By applying the elimination method the value of x is - 2 and y is 7.
This is a problem from algebraic equations and we have to apply the elimination method. We can solve this problem by following a few steps.
So, the given equation according to the question is,
− 2x = 4 ................ ( equation 1 )
4x + 2y = 6 ............... ( equation 2 )
While applying the elimination method we have to multiply equation (1) with the positive coefficient of x in the second equation and vice versa.
Here the coefficient of x in the first equation is 2 and in the second equation is 4.
Now, we have to multiply equation ( 1 ) with 4 and equation ( 2 ) with 2.
Therefore,
− 2x = 4 ................ ( equation 1 ) × 4
4x + 2y = 6 ............... ( equation 2 ) × 2
Now, we can rewrite the equations as,
− 8x = 16 .................. ( equation 3 )
8x + 4y = 12 .................. ( equation 4 )
Now the coefficient of x in both equations are same but opposite sign. So, we have to add the equations.
Here we get , -8x + 8x + 4y = 16 + 12
Or, 4y = 28
Or, y = 7
Now, we have to put the value of y in any equation.
4x + 2.7 = 6 ( equation 2 )
Or, 4x = 6 - 14 = -8
Or, x = -2
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The correct question :
By applying the elimination method, solve the following pair of simultaneous equations:
− 2x = 4
4x + 2y = 6
Graph the line with the given point and slope.
The line through (-1,-2) with slope
6/5
The graph of the line passing through the points (-1,-2) with the slope 6/5 has been plotted
The line passing through the points = (-1,-2)
The slope of the line = 6/5
The slope of the line the change in y coordinates with respect to change in x coordinates of the line
We know
Point slope form [tex](y-y_{1})=m(x-x_{1})[/tex]
Where m is the slope of the line
Substitute the values in the equation
(y-(-2))= 6/5(x-(-1))
y+2 = 6/5(x+1)
y+2 = (6/5)x+6/5
y = (6/5)x+(6/5)-2
y = (6/5)x+(-4/5)
Draw the graph
Hence, the graph of the line passing through the points (-1,-2) with the slope 6/5 has been plotted
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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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The perimeter of the pentagon below is 62 units. Find the length of side QR.
Write your answer without variables
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.
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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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.
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
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]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 ^^
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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Destiny borrowed $1600 at 6% simple interest to be paid back in 3 years. How much interest will she pay?
The amount of interest to be paid by Destiny on the $1600 loan at 6% rate for 3 years is $288.00.
What is the amount of interest earned over the given time?Interest is simply the amount of money a lender or financial institution receives for lending out money or pays for receiving money.
The formula calculating simple interest is expressed as;
I = P × r × t
Where P is principal, r is rate and t is time.
Given the data in the question;
Principal P = $1,600Interest rate r = 6%Time t = 3 yearsInterest I = ?First, convert the rate from percent to decimal.
Rate r = 6%
Rate r = 6/100
Rate r = 0.06
Now plug the values into the formula and solve for I
I = P × r × t
I = $1,600 × 0.06 × 3
Interest I = $288.00
Therefore, the interest accumulated by Destiny is $288.00.
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Ryan has two jobs. He earns $9 per hour for x hours babysitting his cousins and he earns $18 per hour for y hours working at the coffee shop. Ryan will work both jobs. He is able to work no more than 10 hours a week, due to school commitments. Ryan wants to earn at least $72 a week, working a combination of both jobs. A write a system of inequalities that can be used to represent the situation.B. Graph these inequalities C. Determine and state one combination of hours that will allow Ryan to earn at least $72 per week while working no more than 10 hours
Let x and y be the number of hours Ryan works on each job respectively. He can work no more that 10 hours a week, it means that the sum of x and y must be less than or equal to 10:
[tex]x+y\le10[/tex]He also need to earn at least $72 a week, which means that the sum of 9 times x and 18 times y must be greater than or equal to 72:
[tex]9x+18y\ge72[/tex]The system of inequalities is:
[tex]\begin{gathered} x+y\le10 \\ 9x+18y\ge72 \end{gathered}[/tex]To graph these inequalities, we have to graph the boundary lines which are x+y=10 and 9x+18y=72, and then shade the region depending on the inequality. For the first inequality which is a less than or equal to, the shaded region must be under the boundary line (which is a continuous line) and for the second one, the shaded region must be above the boundary line (which is also continous).
In this case we only can take the solutions that have positive values of x and y, since Ryan can't work a negative number of hours. For example, one combination that will allow Ryan reach his goal is 5 hours as babysitter and 5 hours at the coffee shop.
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
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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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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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
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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Simply the following ratios:
4:6
14:8
15:10
6:15
Answer:
Divide them by 100 or use fraction
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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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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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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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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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
point G(6,-2) is translated using the rule (x,y) -> (x-4, y+7).
what is the x-coordinate of G
what is the y-coordinate of G
IT MEANS THAT THE X COORDINATE CHANGED BY -4
[tex]x = 6 - 4 \\ x = 2[/tex]
THE NEW COORDINATE OF X IS 2
AND THE Y COORDINATE CHANGED BY +7
[tex]y = - 2 + 7 \\ y = 5[/tex]
THE NEW COORDINATE OF Y IS 5
(2,5)
ATTACHED IS THE SOLUTION
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
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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Please help I’ll mark you as brainliest if correct!
The value of each letter in the given magic square is a = 30, b = 6 , c = 18 and d = 4.
What is a magic square?A magic square is one that has several different integers placed in such a way that the sum or total of the numbers is the same on all of the diagonals, as well as in every row, column, and major diagonal.
Given:
A magic square where all rows, columns, and diagonals sum to the same number.
Sum of the numbers in the diagonal of the magic square,
5 + 17 + 29 = 51
In the first row, the sum of numbers will also be 51
5 + a + 16 = 51
a = 51 - 21 = 30
Similarly, the sum in the first column
5 + 28 + c = 51
c = 51 - 33 = 18
And the sum in the last row,
c + d + 29 = 51
Putting the value of c, we get
18 + d + 29 = 51
d = 51 - 47 = 4
Now to find the value of b the sum of the last column,
16 + b + 29 = 51
b = 51 - 45 = 6
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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
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]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.