As the density of Mercury is higher than that of both Copper and Zinc, so both the new & old penny will float on mercury.
Define density of a metal?By dividing the object's mass by its volume, we may determine the density of metal.
Mass/volume equals density.
For ex, the object would have a density of 0.284 per cubic inch if its mass were 7.952 pounds and its volume were 28 cubic inches.
Now here in the given question,
Density of copper = 8.8g/cm³
Density of zinc = 7.2g/cm³
Here, both the densities are lesser than that of mercury.
Hence, both the metal pennies will float when dropped into a beaker of mercury.
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Select the correct triangle.
Which triangle represents a reflection of triangle A across line m?
A
B
m
D
с
Answer:
Step-by-step explanation:
(D)
if you can complete this thing with full explanation i will mark rainliest
Answer:
A kite
Step-by-step explanation:
A kite shape is a quadrilateral in which two pairs of adjacent sides are of equal length. No pair of sides in a kite are parallel but one pair of opposite angles are equal
The diagonals bisect at right angles but all four sides are not equal, the sides are not parallel and there is only one line of symmetry
Three friends, Jessa, Tyree, and Ben, are collecting canned food for a culinary skills class. Their canned food collection goal is represented by the expression 11x2 − 2xy + 6. The friends have already collected the following number of cans:
Jessa: 2xy + 4
Tyree: x2
Ben: 3x2 − 7
Part A: Write an expression to represent the amount of canned food collected so far by the three friends. Show all your work.
Part B: Write an expression that represents the number of cans the friends still need to collect to meet their goal. Show all your work.
The expression that represents the amount of canned food collected so far by the three friends is [tex]$4x^2 + 2xy - 3$[/tex] and the expression that represents the number of cans the friends still need to collect to meet their goal is [tex]7x^2 + 9$.[/tex]
What is an expression?
In mathematics, an expression is a combination of numbers, variables, operators, and/or functions, which when arranged in a meaningful way, represents a mathematical relationship or a quantity.
Part A:
To find the amount of canned food collected so far by the three friends, we need to add up the number of cans collected by each friend. So, we can write:
Amount collected [tex]$= \text{Jessa's collection} + \text{Tyree's collection} + \text{Ben's collection}$[/tex]
Substituting the given expressions, we get:
Amount collected [tex]$= (2xy + 4) + x^2 + (3x^2 - 7)$[/tex]
Simplifying the expression, we get:
Amount collected [tex]$= 4x^2 + 2xy - 3$[/tex]
Therefore, the expression that represents the amount of canned food collected so far by the three friends is [tex]$4x^2 + 2xy - 3$[/tex].
Part B:
To find the number of cans the friends still need to collect to meet their goal, we need to subtract the amount collected by the three friends from the goal expression. So, we can write:
Number of cans needed [tex]$= \text{Goal} - \text{Amount collected}$[/tex]
Substituting the given expressions, we get:
Number of cans needed [tex]$= (11x^2 - 2xy + 6) - (4x^2 + 2xy - 3)$[/tex]
Simplifying the expression, we get:
Number of cans needed [tex]$= 7x^2 + 9$[/tex]
Therefore, the expression that represents the number of cans the friends still need to collect to meet their goal is [tex]7x^2 + 9$.[/tex]
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100 points please help
Answer:
(8x + 1) (8x - 1)
Step-by-step explanation:
64x² - 1
Rewrite 64x² as (8x)²
(8x)² - 1
Rewrite 1 as 1²
(8x)² - 1²
Since both terms are perfect squares, factor using the difference of squares formula, a² - b² = (a + b) (a - b) where a = 8x and b = 1
So, our answer is (8x + 1) (8x - 1)
the function f(x)=6x^2-180x=1000 represents the profit f(x) in thousands of dollars of selling x items. what is the meaning of the extreme value
Answer:
To find the extreme value of the function f(x) = 6x^2 - 180x + 1000, we can first take the derivative of the function and set it equal to zero:
f'(x) = 12x - 180 = 0
Solving for x, we get x = 15. Substituting this value back into the original function, we get:
f(15) = 6(15)^2 - 180(15) + 1000 = 1250
So the extreme value of the function is 1250, which represents the maximum profit in thousands of dollars that can be earned by selling a certain number of items.
More specifically, the value x = 15 is the value of x that maximizes the profit, and the maximum profit is $1,250,000. This means that if the company sells 15 items, they will make the most profit possible.
Step-by-step explanation:
Preston and Kim are fostering homeless kittens. Together they have fostered 47 kittens. Preston has fostered one less than one third as many kittens as Kim. How many kittens has Preston and Kim each fostered?
Answer:
Let's use variables to represent the number of kittens each person has fostered.
Let x be the number of kittens Kim has fostered.
Then, according to the problem, Preston has fostered one less than one third as many kittens as Kim, so Preston has fostered:
(1/3)x - 1
We know that the total number of kittens fostered is 47. Therefore, we can write an equation:
x + (1/3)x - 1 = 47
Simplifying and solving for x:
(4/3)x = 48
x = 36
So Kim has fostered 36 kittens.
To find out how many kittens Preston has fostered, we can substitute x = 36 into the expression we found earlier:
(1/3)x - 1 = (1/3)(36) - 1 = 11
Therefore, Preston has fostered 11 kittens.
In summary, Kim has fostered 36 kittens and Preston has fostered 11 kittens.
Answer:
36, 11
Step-by-step explanation:
Preston and Kim 47 kittens
Kim has fostered X number of kittens
Preston has fostered X/3 - 1 ( 1/3 of Kim - 1)
Total number of kitten will be Preston +Kim
X +1/3X - 1 = 47
Add 1 to both sides
X + 1/3X = 48
If 4/3X is 48, X is 36
If Kim has 36kittens, Preston fostered 47- 36 =11
To check
1/3 of 36 = 12
Subract 1 = 11
You have 24 juice cans.
Show all of the ways you
can arrange these cans into
arrays. Draw the arrays on a
separate sheet of paper.
Teyo has 25 juice cans. Show all
of the ways he can arrange his
cans into arrays. Draw the
arrays on a separate sheet of
paper.
1. For your 24 cans of juice, the possibilities of organizing them in arrays can be:
24 cans in a single row12 cans in two rows of 68 cans in three rows of 3, with two cans left6 cans in four rows of 2, with six cans left4 cans in six rows of 1, with 8 cans left3 cans in eight rows of 1, with 0 cans left2 cans in twelve rows of 1, with 0 cans left1 can in twenty-four rows of 1, with 0 cans left2. For Teyo's 25 cans of juice, the possible arrays are:
25 cans in a single row12 cans in two rows of 6, with 1 can left10 cans in two rows of 5, with 5 cans left8 cans in three rows of 2, with 1 can left6 cans in four rows of 1, with 1 can left5 cans in five rows of 1, with 0 cans left2 cans in twelve rows of 1, with 1 can left1 can in twenty-five rows of 1, with 0 cans left over.How to find these possible arrays?You must first consider the factors of the total number of juice cans you own. For activity 1, you must consider the factors of the 24 cans of juice, that is, the factors of 24, which are 1,2,3,4,6,8,12 and 24, and then find the combinations of these factors to sort them into arrays.
Using the information above, you can effectively draw the arrays on a separate sheet of paper.
Therefore, matrices are meant to represent a set of objects or values in a rectangular shape, arranged in rows and columns and are intended to represent a variety of numerical data, text and images.
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William bought a 0. 5 liter bottle of liquid plant food he uses 40 milliliters a week what measurements are given
One bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.
William uses 40 milliliters of liquid plant food per week, so to find out how much plant food he needs for 12 weeks, we can simply multiply the weekly usage by the number of weeks:
Amount of plant food needed for 12 weeks = 40 milliliters/week x 12 weeks = 480 milliliters
So, William needs 480 milliliters of liquid plant food for 12 weeks.
Since the bottle of liquid plant food, William purchased contains 0.5 liters or 500 milliliters of liquid plant food, we can see that one bottle is enough for 12 weeks since 480 milliliters is less than the total amount of liquid plant food in the bottle.
In fact, we can calculate how many weeks one bottle of liquid plant food will last William by dividing the total amount of liquid plant food in the bottle by the amount used per week:
Time to use up the liquid plant food = (Total amount of liquid plant food) / (Amount used per week) = 500 ml / 40 ml/week ≈ 12.5 weeks
So, we can say that one bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.
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The correct question should be:
William bought a 0.5 -liter bottle of liquid plant food. He uses 40 milliliters each week? How much plant food does William need for 12 weeks? Is one bottle enough for 12 weeks?
Hey I need help with these questions ASAP
We find the following conclusions concerning the telegraph wire:
Case 1: The perimeter of the circle is equal to 20π centimeters.
Case 2: The extra length for the telegraph wire is equal to 10π meters.
How to determine the perimeter of a circleIn this problem we find two cases where the perimeter of a circle must be computed for a telegraph wire, this can be done by using the following formula:
s = 2π · r
Where:
s - Perimeterr - RadiusNow we proceed to determine the perimeter for each case.
Case 1: (Please notice that diameter is twice the radius)
s = 2π · (20 / 2)
s = 20π cm
The circle has a perimeter of 20π centimeters.
Case 2: (The Earth has a radius of 6371000 meters)
Δs = 2π · (6371005 - 6371000)
Δs = 2π · 5
Δs = 10π m
An extra length of 10π meters is required for the telegraph wire.
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6. The value, V(t), of a new car is decreasing according to the function V(t) = 22,465 (0.88)', where time t is
measured in years and V(t) is given in dollars. Which of the following represents the average rate of decrease
in the value of the car over the first 5 years of ownership?
An expression that represent the average rate of decrease in the value of the car over the first 5 years of ownership is: 3. 11,855.50 per year.
How to determine the average rate of decrease after 5 years?In Mathematics and Statistics, a population or physical asset that decreases at a specific period of time represent an exponential decay. This ultimately implies that, a mathematical model for any population or physical asset that decreases by r percent per unit of time is an exponential equation of this form:
P(t) = I(1 - r)^t
Where:
P(t ) represents the population.t represents the time or number of years.I represents the initial value of car.r represents the decay rate.By substituting given parameters, we have the following:
P(t) = I(1 - r)^t
P(5) = 22,465(0.88)^5
P(5) = 22,465(0.5277319168)
P(5) = 11,855.50 per year.
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4.02 Lesson check ! (10)
Answer:
yes
d = -30.
the difference between each successive term will give you -30, that's the common difference.
E.g -62 - ( -32) = -62 + 32 = -30
Answer:
Yes (choice 1)
d = - 30 (choice 4)
Step-by-step explanation:
It is an arithmetic sequence because the difference between successive terms is -30
-32 - (-2) = -32 + 2 = -30
-62 - (-32) = -62 + 32 = -30 etc.
Therefore the common difference is -30
you have $30.00 in your wallet when you drive through Steak-n-Shake. You want to order 5 meals from the $4 per meal menu. You also want to buy as many shakes as possible. The shakes are $3 each. Write and solve an equation that represents the situation. How many shakes can you afford? Round appropriately.
Answer:
Let x be the number of shakes you can buy.
The cost of 5 meals is:
5 * $4 = $20
The total cost of the meals and shakes is:
$20 + $3x = $30
Subtracting $20 from both sides of the equation:
$3x = $10
Dividing both sides of the equation by $3:
x = 3.33
Rounding down to the nearest whole number, you can buy 3 shakes.
I hope this helps!
Please ASAP Help
Will mark brainlest due at 12:00
Answer:
D is (3, -2)
Option D
Step-by-step explanation:
If E is the midpoint of DF then the x-distance between D and E must be the same as that between E and F and similarly for the y-distance
In addition, the x, y coordinates of D must be less than the x, y coordinates for E
x-distance from E to F = 5- 4 = 1
x-distance from D to E = 1 so x-coordinate of D = 4 - 1 = 3
y-distance from E to F = 8 - 3 = 5
y-distance from D to E = 3 - 5 = -2
So coordinate of D is(3, -2)
Suppose the standard deviation of the ages of all Florida panthers is 14.3 years. Let be the mean age for
a sample of a certain number of Florida panthers. What sample size will give the standard deviation of
equal to 0.8 years?
Round the solution up to the nearest whole number, if necessary.
A sample size οf 805 Flοrida panthers will give a standard deviatiοn οf 0.8 years.
What is revealed by standard deviatiοn?It displays the average deviatiοn οf each scοre frοm the mean. In a nοrmal distributiοn, a high standard deviatiοn indicates that values are spread οut frοm the mean, whereas a lοw standard deviatiοn indicates that values are clustered clοse tο the mean.
We can use the fοllοwing fοrmula tο calculate the sample size that will result in a standard deviatiοn οf 0.8 years:
n = (z * σ / E)²
Where:
The sample size is denοted by n.
z is the desired cοnfidence level's z-scοre (we'll assume 95% cοnfidence, sο z = 1.96)
is the standard deviatiοn οf the pοpulatiοn (given as 14.3 years)
E represents the margin οf errοr (given as 0.8 years)
The fοllοwing results are οbtained when the given values are substituted:
[tex]n = (1.96 * 14.3 / 0.8)^2 \sn = 804.57[/tex]
We get the fοllοwing when we rοund up tο the nearest whοle number:
n = 805
A sample size οf 805 Flοrida panthers results in a standard deviatiοn οf 0.8 years.
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The population of some bacteria increases by 15% every day. If the original
population was 6000 bacteria, calculate the size of the population after 10 days
Answer:
To solve this problem, we can use the formula for exponential growth:
N = N0 * (1 + r)^t
Where:
N0 = the initial population size
N = the population size after t time periods
r = the growth rate per time period
t = the number of time periods
In this case, we know that the initial population (N0) is 6000, the growth rate (r) is 15% per day, and we want to find the population size (N) after 10 days (t = 10).
First, we need to convert the growth rate from a percentage to a decimal:
r = 15% / 100% = 0.15
Now we can plug in the values and solve for N:
N = 6000 * (1 + 0.15)^10
N = 6000 * 3.439
N ≈ 20,634
Therefore, the population of bacteria after 10 days would be approximately 20,634.
Is the function y= 7(2/3)^x exponital growth or exponential decay
Answer: The function y = 7(2/3)^x is an example of exponential decay.
This is because the base of the exponential function, 2/3, is between 0 and 1, which means that the function is decreasing as x increases. As x increases, the value of (2/3)^x becomes smaller and smaller, which causes the overall value of the function y to decrease over time.
Exponential decay is a type of exponential function where the value of the function decreases over time. In contrast, exponential growth is a type of exponential function where the value of the function increases over time, and the base of the function is greater than 1.
Step-by-step explanation:
It takes Andrew
720
720720 seconds to take a shower. He spends an additional
420
420420 seconds eating breakfast.
start fraction, 4, divided by, 5, end fraction of the distance to the hole. On his second stroke, the ball traveled
79
7979 meters and went into the hole
To convert the total time from seconds to minutes, we need to divide by 60. So, the total time in minutes would be: (720 + 420) / 60 = 1140 / 60 = 19 minutes.
To find the total time it takes Andrew to take a shower and eat breakfast, we need to add the time it takes for each activity. Andrew takes 720 seconds to take a shower and 420 seconds to eat breakfast. To convert seconds to minutes, we divide the total time in seconds by 60. So the total time it takes Andrew to take a shower and eat breakfast is (720 + 420) / 60 = 19 minutes. Therefore, it takes Andrew 19 minutes to take a shower and eat breakfast.
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Complete question:
It takes Andrew 720 seconds to take a shower. He spends an additional 420 seconds eating breakfast. How many minutes does it take Andrew to take a shower and eat breakfast?
Use the figure.
A
D
B
1. Given AB = = DC, m/ABD = 35°,
and m/BDC
25°. How does AD
compare to BC?
-
The required length of AD is equal to the length of BC.
Explain about Quadrilateral?
A polygon with four edges, four angles, and four vertices is called a quadrilateral. The Latin terms quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral. A quadrilateral is shown in the above picture as an example.
According to question:First, we draw the quadrilateral ABCD and label the given angles:
[tex]$\begin{align*}\angle ABD &= 35^\circ \\angle BDC &= 25^\circ\end{align*}[/tex]
Since opposite sides of quadrilateral ABCD are equal, we have:
[tex]$\begin{align*}AB &= DC\end{align*}[/tex]
We can use this fact to draw diagonal BD and label its length as x:
[tex]$\begin{align*}AB &= DC \AD + DB &= BC + DB \AD &= BC\end{align*}[/tex]
Therefore, we can conclude that:
[tex]$\begin{align*}AD &= BC\end{align*}[/tex]
Thus, the length of AD is equal to the length of BC.
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Write 16 over 28 in simplest form
Answer:
4/7
Step-by-step explanation:
16/28= 8/14= 4/7
Lety=f(x)be a function with domainD=[−12,−8]and rangeR=[−16,−10]. Find the domainDand rangeRfor each function. (Enter your answers using interval notation. If there is no solution, enter NO SOLUTION.) (o)y=21f(x)domainD=rangeR=(b)y=f(2x)domainD=rangeR=(c)x=f(x−2)+5domainD=rangeR=(d)y=(x+4)−1domain0=rangeft=(d)y=f(x+4)−1domainD=rangeR=(e)y=f(−x)domainD=rangeR=(f)y=−f(x)domainD=rangeR=(g)y=∣f(x)∣domainD=rangeR=
Answer:Park rangers released 4 fish into a pond in year 0. Each year, there were three times as many fish as the year before. How many fish were there after x years? Write a function to represent this scenario.
Step-by-step explanation:
An function which best represent the given scenario is, 4 x 3ˣ. So option B is correct.
What is geometric progression?
In algebra, in sequence we study various progressions, one of the progression is geometric, in this progression for every two consecutive terms, the common ratio is the same.
Formula for nth term of G.P.,
Tₙ = a×rⁿ
where a is first term and r is common ratio
Given that,
Park rangers released 4 fish into a pond in year 0.
Each year, there were three times as many fish as the year before.
The number of fish after x years = ?
After 1 year,
the number of fish = 4 x 3
After 2 year,
the number of fish = 4 x 3 x 3
= 4 x 3²
After 3 year,
the number of fish = 4 x 3² x3
= 4 x 3³
Similarly, after x years
the number of fish = 4 x 3ˣ
Hence, the expression is 4 x 3ˣ
ū = (–7, 2)
Find the direction angle of u.
Enter your answer as an angle in degrees between 0° and 360° rounded to the
nearest hundredth.
The direction angle of the vector Ū is approximately 16.26°.
A vector's direction angle is the angle, measured anticlockwise, between the positive x-axis and the vector in standard position.
Trigonometry can be used to determine the direction angle of the vector = (-7, 2).
The direction angle is determined by:
θ = tan^-1(y/x)
where y is the vector's vertical component and x is its horizontal component (in this example, -7). (in this case, 2).
θ = tan^-1(2/-7)
We can determine: Using a trigonometric table or a calculator
θ ≈ 16.26°
As a result, the vector's direction angle is roughly 16.26°.
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The width of a rectangular field is 20 feet less than its length. The area of the field is 12,000 ft2. What is the length of the field?
80 ft
100 ft
120 ft
140 ft
Answer:
120 ft
Step-by-step explanation:
Let's assume that the length of the field is x feet. Then, according to the problem statement, the width of the field is (x - 20) feet.
The area of a rectangle is given by the formula A = length x width. So, we can write:
x(x - 20) = 12,000
Expanding the left-hand side, we get:
x^2 - 20x = 12,000
Bringing all the terms to one side, we have:
x^2 - 20x - 12,000 = 0
Now, we can solve this quadratic equation using the quadratic formula:
x = (-(-20) ± sqrt((-20)^2 - 4(1)(-12,000))) / (2(1))
x = (20 ± sqrt(20^2 + 48,000)) / 2
x = (20 ± 220) / 2
We discard the negative root, since a length cannot be negative, and we get:
x = 120
Therefore, the length of the field is 120 feet.
Kenny saved $10 every week. Which expression represents the amount of money, in dollars, Kenny will save in x weeks?
Please help
The equation represents the amount of money, in dollars, Kenny will save in x weeks is y = $10*x
Which expression represents the amount of money Kenny will save in x weeks?We know that Kenny saved 10 dollars every week.
Then, if we define the variable y as the savings, after one week we know that:
y = 10
After another week:
y = 20
And so on.
We can define x as the number of weeks, and now we know that after x weeks, the amount of money that Kenny has saved is x times $10, this gives the linear equation.
y = $10*x
That is the equation we wanted.
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On a map, 2 cm = 40 miles. If two cities on the map are 4.8 cm apart, determine the actual distance between the two cites. Show how you determined your answer.
In reality, [tex]96[/tex] miles distance separate the two cities.
In one words, define distance.We kept an eye on them from afar. Compared to earlier, she perceives a gap between her and her brother. They had been close friends earlier, but now there was a great distance between them. He desires to disassociate himself from his old employer.
Class 6 distance: what is it?Mileage is a vector variable that quantifies "how much space an object has travelled through" while in motion. An object's dependent and independent variables in position is referred to as displaced, a vector variable that measures "the extent to which place an item is."
Using the scale provided, we can establish the proportion:
[tex]2 cm / 40 miles = 4.8 cm / x[/tex]
where [tex]x[/tex] is the actual distance between the two cities in miles.
To solve for [tex]x[/tex], we can cross-multiply:
[tex]2 cm * x = 40 miles * 4.8 cm[/tex]
Simplifying:
[tex]2x = 192[/tex]
[tex]x = 96[/tex]
Therefore, the actual distance between the two cities is [tex]96[/tex] miles.
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What attributes do a right pyramid and a sphere have in common?
Both shapes have 1 apex and a curved surface.
Both shapes have a curved surface and at least 2 edges.
Both shapes have a circular base and a circular face.
These shapes do not share any common attributes.
The common attributes of a right pyramid and a sphere are that they both have an apex and a curved surface.
What is a shape?
Shape can be defined as the external physical outline, structure or form of an object or entity. It refers to the appearance or visual characteristic of an object or entity, and is often determined by its edges, contours, curves, angles, or other physical attributes.
A right pyramid and a sphere have some similarities and differences in their attributes.
Similarities:
Both shapes have a single point at the top which is called the apex.
Both shapes have a curved surface. In the case of the right pyramid, the curved surface is a set of triangles that converge to the apex. In the case of the sphere, the curved surface is a continuous, smooth surface.
Both shapes are three-dimensional objects that occupy space.
Differences:
The base of a right pyramid is a polygon, whereas a sphere has no edges or vertices.
The curved surface of a right pyramid is made up of flat triangles, whereas a sphere's curved surface is continuous and has no flat faces.
A right pyramid has edges where the flat faces meet, whereas a sphere has no edges or corners.
A right pyramid has a finite number of vertices and edges, whereas a sphere has an infinite number of points on its curved surface.
A right pyramid can have different base shapes and sizes, whereas a sphere has only one size and shape.
Therefore, the common attributes of a right pyramid and a sphere are that they both have an apex and a curved surface.
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–69u − 47 =
i just need an answer asp
Answer:
-116u
Step-by-step explanation:
-69-47 is 116. The varblie stays making it -116u
Which equation would be the best to solve by completing the square?
3x^2 + 4x = -2
x^2 + 8x = 20
x^2 + 11x = 40
x^2 = 36
The equation [tex]x^2 + 4x + 4 = 0[/tex] can be solved by completing the square.
To solve an equation by completing the square, first move the constant term to the other side of the equation. So for the equation [tex]x^2 + 4x + 4 = 0[/tex], we can move the 4 to the right side to get [tex]x^2 + 4x = -4[/tex]. Then divide the coefficient of the x-term (4 in this case) by 2, and square the result. 4 divided by 2 is 2, and 2 squared is 4, so we add 4 to both sides: [tex]x^2 + 4x + 4 = -4 + 4[/tex], which simplifies to [tex]x^2 + 4x = 0[/tex]. Then divide the coefficient of the x-term (4 in this case) by 2, and square the result. 4 divided by 2 is 2, and 2 squared is 4, so we add 4 to both sides.
[tex]x^2 + 4x + 4 = 0[/tex]
[tex]x^2 + 4x = -4[/tex]
[tex]x^2 + 4x + 4 = -4 + 4[/tex]
[tex]x^2 + 4x = 0[/tex]
[tex]x^2 + 4x + 4 = 0[/tex]
[tex](x + 2)^2 = 0[/tex]
This gives us [tex]x^2 + 4x + 4 = 0[/tex]. Next, we can factor the left side of the equation: [tex](x + 2)^2 = 0[/tex]. Then we can take the square root of both sides and solve for x: x + 2 = 0 or x = -2.
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Solve the equation. Check your solutions.
∣2x+1∣=∣3x−11∣
To solve this equation, we need to consider two cases, one where 2x + 1 is positive and another where it is negative. We will then solve for x in each case and check our solutions to make sure they satisfy the original equation.
Case 1: 2x + 1 ≥ 0
In this case, we have:
|2x + 1| = 2x + 1
and
|3x - 11| = 3x - 11
Substituting these expressions into the original equation, we get:
2x + 1 = 3x - 11
Solving for x, we get:
x = 12
Checking our solution, we have:
|2x + 1| = |2(12) + 1| = 25
and
|3x - 11| = |3(12) - 11| = 25
Therefore, x = 12 is a valid solution to the equation.
Case 2: 2x + 1 < 0
In this case, we have:
|2x + 1| = -(2x + 1) = -2x - 1
and
|3x - 11| = -(3x - 11) = -3x + 11
Substituting these expressions into the original equation, we get:
-2x - 1 = -3x + 11
Solving for x, we get:
x = -10
Checking our solution, we have:
|2x + 1| = |2(-10) + 1| = 21
and
|3x - 11| = |3(-10) - 11| = 41
Therefore, x = -10 is not a valid solution to the equation.
Therefore, the only solution to the equation |2x + 1| = |3x - 11| is x = 12.
Find the total amount given the original price and tax or tip
123. 28,7. 5%
If the total amount given the original price and tax or tip are 123.28,7. 5%, the total amount including tax is $132.52.
To find the total amount given the original price and tax or tip, we need to add the amount of tax or tip to the original price.
In this case, the original price is $123.28 and the tax is 7.5%. To find the amount of tax, we can multiply the original price by the tax rate expressed as a decimal.
Tax = 0.075 x $123.28 = $9.24
Therefore, the amount of tax is $9.24. To find the total amount, we simply add the original price and the amount of tax:
Total amount = $123.28 + $9.24 = $132.52
Note that if the 7.5% was a tip instead of a tax, we would calculate it in the same way by multiplying the original price by the tip rate expressed as a decimal.
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Suppose that the total interest that will be paid on a 40-year mortgage from a home loan of $100,000 is going to be $480,000. What will be the payments each month if the payments are to pay off both the loan and the interest (rounded to the nearest hundredth)?
Since, that the total interest that will be paid on a 40-year mortgage from a home loan of $100,000 is going to be $480,000. Then, the payments each month if the payments are to pay off both the loan and the interest will be $1,504.
The 40-year loan has the lowest monthly payment at $1,504. But that only means "saving" $183 per month on the 30-year loan. When considering the total price of the house in this example, adding an additional 10 years to the term of the loan seems overkill, reducing the monthly payment by less than $200.
A 40-year loan doesn't sound like a good deal. But for homeowners struggling to meet their monthly payments and get a 40-year loan modification, the lower payments could have a big impact.
Comparing the 30-year and 15-year numbers is even more extreme. The monthly payment on the 15-year loan is an additional $700. Some buyers can afford higher payments. The advantage of the 15-year loan is that the total interest paid on the loan is $103,218, compared to $289,970 for the 30-year loan. Fifteen years seems to pass so quickly, and it's an exciting feeling to stop paying.
Objections to the 15-year loan could include a missed opportunity. With an interest rate of 4.67% on the 30-year loan, one can expect a higher rate of return in the long run by investing heavily in the stock market. But that raises the question of whether the $700 a month in cash freed up by the 30-year loan will be invested. It might be tempting to spend that money on a more expensive car than the one you would otherwise have purchased.
A family's needs, including space, savings and investment for retirement and education, as well as many household expenses should be considered when deciding which home to buy and the term of the loan. At a minimum, homebuyers need to understand how the different types of loans work.
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