The solution to the system of equations are, x + 2y = 8 and -3x-2y = 12 is: X = -10 , Y = 9
The given system of equations:
x + 2y = 8 (Equation - 1)
-3x - 2y = 12 (Equation - 2)
This can be written in matrix form as shown:
[tex]\left[\begin{array}{ccc}1&2&\\-3&-2&\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex] [tex]= \left[\begin{array}{ccc}8\\12\\\end{array}\right][/tex]
Let us assume, D = [tex]\left[\begin{array}{ccc}1&2\\-3&-2\\\end{array}\right][/tex]
We can use cross multiplication,
= (-2)(1) - (-3)(2)
= -2 + 6
= 4 ≠ 0
So the system has a unique solution,
Then,
[tex]D_{1} = \left[\begin{array}{ccc}8&2\\12&-2\\\end{array}\right][/tex]
We can use cross multiplication,
[tex]D_{1} = (8)(-2)-(12)(2)\\D_{1} = -16-24\\D_{1} = -40[/tex]
[tex]D_{2} =\left[\begin{array}{ccc}1&8\\-3&12\\\end{array}\right][/tex]
We can use cross multiplication,
[tex]D_{2} = (12)(1)-(-3)(8)\\D_{2} = 12+24\\D_{2} = 36[/tex]
So, they can solve the X and Y values,
X = D1 / D
X = -40/4
X = -10
Y = D2 / D
Y = 36/4
Y = 9
Therefore,
The solution to the system of equations are, x + 2y = 8 and -3x-2y = 12 is: X = -10 , Y = 9
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A student is purchasing new clothes for the school year. She
can choose any combination of shirts and pants, and she does not
want to spend more than $125. If shirts cost $12.99 each and
pants cost $15.99 each, write an inequality that represents all
possible combinations of x shirts and y pants.
An inequality that represents all possible combinations of x shirts and y pants is (12.99x + 15.99y) ≤ 125.
What are Inequalities?An inequality in algebra is a mathematical expression that uses the inequality symbol to show the relationship between two expressions. The expressions on either side of an inequality symbol are not equal. When the symbols ">," <","≤ ", or "≥" are used to connect two real numbers or algebraic expressions, the relationship is referred to as an inequality.Given:
Cost of each shirt = $12.99
Cost of each pant = $15.99
Let's assume the number of shirts is x and the number of pants is y.
Total cost of x shirts = $12.99x
Total cost of y pants = $15.99y
Total cost = $(12.99x+15.99y).
Now, she does not want to spend more than $125 which means she can spend equal to or less than 125 dollars.
An inequality that represents all possible combinations of x shirts and y pants is,
(12.99x + 15.99y) ≤ 125
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The expression 55 + 14m - 2n + 3p has__ terms.A. 2B. 3C. 4D. 5
4 terms.
1) Terms of an expression denotes the constant terms, and the constant ones (numbers).
2) As we can see all the variables are different so we can tell these terms can't combine with any other one.
3) And therefore, we can tell that this expression has 4 terms.
Simply the following ratios:
4:6
14:8
15:10
6:15
Answer:
Divide them by 100 or use fraction
3(x + 3) – 2 < 4 or 1 – x ≤ –1
The solution of the inequality 3(x + 3)–2 < 4 or 1– x ≤ –1 has been plotted on the number line
The inequalities are 3(x + 3)–2 < 4 or 1– x ≤ –1
The inequality shows the relationship between two values in an algebraic expression, the relationship are greater than or equal to, greater than, less than and less than or equal to.
The first inequality 3(x + 3) – 2 < 4
3(x + 3)–2 < 4
3x+9-2 < 4
3x+7 < 4
3x < 4-7
3x < -3
x < -1
The second inequality 1-x ≤ -1
-x ≤ -2
x ≥ 2
Plot the inequalities on the number line
Hence, the solution of the inequality 3(x + 3)–2 < 4 or 1– x ≤ –1 has been plotted on the number line
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2x(3x-4)-3x(5x+6)
Can somebody help explain how to get the awnser for this like step by step!
By using basic algebra we get x = 0 and x =[tex]\frac{-26}{9}[/tex]
What is basic algebra ?Algebra is a branch of mathematics that helps translate real-world situations or problems into mathematical truths. Mathematical operations like addition, subtraction, multiplication, and division are needed in addition to variables like x, y, and z to construct a meaningful mathematical expression. All branches of mathematics, such as calculus, trigonometry, and coordinate geometry, employ algebra. A fundamental algebraic equation is 2x + 4 = 8. Algebraic expressions serve as the mathematical statement when operations such as addition, subtraction, multiplication, division, etc. are done on variables and constants.
2x(3x-4)-3x(5x+6)
[tex]6x^{2} -8 -15x^{2} -18x\\-9x^{2} -26x = 0\\9x^{2} +26x = 0\\x(9x +26)=0\\x = 0\\ x = \frac{-26}{9}[/tex]
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nine sales representitives for a company are to br chosen at random to participate in a training program. the company has twelve sales representatives, three in each of four regions. what is the probability that the nine sales representatives chosen to participate in the training program will be from only three of the four regions?
The probability is 6/70.
What is probability ?
probability is concerning about numerical description is how likely is an event is occur or how likely it is true.
Sol-
way will be selecting 84 out of eight since representative so 84 which is equal to at 70. And we need that we since we are things. There are two things representing the regions, so the four selected sales representatives are from only two off the regions. So if we select to sales representative from the two regions while we select de o sales representative from the other two regions, so four is it to selected from the four and to select from the two region and to select from two regions on day zero selected from the two regions and they're selected from the two regions. So is equal to four factorial over two factorial, two factorial times two factorial over to Victoria, zero factorial times too times Sorry, that was two factorial over to factory a factory times two factorial zero factorial two factorial which is equal to six for the
Thus,
probability is 6/70 which is equal toe open toe eight 57.
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Question
Solve: n- 5/11=-1/3
N=?
Answer: 26/33
Step-by-step explanation:
Step-by-step explanation:
app called maple calculator
Sales of SUVs (sport utility vehicles) in the United States (in millions) for the years 1990-1999 can be modeled by the quadratic equation shown below.y = 0.016x^2 +0.124x +0.787Here x = 0 represents 1990, x = 1 represents 1991, and so on. Use the model to approximate sales in 1995, Sales in 1995 were approximately ____ million SUVs.(Round to the nearest tenth as needed.)
The sales in 1995 were approximately 1.8 millions.
Explanation:
Since x = 0 is 1995, x = 1 is 1991 and so on, if we want to find the approximate amount of sales, we need to evaluate the expression for x = 5:
[tex]y=0.016x^2+0.124x+0.787[/tex][tex]\begin{gathered} y=0.016\cdot5^2+0.124\cdot5+0.787 \\ y=0.016\cdot25+0.62+0.787 \\ y=0.4+0.62+0.787 \\ y=0.4+0.62+0.787 \\ y=1.807 \end{gathered}[/tex]To the nearest tenth, the sales of SUV were approximately 1.8 millions
Point A is at (-1, -9) and point B is at
(2, 4).
What is the midpoint of line segment AB?
-9-8-7 -6 -5 -4 -3 -2
The most appropriate form of midpoint of line segment will be given by-
Coordinate of midpoint of AB = ([tex]\frac{1}{2}, -\frac{5}{2}[/tex])
What is midpoint of a line segment?
At first, it is important to know about section formula. Let the coordinate of end point of a line segment is ([tex]x_1, y_1[/tex]) and ([tex]x_2, y_2[/tex]) respectively. Let another line intersects the line in the ratio m : n. Coordinate of point of intersection =[tex](\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m + n})[/tex].
If m = n =1, we get the coordinate of midpoint.
Coordinate of midpoint = [tex](\frac{x_1+y_1}{2}, \frac{x_2, y_2}{2})[/tex]
Midpoint of a line segment is that point which is equidistant from both the end points.
Here,
Coordinate of A = (-1, -9)
Coordinate of B = (2, 4)
Coordinate of midpoint of AB = ( [tex]\frac{-1 + 2}{2}, \frac{-9 + 4}{2}[/tex])
= ([tex]\frac{1}{2}, -\frac{5}{2}[/tex])
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A coin is weighted so that there is a 58% chance that it will come up "heads" when flipped. The coin is flipped four times. Find the probability of getting two "heads" and two "tails". Round your answer to four decimal places.
P(A) =Probability of heads
P(B) = Probability of tails
P(B)= 1 - P(A) = 1 - 58 = 42%
The events are independent, so, let's assume that we flip the coin and the first two results are heads, so:
P(A) =0.58
Now, let's assume the last two results are tails so:
P(B) = 0.42
Therefore:
[tex]\begin{gathered} P(A\cap A\cup B\cap B)=P(A)\cdot P(A)\cdot P(A)+P(B)\cdot P(B) \\ P(A\cap A\cup B\cap B)=0.58\cdot0.58+0.42\cdot0.42=0.3364+0.1764=0.5128 \end{gathered}[/tex]Which statement best describes a graph of paired points that form a proportional relationship?
A straight line can be drawn through all the points, and the line passes through the point (0, 0) .
A straight line can be drawn through all the points, and the line passes through the point (2, 1) .
A straight line can be drawn through all the points, and the line passes through the point (10, 5) .
The statement that best describes the graph of a proportional relationship with paired points is: A. A straight line can be drawn through all the points, and the line passes through the point (0, 0).
What is the Graph of a Proportional Relationship?A graph that represents a proportional relationship between two variables can be described as a graph that connects all the given points and goes through the point of origin, (0, 0).
A proportional relationship graph is also a straight line graph. Every point in the relationship are located on the line.
An example of a graph that represents a proportional relationship between two variables is the graph given in the diagram above.
As you can observe, all points are connected by a straight line and it passes through the point of origin, (0, 0).
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Is trangle ABC ~ trangle XYZ ? if so , what sequence of transformation maps trangle ABC to XYZ
You have the figurew ABC with the following vertices:
A(-2,-4)
B(0,-1)
C(2,-4)
First, multiply all points by 2 (this is the first transformation)
A => A'(-4,-8)
B => B'(0,-2)
C => C'(4,-8)
Next, translate the previous points 6 units upward (which means add 6 units to each y-coordinate).
A' => X(-4,-2)
B' => Y(0,4)
C' => Z(4,-2)
as you can notice, with the previous transformation you obtain the vertices X, Y, and Z and form the figure XYZ.
Answer: a dilation by and a translation
Step-by-step explanation: just did on edge
Solve the system[tex]\begin{bmatrix}4x-2y=8\\ 3x+y=2\end{bmatrix}[/tex]
The value of x= 1.2 and the value of y = -1.6
Given two equations
[tex]4x-2y=8[/tex]
[tex]3x+y=2[/tex]
Since there are two equations and two unknowns we can solve the equations by arithmetical methods.
Initially multiply second equation by 2 and add it it to first equation.
[tex]3x+2y=2[/tex] × 2
[tex]6x+2y=4[/tex]
Now adding this to equation 1
[tex]4x-2y=8 + 6x+2y=4[/tex]
[tex]10x=12[/tex]
[tex]x=1.2[/tex]
To get y value substitute x value in any of the equation
[tex]4(1.2)-2y=8[/tex]
[tex]-2y = 3.2[/tex]
[tex]y = -1.6[/tex]
Therefore x and y values are 1.2 and [tex]-1.6[/tex] respectively.
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Find the difference.
(-9ab-4a+8) - (-2ab+4)
Enter the correct answer.
Answer:
-7ab-4a+4
Step-by-step explanation:
simplify the expression
hope this helped
have a great day ^^
Over the last three evenings, Karen received a total of 130 phone calls at the call center. The second evening, she received 4 times as many calls as the third evening. The first evening, she received 10 more calls than the third evening. How many phone calls did she receive each evening?
CORRECT ANSWERS ONly
Answer first evening she received 130 second evening she received 520 third evening she received 1300
Step-by-step explanation: that's the right one for shure i worked it out
A company XYZ issued 30 year bonds with 10% annual coupon rate at their par value of $1000 in 2010. The Bonds had a 7% call premium, with 5 years of call protection. Today XYZ called the bonds. Compute the realized rate of return for an investor who purchased the bonds when they were issued in 2010. Briefly explain why the investor should or should not be happy.
1. Tha rate of return is 11.12%
2. The investor will not be happy in case the market interest rates fall
How to illustrate the information?n is NPER 5 (called back in 5yrs)
Coupon payment / PMT = 1000 * 10% = 100,
Purchase price PV (PV is entered as a negative value) -1000
Called for value is FV Call premium is 7% hence FV = 107% * 1000 = 1070
You can use the RATE function in excel
Rate(nper, PMT, PV,FV, Type)
RATE(5,100,-1000,1070)
= 11.12%
The investor was promised a fixed return rate of 10%, but since the bond was called after 5 years, the actual return was 11.12%, so the investor had good reason to be pleased.
In the event that market interest rates decline, the investor will not be pleased because, had the bond not been called, he would have continued to receive his fixed 10% coupon payments of $100 per year.
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Please answer this question, I need help.
Answer:3 8 10
Step-by-step explanation:
5. Devon is considering taking out a 7,000 loan. He went to two banks, Stevenson Trust Company offered him an 8-year loan with an interest rate of 8.6%First National Bank offered him a 5-year loan with an interest of 10%Which loan will have the lower interest over its lifetime ?
The loan from National bank will have lower interest over its lifetime.
Interest is the additional payment made by a borrower or deposit-taking financial institution to a lender or depositor at a predetermined rate over and above the principal sum (the amount borrowed).
Interest differs from any fees the borrower may be required to pay to the lender or another party.Interest contrasts from a dividend, which is cash distributed to shareholders (owners) by a corporation from its profit or reserve, but not at a predefined rate or proportionally; rather, it is a portion of the reward gained by risk-taking businessmen when revenue is made that surpasses all expenditures.The principal or the amount to be taken loan is $7000.
Let us consider each bank and find the interest to be owed from the loan.
Stevension trust :
Rate = 8.6% = 0.086
time = 8 years
Interest = principal × time × rate = 7000 × 8 × 0.086 = $ 4816
First national bank :
Rate = 10% = 0.1
Time = 5 years
Interest = 7000 × 5 × 0.1 = $3500
Hence the loan from national bank will have lower interest over its lifetime.
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Which of the following quantities are directly proportional? (Answer if they are directly proportional or not) PLS HELP ASAP
A) distance and time traveled if speed is a constant 77 mph
B) speed and time if the distance traveled is 110 miles
C) the price per item and the number of items bought if the amount of money spent is constant
Based on the given quantities, the quantity that is directly proportional is B) speed and time if the distance traveled is 110 miles.
How to find directly proportional quantities?Two quantities are said to be proportional if the increase or decrease between the two quantities is constant. For instance, if a single unit in one will always lead to the same increase in the other quantity.
When people are travelling at a constant 77 mph then it means that for every hour(time) that passes, the distance would increase by 77 miles. The distance and time here are therefore proportional.
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The coordinate 3 has a weight of 1 , and the coordinate 6 has a weight of 2 .
For the coordinates and their weights, the weight average is 5
How to determine the weight average?The given parameters are:
Coordinate 3 has a weight of 1
Coordinate 6 has a weight of 2
The weight average is then calculated as:
Weight average = Sum of (Weight * Coordinate)/Sum of Weights
Substitute the known values in the above equation
So, we have the following equation
Weight average = (3 * 1 + 6 * 2)/(1 + 2)
Evaluate the product in the above equation
So, we have the following equation
Weight average = (3 + 12)/(1 + 2)
Evaluate the sum in the above equation
So, we have the following equation
Weight average = (15)/(3)
Evaluate the quotient in the above equation
So, we have the following equation
Weight average = 5
Hence, the weight average of the coordinates is 5
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Complete question
The coordinate 3 has a weight of 1 , and the coordinate 6 has a weight of 2 .
Find the weighted average.
a 4x³ - 6x² + 4 para x = -2, 3 y 1.
3
For value 4x³- 6x² + 4 is
If para x = -2
4x³ - 6x² + 4
=4(-2)³ - 6(-2)² + 4
=4(-8) - 6(4) + 4
=-32 - 24 + 4
=-52
If para x = 3
=4x³ - 6x² + 4
=4(3)³ - 6(3)² + 4
=4(27) - 6(9) + 4
=108 - 54 + 4
=58
If para x = 1
4x³ - 6x² + 4
=4(1)³ - 6(1)² + 4
=4 - 6 + 4
=2
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Find the inverse function off(x)=20x-4
Given:
[tex]f(x)=20x-4[/tex]Required:
To find the inverse of the given function.
Explanation:
Consider
[tex]f(x)=20x-4[/tex]Rewrite f(x) as y,
[tex]y=20x-4[/tex]Swap x and y,
[tex]x=20y-4[/tex]Solve for y, we get
[tex]\begin{gathered} x=20y-4 \\ \\ x+4=20y \\ \\ y=\frac{x+4}{20} \end{gathered}[/tex]Final Answer:
The inverse of the given function is
[tex]f^{-1}(x)=\frac{x+4}{20}[/tex]c. Suppose you have a 32 ounce bottle of weed killer concentrate. The directions say to mix 2 1/2 ounces of weed killer concentrate with enough water to make a gallon. How many gallons of weed killer will you be able to make from this bottle?
ANSWER
EXPLANATION
e have a 32 ounce bottle of weed killer concerntrate.
The directions say to mix 2 1/2 ounces of weed killer to water to make a gallon.
To find out how many gallons we will b able to make, we have to divide the total amount of the weed killer by the amount it takes to make one gallon.
That is:
[tex]\begin{gathered} \frac{32}{2\frac{1}{2}} \\ \Rightarrow\text{ }\frac{32}{\frac{5}{2}} \\ \Rightarrow\frac{32}{5}\cdot\text{ 2 = 12.8 }\cong13 \end{gathered}[/tex]They can make 12.8 (approximately 13) gallons of the weed killer.
Is it possible for a system of linear equations to have exactly two solutions?
Answer:
Most linear systems you will encounter will have exactly one solution. However, it is possible that there are no solutions, or infinitely many. (It is not possible that there are exactly two solutions
The perimeter of the pentagon below is 62 units. Find the length of side QR.
Write your answer without variables
100 ft 40 ft 140 ft What is the area of this trapezoid? square feet
According to the given data we have the following:
Length of side a=100 ft
Lenght of side b=140 ft
Height of side h=40 ft
In order to calculate the area of this trapezoid we would have to make the following calculation:
area of this trapezoid=(a + b)/2)h
area of this trapezoid=(100+140)/2)40
area of this trapezoid=120*40
area of this trapezoid=4,800
Solve. Todd sold bunches of flowers on a street corner on Friday afternoons. Each bunch sold for $2.75. One Friday he made $71.50. How many bunches of flowers did he sell that day?
Todd sold 26 bunches of flowers on a street corner on Friday afternoon
The selling price of each flower bunch = $2.75
Total money made by Todd on Friday = $71.50
Arithmetic: The foundational subject in mathematics is arithmetic, which covers operations with numbers. These include multiplication, division, addition, and subtraction. One of the crucial branches of mathematics, arithmetic serves as the cornerstone of the field of mathematics.
Finding the number of flower bunches sold by Todd:
Number of bunches sold by Todd = Total money made by Todd/Selling price of each flower bunch
= 71.50/2.75
= 26
Number of bunches sold = 26
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3. Find the value of x?
Answer: 7
Step-by-step explanation:
y = 180 - (17x+13) = 167 - 17x
As sum of the angles of a triangle is 180, we get that (4x+7) + 97 + 167 - 17x = 180
-13x + 271 = 180
-13x = -91
x = 7
hello, i need help with this question
The area of a triangle is given by the formula:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ \text{ Where b is the base and} \\ h\text{ is the height of the triangle} \end{gathered}[/tex]From the information given you know that the measure of the height of the triangle EFG is 16 cm but the measure of the base of the triangle is unknown.
To find the measure of the base, you can first find the measure of the middle of the segment EG using the Pythagorean theorem, since the triangle formed by the vertices F, G, and EG/2 form a right triangle. Graphically,
The formula of the Pythagorean Theorem is
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{ Where c is the hypotenuse and} \\ a,b\text{ are the sides of the triangle} \end{gathered}[/tex]So, you have
[tex]\begin{gathered} a=16 \\ b=\frac{EG}{2} \\ c=20 \\ (16)^2+b^2=(20)^2 \\ 256+b^2=400 \\ \text{ Subtract 256 from both sides of the equation} \\ 256+b^2-256=400-256 \\ b^2=400-256 \\ b^2=144 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{b^2}=\sqrt[]{144} \\ b=12 \\ \text{ Then} \\ \frac{EG}{2}=12 \end{gathered}[/tex]Then, the measure of the segment EG, that is, the measure of the base of the triangle EFG is
[tex]\begin{gathered} \frac{EG}{2}=12 \\ \text{ Multiply by 2 on both sides of the equation} \\ \frac{EG}{2}\cdot2=12\cdot2 \\ EG=24 \end{gathered}[/tex]Finally, the area of triangle EFG will be
[tex]\begin{gathered} b=24\operatorname{cm} \\ h=16\operatorname{cm} \\ A=\frac{b\cdot h}{2} \\ A=\frac{24\operatorname{cm}\cdot16\operatorname{cm}}{2} \\ A=\frac{384\operatorname{cm}^2}{2} \\ A=192\operatorname{cm}^2\text{ } \end{gathered}[/tex]Therefore, the area of the triangle EFG is 192 square centimeters.
How many seven-digit numbers are there when 0 and 8 cannot be the leading number?
There are_____such seven-digit numbers.
Answer:
With the restrictions that 0 or 8 cannot be the leading digit, the leading digit can be one of [1, 2, 3, 4, 5, 6, 7, 9] = 8 choices.
The other six digits can be one of [1, 2, 3, 4, 5, 6, 7, 8, 9, 0] = 10 choices each.
Therefore, there are:
8*10*10*10*10*10*10 = 8*10^6 = 8,000,000 7-digit numbers under the given restrictions.
Step-by-step explanation:
hope this helps