The linear system of equation has one solution as x = 16 and y = -12.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
The given system of equation are :
y=-x+4..........(1)
x + 2y = -8......(2)
Now, solving the above using substitution of y in equation (2) :
x + 2y = -8
x+2(-x+4) = -8
x-2x+8 = -8
-x = -16
x = 16
Now, substituting back x value in equation (1) we get :
y = -x+4
y = -16 +4
y = -12
Therefore, The linear system of equation has one solution as x = 16 and y = -12.
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John buys a phone for $4 500 and sells it to his brother who pays him in three instalments of $1 200.
(a) Determine with the appropriate working if John made a profit or a loss. [2] (b) What was his percentage profit/loss?
a decimal point is used when working with dollars but the decimal point is not necessary when working with cent for each dollar amount give the equivalent amount expressed as cents $5.74 and $0.16
A decimal point is used when working with dollars but the decimal point is not necessary when working with cent for each dollar amount, the equivalent amount expressed as cents of $5.74 is 574 cents and $0.16 is 16 cents
We know that 1 dollar is equal to 100 cents
So, x dollar = x(100) cents
For $5.74 = 5.74(100) cents
= 574 cents
For $0.16 = 0.16(100) cents
= 16 cents
What is a decimal point?Integer and non-integer numbers are represented using the decimal numeral system, also known as the base-ten positional numeral system, denary, or decanary. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the term used to describe how numbers are represented using the decimal system.
It is indicated by a '.', for instance, 3.14
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After 30 baseball games Aaron Smith had 24 hits. If after 100 games he had 80 hits, what is his average hits per baseball game?
Aaron Smith would has average hits per baseball game as 0.79 hits per game.
What is the interpretation of average?Average provides ill information in case of skewed data.
Arithmetic mean is the best central measure available for representing the values of a data set. It is also called average of the values of the considered data set. It serves as predicted value(in case no other information of the data is available) of that data set.
WE have been given that After 30 baseball games Aaron Smith had 24 hits. If after 100 games he had 80 hits, then he would has average hits per baseball game;
Average = Hits in game / number of games
Average = 24- 80 / 30-100
Average = 56 / 70
Average = 0.79 hits per game
Hence, Aaron Smith would has average hits per baseball game as 0.79 hits per game.
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Find the LCM and
GCF of: 25 and 100
Answer:
Look below
Step-by-step explanation:
The LCM of 25 and 100 is 100
The GCF of 25 and 100 are 25.
Find an equation for the line graphed below:
Answer: y = -1/5x -3
Step-by-step explanation:
Answer:
Answer given by bryc31 is correct: [tex]y = -\frac{1}{5}x -3[/tex] is correct
I am simply providing an explanation in case you need it
Step-by-step explanation:
The slope-intercept form equation of a straight line in 2D coordinates is given by y = mx + b
where m is the slope(rise/run) and b the y-intercept i.e. the y value where the line intersects the y axis
Given two points (x₁, y₁) and (x₂, y₂) on the straight line, we can compute the slope as follows
m = [tex]\frac{y_2 - y_1}{x_2-x_1}[/tex]
Two distinct points on the line are at (0, -3) and (5,-4)
[tex]m = \frac{-4 -(-3)}{5-0} = \frac{-4 + 3)}{5-0} = \frac{-1}{5} = - \frac{1}{5}[/tex]
So we know the equation to be
[tex]y = - \frac{1}{5}x + b[/tex]
To find b, take any point on the straight line, plug in y and x values in the above equation and solve for b
However, looking at the graph we see that the line crosses the y axis at
y = -3. So this is the value for the y intercept i.e. b
The equation of the line is therefore
[tex]y = - \frac{1}{5}x - 3[/tex]
Figure LMNO is dilated to form figure L'M'NO'.
Where is the center of dilation located?
inside figure LMNO
outside figure LMNO
on a vertex of figure LMNO
L
M
L'
M'
O
-0'-
The location of a center of dilation in the figure is at the point where the corresponding vertex of the pre–image and image overlaps, which is point N, the correct option is therefore;
On a vertex of figure LMNOHow can the center of dilation be found?The given pre–image = Parallelogram LMNO
The image obtained from the pre–image = Parallelogram L'M'N'O'
Required: The location of the center of dilation
Solution:
The center of dilation is the point about which the figure or image is dilated.
It is the point that does not change following the dilation.
A vertex on the pre–image that gives an image vertex at the same point, is at the center of dilation which does not change in both the pre–image and image.
Therefore, given that point N and N' coincides, which indicates that the distance the pre–image point N is dilated to get the image point, N is 0. The center of dilation is at the vertex N.
The correct option is therefore;
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Answer:
On a vertex of figure LMNO
Step-by-step explanation:
For the function f(x) = (2e)5, find
ƒ−¹(x).
Answer:
no
Step-by-step explanation:
89382
Find the HCF:
3x³ + 15x² and 2x³ - 50x
H.C.F of 3x³+15x² and 2x³-50x is x(x+5)
What is Number system?A number system is defined as a system of writing to express numbers.
The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.
3x³ + 15x²
Factorize the given expression by taking out 3x²
3x²(x+5)
and the expression 2x³ - 50x
2x(x²-25)
2x(x+5)(x-5)
H.C.F of 3x³+15x² and 2x³-50x is x(x+5)
Hence, H.C.F of 3x³+15x² and 2x³-50x is x(x+5)
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The speed of an object is given by the following formula: where s is the speed of the object, d
is the distance traveled in miles, and t is the time traveled in hours. If a car travels 312 miles at a
rate of 52 mph, how long did it take?
A map is drawn to a scale of 1/2 inch = 20 miles How many miles apart are two cities that are 3 1/4 inches apart on the map?
Work Shown:
1/2 = 0.5
1/4 = 0.25
0.5 inch = 20 miles, which is the given scale
1 inch = 40 miles, after multiplying both sides by 2
3.25 inches = 130 miles after multiplying both sides by 3.25
the angle bisector bisect the opposite side inti the two length ,2 and 4 unit long. the length of the height on that side is 225 units. determine the length of the other two sides of a triangle.
The lengths of the other two sides of the triangle is 8√6 units.
What will be the length?
Given that,
AD is the angle bisector of ∠A .
BD = 2 units .
DC = 4 units .
AE ⟂ BC and √15 units .
So, AB / AC = BD / DC { By angle bisector theorem }
AB / AC = 2/4
AB / AC = 1/2 ......... Eqn.(1)
Also, BC = BD + DC = 2 + 4 = 6 units .
Now let BE = x units .
So, in right-angled ∆AEB ,
AB = √(15 + x²) { By pythagoras theorem }
In right angled ∆AEC ,
AC = √{15 + (x - 6)²} { By pythagoras theorem }
Putting both values in Eqn.(1),
AB/AC = 1/2
√(15 + x²)/√(15 + x² + 36 - 12x) = 1/2
Squaring both sides,
(15 + x²) / (x² - 12x + 51) = 1/4.
4(15 + x²) = x² - 12x + 51.
60 + 4x² = x² - 12x + 51.
4x² - x² + 12x + 60 - 51 = 0.
3x² + 12x + 9 = 0.
3x² + 3x + 9x + 9 = 0.
3x(x + 1) + 9(x + 1) = 0.
(3x + 9)(x + 1) = 0.
x = (-3) and (-1) .
Taking x = (-1),
AB = √(15 + x²) = √(15 + 1) = 4 units .
So, AC = 4 * 2 = 8 units .
Taking x = (-3),
AB = √(15 + 9) = √24 = 4√6 units.
So, AC = 2 * 4√6
= 8√6 units .
Hence, the lengths of the other two sides of the triangle is 8√6 units.
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The cubic function p(x) = ax^3 + bx^2 + cx + d has a tangent equation y = 3x + 1 at the point (0, 1) and has a turning point at (-1, -3). Find the values of a, b, c and d. ( Show all ways of solving this math) btw the answer is a = -5, b = -6, c = 3, d = 1. show me the clearest workout
Answer:
[tex]p(x) = -5x^3 -6x^2 + 3x + 1[/tex]
Step-by-step explanation:
Given cubic function:
[tex]p(x) = ax^3 + bx^2 + cx + d[/tex]
As point (0, 1) is on the curve, substitute x = 0 into the function, set it to 1, and solve for d:
[tex]\begin{aligned} p(0) & = 1\\ \implies a(0)^3 + b(0)^2 + c(0) + d & = 1\\ \implies d & = 1 \end{aligned}[/tex]
Differentiate the function:
[tex]\begin{aligned} p(x)& = ax^3 + bx^2 + cx + d\\\implies p'(x)&=3 \cdot ax^{3-1}+2 \cdot bx^{2-1}+1 \cdot cx^{1-1}+0 \\p'(x)&=3ax^2+2bx+c\end{aligned}[/tex]
The tangent equation at the point (0, 1) is y = 3x + 1.
Therefore, the gradient of the tangent equation when x = 0 is 3.
To find the gradient of the function at a given point, substitute the x-value of that point into the differentiated function. Therefore, substitute x = 0 into the differentiated function, set it to 3, and solve for c:
[tex]\begin{aligned}p'(0) & =3 \\ \implies 3a(0)^2+2b(0)+c & =3\\ \implies c & = 3\end{aligned}[/tex]
Substitute the found values of c and d into the function:
[tex]p(x) = ax^3 + bx^2 + 3x + 1[/tex]
Substitute point (-1, -3) into the function and solve for b:
[tex]\begin{aligned}p(-1) & = -3\\\implies a(-1)^3 + b(-1)^2 + 3(-1) + 1 & = -3\\-a+b-3+1&=-3\\-a+b&=-1\\b&=a-1\end{aligned}[/tex]
To find the turning points of a function, set the differentiated function to zero and solve for x.
As there is a turning point of function p(x) when x = -1, substitute x = -1 into the differentiated function and set it to zero (remembering to substitute the found value of c = 3 into the differentiated function):
[tex]\begin{aligned} p'(-1) & =0\\\implies 3a(-1)^2+2b(-1)+3 & = 0\\3a-2b+3&=0\end{aligned}[/tex]
Substitute the found expression for b into the equation and solve for a:
[tex]\begin{aligned}3a-2b+3&=0\\\implies 3a-2(a-1)+3&=0\\3a-2a+2+3&=0\\a+5&=0\\a&=-5\end{aligned}[/tex]
Finally, substitute the found value of a into the found expression for b and solve for b:
[tex]\begin{aligned}b & = a-1\\\implies b & = -5-1\\b & = -6\end{aligned}[/tex]
Therefore:
a = -5b = -6c = 3d = 1Differentiation Rules
[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\dfrac{\text{d}y}{\text{d}x}=nax^{n-1}$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{4cm}\underline{Differentiating a constant}\\\\If $y=a$, then $\dfrac{\text{d}y}{\text{d}x}=0$\\\end{minipage}}[/tex]
Determining the Input Value to Produce the Same Output Value for Two Graphed Functions A coordinate plane with 2 lines. The first line is labeled y equals f(x) and passes through (negative 1, 2), (0, 2), and (2, 2). The second line is labeled y equals g(x) and passes through (negative 0.5, negative 2), points at (0, negative 1), and (1, 1). The lines intersect at (1.5, 2). Use the graph to determine the input value for which f(x) = g(x) is true. x = 0.5 x = 1 x = 1.5 x = 2
Y equals f(x) is written on the first line, The second line, marked y = g(x). When the input is for either of the two functions, the result is x=0 and return the output is same value.
Given that,
Y equals f(x) is written on the first line, which also passes through (-1, 2), (0, 2), and (2, 2). The second line, marked y = g(x), points at (0, -1), passes through (-0.5, -2), and (1, 1). The lines come together at (1.5, 2).
We have to find the input value for which f(x) = g(x) is true using the graph. x = 0.5, x = 1, x = 1.5, x = 2.
The final two actions:
f(x)=-2/3(x+1)
g(x)=1/3(x-2)
The output are equation
f(x)=g(x)
-2/3(x+1)=1/3(x-2)
-2(x+1)=1(x-2)
-2x-2=x-2
-2x-x=-2+2
-x=0
x=0
When x = 0 is used as an input, the first two functions always return the same results.
f(x) traverses (-1,2), (0,2), and (2,2)
The paths that g(x) takes are (-0.5,-2), (0,-1), (1,1)
Therefore, When the input is for either of the two functions, the result is x=0 and return the output is same value.
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make it simple its x=1.5
You are recording intake and output for your patient who has fluid restrictions of 1,000 milliliters per day. During the past 24 hours, the patient has consumed 3 fluid ounces of milk. 725 milliliters of IV fluid and 4 fluid ounces of juice with the potassium supplement. If one fluid ounce is equal to 30 milliliters, how many milliliters of fluids did the patient consume in 24 hours?
The patient consumed 935 milliliters of fluids in 24 hours.
Restrictions of fluid per day = 1000 milliliters
Consumption of fluid by patient in past 24 hours are :
Milk = 3 ounces
IV fluid = 725 Milliliters
Juice = 4 ounces
As we know that,
One fluid ounce = 30 milliliters
Then, Milk = 3 × 30 = 90 milliliters
Juice = 4 × 30 = 120 milliliters
To determine the total amount of fluids we will add the total amount of Milk, IV fluids and Juice.
Fluids consume by patient = 90 + 725 + 120
= 935 milliliters
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Assume the statements below are true. If exactly two of the students went to the movies, who did NOT go to the movies?
If Catherine goes to the movies, then Jessika will go.
If Jessika goes to the movies, then Jorge will go.
If Jorge goes to the movies, then Mike will go.
Answer:Jorge and Mike
Step-by-step explanation:
Nobody goes if Mike goes
The probability of rain in Nevada is 0.3.
If it rains, the probability of the school bus being late is 0.4.
If it does not rain, the probability of the school bus being late is 0.15.
What is the probability that it will not rain?
If it does not rain, the probability of the school bus bring on time is?
What is the probability that it will rain and the school bus will be on time?
Based on the probability of rain in Nevada, the probability that it will not rain is 0.7.
The probability that if it does not rain, the school bus will be on time is 0.85.
The probability that it will rain and the school bus will still be on time is 0.6.
How to find the probability?The probability that it will not rain in Nevada can be found by the formula:
= 1 - probability of rain in Nevada
= 1 - 0.3
= 0.7
The probability that if it does not rain, the school bus will be on time is:
= 1 - probability of the school bus being late if it does not rain
= 1 - 0.15
= 0.85
The probability that it will rain and the school bus will still be on time is:
= 1 - probability of the school bus being late if it rains
= 1 - 0.4
= 0.6
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The height, above the ground, of a block on a vertical spring is a sinusoidal (trigonometric) function of time. In the interval from time 2.1 seconds to time 2.7 seconds, the block's height decreases from its maximum of 48 inches to its minimum of 30 inches. Which function h(t) could model the block's height in inches above the ground at time t seconds?
The sinusoidal function for the given conditions can be written as h(t) = 9cos(1.67π(x - 2.1)) + 39.
What is sinusoidal function?The term sinusoidal refers to a curve, also known as a sine wave or a sinusoidal, that shows smooth, periodic oscillation. It is named after the function y=sin (x). Sinusoidal appear often in mathematics, physics, engineering, signal processing, and many other fields.
A general form of a cosine function is given as shown below,
g(x) = a cos(bx+c) + d
Where the values of the given constant is,
a = amplitude
b = The period is of 2pi/B
c = phase shift
d = vertical shift
Since for the given condition the greatest value is 48 and the smallest value is 30 (a difference of 18), therefore, the amplitude is of the function can be written as,
2a = 18
a = 9
Further, a conventional cosine function with amplitude 9 would fluctuate between -9 and 9, while this one ranges between 30 and 48, resulting in d = 39 vertical shift.
Also, The minimum and maximum values form half the period, therefore, we can write,
π/B = 2.7 - 2.1
B = π/0.6
B = 1.67π.
Furthermore, The maximum value in the normal function is at x = 0, but the greatest value in this function is at x = 2.1, thus, the phase shift is 2.1 units to the right, or c = -2.1.
Hence, the sinusoidal function for the given conditions can be written as h(t) = 9cos(1.67π(x - 2.1)) + 39.
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(-2/3)(6/7)
Please show work if possible!
Find the average rate of change of
The average rate of change of f(x)=[tex]8x^{2} -5[/tex] on the interval [4,b] is [tex]\frac{128-8b^{2} }{4-b}[/tex]
Given,
The function f(x) =[tex]8x^{2} -5[/tex]
The intervals = [4,b]
The average rate of change = [tex]\frac{f(a)-f(b)}{a-b}[/tex]
Where a and b are the interval
f(4)= [tex]8(4)^{2}-5[/tex]
=123
f(b)= [tex]8b^{2}-5[/tex]
The average rate of change = [tex]\frac{123-(8b^{2}-5) }{4-b}[/tex]
[tex]=\frac{123-8b^{2}+5 }{4-b} \\=\frac{128-8b^{2} }{4-b}[/tex]
Hence, The average rate of change of f(x)=[tex]8x^{2} -5[/tex] on the interval [4,b] is [tex]\frac{128-8b^{2} }{4-b}[/tex]
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=?
२०
21090 (x -1 ) + 109.07 = 1
)
The value of "x" which will satisfy the equation [{21090(x -1 ) + 109.07 } = 1] is 1.01.
As per the question statement, we are provided with an equation [tex][{21090(x -1 ) + 109.07 } = 1][/tex].
We are required to solve the above mentioned equation for "x", such that the value of x when substituted in the equation, satisfies the same.
To solve this question, we will simply use the methods of rearranging and opening up of brackets, as shown below.
[tex][{21090(x -1 ) + 109.07 } = 1] \\or, 21090x - 21090+109.07=1\\or, 21090x - (21090-109.07)=1\\or, 21090x - 20980.93=1\\or, 21090x=(1+20980.93)\\or, 21090x=20981.93\\or,x=\frac{21090}{20981.93}\\or,x=1.00515\\or,x=1.01[/tex]
Therefore, the value of "x" which will satisfy the equation
[{21090(x -1 ) + 109.07 } = 1] is 1.01.
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Select the best answer for the question.
12. Which set is an example of like fractions?
A. 1/2 and 3/2
B.2/1 and 2/3
C. 10/10 and 5/5
D. 7/4 and 4/7
Answer:
A. 1/2 and 3/2
Step-by-step explanation:
You want to identify like fractions among the sets {1/2, 3/2}, {2/1, 2/3}, {10/10, 5/5}, and {7/4, 4/7}.
Like fractionsLike fractions are fractions that have the same denominator. Among the sets offered, the only one with denominators the same is ...
{1/2, 3/2}
7.) Given 9x-27y = 81
D.) Does the line RISE or fall?
E.) Why?
Answer: rises; your slope is positive
Every single time your slope is positive, your line goes upward.
Every time your slope is negative, however, your line goes downward.
Rearrange 9x - 27y = 81 to -27y = -9x + 81 because we want to put our equation into slope intercept so that we can eventually get our 'y' all by itself.
Divide by -27 for every variable.
Your slope intercept form should now look like this; y = 1/3x - 3
Now that we're completely done or that we have 'y' by itself, it's safe to say that our answer is 1/3, which is, also, positive.
Hope this helps, dawg.
how many liters make a kilogram
Answer:
One litre of water has a mass of almost exactly one kilogram.kilograms = liters × density of a liquid.
2. Find the roots of the polynomial equation (point)
2x³ + 2x2-19x+ 20 = 0
Answer:
x=-4
Step-by-step explanation:
this is if by roots, the problem is asking for the zeros of the equation
The circle below has center P, and its radius is 6in. Given that =m∠QPR170°, find the length of the major arc QSR.
The length of the major arc QSR is 39.77 inches
How to find the length of the major arc QSR?The given parameters are:
m∠QPR = 170 degree
Radius, r = 6 inches
The length of the major arc QSR is calculated as:
Arc length = (360 - Angle/360) * 2πr
Substitute the known values in the above equation
Arc length = (360 - 170/360) * 2 * 3.14 * 6
Evaluate the difference
Arc length = (190/180) * 2 * 3.14 * 6
Evaluate the product
Arc length = 39.77
Hence, the length of the major arc QSR is 39.77 inches
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What is the answer for this question 2 (6² +2²)÷4-10
Step-by-step explanation:
2 . (6² + 2²) ÷ 4 - 10
= 2 . (36 + 4) ÷ 4 - 10
= 2 . 40 ÷ 4 - 10
= 80 ÷ 4 - 10
= 20 - 10
= 10
The height above ground of a cannon is a function of the time since it was shot.
Question: When time equals 0, why is the height of the cannon ball not equal to 0? Describe the domain of this function. Describe the range.
The height of the cannonball not equal to 0 when time equals 0 because initial height of the cannonball is above the ground
When time equals 0, why is the height of the cannonball not equal to 0?From the graph, we have the y-intercept to be
y-intercept = (0, y), where y > 0
This means that the graph starts above the origin
This in other words mean that the initial height of the cannonball is above the ground (e.g. it could be on a building)
Hence, the height of the cannonball not equal to 0 when time equals 0 because initial height of the cannonball is above the ground
Describe the domain and the range of this functionIn this case, the domain is from t = 0 till the ball lands on the floor, while the range is from the initial height of the cannonball till the maximum height
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Maricopa's Success scholarship fund receives a gift of $ 115000. The money is invested in stocks,
bonds, and CDs. CDs pay 3.75 % interest, bonds pay 4.8 % interest, and stocks pay 7.2 % interest.
Maricopa Success invests $ 45000 more in bonds than in CDs. If the annual income from the
investments is $ 6322.5, how much was invested in each account?
stock=
bonds=
cds=
The value invested in each security will be:
stock= $38000 ,
bonds= $46000
cds= $3000
How to calculate the value?Let the money invested in stocks be 'x', bonds be 'y' and CDs be 'z'.
Total money received as fund = x+y+z = $115000 -(Eqn 1)
$15000 more is invesed in bonds as compared to CDs i.e y = z + $15000 - (Eqn2)
Stocks pay 6.8%, bonds pay 3.6% and CDs pay 4% interest
Interest earned from stocks = 6.8% of x = 0.068x
Interest earned from bonds = 3.6% of x = 0.036x
Interest earned from CDs = 4% of x = 0.04x
Total interest earned = 0.068x + 0.036y + 0.04z = $5840 - (Eqn 3)
x + y + z =$115000 ----(1)
y = z + $15000 -----(2)
0.068x + 0.036y + 0.04z = $5840 ------(3)
Putting y = z+$15000 in Eqn 1 gives us:
x + (z+$15000) + z = $115000 ==> x = $100000 - 2z ----(Eqn 4)
Similarly,
Putting y = z+$15000 in Eqn 3 gives us:
0.068x + 0.036(z+$15000) + 0.04z = $5480 ==> 0.068x + 0.076z = $4940 ----(Eqn 5)
Putting Eqn 4 in Eqn 5,
0.068($100000 - 2z) + 0.076z = $4940
Hence, 0.06z = $1860
z = $31000
Put z = $31000 in Eqn 4 and get x = $100000 - 2z = $38000
Put z = $31000 in Eqn 2 and get y = z + $15000 = $46000
Hence final answer: x = $38000 , y = $46000, z = $31000
where x is the money invested in stocks, y in bonds and z in CDs.
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g(x)=−5x+1, find g(1)
Answer:
-4
Step-by-step explanation:
keep value of x as 1 in 5x+1
g(1)=-5×1+1
=-4
Identify the terms for the simplified expression:
21x^3+3x^2-14x+9x^2+15x
Answer: 21x^3 + 3 + 12x^2 + x
Step-by-step explanation: