Answer:
The amount invested are $2600 and $11400 respectively
Step-by-step explanation:
Let the first amount be x
Given:
(First Investment)
Principal (P1) = x
Rate (R1) = 4.5%
Time (T) = 1 year
(Second Investment)
Principal (P2) = 4x + 1000
Rate (R2) = 6%
Time (T) = 1 year
Income = $801
Calculating the income from the first investment;
[tex]I_1 = \frac{P_1R_1T}{100}[/tex]
Substitute values for P1, R1 and T
[tex]I_1 = \frac{x * 4.5 * 1}{100}[/tex]
[tex]I_1 = \frac{4.5x}{100}[/tex]
Calculating the income from the second investment;
[tex]I_2 = \frac{P_2R_2T}{100}[/tex]
Substitute values for P2, R2 and T
[tex]I_2 = \frac{(4x + 1000) * 6 * 1}{100}[/tex]
[tex]I_2 = \frac{6(4x + 1000)}{100}[/tex]
[tex]I_1 + I_2 = Annual\ Income[/tex]
So:
[tex]\frac{4.5x}{100} + \frac{6(4x + 1000)}{100} = 801[/tex]
Multiply through by 100
[tex]100 * \frac{4.5x}{100} +100 * \frac{6(4x + 1000)}{100} = 801 * 100[/tex]
[tex]4.5x +6(4x + 1000) = 801 * 100[/tex]
[tex]4.5x +24x + 6000 = 80100[/tex]
Collect Like Terms
[tex]4.5x +24x = 80100 - 6000[/tex]
[tex]28.5x = 74100[/tex]
Divide through by 28.5
[tex]x = \frac{74100}{28.5}[/tex]
[tex]x = \$2600[/tex]
Recall that; the second invest
Amount Invested = 4x + 1000
This gives
[tex]Amount = 4 * \$2600 + 1000[/tex]
[tex]Amount = \$11400[/tex]
Hence;
The amount invested are $2600 and $11400 respectively
Simplify:
(4xy^-6)^-3
[tex](4xy^{-6} )^{-3}[/tex]
Answer:
(4^-3)(x^-3) y^(18)
or
y^18/ (64 x^3)
Step-by-step explanation:
(4xy^-6)^-3
Distribute the exponent to all terms in the parentheses
(4^-3)(x^-3) (y^-6)^-3
a^ b^c = a^ (b*c)
(4^-3)(x^-3) y^(-6*-3)
(4^-3)(x^-3) y^(18)
If we do not want negative exponents
a ^ -b = 1/ a^b
y^18/( 4^3 x^3)
y^18/ (64 x^3)
given the point A(-3,-2) and B(6,1), select two possible locations for point P so that P partitions AB in the ratio 2:1
A. (0,3)
B. (3,0)
C. (-1,0)
D. (0,-1)
E. (1,-1)
Answer: (0,3) & (0,-1)
Step-by-step explanation:
Since cos(x) is the derivative of sin(x), then integral 16 sin^2(x) cos(x) dx can be done by substituting u = sin (x) sin (x) and du = cos (x) cos (x)^dx. With the substitution u = sin(x), we get integral 16 sin^2 (x) cos(x) dx = 16 integral u^2 du. which integrates to + C. Substituting back in to get the answer in terms of sin(x), we have integral 16 sin^2 (x) cos (x) dx = + C.
Complete
Find the integral of [tex]f(x) = 16sin^2 (x ) cos(x) dx[/tex]
Answer:
The solution is [tex]\frac{16}{3} sin^{3}x + c[/tex]
Step-by-step explanation:
So
[tex]Let \ u = sin(x)[/tex]
=> [tex]\frac{du}{dx} = cos (x)[/tex]
=> [tex]du = cos(x)dx[/tex]
So
[tex]\int\limits {16sin^2 (x ) cos(x) dx} \, \equiv \int\limits {16u^2 du}[/tex]
=> [tex]\int\limits {16u^2 du} = 16 [\frac{u^3}{3} ] + c[/tex]
Now substituting sin(x) for u
[tex]\frac{16}{3} u^3 + c = \frac{16}{3} sin^{3}x + c[/tex]
So the integral of [tex]f(x) = 16sin^2 (x ) cos(x) dx[/tex] is
[tex]\frac{16}{3} sin^{3}x + c[/tex]
Is there a known infinite product for e? What I mean is, it’s similar to an infinite series.
"e" is an irrational number because it cannot be seen as a quotient of two integers. In the bright side, it can be shown as a continued fraction. "e" may also be used as an infinite product, infinite series, and any other limit to any sequence.
Best of Luck!
AWARDING BRAINLIEST!!
Beth is solving this equation: 1/x+3=3/x
She says “I can multiply both sides by x and get the linear equation 1 + 3x = 3, whose solution is x = 2/3.”
Which of the following statements makes this a correct argument, or shows that it is incorrect? Select all that apply.
Question 1 options:
After multiplying both sides by x you need to subtract 1 from both sides
You can assume x ≠ 0 because both sides are undefined if x = 0.
You cannot multiply both sides by x because you do not know what x is.
The equation is not linear, so you cannot use the methods normally used for solving linear equations.
Answer:
1. After multiplying both sides by x you need to subtract 1 from both sides
2. You can assume x ≠ 0 because both sides are undefined if x = 0.
Step-by-step explanation:
Given
[tex]\frac{1}{x} + 3 = \frac{3}{x}[/tex]
Required
Which of the options shows the validity of Beth's action
The first option answers the question and the reason is as follows;
Multiply both sides by x
[tex]x * (\frac{1}{x} + 3) = \frac{3}{x} * x[/tex]
Open the bracket
[tex]1 + 3x = 3[/tex]
As stated in option 1; Subtract 1 from both sides
[tex]1 - 1 + 3x = 3 - 1[/tex]
[tex]3x = 2[/tex]
Divide both sides by 2
[tex]x = \frac{2}{3}[/tex]
Another correct option is the option 2
Because the expression is undefined if x = 0
See Proof by substituting 0 for x
[tex]\frac{1}{0} + 3 = \frac{3}{0}[/tex]
Division by 0 is undefined.
Hence, option 2 is also correct
The other options (3 and 4) are incorrect
write a quadratic equations given the roots 5/2 and 9
Answer:
(x-5/2)(x-9).
x^2-5/2x-5/2x+45/2.
Multiply the number by 2.
which is 2(x^2-5/2x-5/2x+45/2).
2x^2-5x-5x+45.
2x^2-10x+45.
what is the difference in meaning between |-3| and -3.
Answer: the lines on the outside mean absolute value and the absolute value of -3 is 3
Step-by-step explanation:
20 items per hour x 24 hours per day x 30 days per hour
Answer: 480 items per day, and 14,00 items per mounth.
Step-by-step explanation:
20(24) = 480 items per day
480(30) = 14,400 items per month
Answer:
20x24x30=14,440
Step-by-step explanation:
1
What is an equivalent form of the following function?
f(x) = 4(x - 1)2 + 12
O A. f(x) = 4x2 - 8x + 16
O B. f(x) = 4x2 - 8x + 8
OC. f(x) = 4x2 - 2x + 16
OD. f(x) = 4x2 + 8x + 8
Which list shows these numbers in ascending order?
-V6, 2, -23, 2.5
Please help!!!!!!!!!!!!!!
Answer: 40 peaches
Step-by-step explanation:
Let x represent (1/2) the peaches
and y represent (1/2) the strawberries
Peaches Strawberries Ratio
Alice: x - 3 y 1:4
Bryan: x y - 8 1:3
We can create a system of equations:
Alice: 4(x - 3) = y --> 4x - 12 = y
Bryan: 3(x) = y - 8
Substitute y = 4x - 12 into the Bryan equation:
3x = (4x - 12) - 8
3x = 4x - 20
-x = -20
x = 20
Therefore, Alice and Bryan each had 20 peaches, which means Bryan bought a total of 40 peaches.
Solve the equation. -10x + 1 + 7x = 37
A. X = -15
B. X =-12
C. X = 12
D. X = 15
Answer:
B. X =-12
Step-by-step explanation:
- 10x + 1 + 7x = 37
-10x + 7x = 37 - 1
-3x = 36
x = 36/-3
x = - 12
What is (6x10^6)(4x10^-1) ?
Answer:
Step-by-step explanation:
Multiply the 6 and 4 together. 6*4 = 24
The next part is a bit tricky. Add the powers on the base 10. Keep the base 10.
10^(6 - 1) = 10^5
Now put the two parts together. 24 * 10^5
The number in front of the 10 must be between 1 and 10.
So 24 can be written as 24 = 2.4 * 10^1
2.4 * 10^1 * 10^5 = 2.4 * 10^(5 + 1) = 2.4 * 10^6
HELP! WILL GIVE BRAINLIEST IF YOUR ANSWER IS RIGHT Maria lives in Mexico. Both of her parents are Mexican. Maria is a Mexican citizen. She was born in an American hospital when her parents were on a short vacation in San Diego, California. Was Maria an American citizen at birth? Explain your answer.
Yes, Maria was a "citizen" of America.
What is citizenship?A legal status and relation between an individual and a state that entails specific legal rights and duties.
Given that, Maria lives in Mexico. Both of her parents are Mexican. Maria is a Mexican citizen. She was born in an American hospital when her parents were on a short vacation in San Diego, California.
The answer is yes,
A child born in American soil will be an American citizen.
Hence, Maria an American citizen at birth.
For more references on citizenship, click;
https://brainly.com/question/18099945
#SPJ2
the outdoor temperature was 8 degrees at midnight the. temperature declined 5 degrees during each. of the next 3 hours what was the temperature at 3 A.M.
what exponent will make this true? Enter your naswer in the box 10?=1,000
Answer:
10 to the 2nd power
Step-by-step explanation:
Isabella left a 15% tip for a meal. The total cost of the meal, including the tip, was $23. What was the cost of the meal before the tip was added?
Answer:
the meal was $3.45
Step-by-step explanation:
Answer: cost before tip is $20
Step-by-step explanation:
Tip=20(0.15)
= 3
Total = Cost + Tip
= 20 + 3
= 23
Help please I don’t understand
Answer:
Answer is -6
Step-by-step explanation:
first do from small bracket -(-6)=+6
and then -6-6=-12
do-12+6=-6
hi, need help with math, if you could explain it also.
What is the domain of the given function?
Answer:
Domain = 3, 6, -1, 5, -4
Step-by-step explanation:
The Domain is the first coordinate of a coordinate set so it is x
Hope This Helps :)
Edwin raps for 10 minutes on Monday. On Tuesday he raps for an
hour. Find out how many minutes he has practiced so far this week.
Answer:1 hour and 10 mins
Step-by-step explanation: on Monday he raps for 10
Tuesday he raps for 1 hour
1 h +10m =1 h and 10 min
Which problem can be solved by division of decimals? How much money does Jon need to buy 10.3 gallons of gas that costs $3.79 a gallon? What grade does Maria need on her next test to achieve a total of at least 400 points if she had 4 previous tests that had grades of 75.3, 92.1, 78.6, and 81.0? Helena saved $45.00 toward a dress that costs $78.00. How much more does she need to save? Mica spent $45.50 on 7 indoor baseball sets. How much does it cost for one set?
Answer:
Mica spent $45.50 on 7 indoor baseball sets. How much does it cost for one set?
Step-by-step explanation:
Answer:
ITS D I TOOK THE TEST
Step-by-step explanation:
Perform the indicated operation. 11(-2), 22, 9, -22, -9 which one us it
Answer:
-22
Step-by-step explanation:
When numbers are placed closed like that, and have a parenthesis, you will multiply.
11(-2) = 11 * -2 = -22
-22 is your answer.
~
Answer:
[tex]\Huge \boxed{-22}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
[tex]11(-2)[/tex]
Multiplying,
[tex]\Longrightarrow \ \ 11*-2[/tex]
[tex]\Longrightarrow \ \ -22[/tex]
[tex]\rule[225]{225}{2}[/tex]
Which number is a reasonable estimate for 553 +363?
A 1,300
B 1,000
600
D 200
its b because you can round 363 to 400 and 553 to 600 400 + 600 = 1000
I need help with this question
Answer:
Hey there!
[tex]d= \sqrt{(-1-(-3)^2+(-1-1)^2}[/tex]
[tex]d=\sqrt{8}[/tex]
d is approximately 2.8 units.
Let me know if this helps :)
Oliver reads 28 ½ pages of a book in 1 1/6 hours. Express his speed in pages per hour?
Answer:
Answer: The speed of Oliver is 24\dfrac{1}{3}24
3
1
pages per hour.
Step-by-step explanation: Given that Oliver reads 28\dfrac{1}{2}28
2
1
pages of a book in 1\dfrac{1}{6}1
6
1
hours.
We are to express his speed in pages per hour.
We will be using the UNITARY method to solve the given problem.
Number of pages read by Oliver in 1\dfrac{1}{6}=\dfrac{7}{6}1
6
1
=
6
7
hours is
=28\dfrac{1}{2}=\dfrac{57}{2}.=28
2
1
=
2
57
.
Therefore, the number of pages read by Oliver in 1 hour is given by
\dfrac{57}{2}\times\dfrac{6}{7}=24\dfrac{3}{7}.
2
57
×
7
6
=24
7
3
.
Thus, the speed of Oliver is 24\dfrac{1}{3}24
3
1
pages per hour.
Step-by-step explanation:
Plz Mark me as brainliest
PLEASE HELP ME!I have a really hard time with algebra 2 and I really need to pass:(
Answer:
First problem:
Limiting the Domain to [tex]x\leq 0[/tex] (option A in the list)
Second problem:
All the three statements are true, so pick option D)
Step-by-step explanation:
Recall that a function in order to have inverse needs to be a one-to-one function. In the case of the function they give you in the problem:
[tex]f(x)= 3x^2+1[/tex]
the graph corresponds to a parabola with vertex at x=0 and y=1 (0, 1), and since it has two branches that correspond to equal y-values for opposite pairs of x values, it doesn't satisfy the conditions for the existence of inverse. But if we limit the Domain of it considering just one half of the graph (for example limiting the Domain to the values to one side of the parabola's vertex, then this restricted function is one-to-one and we can find its inverse.
So the option of limiting the Domain to x-values smaller than or equal to zero, suggested in option A of the list of answers will do the job we need.
In the following problem, the three first statements are true for an inverse function, so pick option D that says that all previous statements are true.
you roll a die what is the probability a prime number will come up?
Answer:
1/2 or 50%
Step-by-step explanation:
Total numbers: 1 to 6
Prime numbers: 2, 3, 5
Possible outcomes= 6Favorable outcomes = 3Probability
3/6 = 1/2 or 50%1) What does the equation x = 4 represent in R^2? a) a circle.b) a plane.c) a line.d) a pointWhat does it represent in R^3? a) a plane.b) a line.c) a circle.d) a point.2) What does the equation y + 3x = 2 represent in R^3? a) a plane.b) a circle.c) a line.d) a point.What does z - 4y = 8 represent? a) a line.b) a circle.c) a point.d) a plane.What does the pair of equations y = 2, z = 8 represent? In other words, describe the set or points (x, y, z) such that y = 2 and z = 8. a) a line.b) a circle.c) a plane.d) a point.
Answer:
The equation [tex]x=4[/tex] represents in R^2 c) a line
The equation [tex]x=4[/tex] represents in R^3 a) a plane
The equation [tex]y+3x=2[/tex] represents in R^3 a) a plane
The equation [tex]z-4y=8[/tex] represents d) a plane
The pair of equations [tex]y=2,z=8[/tex] represents a) a line
Step-by-step explanation:
Let's start by studying each question :
1)
In R^2 , [tex]x=a[/tex] with [tex]a[/tex] ∈ IR is the equation of all vertical lines
In this case, the only free variable is the variable ''y''
R^2 has two dimensions (x and y) so if we set [tex]x=4[/tex] we will have only one free variable in R^2 (which is a line in R^2). Therefore, [tex]x=4[/tex] represents a line in R^2
Now, in R^3 we have three dimensions (x, y and z) so if we set [tex]x=4[/tex] we will have only two free variables (y and z) and [tex]x=4[/tex] will represent a plane (which have two dimensions) in R^3.
2) The equation [tex]y+3x=2[/tex] in R^3 has the free variable ''z'' and given that we select a value (for example for ''x'') the another value from the variable ''y'' is determined. Finally, we have the free variables ''z'' and ''x'', and the variable ''y'' restricted for our choice of the variable ''x''.
The equation [tex]y+3x=2[/tex] in R^3 (given that we have two free variables) represents a plane.
Using the same reasoning, the equation [tex]z-4y=8[/tex] represents a plane (given that it has two free variables : ''y'' and ''x'')
Finally, the pair of equations [tex]y=2,z=8[/tex] set values for ''y'' and ''z'' leading us ''x'' as the free variable. With only one free variable we will have a ''one dimensional'' geometric form. The one dimensional forms in R^3 are lines.
The final answer is a) a line.
What is the additive inverse of -7.5? *
Answer:
Step-by-step explanation:
In mathematics, the additive inverse of a number a is the number that, when added to a yields zero. This operation is also known as the opposite (number), sign change, and negation.