Answers
Answer:
[tex]\boxed {x_{1} = 3}[/tex]
[tex]\boxed {x_{2} = -4}[/tex]
Step-by-step explanation:
Solve the following equation:
[tex]\left[\begin{array}{ccc}3&2\\5&5\\\end{array}\right] \left[\begin{array}{ccc}x_{1}\\x_{2}\\\end{array}\right] + \left[\begin{array}{ccc}1\\2\\\end{array}\right] = \left[\begin{array}{ccc}2\\-3\\\end{array}\right][/tex]
-In order to solve a pair of equations by using substitution, you first need to solve one of the equations for one of variables and then you would substitute the result for that variable in the other equation:
-First equation:
[tex]3x_{1} + 2x_{2} + 1 = 2[/tex]
-Second equation:
[tex]5x_{1} + 5x_{2} + 2 = -3[/tex]
-Choose one of the two following equations, which I choose the first one, then you solve for [tex]x_{1}[/tex] by isolating
[tex]3x_{1} + 2x_{2} + 1 = 2[/tex]
-Subtract [tex]1[/tex] to both sides:
[tex]3x_{1} + 2x_{2} + 1 - 1 = 2 - 1[/tex]
[tex]3x_{1} + 2x_{2} = 1[/tex]
-Subtract [tex]2x_{2}[/tex] to both sides:
[tex]3x_{1} + 2x_{2} - 2x_{2} = -2x_{2} + 1[/tex]
[tex]3x_{1} = -2x_{2} + 1[/tex]
-Divide both sides by [tex]3[/tex]:
[tex]3x_{1} = -2x_{2} + 1[/tex]
[tex]x_{1} = \frac{1}{3} (-2x_{2} + 1)[/tex]
-Multiply [tex]-2x_{2} + 1[/tex] by [tex]\frac{1}{3}[/tex]:
[tex]x_{1} = \frac{1}{3} (-2x_{2} + 1)[/tex]
[tex]x_{1} = -\frac{2}{3}x_{2} + \frac{1}{3}[/tex]
-Substitute [tex]-\frac{2x_{2} + 1}{3}[/tex] for [tex]x_{1}[/tex] in the second equation, which is [tex]5x_{1} + 5x_{2} + 2 = -3[/tex]:
[tex]5x_{1} + 5x_{2} + 2 = -3[/tex]
[tex]5(-\frac{2}{3}x_{2} + \frac{1}{3}) + 5x_{2} + 2 = -3[/tex]
Multiply [tex]-\frac{2x_{2} + 1}{3}[/tex] by [tex]5[/tex]:
[tex]5(-\frac{2}{3}x_{2} + \frac{1}{3}) + 5x_{2} + 2 = -3[/tex]
[tex]-\frac{10}{3}x_{2} + \frac{5}{3} + 5x_{2} + 2 = -3[/tex]
-Combine like terms:
[tex]-\frac{10}{3}x_{2} + \frac{5}{3} + 5x_{2} + 2 = -3[/tex]
[tex]\frac{5}{3}x_{2} + \frac{11}{3} = -3[/tex]
-Subtract [tex]\frac{11}{3}[/tex] to both sides:
[tex]\frac{5}{3}x_{2} + \frac{11}{3} - \frac{11}{3} = -3 - \frac{11}{3}[/tex]
[tex]\frac{5}{3}x_{2} = -\frac{20}{3}[/tex]
-Multiply both sides by [tex]\frac{5}{3}[/tex]:
[tex]\frac{\frac{5}{3}x_{2}}{\frac{5}{3}} = \frac{-\frac{20}{3}}{\frac{5}{3}}[/tex]
[tex]\boxed {x_{2} = -4}[/tex]
-After you have the value of [tex]x_2[/tex], substitute for [tex]x_{2}[/tex] onto this equation, which is [tex]x_{1} = -\frac{2}{3}x_{2} + \frac{1}{3}[/tex]:
[tex]x_{1} = -\frac{2}{3}x_{2} + \frac{1}{3}[/tex]
[tex]x_{1} = -\frac{2}{3}(-4) + \frac{1}{3}[/tex]
-Multiply [tex]-\frac{2}{3}[/tex] and [tex]-4[/tex]:
[tex]x_{1} = -\frac{2}{3}(-4) + \frac{1}{3}[/tex]
[tex]x_{1} = \frac{8 + 1}{3}[/tex]
-Since both [tex]\frac{1}{3}[/tex] and [tex]\frac{8}{3}[/tex] have the same denominator, then add the numerators together. Also, after you have added both numerators together, reduce the fraction to the lowest term:
[tex]x_{1} = \frac{8 + 1}{3}[/tex]
[tex]x_{1} = \frac{9}{3}[/tex]
[tex]\boxed {x_{1} = 3}[/tex]
Related Questions
A company produces circular drink coasters. The equation x2 y2 = 18. 0625, with units in inches, represents the size of a coaster. Each coaster is cut from a square piece of cardboard. What is the minimum possible area of each cardboard piece? 4. 25 in2 8. 5 in2 18. 0625 in2 72. 25 in2.
Answers
The minimum possible area of the square cardboard will be given as
[tex]a= 72.2\ in ^2[/tex]
What will be the area of the dashboard?The area of the square is the product of its two lengths.
We have an equation of the circular drink coaster
[tex]x^2+y^2=18.0625[/tex]
Comparing the above equation from the general form of the circle
[tex]x^2+y^2=r^2[/tex]
We can see that from the equation
[tex]r^2=18.0625[/tex]
[tex]r=4.25\ inch[/tex]
Diameter [tex]d=4.25\times 2=8.50[/tex]
The diameter will be the length of the square since the circle is cut from the square.
So the area of the square will be
[tex]a=d\times d=8.50\times 8.50=72.25\ inch^2[/tex]
Thus the minimum possible area of the square cardboard will be given as [tex]a= 72.2\ in ^2[/tex]
To know more about Area follow
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Carlos was given the problem "Evaluate the expression 2x^2 + 5 when x=3." Carlos wrote the answer 41. Was he correct? Explain.
Answers
explanation: when you insert 3 into the problem hince, 2(3)^2 + 5. you will get 2x9+5. 18+5=23
Mr. Majors ordered six hot dogs and a bucket of popcorn at the concession stand. If the popcorn
was $3.20, and the total was $18.20, what was the price of one hot dog?
Answers
Answer:
The cost of one hot dog is $2.50
Step-by-step explanation:
You need to subtract $3.20 from $18.20 to get $15.00. Then you need to divide $15.00 by 6 to get $2.50.
Solve for x:
3x + 5 = 5x – 9
Answers
Answer:
x=7
Step-by-step explanation:
hi can someone help me with my question, which is 2 ( 3 + x) - 7 = x + 5?
Answers
Answer: x=6
Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
2*(3+x)-7-(x+5)=0
(2 • (x + 3) - 7) - (x + 5) = 0
x - 6 = 0
Solve : x-6 = 0
Add 6 to both sides of the equation :
x = 6
Answer:
x = 6
Step-by-step explanation:
2(3+x)-7=x+5
We move all terms to the left:
2(3+x)-7-(x+5)=0
We add all the numbers together, and all the variables
2(x+3)-(x+5)-7=0
We multiply parentheses
2x-(x+5)+6-7=0
We get rid of parentheses
2x-x-5+6-7=0
We add all the numbers together, and all the variables
x-6=0
We move all terms containing x to the left, all other terms to the right
x=6
Surgical treatment of a broken arm costs $16,911. You have a $1,000 deductible and then your insurance will pay 85% of the remaining cost. Your insurance also has an out-of-pocket maximum charge of $3,500. What is your cost?
Answers
Using proportions, it is found that your cost is of $12,411.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, the treatment costs $16,911, with a deductible of $1,000, hence the price is already of $15,911.
The insurance will pay 85% of the remaining cost, or $3,500, whichever is greater, hence:
0.85 x 15911 = $13,524 > $3,500.
Hence, the insurance pays only $3,500, and your cost is given by:
15911 - 3500 = $12,411.
More can be learned about proportions at https://brainly.com/question/24372153
Which algebraic property is used to rewrite 2(4y + 1) as (4y + 1)(2)?
Answers
Answer:
Commutative property of multiplication
Step-by-step explanation:
POLYNOMIALS MULTIPLICATION
(x^2-3) (4x+x^2-7)
Find the product of the polynomials in standard form
Answers
Answer:
x^4+4x^3-10x^2-12x+21
Step-by-step explanation:
Answer:
:D
Step-by-step explanation:
o_o <3
Which of the following number lines and solution sets show the values of r that make the inequality -2r+3<9 true
Answers
Answer:
"Solving'' an inequality means finding all of its solutions. A "solution'' of an inequality is a number which when substituted for the variable makes the inequality a true statement. When we substitute 8 for x, the inequality becomes 8-2 > 5. Thus, x=8 is a solution of the inequality.
Step-by-step explanation:
Example 1:
Consider the inequality
displaymath173
The basic strategy for inequalities and equations is the same: isolate x on one side, and put the "other stuff" on the other side. Following this strategy, let's move +5 to the right side. We accomplish this by subtracting 5 on both sides (Rule 1) to obtain
displaymath174
after simplification we obtain
displaymath175
Once we divide by +2 on both sides (Rule 3a), we have succeeded in isolating x on the left:
displaymath176
or simplified,
displaymath177
All real numbers less than 1 solve the inequality. We say that the "set of solutions'' of the inequality consists of all real numbers less than 1. In interval notation, the set of solutions is the interval tex2html_wrap_inline187 .
Example 2:
Find all solutions of the inequality
displaymath189
Let's start by moving the ``5'' to the right side by subtracting 5 on both sides (Rule 1):
displaymath190
or simplified,
displaymath191
How do we get rid of the ``-'' sign in front of x? Just multiply by (-1) on both sides (Rule 3b), changing " tex2html_wrap_inline201 " to " tex2html_wrap_inline203 " along the way:
displaymath192
or simplified
displaymath193
All real numbers greater than or equal to -1 satisfy the inequality. The set of solutions of the inequality is the interval tex2html_wrap_inline205 .
Example 3:
Solve the inequality
displaymath207
Let us simplify first:
displaymath208
There is more than one route to proceed; let's take this one: subtract 2x on both sides (Rule 1).
displaymath209
and simplify:
displaymath210
Next, subtract 9 on both sides (Rule 1):
displaymath211
simplify to obtain
displaymath212
Then, divide by 4 (Rule 3a):
displaymath213
and simplify again:
displaymath214
It looks nicer, if we switch sides (Rule 2).
displaymath215
In interval notation, the set of solutions looks like this: tex2html_wrap_inline227 .
What is the solution of the proportion 2/3 = x/14 ? Round to the nearest tenth if necessary.
A. 21
B. 2
C. 7
D. 9.3
Answers
Answer:
D. 9.3
Step-by-step explanation:
Answer:
D ( 9.3)
Step-by-step explanation:
2/3 = x/14 -->
14 *2/3 = x -->
28/3 = x -->
9.33.... = x-->
9.3 = x
Compare 6 x 10^8 to 3 x 10^6
A) 6 x 10^8 is 2,000 times larger then 3 x 10^6
B)6 x 10^8 is 200 times larger then 3 x 10^6
C)6 x 10^8 is 20 times larger then 3 x 10^6
D)6 x 10^8 is 2 times larger then 3 x 10^6
Answers
Answer:
i think B
Step-by-step explanation:
it just seems like the most reliable and best choice
Please help! Thank u so much
Answers
Answer:
x= 11/3
Step-by-step explanation:
6x-8=3+3x
6x-8+8=3+3x+8
6x=3x+11
6x-3x=3x+11-3x
3x=11
3x/3=11/3
x=11/3
You are considering selling your home. You consult with an agent who gives you the asking prices of five homes (comps) in your area: $165,000, $188,000, $175,000, $150,000 and $400,000. The $400,000 is an outlier so you will not include it in your evaluation. In determining a reasonable asking price, what is the mean of the four remaining comps?
Answers
Answer:
$169,500Step-by-step explanation:
Mean is the average of the numbers. It is expressed as the ratio of the sum of the numbers to its sample size.
Mean = sum of the amounts/sample size
Sum of the amounts = $165,000 + $188,000 + $175,000+$150,000
Sum of amounts = $678,000
Sample size = 4 (excluding the outlier)
Mean = $678,000/4
Mean = $169,500
Hence the mean of the four remaining comps is $169,500
plz help pllzz 35 points
Answers
Answer:
$18 an HOUR
Step-by-step explanation:
Noah earned $232.70 working for 13 hours.
We are trying to find each hour,
We can make this into a FRACTION.
232.70/13 = 1/x
Multiply across,
13x=232.70
232.70/13=17.9
We can round this to $18 :D
PLEASE help if you’re able!!
Answers
To find the sum of interior angles of this polygon you have to use the equation
S=180(n-2)
where n is the number of sides
S=180(6-2)
S=180(4)
S=720 degrees
The sum of all angles is 720 degrees
[tex]110 + x + 25 + x - 30 + x + x + 115 = 720[/tex]
[tex]4x = 720 - 110 - 25 - 115 + 30[/tex]
[tex]4x = 720 - 220[/tex]
[tex]4x = 500[/tex]
[tex]x = \frac{500}{4} = 125[/tex]
HELP QUICK which function has the greater rate of change
Answers
Answer:
Function A i think.....
Step-by-step explanation:
pls help this is my last question help!!!!
Answers
Find the slope, midpoint and distance using these points: (6,-5) (-4,8)
Answers
8-(-5) / -4-6
13/-10
Midpoint:
(6 + -4/2, -5 + 8/2)
(1, 3/2)
I don’t know how to type the square root symbol so I’ll just type the equation for distance and give you the answer.
Distance formula: square root of (-4 - 6)^2 + (8 - -5)^2
Answer: 16.40
I’m not sure of the distance answer but I hope this helps!!
4, -8, 16, _, 64
What is the 4th missing term?
Answers
yo lo yolo trol
Step-by-step explanation:
nnsnsns
What is cos 45º?
O A.
1
2
O B. 7 /
O C. 13
1
O D.
E. 1
0
OF A
F. 3
Answers
Answer:
The exact value of cos(45°) is √(2) / 2.
Step-by-step explanation:
Answer:
Answer:√2/2=cos45
√2/2×√2/√2=2/2√2
1/√2
can someone explain this to me
Answers
Answer:
the question is mistyped.. they are trying to ask for the area.. not are.. :P soooo ... to answer the question that is trying to be asked.. and not the one that is being asked.. b/c there isn't really an answer to what is the are.... :/
Step-by-step explanation:
area of a triangle is 1/2 area of the box that the triangle makes 1/2 hmm , hence the fomula.. 1/2*base*height.... b/c base*height is the area for a box... soooo ...
for this triangle it's 1/2* 3 * 4= 6 :)
note: even thou this is not a right triangle.. we still know the height of it.. the graph is showing us that. so our formula still works... for this one if we didn't know height.. we might have to use sin() or cos() to figure out height.. but here it's given. luckily :)
The line y = 0.5x + 8 passes through (-10, a) and (-20, b). Find the values of a and b.
Answers
Answer:
Step-by-step explanation:
Write out the equation y = 0.5x + 8. Now focus on the point (-10, a). In the given equation, let y = a and x = -10: a = 0.5(-10) + 8, so that a = 3.
Next, focus on the point (-20, b). Find b: In y = -0.5x + 8, replace x with -20 and y with b: b = 0.5(-20) + 8, or b = -10 + 8, or b = -2
x = what? (giving brainliest and thanks)
Answers
Answer:
x=12
Step-by-step explanation:
Here is the charge at a car park in Spain.
Car park = 0.024 euros per minute
Jon parked his car in this car park.
Jon drove into the car park at 1045
When he drove out of the car park he had to pay 8.40 euros.
At what time did Jon drive out of the car park?
Answers
Answer:
Given : car park charges 0.018 euros per minute.
claude parked his car in this car park at 13:15.
he had to pay 4.50 euros.
To Find : at what time did claude drive out of the car park
Solution:
car park charges per minute = 0.018 euros
Parking Charges paid = 4.50 Euros
Time car parked for = 4.50/0.018
= 250 minutes
= 4 hr 10 minutes
parked his car at 13:15
Parked for 4 hr 10 min
claude drive out of the car park = 13+4 = 17 hr
15 + 10 = 25 min
claude drive out of the car park at 17 : 25
please mark brinliest
Jon drive out of the car park at 16 : 35
What is Division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Here, car park charges 0.024 euros per minute.
Jon parked his car in this car park at 10:45.
he had to pay 8.40 euros.
Time car parked for = 8.40/0.024
= 350 minutes
= 5 hrs 50 minutes
parked his car at 10:45
Parked for 5 hrs 50 mins
Jon drive out of the car park = 10:45 + 5:50
= 16:35
Thus, Jon drive out of the car park at 16 : 35 .
Learn more about Division from:
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How many perfect cubes are there between 2 to 200 ?
ANSWER fast
Answers
Answer:
Three
Step-by-step explanation:
The perfect cubes between 2 to 200 are
[tex] {3}^{3} = 27 \\ \\ {4}^{3} = 64 \\ \\ {5}^{3} = 125 \\ [/tex]
Hence, there are only three perfect cubes 27, 64 and 125 between 2 to 200.
Which segment is a diameter of this circle?
Ο TX
O VX
Ο XY
Answers
Answer:
The answer is VX.
Step-by-step explanation:
This is because the line segment VX, reaches from one end of the circle to the other, touch both sides of the circle. The other options do not make sense since segment XY does not go through the center of the circle and TX is the radius of the circle. The radius is half the diameter of the circle.
Therefore, the answer is VX.
An angle measures 6° more than the measure of its complementary angle. What is the measure of each angle?
Answers
Answer:
42° and 48°
Step-by-step explanation:
Complementary angles add up to 90°.
So we have one angle x and the other angle x+6 which when added together will equal 90°.
x + x + 6 = 90
2x + 6 = 90
-6 - 6
2x = 84
Divide both sides by 2
2x/2 = 84/2
x = 42
So one angle = 42°, and the other angle = 42° + 6° = 48°.
giving brainlist for correct answer. :))
Answers
Answer:
162 cubes
Step-by-step explanation:
The formula for finding the volume of a rectangular prism is length x width x height.
6 x 3 x 4.5 = 81
Since each cube is only half a centimeter, we need to multiply this by two.
81 x 2 = 162 cubes
In the 1980s, Earth had about five months of very hot weather. In the 1990s, Earth had about
22 months of very hot weather. What is the percent increase in hot weather months from the
1980s to the 1990s? Round to the nearest percent.
Answers
Answer:
340%
Step-by-step explanation:
1980s = 5 months of very hot weather
1990s = 22 months of very hot weather
What is the percent increase in hot weather months from the
1980s to the 1990s?
Percent increase = (22 months - 5 months) / 5 months × 100
= 17 / 5 × 100
= 3.4 × 100
= 340%
Percent increase in hot weather months from the 1980s to the 1990s is 340%
what is square root of 27.04 by long division method?
Answers
Answer:
5.2
Step-by-step explanation: