Solving a Two-Step Matrix Equation
Solve the equation:
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]
Which is true of the models? Check all that apply. Both exact values are less than the approximate value. The percent errors are the same. The top model has a greater percent error. The bottom model has a greater percent error. The absolute error is the same for both.
Answer:
A C E
Both exact values are less than the approximate value.
The top model has a greater percent error.
The absolute error is the same for both.
Step-by-step explanation:
Answer:
Both exact values are less than the approximate value.
The top model has a greater percent error.
The absolute error is the same for both.
Step-by-step explanation:
PLEASE HELP PLEASE HELP!!!!
Write a problem that would result in the expression: -12 + 6(3/4). Solve your problem and show your work.
Answer:
-18 and 3/4
Step-by-step explanation:
Besides 49 and 1, what is one factor of 49??????????????????????
Answer:
See below.
Step-by-step explanation:
The factors of 49 are 1, 7, and 49.
1 x 49 = 49
7 x 7 = 49
-hope it helps
I need help wit the answer
Answer:
Triangle STU is not similar to Triangle VWU
Step-by-step explanation:
For two triangles to be similar, they both should have the same angle measures. To find out if they have the same angle measures, we have to solve for the unknown angles. Remember, a triangle is worth 180°.
Triangle STU:
x + 90 + 42 = 180x + 132 = 180x = 48Triangle VWU:
x + 58 + 90 = 180x + 148 = 180x = 32As you can see, the angles don't have the same angle measures. Thus, they are not similar.
PLEASE HELP! I’ll mark you as brainliest or whatever it’s called❤️
Answer:
45% of 280 is 126
126
Hope This Helps!
35% of 280 is 98. 100% of 280 is 280, therefore 35 percent of 280 equals 98
80% of 280 = 224
45% of 280 = 126
Find the constant of proportionality if y varies directly with x for the values below.
x = 2
y = 11
Answer:
y=5.5x
Step-by-step explanation:
Which equation, when graphed, has x-intercepts at (−1, 0) and (−5, 0) and a y-intercept at (0, −30)? f(x) = −6(x 1)(x 5) f(x) = −6(x − 1)(x − 5) f(x) = −5(x 1)(x 5) f(x) = −5(x − 1)(x − 5).
Answer:
f(x) = −6(x+ 1)(x +5)
Step-by-step explanation:
x-intercepts at (−1, 0) and (−5, 0)
so the roots are -1 and -5 (where the graph intersects the x-axis)
this will give us that f(x) = (x- root1)(x-root2) = (x- -1)(x- -5) = (x+1)(x+5)
y-intercept at (0, −30) is telling us that when x= 0 the y = -30
y = a ( x+1)(x+5) , in general
y = a(0+1)(0+5), is the equation if x=0
-30 = a·1·5, we need y= -30 when x= 0
-30 = 5a , divide both sides of the equation by 5
-6 = a
The correct choice is :
f(x) = −6(x+ 1)(x +5)
f(x) = −6(x − 1)(x − 5)
f(x) = −5(x +1)(x +5)
f(x) = −5(x − 1)(x − 5).
m(x) =5
Find m(2)
I have no idea how to do this help me
Answer:
10
Step-by-step explanation:
All this is saying is when there is one x value it is equal to 5
so, applying that logic, 2 fives is equal to 2*5=10
so when x=2, it is equal to 10
Hope this helps you out!!!
Ingnd mxes 3 6 pounds of almonds with some raisins to make a trail mix She divides the trail mix into 12 equal portions Each portion weighs 0.7 of a pound How many pounds of raisins did she use to make the trail mix? Express the answer to the nearest tenth 2.9 4.8 5.1 7.2
Answer:
The 12 portions weigh a total of 12*0.7 = 8.4 lbs
So, the almonds weigh 8.4 - 3.6 = 4.8 lbs
Answer:
4.8 poundsStep-by-step explanation:
Let raisins weight be x
Then we get equation
(3.6 + x)/12 = 0.7Solving for x
3.6 + x = 12*0.7x + 3.6 = 8.4x = 8.4 - 3.6x = 4.8 poundsOption B is correct one
There are 4 times as many dogs as cats if the total number of dogs and cats is 25 how many dogs are there
Answer:
6 times as many dogs as cats
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
So we know that if we combine all of the dogs and cats, we get 25. We also know that there are 4 times more dogs than cats, so we can call cats x, and dogs 4x.
So 4x + x = 25
5x = 25
x=5
There are 5 cats. Now that we know the number of cats , we just need to multiply that by 4, which is 20 dogs.
There are 6 options on the dessert menu at a restaurant. Akira and Paula like all of the choices equally, so they each choose a dessert at random from the menu. What is the probability that Akira will choose apple pie and Paula will choose strawberry cheesecake for dessert? Express your answer as a decimal. If necessary, round your answer to the nearest thousandth.
0.167
0.028
0.033
0.972
The probability that Akira will choose apple pie and Paula will choose strawberry cheesecake for dessert is; B: 0.028
What is the probability of selection?
We are told that;
There are 6 dessert options menu.
Now, Akira and Paula like all of the choices equally. Thus, probability of selecting any of the 6 menus will be; P(select 1 menu) = 1/6
Thus, probability that they select the preferred menu written in the question is; P(both select 1 menu) = 1/6 * 1/6 = 0.028
Read more about Probability at; https://brainly.com/question/251701
Simplify
7x+[x-(5+x)]
a) 7x-5
b)8x-5
c)9x-5
Answer:
It would be a which is 7x-5
The first step of a staircase that leads to an outdoor deck is above a concrete slab. The height, h, in centimeters of the n step of
the staircase above the ground can be represented by the function h (n) = 25n+ 3. Which of the following is a correct
interpretation of the function? (1 point)
A. The concrete slab is 25 cm tall
B. The height of each step is 3 cm.
C. The first step is 25 cm tall, and the subsequent steps are 3 cm tall
D. The concrete slab is 3 cm tall.
Answer: D
Step-by-step explanation:
Answer:
The correct answer is B. The concrete slab is 3 cm tall.
6. Triangle A is an isosceles triangle with two angles of measure x degrees and one
angle of measure y degrees
a. Find three combinations of x and y that make this sentence true
Answer:
Step-by-step explanation:
Question is in the picture:
Answer:
here
Step-by-step explanation:
For the first one shade 38 squares
For the second one shade 65 of the squares
#1 is 38%
#2 is 65%
Answer:shade 19 out of 50 bloxks
Step-by-step explanation:
it shows on page
what is (3-8y)x(-2.5)
Answer:
20xy−7.5x
Step-by-step explanation:
Simplify the expression:
3(2 + 3v)
HELPPP
Answer:
[tex]\boxed{\sf{6+9v}}[/tex]
Step-by-step explanation:
We only need to use a distributive property to solve this.
Distributive property:
⇒ A(B+C)=AB+AC
3(2+3v)
Multiply.
[tex]\sf{3(2+3v)}[/tex]
[tex]\sf{3*2=6}[/tex]
[tex]\sf{3*3=9}[/tex]
Rewrite the problem.
6+9v
Therefore, the correct answer is 6+9v.
I hope this helps you! Let me know if my answer is wrong or not.
5x+10y=20
graph it using y=mx+b
show your work please
Answer:
y=20-5x 10Step-by-step explanation:
5x+10y=20y=mx+b10y=20-5xdivide by 10 both side10y=20-5x 10 = 10y=20-5x 10answerSolve for x in the equation x ^ 2 + 2x + 1 = 17
O x = - 1 plus/minus sqrt(13)
O x = - 2 plus/minus 2 * sqrt(5)
O x = - 1 plus/minus sqrt(17)
O x = - 1 plus/minus sqrt(15)
Answer:
[tex]x=-1+\sqrt{17},\:x=-1-\sqrt{17}[/tex]
Step-by-step explanation:
[tex]x ^ 2 + 2x + 1 = 17[/tex]
[tex]\mathrm{Subtract\:}17\mathrm{\:from\:both\:sides}[/tex]
[tex]x^2+2x+1-17=17-17[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x^2+2x-16=0[/tex]
[tex]\mathrm{Solve\;with\;Quadratic\;formula}[/tex]
[tex]x_{1,\:2}=\frac{-2\pm \sqrt{2^2-4\cdot \:1\cdot \left(-16\right)}}{2\cdot \:1}[/tex]
[tex]\sqrt{2^2-4 \cdot1\cdot(-16)} =\sqrt[2]{17}[/tex]
[tex]x_{1,\:2}=\frac{-2\pm \:2\sqrt{17}}{2\cdot \:1}[/tex]
[tex]\mathrm{Separate\:the\:solutions}[/tex]
[tex]x_1=\frac{-2+2\sqrt{17}}{2\cdot \:1},\:x_2=\frac{-2-2\sqrt{17}}{2\cdot \:1}[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]
[tex]x=-1+\sqrt{17},\:x=-1-\sqrt{17}[/tex]
Hence, Answer is [C] [tex]x=-1+\sqrt{17},\:x=-1-\sqrt{17}[/tex]
~Lenvy~
Answer:C
Step-by-step explanation:
What is The difference of 3 and a number X
Answer:
"the difference of" means to subtract
Therefore, "the difference of 3 and a number" would be:
3-x
Step-by-step explanation:
The required number is 63 and its 20% will be 12.6.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.
The difference between 3 and the number x of that number is -60.
According to the question, the algebraic form will be as:
⇒ 3 - x = -60
⇒ x = 60 + 3
Apply the addition operation,
⇒ x = 63
So the required number is 63
20% of the number = (20/100) × 63
20% of the number = (0.20) × 63
20% of the number is 12.6.
Therefore, the required number is 63 and its 20% will be 12.6.
Learn more about the number system here:
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The question seems to be incomplete the correct question would be:
The difference between 3 and the number x of that number is -60. What is 20% of that number?
Here is a list of ingredients: 260g of butter, 500g of sugar, 650g of flour, 425g of rice to make 20 biscuits. Michael has 2kg of each ingredient. Work out the greatest number of biscuits that he can make.
Answer: 61 Biscuits
Step-by-step explanation: 13g of butter per biscuit, 25g sugar per biscuit, 32.5g flour per biscuit, 21.25g rice per biscuit
By taking the amount of flour per biscuit (the largest ingredient) and dividing 2000 by it you get 61 which is the most amount of biscuits he can make with his ingredients.
100 points pls right answers only it’s for apex
An outlier point is added to a set of bivariate data. In what way must your analysis change with the addition of the outlier?
A. The sign of the regression coefficient will change from positive to
negative, or vice versa.
B. The value of the correlation coefficient will move closer to 0.
C. The regression constant will change dramatically.
D. All of the above.
Answer:
I already said b in the comment area so I'm just putting it here now
Step-by-step explanation:
(B) The value of the correlation coefficient will move closer to 0.
Bivariate data:Bivariate data in statistics refers to data on two variables, each of which has a value coupled with a value of the other variable. Normally, it would be interesting to look into any potential relationships between the two variables. The association can be investigated using sample statistics that can be utilized for inference, a tabular or graphical display, or both. The approach taken to look into the association would depend on how the variable was measured. Bivariate correlation or bivariate association are terms used to describe the links, which only involve two variables.Therefore, the correct option is (B) The value of the correlation coefficient will move closer to 0.
Know more about Data here:
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Please help!!!!!! Thank you so much!!!!!
Answer:
104 degrees
Step-by-step explanation:
RS is a line, so it is 180 degrees. PO is also a line and point O is touching line RS. The acute measure is 76 degrees, as shown. To find the other angle measure for SOP, subtract 76 from 180. That gives 104 degrees, which is the measure of SOP.
x+4y=12
Solving the equation for y
I’m to lazy to do this right now anyone can give me an answer
Answer:
$75.50
Step-by-step explanation:
What is -1.4d = 0.7? Solve for d.
Answer:
d= -0.5
Step-by-step explanation:
hope it help :)
Need help asap please
Answer:
A
Step-by-step explanation:
[tex] {16}^{2} = {14}^{2} + {x}^{2} [/tex]
[tex]256 - 196 = {x}^{2} [/tex]
[tex]x = \sqrt{60} = 2 \sqrt{15} [/tex]
Which value for x makes the equation x -4.21 = 6.047 true? A. x = 10.68 C. X = 10.247 B. x = 10.257 D. x = 1.837
Answer:
C. X = 10.247
Step-by-step explanation:
X -4.21 = 6.047
just you will add 4.21 to both sides of the equation
X -4.21 + 4.21 = 6.047 + 4.21
X = 10.247
Answer: the answer is B.
what are the missing numbers?
Answer:
5, 30, and 70
Step-by-step explanation:
Multiply by number of quarters by 5 to get the number of nickels.