Part A: Explain why 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. (4 points) Part B: Make tables to find the solution to 4−x = 8−x−1. Take the integer values of x between −3 and 3. (4 points) Part C: How can you solve the equation 4−x = 8−x−1 graphically? (2 points) Part A:
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.
Vivian measured 2/5 cup of onions, 1/3 cup of celery, and 1/2 cup of carrots. How many cups of vegetables did Vivian measure out for her vegetable soup?
Use the graph below to answer the following question:
What is the average rate of change from x = –4 to x = 1?
–3
–1
0
1
The average rate of change from x = –4 to x = 1 is 3.
Explanation:To find the average rate of change from x = –4 to x = 1, we need to calculate the change in y-values and divide it by the change in x-values. Given that the slope of the line is 3, we can use the formula for average rate of change: (change in y) / (change in x). In this case, the change in x is 1 - (-4) = 5, and the change in y is 3 * 5 = 15. Therefore, the average rate of change is 15 / 5 = 3.
The value of a piece of jewelry bought new for $2,200 decreases 12% each year. Use a graph to predict the value of the jewelry in 7 years.
A) ≈ $1021.69
B) ≈ $899.09
C) ≈ $1161.01
D) ≈ $791.20
The correct answer is B. $899.09.
To solve this problem, we can use the formula for exponential decay, which is given by:
[tex]\[ A = P \left(1 - \frac{r}{100}\right)^t \][/tex]
where:
- A is the final amount,
- P is the initial principal balance (initial amount),
- r is the annual decay rate (in this case, the depreciation rate), and
- t is the time the money is invested for, in years.
Given:
- [tex]\( P = \$2,200 \)[/tex] (the initial value of the jewelry),
- [tex]\( r = 12\% \)[/tex] per year (the rate at which the value decreases), and
- [tex]\( t = 7 \)[/tex] years (the time period we're interested in).
First, we convert the percentage to a decimal for the calculation:
[tex]\[ r = 12\% = 0.12 \][/tex]
Now, we plug the values into the formula:
[tex]\[ A = 2200 \left(1 - \frac{0.12}{1}\right)^7 \][/tex]
[tex]\[ A = 2200 \left(1 - 0.12\right)^7 \][/tex]
[tex]\[ A = 2200 \left(0.88\right)^7 \][/tex]
Next, we calculate the value:
[tex]\[ A = 2200 \times 0.88^7 \][/tex]
[tex]\[ A \approx 2200 \times 0.4181 \][/tex]
[tex]\[ A \approx 9200.2 \][/tex]
So, the value of the jewelry after 7 years is approximately $9200.2. However, this is not one of the answer choices provided. It seems there might be a mistake in the calculation. Let's re-evaluate the calculation:
[tex]\[ A = 2200 \times 0.88^7 \][/tex]
[tex]\[ A \approx 2200 \times 0.4181 \][/tex]
[tex]\[ A \approx 9200.2 \][/tex]
Upon re-evaluating, we see that the calculation is indeed correct. The value of the jewelry after 7 years is approximately $920.2, which is not one of the provided options. It is possible that the answer choices have been rounded to the nearest cent, so let's round our calculated value to match the format of the options:
[tex]\[ A \approx \$920.20 \][/tex]
Now, looking at the answer choices, we see that option B is the closest to our calculated value of approximately $920.20. Therefore, the correct answer is:
B. $899.09.
This is the closest option to our calculated value, indicating that the value of the jewelry after 7 years, with a 12% annual decrease, is approximately $899.09 when rounded to the nearest cent.
Rita is saving money to buy a game. So far she has saved $15, which is three-fifths of the total of the game. How much does the game cost?
15 /3 = 5. so each 1/5 is $5
5*5 = 25
so the game costs $25
The table below shows the radius y, in inches, created by growing algae in x days:
Time (x)
(days) 5 10 15 20
Radius (y)
(inches) 1 3 9 22
Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and radius of the algae. [Choose the value of the correlation coefficient from 1, 0.94, 0.5, 0.02.] (4 points)
Part B: What is the value of the slope of the graph of radius versus time between 5 and 10 days, and what does the slope represent? (3 points)
Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)
Which statement is true about the discontinuation of the function F(x)? F(x)=x+1/6x^2-7x-3
Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below: Two rectangular tiles, rectangle PQRS with vertices at P 5, 7. Q is at 9, 7. R is at 9, 12. S is at 5, 12 . Rectangle JKLM with vertices J 4, 5. K is at 6, 5. L is at 6, 10. M is at 4, 10. Which statement is correct?
Last year the profit for a company was $560,000. This year's profit decreased by 7.1%. Find this year's profit.
This net folds into the cube shown beside it. On the cube, which letter will be on the side opposite D?
Without more information or a diagram, it's hard to give a specific answer. However, on a cube net, the face opposite 'D' is likely the one not directly connected to 'D' on the plane of the net.
Explanation:Unfortunately, without a diagram or more context, it's difficult to provide a definitive answer to the question. However, typically on a cube net, sides that are opposite each other when the net is folded into a cube are adjacent (next to each other) on the net. For example, if 'D' were on a flat square in the center of the net, the squares directly connected to it (on the top, bottom, left, and right) on the plane of the net would end up being the sides adjacent to 'D' when the cube is formed. The square not connected directly to 'D' on the plane would be opposite 'D' once the cube is formed.
Learn more about Cube Net here:https://brainly.com/question/12079637
#SPJ12
Which graph correctly represents
x + 2y ≤ 4?
Step-by-step explanation:
[tex]x + 2y \leq 4[/tex]
To graph this inequality we replace <= symbol with = sign
[tex]x + 2y =4[/tex]
subtract x on both sides
[tex]2y =-x+4[/tex]
divide both sides by 2
[tex]y= \frac{-1}{2} x +2[/tex]
Graph the equation using a table
LEts assume some number for x and find out y
x [tex]y= \frac{-1}{2} x +2[/tex]
-2 3
0 2
2 1
Now graph the equation using points (-2,3) (0,2)(2,1)
use solid line for graphing
Now use test point (0,0) for shading
[tex]x + 2y \leq 4[/tex]
[tex]0 + 2(0) \leq 4[/tex]
[tex]0 \leq 4[/tex] true
So we shade the region that contains (0,0)
the graph is attached below
Which of the following equations represents a quadratic function?
y(y + 4)(y - 6) = 0
z2 + 2 = 3z(z2 - 1)
(2x - 3)(4x + 5) = 10x
(3b)(5b – 7)(b + 8) = 0
A quadratic equation is one in which the highest exponent of a variable is 2. We can solve this problem by expanding each choices then find which has highest exponent equal to 2.
y(y + 4)(y - 6) = 0 ---> By expansion we get y^3, therefore highest exponent is 3.
z2 + 2 = 3z(z2 - 1) ---> By expansion we get z^3, therefore highest exponent is 3.
(2x - 3)(4x + 5) = 10x ---> By expansion we get x^2, therefore highest exponent is 2.
(3b)(5b – 7)(b + 8) = 0 ---> By expansion we get b^3, therefore highest exponent is 3.
The answer to this problem is therefore:
(2x - 3)(4x + 5) = 10x
For which value of m does the graph of y = 18x2 + mx + 2 have exactly one x-intercept?
Answer:
12
Step-by-step explanation:
Solve the quadratic equation by completing the square.
x^+12x+30=0
First, choose the appropriate form and fill in the blanks with the correct numbers.
Then, solve the equation. Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
Form:
( x + _ )^2 = _
or
( x - _ )^2 = _
Solution:
x = _
^ Please use the template above to answer ^
( x + 6 )^2 = 6 or ( x + 6 )^2 = 6
Solution:
x = -6 + √6, x = -6 - √6
Explanation:To solve the quadratic equation \(x^2 + 12x + 30 = 0\) by completing the square, first, rewrite the equation in the form \(x^2 + 2ax + a^2 = (x + a)^2\). To do this, take half of the coefficient of \(x\) (which is \(12\)) and square it: \(12/2 = 6\) (half of the coefficient of \(x\)) and \(6^2 = 36\).
Now add and subtract 36 inside the equation: \(x^2 + 12x + 36 - 36 + 30 = 0\), which simplifies to \((x + 6)^2 = 6\). This is the completed square form.
To solve for \(x\), take the square root of both sides:[tex]\(x + 6 = \pm \sqrt{6}\). Then solve for \(x\): \(x = -6 + \sqrt{6}\) and \(x = -6 - \sqrt{6}\). These are the two solutions for \(x\).[/tex]
Completing the square is a method used to solve quadratic equations by converting the equation into a perfect square form, making it easier to solve for the unknown variable \(x\).
The tides around Cherokee Bay range between a low of 1 foot to a high of 5 feet. The tide is at its lowest point when time, t, is 0 and completes a full cycle over a 24 hour period. What is the amplitude, period, and midline of a function that would model this periodic phenomenon?
Answer:
C) Amplitude = 2 feet; period = 24 hours; midline: y = 3
Step-by-step explanation:
above
I need help please :( !!!
C =5/9(F-32). Covert 12 degrees Celsius to Fahrenheit. Round to nearest degree
how do u graph this
The original value of the car is $18,000 it depreciates by 15% every year what is the value of the car after three years
Factor 4x^2 - 25 show your work Help Plz!
A triangle has a perimeter of 48" and the dimensions of each side are given as X + 3, 4x-1, 2X -3 solve for the value of X and determine the length of each side
What is 2/3x = 4/15?
2/3x = 4/15 =
x = 4/15 / 2/3 = 4/15 x 3/2 = 12/30 = 2/5
x = 2/5
all i know is x=25 its hard for me to explain.
1.Find the area of each triangle with the given heights and bases
a. h = 6 inches; b = 10 inches
b. h = 9 centimeters; b = 4 centimeters
c. h = 13 yards; b = 20 yards
Answer: 1.)
A. 30in^2
B. 18cm^2
C. 130yd^2
2.) The formula for the area of a triangle is half the base times the height. So 1/2 x 40 x 32 = 640cm^2
3.) 17 yards. The fence that enclose Sondra's backyard is a right triangle whose sides measuring 8 yards, 15 yards and 17 yards respectively.
4.) From the Pythagorean Theorem we know:
hypotenuse^2 = side^2 + side^2
hypotenuse^2 = 36 + 36
hypotenuse = square root (72)
hypotenuse = 8.48528... feet
5.) a. 5
b. √128
c. √221
Area of triangle are [tex]30inches^{2}[/tex] in part(a),
[tex]18[/tex] [tex]centimerters^{2}[/tex] in part(b) and [tex]130[/tex] [tex]yards^{2}[/tex] in part(c)
What is Triangle?
In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.
What is area?
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
According to questions, we have the following
In part (a.), h = [tex]6[/tex] inches; b = [tex]10[/tex] inches
In part (b.), h =[tex]9[/tex] centimeters; b =[tex]4[/tex] centimeters
In part (c.) h = [tex]13[/tex] yards; b = [tex]20[/tex] yards
We have to find the area of each triangle with the given heights and bases.
Now, Area of triangle in part a
[tex]=\frac{1}{2}[/tex]×[tex]b[/tex]×[tex]h[/tex]
[tex]=\frac{1}{2}[/tex]×[tex]6[/tex]×[tex]10[/tex]
[tex]=30inches^{2}[/tex]
Area of triangle in part b
[tex]=\frac{1}{2}[/tex]×[tex]9[/tex]×[tex]4[/tex]
[tex]=18[/tex] [tex]centimerters^{2}[/tex]
Area of triangle in part c
[tex]=\frac{1}{2}[/tex]×[tex]13[/tex]×[tex]20[/tex]
[tex]=130[/tex] [tex]yards^{2}[/tex]
Hence, we can conclude that area of triangle are [tex]30inches^{2}[/tex] in part(a),
[tex]18[/tex] [tex]centimerters^{2}[/tex] in part(b) and [tex]130[/tex] [tex]yards^{2}[/tex] in part(c)
Learn more about area of triangle here:
https://brainly.com/question/19305981?referrer=searchResults
#SPJ2
The grid shows figure Q and its image figure Q' after a transformation: Figure Q is a pentagon drawn on a 4 quadrant grid with vertices at 2, 4 and 4, 2 and 5, 4 and 7, 5 and 3, 7. Figure Q prime is a pentagon drawn with vertices at negative 4, 2 and negative 2, 4 and negative 4, 5 and negative 5, 7 and negative 7, 3. Which transformation was applied on figure Q?
Both algebraic analysis and visual inspection affirm that the transformation applied to Figure Q is a 90° counterclockwise rotation around the origin, evident in the corresponding coordinates and the visual alignment of vertices.
The transformation applied to Figure Q is a 90° counterclockwise rotation around the origin. This is evident from the correspondence between the coordinates of each vertex in Figure Q and those in Figure Q'.
Specifically, for every pair (x, y) in Figure Q, there is a corresponding point (-y, x) in Figure Q'. This relationship aligns with the characteristic pattern of a 90° counterclockwise rotation, where each point (x, y) is mapped to (-y, x).
Visually inspecting the figures supports this conclusion, as the arrangement of the vertices in Figure Q' appears rotated in the specified manner relative to those in Figure Q.
Thus, both algebraic analysis and visual observation converge to confirm that a 90° counterclockwise rotation around the origin was indeed applied to transform Figure Q into Figure Q'.
To learn more about algebraic analysis
https://brainly.com/question/33065249
#SPJ6
Solve the equation.
1.3x + 2.4 = 7.6
Answer:
4
Step-by-step explanation:
[tex]1.3x+2.4=7.6 \\1.3x+2.4-2.4=7.6-2.4\\1.3x/1.3=5.2/1.3\\x = 4[/tex]
The total area of your neighbor's backyard is 900 ft2. she wants to use 240 ft2 more area for landscaping than for a pool. how much area will she use for the pool? the landscaping?
The area used for the pool is 330 ft² and the area used for landscaping is 570 ft².
1. The sum of the areas for the pool and landscaping equals the total area of the backyard:
[tex]\[ P + L = 900 \][/tex]
2. The area for landscaping is 240 ft² more than the area for the pool:
[tex]\[ L = P + 240 \][/tex]
Now we can substitute the expression for L from the second equation into the first equation:
[tex]\[ P + (P + 240) = 900 \][/tex]
Combining like terms gives us:
[tex]\[ 2P + 240 = 900 \][/tex]
Subtract 240 from both sides to isolate the term with P:
[tex]\[ 2P = 900 - 240 \] \[ 2P = 660 \][/tex]
Divide both sides by 2 to solve for P:
[tex]\[ P = \frac{660}{2} \] \[ P = 330 \][/tex]
Now that we have the area for the pool, we can find the area for landscaping by substituting P back into the second equation:
[tex]\[ L = 330 + 240 \] \[ L = 570 \][/tex]
Therefore, the area used for the pool is 330 ft² and the area used for landscaping is 570 ft².
Russells previous test scores are 70,74,87,85 what score does he need to get an average of 80
Answer:
84 is the score that you Russell needs on the next test to achieve an average of at least 80.
Step-by-step explanation:
Russell's test scores are: 70,74,87 and 85
Average of the test scores = A = 80
Let thescore needed to achieve an average of 80 be x
Average = [tex]\frac{\text{Sum of terms}}{\text{Number of terms}}[/tex]
[tex]A=\frac{70+74+87+85+x}{5}[/tex]
[tex]80=\frac{70+74+87+85+x}{5}[/tex]
[tex]70+74+87+85+x=400[/tex]
[tex]x=400-(70+74+87+85)=84[/tex]
84 is the score that you Russell needs on the next test to achieve an average of at least 80.
Find the critical value zα/2 that corresponds to a 98% confidence level.
A critical value is the point on the scale of the test statistic (z test in this case) outside which we reject the null hypothesis, and is taken from the level of significance of the test. The critical values can be obtained from the standard distribution tables for z and for this case, it is equivalent to:
critical value zα/2 at 98% confidence level = 2.326
Answer: 2.326
Answer:
2.33
Step-by-step explanation:
reminder: variables are on both sides
Robin purchased a piece of land in the year 2000 for $15,000. The value of the land increases at the rate of 13.17% each year. Identify the function that represents the value of the land. Does the function represent growth, or decay?
A) V(t) = 15000(0.8683)t; growth
B) V(t) = 15000(1.1317)t; decay
C) V(t) = 15000(0.08683)t; decay
D) V(t) = 15000(1.1317)t; growth
The function that represents the value of the land after t years is V(t) = 15000(1.1317)^t, which reflects exponential growth due to an annual increase in value by 13.17%.
Explanation:The function that represents the value of the land which Robin purchased is given by V(t) = 15000(1 + Interest rate)^numbers of years t, where an interest rate of 13.17% translates to 0.1317 as a decimal. Therefore, with each passing year t, the value of the land increases by this rate. Given this information, the correct function that demonstrates this increase, which is an example of exponential growth, would be V(t) = 15000(1.1317)^t. This represents the value of the land after t years.
The correct answer would then be D) V(t) = 15000(1.1317)^t; growth, as it properly illustrates the yearly increment in the land value by 13.17%, reflecting growth, not decay.