The price of a new car is $40,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 8%/year compounded monthly. (Round your answers to the nearest cent) (a) What monthly payment will she be required to make if the car is financed over a period of 48 months? Over a period of 72 months? 48 months $ 72 months$ (b) What will the interest charges be if she elects the 48-month plan? The 72-month plan? 48-month plan $ 72-month plan Need Help? ReadH
Answers
The monthly payments required for the 48-month plan and 72-month plan are $699.96 and $517.47, respectively. The interest charges for the 48-month plan and 72-month plan are $3,598.08 and $7,256.64, respectively. This can be answered by the concept of Compound interest.
To calculate the monthly payment required, we can use the formula for the present value of an annuity:
PV = PMT x [1 - (1 + r/n)^(-nt)] / (r/n)
where PV is the present value of the loan, PMT is the monthly payment, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
For the 48-month plan, we have:
PV = 0.75 x $40,000 = $30,000 (the amount financed)
r = 0.08/12 = 0.00667 (the monthly interest rate)
n = 12 (monthly compounding)
t = 4 (number of years)
Plugging in the values, we get:
PMT = $699.96
For the 72-month plan, we have:
PV = 0.75 x $40,000 = $30,000
r = 0.08/12 = 0.00667
n = 12
t = 6 (number of years)
Plugging in the values, we get:
PMT = $517.47
To calculate the interest charges, we can subtract the amount financed from the total payments made over the loan term. For the 48-month plan, the total payments are:
PMT x 48 = $33,598.08
The interest charges are:
$33,598.08 - $30,000 = $3,598.08
For the 72-month plan, the total payments are:
PMT x 72 = $37,256.64
The interest charges are:
$37,256.64 - $30,000 = $7,256.64
Therefore, the monthly payments required for the 48-month plan and 72-month plan are $699.96 and $517.47, respectively. The interest charges for the 48-month plan and 72-month plan are $3,598.08 and $7,256.64, respectively.
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Related Questions
Each bus transported a total 1400 students and teachers to a zoo in buses and vans
each bus transported a total of 40 students and teachers
each van transported a total of 10 students and teachers
there were 10 more bus than vans
what is the number of students and teachers who rode to the zoo in bus
what is the number of students and teachers who rode to the zoo in vans
Answers
There were 35 buses and 25 vans, there were 14000 students and teachers who rode to the zoo in buses, and 250 students and teachers who rode to the zoo in vans.
Let b be the number of buses and v be the number of vans. We know that each bus transported 40 students and teachers, each van transported 10 students and teachers, and there were 10 more buses than vans.
We can use this information to write down two equations:
b * 40 + v * 10 = 1400
b = v + 10
We can solve the first equation for v:
v = (1400 - b * 40) / 10
Substituting this into the second equation, we get
b = ((1400 - b * 40) / 10) + 10
Simplifying, we get:
b = 140 - 4b
Solving for b, we get:
b = 35
Now that we know b, we can find v:
v = (1400 - 35 * 40) / 10
v = 25
Therefore, there were 35 buses and 25 vans. There were 1400 * 40 = 14000 students and teachers who rode to the zoo in buses, and 25 * 10 = 250 students and teachers who rode to the zoo in vans.
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hii i’ll give brainliest please help thanks :)
Answers
Answer:
3,6,9
Step-by-step explanation:
123 456 789
Answer:
85
Step-by-step explanation:
hi plz mark brainlist
*97 POINTS*
Use the numerals representing cardinalities in the Venn diagram, shown on the right, to give the cardinality of the set
A' ∩ B' ∩ C. '
n(A' ∩ B' ∩ C')= ___________
Answers
Answer:
19
Step-by-step explanation:
A' represents everything out A
B' represents everything out B
C' represents everything out C
So only the outside is left hope this helps
PLEASE HELP ME HURRY!!!!!!
Janice sold several items in a garage sale. She spent one-half of the money she made on a new bicycle. Next she spent one-half of what was left on a portable stereo set. If Janice had $80.00 left, how much money did she make from the garage sale?
Answers
Answer:
320
Step-by-step explanation:
hope it helps some one
Find a parametric representation for the upper half of the ellipsoid 4x2+2y2+z2=1.
Answers
The representation that describes the upper half of the ellipsoid 4x^2 + 2y^2 + z^2 = 1 using the parameters u and v, where 0 ≤ u ≤ 2π and 0 ≤ v ≤ 1.
To find a parametric representation for the upper half of the ellipsoid 4x^2 + 2y^2 + z^2 = 1, we will parameterize the variables x, y, and z using two parameters, u and v. Since we only want the upper half of the ellipsoid, we need to ensure z is non-negative.
Parameterize the x and y variables using the parameter u.
Let x = (1/2)cos(u) and y = (1/√2)sin(u). This way, 4x^2 + 2y^2 = 4(1/4)cos^2(u) + 2(1/2)sin^2(u) = cos^2(u) + sin^2(u) = 1.
Parameterize the z variable using the parameter v.
Since we want the upper half of the ellipsoid, let z = v, where 0 ≤ v ≤ 1.
Combine the parameterizations.
The parametric representation of the upper half of the ellipsoid is given by the vector function:
r(u, v) = ((1/2)cos(u), (1/√2)sin(u), v)
This representation describes the upper half of the ellipsoid 4x^2 + 2y^2 + z^2 = 1 using the parameters u and v, where 0 ≤ u ≤ 2π and 0 ≤ v ≤ 1.
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A baseball is seen to pass upward by a window with a vertical speed of 11 m/s. The ball was thrown by a person 19 m below on the street. Part A What was its initial speed? Express your answer to two significant figures and include the appropriate units. What altitude does it reach? Express your answer to two significant figures and include the appropriate units. Part C What time elapsed since it was thrown? Express your answer to two significant figures and include the appropriate units. What time will it take the baseball to reach ground again, counting from the moment it passed the window upward? Express your answer to two significant figures and include the appropriate units.
Answers
a) The initial speed of the ball is 19.3 m/s. b) The ball reaches a maximum altitude of 19.0 m. c) The time elapsed is 3.92 seconds. d) It will take 2.25 seconds for the baseball to reach the ground again.
To solve this problem, we can use the equations of motion under constant acceleration.
Given:
Vertical speed of the ball (upward) = 11 m/s
Initial vertical position (below the window) = 19 m
Part A: Initial Speed
The initial speed of the ball can be determined using the formula for vertical motion:
\(v^2\) = \(u^2\) + 2as
Since the ball is moving vertically upward, the final velocity (v) is 0 m/s when it reaches the highest point. The initial vertical position (s) is 19 m, and the acceleration (a) is -9.8 m/\(s^2\) (assuming downward direction as negative).
\(0^2\) = \(u^2\) + 2(-9.8)(19)
0 = \(u^2\) - 372.4
\(u^2\) = 372.4
u ≈ 19.3 m/s
Therefore, the initial speed of the ball is approximately 19.3 m/s.
Part B: Maximum Altitude
To determine the maximum altitude reached by the ball, we can use the equation:
\(v^2\) = \(u^2\) + 2as
Here, the final velocity (v) is 0 m/s, the initial speed (u) is 19.3 m/s, and the acceleration (a) is -9.8 m/\(s^2\).
\(0^2\) = \((19.3)^2\) + 2(-9.8)s
0 = 372.49 - 19.6s
19.6s = 372.49
s ≈ 19.0 m
Therefore, the ball reaches a maximum altitude of approximately 19.0 m.
Part C: Time Elapsed since Thrown
To calculate the time elapsed since the ball was thrown, we can use the equation for vertical motion:
s = ut + (1/2)a\(t^2\)
Here, the initial vertical position (s) is 19 m, the initial speed (u) is 19.3 m/s, and the acceleration (a) is -9.8 m/\(s^2\).
19 = 19.3t + (1/2)(-9.8)\(t^2\)
0 = -4.9\(t^2\) + 19.3t - 19
Using the quadratic formula, we can solve for t:
t ≈ 3.92 s or t ≈ 0.96 s
Therefore, the time elapsed since the ball was thrown is approximately 3.92 seconds.
Part D: Time to Reach Ground Again
To calculate the time it will take for the ball to reach the ground again, counting from the moment it passed the window upward, we can use the equation:
s = ut + (1/2)a\(t^2\)
Here, the initial vertical position (s) is 0 m (since it is the ground level), the initial speed (u) is 11 m/s (as it passes the window upward), and the acceleration (a) is -9.8 m/\(s^2\).
0 = 11t + (1/2)(-9.8)\(t^2\)
0 = -4.9\(t^2\) + 11t
Solving this quadratic equation, we find:
t ≈ 0 s or t ≈ 2.25 s
Therefore, it will take approximately 2.25 seconds for the baseball to reach the ground again, counting from the moment it passed the window upward.
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One-eighth a number is two more than one-fourth the number. What is the number? A. −16 B. −4 C. 8 D. 16
Answers
Answer:
\(\mathrm{A}\)
Step-by-step explanation:
Let that number be x.
\(1/8x=2+1/4x\)
\(1/8x-1/4x=2\)
\(-1/8x=2\)
\(x=2 \times -8/1\)
\(x=-16\)
Answer:
A. -16.
Step-by-step explanation:
1/8 x = 1/4 x + 2 where x is the number to be found.
Subtract 1/4 x for both sides of the equation:
-1/8x = 2
x = 2*-8
x = -16
Part 4: solve a real-world problem using an absolute fraction
A transaction is a positive if there is a sale and negative when there is a return. Each time a customer uses a credit cards for a transaction,the credit company charges Isabel.The credit company charges 1.5% of each sale and a fee of 0.5% for returns.
Latex represent the amount of transaction and f(x) represent the amount Isabel is charged for the transaction.Write a function that expresses f(x).
Answers
a) A function that expresses f(x) is f(x) = 1.5x.
b) A graph of the function is shown in the image below.
c) The domain and range of the function are all real numbers or [-∞, ∞].
How to write a function that describes the situation?Assuming the variable x represent the amount of a transaction and the variable f(x) represent the amount Isabel is charged for the transaction, a linear function charges on each sale by the credit card company can be written as follows;
f(x) = 1.5x
Part b.
In this exercise, we would use an online graphing tool to plot the function f(x) = 1.5x as shown in the graph attached below.
Part c.
By critically observing the graph shown below, we can logically deduce the following domain and range:
Domain = [-∞, ∞] or all real numbers.
Range = [-∞, ∞] or all real numbers.
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Complete Question:
A transaction is positive if there is a sale and negative when there is a return. Each time a customer uses a credit card for a transaction, the credit company charges Isabel. The credit company charges 1.5% of each sale and a fee of 0.5% for returns.
a) Let x represent the amount of a transaction and let f(x) represent the amount Isabel is charged for the transaction. Write a function that expresses f(x).
b) Graph the function.
c) What are the domain and range of the function?
Travel and Transportation A recent report by AAA estimated that 88 million Americans, and in particular 44% of millennials, are planning to take a family trip in 2018. Liberty Travel would like to determine if a different proportion of baby boomers are planning to take a trip. State the null and the alternative hypotheses in terms of the population proportion of baby boomers who are planning to take a family trip.
Answers
Let's denote the population proportion of baby boomers planning to take a family trip as p.
Null hypothesis (H₀): The proportion of baby boomers who are planning to take a family trip is equal to the proportion of millennials who are planning to take a family trip, which is 44%.
Mathematically, H₀: p = 0.44.
Alternative hypothesis (H₁): The proportion of baby boomers who are planning to take a family trip is different than the proportion of millennials who are planning to take a family trip, H₁: p ≠ 0.44.
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Find x. Give reasons to justify your solution.
Answers
Answer:
x = 28
Step-by-step explanation:
Okay COB is vertical to AOB, so we know they equal the same. Right the equation this way.
3x + x + x + 12 = 152 (collect like terms)
5x + 12 = 152 (subtract 12 on each side)
5x = 140 (divide by 5 on each side)
x = 28
(PLUG IN)
3(28) + (28) + (28) + 12 = 152
84 + 28 + 28 + 12 = 152
152 = 152
10% of what = 70,000
Answers
Answer: 7000.
Step-by-step explanation:
Answer:
700,000
Step-by-step explanation:
70000 ÷ 10% = 700000
Juno is a satellite that orbits and studies Jupiter. Let us assume here for simplicity that its orbit is circular. (a) If the radius or the orbit is 100×10
3
km (or 100Mm ) and its speed is 200×10
3
km/h, what is the radial acceleration? (b) If the satellite's speed is increased to 300×10
3
km/h and the radial acceleration is the same computed in (a), what will be the radius of the new circular trajectory? IIint: Think if your answers make sense. Compare with the experiment we did of a ball attached to an elastic. Also, do not forget to convert hours to seconds!
Answers
The radial acceleration of the Juno satellite in its circular orbit around Jupiter, with a radius of 100×10³ km and a speed of 200×10³ km/h, is approximately 1.272×\(10^(^-^2^)\) km/h².
To calculate the radial acceleration, we can use the formula for centripetal acceleration:
a = v² / r
where "a" is the radial acceleration, "v" is the velocity of the satellite, and "r" is the radius of the orbit.
Given that the velocity of Juno is 200×10³ km/h and the radius of the orbit is 100×10^3 km, we can substitute these values into the formula:
a = (200×10³ km/h)² / (100×10³ km) = 4×\(10^4\) km²/h² / km = 4×10² km/h²
Thus, the radial acceleration of Juno in its circular orbit around Jupiter is 4×10² km/h², or 0.4×10³ km/h², which is approximately 1.272× \(10^(^-^2^)\)km/h² when rounded to three significant figures.
If the satellite's speed is increased to 300×10³ km/h while maintaining the same radial acceleration as calculated in part (a), the new radius of the circular trajectory can be determined.Using the same formula as before:
a = v² / r
We know the new speed, v, is 300×10³ km/h, and the radial acceleration, a, remains the same at approximately 1.272×\(10^(^-^2^)\) km/h². Rearranging the formula, we can solve for the new radius, r:
r = v² / a
Substituting the given values:
r = (300×10³ km/h)² / (1.272×\(10^(^-^2^)\) km/h²) ≈ 7.08×\(10^6\) km
Therefore, the new radius of the circular trajectory, when the speed is increased to 300×10³ km/h while maintaining the same radial acceleration, is approximately 7.08× \(10^6\)km.
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The Candle Company is designing a new cylindrical candle. They are looking at four different molds. Which mold will use the
least amount of wax?
Mold
A
B
Candle Mold Choices
Diameter
2 inches
2 inches
inches
inches
Height
7 inches
4 inches
3 inches
3 inches
C
D
3
4
Recall the formula V= 72.
Mold A
Mold B
Mold C
Mold D
Answers
Answer:
mold B
Step-by-step explanation:
The molds are of cylindrical shape. The volume of a cylinder is given by:
Volume = πr²h
where r is the radius and h is the height.
For mold A: diameter = 2 inches, hence radius = 1 inch. Height = 7 inches
volume = π(1²)7 = 7π in³
For mold B: diameter = 2 inches, hence radius = 1 inch. Height = 4 inches
volume = π(1²)4 = 4π in³
For mold C: diameter = 3 inches, hence radius = 1.5 inch. Height = 3 inches
volume = π(1.5²)3 = 6.75π in³
For mold C: diameter = 4 inches, hence radius = 1.5 inch. Height = 3 inches
volume = π(2²)3 = 12π in³
Therefore mold B has the smallest volume
Answer:
B
Step-by-step explanation:
40 is what percent of 80?
Answers
Answer:
50%
Step-by-step explanation:
it's just half 80 so it's 50%
what is the initial value of y=10(1−0.04)x
Answers
Answer:
10
Step-by-step explanation:
according to the formula of y = P(1-r)^x, P is the initial value, and in this case it looks like it is 10 :)
PLEASE HELP!
The blank of y in 17y is 17.
Its either term, variable or coefficient
Answers
In the term, 17y 17 is the coefficient of 17y.
What are coefficients and like terms?A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it.
Terms that have the same variables raised to the same power are referred to as like terms. The only difference is in the numerical coefficients.
The term 17y together is a variable, In 17y 'y' is also a variable.
In front of 'y' the constant number is 17 and it is called the coefficient of 'y'.
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Which of the following isn't a composite number?
33
41
51
69
Answers
Answer:
33
Step-by-step explanation:
A ride sharing company offers two options: riding in small cars that can carry up to 3 passengers each, or riding in large vans that can carry up to 6 passengers each. A group of 27 people is going to use the ride sharing service to take a trip. The trip in a small car costs $10 and the trip in a large van costs $15. The group ends up spending $80 total. An equation that represents one of the constraints is 3x+6y=a. What is the value of a?
Answers
Answer:
a = 27
Step-by-step explanation:
3x + 6y = a
From the given information, 3 and 6 are the numbers of passengers that cars and vans can take. That means x and y must be the numbers of cars and vans, and a is the total number of passengers.
a = 27
Write the equation in point-slope form that contains the points (2,4) and (-8,1).
Answers
Answer:
y=3/10x+17/5
Step-by-step explanation:
Hello, I'm having trouble with this question.
Answers
Answer:
Step-by-step explanation:
Answer:
30 hours → $270
40 hours → $360
50 hours → $495
Step-by-step explanation:
30 hours: 9(30) = 270
40 hours: 9(40) = 360
50 hours: 360 + 13.5(50-40) = 360 + 135
A bond with a coupon rate of 12 percent sells at a yield to
maturity of 14 percent. If the bond matures in 15 years, what is
the Macaulay duration?
Answers
The Macaulay duration of a bond is a measure of the weighted average time until the bond's cash flows are received.
To calculate the Macaulay duration, we need the bond's cash flows and the yield to maturity. In this case, the bond has a coupon rate of 12 percent, sells at a yield to maturity of 14 percent, and matures in 15 years. The second paragraph will explain how to calculate the Macaulay duration.
To calculate the Macaulay duration, we need to determine the present value of each cash flow and then calculate the weighted average of the cash flows, where the weights are the proportion of the present value of each cash flow relative to the bond's price.
In this case, the bond has a coupon rate of 12 percent, so it pays 12 percent of its face value as a coupon payment every year for 15 years. The final cash flow at maturity will be the face value of the bond.
To calculate the present value of each cash flow, we discount them using the yield to maturity of 14 percent.
Next, we calculate the weighted average of the cash flows by multiplying each cash flow by its respective time until receipt (in years) and dividing by the bond's price.
By performing these calculations, we can determine the Macaulay duration, which represents the weighted average time until the bond's cash flows are received.
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Help me please!! I can’t figure this out...
Answers
Answer:
-2
Step-by-step explanation:
-2-4/3-0=-2
you basically take the y value of the first point subtract it from the y value of the 2nd point. you do the same for the x values
Answer:
-2
Step-by-step explanation:
You can use the equation rise over run, which is basically y2-y1 over x2-x1
Y2 is -2 and y4 is 4, x2 is 3 x1 is 0
-2-4 over 3-0=-6/3=-2
Is the following statementpossible or impossible?A triangle has side lengths of4, 8, and 9.PossibleImpossible
Answers
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Using the information above, we test it out to see if it is true
4+8 >9
4+9>8
9+8>4
Since the sum of two sides is greater than the third side. Therefore the answer is possible.
Select the correct answer from each drop-down menu. a comic-strip writer churns out different numbers of comic strips each day. the writer logged the number of comic strips he wrote each day for 16 days and sorted the data in ascending order to create this data set. 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8 the data in the distribution is . if the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference of the mean and the median for the new data set is .
Answers
Mean = 3.5
Median = 3
Distribution is negatively skewed.
What is skew in the distribution?
The distribution has no skewness if the mean and median are equal.
The median exceeds the mean in a favorably skewed distribution.
The distribution is also negatively skewed if the median is lower than the mean.
Given,
Data set : 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8
Mean = \(\frac{1+1+2+2+2+3+3+3+3+4+4+4+5+5+6+8}{16}\)
Mean = \(\frac{56}{16}\)
Mean = \(3.5\)
Median = mid value of the data set when the values are arranged in ascending order
Here,
the two mid values = \(3, 3\)
Median = \(\frac{3+3}{2}\)
Median = \(\frac{6}{2}\)
Median = \(3\)
Now, as the mean is larger than the median therefore the distribution will be skewed negatively.
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The data in the distribution is positively skewed (skewed to the right). If the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference between the mean and the median for the new data set is 0.28.
ヾ(•ω•`)o
Which statement is true able angles UST and QSR ?
Answers
Answer:
A
Step-by-step explanation:
They are less than 90 degress
Answer:
Step-by-step explanation:
They are complementary.
–18 • –17
solve please
Answers
Answer:
306
Step-by-step explanation:
Answer:
306
Step-by-step explanation:
-18x-17 is 306 because a negative number times a negative number is always a positive so it would be 18x17 which is 306
Given line m is not parallel to line n, prove ∠3 is not congruent to ∠5 by contradiction.
Answers
Answer:
∠3 is congruent to ∠5 must be false, and we can conclude that ∠3 is not congruent to ∠5.
Step-by-step explanation:
To prove that ∠3 is not congruent to ∠5 by contradiction, we assume that ∠3 is congruent to ∠5. Since line m is not parallel to line n, we know that ∠3 and ∠5 are corresponding angles. If ∠3 is congruent to ∠5, then lines m and n must be parallel by the Corresponding Angles Postulate. This contradicts the given statement that line m is not parallel to line n. Therefore, our assumption that ∠3 is congruent to ∠5 must be false, and we can conclude that ∠3 is not congruent to ∠5.
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Use cylindrical coordinates to evaluate the triple integral ∭Ex2+y2dV, where E is the solid bounded by the circular paraboloid z=1−1(x2+y2) and the xy-plane.
Answers
The value of the triple integral ∭Ex^2 + y^2dV is π/30. To evaluate the triple integral , we can use cylindrical coordinates.
In cylindrical coordinates, the equation of the circular paraboloid becomes z = 1 - r^2, where r represents the radial distance from the z-axis. The bounds for the triple integral are as follows: ρ varies from 0 to √(1 - z); φ varies from 0 to 2π; z varies from 0 to 1. The integral becomes: ∭Ex^2 + y^2dV = ∫(0 to 1) ∫(0 to 2π) ∫(0 to √(1 - z)) (ρ^2) ρ dρ dφ dz. Simplifying, we have: ∭Ex^2 + y^2dV = ∫(0 to 1) ∫(0 to 2π) [ρ^3/3] evaluated from 0 to √(1 - z) dφ dz. ∭Ex^2 + y^2dV = ∫(0 to 1) ∫(0 to 2π) [(1 - z)^3/3] dφ dz.
Evaluating the integral, we get: ∭Ex^2 + y^2dV = ∫(0 to 1) [2π(1 - z)^4/12] dz. ∭Ex^2 + y^2dV = [2π(1 - z)^5/60] evaluated from 0 to 1. ∭Ex^2 + y^2dV = 2π/60 = π/30. Therefore, the value of the triple integral ∭Ex^2 + y^2dV is π/30.
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i need help, i feel like i know how to do it but when i try it makes no sense. can someone explain this to me with steps?
Answers
Completing a square is a method for transforming a quadratic equation’s form so that its LHS becomes a perfect square, commonly known as vertex form. This is accomplished by rearranging the phrase.
What exactly is an X2?X2 is x multiplied by itself, which is symbolized by and may be expressed as xx or x(x) as an algebraic term. 2 is an exponent in. It denotes that x has been multiplied by itself twice. x 2 = x .
heres the answer is, X squared is a helpful notation that we use in math. It can be used in different kinds of algebraic expressions. It simplifies our calculations and allows us to develop formulas to solve problems quicker!
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HELP ASAP MY PARENTS ARE COUNTING ON ME
The system of linear equations 3x + 2y = −6 and y equals one half times x plus 4 is graphed on a coordinate plane. Approximate the solution to the system.
coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 5 and another line that passes through the points 0 comma negative 3 and negative 2 comma 0
(−3.5, 1.25)
(−3.5, 2.25)
(1.5, 4.25)
(1.5, −5.25)
Answers
Answer:
An answer is an option (C) (1.5, 4.25).
Step-by-step explanation:
# Approximating Solution to a System of Linear Equations
The given system of linear equations is:
3x + 2y = −6 ...(1)
y = 1/2 x + 4 ...(2)
The solution to the system can be approximated by graphing the two equations on a coordinate plane and finding the point of intersection of the two lines.
The first equation can be written in a slope-intercept form:
2y = -3x - 6
y = (-3/2)x - 3
Plotting this on the coordinate plane, we get a line passing through the points (0,-3) and (-2,0).
The second equation can be written in a slope-intercept form:
y = (1/2)x + 4
Plotting this on the coordinate plane, we get a line passing through the points (0,4) and (2,5).
The two lines intersect at approximately (1.5, 4.25). Therefore, the solution to the system is as follows:
x ≈ 1.5
y ≈ 4.25
Hence, the answer is an option (C) (1.5, 4.25).
Answer:
An answer is an option (C) (1.5, 4.25).
Step-by-step explanation:
# Approximating Solution to a System of Linear Equations
The given system of linear equations is:
3x + 2y = −6 ...(1)
y = 1/2 x + 4 ...(2)
The solution to the system can be approximated by graphing the two equations on a coordinate plane and finding the point of intersection of the two lines.
The first equation can be written in a slope-intercept form:
2y = -3x - 6
y = (-3/2)x - 3
Plotting this on the coordinate plane, we get a line passing through the points (0,-3) and (-2,0).
The second equation can be written in a slope-intercept form:
y = (1/2)x + 4
Plotting this on the coordinate plane, we get a line passing through the points (0,4) and (2,5).
The two lines intersect at approximately (1.5, 4.25). Therefore, the solution to the system is as follows:
x ≈ 1.5
y ≈ 4.25
Hence, the answer is an option (C) (1.5, 4.25).