Using a system of equations, it is found that she invested 318.71 into Fund B.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: Amount invested in Fund A.Variable y: Amount invested in Fund B.The amount she invested in Fund A was 3 times as much as the amount she invested in Fund B, hence:
x = 3y.
Fund A returned a 6% profit and Fund B returned a 15% profit, and the total profit was of 1380, hence:
1.06x + 1.15y = 1380.
We have that x = 3y, hence:
1.06(3y) + 1.15y = 1380.
4.33y = 1380
y = 1380/4.33
y = 318.71.
She invested 318.71 into Fund B.
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Write an algebraic expression for the length of QR
The algebraic expression for the length of QR is 5y+20.
Given that The algebraic expression for the length of PR is 13y+25 , The algebraic expression for the length of PQ is 8y+5 and asked to find The algebraic expression for the length of QR.
The algebraic expression for the length of PR is 13y+25
PR=PQ+QR
⇒The algebraic expression for the length of PR =The algebraic expression for the length of PQ + The algebraic expression for the length of QR
QR=PR-PQ
⇒The algebraic expression for the length of QR=The algebraic expression for the length of PR - The algebraic expression for the length of PQ
⇒The algebraic expression for the length of QR=13y+25 - 8y+5
⇒The algebraic expression for the length of QR=5y+20
Therefore,The algebraic expression for the length of QR is 5y+20.
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Give the number of terms in the algebraic expression and also give the numerical coefficient of the second term.
-3 a + 30b
Answer:
2 termssecond coefficient: 30Step-by-step explanation:
You want the number of terms and the second coefficient in the expression ...
-3a +30b
TermsIn a simplified polynomial expressed as a sum of products, each of the products is a "term." This expression has two terms:
-3a30bThe sign separating terms in the sum is generally considered to be part of the following term. If this were written 30b -3a, one of the terms would still be -3a.
CoefficientIf each variable value is set to 1 in a term of a polynomial expression, the resulting value is the coefficient of that term. In general, this will be the numerical multiplier of the variables.
30b = 30(1) = 30 . . . . . when b=1
The coefficient of the second term is 30.
how many 3 fourths can you cut from a 6 in a half ft ribbon? explain
Answer:Half of 51/8 is 51/16 (you multiply 51/8 by 1/2 and that is your answer.)
Now back to mixed number
51/16 = 3 3/16
So final answer is 3 3/16.
Step-by-step explanation:
To find half of 6 3/8.
6 3/8 is a mixed number.
First will change into fraction.
6 3/8 = ((8*6)+3)/8 = 51/8
(Convert the mixed number 6 3/8 into an improper fraction first by multiplying the denominator (8) by the whole number part (6) and add the numerator (3) to get the new numerator. Place the new numerator (51) over the old denominator (8).)
the line y = 3x + 4 and y = ax + 2 are parallel if a=
Answer:
a =3
Step-by-step explanation:
The number before the x is the slope. Parallel lines have the same slope.
Answer:
Step-by-step explanation:
The length of a rectangle is 6 mi. less than 2 times the width. If the perimeter of the rectangle is 54 mi., find the length and the width.
(Hint - The perimeter of a rectangle is given by: P=2L+2W )
(+3)-(-2)=
(-3)-(+2)=
(-2)-(+3)=
(-2)-(-3)=
(+2)-(-3)=
Answer:
1. +5
2.-5
3.-5
4.+1
5.+5
Answer: 1.) 5 2.) -1 3.)-5 4.)1 5.)5
Step-by-step explanation:
Alex wrote checks on Tuesday for $35 and $45. He also made a
deposit in his checking account of $180. Find the overall change in
the amount in his checking account.
Step 1: Analyze Information
Step 2: Formulate a Plan
Step 3: Solve
Step 4: Justify and Evaluate
1
Write answer for step 2 here.
*||«
r notes
Answer: here is ur answer
He would have $100 in his bank account from the information provided
Step-by-step explanation:i really hope this helps please lmk if i am wrong have a good day/night (:
Evaluate the function
f(x) = 3x^2 + 4x + 19
Find f(-7)
Answer:
Step-by-step explanation:
3
x
2
+
4
x
+
19
−
f
(
x
)
=
0
Enter the missing values in the area model to find 6(2w+5)
Write the quadratic equation whose roots are -5 and 3, and whose leading coefficient is 3.
(Use the letter x to represent the variable.)
Answer: (x-3)(x-5) = x2 - 8x + 15
The roots will be unchanged by multiplication by 3: 3x2 - 24x + 45
Step-by-step explanation:
Answer:
y = 3x² + 6x - 45
Step-by-step explanation:
given roots x = a and x = b then the factors are (x - a) and (x - b)
then the quadratic is the product of its factors
y = a(x - a)(x - b) ← a is a multiplier
here x = - 5 and x = 3 with a = 3 , then factors are
(x - (- 5)) and (x - 3) , that is (x + 5) and (x - 3) , then
y = 3(x - 3)(x + 5) ← expand factors using FOIL
y = 3(x² + 2x - 15) ← distribute parenthesis by 3
y = 3x² + 6x - 45
Plytage-22-23
Examining Intervals in a Table of Values
Which table shows a function that is decreasing over the interval (-2, 0)?
f(x)
f(x)
0
-15
-5
-5
-20
-30
X
-2
-1
0
1
Intro
0
5
X
-2
0
2
4
X
-3
-2
-1
0
f(x)
2
0
-10
-24
Done
English
Answer:
the third one (the outmost right)
Step-by-step explanation:
the first one goes from -2 to 0 through functional values of 0, down to -5, and then back up to 0. so, it does NOT go down between -2 and 0.
the second one goes from -2 to 0 through the functional values of -15 up to -5. so, it goes UP in that interval.
and the third one goes from -2 to 0 through the functional values of 0 down to -10 and then further down to -24. so, this one is truly decreasing in that interval.
Compare √5 and 3.1. Which one is greater
Answer:√5
Step-by-step explanation:
√5 = 2.23...
Answer:
3.1
Step-by-step explanation:
Square root means what number multiplied by another equals the number you need to square (2 then 2nd square root button on calculator.
square root of 5 is 2.2360679775 and 3.1 is greater so 2.2360679775<3.1
Determine whether the sequence is convergent or divergent. If it is convergent, find the limit. (If the quantity diverges, enter DIVERGES.)
an = n^3 − 1/n^3 + 1.
lim an =
n→∞
There are 11 reams of paper in a case. How many total reams of paper are in 23 cases?
Answer: 253 reams of paper
Hope this helps!
The table to the right shows the volume discounts offered by a company, where x is the volume of a purchase in dollars. Assume that the volume discounts in the table apply to the entire purchase. That is, if the volume x satisfies $300≤x<$1,000, the entire purchase is discounted 4%. Answer a) and b) below.
$300≤x<$1,000
$1,000≤x<$3,000
$3,000≤x<$5,000
$5,000≤x
4%
5%
6%
10%
Volume Discount
(Excluding tax)
Volume($x)
Discount Amount
Question content area bottom
Part 1
a) If x is the volume of a purchase before the discount is applied, write a piecewise definition for the discounted price D(x) of this purchase.
D(x)= x if 0≤x<300 enter your response here if 300≤x<1,000 0.95x if 1,000≤x<3,000 enter your response here if 3,000≤x<5,000 0.90x 5,000≤x
The piecewise function for the discounted price of the purchase is given by:
D(x) = 0.96x, 300≤x<1,000.D(x) = 0.95x, 1,000≤x<3,000.D(x) = 0.94x, 3,000≤x<5,000.D(x) = 0.9x, 5,000≤x.What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
For $300≤x<$1,000, the discount is of 4%, hence the discounted price is 96% of the original price, that is:
D(x) = 0.96x, 300≤x<1,000
For $1,000≤x<$3,000, the discount is of 5%, hence the discounted price is 95% of the original price, that is:
D(x) = 0.95x, 1,000≤x<3,000.
For $3,000≤x<$5,000, the discount is of 6%, hence the discounted price is 94% of the original price, that is:
D(x) = 0.94x, 3,000≤x<5,000.
For $5,000≤x, the discount is of 10%, hence the discounted price is 90% of the original price, that is:
D(x) = 0.9x, 5,000≤x.
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Megan cuts pieces of colored felt to
create a logo of a sun behind a
mountain peak. Determine the
approximate total amount of felt used
in the logo.
The approximate total amount of felt used in the logo is 334.34 square cm
How to determine the approximate total amount of felt used in the logo?We have the following parameters on the logo:
Shapes = Semicircle and Triangle
Where
Semicircle:
Diameter = 18 cm
Triangle
Base = 16 cm
Height = 10 cm
The approximate total amount of felt used in the logo is calculated as
Amount = Area of semi-circle + Area of triangle
This gives
Amount = π(d/2)^2 + 0.5bh
So, we have
Amount = 3.14 * (18/2)^2 + 0.5 * 16 * 10
Evaluate
Amount = 334.34
Hence, the approximate total amount of felt used in the logo is 334.34 square cm
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For any two integers a and b, (a - b) squared = a squared - b squared.
^^^^
Determine if the conjecture is true or false.
If False give a counterexample.
a = 1, b = 2 is a counterexample, and with that, we conclude that the conjecture is false.
Is the conjecture true or false?Here we have the conjecture:
"For any two integers a and b, (a - b)^2 = (a^2 - b^2)"
Notice that if we find a single pair of integers a and b such that the equality in the conjecture is false, then we have found a counterexample and that is enough to conclude that the conjecture is false.
If we define=
a = 1
b = 2
Replacing that in the equation of the conjecture we get:
(1 - 2)^2 = (1^2 - 2^2)
(-1)^2 = 1 - 4
1 = -3
This is false, then a = 1, b = 2 is a counterexample, and with that we conclude that the conjecture is false.
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Vera uploaded a hilarious video of a squirrel to a funny videos website. It was viewed 320320320 times on the first day. Each day since then, the number of views was 25\%25%25, percent more than the day before.
Let f(n)f(n)f, left parenthesis, n, right parenthesis be the number of views Vera's video got on the n^\text{th}n
th
n, start superscript, start text, t, h, end text, end superscript day since she uploaded it.
fff is a sequence. What kind of sequence is it?
Solution : [tex]F(n)= (320) 1.25^{n-1}[/tex]
In Maths, Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is also known as a geometric sequence of numbers that follow a pattern. Also, learn arithmetic progression here. The common ratio multiplied here to each term to get a next term is a non-zero number. An example of a Geometric sequence is 2, 4, 8, 16, 32, 64, …, where the common ratio is 2.
A geometric progression or a geometric sequence is the sequence, in which each term is varied by another by a common ratio. The next term of the sequence is produced when we multiply a constant (which is non-zero) by the preceding term. It is represented by:
a, ar, ar2, ar3, ar4, and so on.
Where a is the first term and r is the common ratio.
Note: It is to be noted that when we divide any succeeding term from its preceding term, then we get the value equal to the common ratio.
Suppose we divide the 3rd term by the 2nd term we get:
ar2/ar = r
In the same way:
ar3/ar2 = r
ar4/ar3 = r
General Form of Geometric Progression
The general form of Geometric Progression is:
a, ar, ar2, ar3, ar4,…, arn-1
Where,
a = First term
r = common ratio
ar^(n-1) = nth term
On the first day, the video was viewed = 320 times.
the number of views was 25% more than the day before which means increasing 1.25 per day.
G.P.
Where common ratio r = 1.25
First term = f(1) = 320
The formula of nth term in G.P. =
[tex]F(n)= f(1) r^{n-1}[/tex]
So, nth term of the given situation :
[tex]F(n)= (320) 1.25^{n-1}[/tex]
Where f(n) denotes the number of views on an nth day.
[tex]F(n)= (320) 1.25^{n-1}[/tex]
So, the number of views Vera's video got on an nth day =
[tex]F(n)= (320) 1.25^{n-1}[/tex]
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Which numbers have a digit in the ones place that is 1/10 the value of the digit in the tens place? select all that apply
a. 6,044.7
b 6,339.99
c. 8,101.13
d. 8,066.51
e. 9,777.1
The numbers that have a digit in the ones place that is 1/10 the value of the digit in the tens place is 6,044.7 , 9,777.1 and 8,101.13
The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs. The precise position of a number within a series is assigned a value by a place-value system.
Given that we have to choose the number having a digit in the one place that is 1/10 the value of the digit in the tens place.
The numbers are 6,044.7 , 9,777.1 and 8,101.13 in which a digit in one place has a value that is 1/10 that of a digit in the tens place.
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Math question please help ASAP
Please check the image attached aside to see the representation of the system of inequalities. The points (x, y) = (40, 30) and (x, y) = (10, 40) are solutions of the system of inequalities.
What is the graphic representation of a system formed by two inequalities
In this question we have a system formed by two inequalities represented by linear expressions in implicit form. Now we proceed to rewritte the system into explicit form:
y ≥ (200 - 4 · x) / 6 (1)
y < 75 - x (2)
Then, the solution set of the point is represented by an area below the function (2) and equal and greater to the function (1). Finally, we proceed to graph the system of inequalities. The points (x, y) = (40, 30) and (x, y) = (10, 40) are solutions of the system of inequalities.
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If w # 0, what is the additive inverse of the
expression below?
A. -3w
B.-w/3
C. 3w
D. 3/w
The additive inverse of the expression -3/w is 3/w
How to determine the additive inverse?The expression is given as:
-3/w
The law of additive inverse states that
For an expression x, the additive inverse is -x
This means that the additive inverse of the expression -3/w is 3/w
Hence, the additive inverse of the expression -3/w is 3/w
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If w≠0, what is the additive inverse of the expression below? -3/w
Explain how to find the constant of proportionality for the ratio of robins to cardinals.
Not really sure how this works!! Thank you for all help
The constant of proportionality is 3 for the ratio of robins to cardinals.
We have a table:
Cardinals Robins
5 15
6 18
9 27
10 30
We need to find the constant of proportionality.
The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.
We know that:
Robins ∝ Cardinals
Robins = K × Cardinals
K = the constant of proportionality
15 = k (5)
k = 3
So, we get the constant of proportionality as 3.
Therefore, the constant of proportionality is 3 for the ratio of robins to cardinals.
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Your question was incomplete. Please refer the content below:
Explain how to find the constant of proportionality for the ratio of robins to cardinals.
A 2-column table with 4 rows. Column1 is labeled Cardinals with entries 5, 6, 9, 10. Column 2 is labeled Robins with entries 15, 18, 27, 30.
Huilan is 11 years younger than Thomas. The sum of their ages is 31. What is Thomas's age?
years old
Answer:
21
Step-by-step explanation:
Answer:
21
Step-by-step explanation:
Huilan: x-11
Thomas: x(Assume)
Their Sum = 31
Huilan+Thomas = 31 ...(1)
Possible Equation: x+x-11= 31 ...(2)
Solved:
2x-11= 31
2x = 31+11
x = 42/2
x = 21
Therefore, Thomas' Age is 21.
Before Valentine's Day, a store bought 58 boxes of chocolates. There were 65 chocolates in each box. How many chocolates did the store buy? chocolates
Answer:
The equation would be:
58 times 65
The answer:
3,770
Step-by-step explanation:
What is the product of 4.5 ⋅ 10^5 and 1.6 ⋅ 10^2?
Answer: 450000, 160
Step-by-step explanation:
4.5 ⋅ 10^5 =
4.5*100000=
4*100000+0.5*100000=
400000+50000=450000
1.6 ⋅ 10^2=
1.6*100=
1*100+0.6*100=
100+60=160
Do the shapes with the same volume always have the same surface area?
Answer:
No.
Step-by-step explanation:
They can't have the same surface area, because the surface area is a 2-dimensional measure of a 3-dimensional object(for the most part), while the volume is 3-dimensional, so they would not share the same surface area due to them being mostly different structures despite having the same amount of cubic units.
➲ Hope this helps. Address concerns if needed.
Answer if you know your right, bur dont answer just for the points
Answer:
2/11 = 0.18
22% = 0.22
1.42 = 1.42
That leaves the answers down to B and C.
B has a lesser hundredths place than 0.18.C is greater than 0.18 in the tenths place, making it bigger.Thus, the answer is C, 22%.
Answer:
C
Step-by-step explanation:
2/11 = 0.18181
22% = 0.22
1.42
Please explain Y is the midpoint of line segment XZ
Answer:
d
Step-by-step explanation:
(1,8) is the coordinates of midpoint so ×2 and - one of the x z is ok
1×2 -(-10) = 12
8×2-(-12) = 28
Write the following as an algebraic expression. Then simplify.
The total amount of money (in cents) in x quarters, (x+2) dimes, and 2x nickels. (Hint: The value of a quarter is 25 cents, the value of a dime is 10 cents, and the value of a nickel is 5 cents.)
HELP PLEASEEE !
The algebraic expression that represents the total amount of money in terms of x is:
y = 45*x + 20
How to write the algebraic expression?Here we want to find the total value (in cents) of:
x quarters.x + 2 dimes2x nickels.The total value will be given by the linear equation:
y = x*25 + (x + 2)*10 + (2x)*5
Where y represents the total value in cents.
Now we can simplify that equation to get:
y = x*25 + (x + 2)*10 + (2x)*5
y = x*25 + x*10 + 20 + x*10
y = 45*x + 20
This is the algebraic expression we wanted to get.
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how to solve 10x+25(x-2)=335
Answer:
x = 11 ,
Step-by-step explanation:
isolate the variable by diving each side by factors that don’t contain the variable