Solve the following system of equation using inverse matrix method.
5x + 2y=4
7x + 3y=5
[tex]5x+2y = 4~~~~~~~~~~...(i)\\\\7x +3y = 5~~~~~~~~~~...(ii)\\\\\text{Write in AX = B form.}\\\\~~~~~~\begin{bmatrix}5&2\\7&3 \end{bmatrix} \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\\\\\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\begin{bmatrix}5&2\\7&3 \end{bmatrix}^{-1}\\\\\\[/tex]
[tex]\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\cdot\dfrac{\begin{bmatrix} 3&-7\\-2&5\end{bmatrix}^{T}}{\begin{vmatrix}5&2\\ 7&3 \end{vmatrix}}\\\\\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\cdot\dfrac{\begin{bmatrix} 3&-2\\-7&5\end{bmatrix}}{5(3) -2(7)}\\\\\\[/tex]
[tex]\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\cdot\begin{bmatrix} 3&-2\\-7&5\end{bmatrix}\\\\\\ \implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix}12-10\\-28+25 \end{bmatrix}\\\\\\ \implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix}2\\-3\end{bmatrix}\\\\\\\text{Hence,}~ (x,y) = (2,-3)[/tex]
. Which volume-to-surface-area ratio would be better for an ice cube— the lowest possible or the highest possible? Use the table to help you try different shapes and sizes to make your selection (You can show your work on a separate piece of paper.):
The volume-to-surface-area ratio would be better for an ice cube is the highest possible one.
How to explain the volume?When you put ice into your drink, the goal is to have the ice chill your drink. This takes time. Therefore, you would want the ice to slowly melt and cool the drink for as long as you can.
You would want to have the highest possible volume to surface area ratio in an ice cube. If your ice cube is mostly surface area with less volume, it will melt quickly and water down your drink. If your ice cube has a higher ratio of volume to the surface area, it will stay solid longer and chill your drink longer.
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Tim needs 18 pens. He can buy them in packages containing 6,9, or 12 pens each. He will buy only one type of package. Which packages could Tim buy? Write two different ways of how Tim can buy exactly 18 pens. (Goodluck)
Answer:
9 and 6
Step-by-step explanation:
You see, 9x2=18 and 6x3=18
The formula for the nth term of an arithmetic sequence can be found using the formula a Subscript n Baseline = a Subscript 1 Baseline + (n minus 1) d. Which of the following is equivalent to this equation?
The equation of nth term will be written as for n as will be ([tex]\rm a_n[/tex] - a₁ + d) / d. Then the correct option is D.
The missing options are attached to the picture given below.
What is a sequence?A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.
The formula for the nth term of an arithmetic sequence can be found using the formula given below.
[tex]\rm a_n = a_1 + (n-1)d[/tex]
Then arrange the equation for n, we have
[tex]\begin{aligned} \rm a_n - a_1 & \rm = nd - d\\\\\rm a_n - a_1 + d & \rm =nd\\\\\rm n & \rm = \dfrac{a_n - a_1 + d}{d} \end{aligned}[/tex]
Then the correct option is D.
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Answer: The answer is D
Step-by-step explanation:
took the test
3 x 10³ - 7000
(8 × (-5)) + (4² + 22)
please help!
solve as simplest answer!
Answer:
283038 or 2.83038×10⁵
Step-by-step explanation:
3×10³-7000(-40)+(16+22)3×10³+280000+383×1000+2800383000+28003828303850. a skateboard shop stocks 10 types of board decks, 3 types of trucks, and 4 types of wheels. how many different skateboards can be constructed?
Which number in the monomial 125x18y3z25 needs to be changed to make it a perfect cube? 3 18 25 125
Answer: 25
Reason:
The exponent 25 is not a multiple of 3. If it was something like 24, then we would have a perfect cube as shown below
[tex]w = 125x^{18}y^3z^{24}\\\\w = 5^{1*3}x^{6*3}y^{1*3}z^{8*3}\\\\w=(5^1x^6y^1z^8)^3\\\\w = (5x^{6}yz^{8})^3\\\\[/tex]
When going from step 2 to step 3, I used the rule that [tex](abcd)^e = a^eb^ec^ed^e[/tex]. Basically the exponent e gets applied to each factor inside.
Answer:
25
Step-by-step explanation:
Evaluate each function at the given value using the remainder theorem.
F(x)=x^4+5x^3-18x+1 at x=-4
Please show work , I give brainliest. :)
Answer:
9
Step-by-step explanation:
[tex]f(x) = x^4 +5x^3 -18x +1\\\\f(-4) = (-4)^4 +5(-4)^3 -18(-4) +1\\\\~~~~~~~~~=256+5(-64)+72+1\\\\~~~~~~~~~=329-320\\\\~~~~~~~~~=9[/tex]
What are the exact values of x and y?
x =
y =
Answer:
[tex]x = 2\\y = 2\sqrt{3}[/tex]
Step-by-step explanation:
**Look at the picture
Anyone know the answer
Step-by-step explanation:
-2g(1+g)
-2g - 2g²
(-2)g - (2)g²
PRECISION In November 2010 the average cost of 5 gallons of regular unleaded gasoline in the United States was $14.46. What was the average cost for 16 gallons of gasoline?
Answer:
$46.272
Step-by-step explanation:
Jane had a salad In her refrigerator she ate 2/8 of it for lunch and 3/8 of it dinner and what fraction of the salad is left
Answer:
3/8
Step-by-step explanation:
2 + 3=5, (8/8)-( 5/8) =3/8
Answer:
3/8
Step-by-step explanation:
What is the equivalent to 1 tablespoon?
Answer:
3 teaspoons
Step-by-step explanation:
Three teaspoons are equivalent to one tablespoon
if 6 men. 8 women and 16 boys together can do a piece of work in 288 days by working 6 hours each day in how many days can 12 men, 18 women and 28 boys complete the same & work by working 8 hours each day? The work efficiency of men, women and boys proportion 3:2:1 respectively?
Answer:
144 days
Step-by-step explanation:
Let's put the efficiency in terms of b
m = 3b w = 2b b=b
starting with 6 m = 18 b
8w = 16 b
16b = 16 b total 50 b
then increase 12m = 36b
18w = 36b
28b = 28 b total = 100 b
You doubled 'b' workers so work time will be halved to 144 days
184 is 130% more than what number?
Answer:
80
Step-by-step explanation:
The wording "130% more" suggests that we have the result of adding 130% of the original number to the original number.* This can be expressed as an equation to be solved for the original number.
__
Let x represent the original number. The given relation is ...
184 = x + 130% × x
184 = 2.30x . . . . . . . . . collect terms (130% = 1.3)
80 = x . . . . . . . divide by 2.3
184 is 130% more than 80.
_____
* One needs to be a little careful here. You will often see the wording ...
"<some number> times more".
Usually the intention there is that the result is <some number> times the original amount. That is, percentages are often treated differently from other number expressions in problems like this.
A light bulb consumes 1440 watt-hours per day. How long does it take to consume 6480 watt-hours?
The number of days it will take to consume the given power = 4.5 days
Calculation of energy consumptionThe amount of power consumed per day = 1440watt-hours
Therefore X days = 6480 watt-hours?
Make X the subject formula;
X = 1 × 6480/1440
X = 4.5 days
Therefore, The number of days it will take to consume the given power = 4.5 days.
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Please help me, I really appreciate it! Thanks!
Answer: See the attached images below.
The steps and explanations are on those screenshots, so there's not much for me to mention right here on this main page. The decimal results are approximate to 6 decimal places. Make sure your calculator is in degree mode.
What is a factor of X2–9 X +14
The factors of the expression x^2 - 9x + 14 are (x - 7) and (x - 2)
How to factor the expression?The expression is given as:
x^2 - 9x + 14
Expand
x^2 - 2x - 7x + 14
Factorize the expression
x(x - 2) - 7(x - 2)
Factor out x - 2 from the expression
(x - 7)(x - 2)'
Hence, the factorized expression of x^2 - 9x + 14 is (x - 7)(x - 2)'
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Triangle JKL is transformed to create triangle J'K'L'. The angles in both triangles are shown.
AngleJ = 90° AngleJ' = 90°
AngleK = 65° AngleK' = 65°
AngleL = 25° AngleL' = 25°
Which statement is true about this transformation?
The correct statement is AngleL = 25° AngleL' = 25°.
We have given that,
Triangle JKL is transformed to create triangle J'K'L'.
We have to choose the correct option.
What is the information about the transformed triangle?
The following information should be considered:
In a rigid transformation, the image & pre-image are congruent.
Reflection, translation, and rotation are rigid transformations.
In a non-rigid transformation, the image and pre-image are similar.
Dilation is a non rigid transformation.
In a rigid or nonrigid transformation, the corresponding angles are the same.
If the corresponding sides are the same, then it is a rigid transformation.
If the corresponding sides are proportional, then it is a nonrigid transformation.
It can be a rigid or a nonrigid transformation based on whether the corresponding side lengths have the same measures.
Therefore option 3 is correct.
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Devaughn earns $7.25 per hour working as a waiter at TGI Fridays. He typically pays a total of $89.76 towards deduction. If he works 37 hours, what will Devaughn net?
Hello, the answer should be $178.49.
If Devaughn earns $7.25 an hour at his job, we need to find out how much money he will make if he works for 37 hours.
[tex]37.(7.25)=268.25[/tex]
Next, we need to subtract the deduction amount from the total amount.
Net Equation will be defined as;
[tex]N=T-D[/tex]
[tex]N=(268.25)-(89.76)=178.49[/tex]
Good luck! If you have any questions, then feel free to ask in comments!
i need help with these two questions ASAP and preferably shown work.. Thank you!
Answer:
1: sin B, cos B, and tan B = 36.87°
2: x = 11.7
Step-by-step explanation:
Question 1: As toy can see they all have the same angle answer just different methods of finding it
Question 2:
adjacent is the closest side to the angle
opposite is the side across from the angle
hypotenuse is always the longest side
x = 11.7025
Hope it helps :)
If you have any questions or anymore help lmk, happy to help with any school work!!
Have a nice day, you’ll make it thru <3
DONT BE AFRAID TO ASK IF YOU CANT READ MY HANDWRITTING
Help me please this is due today :((
Show all work for it pleaseee
Answer:
Length C, B= 90 mi
Step-by-step explanation:
The small square in the corner in any shape always represent 90°
Hope it helps!!
Subtract − 3 x 2 + 4 x + 10 −3x 2 +4x+10 from 2 x 2 − 2 x 2x 2 −2x.
Answer:
10+12x
Step-by-step explanation:
1. simplify both sides using PEMDAS.
(2 x 2) − ((2 x 2x) 2) −2x
4-8x-2x
4-10x
− (3 x 2) + 4x + 10 −(3x 2) +4x+10
-6+4x-6x+4x+20
2x+14
2. (2x+14)-(4-10x)= 10+12x
sorry if its rong it was kinda confusing finfing if it was an x or multiplecation.
If Randy sells 8 times as many vacuum cleaners as Janice, and Janice sells 690 vacuum cleaners per year, on average, how many does Randy sell each month
Randy sells, in average, 460 vacuum cleaners per month.
How many vacuum cleaners does Randy sell each month?.
First, we know that Janice sells 690 units per year.
There are 12 months in a year, so the amount that she sells, in average, per month is:
J = 690/12 = 57.5
This means that Janice sells, in average, 57.5 units per month. And Randy sells 8 times as many, then we can solve the product:
R = 8*57.5 = 460
This means that Randy sells 460 units per month.
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The probability distribution for a
random variable x is given in the table.
X
-10 -5 0
5
10 15 20
Probability ,20 15.05 .1
25 .1 .15
Find the probability that -5 ≤x≤5
The correct answer is 0.3
Given as:X : -10 -5 0 5 10 15 20
P(X)=f(x): 0.20 0.15 0.05 0.1 0.25 0.1 0.15
To find:probability of -5≤x≤5
Solution: ∑f(x)= f(-5)+f(0)+f(5)⇒ P(-5≤x≤5) = 0.15 +0.05+0.1 = 0.3
Hence, the answer of the given question is 0.3.
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Answer: 130 degrees
Step-by-step explanation:
If we are assuming this is an isosceles trapezoid, then this means angles B and C are congruent.
x^k=1/x^-1
Someone help me please
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^k~~ = ~~\cfrac{1}{x^{-1}}\implies x^k~~ = ~~x^1\implies k=1[/tex]
What is the (LCD) of 3/5 and 5/6
Answer: 30
Step-by-step explanation:
A LCD, or least common denominator, is the lowest common multiple of both denominators.
Multiples of 5: 0, 5, 10, 15, 20, 25, 30, 35, 40, ...
Multiples of 6: 0, 6, 12, 18, 24, 30, 36, 42, 48, ...
We can see the LCD of 3/5 and 5/6 is:
30
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The first step that we should take before attempting to solve any problem is to understand what the problem statement is asking for us to do and what is given to us to help us achieve that goal. In this case, the problem is asking us to determine the LCD or least common denominator of two numbers. We are provided with two fractions that we will use to help determine our solution. However, before solving for the LCD let us first define what LCD means.
Least Common Denominator ⇒ LCD is a term that is used to help describe a number that can be used in the bottom of the fraction (also known as a denominator) that is common between two numbers. For example, the LCD between 2 and 5 is 10 because that is a time where both of them can be equal to.Looking at our problem we can see that the denominators that are given to us is 5 and 6 so let us determine the multiples of them until we have a duplicate.
Multiples of 5 ⇒ 5, 10, 15, 20, 25, 30Multiples of 6 ⇒ 6, 12, 18, 24, 30Now that we have determine the multiples of 5 and 6 we were able to see that the lowest duplicate that we have is at 30 which means that 30 is our LCD.
Which system has no solutions? x < 3 x < 1 x > 3 x > 1 x < 3 x > 1 x > 3 x < 1
The system of inequalities with no solution is x > 3 x < 1
How to determine the system with no solutions?The systems of inequalities are given as:
x < 3 x < 1
x > 3 x > 1
x < 3 x > 1
x > 3 x < 1
As a general rule, it is impossible for a variable to be greater than a higher number and less than a smaller number.
This means that if x is greater than 3, then it must be greater than 1
Hence, the system of inequalities with no solution is x > 3 x < 1
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←
How many solutions does this linear system have
y =
x+2
6x - 4y = -10
Answer:
This linear system has one solution.
Step-by-step explanation:
First equation: y = x + 2
Second equation: 6x - 4y = -10
Let's change the second equation in slope-intercept form y = mx + b.
Slope-intercept form
y = mx + b
m ... slope
b ... y-intercept
[tex]6x - 4y = -10[/tex]
[tex]6x + 10 = 4y[/tex]
[tex]\frac{6}{4}x + \frac{10}{4} = y[/tex]
[tex]\frac{3}{2}x + \frac{5}{2} = y[/tex]
If two lines have the same slope but different y-intercept, they are parallel - system has no solutions.
If two lines have the same slope and the same y-intercept, they are the same line and are intersecting in infinite many points - system has infinite many solutions.
If two lines have different slopes then they intersect in one point - system has one solution.
We see that lines have different slopes. First line has slope 1 and the other line has slope [tex]\frac{3}{2}[/tex]. So the system has one solution.
You can also check this by solving the system.
Substitute y in second equation with y from first.
6x - 4y = -10
6x - 4(x + 2) = -10
Solve for x.
6x - 4x - 8 = -10
2x = -2
x = -1
y = x + 2
y = -1 + 2
y = 1
The lines intersect in point (-1, 1). <-- one solution