[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{7(g - 10h + 4)}[/tex]
[tex]\large\text{\underline{Distribute} \boxed{\text{7}} \underline{within the parentheses}:}[/tex]
[tex]\mathsf{= 7(g - 10h + 4)}[/tex]
[tex]\mathsf{= 7(g) + 7(-10h) + 7(4)}[/tex]
[tex]\mathsf{= 7g - 70h + 28}[/tex]
[tex]\large\text{We \boxed{\text{cannot}} do anything further because we do NOT have any \underline{like}}\\\large\text{\underline{terms}}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{\mathsf{7g - 70h + 28}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
why does the gcf of the variables of a polynomial have the least exponent of any variable term in the polynomial brainly
The GCF (Greatest Common Factor) of the variables of a polynomial has the least exponent of any variable term in the polynomial because it represents the largest factor that is common to all the terms in the polynomial.
To understand this better, consider a polynomial like 6x²y³ + 9x³y². The GCF of this polynomial would be 3x²y², which is the largest factor that can divide both terms evenly.
Notice that the exponent of each variable in the GCF is the smallest exponent among the corresponding variable terms in the polynomial.
This is because any factor that is common to all terms in the polynomial must be able to divide each term without leaving a remainder. Therefore, the exponent of each variable in the GCF must be less than or equal to the exponent of that variable in every term of the polynomial.
In summary, the GCF of the variables of a polynomial has the least exponent of any variable term in the polynomial because it represents the largest factor that can divide all terms in the polynomial evenly, and therefore, it must have the smallest exponent of each variable among all terms in the polynomial.
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in square units, what is the largest possible area a rectangle inscribed in the triangle shown here can have?
For the triangle shown, the area is (1/2) * 5 * 4 = 10 square units. The largest possible area of a rectangle inscribed in a triangle is equal to the area of the triangle.
The area of the triangle can be calculated using the formula: Area = (1/2) * Base * Height.
Note that the rectangle must be completely within the triangle and all of its sides must be parallel to the sides of the triangle. To calculate the area, the base and height of the triangle must be known. The base is the length of any one side, while the height is the perpendicular distance from the base to the opposite vertex.
In this case, the triangle is 5 units along the base and 4 units in height. The area can then be calculated as (1/2) * 5 * 4 = 10 square units.
It is also important to note that the rectangle can have sides of different lengths and will still have an area of 10 square units.
To summarize, the largest possible area a rectangle inscribed in the triangle shown can have is 10 square units. This can be calculated using the formula (1/2) * Base * Height. The rectangle can have sides of different lengths, but the area will remain the same.
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A certain amount of money is shared between rui feng and vishalin the ratio of 5:9 if rui feng gets 44 dollar less than vishal find total amount of money shared between the two boys
The total amount of money shared between Rui Feng and Vishal is 154 dollars.
Let's assume that the amount of money shared between Rui Feng and Vishal is x dollars.
According to the given ratio, the amount of money received by Rui Feng is 5/14 of the total amount, and the amount received by Vishal is 9/14 of the total amount.
We are also given that Rui Feng receives 44 dollars less than Vishal. We can express this as:
9/14 x - 5/14 x = 44
Simplifying the equation, we get:
4/14 x = 44
Multiplying both sides by 14/4, we get:
x = 154
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This is due tomorrow so please help me ASAP! Thanks!
The value of the given lengths are as follows:
a.) KL = 11.1ft
LO = 5.7ft
b.) m<OMN = 45°
How to calculate the missing length of the given triangles?For Side LO ;
7/11 = 7√2/7√2+LO
7(7√2+LO) = 11×7√3
69.3+7LO = 108.9
7LO = 108.9-69.3
LO = 39.6/7
LO = 5.7 ft
For KL ;
This can be solved using the Pythagorean theorem;
c²= b²+a²
C = 5.7+7√2 = 15.6
b = 11
a²= 15.6²-11²
= 243.36 - 121
= 122.36
a= √122.36
a= 11.1ft
For angle OMN;
This can be solved using SOHCAHTOA.
Sin∅ = opposite/hypotenuse
opposite = 7
hypotenuse = 7√2
sin∅ = 7/7√2
sin∅ = 0.707106781
∅= sin-1 0.707106781
∅ = 45°
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9. a soccer field is a rectangle 90 meters wide and 120 meters long. the coach asks players to run from one corner to the other corner diagonally across. what is this distance? round your answer to the nearest tenth. (4 points)
The distance from one corner to the other corner diagonally across the soccer field is 169.7 meters.
To calculate this, use the Pythagorean theorem, which states that [tex]a^2 + b^2 = c^2[/tex], where a and b are the two sides of a right triangle, and c is the hypotenuse, or the longest side.
In this problem, a is 90 meters, b is 120 meters, and c is the distance from one corner to the other diagonally across the field.
So, [tex]90^2 + 120^2 = c^2[/tex]. To solve this, take the square root of both sides, and c = 169.7 meters.
To round this answer to the nearest tenth, we need to round it to 169.7 meters.
This question can be used to demonstrate the importance of knowing the Pythagorean theorem, which can be used to calculate the distance of a right triangle when the lengths of two sides are known. It is a useful tool to solve a variety of geometry problems.
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for an astm grain size of 8, approximately how many grains would there be per square inch at a magnification of 100? without any magnification?
An ASTM grain size of 8 means that there are 8 grains per square inch at a magnification of 100. Without any magnification, it is not possible to determine the number of grains per square inch.
ASTM grain size is a measure of the size of the grains in a metal sample. The ASTM E112 defines the grain size number as the number of grains per square inch of metal surface area at a magnification of 100 times. So, an ASTM grain size of 8 means that there are 8 grains per square inch at a magnification of 100.
Without any magnification, it is not possible to determine the number of grains per square inch as the grains are too small to be visible to the eye. However, the ASTM grain size number can still provide information about the grain size distribution in the metal sample.
A metal sample with a smaller grain size number (i.e., larger grain size) will have fewer grains per square inch at a magnification of 100 than a metal sample with a larger grain size number (i.e., smaller grain size). This is because larger grains take up more surface area than smaller grains, resulting in fewer grains per unit area.
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how would you interpret the findings of a correlation study that reported a linear correlation coefficient of 0.3?
The linear correlation coefficient of 0.3 indicates a moderate positive correlation between the two variables.
This suggests that when one variable increases, the other variable tends to increase too. However, there is not a strong linear relationship between the two variables, meaning that the increase in one variable does not guarantee a predictable change in the other variable.
When interpreting the findings of a correlation study, it is important to note the strength of the relationship between the two variables. A linear correlation coefficient of 0.3 indicates a moderate positive correlation, meaning that the two variables increase together but there is not a strong linear relationship between the two variables.
This means that the increase in one variable does not guarantee a predictable change in the other variable. To put it another way, the strength of the correlation means that when one variable increases, it is likely that the other will increase as well, but it is not guaranteed.
Therefore, caution should be used when making predictions based on the results of a correlation study.
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What is the area of this figure?
Answer: 75 [tex]m^{2}[/tex]
Step-by-step explanation:
5*5 + 5*10 = 25 + 50 = 75
please mark brainliest
what topics will be covered in this unit? logarithmic functions quadratic functions linear functions matrices exponential functions
The unit will cover linear functions, quadratic functions, exponential functions, logarithmic functions, and matrices.
We have,
Based on the topics, the unit will cover the following topics:
Linear functions: This topic typically includes concepts such as slope, intercepts, equations of lines, and graphing linear functions.
Quadratic functions: This topic covers quadratic equations, factoring, completing the square, quadratic formula, vertex form, and graphing parabolas.
Exponential functions: This topic involves exponential equations, growth and decay, properties of exponential functions, and their graphs.
Logarithmic functions: This topic focuses on logarithmic equations, properties of logarithms, solving logarithmic equations, and the relationship between exponential and logarithmic functions.
Matrices: Matrices are a topic in linear algebra and involve operations on matrices, matrix multiplication, determinants, inverse matrices, and solving systems of linear equations using matrices.
It's important to note that the exact content and depth of each topic may vary depending on the specific curriculum or course.
However, the mentioned topics generally form the core concepts of a unit covering functions, algebra, and matrices.
Thus,
The unit will cover linear functions, quadratic functions, exponential functions, logarithmic functions, and matrices.
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Lin's job pays $12.50 an hour. She also gets paid $25 per week to cover uniform cleaning and
other expenses. To meet her budget, Lin needs to be paid at least $300 per week.
Answer:
I think it is because 3,500
what is 7x=14 show your work
Answer:
x=2
Step-by-step explanation:
7x=14
divide by 7 on each side to get x by itself
x=14/7
x=2
Simplify 4 x + 3 y 2 − 7 z 4 + 5 z 4 + 11 − 4 x + y 2
Answer:
[tex]4y {}^{2} - 2z {}^{4} + 11[/tex]
Step-by-step explanation:
[tex]1. \: (4x - 4x) + (3y {}^{2} + y {}^{2} ) + ( - 7z {}^{4} + 5z {}^{4} ) + 11 \\ 2. \: 4y {}^{2} - 2z {}^{4} + 11[/tex]
What is the area of a circle with the radius of 11.5 meters? Use 3.14 for pi or put pi in your answer for an exact answer.
Answer:
Area = [tex]415.265 m^2[/tex]
Step-by-step explanation:
Area of a circle = [tex]\pi r^2[/tex]
[tex]A = (3.14)(11.5^2)=(3.14)(132.25)=415.265[/tex]
Matt wants to buy a tie. The prices of similar ties offered by four different online retailers are listed. $15.50, $17.50, $16.00, $18.00 What is the mean absolute deviation of the prices of the ties?
Answer: mean-16.75
population size- 4
Step-by-step explanation:
A math teacher gives her class the following problem.
Barry is selling magazine subscriptions for a school fundraiser. He has already sold 15 subscriptions. He plans to sell 3 subscriptions per week until he reaches a total of 30 subscriptions sold. How many weeks will it take Barry to achieve his goal.
One student in the class solves the problem arithmetically as shown below.
The linear expression that could be used to find the number of weeks until he reaches 30 subscriptions is given as follows:
A. 15 + 3x = 30.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the rate of change.b is the y-intercept of the function, which is the initial value.The parameters for this problem are given as follows:
m = 3, as each week, 3 subscriptions are sold.b = 15, which is the initial number of subscriptions.Hence the number of subscriptions after x weeks is given as follows:
y = 3x + 15.
The number of weeks to reach 30 subscriptions (y = 30) is given as follows:
3x + 15 = 30.
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let x be the charge for an oil change, and let the tax on x be 7% so that the actual charge is 1.07x. let y be the number of containers of oil that are needed, and $2 the price per container. then 2y is the price of the oil itself. the cov(x,y) is 5.6. what is the the cov(1.07x, 2y)? select one:a. 11. 984b. 0.3821c. 2.616d. 7.982
let x be the charge for an oil change, and let the tax on x be 7% so that the actual charge is 1.07x. let y be the number of containers of oil that are needed, and $2 the price per container. then 2y is the price of the oil itself. the cov(x,y) is 5.6.
The covariance of 1.07x and 2y is 11.984
What is covariance?
Covariance refers to the way two variables shift together. It is a measurement that evaluates how close two variables are to one another. It examines whether they change in the same direction (positive covariance) or in the opposite direction (negative covariance)
.Calculating Covariance:
Given that Cov(X,Y) = 5.6
we need to find Cov(1.07X,2Y)Hence,
Cov(1.07X,2Y) = 2 * 1.07 * Cov(X,Y) = 2.2996 * 5.6 = 11.984
Therefore, the covariance of 1.07x and 2y is 11.984.
Hence option (a) is the correct answer.
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please help mee I need it
7 is the value of mixed fraction.
What exactly is a mixed fraction?
A mixed fraction is one that is represented by both its remainder and quotient. Two is the quotient and one is the remainder in the mixed fraction 2/3, for instance. Hence, a mixed fraction is created by combining a whole number and a proper fraction. A mixed number is one that includes both a whole number and a legal fraction.
= 6 30/44
= 294/44
= 6.6818
= 7 ( round off )
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DUE FRIDAY WELL WRITTEN ANSWERS ONLY!!!!!!!!!!!
Complete the table
All the trigonometric values for sin θ, cos θ and tan θ are valued below. Each trigonometric value is mentioned.
sin θ has boundaries from 0 to 1.
sin [tex]-\pi /2[/tex] = -1
sin [tex]-\pi /3[/tex] = -0.87
sin [tex]-\pi /6[/tex] = -0.5
sin 0 = 0
sin [tex]\pi /6 \\[/tex] = 0.5
sin [tex]\pi /3[/tex] = 0.87
sin [tex]\pi /2[/tex] = 1
sin [tex]2\pi /3[/tex] = [tex]\sqrt{3}/2[/tex]
sin [tex]5\pi /6[/tex] = 1/2
sin [tex]\pi[/tex] = 1
sin [tex]7\pi /6[/tex] = -0.5
sin [tex]4\pi /3[/tex] = -0.87
sin [tex]3\pi /2[/tex] = -1
sin [tex]5\pi /3[/tex] = -0.87
sin [tex]11\pi /6[/tex] = -0.5
sin [tex]2\pi[/tex] = 0
Similarly cos θ has boundaries.
cos [tex]-\pi /2[/tex] = 0
cos [tex]-\pi /3[/tex] = 0.5
cos [tex]-\pi /6[/tex] = 0.87
cos 0 = 1
cos [tex]\pi /6 \\[/tex] = 0.87
cos [tex]\pi /3[/tex] = 0.5
cos [tex]\pi /2[/tex] = 0
cos [tex]2\pi /3[/tex] = -0.5
cos [tex]5\pi /6[/tex] = -0.87
cos [tex]\pi[/tex] = -1
cos [tex]7\pi /6[/tex] = -0.87
cos [tex]4\pi /3[/tex] = -0.5
cos [tex]3\pi /2[/tex] = 0
cos [tex]5\pi /3[/tex] = 0.5
cos [tex]11\pi /6[/tex] = 0.87
cos [tex]2\pi[/tex] = 1
But tan θ has no boundaries.
tan [tex]-\pi /2[/tex] = undefined
tan[tex]-\pi /3[/tex] = -0.8
tan [tex]-\pi /6[/tex] = -1.73
tan 0 = 0
tan[tex]\pi /6 \\[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex]
tan [tex]\pi /3[/tex] = [tex]\sqrt{3}[/tex]
tan [tex]\pi /2[/tex] = undefined
tan [tex]2\pi /3[/tex] = -3
tan [tex]5\pi /6[/tex] = -0.5774
tan [tex]\pi[/tex] = undefined
tan [tex]7\pi /6[/tex] = -1.73
tan[tex]4\pi /3[/tex] = 1.73
tan [tex]3\pi /2[/tex] = undefined
tan [tex]5\pi /3[/tex] = -1.73
tan [tex]11\pi /6[/tex] = -0.58
tan [tex]2\pi[/tex] = 0
Hence, all the values mentioned in the table, were written above.
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which is bigger 4.03 or 4.01
Answer:
4.03
Step-by-step explanation:
if the cost for your car repair is in the lower of automobile repair charges, what is your cost (to two decimals)?
The cost of your car repair will depend on the type of repair being performed, as well as the cost of the necessary parts and labour. To find out the exact cost, you will need to consult a qualified mechanic.
Assuming that the cost of your repair is in the lower range of automobile repair charges, you can calculate the cost by multiplying the cost of the parts and the cost of the labour together. You can then round the result to two decimal places. For example, if the cost of the parts is $100 and the cost of the labour is $200, the total cost of the repair will be $300. This can be rounded to two decimal places, giving you a cost of $300.00.\
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Really appreciated :) 25 points
Answer:
a. 9
b. 4
c. 4/9
Step-by-step explanation:
a. If we are picking 1 card out of 9, then there are 9 possible outcomes:
1, 2, 3, 4, 5, 6, 7, 8, or 9
This can also be represented as 9 choose 1 ([tex]_9C_1[/tex]).
b. We have to identify the number of prime numbers in the set:
2, 3, 5, 7
↑ 4 numbers
Note: Prime numbers can only be divided by themselves and 1 to result in a whole number.
c. We can represent the probability of selecting a prime number by dividing the number of prime numbers by the total number of numbers.
# of primes / # of numbers = 4 / 9
Penny Banks purchased a new washer and dryer for $1,526.39. She used the store's credit plan and made a 25% down payment. How much did she finance?
Penny Banks made a 25% down payment, which means she paid 75% of the total cost through financing.
The amount she paid as a down payment is:
25% of $1,526.39 = 0.25 x $1,526.39 = $381.60
So the amount she financed is:
$1,526.39 - $381.60 = $1,144.79
Therefore, Penny Banks financed $1,144.79.
how many ways can patricia choose 4 pizza toppings from a menu of 19 toppings if each topping can only be chosen once?
There are 3876 ways in which Patricia can choose 4 pizza toppings from a menu of 19 toppings if each topping can only be chosen once. In permutation, the order is very important, and it is denoted by "P." which means that each item can only appear once in the lineup, and there are no duplicates. The formula for permutation is given as: P(n, r) = n!/(n-r)!
What is combination?In a combination, the order is not essential, and it is denoted by "C." It means that things can be jumbled up, and there are no duplicates. The formula for a combination is given as: C(n, r) = n! / (r! * (n-r)!)How to calculate the number of ways to choose 4 pizza toppings from a menu of 19 toppings?
To calculate the number of ways to choose 4 pizza toppings from a menu of 19 toppings, we need to use the combination formula, which is: C(n, r) = n! / (r! * (n-r)!)Here, n = 19 and r = 4, so the formula becomes: C(19,4) = 19!/(4!(19-4)!) = 19!/(4!15!) = (19*18*17*16)/(4*3*2*1) = 38,76. Therefore, there are 3876 ways in which Patricia can choose 4 pizza toppings from a menu of 19 toppings if each topping can only be chosen once.
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an ai that plays the game of go has a 90\% chance of winning each game it plays against a human grandmaster. what is the binomial probability of the human beating the ai 1 out of 3 games?
The probability of the human Grandmaster winning one out of three games against the AI is approximately 0.243 or 24.3%.
Let's denote the probability of the human Grandmaster winning one game as p. Then the probability of the AI winning one game is 0.9, which means the probability of the human winning one game is 0.1. Since we want to calculate the probability of the human winning one game out of three, we can use the binomial distribution formula:
[tex]P(X=k) = (^n _k) \times p^k \times (1-p)^{(n-k)}[/tex]
Where:
P(X=k) is the probability of getting k successes in n trials
(n choose k) is the binomial coefficient, which is the number of ways to choose k successes from n trials
p is the probability of success in one trial
(1-p) is the probability of failure in one trial
k is the number of successes we are interested in (in this case, k=1)
n is the total number of trials (in this case, n=3)
Plugging in the values, we get:
P(X=1) = (3 choose 1) * 0.1^1 * 0.9^(3-1) = 3 * 0.1 * 0.81 = 0.243 or 24.3%
This means that there is a decent chance for the human to win at least one game, but it is still more likely for the AI to win all three games.
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Can someone help me?!??
Answer:
4,320
Step-by-step explanation:
answer is 4,320
9x2x3x8x2x5
Answer:
66 km²
Step-by-step explanation:
To solve this, you should find the area of the rectangle as if it were complete and then subtract the area of the missing section.
Step one: Finding the area of the big rectangle
A = length x width
A = 9 x 8
A = 72 km²
Step two: Find the area of the smaller rectangle
A = 2 x 3 = 6 km²
Step three: Subtract the area of the small rectangle from the area of the big rectangle
72 - 6 = 66
I just need help with this, please! 10 points!
The given data comprises of a right triangle in which the base is denoted by x whose value is found to be 10.01.
Define trigonometric identity of sine?It states that the ratio of the length of the side opposite to the angle to the length of the hypotenuse is equal to the sine of the angle.
The given data comprises of a right triangle in which the base is denoted by x and the perpendicular is 8. The angle formed between the base and hypotenuse is 53 degree.
To solve this problem, we can use the trigonometric identity of sine.
Mathematically, it can be expressed as:
sin 53° = Perpendicular/Hypotenuse
8/x = sin 53°
x = 8/sin 53°
x = 8/ 0.7986
x ≈ 10.01
Hence, the value of x is 10.01.
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a farmer wants to build a rectangular enclosure, using the side wall of his barn and the other 3 sides created by fencing. he has 70 meters of fencing. what is the largest area he can fence in?
The largest area a farmer can fence in is 612.5 m².
The given question is based on finding the largest area a farmer can fence in for building a rectangular enclosure.
The farmer is given with 70 meters of fencing for fencing 3 sides of a rectangular enclosure.
The enclosure's fourth side is the wall of the farmer's barn.
To find the largest area fenced in, the farmer must try to use all 70 meters of fencing to enclose as large an area as possible.
First, let's assume that the rectangular enclosure's width is x.
So, we can find the length by dividing the remaining length of fencing after subtracting the width of the fence from the total length of fencing.
The remaining length of fencing is 70 - 2x.
After calculating the length, the area of the rectangular enclosure can be calculated by multiplying length and width.
The formula for calculating the area of the rectangle is A = l x w.
A = (70 - 2x)x
= 70x - 2x²
To find the maximum area fenced in, differentiate A with respect to x and equate it to zero.
dA/dx = 70 - 4x
=0x = 17.5 meters.
After finding x, the length of the enclosure can be calculated by subtracting the width from the total length of fencing.
l = 70 - 2x = 70 - 2(17.5) = 35 meters.
Therefore, the largest area fenced in will be A = l x
w = 35 x 17.5 = 612.5 m².
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solve these questions
Answer:
a) The perimeter of a rectangle is given by the formula:
P = 2L + 2W
where P is the perimeter, L is the length, and W is the width. We are given that the width of the rectangle is 2x and the length is three times the width. So we can set up an equation that represents the given information:
P = 2L + 2W
168 = 2(3W) + 2W
168 = 8W
b) To solve for W, we can divide both sides of the equation by 8:
168/8 = W
21 = W
Therefore, the width of the rectangle is 21cm.
c) To find the length of the rectangle, we can use the expression that represents the length in terms of the width:
L = 3W
L = 3(21)
L = 63
Therefore, the length of the rectangle is 63cm.
The width and length of the rectangle are 21cm and 63cm, respectively.
BRAINLIST! HELP ME PLS
SHOW HOW U GOT IT AND SHOW ALL STEPS! IF CORRECT WILL MAKE U BRAINLIST!
Answer: 948 [tex]ft^{2}[/tex]
Step-by-step explanation:
2(18*20) + 2(18*3) + 2(20*3) = 2(360) + 2(54) + 2(60) = 720 + 108 + 120 = 948
James invested 20,000 for one year and earned 1470 interest. If part of the money is invested at 10% and the remainder is invested at 6% how much is the invested at each rate
Linear equation.
Answer:
Let's represent the amount invested at 10% as x and the amount invested at 6% as y. Then we can set up a system of two equations to represent the given information:
x + y = 20,000 (since the total amount invested is 20,000)
0.10x + 0.06y = 1,470 (since the interest earned is 1,470 and the interest rate at which x is invested is 10% and the interest rate at which y is invested is 6%)
We can use the first equation to solve for one of the variables in terms of the other:
x = 20,000 - y
Now we can substitute this expression for x into the second equation and solve for y:
0.10(20,000 - y) + 0.06y = 1,470
2,000 - 0.10y + 0.06y = 1,470
-0.04y = -530
y = 13,250
So $13,250 was invested at 6%. We can find the amount invested at 10% by plugging in this value of y into the first equation:
x + 13,250 = 20,000
x = 6,750
So $6,750 was invested at 10%.