-2n + 3 = 8
-2n = 8 - 3
-2n = 5
n = -5/2
The following equations are givenEquation #1 3x+z+y=8Equation #2 5y-x=-7Equation #3 3z+2x-2y=15Equation #4 4x+5y-2z=-3a. is it possible to solve for any of the variables using only Equation #1 and Equation #27 Explain your answer. If possible, solve for the variables using only equations #1 and #2b. is it possible to solve for any of the variables using only Equation #1, Equation #2, and Equation #37 Explain your answer if possible, solve for the variables using only equations #1, #2, and #3c. if you found solutions in part b, do these solutions also hold for Equation #4?
Solution
(a). For any number of equations to be solved simultaneously, the number of equations, must be same as number of variables.
Hence, Equation (1) & (2) can't be solved simultaneously, because, only two equations are given to solve for 3 variables.
(b) From the explanation above, it is obvious that, Equation (1), (2), and (3), can be solved simultaneously, because, we have 3 variables (x, y, z), with 3 equations to solve with.
Next we do is to solve Equation (1), (2), and (3) simultaneously using substitution method.
[tex]\begin{bmatrix}3x+z+y=8\\ 5y-x=-7\\ 3z+2x-2y=15\end{bmatrix}[/tex]From the Equation 2, make y the subject of formula
[tex]\begin{gathered} 5y-x=-7 \\ 5y=-7+x \\ y=\frac{-7+x}{5} \end{gathered}[/tex]We substitute, for y in equation (1), and (3).
[tex]\begin{bmatrix}3x+z+\frac{-7+x}{5}=8\\ 3z+2x-2\cdot \frac{-7+x}{5}=15\end{bmatrix}[/tex]Simplifying,
[tex]\begin{bmatrix}z+\frac{-7+16x}{5}=8\\ 3z+\frac{14+8x}{5}=15\end{bmatrix}[/tex]make z the subject of formula
[tex]z=8-\frac{-7+16x}{5}[/tex]Substitute z in the second equation,
[tex]\begin{gathered} \begin{bmatrix}3\left(8-\frac{-7+16x}{5}\right)+\frac{14+8x}{5}=15\end{bmatrix} \\ simplifying \\ \begin{bmatrix}-8x+31=15\end{bmatrix} \\ simplifying \\ -8x=15-31=-16 \\ x=\frac{-16}{8}=-2 \end{gathered}[/tex]Now, we have the value of x, remaining y, and z, and we substitute the value of x = -2, in the equation above for z.
[tex]\begin{gathered} z=8-\frac{-7+16x}{5} \\ z=8-\frac{-7+16(2)}{5}=\frac{-7+32}{5} \\ z=\frac{25}{5}=5 \end{gathered}[/tex][tex]\begin{gathered} y=\frac{-7+x}{5}=\frac{-7+2}{5}=\frac{5}{5}=1 \\ y=1 \end{gathered}[/tex]Hence, x = -2, y = 1, z = 5
(c)
Next, we proof for the values of x, y, and z in equation (4)
Substitute, x = -2, y = 1, z = 5 in equation (4)
[tex]\begin{gathered} 4x+5y-2z=-3 \\ 4(-2)+5(1)-2(5)=-8+5-10=-13\ne-3 \\ \end{gathered}[/tex]Hence, the solution doesn't hold for the equation (4).
i need to solve c pls help were working on on srthemic sequence formula sn=n/2(u1+un)
Answer: 78,800
The formula is given as
Sn = n/2(u1 + Un)
Let n = 16
u1 = first term
Un = Last term
According to the table given
U1 = 6800
U16 = 3050
S16 = 16/2( u1 + u16)
S16 = 16/2(6800 + 3050)
Firstly, solve the expression inside the parenthesis
S16 = 16/2 (9850)
S16 = 8 x 9850
S16 = 78,800
The answer is 78,800
Find the measures of angles `CFE` and `DEF.` Explain or show your answer.
We can put a circle on quadrangle only if :
So,
7. Consider the line below.A. Find two points on this line with whole number coordinates.B. Find an equation for this line in point slope form.C. Find the equation for this line in slope intercept form. Be sure to show your work-550-5
Let take the x-intercept and the y-intercept.
• From the graph, the x-intercept (x-axis cutting point) is >>>
[tex](x_1,y_1)=(1,0)[/tex]• The y-intercept (y-axis cutting point) is >>>
[tex](x_2,y_2)=(0,-1)[/tex]Now, let's find the point slope and slope intercept form of the line.
B.Point Slope Form
[tex]y-y_1=m(x-x_1)[/tex]Where m is given by the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, let's substitute the the points and find the point slope form:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-0=\frac{-1-0}{0-1}(x-1) \\ y-0=\frac{-1}{-1}(x-1) \\ y-0=1(x-1) \end{gathered}[/tex]Thus, the point-slope form is
[tex]y-0=1(x-1)[/tex]C.The slope intercept form is given by
[tex]y=mx+b[/tex]Where
m is the slope and b is the y-intercept
Just re-arranging the point slope form will give us the slope intercept form. Shown below:
[tex]\begin{gathered} y-0=1(x-1) \\ y=1(x-1) \\ y=x-1 \end{gathered}[/tex]The slope intercept form is
[tex]y=x-1[/tex]Each side of a square is increased 5 inches. When this happens, the area is multiplied by 9. How many inches in the side of the original square?
The side of the original square is 2.5 inches
Define square.In geometry, a square is a flat shape with four equal sides and four right angles (90°). A square is an unique sort of parallelogram as well as an equilateral rectangle (an equilateral and equiangular one).
Let side of a square be x
The area of this square will be [tex]x^{2}[/tex]
The second square has a side that has 5 more,
Therefore, side of second square= x+5
The area of second square= [tex](x+5)^{2}[/tex]
Thee area of the second square which is 9 times the original square =
[tex](x+5)^{2}[/tex]= 9([tex]x^{2}[/tex])
use foil to multiply (x+5)(x5) = [tex]x^{2}[/tex]+10x+25 = 9[tex]x^{2}[/tex]
That is, 0 = 8[tex]x^{2}[/tex]-10x-25
Factoring quadratic expressions
0= (4x+5)(2x-5)
0 = 4x+5 or 0=2x-5
Therefore, x= -5/4 or x= 2.5.
Reject -5/4 as length cannot be negative and accept the value 2.5.
That is side of the original square x=2.5 sq in
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A sales person is given a choice of two salary plants plan one is a weekly salary of 800 plus 3% commission of sales. plan 2 is a straight commission of 11% of sales. how much in sales must she make in a week for both plans to result in the same salary
SOLUTION:
Let us represent the amount in sales that we are to calculate with "x".
For both plans to result in the same salary, we have;
Plan 1 = Plan 2
[tex]800\text{ + 3 \% of x = 11 \% of x}[/tex][tex]\begin{gathered} 800\text{ + 0.03x = 0.11x} \\ 800\text{ = 0.11x - 0.03x} \\ 800\text{ = 0.08x} \\ \\ \frac{0.08x}{0.08}\text{ = }\frac{800}{0.08} \\ \\ x\text{ = 10,000} \end{gathered}[/tex]The amount in sales she must make in a week for both plans to result in the same salary is 10,000
Find a.Round to the nearest tenth:2 cmс1501050a=a = [ ? ]cmLaw of Sines: sin A=sin Bb=sin Cсa
In the given triangle ABC ,
Sum of the angles of of a triangle is 180 degrees.
Therefore,
[tex]\begin{gathered} \angle A\text{ + }\angle B\text{ + }\angle C\text{ = 180} \\ \angle A\text{ + 105 + 15 = 180} \\ \angle A=\text{ 180 - 120} \\ \angle A\text{ = 60} \end{gathered}[/tex]By using sine rule,
[tex]\frac{a}{\sin A}\text{ = }\frac{b}{\sin B}[/tex]Substituting the given values in the given equation,
[tex]\begin{gathered} \frac{a}{\sin60}\text{ = }\frac{2}{\sin 105} \\ a\text{ = }\frac{2\sin 60}{\sin 105} \\ a\text{ = 1.7931 } \\ a\text{ }\approx\text{ 1.8 }cm \end{gathered}[/tex]Which equation represents a line which is parallel to the line y = 1/3x +6x+3y=243y-x=-183y−x=−183x-y=73x−y=73x+y=-83x+y=−8
Recall that two lines are parallel if they have the same slope.
Now, the given equation is in the form
[tex]y=mx+b,[/tex]where m is the slope. Therefore, the slope of the given line is
[tex]\frac{1}{3},[/tex]and it has to be the slope of the parallel line.
Taking the options to their slope-intercept form, we can determine which equation represents a parallel line to the given line.
Answer: An equation of the form:
[tex]y=\frac{1}{3}x+b\text{.}[/tex]Where b is a constant.
TS and TV are tangent to circle P. What is the value of x?
tangent = tangent
x^2-1 = 24
Add 1 to each side
x^2 -1 +1 = 24+1
x^2 = 25
Take the square root of each side
sqrt(x^2) = sqrt(25)
x = 5
x cannot be negative, because distances cannot be negative
Complete the function table.Input (n) Output (n + 5)-242
Answer
To complete the table, you need to substitute the values of the inputs (n) given into the output (n+5) given.
Football game admission is $2.00 for general admission and $6.50 for reserved seats . The receipts were $3953.00 for 1297 paid admissions .How many of each ticket were sold? (round to the nearest intergar if necessary .) ___ general admission tickets sold .____reserved seating tickets sold.
Let x represent the number of general admission tickets sold.
Let y represent the number of reserved seating tickets sold.
We were told that general admission ticket costs $2 each and reserved seating ticket costs $6.50 each. This means that the cost of x general admission tickets and y reserved seating tickets would be
2x + 6.5y
The total amount received was $3953. It means that
2x + 6.5y = 3953
Also, the total number of tickets sold was 1297. It means that
x + y = 1297
x = 1297 - y
Substituting x = 1297 - y into 2x + 6.5y = 3953, it becomes
2(1297 - y) + 6.5y = 3953
2594 - 2y + 6.5y = 3953
- 2y + 6.5y = 3953 - 2594
4.5y = 1360
y = 1360/4.5
y = 302.22
Rounding to the nearest integer,
y = 302
x = 1297 - y = 1297 - 302
x = 995
995 general admission tickets were sold .
302 reserved seating tickets were sold
y-(-4)= x-(-5)what is y
In this figure, the curve y= 3x+2-2x^2 cuts the x-axis at two points A and B, and the y-axis at the point C. Find the coordinates of A, B and C
To find the x-coordinates of A and B, find the zeroes of the equation (set y=0 and solve for x).
[tex]y=3x+2-2x^2[/tex]If y=0 then:
[tex]0=3x+2-2x^2[/tex]Writing this quadratic equation in standard form, we get:
[tex]2x^2-3x-2=0[/tex]Use the quadratic formula to find the solutions for x:
[tex]\begin{gathered} \Rightarrow x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(2)(-2)}}{2(2)} \\ =\frac{3\pm\sqrt[]{9+16}}{4} \\ =\frac{3\pm\sqrt[]{25}}{4} \\ =\frac{3\pm5}{4} \\ \Rightarrow x_1=\frac{3+5}{4}=\frac{8}{4}=2 \\ \Rightarrow x_2=\frac{3-5}{4}=\frac{-2}{4}=-\frac{1}{2} \end{gathered}[/tex]Then, the x-coordinate of A is -1/2, and the x-coordinate of B is 2. Both the y-coordinate of A and B are 0.
On the other hand, to find the y-coordinate of C, which is the point where the graph crosses the Y-axis, replace x=0:
[tex]\begin{gathered} y=3(0)+2-2(0)^2 \\ =2 \end{gathered}[/tex]Therefore, the coordinates of A, B and C are:
[tex]\begin{gathered} A(-\frac{1}{2},0) \\ B(2,0) \\ C(0,2) \end{gathered}[/tex]
Which of the following illustratesthe associative property ofmultiplication?Enter a, b, c, d, or e.(a + b)(cd) =a. acd + bcdb. (b + a)(cd)c. (ac + bc)d d. [(a + b)c]de. (cd)(a + b)
The associative property of multiplication states that
[tex](a\cdot b)\cdot c=a\cdot(b\cdot c)[/tex]Given that (a+b)(cd), then its associative counterpart is
[tex](a+b)\mleft(cd\mright)=\lbrack(a+b)c\rbrack d[/tex]Write a quadratic equation in factored form if it has x-intercepts 2 and -1 and y-intercept 6.
We have to write a quadratic equation, in factored form, that has an x-intercept at x=2 and x=-1, and a y-intercept 6.
As the x-intercepts are the roots of the function, we can write the equation as:
[tex]y=a(x-2)(x+1)[/tex]The parameter a will be defined in order to have a y-intercept at y=6. That means that, when x is 0, the value of the function is y=6.
Then, we can replace x with 0 and y with 6 and find the value of a:
[tex]\begin{gathered} y=a(x-2)(x+1) \\ 6=a(0-2)(0+1) \\ 6=a(-2)(1) \\ 6=-2a \\ a=\frac{6}{-2} \\ a=-3 \end{gathered}[/tex]With the value of a=-3, we can write the factorized form of the equation as:
[tex]y=-3(x-2)(x+1)[/tex]Graph:
Answer: y=-3(x-2)(x+1)
You leave your house and run 6 miles due west followed by 3.5 miles due north. At that time, what is your bearing from your house?
N 60° W
Explanation
Step 1
draw the situation
we have a right triangle, so we can use a trigonometric function to find the missing angle,
then
Let
[tex]\begin{gathered} \text{opposite side= 3.5 m} \\ \text{adjacent side=6 mi} \end{gathered}[/tex]so, we need a function that relates those values
[tex]\tan \alpha=\frac{opposite\text{ side}}{\text{adjacent side}}[/tex]replace
[tex]\begin{gathered} \tan x=\frac{3.5}{6} \\ \text{ Inverse tan in both sides} \\ \tan ^{-1}(\tan x)=\tan ^{-1}(\frac{3.5}{6}) \\ x=30.25 \\ \text{rounded } \\ x=30\text{ \degree} \end{gathered}[/tex]so, the direction is
N 60° W
3) Select all ratios that are equivalent to 4:5 A. 2: 2.5 B. 2:3 C. 3: 3.75 D. 7:8 E. 8:10 F. 14: 27.5
For two ratios to be equivalent, its means and extremes if multiplied must be equal to each other.
[tex]\begin{gathered} \frac{a}{b}=\frac{c}{d} \\ ad=bc \end{gathered}[/tex]Let's start with Option A.
[tex]\begin{gathered} \frac{4}{5}=\frac{2}{2.5} \\ 4\times2.5=2\times5 \\ 10=10 \end{gathered}[/tex]Since they are equal, then Option A is equivalent to 4/5.
Let's check Option B.
[tex]\begin{gathered} \frac{4}{5}=\frac{2}{3} \\ 4\times3=2\times5 \\ 12\ne10 \end{gathered}[/tex]Let's check Option C.
[tex]\begin{gathered} \frac{4}{5}=\frac{3}{3.75} \\ 4\times3.75=5\times3 \\ 15=15 \end{gathered}[/tex]Let's check Option D.
[tex]\begin{gathered} \frac{4}{5}=\frac{7}{8} \\ 4\times8=5\times7 \\ 32\ne35 \end{gathered}[/tex]Let's check Option E.
[tex]\begin{gathered} \frac{4}{5}=\frac{8}{10} \\ 4\times10=5\times8 \\ 40=40 \end{gathered}[/tex]FInally, let's check Option F.
[tex]\begin{gathered} \frac{4}{5}=\frac{14}{27.5} \\ 4\times27.5=5\times14 \\ 110\ne70 \end{gathered}[/tex]Hence, only Option A, Option C, and Option E are equivalent to ratio 4/5.
What is the y-intercept of function f? f(x)={-3x-2, -infinity
======================================================
Explanation:
The y intercept always occurs when x = 0.
Visually this is where the function curve crosses or touches the vertical y axis.
The input x = 0 fits into the interval [tex]-2 \le \text{x} < 3[/tex] since [tex]-2 \le 0 < 3[/tex] is a true statement. This means we'll go for the second piece of the piecewise function.
Plug x = 0 into this middle piece to get...
f(x) = -x+1
f(0) = -0+1
f(0) = 1
Does the following equation represent a growth of a decay of an exponential function? What isthe rate of the growth/decay?y = 1/2(1.5)^x
It represents a growth
The growth rate is 1.5
the equation 0 -b=-b is an example of which property
Recall that the identity property of addition states that:
[tex]0+x=x+0=x\text{.}[/tex]Answer: Third option.
In a game, a spinner with 8 equally sized sections numbered 1 to 8 is spun and a die is tossed. What is the probability of landing on an odd number on the spinner and rolling aneven number on the die?
ANSWER
1/4
EXPLANATION
The spinner has 8 equally sized sections numbered 1 to 8.
The die has 6 faces.
On the spinner there are 4 sections with odd numbers and 4 sections with even numbers.
On a die, there are 3 faces with even numbers and 3 faces with odd numbers.
To find the probability of both events occuring, we need to find their individual probabilities and then multiply them together.
The probability of landing on an odd number on the spinner is:
4/8 i.e. 1/2
The probability of rolling an even number on the die is:
3/6 i.e. 1/2
Therefore, the probability of landing on an odd number on the spinner and rolling an even number on the die is:
[tex]\begin{gathered} \frac{1}{2}\cdot\text{ }\frac{1}{2} \\ \text{= }\frac{1}{4} \end{gathered}[/tex]what is the degree of the polynomial5z^3-2z^4-9z^2+z
The degree of a polynomial is the highest power in the inividual terms
Hence the degree of this polynomial is 4
PLEASE HELP ME
Describe the transformation that was performed on parallelogram EFGH to create parallelogram E’F’G’H’. Show or explain how you got your answer.
The transformation of (x,y) from EFGH to E'F'G'H' is (x + 4, y - 2).
We can see that the coordinates of E are (3,6) and the coordinates of E' are (7,4)
Hence, we can see that,
x coordinate is increased by 3 and y-coordinate is decreased by 2.
Also, the coordinates of F are (5,6) and the coordinates of F' are (9,4).
Here also, x coordinate is increased by 3 and y-coordinate is decreased by 2.
This is happening in all vertices of the parallelogram.
Hence,
The transformation of (x,y) from EFGH to E'F'G'H' is (x + 4, y - 2).
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An equation is shown below:5(2x − 3) = 5Part A: How many solutions does this equation have? (4 points)Part B: What are the solutions to this equation? Show your work.
Part A
The given equation is
[tex]5(2x\text{ -3\rparen=5}[/tex]as there is only one variable, the equation either has 1 solution or no solution. However, note that on the left we have a polynomial of degree 1 (a line), whenever we make it equal to a constant, we always have a solution. So in this case the solution is 1.
Part B
Now, to solve this equation first we divide both sides by 5. So we get
[tex]2x\text{ -3=1}[/tex]Then, we add 3 on both sides to get
[tex]2x=1+3=4[/tex]Finally we divide both sides by 2 to get
[tex]x=\frac{4}{2}=2[/tex]so the unique solution of the equation is x=2
On the coordinate plane, rectangle WXYZ has vertices W(–
3,–
7), X(3,2), Y(6,0), and Z(0,–
9).
What is the area of rectangle WXYZ? If necessary, round your answer to the nearest tenth.
The area of rectangle WXYZ is 39 units sq.
What is the distance between two points?Distance between two points is the length of the line segment that connects the two given points and is find by formula
√ (x2 -x1)² + (y2-y1)²
Given that, On the coordinate plane, rectangle WXYZ has vertices W(-3,-7), X(3,2), Y(6,0), and Z(0,-9).
In the given rectangle, WX = YZ
Area of rectangle = length*width
Here, length = XY and width = WX
XY = √(6-3)²+(0-2)² = √13 units
WX = √(3+3)²+(2+7)² = √117 units
Area = XY*WX = √13*√117 = 39 units sq.
Hence, the area of rectangle WXYZ is 39 units sq.
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write the function value in term of the cofunction of a complementary angle .
Answer:
Explanations:
Note that the secant and cosecant functions are cofunctions and are also complements.
Therefore, they are related mathematically as:
csc x = sec ( 90° - x)
x = 64°
csc 64° = sec (90° - 64°)
csc 64° = sec 26
The landscaper recommended a mix of 3 pounds of rye grass seed with 44 pound of blue grass.seed. If the lawn needs 544 pounds of rye grass seed; how many pounds of blue grass seed would that be?
Let's use a rule of three:
Therefore,
[tex]\begin{gathered} x=\frac{544\cdot44}{3} \\ \Rightarrow x=7978.67 \end{gathered}[/tex]We would neeed 7978.67 lb of blue grass seed.
9) At Go and Shop, apples cost $3 each and oranges cost $2.50 each. Maggie bought three times as manyapples as she did oranges. If her total was $46, how many of each fruit did she buy?
We have:
Let x = number of apples
Let y = number of oranges
Maggie bought three times as many apples as she did oranges, this is:
x = 3y
$3 each apple
$2.50 each orange
Total cost $46
Then, we have the expression:
[tex]3x+2.50y=46[/tex]Next, solve the system of equations:
we replace x = 3y in the second equation
[tex]3(3y)+2.50y=46[/tex]And solve for y
[tex]\begin{gathered} 9y+2.50y=46 \\ 11.5y=46 \\ \frac{11.5y}{11.5}=\frac{46}{11.5} \\ y=4 \end{gathered}[/tex]Therefore, x is:
[tex]undefined[/tex]I need help with my math
Answer
5².2÷10 + 3.2 - 1 = 10
Explanation
To solve this, we will use the order of operation mnemonic to solve it.
PEMDAS explains that we solve the expression with power first, then multiplication, division and then the addition and then subtraction
5².2÷10 + 3.2 - 1
= (25.2÷10) + (3.2) - 1
= (50÷10) + 6 - 1
= 5 + 6 - 1
= 11 - 1
= 10
Hope this Helps!!!
which of the following values are solutions to the inequality -6<-7-4x?1. 12. -83. 5or none
The Solution:
Given:
Required:
Find f(2):
[tex]\begin{gathered} f(2)=\sqrt{[(-5\times2)+14]}=\sqrt{-10+14}=\sqrt{4}=2 \\ \\ f(2)=2 \end{gathered}[/tex]Find g(-5):
[tex]\begin{gathered} g(-5)=\frac{-5}{(-5)^2-7}=\frac{-5}{25-7}=-\frac{5}{18} \\ \\ g(-5)=-\frac{5}{18} \end{gathered}[/tex]Find h(-1/2):
[tex]\begin{gathered} h(-\frac{1}{2})=|6(-\frac{1}{2})|-9=|-3|-9=3-9=-6 \\ \\ h(-\frac{1}{2})=-6 \end{gathered}[/tex]Answer:
f(2) =
[tex]-6<-7-4x[/tex]now we can solve the inequalty for x by passing the -7 to the other side:
[tex]\begin{gathered} 7-6<-4x \\ 1<-4x \end{gathered}[/tex]Now to change the sign of the -4x we have to invert the inequality:
[tex]\begin{gathered} -1>4x \\ \frac{-1}{4}>x \end{gathered}[/tex]so the only solution is -8 and we can prove it:
[tex]-6<-7-4(-8)[/tex]