The answers to all parts shown below.
What is Matrix?A set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix.
Given:
a) The system of linear equations
3A + 2B + 6C = 71, 000
3A + 2B +4C = 81, 000
5A + 7B + 0C= 92, 000
B) The equation for the system of linear equations
Y = [tex]\left[\begin{array}{ccc}3&2&6\\3&2&4\\5&7&0\end{array}\right][/tex] , Z = [tex]\left[\begin{array}{ccc}71000\\81000\\92000\end{array}\right][/tex]
So, YX = Z
X = Z[tex]Y^{-1[/tex]
C) The inverse matrix method
14/11 21/11 -2/11
= 1/22 10/11 -15/11 3/11
1/2 -1/2 0
= 7/ 121 21/ 242 -1/121
5/121 -15/242 3/242
1/44 -1/44 0
and, X = Z[tex]Y^{-1[/tex]
X = [tex]\left[\begin{array}{ccc}71000\\81000\\92000\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}7/ 121 &21/ 242& -1/121\\ 5/121&-15/242&3/242\\1/44&-1/44&0\end{array}\right] \\[/tex]
A= 10,376.03
B = 946.28
C= 227.72
d) The production for A = RM 7,263.221
The production for B = RM 473.14
The production for C = RM 204.948
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8/10 of 3/9 is what?
From IXL
Answer:
7/15
Step-by-step explanation:
Work out 1 1 2 + 2 3 7 Give your answer as a mixed number where appropriate.
Solution of 1 1/2 + 2 3/7 is 3 13/14
What is mixed number?A mixed number is formed by combining three parts: a whole number, a numerator, and a denominator. The numerator and denominator are part of the proper fraction that makes the mixed number.
Given expression,
1 1/2 + 2 3/7
it can be written as
= 3/2 + 17/7
= (21 + 34)/14
= 55/14
= 3 13/14
Hence, 3 13/14 is the solution of 1 1/2 + 2 3/7
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Which of these numbers is NOT divisible by 3?
300
321
241
8.910
Answer: 241
300 / 3 = 100
321 / 3 = 107
241 / 3 = 80.333
8.910 / 3 = 2.97
If the terminal side of angle A goes through the point (−24/25,7/25) on the unit circle, then what is sin(A)?
The value of sin A is, 7/25.
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
The terminal side of angle A goes through the point (−24/25,7/25) on the unit circle.
Now, By definition we get;
⇒ cos A = - 24/25
⇒ Sin A = 7/25
Thus, The value of sin A is, 7/25.
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what is the correlation between the amount of rain (mm) in the summer and the amount of water (m2) used for watering the lawn
The correlation between the amount of rain (mm) in the summer and the amount of water (m2) used for watering the lawn is directly proportion to each other
The classification of rainBased on the grain size, the classification of rain is divided into four, namely:
Drizzle is a small amount of rain precipitation that can even be called light, which generally has a diameter of less than 0.5 mm. Drizzle is caused by small stratus clouds and stratocumulus clouds. Snowfall or snow is rain from small crystals of water that turn into ice and have temperatures below freezing. Hail hailstones are ice cubes that fall from clouds that have temperatures below 0° degrees Celsius which occur in hot weather Heavy rain is an outpouring of water that has grains of approximately 7 millimeters and comes from clouds that have temperatures above 0°.Learn more about amount of rain at https://brainly.com/question/30487357
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A rectangular garden has a walkway around it. The area of the garden is 6(4.5x + 2.5). The combined area of the garden
and the walkway is 6.5(6x + 6). Find the area of the walkway around the garden as the sum of two terms.
Answer:
2w^2.
Step-by-step explanation:
Let "w" be the width of the walkway. Then, the length of the garden is 6.5(6x + 6) - 2w and the width of the garden is 6.5(6x + 6) - 2w.
The area of the garden is 6(4.5x + 2.5) = 6 * 4.5 * x + 6 * 2.5 = 27x + 15
The area of the garden and walkway is (6.5(6x + 6) - 2w)^2 = 27x + 15 + 2w^2
Equating the two expressions for the area of the garden:
27x + 15 = 27x + 15 + 2w^2
Thus, the area of the walkway is:
Julie purchased a bottle of vegetable oil for $4.58. The cashier gave Julie $2.82 in change. How much money did Julie give the cashier?
Answer:
7.40
Step-by-step explanation:
4.58+2.82 = 7.40
6x6 foot area. Use this value to estimate the size of a crowd that is 5 feet deep on both sides of the street along a 3-mile section of a parade route.
22000
44000
4800
8400
The size of the crowd that is 5 feet deep on both sides of the street along a 3-mile section of a parade route is 44000 people.
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given that, the size of a crowd that is 5 feet deep on both sides of the street along a 3-mile section of a parade route,
The number of people that can fit comfortably in a 6 feet by 6 feet area = 10
The ratio of the number of people per unit area = 10/(6 × 6) = 10/36
The area, A, occupied by the crowd = 5 feet × 3 mile × 2
3 miles = 15840 feet
∴ A = 5 feet × 15840 feet × 2 = 158400 ft²
We then have;
Number of people / 158400 = 10/36
Number of people = 44000
Hence, the size of the crowd that is 5 feet deep on both sides of the street along a 3-mile section of a parade route is 44000 people.
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Han wants to buy a $30 ticket to a game, but the pre-order tickets are sold out. He knows there will be more tickets sold of the day of the game, with a markup of 200%. How much should Han expect to pay for the ticket if he buys it the days of the game?
Han should expect to pay $90 for the ticket if he buys it the day of the game.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Han should expect to pay $90 for the ticket if he buys it the day of the game
The current ticket fee = $30
The markup = 200%
The markup = 200% of the current price
Markup = 200/100 ×30
= $60
The ticket fee on the game day = The current fee + The markup
The ticket fee on the game day = $30 + $60
The ticket fee on the game day = $90
Hence, Han should expect to pay $90 for the ticket if he buys it the day of the game.
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Mike bought several packs of lacrosse trading cards to add to his collection
to pay for his cards packs , he paid with 1 quarter, 2 dimes 4 nickels and 4 pennies
What was the cost of the packs of cards that mike bought ?
The cost of the packs of cards that Mike bought can be calculated by adding up the value of the coins he used to pay for them.
1 quarter is worth 25 cents.
2 dimes are worth 2 * 10 cents = 20 cents.
4 nickels are worth 4 * 5 cents = 20 cents.
4 pennies are worth 4 cents.
So, the total value of the coins that Mike used to pay for the packs of cards is 25 + 20 + 20 + 4 = 69 cents.
Therefore, the cost of the packs of cards that Mike bought was 69 cents.
Select the correct answer.
Where does the graph of y= sin x from x = 0 to x = 277 start?
OA.
OB.
O C.
O D.
at its minimum
at an x-intercept
at its maximum
between an x-intercept and its maximum
Answer:
At an x-intercept
Step-by-step explanation:
y = sin x
y = sin 0
y = 0
(0,0) is an x-intercept but not it's maximum or minimum.
Reid found 6 coins that totaled 61c in all. What coins did the find?
Answer:
1 quarter, 3 dimes, 1 nickel, 1 penny
Step-by-step explanation:
25c + 10c+10c+10c+5c+1c =61c
3. Determine the cost to lay down pebbel in the seating area one bag of pebbels covers 5 ft² and costs $8.99
The total amount to lay down the pebbles in the seating area would be - ${(A/5) x 8.99}.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that one bag of pebbles covers 5 ft² and costs $8.99.
Assume that the area of the seating place is A ft². Now -
1 bag will cover - 5 ft²
1 ft² will be covered in (1/5) bags
A ft² will be covered in (A/5) bags
The total cost of laying the pebbles -
(A/5) x 8.99
Therefore, the total amount to lay down the pebbles in the seating area would be - ${(A/5) x 8.99}.
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♦️ANSWER NEEDED QUICK, SHOW YOUR WORK♦️
Savvas Realize
Jamilas mom wants to make a size 10 dress and jacket. About how much yards of fabric does she need?
Answer:
[tex]2\frac{7}{8}[/tex]
Step-by-step explanation:
size 10 dress requires 2 1/4 yards of fabric while a jacket requires 1 5/8 yards so we add them
2 1/4+1 5/8
we make similar fractions and turn the denominator to 8
2 2/8+ 1 5/8
and now we can add the whole numbers first
2+1=3
now the fractions
2/8+5/8
7/8
final answer is 2 7/8
hopes this helps
Choose the justification for each step in the solution to the given equation.
- division property of equality
- simplification
- multiplication property of equality
-Addition property of equality
-Subtraction property of equality
The properties are used to manipulate equations in order to isolate a variable, find a solution, or simplify the equation
What are the properties of equality?
The "division property of equality" states that if you divide both sides of an equation by the same non-zero number, the two sides will remain equal.
The "simplification" step is used to simplify an expression by combining like terms, reducing fractions, or performing other operations to simplify the expression.
The "multiplication property of equality" states that if you multiply both sides of an equation by the same non-zero number, the two sides will remain equal.
The "addition property of equality" states that if you add the same number to both sides of an equation, the two sides will remain equal.
The "subtraction property of equality" states that if you subtract the same number from both sides of an equation, the two sides will remain equal.
These properties are used to manipulate equations in order to isolate a variable, find a solution, or simplify the equation.
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Write a story problem that can be solved using 1 3/4 / 1/2. Drraw a picture to match your story and Illustrate the answer.
Answer: A baker needs to make a dessert for a party. The recipe calls for 1 3/4 cups of sugar, but the baker only has 1/2 cup measuring cups. How many measuring cups does the baker need to measure out the sugar for the recipe?
We can start by converting the mixed number 1 3/4 into an improper fraction: 1 3/4 = 7/4. Then, we can divide 7/4 by 1/2:
7/4 ÷ 1/2 = 7/4 * 2/1 = 14/4 = 3 1/4
The baker needs 3 1/4 measuring cups to measure out the sugar for the recipe.
[Image: Three and a quarter measuring cups filled with sugar]
Step-by-step explanation:
what is the value of the expression hurry please!
Answer:
50
Step-by-step explanation:
An antique vase costs $2000, and its price increases by 4.5% each year.
y = ____
The price of vase next year is $2090.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
We need to Write the percent as a fraction in simplest form
16.24%
So, we can rewrite it as;
16.24 / 100
16 and 24/100 or 16 6/25
So the percent as a fraction is 16 6/25
Given;
An antique vase costs $2000
Its price increases by 4.5%
Now,
Let the 4.5% of price be x
x*100/2000=4.5
x=20*4.5
x=90
Therefore, the price next year by 4.5 percent increase will be $2090.
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Answer:
Step-by-step explanation:
it equals 90
PLS HELP ME SOLVE THIS
Answer:
Below
Step-by-step explanation:
According to the triangle bisector theorem
x/18 = 45/20
x = 40.5 units
Math on the Spot An arcade deducts 3.5 points from
a 50-point game card for each game played. The linear
equation y= -3.5x + 50 represents the number of
points y on a card after x games played. Graph the
equation using the slope and y-intercept.
For the linear equation y = -3.5x + 50 the graph is plotted with points (0,50) and (14.28,0).
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The linear equation is y = -3.5x + 50.
An arcade deducts 3.5 points from a 50-point game card for each game played.
The graph will represent the x axis as number of games played.
The graph will represent the y axis as points earned.
Substitute the value x = 0 in the equation -
y = -3.5(0) + 50
y = 50
The coordinate point is (0,50).
Substitute the value y = 0 in the equation -
0 = -3.5x + 50
-50 = -3.5x
x = 14.28
The coordinate point is (14.28,0).
Plot both the coordinate points and join the line.
Therefore, the graph is plotted for the linear equation.
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51) On a map, 1.00 cm represents 2.00 km. If a bike trail is 7.40km, what would be the length of the trail on the map?
The length of the trail on the map would be 3.7 cm when a bike trail is 7.40km.
What is a scale image?Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions on the actual figure or object
On a map, 1.00 cm represents 2.00 km.
Let the required length of the trail on the map would be x cm, when a bike trail is 7.40km
As per the information, we can write the ratio would be as:
1.00 cm : 2.00 km = x cm : 7.40km
1/2 = x/7.40
Apply cross-multiplication operation, and we get
x = 7.40/2
x = 3.7
Thus, the required length of the trail on the map would be 3.7 cm.
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Seth owns a printing shop that makes customized T-shirts. The cost to make T-shirts is proportional to the number of T-shirts he makes. Seth graphs a line that shows the cost per customized T-shirt. Two points on the line are (2, 8) and (4, 16). What does the slope of the line mean in this situation?
Group of answer choices
a. The cost is $4 per T-shirt.
b. The cost is $2 per T-shirt.
c. The cost is $0.25 per T-shirt.
d. The cost is $8 per T-shirt.
the slope of the line means in this situation "a. The cost is $4 per T-shirt".
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, Seth owns a printing shop that makes customized T-shirts.
Since The cost to make T-shirts is proportional to the number of T-shirts he makes.
Thus,
The y-intercept of the line will be 0 cause the line is passing through the origin point.
The general formula of the equation of a line:
y=mx+b,
where m is the slope
b is the y-intercept
since, slope = (y - y')/(x -x')
In our case,
b = 0
m = (8 - 4)(2-1)
m = 4
And m represents The cost is $4 per T-shirt.
therefore, the slope of the line means in this situation "a. The cost is $4 per T-shirt".
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Find the equation of the line through the point (7,-9) with slope -5/7 The equation is (Be sure to enter your answer as an equation)
Required the equation of the line is y = -5/7 *x -4.
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
the line through the point (7,-9) with slope -5/7
so, m= -5/7
now, y= mx+c
solving with the given values we get,
c= -9 +5
= -4
Hence, Required the equation of the line is y = -5/7 *x -4.
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6. In a market economy
a. an individual consumer has a great influence on the price of goods and services.
b. consumers do not influence the price of goods and services.
c. all consumers collectively have a great influence on the price of goods and services
d. all consumers collectively have no influence on the price of goods and services.
nomic terms?
In a market economy, option C. all consumers collectively have a great influence on the price of goods and services.
What is a market economy?A market economy is an economic system in which goods and services are traded in a market, and prices are determined by supply and demand. The decisions of individual consumers and producers, operating through the market mechanism, determine what goods and services are produced and how they are distributed.
Therefore, the correct answer is as given above. It could be concluded that market economy allow individuals to influence the price of goods and services
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Use the graph of f to evaluate the following
The average rate of change of f from 2 to 5
By using the graph, the average rate of change of the function f from 2 to 5 is equal to -1.
How to determine the average rate of change?In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of the function f from the graph over the interval [2, 5]:
a = 2; f(a) = 4
b = 5; f(b) = 1
Substituting the given parameters into the average rate of change formula, we have the following;
Average rate of change = (1 - 4)/(5 - 2)
Average rate of change = -3/3
Average rate of change = -1.
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20 points!!
A EF = 22
B EF = 11
C EF = 16
D EF = 20
Answer:
A
Step-by-step explanation:
the midsegment EF of the trapezoid ABCD is half the sum of the parallel bases, that is
EF = [tex]\frac{AB+DC}{2}[/tex] ( substitute values )
x + 6 = [tex]\frac{2x-9+x+5}{2}[/tex]
x + 6 = [tex]\frac{3x-4}{2}[/tex] ( multiply both sides by 2 to clear the fraction )
2x + 12 = 3x - 4 ( subtract 3x from both sides )
- x + 12 = - 4 ( subtract 12 from both sides )
- x = - 16 ( multiply both sides by - 1 )
x = 16
Then
EF = x + 6 = 16 + 6 = 22
Help pic is included y(x^2+1)=1
Answer:
C.
Step-by-step explanation:
The answer is C (-1, 1/2)
An amount is divided among A, B and
C in the ratio 2:5:7 respectively. B
gets R30.
How much does A get?
On solving the provided question, we can say that ratio is = 2:5:7 => 2x + 5x + 7x = 84 => x = 6 and A gets = 2x = 12 rs.
what is ratio?Ratios show how often one number is contained in another in mathematics. For instance, the ratio of oranges to lemons in a fruit dish is 8 to 6 if there are 8 oranges and 6 lemons present. In a similar vein, the proportion of oranges to whole fruit is 8, while that of lemons to oranges is 6:8. A ratio is an ordered pair of numbers a and b that is expressed as a / b, with b not equal to zero. An equation equating two ratios is known as a ratio. The ratio can be expressed as 1:3, for instance, if there is 1 boy and 3 girls (for every boy she has 3 girls) 3/4 are girls, while 1/4 are boys.
ratio is = 2:5:7
2x + 5x + 7x = 84
14x = 84
x = 84/14 = 6
a gets = 2x = 12 rs.
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Physics shows that when an object is thrown upward with an initial velocity of v_0, then its approximate height is given by this quadratic function.
s = -4.9t^2 + v_0^t + h
A ball is thrown upward from the top of a building 15 meters high, at a velocity of 3.1m/sec. Answer the following questions. Be sure to show and explain all work.
A. Find the maximum height and the time in which it was attained (round to 3 decimal places)
B. When does it reach the ground? (round to 3 decimal places)
C. Sketch a graph to illustrate your answers.
The answers to each part is given above.
Explain Maxima and Minima in mathematics?Maxima and Minima are known as the extrema of a function. Maxima and minima are the maximum or the minimum value of a function within the given set of ranges. For the function, under the entire range, the maximum value of the function is known as the absolute maxima and the minimum value is known as the absolute minima.Local Maxima : A point x = b is a point of local maximum for f(x) if in the neighborhood of b i.e in (b−, b+) where can be made arbitrarily small, f(x) < f(b) for all x ∈ (b−, b+)∖{b}. This simply means that if we consider a small region (interval) around x = b, f(b) should be the maximum in that interval.Local Minima : A point x = a is a point of local minimum for f(x) if in the neighbourhood of a, i.e. in (a−,a+), (where can have arbitrarily small values), f(x) > f(a) for all x ∈ (a−,a+)∖{a}. This means that if we consider a small interval around x = a, f(a) should be the minimum in that interval.Given is that when an object is thrown upward with an initial velocity of v{0}, then its approximate height is given by this quadratic function -
S = - 4.9t² + [tex]$v_{o} ^{t}[/tex] + h
The approximate height is given by this quadratic function -
S = - 4.9t² + [tex]$v_{o} ^{t}[/tex] + h
{ 1 } - For the maximum height :
dS/dt = 0 ... Eq{ 1 }
dS/dt = -9.8t + [tex]$3.1^{t}[/tex] log(3.1) + 0 = 0
- 9.8t + [tex]$3.1^{t}[/tex] log(3.1) = 0
Refer to the graph attached. At t = 3.8 {possible value}, the function is 0.
So we get -
t = 3.8 s ... Eq{ 2 }
Maximum height achieved -
h{max} = - 9.8t + [tex]$3.1^{t}[/tex] log(3.1) + 15
h{max} = - 9.8 x 3.8 + [tex]$3.1^{3.8}[/tex] log(3.1) + 15
h{max} = - 37.24 + 73.65 x 0.50 + 15
h{max} = 14.585 m
{ 2 } -
0 = 3.1 t + 9.8/2 t²
0 = 3.1 t + 4.9 t²
Solving graphically, we get -
|t| = 0.6 s
Total time taken to reach ground -
T = 2 x 3.8 + 0.6
T = 8.2 seconds ... Eq{ 3 }
Therefore, the answers to each part is given above.
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47) A convention manager finds that she has $1370, made up of twenties and fifties. She has a total of 46 bills. How many fifty-dollar bills does the manager have?
The number of fifty dollars with the manager are 31.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that a convention manager finds that she has $1370, made up of twenties and fifties.
20x+50y=1370
She has a total of 46 bills.
x+y=46
x=46-y
Now we have to plug in x value in equation 1
20(46-y)+50y=1370
920-20y+50y=1370
920+30y=1370
Subtract 920 on both sides
30y=450
Divide both sides by 30
y=15
Now plug in y value in x+y=46
x+15=46
Subtract 15 on both sides
x=46-15
x=31
Hence, the number of fifty dollars with the manager are 31.
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