Use the table provided to determine the total amount paid on a 30 year fixed loan, at 6.0%, of $75,000.
$162,000
c.
$143,820
b.
$153,750
d.
$133,250
Answer:
162000
Step-by-step explanation:
For 75000 paying in 30 years at 6% we have
Mortgage Summary
Monthly Payment $449.66
Total Interest Paid $86,879
9
Total of 360 Payments $161,879
Pay-off Date Feb, 2049
We find out of 4 options given 162000 is nearer to this 161879
Hence option of 162000 is the right answer.
An equilateral triangle has an altitude length of 36 feet. Determine the length of a side of the triangle.
question 1.) simplify 6(2 + 0.3)5
A.) about 0.03
B.) about 12.01
C.) about 85.19
D.) about 386.18
question 2.) solve 32x = 7
A.) x = 0.22
B.) x = 4.57
C.) x = 25
D.) x = 39
Answer: Q1) 386.18
Step-by-step explanation:
Q1): You do the parenthesis first.
6(2+0.3)^5
2+0.3 = 2.3^5 = 64.36343
then do 6(64.36343) = 386.18
For Q2 I believe the answer is 0.22 if you do 7 divided by 32 you get 0.21875 and you round that to get 0.22
Identify a possible first step using the elimination method to solve the system and then find the solution to the system.
12x – 3y = 6
2x – y = 2
A) multiply second equation by 6, solution (2,0)
B) multiply second equation by 6, solution (-2,0)
C) multiply second equation by -6, solution (0,2)
D) multiply second equation by -6, solution (0,-2)
Answer:
D) multiply second equation by -6, solution (0,-2)
Step-by-step explanation:
This pair of linear equations may be solved simultaneously by using the elimination method. This will involve ensuring that the coefficient of one of the unknown variables is the same in both equations.
As such, in the given set of equations
12x – 3y = 6
2x – y = 2
We may make the coefficients of x the same by multiplying the second by 6 or the coefficient of y by multiplying the second by 3. Using the first
12x – 3y = 6
12x – 6y = 12
equation 1 - equation 2
3y = -6
y = -2
2x + 2 = 2
x = 0
Steve drew a floorplan of his living room. The floorplan is represented by rectangle ABCD. He drew a dilation of his represented by rectangle A’B’C’D’ on the coordinate plane below. Each square unit on the coordinate plane represents a square with 1-foot sides. I WILL GIVE THE FIRST ANSWER BRAIN!
What number should be added to the expression x²+14x to change it into a perfect square trinomial?
7
14
28
49
Final answer:
To transform x²+14x into a perfect square trinomial, add 49 to it, which is the square of half the coefficient of x.
Explanation:
The number that should be added to the expression x²+14x to change it into a perfect square trinomial is obtained by taking half of the coefficient of x, which is 14, and then squaring that value. Therefore, (14 / 2)² = 7² = 49. So, the number to be added to make x²+14x a perfect square trinomial is 49.
What does (p⋅c)(2) mean about the horse-drawn carriage tour company?
c(2) = 50 +5(2) = 60
p(2) = 80-2(2) = 76
60 * 76 = 4560 when the price is 60
What is the Greatest Common Factor of 12 and 36? (1 point)
2
4
6
12
The greatest Common factor of 12 and 36 is 12.
A number that divide another number is called factor.
Factors of 12 is 2, 3, 4, 6, 12
Factors of 36 are 2, 3, 4, 6, 9, 12, 18, 36.
Therefore, the greatest common factor of 12 and 36 is 12.
Learn more about factor here:
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What is the measure of EG?
Which of the following is false?
the number of hours a person studies and the numerical score on the exam is a positive correlation
the speed of a vehicle and the time it takes the vehicle to travel 60 miles is a positive correlation
none, since all of the other answer choices are true
a child’s age and the height of a child is a positive correlation
Answer:
the speed of a vehicle and the time it takes the vehicle to travel 60 miles is a positive correlation
The swimming relay race is 1/4mile long. Each of 3 swimmers in the relay swim the same distance. How far does each swimmer swim
If f(x)=3x^2-1 and g(x)=x+2, find (f+g)(x)
Answer:
Step-by-step explanation:
X^2+3x-1 apex
Explain how the exponent of 10 changes when you multiply a number written in scientific notation by 100. Show an example.
Final answer:
When a number in scientific notation is multiplied by 100, its exponent of 10 increases by 2 since 100 is equivalent to 10 squared (10²). For example, 3.14 x 10⁴ multiplied by 100 becomes 3.14 x 10⁶.
Explanation:
When you multiply a number in scientific notation by 100, the exponent of 10 increases by 2.
This is because 100 can be written as 10² or 10 squared.
So, if we have a number like 3.14 × 10⁴ and we multiply by 100, we are essentially multiplying by 10².
We keep the coefficient the same (3.14) and add the exponents of 10:
3.14 × 10⁴ × 102 = 3.14 × 10⁴+23.14 × 10⁴ × 100 = 3.14 × 10⁶The resulting scientific notation is 3.14 × 10⁶, which means the exponent of 10 increased by 2 as we multiplied by 100.
What is the length of a leg of an isosceles right triangle whose hypotenuse measures 6 inches? Let c represent the value of the hypotenuse. If the hypotenuse is c = a, then 6 = a. In inches, what is the value of a? 3 6
In iscosceles right triangle the value of the unknown sides is equal to [tex]3\sqrt{2}[/tex] and it can be deteremine by using pythagorean theorem.
Given :
Iscosceles right triangle.Hypotenuse = 6.Both remaining sides are equal.Let the length of unknown sides be 'a'. Than to deteremine the value of a, pythagorean theorem can be used.
[tex]\rm (Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2[/tex]
[tex]6^2 = a^2+a^2[/tex]
[tex]2a^2 = 36[/tex]
[tex]a^2 =\dfrac{36}{2}[/tex]
[tex]a = \sqrt{18} =3\sqrt{2}[/tex]
Therefore, by applying pythagorean theorem the value of a which is [tex]3\sqrt{2}[/tex] can be determine.
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If b is the midpoint of \frac{ }{ac} a c , d is the midpoint of \frac{ }{ce} c e , and bd = 19 , find ae .
The amount of money, in dollars, in an account after t years is given by A = 1000(1.03)t. The initial deposit into the account was $ a0 and the interest rate is a1% per year. Only enter numbers in the boxes. Do not include any commas or decimal points.
An element with mass 430 grams decays by 27.4% per minute. How much of the element is remaining after 19 minutes, to the nearest 10th of a gram?
WILL GIVE BRAINLIEST TO PERSON WHO ANSWERS CORRECTLY!!!!!! PLEASE HELP ASAP!!!!!
A roller coaster car follows a parabolic path over the first hill on its track. The height of the car, in feet, t seconds after the ride starts can be shown by the function given below.
h ( t ) = -3t^2 + 15t + 18
Which of the statements is true?
* The domain of the function is [0, 6], and it represents the car's time to reach maximum height.
* The domain of the function is [-1, 6], and it represents the car's time to reach maximum height.
* The domain of the function is [0, 6], and it represents the car's time to complete the hill.
* The domain of the function is [-1, 6], and it represents the car's time to complete the hill.
None of the options are entirely correct. The domain of the function is [tex]\( t \geq 0 \)[/tex] , and it does not directly represent the time to complete the hill or reach maximum height.The domain is representing all real numbers. The function doesn't directly indicate completion time or maximum height.
Let's analyze the given function [tex]\( h(t) = -3t^2 + 15t + 18 \)[/tex] to determine the domain and its meaning:
1. **Domain of the function**:
The domain of a quadratic function is all real numbers unless there are restrictions. In this case, there are no restrictions mentioned in the problem, so the domain is all real numbers. However, in the context of the roller coaster ride, the time ( t ) cannot be negative because it doesn't make sense for time to be negative in this scenario. Therefore, the practical domain is [tex]\( t \geq 0 \).[/tex]
2. **Time to reach maximum height**:
The time to reach the maximum height of the roller coaster can be found using the vertex formula: [tex]\( t = -\frac{b}{2a} \)[/tex] , where [tex]\( a = -3 \) and \( b = 15 \)[/tex] (coefficients from the quadratic function). Substituting these values into the formula:
[tex]\[ t = -\frac{15}{2(-3)} = -\frac{15}{-6} = \frac{15}{6} = \frac{5}{2} \][/tex]
Since time cannot be negative in this context, the time to reach the maximum height is [tex]\( t = \frac{5}{2} = 2.5 \)[/tex] seconds.
Now, let's analyze the given options:
- **Option 1: The domain of the function is [0, 6], and it represents the car's time to reach maximum height.**
- The domain given is correct [tex](\( t \geq 0 \)),[/tex] but it incorrectly states that it represents the time to reach maximum height. The correct time to reach maximum height is [tex]\( t = 2.5 \)[/tex] seconds, not 6 seconds.
[tex]\( t \geq 0 \),[/tex]
- **Option 2: The domain of the function is [-1, 6], and it represents the car's time to reach maximum height.**
- This option gives an incorrect domain. The domain is [tex]\( t \geq 0 \), not \( t \geq -1 \).[/tex]
- **Option 3: The domain of the function is [0, 6], and it represents the car's time to complete the hill.**
- This option correctly identifies the domain as [tex]\( t \geq 0 \).[/tex] However, it incorrectly states that it represents the time to complete the hill. The function does not directly represent the time to complete the hill; it represents the height of the car at any given time.
- **Option 4: The domain of the function is [-1, 6], and it represents the car's time to complete the hill.**
- This option gives an incorrect domain. The domain is [tex]\( t \geq 0 \),[/tex] not [tex]\( t \geq -1 \).[/tex]
Therefore, none of the options are entirely correct. The domain of the function is [tex]\( t \geq 0 \)[/tex] , and it does not directly represent the time to complete the hill or reach maximum height.
A system of equations is graphed on the coordinate plane. y=−x+5y=2x−1 What is the solution to the system of equations? Enter the coordinates of the solution in the boxes.
Answer:
[tex](2;3)[/tex]
Step-by-step explanation:
We can find the solution directly on the graph. The solution of a system of equations is the intersections between the two lines. Remember that each equation in this case represent a line, where the common points are always shown as an intersection.
To prove this result, we can apply other methods. Using the substitution method, we have to isolate one variable from one equation and then replace it in the other equation, like this:
[tex]\left \{ {{y=-x+52'} \atop {y=2x-1}} \right.[/tex]
The variable y is already isolated, now we just replace the first equation in the second:
[tex]-x+5=2x-1\\5+1-2x+x\\6=3x\\x=\frac{6}{3}=2[/tex]
Then, we replace the x-value in one equation, no matter which one:
[tex]y=2x-1\\y=2(2)-1\\y=4-1=3[/tex]
Therefore, we found that the solution is[tex](2;3)[/tex]
Write g(x) = –16x + x2 in vertex form. Write the function in standard form. Form a perfect square trinomial by adding and subtracting . Write the trinomial as a binomial squared. Write the function is in vertex form, if needed. g(x) = x2 – 16x b = –16, so = 64 g(x) = (x2 – 16x + 64) – 64 g(x) = (x – )2 –
Answer:
g(x) = (x - 8)² - 64 will be the answer.
Step-by-step explanation:
The given function in the standard form is g(x) = -16x + x²
We have to write this function in the vertex form.
Since vertex form of a quadratic function is in the form of
f(x) = (x - h)² + k
Therefore, g(x) = x² - 16x may be written as
g(x) = x² - 16x + 64 - 64
= x² - 2(8x) + 64 - 64
= (x - 8)² - 64
Therefore, g(x) = (x - 8)² - 64 will be the answer.
The Temple in Jerusalem was destroyed in the year A.D.________.
46
63
70
80
The provincial governors in Rome were given orders to openly persecute the Christians by Emperor ________.
Caligula
Caesar
Trajan
Constantine
The Roman emperor who passed a decree to require everyone to participate in the cult of emperor worship was:
Caligula
Caesar
Trajan
Decius
Fill in the blanks.
1 Peter 3:17: "For it is__________if God should will it so, that you suffer for doing what is right rather than for doing what is wrong."
What was the most damaging charge brought against the Christians in Rome?
They were constant law-breakers who did not discharge their duties to the state.
They were somewhat secretive in their worship.
They stirred up riots.
They would not engage in emperor worship.
1. The Temple in Jerusalem was destroyed in the year of 70 AD.
The first Temple was built by King Solomon for seven years in the 10th century BC. The first Temple was destroyed by the Babylonians in 586 BC. The construction of the new Temple began 535 BC and it is completed in 516 BC. The rebuilding of the Temple was approved by Darius I. It was, however, destroyed by the Romans in 70 AD. Despite the fact that the Temple was destroyed, all the outer walls still stand, and for a long time, it was believed that only the west wall stood.
The provincial governors in Rome were given orders to openly persecute the Christians by Emperor Trajan.
This can be concluded from the letter sent to him by Pliny, governor of Bithynia (province of Asia Minor). He had doubts about the investigation and the way of punishing those who were accused as Christians because he never been present at any trials of Christians. This implies that there have already been trials for Christians and that he did not know the details about Trajan’s decree of prosecuting Christians.
The Roman emperor who passed a decree to require everyone to participate in the cult of emperor worship was Decius.
Emperor Decius (249-251) announced the edict that orders everyone to do sacrifice to the Roman gods and to him personally. According to the edict, the sacrifice had to be carried out in the presence of a Roman magistrate who issued a certificate that this had been done. There is no evidence that it was directed against the Christians, but it was fatal for them because was contrary to their beliefs.
1 Peter 3:17: "For it is better, if God should will it so, that you suffer for doing what is right rather than for doing what is wrong."
The quote is from the First Epistle of Peter, which is part of the New Testament. It is written by Peter the Apostle in Rome (where he was a bishop) as the letter which is sent to believers in Asia Minor who were persecuted and tortured.
The most damaging charge brought against the Christians in Rome was that they were constant law-breakers who did not discharge their duties to the state.
The Roman authorities consider Christians as opponents of the state that promoted treasonous activities and they were apprehended for disobedience. Suspected Christians have often refused to deviate from Christianity in order to comply themselves with acts of a state cult, which was understood as a public cancellation of loyalty to the state.
Identify the cross section shown.
a. rectangle
b. circle
c. trapezoid
d. pentagon
Option : a is the correct answer.
a. rectangle.
Step-by-step explanation:From the figure that is provided to us we see that the cross-section is in the shape of a quadrilateral such that it has two pair of parallel sides.
b)
circle
A circle does not have any edge or sides.
Hence, option: b is incorrect.
c)
Trapezoid
A trapezoid is a quadrilateral with one pair of parallel sides and one pair of unparallel sides.
Hence, option: c is incorrect.
d)
Pentagon
A pentagon is a polygon with 5 sides.
Hence, option: d is incorrect.
Hence, the best possible answer is:
Rectangle
Quadrilateral RJFT is similar to quadrilateral SYPA . JF=60 mm , AP=40 mm , and YP=25 mm . What is TF ?
Final answer:
To find the length of FT in the similar quadrilaterals RJFT and SYPA given specific side lengths, apply the scale factor method to determine FT = 37.5 mm.
Explanation:
Quadrilateral RJFT is similar to quadrilateral SYPA. Given that JF=60 mm, AP=40 mm, and YP=25 mm, we can solve for FT.
Calculate the scale factor between the two similar quadrilaterals using side lengths: JF/AP = FT/YP.
Substitute the given values to find the length of FT.
Calculate FT = (60 mm * 25 mm) / 40 mm = 37.5 mm.
Graph the following inequality. Then click to show the correct graph.
3x - 2y ≥ 6
One column of numbers consists of 33, 58, and 17. When the digits of the numbers are added together, the result is 3 + 3 + 5 + 8 + 1 + 7 = 27, and when the digits of 27 are then added together, the end result is 2 + 7 = 9. If the same process is performed on the numbers in a second column, what can be concluded? a.If the end result from the second column is also 9, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column. b.If the end result from the second column is also 9, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column. c.If the end result from the second column is not 9, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column. d.If the end result from the second column is not 9, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column.excel sum values based on another columnsum if greater than
Bax invested a total of $2000 in two simple interest accounts. Account A earns 3% interest and Account B earns 5% interest. Bax earned a total of $75 interest after one year. How much did Bax invest in each account?
Bax invested a total of $2000 in two simple interest accounts. Account A earns 3% interest and Account B earns 5% interest. Bax earned a total of $75 interest after one year. How much did Bax invest in each account?
Let, The amount invested in Account A=x
Then, the amount invested in Account B=2000-x
The formula of Simple Interest =[tex] \frac{Principle*Rate*Time}{100} [/tex]
Interest earned in Account A in 1 year=[tex] \frac{x*3*1}{100} [/tex]
Interest earned by Account A=[tex] \frac{3x}{100} [/tex]
Interest earned in Account B in 1 year=[tex] \frac{(2000-x)*5*1}{100} [/tex]
Interest earned by Account B=[tex] \frac{5(2000-x)}{100} [/tex]
Total Interest Earned= Interest earned by Account A+ Interest earned by Account B
Total Interest Earned=[tex] \frac{3x}{100} [/tex]+[tex] \frac{5(2000-x)}{100} [/tex]
75=[tex] \frac{3x}{100} [/tex]+[tex] \frac{10000-5x)}{100} [/tex]
75=[tex] \frac{3x+10000-5x)}{100} [/tex]
Multiply by 100 on both sides
75*100=[tex] \frac{100(10000-2x))}{100} [/tex]
7500=10000-2x
Let us subtract 7500 from both sides
7500-7500=10000-7500-2x
0=2500-2x
Adding 2x on both sides, we get
0+2x=2500-2x+2x
2x=2500
To solve for x, divide by 2 on both sides
2x/2=2500/2
x=1250
So, The Amount invested in Account A= $1250
The Amount invested in Account B= $2000-1250=$750
Noelle stands at the edge of a cliff and drops a rock. The height of the rock, in meters, is given by the function f(x)=−4.9x^2+17 , where x is the number of seconds after Noelle releases her rock. Cesar, who is standing nearby on the ground, throws a rock straight up in the air. The height of Cesar’s rock, in meters, is given by the function g(x)=−4.9x^2+13x , where x is the number of seconds after he releases his rock. There is a moment when the rocks are at the same height.
The rocks are at the same height approximately 1.31 seconds after Noelle drops her rock and Cesar throws his, and at this time, they are both at a height of approximately 8.57 meters.
To determine the moment when Noelle's and Cesar's rocks are at the same height, we need to set the two functions equal to each other and solve for x. Noelle's rock has the height function f(x) = -4.9x² + 17 and Cesar's rock has the height function g(x) = -4.9x² + 13x.
We solve for x when f(x) = g(x):
-4.9x² + 17 = -4.9x² + 13x
This simplifies to:
17 = 13x
Solving for x gives us:
x = 17/13
x ≈ 1.31 seconds
At approximately 1.31 seconds after Noelle drops her rock and Cesar throws his, both rocks are at the same height. To find this height, we substitute x back into either f(x) or g(x). Using Noelle's function, we get:
f(1.31) = -4.9(1.31)² + 17 ≈ 8.57 meters
Therefore, both rocks are at a height of approximately 8.57 meters 1.31 seconds after their respective releases.
Answer:
8.6
Step-by-step explanation:
I took the test
grayson charges $35 per hour plus a $35 administration fee for tax preparation. Ian charges $45 per hour plus a $15 administration fee. If h represent the number of hours of tax preparation, for what number of hours does Grayson charge more than Ian?
We find that Grayson charges more than Ian when the number of hours of service h is less than 2.
To determine for how many hours Grayson charges more than Ian, we can set up an equation where the cost of Grayson's tax preparation service is greater than Ian's service. Grayson charges $35 per hour plus a $35 administration fee, while Ian charges $45 per hour plus a $15 administration fee. The number of hours for which the service is required is represented by h.
Grayson's total charge for h hours would be:
Grayson's Cost = $35h + $35
Ian's total charge for h hours would be:
Ian's Cost = $45h + $15
To find the number of hours where Grayson's cost is more than Ian's cost, we set Grayson's Cost > Ian's Cost:
$35h + $35 > $45h + $15
Simplifying, we get:
$35h - $45h > $15 - $35
-$10h > -$20
Dividing both sides by -10 (and remembering to reverse the inequality when dividing by a negative):
h < 2
Thus, Grayson charges more than Ian for fewer than 2 hours of tax preparation.
What is the probability that mattias picks an outfit at random that includes red shoes?
The probability that mattias picks an outfit at random that includes red shoes is 0.5
Calculating the probability that mattias picks an outfit at random that includes red shoes?
From the question, we have the following parameters that can be used in our computation:
The tree diagram
On the tree diagram, we have
Total Outfits = 12
Outfits with red = 6
So, we have the probability to be
P = Outfits with red /Total Outfits
This gives
P = 6/12
Evaluate
P = 0.5
Hence, the probability is 0.5
Question
Mattias gets dressed in the dark one morning and chooses his clothes at random. He chooses a shirt (green, red or yellow), a pair of pants (black or blue), and a pair of shoes (checkered or red).
What is the probability that mattias picks an outfit at random that includes red shoes?
A 5-digit combination lock with digits 0-9 can be opened only if a correct combination of digits is chosen. Find the probability of guessing the correct combination if: