In matrix form, the system is
[tex]\begin{bmatrix}1&2&-1\\1&2&1\\-1&-1&2\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}=\begin{bmatrix}-4\\2\\6\end{bmatrix}[/tex]
Solving this "using matrices" is a bit ambiguous but brings to mind two standard methods.
Using inverses:Compute the inverse of the coefficient matrix using the formula
[tex]\mathbf A^{-1}=\dfrac1{\det\mathbf A}\mathbf C^\top[/tex]
where [tex]\mathbf A[/tex] is the coefficient matrix, [tex]\det\mathbf A[/tex] is its determinant, [tex]\mathbf C[/tex] is the cofactor matrix, and [tex]\top[/tex] denotes the matrix transpose.
We compute the determinant by a Laplace expansion along the first column:
[tex]\det\mathbf A=\begin{vmatrix}1&2&-1\\1&2&1\\-1&-1&2\end{vmatrix}[/tex]
[tex]\det\mathbf A=\begin{vmatrix}2&1\\-1&2\end{vmatrix}-\begin{vmatrix}2&-1\\-1&2\end{vmatrix}-\begin{vmatrix}2&-1\\2&1\end{vmatrix}[/tex]
[tex]\det\mathbf A=5-3-4=-2[/tex]
The cofactor matrix is
[tex]\mathbf C=\begin{bmatrix}5&-3&1\\-3&1&-1\\4&-2&0\end{bmatrix}\implies\mathbf C^\top=\begin{bmatrix}5&-3&4\\-3&1&-2\\1&-1&0\end{bmatrix}[/tex]
which makes the inverse
[tex]\mathbf A^{-1}=\begin{bmatrix}-5/2&3/2&-2\\3/2&-1/2&1\\-1/2&1/2&0\end{bmatrix}[/tex]
Finally,
[tex]\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}=\mathbf A^{-1}\begin{bmatrix}-4\\2\\6\end{bmatrix}\implies\boxed{x_1=1,x_2=-1,x_3=3}[/tex]
Gauss-Jordan elimination:Take the augmented matrix
[tex]\begin{bmatrix}1&2&-1&-4\\1&2&1&2\\-1&-1&2&6\end{bmatrix}[/tex]
Subtract row 1 from row 2, and -(row 1) from row 3:
[tex]\begin{bmatrix}1&2&-1&-4\\0&0&2&6\\0&1&1&2\end{bmatrix}[/tex]
Multiply row 2 by 1/2:
[tex]\begin{bmatrix}1&2&-1&-4\\0&0&1&3\\0&1&1&2\end{bmatrix}[/tex]
The second row tells us that
[tex]x_3=3[/tex]
Then in the third row,
[tex]x_2+x_3=2\implies x_2=-1[/tex]
Then in the first row,
[tex]x_1+2x_2-x_3=-4\implies x_1=1[/tex]
Answer:
1
-1
3
Step-by-step explanation:
j did it on edge
the percent of working students increased 21.7% to 8.9%, what was the percent prior to increase
Answer:
Approximately 7.3%.
Step-by-step explanation:
What is percentage increase?
[tex]\displaystyle \text{Percentage Increase} = \frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \times 100\%[/tex].
For this question:
[tex]\text{Percentage Increase} = 21.7\%[/tex],[tex]\text{Final Value} = 8.9\% = 0.089[/tex], and[tex]\text{Initial Value}[/tex] needs to be found.Let [tex]\text{Initial Value} = x[/tex].
[tex]\displaystyle \frac{0.089 - x}{x} = 0.217[/tex].
Assume that [tex]x \ne 0[/tex]. Multiply both sides of the equation by [tex]x[/tex]:
[tex]0.089 - x = 0.217x[/tex].
Add [tex]x[/tex] to both sides of the equation:
[tex]0.089 = (1 + 0.217)x[/tex].
[tex]\displaystyle x = \frac{0.089}{1 + 0.217} = 0.0731 \approx 7.3\%[/tex].
In other words, the initial percentage is approximately 7.3%.
Mark purchased a Playstation on sale at a 40%
discount. The original list price was $350.
What was the amount of the discount?
The legs of a right to
have lengths of 4 and 5 units. Find the length of the hypotenuse
3
3.5
6.4
Answer:
√ 41 (or 6.40 in decimal form)
Step-by-step explanation:
By Pythagorean theorem,
for a right triangle with sides a and b and hypotenuse h, the following formula is true:
a² + b² = h²
or
h = √ (a² + b²).
in this case, it is given that a and b are 4 and 5 units respectively
hence
h = √ (4² + 5²) = √ (16 + 25) = √ 41 = 6.40
Answer: last option.
Step-by-step explanation:
You need to apply the Pythagorean Theorem, which states that:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse of the right triangle and "b" and "c" are the legs of the right triangle.
Knowing that the legs of this right triangle have lengths of 4 units and 5 units, you can solve for the hypotenuse "a".
Then:
[tex]a^2=(4units)^2+(5units)^2\\\\a=\sqrt{(4units)^2+(5units)^2}\\\\a=6.4units[/tex]
strategies that encourage to buy products include ___.
Answer:
Offer lots of information. Consumers look for trustworthy, knowledgeable individuals to educate them on a purchase. .
Step-by-step explanation:
A bag has 2 blue marbles, 3 red marbles, and 5 white marbles. Which events have a probability greater than 5 ? Chec
apply.
choosing 1 blue marble
choosing 1 red marble
choosing 1 red marble, not replacing it, and then choosing a blue marble
choosing 1 white marble, replacing it, and choosing another white marble
choosing 1 white marble
Answer:
the required answer of this question is 1/10
Answers;
A) 135 degree’s
B) 30 Degree’s
C) 180 or 0 Degree’s
D) 90 Degree’s
Answer:
C). 0 degrees
Step-by-step explanation:
The given equation is:
-4 + 6 sinx = -4 + 4 sinx
adding 4 on both sides:
4 - 4 + 6 sinx = 4 - 4 + 4 sinx
6sinx = 4sinx
dividing by 2 on both sides, we get:
6sinx/2 = 4sinx/2
3 sinx = 2 sinx
subtracting 2 sinx from both sides we get:
sin x = 0
x = sin⁻¹ (0)
x = 0 degrees
The polynomial 6x2 + x − 15 has a factor of 2x − 3. What is the other factor?
3x − 5
3x + 5
4x − 5
4x + 5
Answer:
[tex](3x+5)[/tex]
Step-by-step explanation:
The given polynomial expression is:[tex]6x^2+x-15[/tex]
We compare to [tex]ax^2+bx+c[/tex] and have a=6,b=1,c=-15
The product [tex]ac=6\times -15=-90[/tex]
Two factors of -90 that sums to 1 are -9 and 10
We split the middle term to get:
[tex]6x^2+10x-9x-15[/tex]
[tex]2x(3x+5)-3(3x+5)[/tex]
[tex](3x+5)(2x-3)[/tex]
Therefore the other factor is:
[tex](3x+5)[/tex]
Answer: B
Step-by-step explanation:
each equation and the solution is 1 point for each. Round the solution to two decimal places. a. 4x – 5 = 16 b. 35 + 3x – 11 = 23
Answer:
a: 5.25 b: -0.33
Step-by-step explanation:
a:
4x - 5 = 16
isolate the variable. this is done by putting only the variable on the left side and the numbers on the right side. when moving the 5 to the right side, it is counted as a -5 because of the minus in front. when moving it, be sure to change from - to + and vice versa.
4x = 16 + 5
4x = 21
x = 21/4
x = 5.25
b:
same process
35 + 3x - 11 = 23
move the 35 to the right, changing it to a -35
3x - 11 = 23 - 35
move the -11
3x = 23 - 35 + 11
3x = -12 + 11
3x = -1
x = -1/3
x = -0.33
Hope I could help! If you have any trouble, tell me in the comments.
Answer:
a. [tex]x=5.25[/tex]
b. [tex]x=-0.33[/tex]
Step-by-step explanation:
You need to solve for the variable "x" in each equation. Then:
a. You need to add 5 to both sides of the equation:
[tex]4x - 5 +(5)= 16+(5)\\\\4x= 21[/tex]
Now you need to divide both sides of the equation by 4, getting:
[tex]\frac{4x}{4}=\frac{21}{4}\\\\x=5.25[/tex]
b. You need to subtract 35 from both sides of the equation:
[tex]35 + 3x - 11-(35)= 23-(35)\\\\3x-11=-12[/tex]
Add 11 to both sides:
[tex]3x-11+(11)=-12+(11)\\\\3x=-1[/tex]
Now you need to divide both sides of the equation by 3, getting:
[tex]\frac{3x}{3}=\frac{-1}{3}\\\\x=-0.33[/tex]
evaluate the dot product of (2,4) (-1,2)
Answer:
6
Step-by-step explanation:
Given (x1, y1) and (x2, y2) dot product = (x1*x2 + y1*y2)
SO... given (2, 4) and (-1, 2) dot product = (2*-1 + 4*2)
= -2 + 8
= 6
Which is an equation of the line with slope –3 and passes through (2, –1)?
Question 2 options:
a)
3x + y = 5
b)
–3x + y = 5
c)
y = 5x – 3
d)
y = –3(x + 5)
Answer:
a) 3x + y = 5
Step-by-step explanation:
Insert the coordinates into the Point-Slope Formula FIRST, y - y₁ = m(x - x₁), with their CORRECT signs. Remember, in the Point-Slope Formula, all the negative symbols give the OPPOSITE term of what they really are. So, with that being stated, here is how you will set it up: y + 1 = -3(x - 2). After this [Distributive Property], convert to Slope-Intercept Form by moving "-1" to the right side of the equivalence symbol, resulting in y = -3x + 5. Go to your answer choices and see if this is there. No. So then, we try going from Slope-Intercept to Standard by moving "3x" to the left side of the equivalence symbol to end up with 3x + y = 5. This answer choice is found, there you are finished.
use the squared identities to simplify sin^2x cos^2x
Answer:
[tex]\frac{1-cos^2(2x)}{4}[/tex]
Step-by-step explanation:
We have the following expression
[tex]sin^2x *cos^2x[/tex]
Whe know that:
[tex]sin^2(x) = \frac{1-cos(2x)}{2}\\\\cos^2(x)=\frac{1+cos(2x)}{2}[/tex]
Now replace these equations in the main expression and simplify
[tex](\frac{1-cos(2x)}{2})*(\frac{1+cos(2x)}{2})[/tex]
[tex](\frac{(1-cos(2x))(1+cos(2x))}{4})[/tex]
Apply the following property
[tex](a + b) (a-b) = a ^ 2 -b ^ 2[/tex]
Then
[tex](\frac{(1-cos(2x))(1+cos(2x))}{4})=\frac{1^2-cos^2(2x)}{4}[/tex]
Finally:
[tex](\frac{(1-cos(2x))(1+cos(2x))}{4})=\frac{1-cos^2(2x)}{4}[/tex]
Eight friends ate 5/8 of a bag of chips what fraction of the bag did each person eat assuming that they each ate the same amount?
Given: 8 friends ate (5/8)TH fraction of a bag of chips.
And Each one ate the same fraction.
Then; The fraction of chips consumed by one person is (1/8)TH of (5/8)
i.e. =
[tex] \frac{1}{8} ( \frac{5}{8} ) \\ = \frac{5}{64} [/tex]
Hope it helps...
Regards;
Leukonov/Olegion.
Answer:
Option B. [tex]\frac{5}{64}[/tex] of the bag.
Step-by-step explanation:
Eight friends ate [tex]\frac{5}{8}[/tex] of a bag of chips in the same amount.
We have to find the quantity that each person ate the chips.
Each friend ate = [tex]\frac{5}{8}[/tex] ÷ 8
= [tex]\frac{5}{8}[/tex] × [tex]\frac{1}{8}[/tex]
= [tex]\frac{5}{64}[/tex]
Therefore, each friend ate [tex]\frac{5}{64}[/tex] of the bag of chips.
Option B is the answer.
The product of a binomial and trinomial is x^3+3x^2-x+2x^2+6x-2 which expression is equivalent to this product after it has been fully simplified?
Answer: First option.
Step-by-step explanation:
You know that the product obtained by multiplying a binomial and a trinomial is:
[tex]x^3+3x^2-x+2x^2+6x-2[/tex]
Then, in order to simplify this product, it is necessary to add the like terms.
Therefore, the expression that is equivalent to this product after it has been fully simplified is:
[tex]=x^3+(3x^2+2x^2)+(6x-x)-2\\\\=x^3+5x^2+5x-2[/tex]
You can observe that this matches with the first option.
solve for x
-2x+3b>5
Answer:
x < -5 + 3b
Step-by-step explanation:
-x + 3b >5
-x > 5 - 3b ..... flip inequality when multiplying both sides by -1
x < -5 + 3b (Answer)
Answer:
x<-5/2 + 3b/2 ( the fractions are supposed to be 5 over 2 and 3b over 2 btw)
Step-by-step explanation:
pls mark brainiest.
Your parents allow you to borrow a car to get to your part-time job, but you have to pay for a tank of gas each month. Gasoline costs $2.76/gallon and the tank takes 15 gallons. You have 2 coworkers who are each willing to pay for a quarter of a tank each month to carpool with you to work. How much do you save each month? $20.70 $16.46 $18.55 $15.91
By having two coworkers pay for a quarter of the tank each, the student saves $20.70 per month on gasoline.
The question asks us to calculate how much a student would save on gasoline for a month by having two coworkers pay for a quarter of a tank each. With gasoline costing $2.76\/gallon and the tank capacity of 15 gallons, the cost of a full tank is 15 gallons x $2.76\/gallon = $41.40.
Each coworker would pay for a quarter of that amount, which is 0.25 x $41.40 = $10.35. Since there are two coworkers, the total contribution would be 2 x $10.35 = $20.70. Therefore, the student saves $20.70.
A merchant selling sunglasses can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment he sent a total of 124 boxes of sunglasses. If there are more large boxes than smaller boxes, how many cartons did he ship?
64 large boxes and 60 small boxes.
Step-by-step explanation:Here we must use the concept of multiples. A multiple of a number result of the multiplication of that number by an integer. For instance, 2, 4, 6, 8 are multiples of 2. The following chart shows our statement:
[tex]\begin{array}{cccccccccc}Number\,of\,boxes & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\\Large & 8 & 16 & 24 & 32 & 40 & 48 & 56 & 64 & 72\\Small & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 & 90\end{array}[/tex]
So we need to choose the number of small and large boxes such that the sum is 124 boxes of sunglasses and the number of large boxes is greater than the number of small boxes. From the table, the correct solution is:
64 large boxes and 60 small boxes because 64 + 60 = 124 and 64 > 60
Answer:
A merchant selling sunglasses can place 8 large boxes or 10 small boxes into a carton for shipping.
If a total of 124 boxes are shipped, then the large boxes in the cartons must be a multiple of 8 which means either 16,56,64, 72,104.
We will choose that multiple of 8, which when subtracted from 124, gives the number that is divisible by 10.
As the larger boxes are more in quantity, we will choose 64 and 104.
[tex]124-64=60[/tex]
[tex]64/8=8[/tex] cartons
[tex]60/10=6[/tex] cartons
Total cartons are =[tex]8+6=14[/tex]
Also, [tex]124-104=20[/tex]
[tex]104/8=13[/tex] cartons
[tex]20/10=2[/tex] cartons
So, total cartons shipped = [tex]13+2=15[/tex]
So, both can be answers. As any options are not given, you can solve it whatever way you like.
Easy!!!
if f(x)=-9x-9 and g(x)=√x-9, find f(g)(10)
I have 8 other problems and everyone says this is really easy but I don't get it and I'm freaking out
Step-by-step explanation:
f(g(10))
This is called a composite function. It's when you plug one function into another.
First, find g(10):
g(x) = √(x-9)
g(10) = √(10-9)
g(10) = √1
g(10) = 1
Then plug that into f(x):
f(x) = -9x - 9
f(g(10)) = -9 g(10) - 9
f(g(10)) = -9 (1) - 9
f(g(10)) = -9 - 9
f(g(10)) = -18
A rectangular box has length x and width 3. The volume of the box is given by y = 3x(8 – x). The greatest x-intercept of the graph of this polynomial equals which of the following? Choose all that apply.
Answer:
The maximum length (x) of the rectangular box
The minimum volume (y) of the rectangular box
The minimum height (8-x) of the rectangular box
Step-by-step explanation:
we have
[tex]y=3x(8-x)[/tex]
This is the equation of a vertical parabola open downward
The vertex is a maximum
Remember that
The x-intercept is the value of x when the value of y is equal to zero
The x-intercepts of the equation are
(0,0) and (8,0)
therefore
The greatest x-intercept is the point (8,0)
see the attached figure
Remember that x represent the length of the box
therefore
The greatest x-intercept of the graph of this polynomial equals to
The maximum length (x) of the rectangular box
The minimum volume (y) of the rectangular box
The minimum height (8-x) of the rectangular box
A circle is centered at the point (3, 2) and the length of the radius is 5. What is the equation of the circle?
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{3}{ h},\stackrel{2}{ k})\qquad \qquad radius=\stackrel{5}{ r} \\\\\\ (x-3)^2+(y-2)=5^2\implies (x-3)^2+(y-2)=25[/tex]
Answer:
(x-3)² + (y-2)² = 25
Step-by-step explanation:
apeex
If f(x) = 1/9 x-2, what is f^-1 (x)?
Answer:
A
Step-by-step explanation:
let y = f(x) and rearrange making x the subject
Given
y = [tex]\frac{1}{9}[/tex] x - 2
Multiply through by 9
9y = x - 18 ( add 18 to both sides )
x = 9y + 18
Change y back into terms of x, hence
[tex]f^{-1}[/tex] (x) = 9x + 18
Answer:A
Step-by-step explanation:Right on edge
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Name Score
Julia 650
Andrew 550
Jason 380
Cathy 720
Jessica 710
Robert 550
The table gives the scores of 6 students from a class of 25 in a competitive exam. The point estimate of the mean score for the students is
Answer:
The mean point estimate is 593
Step-by-step explanation:
650 + 550 + 380 + 720 + 710 + 550 = 3560
3560/6 = 593.33
Answer:
593.3
Step-by-step explanation: plato family
Find the vertex of the graph of the function.
f(x) = 2x^2 + 8x + 10
Answer:
The vertex is (-2, 2).
Step-by-step explanation:
2x^2 + 8x + 10
Convert to vertex form:
= 2(x^2 + 4x) + 10
= 2 [ (x + 2)^2 - 4] + 10
= 2(x + 2)^2 - 8 + 10
= 2(x + 2)^2 + 2.
Compare this with a(x - b)^2 + c:
b = -2 and c = 2.
The vertex is at
Answer:
2
Step-by-step explanation:
Jake is comparing the prices of two mattress cleaning companies. Company A charges $30 per mattress and an additional $13 as service charges. Company
B charges $28 per mattress and an additional $15 as service charges.
Part A: Write equations to represent Company A's and Company B's total mattress cleaning charges for a certain number of mattresses. Define the variable
used in the equations. (4 points)
Part B: Which company would charge less for cleaning 4 mattresses? Justify your answer. (3 points)
Part C: How much money is saved by using the services of Company B instead of Company A to clean 7 mattresses? (3 points)
Answer:
A) A = 30m + 13 B = 28m + 15
B) Company B would charge $6 less for 4 mattresses
C) Company B would charge $12 less for 7 mattresses
Step-by-step explanation:
A. : Write equations to represent Company A's and Company B's total mattress cleaning charges for a certain number of mattresses. Define the variable used in the equations.
Let's define the variable m to represent the number of mattresses to be cleaned.
For company A, we have a cost per mattress of $30 plus a fixed service fee of $13. So the equation will be:
A = 30m + 13
While company B charges $28 per mattress, with a fixed service fee of $15:
B = 28m + 15
That way, we have a good representation of both price structures, using a meaningful variable.
B. Which company would charge less for cleaning 4 mattresses? Justify your answer.
We just have to calculate the cost of cleaning 4 mattresses at both companies:
A = 30m + 13 = 30 (4) + 13 = 120 + 13 = $133
B = 28m + 15 = 28 (4) + 15 = 112 + 15 = $127
Company B would charge $6 less for 4 mattresses
C. How much money is saved by using the services of Company B instead of Company A to clean 7 mattresses?
Again, all we have to do is calculate the cost to clean 7 mattresses at both companies:
A = 30m + 13 = 30 (7) + 13 = 210 + 13 = $223
B = 28m + 15 = 28 (7) + 15 = 196 + 15 = $211
Company B would charge $12 less for 7 mattresses
At a market Denine buys a bag of 6 mangoes for 15 pesos. What is the unit
price for 1 mango?
Answer:
2.5 pesos/mango
Step-by-step explanation:
You are looking for the price per mango. "Per" means to divide.
Price per mango means to divide the price of all the mangoes by the number of mangoes.
(15 pesos)/(6 mangoes) = (5 pesos)/(2 mangoes) = 2.5 pesos/mango
Anna and her friends ate pizza for lunch. There were 5 pizzas with 12 slices. If Anna and her 12 friends had 4 slices each, how many slices were left over?
Answer:
the answer is 12. hoped this helped
Step-by-step explanation:
first find out what 5* 12 is. 5* 12= 60
then 12* 4. 12* 4=48
finally subtract 60 and 48 witch is 12
Which equation can be used to represent “six added to twice the sum of a number and four is equal to one-half of the difference of three and the number”?
6 + 2(x + 4) = (3 – x)
6 + 2(x + 4) = (x – 3)
(6 + 2)(x + 4) = (3 – x)
(6 + 2)(x + 4) = (x – 3)
Answer:
a. 6 + 2(x + 4) = (3 – x)
Step-by-step explanation: just took the test
Find expressions for the possible dimensions of the rectangular prism.
V=5y3 = 37y2 + 14y
The possible dimensions of the rectangular prism are
(Use a comma to separate answers as needed.)
Answer:
The possible dimensions are y, 5y + 2 and y + 7.
Step-by-step explanation:
V = 5y^3 + 37y^2 + 14 y
y is common to all 3 terms so
V = y(5y^2 + 37y + 14)
V = y (5y + 2)(y + 7)
The expressions for the possible dimensions of the rectangular prism.
[tex]V = 5y^3 + 37y^2 + 14 y[/tex]. The possible dimensions are y, 5y + 2, and y + 7.
How to find the volume of a right rectangular prism?Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units,
then its volume is given as:
[tex]V = a\times b \times c \: \: unit^3[/tex]
The given expressions for the possible dimensions of the rectangular prism.
[tex]V = 5y^3 + 37y^2 + 14 y[/tex]
y is common to all 3 terms
so,
[tex]V = y(5y^2 + 37y + 14)\\V = y (5y + 2)(y + 7)[/tex]
By the comparison of the volume
[tex]V = a\times b \times c \: \: unit^3[/tex]
Therefore, the dimensions are a = y, b = 5y + 2, c = y + 7.
Learn more about the volume of a right rectangular prism here:
https://brainly.com/question/21308574
#SPJ2
prove that the line whose intercepts on the axes of x and y. are respectively -2and3 pass Through the point 2 and 6
Answer:
see explanation
Step-by-step explanation:
Using the intercept form of the equation of a straight line
[tex]\frac{x}{a}[/tex] + [tex]\frac{y}{b}[/tex] = 1
where a is the x- intercept and b the y- intercept
here a = - 2 and b = 3, hence
[tex]\frac{x}{-2}[/tex] + [tex]\frac{y}{3}[/tex] = 1
Multiply through by - 6
3x - 2y = - 6 ← equation in standard form
Substitute x = 2 and y = 6 into the left side of the equation and if equal to the right side then (2, 6) lies on the line
left side = (3 × 2) - 2(6) = 6 - 12 = - 6
Hence line passes through (2, 6)
Solve 4x+2 = 12 for x using the change of base formula log base b of y equals log y over log b.
To solve the equation 4x + 2 = 12, we subtract 2 from both sides and then divide by 4, finding that x = 2.5. The change of base formula mentioned is not needed for solving this equation.
Explanation:The question asks to solve the equation 4x + 2 = 12 for x, but references the change of base formula which is not relevant to solving this linear equation. Instead, we will solve it through simple algebraic manipulation.
First, subtract 2 from both sides of the equation: 4x + 2 - 2 = 12 - 2, which simplifies to 4x = 10.Next, divide both sides by 4 to isolate x: 4x / 4 = 10 / 4, resulting in x = 2.5.Therefore, the solution to the equation 4x + 2 = 12 is x = 2.5.
Triangle ABC is rotated 180 using the Irgun as the center rotation. Which sequence of transformations will produce the same result?
Answer:
Option C is correct.
A reflection over the x-axis and then a reflection over the y-axis
Step-by-step explanation:
From the given figure:
The coordinates of ABC are:
A(-4, -3), B(-5, -2) and C(-3, -2).
and the coordinate of A'B'C' are:
A'(4, 3), B'(5, 2) and C(3, 2)
The rule of reflection over x-axis is given by:
then,
The rule of reflection over y-axis is given by:
Therefore, the triangle ABC is rotated 180 degree using the origin as the center of rotation is: A reflection over the x-axis and then a reflection over the y-axis
Step-by-step explanation:
Please mark brainliest and have a great day!
Answer:
It's C
Step-by-step explanation:
Just took the test