florida Mockingbird to me, I'll do more research and comment on any new finds. Hope this helps.

Step-by-step explanation:

Answer:

yeah it might be a florida mocking bird i got a lot around where i live

Step-by-step explanation:

Using the description, area of triangle ACE is solved to be 150 square units

from the given data we fine AE using Pythagoras rule, as AE is the hypotenuse of the triangle AEM. So we solve as:

AE^2 = ME^2 + AM^2

AE^2 = 10^2 + 22^2

AE = √(100 + 484)

AE = √584

note AM is half of AB which is 44, it was given that M is the mid point of line AB, this makes AM = AB / 2 = 22

Area of triangle ACE

area of triangle when two sides and one angle is given is solved by the formula

= a b sin ∅ / 2

angle at A/2 = arc tan (10/22) = 24.44

= AC * AE * sin A/2 / 2

= 30 * √584 * sin 24.44 / 2

= 299.95 / 2

= 149.98 ≅ 150

Hence area of triangle ACE is solved to be 150 square units

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A counterexample that disproves her conjecture is that Easter date fell outside the first 22 days in April in the year 2024, 2027, 2032 and 2038.

Easter Sunday might come between March 22 and April 25. Easter is always celebrated on the Sunday immediately following the Paschal Full Moon date of the year. The Paschal Full Moon is the first Ecclesiastical Full Moon date after March 20. So, in Western Christianity, Easter is always celebrated on the Sunday immediately following the Paschal Full Moon.

Her conjecture over 2018 to 2021 is not a full reflection of the changes that occurs in these dates. To draw a more concrete assumptions, a wider range of year would need to be considered. Hence, the date variations between 2018 and 2021 is not enough for such conjectures.

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Answer:

- 3b + 21

Step-by-step explanation:

- 3(b - 7) ← multiply each term in the parenthesis by - 3

= - 3b + 21

The equation that can be use to represent the relationship between the actual length(a) in feet, and the length of the model (m), in inches is a = 2.4m or m = a / 2.4

The actual length of the car is 12 feet and is represented by 5 inches in the model.

The equation that can be use to represent the relationship between the actual length(a) in feet, and the length of the model (m), in inches is as follows:

12 feet = 5 inches

Hence,

m = 5 / 12 a

a = 2.4m

where

or

m = a / 2.4

Therefore, the  equation that can be use to represent the relationship between the actual length(a) in feet, and the length of the model (m), in inches is a = 2.4m or m = a / 2.4

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There is 0.329 probability or chance that the software really has a virus.

The calculation will be based on Bayes' theorem which relates the probability and statistics, as is mentioned in the given question. The values provided are True positive = 97%, False positive = 2% and Prevalence = 1%.

Probability = (True positive × user) ÷ (True positive × user) + (false positive × non user)

Keep the values in formula to find the probability

Probability = (0.97 × 0.01) ÷ (0.97 × 0.01) + (0.02 × 0.99)

Probability = 0.0097 ÷ (0.0097 + 0.0198)

Probability = 0.0097 ÷ 0.0295

Probability = 0.329

Thus, there is 0.329 chance that the software really has a virus.

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Answer:

Steps below.

Step-by-step explanation:

Unit Conversion is definitely needed in this question. Therefote, we will do some conversions first.

[tex]1m = 1000 mm \\ 1 {m}^{2} = {(1000)}^{2} {mm}^{2} \\ 1 {m}^{2} = 1000000 {mm}^{2} [/tex]

Now we can use the above converted unit to solve for the question.

[tex]32 {m}^{2} = 32 \times 1000000 \\ = 32000000 {mm}^{2} [/tex]

Answer: its 56

Step-by-step explanation:

plug #'s in

t=72-8x2

t=56

Step-by-step explanation:

To find a line perpendicular to one another and passing through the point we take the slope of the original line and apply its reciprocal in point slope form.

Reciprocal of [tex]\frac{1}{4}[/tex] is [tex]\frac{-4}{1}=-4[/tex]

Now plug the slope into point-slope form with the known x and y values:

[tex]x-(-2)=-4(y-4)\\x+2=-4(y-4)\\x+2=-4y+16\\x+2+4y=16\\4y=16-x-2\\y=4-\frac{x}{4}-\frac{2}{4}\\y=3.5-\frac{x}{4}[/tex]

Answer:

3n+5

Step-by-step explanation:

you don’t know the official age, all you know is that his age is 3 times whatever number

Answer:

x = 8 and x = 2 are both valid solutions.

There are no extraneous answers.

Step-by-step explanation:

Given absolute value function:

[tex]|2(x-5)|+11=17[/tex]

To solve an equation containing an absolute value, isolate the absolute value on one side of the equation:

[tex]\implies |2(x-5)|+11=17[/tex]

[tex]\implies |2(x-5)|+11-11=17-11[/tex]

[tex]\implies |2(x-5)|=6[/tex]

Set the contents of the absolute value equal to both the positive and negative value of the number on the other side of the equation, then solve both equations.

Equation 1 (positive)

[tex]\implies 2(x-5)=6[/tex]

[tex]\implies \dfrac{2(x-5)}{2}=\dfrac{6}{2}[/tex]

[tex]\implies x-5=3[/tex]

[tex]\implies x-5+5=3+5[/tex]

[tex]\implies x=8[/tex]

Equation 2 (negative)

[tex]\implies 2(x-5)=-6[/tex]

[tex]\implies \dfrac{2(x-5)}{2}=\dfrac{-6}{2}[/tex]

[tex]\implies x-5=-3[/tex]

[tex]\implies x-5+5=-3+5[/tex]

[tex]\implies x=2[/tex]

Therefore, the solutions are x = 8 and x = 2.

Check if the solutions are valid by substituting them into the original equation:

[tex]\begin{aligned}x=8 \implies |2(8-5)|+11 & =17\\|2(3)|+11 & =17\\|6|+11 & =17\\6+11 & =17\\ 17 & = 17\end{aligned}[/tex]

[tex]\begin{aligned}x=2 \implies |2(2-5)|+11 & =17\\|2(-3)|+11 & =17\\|-6|+11 & =17\\6+11 & =17\\ 17 & = 17\end{aligned}[/tex]

Therefore, both solutions are valid and there are no extraneous answers.

Note:  An extraneous solution is a solution that is produced by solving the problem, but is not a valid solution to the problem.