The interest that will accrue while the college freshman is still in school and over the 6-month grace period for this freshman year loan is, approximately, B. $2,915.06.
How is the interest determined?The interest for federal college loans is based on the simple interest formula instead of compounding.
By compounding, we mean that interest is computed on the principal and accumulated interest.
Federal Direct Unsubsidized Loan = $15,100
Number of years for college = 4 years
The number of years before repayment = 4.5 years (4 years + 6 months)
Simple interest for 4.5 years = $2,915.06 ($15,100 x 4.29% x 4.5 years)
On the other hand, one can compute the compounded interest using an online finance calculator.
Compounded Interest:N (# of periods) = 4.5 years
I/Y (Interest per year) = 4.29%
PV (Present Value) = $15,100
PMT (periodic payment) during the 4.5 years = $0
Results:
FV = $18,241.85
Total Interest = $3,141.85
Thus, the interest is Option B.
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PLEASE HELP
OFFERING 10 POINTS
Answer: AAS
Step-by-step explanation:
Two sides are congruent, two angles are congruent, and vertical angles are congruent
Question 3(Multiple Choice Worth 2 points)
(01.06 MC)
Simplify √√-72-
--6√√2
6√-2
6√√2i
061√2
Answer:
[tex]6i\sqrt{2}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sqrt{-72}[/tex]
Rewrite -72 as the product of 6 · -1 · 2:
[tex]\implies \sqrt{36 \cdot -1 \cdot 2}[/tex]
Apply the radical rule [tex]\sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies \sqrt{36} \sqrt{-1} \sqrt{2}[/tex]
Carry out the square root of 36:
[tex]\implies 6\sqrt{-1}\sqrt{2}[/tex]
Apply the imaginary number rule [tex]\sqrt{-1}=i[/tex] :
[tex]\implies 6i\sqrt{2}[/tex]
Fill in the missing statements and reasons in each proof shown below. You must mark the diagram forcredit.15.Given: g | h and 21 22Prove: p | r3рStatementReason2.ghgh21 2 2321 2222 223pllr
To prove that p || r, we will complete the data in the given table
[tex]\begin{gathered} \text{Statement: g}\mleft\Vert h\mright? \\ R\text{eason : Given} \end{gathered}[/tex][tex]\begin{gathered} \text{Statement: <1}\cong<3 \\ \operatorname{Re}\text{ason: Corresponding angles} \end{gathered}[/tex][tex]\begin{gathered} \text{Statement: <1}\cong<2 \\ \operatorname{Re}\text{ason:Given} \end{gathered}[/tex][tex]\begin{gathered} Statement\colon\text{ <2}\cong<3 \\ Re\text{ason: Alternate exterior angle} \end{gathered}[/tex][tex]\begin{gathered} \text{Statement: P}\mleft\Vert r\mright? \\ \operatorname{Re}\text{ason:<2}\cong<3 \end{gathered}[/tex]Function g can be thought of as a translated (shifted) version of f(x) = x?Y Y6+5+432f7 6 5 4 3 21 2 3 4 5 6 7-2--3+-6-7Write the equation for g(x).
Answer:
g(x) = (x + 5)²
Explanation:
g is the same function f shifted 5 units to the left.
Then, if we have a function h(x) =f(x+c), h(x) is f(x) shifted c units to the left.
So, to translate f 5 units to the left, we need to replace x by (x + 5), to get:
[tex]\begin{gathered} f(x)=x^2 \\ g(x)=f(x+5) \\ g(x)=(x+5)^2 \end{gathered}[/tex]So, the equation for g(x) is:
g(x) = (x + 5)²
Question number 3: which of the following is equal to 18x*7 y*6?
Solution:
Given:
[tex]\sqrt{18x^7y^6}[/tex]Splitting the expressions further to get the perfect squares out:
[tex]\begin{gathered} \sqrt{18x^7y^6}=\sqrt{9\times2\times(x^6\cdot x)\times(y^3)^2} \\ =\sqrt{9\times2\times(x^3)^2\cdot x\times(y^3)^2} \end{gathered}[/tex][tex]\begin{gathered} \sqrt{18x^7y^6}=\sqrt{9\times2\times(x^3)^2\cdot x\times(y^3)^2} \\ =3x^3y^3\sqrt{2x} \end{gathered}[/tex]Therefore, the correct answer is:
[tex]3x^3y^3\sqrt{2x}[/tex]Find the values of w and x that makeup NOPQ a parallelogram. A. W = 1/2 X = 1/2 B. W = 3 X = 2 C. W = 2 X = 2 D. W = 3 X = 1/2 Please select the best answer from the choices Provided
Solution
Step 1:
Properties of Parallelograms Explained
1. Opposite sides are parallel. ...
2. Opposite sides are congruent. ...
3. Opposite angles are congruent. ...
4. Same-Side interior angles (consecutive angles) are supplementary. ...
5. Each diagonal of a parallelogram separates it into two congruent triangles. ...
6. The diagonals of a parallelogram bisect each other.
Step 2:
The diagonals of a parallelogram bisect each other.
[tex]\begin{gathered} The\text{ }diagonals\text{ }of\text{ }a\text{ }parallelogram\text{ }bisect\text{ }each\text{ }other. \\ w\text{ + 7 = 5w - 5} \\ and \\ \frac{3}{2x}\text{ = 3} \end{gathered}[/tex]Step 3
[tex]\begin{gathered} Solve\text{ for w:} \\ w\text{ + 7 = 5w - 5} \\ Add\text{ similar terms} \\ 7\text{ + 5 = 5w - w} \\ 12\text{ = 4w} \\ w\text{ = }\frac{12}{4} \\ w\text{ = 3} \end{gathered}[/tex]Step 4
[tex]\begin{gathered} Solve\text{ for x:} \\ \frac{3}{2x}\text{ = 3} \\ 3\times2x\text{ = 3} \\ \\ 6x\text{ = 3} \\ \\ x\text{ = }\frac{3}{6} \\ \\ x\text{ = }\frac{1}{2} \end{gathered}[/tex]Final answer
[tex]\text{w = 3 . x = }\frac{1}{2}[/tex]Use long division or a calculator to write 4/99 as a decimal. Then tell whether the decimal is terminating or repeating
0.0404
Repeating decimal (periodic)
1) Let's proceed with the long division of 4 by 99:
1.1) Since 4 is way smaller than 99 let's add one zero to the dividend and another for the quotient followed by a dot.
But 40 is still lesser than 99, so let's add another zero after the dot to make it 400. Now we can divide 400 by 99
1.2) Again to proceed with that division we'll need to write a zero at that 4 and another one in the quotient.
As and we can see already this a repeating decimal or periodic. This division will yield 0.0404040404.....
2) Hence, the answer is 0.0404
Julia found the equation of the line perpendicular toy = -2x + 2 that passes through (5.-1).Analyze Julia's work. Is she correct? If not, what washer mistake?1 y25= 1/2 (-2) + 6Yes, she is correct,No, she did not use the opposite reciprocal for theslope of the perpendicular line.No, she did not substitute the correct x and yvaluesNo she did not apply inverse operations to solve forthe y-intercept.3+5b=555y=x5.5
The given line is
[tex]y=-2x+2[/tex]The line passes through (5, -1),
Perpendicular lines have opposite slopes, so we use the following equation to find the new slope knowing that the slope of the given line is -2.
[tex]\begin{gathered} m\cdot m_1=-1 \\ m\cdot(-2)=-1 \\ m=\frac{-1}{-2} \\ m=\frac{1}{2} \end{gathered}[/tex]Now, we use the slope, the point, and the point-slope formula to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-1)=\frac{1}{2}(x-5) \\ y+1=\frac{1}{2}x-\frac{5}{2} \\ y=\frac{1}{2}x-\frac{5}{2}-1 \\ y=\frac{1}{2}x+\frac{-5-2}{2} \\ y=\frac{1}{2}x-\frac{7}{2} \end{gathered}[/tex]Therefore, the equation of the new perpendicular line is[tex]y=\frac{1}{2}x-\frac{7}{2}[/tex]So, she's not correct, she didn't substitute the correct x and y values.
The right answer is C.NEED ASAP IF CORRECT ILL GOVE BRAINLIEST
Answer:
I believe the answer is g(x)=x+10
Step-by-step explanation:
it moves 4 units to the right making it positive, adding to the previous 6 units, making it move 10 units to the right
What value of t makes the following equation true?
5t−2=6t−7
Factor each polynomial by factoring out the greatest common factorminimum steps please
we are given the following expression:
[tex]12x^4+6x^3-8x^2[/tex]The greatest common factor between 12, 6, and 8 is 2. And the greatest common factor between the variables is:
[tex]\text{GCF(x}^4,x^3,x^2)=x^2[/tex]Therefore, the factorization is:
[tex]12x^4+6x^3-8x^2=2x^2(6x^2+3x-4)[/tex]help meee pleaseeee pleasee
Answer:
f(4) = (16/7)
f(0) = -12
f(-5) = (-7/11)
Step-by-step explanation:
x + 12
f(x) = -----------
2x - 1
(4) + 12 16
f(4) = ----------- = ---------
2(4) - 1 7
(0) + 12 12
f(0) = ----------- = ------- = -12
2(0) - 1 -1
(-5) + 12 7 -7
f(-5) = ------------ = ----------- = -------
2(-5) - 1 -11 11
I hope this helps!
distance between (11,-5) and (0,1)
Here,point can be written as:
[tex]\begin{gathered} x1=11, \\ y1=-5 \\ x2=0 \\ y2=1 \end{gathered}[/tex]The formula for the distance between the points as follows;
[tex]\begin{gathered} d=\sqrt{(x1-x2)^2+(y1-y2)^2} \\ d=\sqrt{(11-0)^2+(-5-1)^2} \\ d=\sqrt{121+36} \\ d=\sqrt{157} \\ d=12.53 \end{gathered}[/tex]Thus, the distance between the point is 12.53.
69=2g-24 I NEED TO FIND G
help meeeeeeeeee pleaseee !!!!!
The composition will be:
(g o h)(x) = 5*√x
By evaluating in x = 0, we get:
(g o h)(0) = 0
How to evaluate the composition?Here we have the two functions:
g(x) = 5x
h(x) = √x
And we want to get the composition:
(g o h)(x) = g( h(x))
So we need to evaluate g(x) in h(x), we will get:
g( h(x)) = 5*h(x) = 5*√x
And now we want to evaluate this in x = 0, we will et:
(g o h)(0) = 5*√0 = 0
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How do I find the linear equation for this? (y=mx+b)
Okay, here we have this:
Considering the provided table, we are going to find the corresponding linear equation, so we obtain the following:
To do this we will start using the information in the slope formula, then we have:
m=(y2-y1)/(x2-x1)
m=(190-(-30))/(19-9)
m=220/10
m=22
Now, let's find the y-intercept (b) using the point (9, -30):
y=mx+b
-30=(22)9+b
-30=198+b
b=-30-198
b=-228
Finally we obtain that the linear equation is y=22x-228
Answer:
Step-by-step explanation:
These are the two methods to finding the equation of a line when given a point and the slope: Substitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b. Use the m given in the problem, and the b that was just solved for, to create the equation y = mx + b.
1a. 100 foot-long rope is cut into 3 pieces.The first piece of rope is 3 times as long asthe second piece of rope. The third piece istwice as long as the first piece of rope.What is the length of the longest piece ofrope?
To solve the exercise, it is easier to make a drawing, like this
So, you have
[tex]\begin{gathered} z=3y \\ y=y \\ x=2z \\ z+y+x=100 \end{gathered}[/tex]Now solving
[tex]\begin{gathered} x=2z \\ x=2(3y) \\ x=6y \end{gathered}[/tex][tex]\begin{gathered} z+y+x=100 \\ 3y+y+6y=100 \\ 10y=100 \\ \frac{10y}{10}=\frac{100}{10} \\ y=10\text{ ft} \end{gathered}[/tex][tex]\begin{gathered} x=6y \\ x=6(10) \\ x=60\text{ ft} \end{gathered}[/tex][tex]\begin{gathered} z=3y \\ z=3(10) \\ z=30\text{ ft} \end{gathered}[/tex]Therefore, the length of the longest piece is 60ft.
20. Two teachers measured the shoe size of each of their students. The datawere used to create the box plots shown.Mrs. Norris's Class567891011121314Shoe SizeMrs. Ganger's Class5 6+87111213149 10Shoe SizeBased on the data, which statement about the results must be true?The average shoe size is the same for both classes.The shoe sizes 6 and 13 are outliers for both classes.© Mrs. Norris's class and Mrs. Ganger's class have the sameinterquartile range.© The median shoe size for Mrs. Norris's class is greater than forMrs. Ganger's class.
The correct answer is the last sentence.
"The median shoe size for Mrs. Norris's class is greater than for
Mrs. Ganger's class".
What is the mean and median of the data set
The mean of a data set is the sum of the data divided by the total number of data.
The median of a data set is the middle number in the set (after the numbers have been arranged from least to greatest, or, if there is an even number of data, the median is the average of the two middle numbers.
You have the next data set:
[tex]\begin{gathered} \lbrace11,11,11,11,12,12,12,13,13,13,13,13,13,14,15,15,15,15,15, \\ 15,16,16,16,16,16,17,17,17\rbrace \end{gathered}[/tex]A total of 28 data.
The mean is equal to the sum of the 28 numbers and then divided into 28:
[tex]undefined[/tex]if Maria collected R rocks and Javy collected twice as many rocks as Maria and Pablo collected 5 less than Javy. What is the sum of rocks collected by Pablo and Maria?
This problem deals with the numbers expressed in a more general way: letters or variables
That belongs to Algebra
We know Maria collected R rocks. Let's put this in a separate line:
M = R
Where M is meant to be the number of rocks collected by Maria
Now we also know Javy collected twice as many rocks as Maria did. Thus, if J is that variable, we know that
J = 2R
Pablo collected 5 less rocks than Javy. This is expressed as
P = J - 5
or equivalently:
P = 2R - 5
since J = 2R, as we already stated
We are now required to calculate the sum of rocks collected by Pablo and Maria.
This is done by adding P + M:
P + M = (2R - 5) + (R)
We have used parentheses to indicate we are replacing variables for their equivalent expressions
Now, simplify the expression:
P + M = 2R - 5 + R
We collect the same letters by adding their coefficients:
P + M = 3R - 5
Answer: Pablo and Maria collected 3R - 5 rocks together
12 + 24 =__(__+__)
Find the GCF. The first distributing number should be your GCF
A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, the numbers 12, 20, and 24 share the components 2 and 4.
Therefore, 12 and 24 have the most things in common. Figure 2: LCM = 24 and GCF = 12 for two numbers.
Find the other number if one is 12, then. What does 12 and 24's GCF stand for?
Example of an image for 12 + 24 = ( + ) Locate the GCF. You should distribute your GCF as the first number.
12 is the GCF of 12 and 24. We must factor each number individually in order to determine the highest common factor of 12 and 24 (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 24 = 1, 2, 3,.
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Cameron has 21 coins in his pocket, all of which are dimes and quarters. If the total value of his change is315 cents, how many dimes and how many quarters does he have?
Given:
Cameron has 21 coins in his pocket, all of which are dimes and quarters.
Let, x be the number of quarters and y be the number of dimes.
The total cost is 315 cents.
The equations are,
[tex]\begin{gathered} x+y=21\ldots\ldots\ldots\text{.}(1) \\ 25x+10y=315\ldots.\ldots\ldots....\ldots(2) \end{gathered}[/tex]Solve the equation,
[tex]\begin{gathered} x+y=21 \\ x=21-y\text{ put this value in equation (2)} \\ 25(21-y)+10y=315 \\ 525-25y+10y=315 \\ 525-315=15y \\ y=\frac{210}{15} \\ y=14 \end{gathered}[/tex]Put the value of y in equation (1),
[tex]\begin{gathered} x+y=21 \\ x+14=21 \\ x=21-14 \\ x=7 \end{gathered}[/tex]Thus, the number of quarters are 7 and dimes are 14 .
what does frilling mean
Answer:
A ruffled, gathered, or pleated border or projection, such as a fabric edge used to trim clothing.
Step-by-step explanation:
Brainlest, Please!
A business woman buys a new computer for $4000. for each year that she uses it the value goes depreciates by $400 the equation below gives the value y of the computer after x years. What does the x intercept mean in this situation? Find the x intercept. After how many years will the value of the computer be $2000Y=-400x+4000
Step 1: Write the equation
y = -400x + 4000
Step 2:
The intercept in the equation represents time in years.
x-intercept represents the total length of time taken in years for the computer to values to depreciate to $0.
step 3: Find the x-intercept
To find the x-intercept, you will have to find the time taken for the computer value to depreciate to $0.
y = $0
[tex]\begin{gathered} \text{From the equation.} \\ y\text{ = -400x + 4000} \\ 0\text{ = -400x + 4000} \\ 400x\text{ = 4000} \\ x\text{ = }\frac{4000}{400} \\ x\text{ = 10} \end{gathered}[/tex]The x-intercept = 10 years
Step 4:
To find the number of years take for the computer value to depreciate to $2000.
You will substitute the value of y = $2000 and find the value of x.
Therefore
[tex]\begin{gathered} y\text{ = -400x + 4000} \\ 2000\text{ = -400x + 4000} \\ 400x\text{ = 4000 - 2000} \\ 400x\text{ = 2000} \\ x\text{ = }\frac{2000}{400} \\ \text{x = 5 years} \end{gathered}[/tex]It will take 5 years for the value of the computer to depreciate to $2000.
Use the graph of y = f (x) to find the following value of f. f(2) =
Answer:
f(2)=4
Explanation:
Consider the graph below:
When x=2, the value of f(x) = 4 (the poiny circled in blue above).
Therefore:
[tex]f(2)=4[/tex]The value of f(2) is 4.
Choose the best description of its solution. If applicable, give the solution.
Given:
[tex]\begin{gathered} -x-3y=-6\ldots\text{ (1)} \\ x+3y=6\ldots\text{ (2)} \end{gathered}[/tex]Adding equation(1) and equation(2)
[tex]\begin{gathered} -x-3y+x+3y=-6+6 \\ 0=0 \end{gathered}[/tex]The system has infinitely many solution .
They must satisfy the equation:
[tex]y=\frac{6-x}{3}[/tex]Help with number one a and b is both parts of number one
Solving the operation_
We are given two figures that represent a garden. We are asked to determine its areas.
The shape of figure A is a rectangle of 9 ft by 12 ft. The area of a rectangle is the product of its dimensions therefore, we have:
[tex]A_A=\left(9ft\right)\left(12ft\right)[/tex]Solving the operations:
[tex]A_A=108ft^2[/tex]The shape of figure B is a circle of radius 5ft. The area of a circle is:
[tex]A_B=\pi r^2[/tex]Where "r" is the radius. Substituting we get:
[tex]A_B=\pi\left(5ft\right)^2[/tex][tex]A_B=25\pi ft^2[/tex]In decimal notation, the area is:
[tex]A_B=78.54ft^2[/tex]Question 23 of 25
What is the effect on the graph of f(x) = when it is transformed to
g(x) = +17?
A. The graph of f(x) is shifted 17 units down.
B. The graph of f(x) is shifted 17 units to the right.
OC. The graph of f(x) is shifted 17 units up.
OD. The graph of f(x) is shifted 17 units to the left.
Answer:
C. The graph of f(x) is shifted 17 units up.
Step-by-step explanation:
When + is outside the equation, it means up.
Challenge A family wants to rent a car to go on vacation. Company A charges $75.50 and14¢ per mile. Company B charges $30.50 and 9¢ per mile. How much more does Company Acharge for x miles than Company B?For x miles, Company A charges dollars more than Company B.(Simplify your answer. Use integers or decimals for any numbers in the expression.)
Company A charges $75.50 and 14¢ per mile, then for x miles, Company A charges 75.5 + 0.14x dollars
Company B charges $30.50 and 9¢ per mile, then for x miles, Company B charges 30.5 + 0.09x dollars
Subtracting the second equation to the first one,
75.5 + 0.14x
-
30.5 + 0.09x
----------------------
45 + 0.05x
For x miles, Company A charges 45 + 0.05x dollars more than Company B.
At a local school, 164 students play soccer and 112 students play baseball. What is the ratio of soccer players to baseball players?41:2828:4113:2828:13
Given
The number of students who play soccer is 164.
The number of students who play baseball is 112
Explanation
To find the ratio of soccer player to baseball players .
Divide the number of soccer player by the number of baseball player.
[tex]\frac{164}{112}=\frac{41}{28}[/tex]Answer
Hence the ratio of soccer players to baseball players is
[tex]41:28[/tex]