The solution for the given system of equations is x[1] = -1 and x[2] = 2.
What is system of equations?A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.
Given are the following equations as -
5 x[1] + 5 x[2] = 5
2 x[1] + 3 x[2] = 4
Assume that -
x[1] = a
x[2] = b
Then, we can write the equations as -
5a + 5b = 5
2a + 3b = 4
Now -
5a + 5b = 5
5(a + b) = 5
a + b = 1
a = 1 - b
So, we can write -
2a + 3b = 4
as
2(1 - b) + 3b =4
2 - 2b + 3b = 4
b = 4 - 2
b = 2 = x[2]
Then
a = 1 - 2
a = -1 = x[1]
Therefore, the solution for the given system of equations is x[1] = -1 and x[2] = 2.
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Two standard 6-
sided dice are
rolled. How would
you describe the
following events
of having their
sum be EVEN OR
GREATER THAN 9?
The probability of having an even or a number greater than 9 is 2/3.
What is the probability?Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1.
The sample space of two 6-sided dice would be 36
Of this 36, there would be 18 which would have an even sum.
There would be 6 with a sum greater than 9.
The probability of having an even or a number greater than 9 = (18/36) + (6/36) = 24 / 36 = 2/3
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Answer:
5/9
Step-by-step explanation:
You want the probability that a roll of 2 dice will produce a sum that is even or greater than 9.
EvenHalf the numbers on each die are even. Their sum will be even when the dice show ...
even + even . . . . p = (1/2)(1/2) = 1/4
odd + odd . . . . . . p = (1/2)(1/2) = 1/4
So, the 36 possible outcomes will produce an even sum (1/4) +(1/4) = 1/2 of the time. That is, there are 1/2(36) = 18 outcomes with an even sum.
Greater than 9The sums that are greater than 9 are 10, 11, 12. Of these, 10 and 12 are outcomes that are even, so are already counted.
The sum 11 can be made two ways: 6 +5 or 5 +6.
So, "or greater than 9" adds 2 outcomes to the 18 we have already counted.
Final tallyThe final tally of outcomes of interest is ...
18 + 2 = 20 . . . . of 36 possible outcomes
That is ...
P(even or >9) = 20/36 = 5/9
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Find the values of the variables so that the figure is aparallelogram.
Answer:
The image is given below as
From the image above, we can deduce that
[tex]\begin{gathered} \angle GEF=\angle DFE(altenate\text{ angles are equal)} \\ \angle GEF=64^0 \\ \text{hence,} \\ \angle DFE=64^0 \end{gathered}[/tex][tex]\begin{gathered} \angle GEF=\angle BGH(correspond\in g\text{ angles are equal)} \\ \angle GEF=64^0 \\ \text{Hence,} \\ \angle BGH=64^0 \end{gathered}[/tex][tex]\begin{gathered} \angle DFE+\angle HFE=180^0(\text{ linear pair sum up to give 180)} \\ \angle DFE=64^0 \\ \angle HFE=y \\ 64^0+y=180^0 \\ \text{collect similar terms, we will have} \\ y=180^0-64^0 \\ y=116^0 \end{gathered}[/tex]From the image also, we will have that
[tex]\begin{gathered} \angle BGH=\angle FHG(alternate\text{ angles)} \\ \angle BGH=64^0 \\ \angle FHG=x \\ \text{hence,} \\ x=64^0 \end{gathered}[/tex]Hence,
The value of x= 64°
The value of y = 116°
Two-eighths of the movies in Beth's collection are
action movies. Another of the movies are come
What fraction of Beth's movies are either action
movies or comedies?
The answer is ..
Action moviesMental Math Using the slope formula, find the slope of the line through the points (0,0) and (3,6).Use pencil and paper. Explain how you can use mental math to find the slope of the line.
Given the points (0,0) and (3,6)
slope = y2 - y1 / x2 -x1
x1= 0, y1 = 0 , x2= 3, and y2 = 6
slope = 6 - 0 / 3 - 0
slope = 6 / 3
slope = 2
the answer is 2
what are the correct answers for each blank using the dropbox's provided for each blank?Dropbox 1: Congruent, Similar, Not congruent or similarDropbox 2: Proportional, Not proportional, CongruentDropbox 3: Proportional Not proportional, Congruent
The pair of triangles shown are similar because the sides are proportional and corresponding angles are congruent.
If a Ferrari, with an initial velocity of 10 km/h, accelerates at a rate of 50 km/h/min for 3 minutes, what will its final velocity be (in km/h)?
The final velocity of the Ferrari will be 84.53 km/h. with an initial velocity of 10 km/h, accelerates at a rate of 50 km/h/min for 3 minutes.
This is a typical question from Newtonian mechanics. To solve this problem we have to convert all the given data into a standard unit like C.G.S.
Now, we will convert 10 km/h and 50 km/h by using the formula. (km/h × 5/18 = m/s )
10 km/h = 10× 5/18 = 2.78 m/s
50 km/h = 50× 5/18 = 13.89 m/sec/min = 0.23 m/s²
3 min = 3 × 60 = 180 sec. ( 1 min = 60 sec )
Now, we have to use the formula from Newton's law of motion,
v = u + at/2 .
Here, u is the initial velocity which is 2.78 m/s.a is the acceleration which is 0.23 m/s²t is the period which is 180 sec. v is the final velocity.Now we can calculate the final velocity,
v = 2.78 + (0.23 × 180)/2 = 2.78 + 20.7 = 23.48 m/s
Now, we have to calculate the velocity in km/h, which is (23.48 × 5 )/8 = 84.53 km/h. as we know (km/h = m/s ×18/5 ).
Therefore, the final velocity will be 23.48 m/s according to the given inputs and criteria.
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help l need help with this
Answer:
Step-by-step explanation:
Answer: Y = 3x + 3
Simply plug in points on graph calculator.
Answer:
Step-by-step explanation:
I think it might be y=3/1+6 ??? i might be wrong
A random sample of 89 observations produced a mean x = 25.4 and a standard deviation s = 2.4.a. Find a 95% confidence interval for u.b. Find a 90% confidence interval for H.c. Find a 99% confidence interval for u.a. The 95% confidence interval is O.(Use integers or decimals for any numbers in the expression. Round to two decimal places as needed.)
The formula for the confidence interval is;
Where:
[tex]undefined[/tex]Given:
The mean is 25.4, the sample size n is 89, the standard deviation s is 2.4.
a. For the 95% confidence interval, the z-score for a 95% interval is 1.96.
Therefore, the 95% confidence interval is;
[tex]\begin{gathered} CI=25.4-1.96\frac{2.4}{\sqrt[]{89}}<\operatorname{mean}<25.4+1.96\frac{2.4}{\sqrt[]{89}} \\ CI=24.90<\operatorname{mean}<25.90 \end{gathered}[/tex]Answer: (24.90, 25.90)
b. For the 90% confidence interval, the z-score for a 90% interval is 1.645.
Therefore, the 90% confidence interval is;
[tex]\begin{gathered} CI=25.4-1.645\frac{2.4}{\sqrt[]{89}}<\operatorname{mean}<25.4+1.645\frac{2.4}{\sqrt[]{89}} \\ CI=24.98<\operatorname{mean}<25.82 \end{gathered}[/tex]Answer: (24.98, 25.82)
c. For the 99% confidence interval, the z-score for a 99% interval is 2.576.
Therefore, the 99% confidence interval is;
[tex]\begin{gathered} CI=25.4-2.576\frac{2.4}{\sqrt[]{89}}<\operatorname{mean}<25.4+2.576\frac{2.4}{\sqrt[]{89}} \\ CI=24.74<\operatorname{mean}<26.06 \end{gathered}[/tex]Answer: (24.74, 26.06)
Use the Multiplication Property of One to rewrite the statement.8+1=x1) = 0
We need to isolate on the equation
[tex]8+(z\times1)=0[/tex]since any number multiplied by one is the same, then z times 1 is z, so we can write
[tex]8+z=0[/tex]Now, we can add -8 to both side and get
[tex]8-8+z=-8[/tex]since 8 - 8 is zero, we have
[tex]z=-8[/tex]then, z is equal to -8.
2. Multiply the matrices.
Result of matrix multiplication [tex]\left[\begin{array}{ccc} - 1&2&0\\3&2&4\\ - 5& - 1&6\end{array}\right] \times \left[ \begin{array}{cc} 2& - 3 \\ 7& - 1 \\ 1&2 \end{array} \right] = \left[\begin{array}{ccc} 12&1\\ - 4 &1\\ - 11&28\end{array}\right] [/tex].
What is a matrix?A matrix is a series of numbers forming a square or rectangle arranged in rows and columns enclosed in square brackets [ ] or regular brackets ( ).
Solution:
[tex]\left[\begin{array}{ccc} - 1&2&0\\3&2&4\\ - 5& - 1&6\end{array}\right] \times \left[ \begin{array}{cc} 2& - 3 \\ 7& - 1 \\ 1&2 \end{array} \right] [/tex]
[tex] \left[ \begin{array}{cc} - 1 \times 2 + 2 \times 7 + 0 \times 1 & - 1 \times ( - 3) + 2 \times ( - 1) + 0 \times 2 \\3 \times 2 + ( - 2) \times 7 + 4 \times 1&3 \times ( - 3) + ( - 2) \times ( - 1) + 4 \times 2\\ - 5 \times 2 + ( - 1) \times 7 + 6 \times 1&( - 5) \times ( - 3) + ( - 1) \times ( - 1) + 6 \times 2 \end{array}\right ][/tex]
[tex]\left[\begin{array}{ccc} 12&1\\ - 4 &1\\ - 11&28\end{array}\right ][/tex]
Molly has 250 trading cards. She gives n trading cards to her friend Carol. Marcus has 430 trading cards. He gives away three times as many cards as Molly does. How many trading cards did Molly give away if Molly and Marcus have the same number of trading cards left?
Molly gave away 90 trading cards out of 250 trading cards to her friend Carol.
Initially molly had 250 cards.
She gave away n trading cards to her friend.
Now molly has (250 - n) trading cards.
Initially Marcus had 4430 trading cards.
The number of cards that Marcus gave away is is three times of molly.
Cards gave away by Marcus = 3n
Now, Marcus is left out with (430 - 3n) trading cards/
After giving away the cards,
Molly and Marcus had same number of trading cards.
So, we can write,
250-n = 430-3n
Now, we have a linear relation between the number of cards given away and the remaining cards,
Further solving,
2n = 180
n = 90.
So, Molly gave away 90 cards.
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718-119x+719 for x =0
please simplify and find the value
find the perimeter of ABC with vertices A(-4,4), B(4,-1) and C(-4,-1)
Answer: A=-16 B=-5 C=-3
Step-by-step explanation:
write an email as if
you wanted to set up
an interview with
someone
Answer:Dear Mikey,
I saw your progress on how to serve the best food and we wanted to see if you could help us or join our company if you want.
Call 923-456-2483
Sincerely Johns Bagel Company
Step-by-step explanation:
A store generates Monday through Thursday sales of $150, $125, $75, and $180. What sales on Friday would give a weekday average of $150?
Answer:
mi cola es grande
Step-by-step explanation:
uhh
The length of a rectangle is double its width. If the rectangle has a perimeter of 138cm, find its length (in cm).
Answer:
length = 46cm
Step-by-step explanation:
The length of a rectangle is double its width. If the rectangle has a perimeter of 138cm, find its length (in cm).
p = 2l + 2w
when l = 2w, substitute in to equation:
138 = 2(2w) + 2w
138 = 4w + 2w
138 = 6w
divide both sides by 6:
138/6 = 6w/6
so width = 23cm
and we know that length = 2 width so:
length = 23cm × 2
length = 46cm
write the missing power of 10 in the exponential form…….*0.006=0.6
Answer:
10 to the second power
[tex]10^2[/tex]Explanation:
Let the unknown value be x
The given expression can be rewritten as:
[tex]x\times0.006=0.6[/tex]Express as a fraction;
[tex]\begin{gathered} x\times\frac{6}{1000}=\frac{6}{10} \\ \frac{6x}{1000}=\frac{6}{10} \\ \end{gathered}[/tex]Cross multiply
[tex]\begin{gathered} 6x\times10=6\times1000 \\ 60x=6000 \\ x=\frac{6000}{60} \\ x=100 \\ x=10^2 \end{gathered}[/tex]Hence the required unknown number in the exponential power of 10 is 10^2
Given the replacement set: {−9, −10, −11, −12}.
Which value of x correctly solves this equation?
3.2x−5=−40.2
Enter your answer in the box.
Answer:
x = -11
Step-by-step explanation:
You want to know the value of x that correctly solves the equation 3.2x -5 = -40.2.
SolutionThis 2-step linear equation is solved in the usual way:
Step 1: isolate the variable term
3.2x -5 +5 = -40.2 +5 . . . . . . . . . add 5 to both sides
3.2x = -35.2 . . . . . . . . . . . . . simplify
Step 2: isolate the variable
3.2x/3.2 = -35.2/3.2 . . . . . . . . . . divide both sides by the coefficient of x
x = -11 . . . . . . . . . . . . . . . . . . simplify
Which of the following lines best fits the data shown in the scatter plot? 10 9 8 7 6 1 2 3 4 5 6 7 8 9 x Line a A С Line c Line b B. D None of the lines fit the data well
Scatter drawing plot
Emily is a sales representative. She receives 7% commission on all sales. At the end of the year she receives a bonus of 5% of her commission. If Emily's sales for the year total $412,454, calculate: 1) 7% Commission on Sales 2) 5% Bonus on Commission 3) Total Gross Pay for the year 4) Monthly Income
start by calculating the 7% of all the sales
[tex]\begin{gathered} \text{Comission}=(0.07)\cdot412,454 \\ \text{comission}=28,871.78 \end{gathered}[/tex]Calculate the bonus from the comission
[tex]\begin{gathered} \text{Bonus}=(28,871.78)\cdot(0.05) \\ \text{Bonus}=1,443.59 \end{gathered}[/tex]The total gross pay will be the addition between the comission and bonus
[tex]\begin{gathered} G.\text{ Income=28,871.78+1,443.59} \\ G\text{. income=30,315.37} \end{gathered}[/tex]The monthly income will be the division between 12 months of the year
[tex]\begin{gathered} \text{Monthly income} \\ \frac{30,315.37}{12}=2526.28 \end{gathered}[/tex]There are 6 roses in a vase of 14 flowers. The rest are daisies. What is the ratio of all flowers in the vase to daisies?
Given:
There are 6 roses in a vase of 14 flowers.
Required:
To find the ratio of all flowers in the vase to daisies.
Explanation:
The total number of daisies in the vase are
[tex]\begin{gathered} =14-6 \\ =8 \end{gathered}[/tex]So the ratio of all flowers in the vase to daisies is,
[tex]14:8[/tex][tex]7:4[/tex]Final Answer:
[tex]7:4[/tex]order the following number from smallest to largest. 25, 10, -15, 0, -5
Answer:
-15, -5, 0, 10, 25
Step-by-step explanation:
Answer:-
15, -5, 0, 10, 25
Least -> greatest
Step-by-step explanation:
ANSWERS ASAPP
i got a 57 in this class
Answer:
Y=-1/4x+-6
Step-by-step explanation:
convert the line to slope intercept form
x is the slope and the last thing is the y intercept
Name The Transformations Y=(x+3)^2-5
Answer: move three units to the left, and 5 units down would be the answer to it
Step-by-step explanation: hope i helped
The lines shown below are parallel. If the green line has a slope of 5, what isthe slope of the red line?.O A.OB. 55O C.C. -//OD. -5(1)→
The slope of the red line is 5. The correct answer is option B. 5
Two parallel lines, always have the same slope. Since the green and red line are parallels and the green line has slope 5, the slope of the red line is also 5.
A car was valued at $41,000 in the year 1994. The value depreciated to $13,000 by the year 2004
Firstly, we have to write the general depreciation fomula as follows;
[tex]V(t)=I(1-r)^t[/tex]where V(t) represents the value of the commodity after a certain t years
I is the initial value of the item
r is the annual percentage change (rate of depreciation)
t is the number of years
a) Here, we want to calculate the annual rate of change
According to the data given in the question;
V(t) = $13,000
I = $41,000
r = ?
t = 2004-1994 = 10 years
Now, we proceed to substitute these values, to find the find of r as follows;
[tex]\begin{gathered} 13,000=41,000(1-r)^{10} \\ (1-r)^{10\text{ }}\text{ = }\frac{13,000}{41,000} \\ (1-r)^{10\text{ }}=\text{ }\frac{13}{41} \\ \\ (1-r)\text{ = }\sqrt[10]{\frac{13}{41}} \\ \\ 1-r\text{ = 0.8915} \\ r\text{ = 1-0.8915} \\ r\text{ = 0.1085} \end{gathered}[/tex]b) To write r in percentage form, we have to multiply the answer in 'a' above by 100
We have this as ;
[tex]0.1085\times100\text{ = 10.85 \%}[/tex]c) Here, we want to get the car value by year 2009
In that instance;
V(t) = ?
I = $41,000
r = 0.1085
t = 2009-1994 = 15
Substituting these values, we have;
[tex]\begin{gathered} V(15)=41,000(1-0.1085)^{15} \\ V(15)\text{ = \$7,321.56} \end{gathered}[/tex]To the nearest 50 dollars, this is $7,300
Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the equation.
(-2, 3); y=-3/4x+4
Answer:
y=4/3x+17/3
Step-by-step explanation:
Perpendicular lines have reciprocal negative slopes, find the slope of the new line:
-3/4 --> m = 4/3
Write line in point slope form:
y-3 = 4/3(x+2)
Distribute:
y-3=4/3x+8/3
Simplify:
y=4/3x+17/3
Gabe has just moved to a new town and wants to share plates of baked goods with his neighbors. He has 16 cookies and 24 brownies to share, and wants to split them equally among the plates with no food left over. What is the greatest number of plates he can make to share?
The greatest number of plates he can make to share is 6.
What is the greatest number of plates he can make to share?From the information, Gabe has just moved to a new town and wants to share plates of baked goods with his neighbors and he has 16 cookies and 24 brownies to share.
It should be noted that this illustrates that we have to find the highest common factor for 16 and 24.
This will be:
18 = 2, 3, 6, 9 and 18.
24 = 2, 3, 4, 6, 8, 12 and 24
The highest common factor is 6.
Therefore, the number will be 6 plates.
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7 is added to 11 divided by a number r write the algebraic expression
Answer: 7+(11/r)
Step-by-step explanation:
I'll give brainliest!
Answer:
The answer is A