A. We have two lines: y = 4-x and y = 8-x^-1
Given two simultaneous equations that are both to be true, then the solution is the points where the lines cross. The intersection is where the two equations are equal. Therefore the solution that works for both equations is when
4-x = 8-x^-1
This is where the two lines will cross and that is the common point that satisfies both equations.
B. 4-x = 8-x^-1
x 4-x 8-x^-1
______________
-3 7 8.33
-2 6 8.5
-1 5 9
0 4 -
1 3 7
2 2 7.5
3 1 7.67
The table shows that none of the x values from -3 to 3 is the solution because in no case does
4-x = 8-x^-1
To find the solution we need to rearrange the equation to find for x:
4-x = 8-x^-1
Multiply both sides with x:
4x-x^2 = 8x-1
x^2+4x-1=0
x= -4.236, 0.236
Therefore there are two points that satisfies the equation.
Find y:
x=-4.236
y = 4-x = 4 – (-4.236) = 8.236
y = 8-x^-1 = 8-(-4.236)^-1 = 8.236
x=0.236
y = 4-x = 4 – (0.236) = 3.764
y = 8-x^-1 = 8-(0.236)^-1 = 3.764
Thus the two lines cross at 2 points:
(-4.236, 8.236) & (0.236, 3.764)
C. To solve graphically the equation 4-x = 8-x^-1
We would graph both lines: y = 4-x and y = 8-x^-1
The point on the graph where the lines cross is the solution to the system of equations.
Just graph the points on part B on a cartesian coordinate system and extend the two lines. The solution is, as stated, the point where the two lines cross on the graph.
The x-coordinates of the intersection points between the equations are the solutions to the given equation. Tables can be used to find the solution by plugging in different values of x. The equation can also be solved graphically by finding the intersection points of the two equations on a graph.
Explanation:Part A:
The x-coordinates of the points where the graphs of the equations y = 4−x and y = 8−x−1 intersect are the solutions of the equation 4−x = 8−x−1. To find the intersection points, we set the two equations equal to each other and solve for x.
Part B:
To find the solution to 4−x = 8−x−1, we can create a table by plugging in different integer values of x between -3 and 3. Substitute each value of x into the equation and solve for y. The values of x and y that make the equation true are the solutions.
Part C:
The equation 4−x = 8−x−1 can be solved graphically by plotting the two equations on a graph and finding the points of intersection. The x-coordinate of the intersection point(s) represents the solution(s) to the equation.
Max is in a control tower at a small airport. He is located 50 feet above the ground when he spots a small plane on the runway at an angle of depression of 27. What is the distance of the plane from the base of the tower? Round to the nearest foot. A. 25 feet B. 110 feet C. 56 feet D. 98 feet
The distance of the plane from the base of the tower is:
Option: D
D. 98 feet
Step-by-step explanation:Let x denotes the distance of the plane from the base of the tower.
Now, in the right angled triangle we will need to use trignometric identity corresponding to 63°.
Based on the figure we have:
[tex]\tan 63=\dfrac{x}{50}\\\\\\x=50\times \tan 63[/tex]
[tex]x=50\times 1.9626\\\\\\x=98.13\ feet[/tex]
which to the nearest feet is:
98 feet
QUESTION 18 I want to build a right triangular garden on the side of my house. Find the sides of the triangle if the hypotenuse is 6 feet and the two sides are equal in length.
What is the probability of drawing two yellow marbles if the first one is NOT placed back into the bag before the second draw? Their is 10 marbles total, 2 yellow, 3 pink, and 5 blue
Final answer:
The probability of drawing two yellow marbles in succession without replacement from a bag of 10 marbles, where 2 are yellow, is 1/45.
Explanation:
The student is asking about the probability of drawing two yellow marbles successively without replacement from a bag containing a total of 10 marbles with different colors. To solve this problem, we use conditional probability. The probability of drawing the first yellow marble is 2 out of 10 since there are 2 yellow marbles among 10 total marbles. This can be written as P(Y1) = 2/10 or 1/5. After the first yellow marble is drawn, there is only 1 yellow left among 9 total marbles, so the probability of drawing a second yellow marble is P(Y2|Y1) = 1/9.
The two events are dependent since the outcome of the first draw affects the second draw. Therefore, to find the overall probability of both events happening, we multiply their probabilities: P(Y1 and Y2) = P(Y1) × P(Y2|Y1) = (1/5) × (1/9) = 1/45. So, the probability of drawing two yellow marbles successively without replacement is 1/45.
Drag the tiles to the correct boxes to complete the pairs. Match the numerical expressions to their simplified forms.
Drag the tiles to the correct boxes to complete the pairs. Match the numerical expressions to their simplified forms
Tiles:
A).
(P^5) ^1/4
---------------
(P^-3 Q^-4)
B).
(P^2Q^7) ^1/2
----------
(Q^4)
C).
(P^6Q^3/2)^1/3
D).
(PQ^3)^1/2
--------------
(PQ)^-1/2
Pairs:
1.)
P^2Q^1/2
2.)
PQ^2
3.)
P^2Q
4.)
PQ^3/2
find the magnitude of 6+2i
Final answer:
The magnitude of 6 + 2i is 2√10.
Explanation:
To find the magnitude of the complex number 6 + 2i, we can use the Pythagorean theorem. The magnitude, or absolute value, of a complex number is found by taking the square root of the sum of the squares of its real and imaginary parts. In this case, the real part is 6 and the imaginary part is 2. So the magnitude is:
|6 + 2i| = √(6^2 + 2^2) = √(36 + 4) = √40 = 2√10
Therefore, the magnitude of 6 + 2i is 2√10.
True or false some drugs like Tylenol or available over-the-counter because they are safe in any dose
Using the Rational Root Theorem, what are all the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x – 12?
Answer: The all possible rational roots are [tex]x=\pm1,\pm2,\pm3,\pm4,\pm6,\pm12,\pm\frac{1}{2},\pm\frac{3}{2},\pm\frac{1}{4},\pm\frac{3}{4},\pm\frac{1}{10},\pm\frac{1}{5},\pm\frac{3}{5}\pm\frac{3}{10},\pm\frac{2}{5},\pm\frac{6}{5},\pm\frac{1}{20},\pm\frac{3}{20},\pm\frac{4}{5},\pm\frac{12}{5}[/tex].
Explanation:
The given polynomial is,
[tex]f(x)=20x^4+x^3+8x^2+x-12[/tex]
The Rational Root Theorem states that the all possible roots of a polynomial are in the form of a rational number,
[tex]x=\frac{p}{q}[/tex]
Where p is a factor of constant term and q is the factor of coefficient of leading term.
In the given polynomial the constant is -12 and the leading coefficient is 20.
All possible factor of -12 are [tex]\pm1,\pm2,\pm3,\pm4,\pm6,\pm12[/tex].
All possible factor of 20 are [tex]\pm1,\pm2,\pm4,\pm5,\pm10,\pm20[/tex].
So, the all possible rational roots of the given polynomial are,
[tex]x=\pm1,\pm2,\pm3,\pm4,\pm6,\pm12,\pm\frac{1}{2},\pm\frac{3}{2},\pm\frac{1}{4},\pm\frac{3}{4},\pm\frac{1}{10},\pm\frac{1}{5},\pm\frac{3}{5}\pm\frac{3}{10},\pm\frac{2}{5},\pm\frac{6}{5},\pm\frac{1}{20},\pm\frac{3}{20},\pm\frac{4}{5},\pm\frac{12}{5}[/tex]
Answer:
A.) -4/5 and 3/4
Step-by-step explanation:
Help please:((((((((((((((((
Answer:
B. The amount spent on grapes compared with the weight of the purchase.
Step-by-step explanation:
Grapes are usually sold at some dollar amount per pound. That dollar amount is the "rate of change," and it is generally constant.
___
In the case of pizza delivery or bus ridership, it is hard to imagine what the "rate of change" might be, as the relationship is probably not a function.
Find all solutions in the interval [0, 2π). 7 tan3x - 21 tan x = 0
The state of wyoming has roughly the shape of a rectangle that is 3.6 x 102 miles long and 2.8 x 102 miles high. what is the approximate area of wyoming? hint: the area of a rectangle is product of its length and width.
Assuming a regularly shaped rectangle, the formula for the area is given as:
A = L * W
where L and W are the length and width respectively
A = 3.6 x 10^2 miles * 2.8 x 10^2 miles
A = 100,800 square miles
or
A = 10.08 x 10^2 miles
Answer: The area of wyoming is [tex]A=1.008\times 10^{5}\, miles^{2}[/tex]
Step-by-step explanation:
The shape of wyoming is rectangular with length , [tex]L=3.6\times 10^{2}\, miles[/tex]
and height , [tex]H=2.8\times 10^{2}\, miles[/tex]
Area of rectangle , [tex]A=L\times W[/tex]
=> [tex]A=(3.6\times 10^{2})\times (2.8\times 10^{2})\, miles^{2}[/tex]
=>[tex]A=1.008\times 10^{5}\, miles^{2}[/tex]
Thus the area of wyoming is [tex]A=1.008\times 10^{5}\, miles^{2}[/tex]
A ramp 28 ft long rises to a platform. the bottom of the platform is 15 ft from the foot of the ramp. find x , the angle of elevation of the ramp
What is the graph of the function f(x) = the quantity of 3 x squared plus 2 x plus 10, all over x plus 3
A) a graph is shown with a vertical asymptote at x = -3 increasing from negative infinity to just under -35 and then decreasing back to negative infinity as well as decreasing to just under five and increasing to infinity
B) graph with vertical asymptote of x equals 3, and oblique asymptote of y equals x minus 1
C) graph with vertical asymptote of x equals 3, and oblique asymptote of y equals negative x minus 1
D) graph with vertical asymptote of x equals negative 3, and oblique asymptote of y equals negative x minus 1
Arrange the functions in ascending order, starting with the function that eventually has the lowest value and ending with the function that eventually has the greatest value.
2x+5
2^x+3
2^x+10
2x
x²+2
x²
PLEASE HELP 20 POINTS PROVIDED
A Web music store offers two versions of a popular song. The size of the standard version is 2.8 megabytes (MB). The size of the high-quality version is 4.9 MB. Yesterday, there were 1070 downloads of the song, for a total download size of 3521 MB. How many downloads of the high-quality version were there?
x= standard
y = high quality
x +y = 1070
y=1070-x
2.8x + 4.9y =3521
2.8x +4.9(1070-x) = 3521
2.8x+5243-4.9x =3521
-2.1x=-1722
x=-1722/-2.1 = 820
820*2.8 =2296
1070-820 =250
250*4.9 = 1225
1225+2296 = 3521
there were 250 high quality downloads
Mr. Rr the Rreliable Rrobot has been programmed to whistle every $18$ seconds and do a jumping jack every $42$ seconds, starting from the moment he is turned on. (For example, he does his first jumping jack $42$ seconds after he is turned on.)
How many times during the first $15$ minutes after activation will Mr. Rr whistle and do a jumping jack at the same instant?
Answer:
7 times during the first 15 minutes
Step-by-step explanation:
Remember that
[tex]1\ min=60\ sec[/tex]
so
[tex]15\ min=15(60)=900\ sec[/tex]
Decompose the numbers 18 and 42 in prime factors
we know that
[tex]18=(2)(3^2)[/tex]
[tex]42=(2)(3)(7)[/tex]
Find the least common multiple (LCM)
The LCM is
[tex](2)(3^2)(7)=126\ sec[/tex]
we need to find all multiples of 126 that are less than or equal 900.
[tex]126*1=126\ sec\\126*2=252\ sec\\126*3=378\ sec\\126*4=504\ sec\\126*5=630\ sec\\126*6=756\ sec\\126*7=882\ sec[/tex]
therefore
7 times during the first 15 minutes
Jayla has a USB stick that transfers data at 2.4 x 10^9 bytes per second. Her modem transfers data at 1.2 x 10^7 bytes per second. Which statement is true?
A.There is no way to compare the transfer rates.
B.The transfer rate of the USB is 2 times the transfer rate of the Modem.
C.The transfer rate of the USB stick is 200 times the trasnfer rate of the modem
D.The transfer rate of the USB stick is 2,000 times the transfer rate of the modem
Answer: C.The transfer rate of the USB stick is 200 times the transfer rate of the modem .
What is the slope of a line that is perpendicular to the line x=-3?
A(-3
B(0
C(1/3
D(underfined
The slope of a line perpendicular to x = -3 is 0. Option B is correct answer.
What is the slopes of perpendicular lines?Perpendicular line slopes are the negative reciprocals of one another. In other words, if one line has a slope of m, a line perpendicular to it has a slope of -1/m. The definition of perpendicular lines, which states that the angles created by the lines are 90 degrees, may be used to demonstrate this relationship. The product of the slopes of perpendicular lines must be -1 in order to meet the requirement that the tangent of a 90 degree angle be specified.
Given the line x = -3.
Any line perpendicular to this line will have slopes of negative reciprocals of each other.
The slope of a horizontal line is 0, since the line does not change in the y-direction.
Hence, the slope of a line perpendicular to x = -3 is 0.
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PLEASE HELP ME ON THESE PROBLEMS, ITS URGENT! (Help for any of these would be greatly appreciated!)
1. A grocer mixes two grades of coffee which sell for 70 cents and 80 cents per pound, respectively. How much of each must he take to make a mixture of 80 pounds which he can sell for 76 cents per pound?
2. How many quarts of pure alcohol must be added to 40 quarts of a mixture that is 35% alcohol to make a mixture that will be 48% alcohol?
3. If a container contains a mixture of 5 gallons of white paint and 11 gallons of brown paint, how much white paint must be added to the container so that the new mixture will be two-thirds white paint?
4. Can the sum of three consecutive odd integers be (a) 25? (b) 45?
5. A tank can be filled in 9 hours by one pipe alone, in 12 hours by a second pipe alone, and can be drained when full, by a third pipe, in 15 hours. How long would it take to fill the tank if it is empty, and if all pipes are in operations?
5/3(6x+3)<2x-7 what is the solution for the iniquality
Which of the following is the sum of the polynomials 5x2 - 4x + 1 and -3x2 + x - 3 ?
2x2 + 3x + 2
8x2 - 5x - 2
2x2 - 3x - 2
-8x2 - 3x - 2
Find the possible value or values of n in the quadratic equation 2n2 – 7n + 6 = 0
Answer:
[tex]n=\frac{3}{2},\,\,n=2[/tex].
Step-by-step explanation:
The equation you have is a quadratic equation because the polynomial [tex]2n^{2}-7n+6[/tex] has degree 2. One of the methods available to solve kind of equations is to factorize the polynomial on the left hand side. To factorize you can do the following:
(1) [tex]2n^2-7n+6[/tex]. The given polinomial
(2) [tex]\frac{2\times(2n^2-7n+6)}{2}=\frac{(2n)^{2}-7(2n)+12}{2}[/tex]. Multiply and divide by 2, because it is the coeficient of [tex]n^{2}[/tex]
(3) [tex]\frac{(2n)^{2}-7(2n)+12}{2}=\frac{(2n-\_\_)(2n-\_\_)}{2}[/tex]. Separate the polynomial in two factors, each one with [tex]2n[/tex] as a first term. The sign in the first factor is equal to the sign in the second term of the polynomial, that is to say, [tex]-7n[/tex]. The sign in the second factor is the sign of the second term multiplied by the sign of the third term, that is to say [tex](-)\times(+)=(-)[/tex] . In the blanks you should select two numbers whose sum is 7 and whose product is 12. Those numbers must be 3 and 4.
(4)The polynomial factorized is [tex]\frac{(2n-4)(2n-3)}{2}[/tex]
(5)Use the common factor in the numerator to cancel the number 2 in the denominator to obtain [tex](n-2)(2n-3)[/tex]
Then the given equation can be written as:
[tex]{(2n-3)(n-2)=0[/tex]
The product of two expression equals zero if and only if one of the expression is zero. From here we have that
[tex]2n-3=0[/tex] or [tex]n-2=0[/tex]
From the first equality we obtain that [tex]n=\frac{3}{2}[/tex]. From the second equality we obtain that [tex]n=2[/tex].
Let $AB = 6$, $BC = 8$, and $AC = 10$. What is the area of the circumcircle of $\triangle ABC$ minus the area of the incircle of $\triangle ABC$?
Help which is the correct function
please help , show your steps , thanks
5 + 2*SQRT(x) = 15
subtract 5 from each side
2*SQRT(x) = 10
(2*SQRT(x))^2 =10^2
2^2 *x = 100
4x=100
x=400/4
x = 25
Find S8 for the geometric series 3 + -6 + 12 + -24 +…
the sum of the first 8 terms of the series is [tex]\( -255 \)[/tex].
To find the sum [tex]\( S_8 \)[/tex] of the geometric series [tex]\( 3 - 6 + 12 - 24 + \ldots \)[/tex], we need to determine the common ratio [tex](\( r \))[/tex] and the first term [tex](\( a \)).[/tex]
The general form of a geometric series is [tex]\( a + ar + ar^2 + \ldots + ar^{n-1} \)[/tex], where:
- [tex]\( a \)[/tex] is the first term,
- [tex]\( r \)[/tex] is the common ratio,
- [tex]\( n \)[/tex] is the number of terms.
In our series:
- [tex]\( a = 3 \)[/tex] (the first term),
- To find the common ratio [tex](\( r \))[/tex], we can divide any term by its preceding term:
- [tex]\( \frac{-6}{3} = -2 \)[/tex]
- [tex]\( \frac{12}{-6} = -2 \)[/tex]
- [tex]\( \frac{-24}{12} = -2 \)[/tex]
So, [tex]\( r = -2 \)[/tex].
Now, [tex]\( S_n \)[/tex], the sum of the first [tex]\( n \)[/tex] terms of a geometric series, is given by the formula:
[tex]\[ S_n = \frac{a(1 - r^n)}{1 - r} \][/tex]
Substituting the values of [tex]\( a \), \( r \)[/tex], and [tex]\( n = 8 \)[/tex], we get:
[tex]\[ S_8 = \frac{3(1 - (-2)^8)}{1 - (-2)} \][/tex]
[tex]\[ S_8 = \frac{3(1 - 256)}{1 + 2} \][/tex]
[tex]\[ S_8 = \frac{3(-255)}{3} \][/tex]
[tex]\[ S_8 = -255 \][/tex]
So, the sum of the first 8 terms of the series is [tex]\( -255 \)[/tex].
Find the length of arc VZX in circle C
Length of arc VZX is 27.92 units.
What is arc?
The arc is a portion of the circumference of a circle.
Given,
Radius of circle = 8 units
∠VCX = 160°
Let length of arc VZX = x
x = area of circle×(360°- ∠VCX)/360°
x = 2π×8×(360-160)/360
x = 2π×8×(200)/360
x = 400π/45
x = 80π/9
x = 27.92 units
Hence, length of arc VZX is 27.92 units.
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You will be charged 12.5% interest on a loan of $678. how much interest will you pay on the loan?
It is given in the question that
You will be charged 12.5% interest on a loan of $678.
So to find the interest, we have to find 12.5% of 678. And 12.5% = 0.125
So we have to find the value of 0.125 of 678.
[tex]0.125*678 = 84.75[/tex]
Therefore the interest that you will have to pay on loan is $84.75 .
Solve for x and y: 28x-49y=35 and 4x-7y=5
What is 78% written as a decimal
What is the equation of a line that goes through the point
(0,
5
6
)
(0,56)
and has a slope of 1?
Select one:
a.
y=x+
5
6
y=x+56
b.
5
6
y=x
56y=x
c.
y=−x+
5
6
y=−x+56
d.
y=
5
6
x+1
y=56x+1