answer
(z+2)(z-2)
steps
its a rule
a²-b²= (a+b) (a-b)
vedantu
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
The equivalent equations that have the value x = 3 are:
2 + x = 5, x + 1 = 4, and (-5) + x = -2.
Equations are considered equivalent if they have the same solution(s). In other words, if you solve each equation for the variable, you should end up with the same value(s).
Let's look at the options given:
2 + x = 5: This equation can be solved by subtracting 2 from both sides, leaving x = 3.
x + 1 = 4: This equation can be solved by subtracting 1 from both sides, leaving x = 3.
9 + x = 6: This equation can be solved by subtracting 9 from both sides, leaving x = -3.
x + (-4) = 7: This equation can be solved by adding 4 to both sides, leaving x = 11.
-5 + x = -2: This equation can be solved by adding 5 to both sides, leaving x = 3.
So, we can see that the first, second, and fifth equations are equivalent since they all simplify to x = 3. The third and fourth equations are not equivalent to any of the other equations, since they have different solutions.
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50 Points
In the figure below ABC~YXZ. Find sinX, tanX, and cosX. Round your answers to the nearest hundredth.
The table below shows the cost of different numbers of goldfish at a pet store.
Number of Goldfish Cost
5 $1.50
10 $3.00
15 $4.50
20 $6.00
The cost is a linear function of the number of goldfish. Which statement describes the rate of change of this function?
A
The cost increases $0.30 each time 1 goldfish is added.
B
The cost increases $1.50 1 goldfish is added.
C
The cost increases $3.00 5 goldfish are added.
D
The cost increases $6.00 5 goldfish are added.
Answer:Option A
Step-by-step explanation:
It will option because if you 3/10 it would give 0.3 which can turned into $0.30 and we try it for example 5x0.30, it will give us $1.50 which proves that the cost increases$0.30 each time 1 goldfish is added
does 3 (x - 5) - 7=ax + b has a solution
Whether the equation 3(x - 5) - 7 = ax + b has a solution depends on the value of a.
To determine if the equation 3(x - 5) - 7 = ax + b has a solution, we need to compare the coefficients of x on both sides of the equation.
In the given equation, the coefficient of x on the left side is 0 (since 3(x - 5) - 7 does not have an x term), and the coefficient of x on the right side is a.
For the equation to have a solution, the coefficients of x on both sides should be equal.
Therefore, we need to equate 0 and a:
0 = a.
If a = 0, then the equation has a solution. However, if a ≠ 0, then there is no solution.
Therefore, whether the equation 3(x - 5) - 7 = ax + b has a solution depends on the value of a.
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PLEASE HELP
Which expressions are equivalent to the one below? Check all that apply.
27^x/9^x
Will Give Brainliest Please Help!
simplify the expression 6 - 5/4 X 6 -8/7
The solution of the expression is,
⇒ - 37/14
We have to given that;
Expression to solve is,
⇒ 6 - 5/4 × 6 - 8/7
Now, We can simplify the expression as,
⇒ 6 - 5/4 × 6 - 8/7
⇒ 6 - 5/2 × 3 - 8/7
⇒ 6 - 15/2 - 8/7
⇒ (12 - 15)/2 - 8/7
⇒ - 3/2 - 8/7
⇒ (- 21 - 16) / 14
⇒ - 37/14
Thus, The solution of the expression is,
⇒ - 37/14
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2. A linear model for the data in the table is shown in the scatter plot. X 1 2 5 6 7 9 y 2 6 9 9 13 Variable y 14 10 8 LT 5 4 321 0 1 2 3 4 5 6 7 8 9 10 11 Variable x (a) Which two points should you use to find the equation of the model? 6,9 and 10,13. (b) What is the slope of the linear model? 1 (c) What is the equation of the linear model in point-slope form? Y-9 =(x-6) (d) What is the slope-intercept form of the equation you wrote in Part (c)? y=x+3 (e) What is the equation for the least squares regression line? y = bx + a (f) decimal places. Answer: Y= 1.028x + 2.271
pls check my answers
correct any mistakes pls
thanks!
You answered 6,9 and 10,13. The correct answer is 6,9 and 7,13 to find the equation of the linear model.
(a) The two points you selected are (6,9) and (10,13). This is correct.
(b) To find the slope of the linear model, we can use the formula: slope = (change in y) / (change in x). By using the points (6,9) and (10,13), we have (13-9) / (10-6) = 4/4 = 1. So, the slope is indeed 1. This is correct.
(c) The equation of the linear model in point-slope form is given as: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values (6,9) as the point and 1 as the slope, we get y - 9 = 1(x - 6). This simplifies to y - 9 = x - 6. This is not the same as the equation you provided. It seems you made a mistake here.
(d) The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. To convert the equation y - 9 = x - 6 to slope-intercept form, we can add 9 to both sides: y = x - 6 + 9, which simplifies to y = x + 3. This matches the equation you provided. So, this is correct.
(e) The equation for the least squares regression line is in the form y = bx + a, where b is the slope and a is the y-intercept. In this case, the slope is 1, and we need to find the y-intercept.
We can use the point (6,9) and the slope-intercept form equation y = x + 3 to find the y-intercept: 9 = 6 + 3. Solving this equation, we find that the y-intercept is 3.
Therefore, the equation for the least squares regression line is y = x + 3. This does not match the equation you provided. It seems you made a mistake here.
(f) Based on the correct equation from part (d) (y = x + 3), the correct equation for the least squares regression line is y = 1x + 3. When rounded to three decimal places, this would be y = 1.000x + 3.000.
The equation you provided (Y = 1.028x + 2.271) is slightly different, so it appears you made a mistake in the calculations or rounding.
To summarize, your answers in parts (a) and (b) are correct. However, there are mistakes in parts (c), (e), and (f). The corrected answers are:
(c) The equation of the linear model in point-slope form: y - 9 = x - 6.
(d) The slope-intercept form of the equation: y = x + 3.
(e) The equation for the least squares regression line: y = 1x + 3.
(f) When rounded to three decimal places, the equation is: y = 1.000x + 3.000.
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Can someone help me with 6-11. Directions: Find the volume of each figure. Round to the nearest hundredth when necessary.
The calculated volumes of the figures are 11264 cubic units, 14482.28 cubic units, 3744 cubic units, 475.2 cubic units, 18824.14 cubic units and 91.99 cubic units
How to find the volume of the figuresThe cylinder
The volume is calculated as
V = πr²h
Where
r = Radius
h = Height
So, we have
V = 22/7 * (32/2)² * 14
Evaluate
Volume = 11264
The cylinder
The volume is calculated as
V = πr²h
Where
r = Radius
h = Height
So, we have
(2r)² = 40² - 32²
(2r)² = 576
So, we have
r = 12
So, we have
V = 22/7 * (12)² * 32
Evaluate
Volume = 14482.28
The rectangular prism
The volume is calculated as
V = lwh
Where
l = Length
w = Width
h = Height
So, we have
V = 8 * 12 * 39
Evaluate
Volume = 3744
The triangular prism
The volume is calculated as
V = 1/2lwh
Where
l = Length
w = Width
h = Height
So, we have
V = 1/2 * 11 * 5.4 * 16
Evaluate
Volume = 475.2
The sphere
The volume is calculated as
V = 4/3πr³
Where
r = Radius
So, we have
V = 4/3 * 22/7 * (33/2)³
Evaluate
Volume = 18824.14
The sphere
The volume is calculated as
V = 4/3πr³
Where
r = Radius
So, we have
V = 4/3 * 22/7 * 2.8³
Evaluate
Volume = 91.99
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side of balls and placed in a bag.
Three balls are drawn, one at a time
and not placed back.
Which set of results could not have
been drawn from the bag?
2, 3, 7
10, 4, 3
FREE HINTS
3, 5, 5
FREE SOLVE
8, 6, 10
The set of results that could not have been drawn from the bag is 3, 5, 5.
Let's assume there are three balls in the bag, labeled A, B, and C. The possible combinations are:
ABC, ACB, BAC, BCA, CAB, CBA
Now, let's analyze each set of results:
2, 3, 7: This set of results could have been drawn from the bag. For example, if A = 2, B = 3, and C = 7, the results would be 2, 3, 7.
10, 4, 3: This set of results could have been drawn from the bag. For example, if A = 10, B = 4, and C = 3, the results would be 10, 4, 3.
3, 5, 5: This set of results could not have been drawn from the bag, because there is only one ball labeled 3 in the bag. Therefore, it is impossible to draw two balls labeled 5 and one ball labeled 3.
8, 6, 10: This set of results could not have been drawn from the bag, because there is no ball labeled 8 in the bag. Therefore, it is impossible to draw a ball labeled 8.
So, the set of results that could not have been drawn from the bag is 3, 5, 5.
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what is the rage of 0,0,0,1,1,2,2,3,3,4,5
The range of the set {0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 5} is 5.
The range of a set of numbers is the difference between the largest and smallest numbers in the set.
The set is {0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 5}.
The range first need to identify the smallest and largest numbers in the set.
The smallest number is 0 appears three times.
The largest number is 5.
The range is:
5 - 0 = 5
The range of the set {0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 5} is 5.
The range is a measure of the spread or variability of a set of numbers.
It tells us how much the values in the set differ from each other.
The range of 5 indicates that the values in the set are spread out over a range of 5 units.
The set includes consecutive integers from 0 to 5 with multiple occurrences of some of these integers.
While the range provides a measure of the spread it is only one of many measures that can be used to describe the characteristics of a set of data.
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approximate the area under the curve y=x^3 from x=3 to x=6
To approximate the area under the curve y=x^3 from x=3 to x=6, we can use the midpoint rule with four subintervals.First, we need to find the width of each subinterval:delta x = (6 - 3) / 4 = 0.75Next, we can find the midpoint of each subinterval:x1 = 3 + 0.5 * delta x = 3.375
x2 = x1 + delta x = 4.125
x3 = x2 + delta x = 4.875
x4 = x3 + delta x = 5.625Now, we can evaluate the function at each midpoint:y1 = x1^3 = 40.39
y2 = x2^3 = 71.25
y3 = x3^3 = 106.29
y4 = x4^3 = 146.48Finally, we can use the midpoint rule formula to approximate the area:A ≈ delta x * (y1 + y2 + y3 + y4)
= 0.75 * (40.39 + 71.25 + 106.29 + 146.48)
= 267.98Therefore, the approximate area under the curve y=x^3 from x=3 to x=6 is 267.98 square units.
5.
14 ft
8 ft
V =
Hello guys I'm stuck
Answer:
2816 ft^3
Step-by-step explanation:
Solution Given:
Radius(r)=8ft.
Height(h)=14 ft.
Now
To find the volume of a cylinder, you can use the formula:
[tex]\boxed{\bold{Volume = \pi * r^2 * h}}[/tex]
where:
π (pi) is a mathematical constant approximately equal to 3.14
r is the radius of the base of the cylinder
h is the height of the cylinder
Now Substituting value
[tex]Volume = \pi * r^2 * h\\Volume=3.14*8^2*14\\Volume=2816 ft^3[/tex]
Find the determinant of a 10 x 10 matrix which had a 2 in each main diagonal entry and zeros everywhere else.
The determinant of the given 10 x 10 matrix is 1024.
What is a matrix?A matrix is described as a rectangular array or table with rows and columns and numbers, symbols, or expressions that is used to represent a mathematical object or a property of such an object.
We apply the knowledge that the determinant of a diagonal matrix is the product of its diagonal entries in order to find the determinant of a 10 x 10 matrix with 2s on the main diagonal and zeros elsewhere,
Determinant = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2
We then calculate for the product and have:
Determinant = [tex]2 ^ 1^0[/tex] = 1024
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PLEASE HELP ME I HAVE TO ANSWER THIS AND THERES A TIME LIMIT
The value of m∠ECD is 50°
What is an equation?An equation is an expression that is used to show how numbers and variables are related using mathematical operators
In the right triangle, m∠B = 90°, hence:
m∠A + m∠B + m∠C = 180° (sum of angles in a triangle)
40 + 90 + m∠C = 180
m∠C = 50°
Also:
m∠C = m∠ECD (opposite angles are equal)
m∠C = m∠ECD = 50°
m∠ECD is 50°
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What is the measure of GEF?
OA. 50°
OB. 60°
OC. 160°
OD. 110°
110°
G
✓
The measure of angle CDE is 70°.
Option C) 70° is correct.
Angle BAC measures 80°.
Point D is located on side BC such that BD = CD.
Angle ADE measures 30°.
To find: Measure of angle CDE.
Since angle BAC measures 80° and angle ADE measures 30°, we can determine the measure of angle CDE by subtracting the sum of these two angles from 180° (the total measure of angles in a triangle).
Measure of angle CDE = 180° - (80° + 30°)
= 180° - 110°
= 70°
Therefore, the measure of angle CDE is 70°.
The correct answer is:
C) 70°
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The complete question may be like;
In the diagram below, triangle ABC is shown. Angle BAC measures 80°. Point D is located on side BC such that BD = CD. Angle ADE measures 30°. What is the measure of angle CDE?
A) 50°
B) 60°
C) 70°
D) 80°
Please let me know if you have any specific requirements or if there's anything else I can assist you with.
What is 5.7% of 134 m?
Give your answer as a decimal in metres
(m).
PLEASE DO IT
Answer:
7.638m
Step-by-step explanation:
Please help ASAP. I have been having trouble
Vertical Angles
---Vertical angles are congruent and can often be found where two lines intersect and make an "X" shape.
The vertical angles in this figure are XAW and UAY.
Adjacent angles that are neither complementary nor supplementary
---Adjacent angles are angles that share a line and are, as a result, next to each other.
Two adjacent angles in this figure that are neither complementary nor supplementary are XAW and ZAY.
Supplementary Angles
---Supplementary angles form a straight line, or 180 degree angle.
The supplementary angles in this figure are XAW and WAU.
Complementary Angles
---Complementary angles form a right, or 90 degree angle.
The complementary angles in this figure are XAW and XAZ.
Hope this helps!
Step-by-step explanation:
See image
A group of 6 students was asked, "How many hours did you watch television last week?" Here are their responses.
20,4,7,7, 10, 10
Find the median and mean number of hours for these students.
If necessary, round your answers to the nearest tenth.
(a) Median:
(b) Mean:
hours
hours
Answer: median = 8.5
mean=
9.7
total = 58
Answer:
median=8.5 hours Mean=9.7 hours
Step-by-step explanation:
First you take the values and add them together, find the sum.
20+4+7+7+10+10=x
x=58
now take 58 and divide it by the number of students
58/6=9.66666
the mean would be 9.7 hours since it asks to round to the nearest 10th
and for the median sort it from lowest to highest
4,7,7,10,10,20
now since in the middle are 7 and 10, add those together and divide by 2
10+7=17
17/2=8.5
the median is 8.5
Record the information you found for steps 2 and 3 here. Make sure you discuss how the company got money to start the
business, employee data, and what products or services the company provides in comparison with what other similar
business plans are offering.
BIVE &
BIVE & is a company that provides a platform for businesses to connect with and engage with their customers.
What is the company about?The company was founded in 2015 by two entrepreneurs, and it has since raised over $10 million in funding. BIVE & offers a variety of features that allow businesses to create and manage their own social media profiles, as well as to track and measure their social media engagement. The company also offers a variety of tools that allow businesses to create and manage their own email marketing campaigns.
BIVE &'s employee data is not publicly available. However, the company has stated that it has over 50 employees. BIVE &'s products and services are similar to those offered by other social media marketing platforms, such as Hootsuite and Buffer. However, BIVE &'s platform is designed specifically for businesses that want to connect with and engage with their customers on a social level.
BIVE &'s main source of revenue is from its subscription fees. The company offers a variety of subscription plans, starting at $29 per month. BIVE & also offers a free trial of its platform.
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How to right 0.481 in standard form
Answer:
4.81 × 10-1
Also its "write"
Also I have your IP
Also I'm kidding relax
In a Leichtman Research Group survey of 1000 TV households, 74.8% of them had at least one Internet-connected TV device (for example, Smart TV, standalone streaming device, connected video game console). A marketing executive wants to convey high penetration of Internet-connected TV devices, so he makes the claim that the percentage of all homes with at least one Internet-connected TV device is equal to 78%. Test that claim using a 0.01 significance level. Use the P-value method. Use the normal distribution as an approximation to the binomial distribution.
W do not have sufficient evidence at the 0.01 level of significance to reject the claim made by the marketing executive
How to explain the normal distributionWe'll perform a one-sample z-test for proportions.
From the survey, we know:
Sample size (n) = 1000
Sample proportion) = 0.748
Under the null hypothesis:
Proportion (p0) = 0.78
Now we can calculate the z-score:
z = (0.748 - 0.78) / ✓(0.78 * (1 - 0.78)) / 1000]
= -0.032 / ✓(0.1716 / 1000]
= -0.032 / 0.0131
≈ -2.44
From the z-table, the P-value for -2.44 is approximately 0.015.
However, we need to double this value to get the two-tailed P-value: 2 * 0.015 = 0.03.
If the P-value is less than the significance level (α = 0.01), we reject the null hypothesis. In this case, the P-value (0.03) is greater than α, so we do not reject the null hypothesis.
Based on the data from the Leichtman Research Group survey, we do not have sufficient evidence at the 0.01 level of significance to reject the claim made by the marketing executive.
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The figure shown is composed of two congruent triangles and a square. Measurements are given in inches. 1 4 7 What is the total area of the figure in square inches? Enter your answer in the box. X 2 5 8 5 in. 0 4 in. 5 in. 3 6 9 6 in. pla 5 in. 4 in. 5 in.
The total area of the figure formed by the congruent triangles and the square is 60 sq in
For square
A = s²
where s is the side
Given:
s = 6 in
Area = 6 * 6
= 36 sq in
Area of triangle = 0.5bh
where b is the base
h is the height
Given:
b = 6 in
h = 4 in
A = 0.5 * 6 * 4
= 12 sq in
Total area of the figure = 2 * Area of triangle + area of square
= 2 * 12 + 36
= 24 + 36
= 60 sq in
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Goran bought 8 pounds of rice for $4.
How many pounds of rice did he get per dollar?
PLEASE HELP ME
Answer:
Step-by-step explanation:
32
Mark brought $43.00 to the state fair. He bought a burger, a souvenir, and a pass. The burger was
1
4
as much as the souvenir, and the souvenir cost
2
3
the cost of the pass. Mark had $4.50 left over after buying these items.
What was the cost of each item?
The cost of the burger is $10.50, the cost of the souvenir is $28.00, and the cost of the pass is $42.00.
Let's assume the cost of the pass is x dollars.
According to the given information:
The burger costs 1/4 of the souvenir, so the burger's cost is[tex](1/4) \times x[/tex]dollars.
The souvenir costs 2/3 of the pass, so the souvenir's cost is [tex](2/3) \times x[/tex]dollars.
Mark had $4.50 left over after buying these items, so we can set up the following equation:
[tex]43.00 - [(1/4) \times x + (2/3) \times x] = $4.50[/tex]
Simplifying the equation, we have:
[tex]43.00 - [(1/4) \times x + (2/3) \times x] = $4.50[/tex]
[tex]43.00 - (1/4 + 2/3) \times x = $4.50[/tex]
[tex]43.00 - (3/12 + 8/12) \times x = $4.50[/tex]
[tex]43.00 - (11/12) \times x = $4.50[/tex]
To solve for x, we'll isolate the variable on one side of the equation:
$43.00 - $4.50 = (11/12) * x
$38.50 = (11/12) * x
Now, we can solve for x by multiplying both sides of the equation by (12/11):
[tex](12/11) \times $38.50 = x[/tex]
$42.00 = x
Therefore, the cost of the pass is $42.00.
Now we can find the costs of the burger and the souvenir:
The burger costs 1/4 of the souvenir, so its cost is (1/4) * $42.00 = $10.50.
The souvenir costs 2/3 of the pass, so its cost is (2/3) * $42.00 = $28.00.
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A bag contains 8 red marbles 3 blue marbles and 6 Green marbles is three marbles are
drawn out of the bag. What is the probability to the nearest thousand that all three marbles will be red
The probability to the nearest thousand that all three marbles drawn will be red is approximately 0.080.
There are 8 red marbles, 3 blue marbles, and 6 green marbles in the bag so the total possible outcomes in this scenario are:
8+3+6=17.
The probability of getting a red marble on the first draw is simply equal to:
= 8/17
The probability of getting a red marble on the second draw without replacement is equal to:
= 7/16
The probability of getting a red marble on the third draw without replacement is equal to:
= 6/15
The probability of getting three red marbles in a row is:
= [tex]\frac{8}{17}*\frac{7}{16}*\frac{6}{15}[/tex]
=[tex]\frac{7}{85}[/tex]
or 0.082
after rounding it to the nearest thousand, we get the probability [tex]^\sim_\sim[/tex] 0.080
Therefore, the probability to the nearest thousand that all three marbles drawn will be red is approximately 0.080.
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Select the correct answer. What are the x- and y-intercepts of the function g(x) = (x + 1)(x2 − 10x + 24)? A. x-intercepts: -1, 4, 6; y-intercept: 24 B. x-intercepts: -6, -4, and 1; y-intercept: 24 C. x-intercepts: -4, -1, 6; y-intercept: -24 D. x-intercepts: -6, -1, 4; y-intercept: -24
The x- and y-intercepts of the function g(x) = (x + 1)(x² − 10x + 24) include the following: A. x-intercepts: -1, 4, 6; y-intercept: 24.
What is the x-intercept?In Mathematics, the x-intercept is also referred to as horizontal intercept and the x-intercept of the graph of any function simply refers to the point at which the graph of a function crosses or touches the x-coordinate (x-axis) and the y-value or value of "y" is equal to zero (0).
When y = 0, the x-intercepts can be calculated as follows;
g(x) = (x + 1)(x² − 10x + 24)
0 = (x + 1)(x² − 10x + 24)
0 = (x + 1)(x² − 6x - 4x + 24)
0 = (x + 1)x(x − 6) -4(x - 4)
0 = (x + 1)(x - 6)(x - 4)
x = -1, 4, 6.
When x = 0, the y-intercept can be calculated as follows;
g(x) = (x + 1)(x² − 10x + 24)
g(0) = (0 + 1)(0² − 10(0) + 24)
g(0) = 24.
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What is the probability that a student who plays an instrument does not play a sport?
What is the probability that a student plays an instrument given that they play a sport?
Answer:
.2222
Please give the brainliest, really appreciated. Thank you
what value of x is in the solution set of the inequality 2(3x-1)>4x-6
Answer: the solution set of the inequality 2(3x-1)>4x-6 is all values of x greater than -2.
Step-by-step explanation: To solve the inequality 2(3x-1)>4x-6, we first simplify the left side by distributing the 2, which gives us 6x-2. Substituting this back into the original inequality, we get:
6x-2 > 4x-6
Next, we isolate the variable term (6x) by subtracting 4x from both sides:
2x-2 > -6
Then, we add 2 to both sides to isolate the variable term completely:
2x > -4
Finally, we divide both sides by 2 to solve for x:
x > -2
Therefore, the solution set of the inequality 2(3x-1)>4x-6 is all values of x greater than -2.
Norbit buys a car for $32,550. If he finances it for 4 years at an annual
interest rate of 8%, what will his monthly payment be? show your work
Norbit is looking to buy a car for $32,550 and finance it over 4 years. Using an annual interest rate of 8%, we can calculate his monthly payment.
First, we will calculate the total amount of interest over the 4-year period. To do this, we multiply the interest rate (8%) by the amount borrowed ($32,550) and then by the number of years (4).
0.08 × $32,550 × 4 = $10,620Next, we need to find the total amount that Norbit will pay over the 4-year period. To do this, we add the amount borrowed ($32,550) to the total interest ($10,620).
$32,550 + $10,620 = $43,170.Finally, to calculate the monthly payment, we divide the total amount by the number of months in 4 years (48). q
$43,170 ÷ 48 = $899.37Therefore, if Norbit finances his car for 4 years at an annual interest rate of 8%, his monthly payment will be $899.37
Hope this helps! Have a nice day. :)