To achieve an annual income of $18,930, the woman should invest $77,700 at the 10% rate and $62,000 at the 18% rate.
To determine how much a woman should invest at each rate to achieve an income of $18,930 per year, we can set up a system of linear equations. Assuming she invests x dollars at the 10% rate and y dollars at the 18% rate, we can use the following equations:
x + y = $139,700: This equation represents the total amount of money she has to invest.
0.10x + 0.18y = $18,930: This equation represents the annual income from the investments.
To solve:
Multiply the first equation by 0.10:
0.10x + 0.10y = $13,970
Subtract this from the second equation:
0.18y - 0.10y = $18,930 - $13,970
0.08y = $4,960
Divide by 0.08 to find y:
y = $62,000
Substitute y back into the first equation to find x:
x + $62,000 = $139,700
x = $77,700
Therefore, the woman should invest $77,700 at the 10% rate and $62,000 at the 18% rate to achieve her desired income.
What is the solution to the following system of equations? 3x-2y=12 and 6x-4y=24
Answer:
A. It has infinitely many solutions
Step-by-step explanation:
I took the Solving Linear Systems By Substitution Quiz on Edge
The given system of equations 3x-2y=12 and 6x-4y=24 has no solution.
As per the question, we have to determine the solution to the following system of equations, 3x-2y=12 and 6x-4y=24
What is the equation?The equation is the relationship between variables and is represented as y =ax +b is an example of a polynomial equation.
Here,
Given a system of the equation,
3x-2y = 12
x = 12 + 2y / 3 - - - - -(1)
6x - 4y =24 - - - - -(2)
Put the value of equation 1 in the equation
6 (12 + 2y / 3) - 4y = 24
2 (12 + 2y) - 4y = 24
24 +4y - 4y = 24
24 = 24
Thus, the given system of equations 3x-2y=12 and 6x-4y=24 has no solution.
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This graph shows the costs of purchasing two types of flowers. Which statement is true?
Flower A is less expensive than Flower B.
Flower B is less expensive than Flower A.
Flower A and Flower B cost about the same.
The graph shows the costs of purchasing two types of flowers.
Select some value [tex]x_0[/tex] for x and draw vertical line
[tex]x=x_0.[/tex]
This line intersects the graphs of Flower A and the graph of Flower B in points A and B, respectively. The point A lies on this vertical line higher than the point B. This means that y-coordinate of point A is greater than y-coordinate of point B.
If y-coordinate of point A is greater than y-coordinate of point B, then Flower A is more expensive than Flower B (or Flower B is less expensive than Flower A).
Answer: correct choice is B
The product of 2, and a number increased by 6, is -24
The mathematical expression is,
⇒ 2x + 6 = - 24
And, The value of number = - 15
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
''The product of 2, and a number increased by 6, is -24''
Now,
Since, The algebraic expression is,
''The product of 2, and a number increased by 6, is -24''
Let a number = x
Hence, We can formulate;
⇒ 2x + 6 = - 24
Solve for x as;
⇒ 2x = - 24 - 6
⇒ 2x = - 30
⇒ x = - 15
Thus, The value of number = - 15
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Planes flies 2951 miles in 6.5 hours what is the speed of the airplane miles per hour
5.5-x=-4.5-x. how do you solve this?
The equation 5.5 - x = -4.5 - x has no solution. After cancelling out the variable x, we are left with 5.5 = -4.5, which is a contradiction.
Explanation:To solve the equation 5.5 - x = -4.5 - x, we first notice that the variable x is present on both sides of the equation. We can simply subtract or add x to both sides to cancel it out. This will give us an equation without variables:
5.5 - x + x = -4.5 - x + x
5.5 = -4.5
This equation suggests that 5.5 is equal to -4.5, which is not true. Therefore, we can conclude that there is no solution to the equation since the two sides of the equation do not balance.
Moreover, this type of equation is an example of a contradiction, meaning that it presents a statement that is inherently false regardless of the value of x. As there is no value of x that can make the equation true, we say that the equation has no solution.
Final answer:
The equation 5.5 - x = -4.5 - x simplifies to 5.5 = -4.5 when the x terms are cancelled out. Since 5.5 does not equal -4.5, the equation has no solutions.
Explanation:
To solve the equation 5.5 - x = -4.5 - x, we can first try to simplify it by adding or subtracting the same value from both sides. This method is based on the principle that whatever you do to one side of the equation, you must do to the other to maintain balance.
In this case, if we add x to both sides of the equation, the x terms will cancel out on both sides, which leaves us with 5.5 = -4.5. Here, we notice that both sides of the equation represent constant values and no longer contain the variable x.
Therefore, since 5.5 and -4.5 are not equal, we can conclude that there is no value of x that can satisfy this equation. This equation is a contradiction, which means there are no solutions.
I really need help on this question
Ryan uses 3 bars of clay for a sculpture. The first bar is 1.15 centimeters long. The second bar is 3.92 centimeters long. What is the total length of 2 bars?
Enter your answer in the box.
Nick is driving to a town 30 miles away. He is averaging about 45 miles per hour. If he makes no stops, how long will the trip take (in minutes)?
Write an expression from the description. Then evaluate the expression. 8 less than the product of 5 and -4.
Answer:
5(-4) - 8 is the expression.
Evaluate: -20 - 8 -28 is your answer
Inez has 2 1/4 pounds of potatoes for the picnic, she needs 8 1/2 pounds of potatoe. How many more pounds of potatoes does Inez need to buy?
subtract 2 1/4 from 8 1/2
make fractions have same denominator
8 1/2 = 8 2/4
8 2/4 - 2 1/4 = 6 1/4 more pounds
write a trinomial expression equivalent to (2x+5)(3x-2)
The required trinomial expression that is equivalent to (2x+5)(3x-2) is 6x² + 11x - 10.
According to the question, we have to determine the trinomial expression that is equivalent to the (2x+5)(3x-2).
A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the quadratic equation, cubic equation, etc. ax+b is a polynomial.
Here,
Given expression in the question,
= (2x+5)(3x-2)
Following the distributive property
= 2x (3x - 2) + 5 (3x - 2)
= 6x² - 4x + 15x - 10
= 6x² - 11x - 10
Thus, the required trinomial expression that is equivalent to (2x+5)(3x-2) is 6x² + 11x - 10.
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Final answer:
The trinomial expression equivalent to (2x+5)(3x-2) is calculated using the FOIL method, resulting in 6x² + 11x - 10.
Explanation:
To write a trinomial expression equivalent to the product of two binomials, (2x+5)(3x-2), we perform the multiplication by using the distributive property (also known as the FOIL method).
Multiply the first terms: 2x × 3x = 6x²
Multiply the outside terms: 2x × (-2) = -4x
Multiply the inside terms: 5 × 3x = 15x
Multiply the last terms: 5 × (-2) = -10
Combine like terms:
6x² + (15x - 4x) - 10 = 6x² + 11x - 10
The trinomial expression equivalent to (2x+5)(3x-2) is 6x² + 11x - 10.
Rachel earned 34$, 34 in 4 hours at her job today
Mrs.Cranston bought five bottles of water for $0.90 each and 8 pounds of meat. She paid a total of $26.90 for these items, not including tax. What was the price per pound of the meat?
Jodie uses her college printer to print pages at the rate of $0.06 per page. She decides to rent a printer for $80 a year. The cost of printing using the rented printer is $0.02 per page.
Part A: Write an inequality that can be used to calculate the number of pages that Jodie should print in a year so that the amount she pays for the rented printer is less than the college printer. Define the variable used. (5 points)
Part B: How many pages should Jodie print in a year to justify renting the printer? Show your work.
the calendar shows the number of days carlota rides her bike each month. each time ahe rides her bike, she travels 10 miles.is it rwasonable to say that carlota will bike more than 500 miles in 6 months?
Find the volume of this cuboid? 1.7m 2.3m and 0.8m
Please someone help me this is the second time I posted this question....
What is the equation, in point-slope form, for a line that goes through (8, −4) and has a slope of −5/6 ?
A. y−4=−5/6(x−8)
B. y+4=−5/6(x−8)
C. y−4=−5/6(x+8)
D. y+4=−5/6(x+8)
Please provide an explanation on how to do this.
The ph of water samples from a specific lake is a random variable y with probability density function given by f (y) = $ (3/8)(7 − y) 2 , 5 ≤ y ≤ 7, 0, elsewhere. a find e(y ) and v(y ). b find an interval shorter than (5, 7) in which at least three-fourths of the ph measurements must lie. c would you expect to see a ph measurement below 5.5 very often? why?
Jordan is playing a video game. For every 35 stars she collects, she gets 4,000 points. Her record is 86,000 points. Which of the following proportions could she use to determine x, the number of stars she needs to tie her record?
During a certain period of time, a car can cover the distance of 120 miles, going at an average speed of 55 mph. What distance over the same period of time would cover a truck, going at an average speed of 44 mph
In a number of identical boxes of chocolates there are 90 dark ginger, 198 white and 126 hazelnut. What is the largest possible number of boxes of chocolates?
The problem involves finding the Greatest Common Divisor (GCD) of the three numbers. The GCD of 90, 198, and 126 is 18. Hence, the largest possible number of identical boxes of chocolates is 18.
Explanation:The problem involves finding the Greatest Common Divisor (GCD) of the three quantities to find the largest possible number of identical boxes of chocolates. The GCD is the largest number that divides all three quantities evenly. So, let's first calculate the GCD of the given quantities: 90 dark ginger, 198 white, and 126 hazelnut chocolates.
We use the Euclidean Algorithm to find the GCD. Start with the two largest numbers, 198 and 126. The remainder of 198 divided by 126 is 72. Then, divide the initial divisor 126 by this remainder 72 to get another remainder 54. Continue this process with 72 and 54 to get a remainder 18. Now, the number 18 divides 54 exactly with 0 remainder, so 18 is the GCD of 198 and 126. When we test 18 with the third number, 90, it also divides evenly, hence the GCD of all three numbers is 18.
This means that the largest possible number of identical boxes of chocolates is 18.
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What are the values of the function y = –2x – 4 for x = 0, 1, 2, and 3?
A.0, –6, –8, –10
B.–4, –6, –8, –10
C.-4, –2, 0, 2
D.0, 6, 8, 10
y =-2x-4
x = 0, y = -2(0)-4 = -4
x=1, y = -2(1) -4 =-2-4 = -6
x=2, y = -2(2)-4 = -4-4 =-8
x=3, y = -2(3) - 4 = -6-4 =-10
Answer is B
Answer:
B
Step-by-step explanation:
Find dy/dx by implicit differentiation 4x^3 + x^2y − xy^3 = 6
Answer: dy/dx = y^3 - 12x^2 - 2yx / x(x-3y^2)
Step-by-step explanation: Differentiate each term with respect to x, then solve for y.
I hope this helps you out!
If point a is located at coordinates (5, 3) and point b is located at coordinates (-3, 9), what is the distance from a to b if the units of the coordinated system are meters?
The distance from a to b if the units of the coordinated system are meters is 10m.
What is a line segment?A line that has two endpoints and a fixed measurement is called a line segment.
It is given that point a is located at coordinates (5, 3) and point b is located at coordinates (-3, 9)
D = √[(x-p)² + (y-q)²]
Substituting the points we get;
D = √[(-3 - 5)² + (9 - 3)²]
D = √[(-8)² + (6)²]
D = √[(64) + (36)]
D = √100
D = 10
Hence, the distance from a to b if the units of the coordinated system are meters is 10 m.
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Final answer:
The distance between point A (5, 3) and point B (-3, 9) is calculated using the distance formula, resulting in a distance of 10 meters.
Explanation:
The question is asking for the distance between two points in a coordinate system. To find the distance between point A (5, 3) and point B (-3, 9), we can use the distance formula which is derived from Pythagorean theorem. The distance d between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)² + (y2 - y1)²)
For point A and point B, we substitute the coordinates into the formula:
d = √((-3 - 5)² + (9 - 3)²)
= √(64 + 36)
= √100
= 10 meters
Therefore, the distance from A to B is 10 meters.
How do you simplify sqrt of x^20?
Maria wants to find the product of 5 3/20 multiplied by 3 4/25 using decimals instead of fractions how can she rewrite the problem using decimals
Answer:
[tex] 5.15\times 3.16=16.2740[/tex]
Step-by-step explanation:
Maria wants to find the product of [tex]5\frac{3}{20}[/tex] multiplied by[tex]3\frac{4}{25}[/tex]
First we change mixed fraction to fraction and then change into decimal.
#First fraction:
Change mixed to fraction[tex]5\frac{3}{20}\Rightarrow \dfrac{103}{20}[/tex]
Change fraction to decimal[tex]\dfrac{103}{20}\Rightarrow \dfrac{103\times 5}{20\times 5}=5.15[/tex]
#Secondfraction:
Change mixed to fraction[tex]3\frac{4}{25}\Rightarrow \dfrac{79}{25}[/tex]
Change fraction to decimal[tex]\dfrac{79}{25}\Rightarrow \dfrac{79\times 4}{25\times 4}=3.16[/tex]
Now we find the product of both decimal
[tex]\Rightarrow 5.15\times 3.16[/tex]
Using calculator product of 515 and 316 = 162740
Both number has decimal digits two
So, total number of decimal digits is 4
In multiply result write decimal before 4 digits from right.
Therefore,
[tex] 5.15\times 3.16=16.2740[/tex]
23,769 rounded to the nearest thousand
—
Is 1.0227 a rational number?
The beads in 7 bracelets if 4 bracelets have 96 bead
The farmer market sells apples by the bushel ,each bushel of apples weights 42 pounds.a bushel of large apples contains 84 apples. If a bushel of sa all apples contains twice as many apples as a bushel of large apples, how many small apples are in 1pound of apple
Answer:
2 apples
Step-by-step explanation:
84/42 = 2
each pound has 2 apples