Answer:
[tex]\textsf{1.} \quad a_n=174-6n[/tex]
[tex]\textsf{2.\;a)} \quad A=5000\left(1.019\right)^{4t}[/tex]
b) 9.25 years (to the nearest quarter)
Step-by-step explanation:
Question 1[tex]\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a_n$ is the nth term. \\ \phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given terms of an arithmetic sequence:
[tex]a_{28}=6[/tex][tex]a_{22}=42[/tex]Substitute the given values into the arithmetic sequence formula to create two equations:
[tex]\implies a_{28}=a+27d=6[/tex]
[tex]\implies a_{22}=a+21d=42[/tex]
Subtract the second equation from the first equation to eliminate a and solve for d:
[tex]\implies 6d=-36[/tex]
[tex]\implies d=-6[/tex]
Substitute the found value of d into one of the equations and solve for a:
[tex]\implies a+27(-6)=6[/tex]
[tex]\implies a-162=6[/tex]
[tex]\implies a=168[/tex]
Substitute the found values of a and d into the formula to create an equation for the nth term of the sequence:
[tex]\implies a_n=168+(n-1)(-6)[/tex]
[tex]\implies a_n=168-6n+6[/tex]
[tex]\implies a_n=174-6n[/tex]
Question 2[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given values:
P = $5000r = 7.6% = 0.076n = 4 (quarterly)Substitute the given values into the compound interest formula to create an equation with respect to time, t:
[tex]\implies A=5000\left(1+\dfrac{0.076}{4}\right)^{4t}[/tex]
[tex]\implies A=5000\left(1.019\right)^{4t}[/tex]
To find when the value of the investment will be worth more than $10,000, substitute A = 10000 into the equation:
[tex]\implies 10000 < 5000\left(1.019\right)^{4t}[/tex]
[tex]\implies 2 < \left(1.019\right)^{4t}[/tex]
[tex]\implies \ln 2 < \ln\left(1.019\right)^{4t}[/tex]
[tex]\implies \ln 2 < 4t\ln\left(1.019\right)[/tex]
[tex]\implies \dfrac{\ln 2}{4 \ln\left(1.019\right)} < t[/tex]
[tex]\implies t > 9.20672924...[/tex]
Therefore, the investment will be worth more than $10,000 from 9.25 years (to the nearest quarter).
The demand for a given product demand is formulated by the linear trend equation: y= 50 – 6t.
Based on this information, when would be the first period that there is NO demand at all for this product?
Answer:
t >= [tex]\frac{25}{3}[/tex] or 8.33333333333
Step-by-step explanation:
We need to set up an inequality where demand is less than or equal to 0. The inequality looks like this:
50 - 6t <= 0
50 <= 6t
t >= [tex]\frac{25}{3}[/tex] or 8.33333333333
What is the equation of the line that is parallel to line R, y = 2x + 5, and passes through the
point (-2, 2)?
Answer:
y = 2x + 6
Step-by-step explanation:
We are given the line R, which is y=2x+5, and we want to find the equation of the line that is parallel to this line, and that also passes through the point (-2, 2).
Parallel lines have the same slope, yet different y-intercepts.
So, we should first find the slope of y=2x+5.
The line is written in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept.
As 2 is in the place of where m (the slope) should be, 2 is the slope of the line.
It is also the slope of the line parallel to it.
We can write the equation of the new line in slope-intercept form as well; here is the equation so far, with what we know:
y = 2x + b
We need to find b.
As the equation passes through the point (-2, 2), we can use its values to help solve for b.
Substitute -2 as x and 2 as y.
2 = 2(-2) + b
Multiply.
2 = -4 + b
Add 4 to both sides.
6 = b
Substitute 6 as b.
y = 2x + 6
Which is the graph of the function f(x) = 1/2x^2+2x-6?
See the graph in the attached image.
The vertices of a quadrilateral are A(-3,-1), B(1,5), C(5,5), and D(5,-1). Select the statement that represents this quadrilateral. A. ABCD is a rectangle because it has exactly one pair of right angles. B. ABCD is a trapezoid because it has at least one pair of parallel sides. C. ABCD is a square because it has all equal sides. D. ABCD is a parallelogram because it has two pairs of parallel sides.
Answer:
B. ABCD is a trapezoid because it has at least
one pair of parallel sides.
Step-by-step explanation:
the two points A(-3,-1) and D(5,-1) have the same y-coordinates
Then
The line AD is parallel to the x-axis
On the other hand,
the two points B(1,5) and C(5,5) have the same y-coordinates
Then
The line BC is parallel to the x-axis.
We obtain :
• AD is parallel to the x-axis
• BC is parallel to the x-axis.
Therefore
AD // BC
Conclusion:
ABCD is a trapezoid because it has at least
one pair of parallel sides.
Answer:
b
Step-by-step explanation:
plato
_ May Occur if the chosen sample is too small for a study.
a) Participation Bias
b) response Bias
c)non-response Bias
d) sampling Bias
e) Reasearcher Bias
The non response bias can happen if the chosen sample is too small for a study.
What is the non response bias?This is the term that is used to refer to the type of bias that happens in a research study because the some of the study participants could not participate in the study.
This type of bias is a very serious matter of concern while carrying out research.
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Which statement is true about the function f(x) = 6x7?
The function is even because f(–x) = f(x).
The function is odd because f(–x) = –f(x).
The function is odd because f(–x) = f(x).
The function is even because f(–x) = –f(x).
Answer: The function is odd because f(–x) = –f(x).
Step-by-step explanation:
[tex]f(x)=6x^7\\\\f(-x)=6(-x)^7 = -6x^7\\\\\therefore f(x)=-f(-x)[/tex]
The function is odd because f(–x) = –f(x).
How to determine the true statement?The function is given as:
f(x) = 6x^7
A function is odd if the following is true
f(-x) = -f(x)
Calculate f(-x)
f(-x) = 6(-x)^7
f(-x) = -6x^7
Calculate -f(x)
-f(x) = -6x^7
By comparison;
f(-x) = -f(x) = -6x^7
Hence, the function is odd because f(–x) = –f(x).
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Please Help! Multiple Choice
Using the z-distribution, the z-statistic would be given as follows:
c) z = -2.63.
What are the hypothesis tested?At the null hypothesis we test if the means are equal, hence:
[tex]H_0: \mu_D - \mu_C = 0[/tex]
At the alternative hypothesis, it is tested if they are different, hence:
[tex]H_1: \mu_D - \mu_C \neq 0[/tex]
What are the mean and the standard error for the distribution of differences?For each sample, they are given as follows:
[tex]\mu_D = 12, s_D = \frac{5.2}{\sqrt{73}} = 0.6086[/tex][tex]\mu_C = 14, s_C = \frac{4.1}{\sqrt{81}} = 0.4556[/tex]Hence, for the distribution of differences, they are given by:
[tex]\overline{x} = 12 - 14 = -2[/tex].[tex]s = \sqrt{0.6086^2 + 0.4556^2} = 0.76[/tex]What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Hence:
[tex]z = \frac{\overline{x} - \mu}{s}[/tex]
[tex]z = \frac{-2 - 0}{0.76}[/tex]
z = -2.63.
Hence option B is correct.
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(07.06) There are currently 4 people signed up to play on a baseball team. The team must have at least 9 players.
Which of the following graphs includes the possible values for the number of people who still need to sign up for the team?
Number line with closed circle on 5 and shading to the left
Number line with closed circle on 5 and shading to the right.
Number line with open circle on 5 and shading to the left.
Number line with open circle on 5 and shading to the right.
A graph which includes the possible values for number of people who can still sign up for the team is: B. number line with closed circle on 5 and shading to the right.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains numerical values (positive and negative numbers) that are placed at equal intervals along its length.
Let the number of people who can still sign up for the team be represented by x. Thus, the inequality is given by:
x + 4 ≥ 9
x ≥ 9 - 4
x ≥ 5.
This ultimately implies that, there could be five (5) or more people that can still sign up for the team and a graph which includes these possible values is a number line with closed circle on five (5) and shading to the right because it can get larger.
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Andy is preparing the company's income statement. His first line item is the company's service revenue. What will he deduct from this line item to obtain the net income?
Andy needs to subtract _______ from the service revenue.
Fill in the blank
Andy needs to subtract cost from the service revenue.
What does Andy need to subtract?
Revenue is the total income earned before any deductions are made. Net income is the total revenue less total expenses or cost.
Net income = total revenue - cost
For example, if a company sold 100 loaves of bread for $100 dollars. The cost of making the bread is $50. The revenue is $100 and the net income is $50 (100 - 50).
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Find the point of intersection for the pair of linear equations. A. (5.1, 2.6) B. (-3.1, 2.4) C. (3.6, 2.2) D. (-4.6, 4.1) √x+y=-0.7 y = 3x + 11.7
The point of intersection for the pair of linear equations is (-5.5, -4.8)
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the point of intersection for the pair?The pair of linear equations is given as:
x + y = 0.7
y = 3x + 11.7
Substitute y = 3x + 11.7 in x + y = 0.7
x + 3x + 11.7 = 0.7
Evaluate the like terms
2x = -11
Divide both sides by 2
x = -5.5
Substitute x = -5.5 in y = 3x + 11.7
y = 3*-5.5 + 11.7
Evaluate
y = -4.8
So, we have
x = -5.5 and y = -4.8
Express the above points as an ordered pair, to determine the point of intersection
(x, y) = (-5.5, -4.8)
Hence, the point of intersection for the pair of linear equations is (-5.5, -4.8)
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Can you guys show me what process you would use for this? I mostly need the process
The value of the expression for the given values of the variables is 1/9
Evaluating an ExpressionFrom the question, we are to determine the value of the expression for the given values of the variables
The given expression is
[tex](\frac{4x^{3} -2y-2z^{3} }{4y^{2}-16x^{2} }) ^{2}[/tex]
From the given information,
x = 2
y = -5
z = 3
Putting the values of the variables into the expression
[tex](\frac{4(2)^{3} -2(-5)-2(3)^{3} }{4(-5)^{2}-16(2)^{2} }) ^{2}[/tex]
[tex](\frac{4(8) +10-2(27) }{4(25)-16(4) }) ^{2}[/tex]
[tex](\frac{32 +10-54 }{100-64 }) ^{2}[/tex]
[tex](\frac{-12 }{36 }) ^{2}[/tex]
[tex](\frac{-1 }{3 }) ^{2}[/tex]
[tex]= \frac{1}{9}[/tex]
Hence, the value of the expression for the given values of the variables is 1/9
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Math man fell from the top of a 500 meter building. The equation d = t squared * 0.25 describes math man's distance from the ground as he falls. How long does math man spend falling if he falls all the way from the top of the building to the ground? Round your answer to the nearest tenth.
Based on the equation of the function of the height of the building, it takes the man 44.7 seconds to fall from the top
How to determine how long it takes the math man to fall?The function of the height where the man falls is a quadratic function, and the equation of the function is given as:
d = t^2 * 0.25
The height of the building is 500
This means that the value of d is 500.
So, we have;
d = 500
Substitute 500 for d in the equation d = t^2 * 0.25
500 = t^2 * 0.25
Divide both sides of the above equation by 0.25
500/0.25 = t^2 * 0.25/0.25
Evaluate the quotient in the above equation
t^2 = 2000
Take the square root of both sides in the above equation
√t^2 = √2000
Evaluate the exponent
t = 44.7
Hence, it takes the man 44.7 seconds to fall
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On a piece of graph paper, plot the following points: A (3, 1), B (1, 5), C (9, 9), and D (11, 5). These coordinates will be the vertices of a quadrilateral. How would you use the distance formula and the slope formula to prove that this figure is actually a rectangle?
The given coordinates are actually a rectangle
How to determine the quadrilateral type?
The coordinates are given as:
A (3, 1), B (1, 5), C (9, 9), and D (11, 5).
Calculate the distance between the coordinates using:
[tex]d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2[/tex]
So, we have:
[tex]AB = \sqrt{(3 -1)^2 +(1-5)^2} =\sqrt {20[/tex]
[tex]BC = \sqrt{(1 -9)^2 +(5-9)^2} =\sqrt {80[/tex]
[tex]CD = \sqrt{(9 -11)^2 +(9-5)^2} =\sqrt {20[/tex]
[tex]DA = \sqrt{(11 -3)^2 +(5-1)^2} =\sqrt {80[/tex]
The above shows that the opposite sides are congruent
Next, we calculate the slopes using:
m = (y2- y1)/(x2- x1)
So, we have:
AB = (1- 5)/(3-1) = -2
BC = (5- 9)/(1-9) = 1/2
CD = (9- 5)/(9-11) = -2
DA = (5- 1)/(11-3) = 1/2
The slopes of adjacent sides are opposite reciprocals.
This means that the sides are perpendicular
Hence, the given coordinates are actually a rectangle
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Lamonte has 50 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 288 square meters. List each set of possible dimensions (length and width) of the field.
The dimensions of the length and width are 25 meters and 12. 5 meters respectively.
How to determine the valuesArea of a rectangle
area of rectangle = l × w
where
l = length
w = width
Note that,
Perimeter = 2w+ l
50 = 2w + l
l = 50 - 2w
Hence,
area = w(50 - 2w)
288 = 50w - 2w²
-2w² + 50w - 288 = 0
-w² + 25w - 144 = 0
The dimension w can be found as follows;
w = - b / 2a
where
a = -1
b = 25
w = - 25 / 2 × -1
w = 12.5 meters
Then, we have that
l = 50 - 2w
Substitute the value of w
l = 50 - 2(12.5)
l = 50 - 25
I = 25 meters
Thus, the dimensions of the length and width are 25 meters and 12. 5 meters respectively.
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Pamela is 9 years younger than Jiri and the sum of their ages is 41 what is jiri's age
Answer:
Jiri is 25 years old.
Step-by-step explanation:
1)Pamela =Jiri-9 ( Pamela is 9 years younger than Jiri)
2)Pamela +Jiri=41
Substitute equation 1 into equation 2
(J-9)+J= 41
2J-9=41
Add 9 to both sides:
2J=41+9
Divide by 2:
2J=50
J=25
the required Jiri's age is 25 years.
Pamela is 9 years younger than Jiri and the sum of their ages is 41. What is Jiri's age is to be determined.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
Let the age of Pamela and Jiri is x and y respectively
Pamela is 9 years younger than Jiri. so,
y = x + 9 - - - - (1)
the sum of their ages is 41
x + y = 41 - - - - (2)
From equation 1 put y in equation 2
x + x + 9 = 41
2x + 9 = 41
2x = 41 - 9
2x = 32
x = 32/2
x = 16
Now put this x =16 in equation 1
y = 16 + 9
y = 25
Thus, the required Jiri age is 25 years
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Johnny picks up a baseball and throws it to Rob who is exactly 130 feet away at a direction of 50 degrees. Rob then throws the ball to Patrick who is 50 feet from Rob in a direction of 30 degrees. Find the exact distance and direction that Patrick is from Johnny.
I need to sketch a triangle.
The exact distance and direction that Patrick is from Johnny is; 177.81 ft and 215.52°
How to utilize trigonometric ratios?Let the distance of Johnny to Patrick be x.
The angle opposite x would be; (90 - 50) + 90 + 30 = 160°
We will therefore use the cosine rule to find x;
X² = A² + B² - 2ABcosx
Where;
A and B are the distance of Johnny to Rob and Rob to Patrick respectively. Thus;
X² = 130² + 50² - 2(130)(50)cos160
X²= 16900 + 2500 + 12216.004
X² = 31616.004
X = 177.81 ft
To get the direction "y" we will use sine rule;
50/siny = 177.809/sin160
50/siny = 177.809/0.342
50/siny = 519.9094
Siny = 50/519.904
Siny = 0.09617
y = sin⁻¹(0.09617)
y = 5.52°
The bearing of Patrick from Johnny is;
5.52 + 30 + 180 = 215.52°
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When the sum of a number and 3 is subtracted from 10 the result is 5 solve om algebraic equation?
Answer:
y = 2
Step-by-step explanation:
Algebraic Equation is an equation where alphabets are used to represent numbers.
Solving the above question,
Let the number = y
Therefore,
Sum of the number = y + 3
If it's subtracted from 10 it becomes
10 - ( y + 3 )
The result : 10 - y - 3 = 5
- y = 5 - 10 + 3
- y = -2
Therefore,
y = 2
can two equilateral triangles always be congrunet ? give resons
SOLUTION :
YES as well as NO , two equilateral ∆s can be congruent if any of their side matched to one another,
& CANNOT be congruent if any of their side didn't matched in terms of length (magnitude).
________________________________
MARK BRAINLIEST!
1!+2(2!)+3(3!)+...+n(n!)=(n+1)!-1
Step-by-step explanation:
OK, let's assume it this way:
Sn=1.1!+2.2!+3.3!+...+n.n!=(2‐1).1!+(3-1).2!+(4-1)3!+...+((n+1)-1).n!
Sn=1.1!+2.2!+3.3!+...+n.n!=(2‐1).1!+(3-1).2!+(4-1)3!+...+((n+1)-1).n!=(2.1!-1!)+(3.2!-2!)+(4.3!-3!)+...+((n-1)n!-n!)=(2!-1!)+(3!-2!)+(4!-3!)+
Sn=1.1!+2.2!+3.3!+...+n.n!=(2‐1).1!+(3-1).2!+(4-1)3!+...+((n+1)-1).n!=(2.1!-1!)+(3.2!-2!)+(4.3!-3!)+...+((n-1)n!-n!)=(2!-1!)+(3!-2!)+(4!-3!)+...+(n+1)!-n!=(n+1)!-1!=(n+1)!-1
and boom problem solved
What is the measure of
Which function is graphed?
Answer: [tex]f(x)=\begin{cases} x^2 +4, x < 3 \\ -x+4, x \geq 3 \end{cases}[/tex]
Step-by-step explanation:
By inspection, we know the equation of the parabola is [tex]y=x^2 +4[/tex] and the equation of the line is [tex]y=-x+4[/tex].
Since there is an open hole at x=3 for the parabola and a closed hole at x=3 for the line, the function is
[tex]f(x)=\begin{cases} x^2 +4, x < 3 \\ -x+4, x \geq 3 \end{cases}[/tex]
Please Solve the equation by factoring: x2+2x−15=0
Answer:
x = 3, -5
Step-by-step explanation:
I just know
Answer:
x= -5
x=3
Step-by-step explanation:
You are factoring here. The standard form of an equation is Ax² + Bx + C.
The 2 factors must multiple together to be C, but add together to be B. The easiest way to do this is to factor C.
C is -15. Factoring this, we find the only factors of 15 that will add together to be 2 are 5 & -3.
Therefore, the factors are (x+5) and (x-3). If you set each of these factor pairs to 0 and solve, the answers are:
x+5=0
x = -5
x-3 = 0
x=3
I need help figuring out any details that are in this graph and what you can make of it.
The graph shows the comparison of the human welfare and ecological footprints.
What is a graph?A graph simply means a diagram that shows the relationship between variables.
From the graph, it can be seen that countries such as Norway, Canada, USA, and Australia meet the minimum criteria for sustainability.
The graph also shows that Sierra Leone is the least developed country among the countries compared as it has the lowest human development index.
The threshold for high human development as given as 0.8. Most African countries had a human development index of 0.5 and below.
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A line passes through the point −8, 4 and has a slope of −3/4.
Answer:
y = (-3/4)x + 2
Step-by-step explanation:
y = m * x + b where m is the slope and b is the y-intercept
y = (-3/4)x + b substituting the slope
4 = 6 + b => b = 2 substituting the point given
y = (-3/4)x + 2
There are 18 apple candies and 12 cherry candies mixed in a bag. If one candy is chosen from that bad, the odds of picking an apple candy are:
A: 1 out of 18
B: 2 out of 5
C: 3 out of 5
D: 3 out of 8
What is the area of a poster that is 1 1/2 feet by 2 1/2 feet?
The area of the poster is 28.75 feet square.
How to determine the areaNote that the area of a rectangle is given as;
Area = length × width
Length = 11. 5 feet
Width = 2. 5 feet
Area = 11. 5 × 2. 5
Area = 28. 75 feet square
Thus, the area of the poster is 28.75 feet square.
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If $11,000 is invested in an account for 25 years. Find the value of the investment at the end of 25 years if the interest is:
If $11,000 is invested, $33,000 is the value of the investment at the end of 25 years if the interest is 8% simple interest and $75,333.23 is the value of the investment at the end of 25 years if the interest is 8% compounded annually. This can be obtained by using formulas for simple interest and compound interest.
What is the formulas of simple interest and compound interest?Simple interestA = P(1 +Rt/100) , P = principle amount ,R = rate of interest, t = time(in years)
Compound interest (annually)A = P(1 + R/100)^t , P = principal amount, R = rate of interest, t = time(in years)
What is the value of investment?
Given that,
P = $11,000 , R = 8%, t = 25 years
8% simple interestA = P(1 +Rt/100) = [tex]11000(1+\frac{(8)(25)}{100} )[/tex] = $33,000
8% compounded annuallyA = P(1 + R/100)^t = [tex]11000(1+\frac{8}{100} )^{25}[/tex] = [tex]11000(1.08 )^{25}[/tex] = $75,333.23
Hence If $11,000 is invested, $33,000 is the value of the investment at the end of 25 years if the interest is 8% simple interest and $75,333.23 is the value of the investment at the end of 25 years if the interest is 8% compounded annually.
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: If $11,000 is invested in an account for 25 years. Find the value of the investment at the end of 25 years if the interest is:
(a) 8% simple interest
(b) 8% compounded annually
Suppose that X is a Bernoulli random variable with success probability 0.8. (Note: If this number is not already rounded to two decimal places, round it to two decimal places before proceeding.)
Calculate the probability of failure.Round your answer to two decimal places and enter it as a decimal number (as opposed to a fraction percentage or a fraction).
Considering the probability of success of 0.8 in the Bernoulli trial, the probability of failure is of 0.2.
What is the probability of failure in a Bernoulli trial?
The probability of failure in a Bernoulli trial is one subtracted by the probability of a success.
In this problem, the probability of a success is of 0.8, hence the probability of failure is:
pF = 1 - 0.8 = 0.2.
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I am odd I am less than 40 both of my digits are perfect squares t-u=0
Answer:
19 or 14
Step-by-step explanation:
Since the number is odd you can disqualify all even numbers up to 40 including 0.
Next since this number has 2 digits you can take out all 1 digit numbers.
After that, find perfect squares that also are 1 digit each.
Lastly merge the combination of the numbers as each digit on each sides in such a way that the result is less than 40.
Someone help quickly pls :(
Assignment
Practice finding solutions to systems of equations using
substitution.
The value of x in this system of equations is 1.
3x + y = 9
y=-4x+10
1. Substitute the value of y in the first equation:
2. Combine like terms:
3. Apply the subtraction property of equality:
4. Apply the division property of equality:
What is the value of y?
y=
3x + (-4x+10) = 9
-x+10=9
-x=-1
x=1
Answer:
y = 6
Step-by-step explanation:
Solving system of linear equation using substitution method:3x + y = 9 ---------------(I)
y = -4x + 10 -----------------(II)
Substitute y = -4x + 10 in equation (I)
3x - 4x + 10 = 9
Combine like terms,
-x + 10 = 9
Subtract 10 from both sides. (subtraction property of equality)
-x = 9 - 10
-x = -1
Divide both sides by (-1). {Division property of equality}
[tex]\sf \dfrac{-x}{-1}=\dfrac{-1}{-1}\\\\ \boxed{x = 1}[/tex]
Now, substitute x = 1 in equation (II) and find the value of y.
y = -4*1 + 10
= -4 + 10
[tex]\sf \boxed{\bf y = 6}[/tex]