Answers
The logarithmic form of the equation (1/7)³ = 1/343 is given as follows:
[tex]\log_3{\left(\frac{1}{343}\right)} = \frac{1}{7}[/tex]
How to represent a logarithm?A logarithm is a mathematical function that represents the power to which a given base must be raised in order to obtain a given number. Logarithms are often used to simplify calculations involving very large or very small numbers.
In this problem, we raise 1/7 to the third power to obtain the number 1/343, hence the logarithm of base 3 of the number 1/343 is of 1/7, and then the expression is given as follows:
[tex]\log_3{\left(\frac{1}{343}\right)} = \frac{1}{7}[/tex]
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Related Questions
50 points! Multiple choice algebra question. Gilda used the formula f(x) = x/144 to convert square inches to square feet. Find the inverse of f(x). Photo attached. Thank you,
Answers
To find the inverse of f(x), we need to switch x and f(x) and solve for x:
x = f(f^(-1)(x))
In this case, f(x) = x/144, so we have:
x = f(f^(-1)(x))
x = (f^(-1)(x))/144
Simplifying for f^(-1)(x), we multiply each side by 144:
144x = f^(-1)(x)
Therefore, the inverse of f(x) is:
f^(-1)(x) = 144x
Describe what happens as the number of sides of the bases of a prism increases.
THIS IS NOT COLLEGE LEVEL IT IS MIDDLE SCHOOL
Answers
Answer:
As the number of sides of the bases of a prism increases, the shape of the prism becomes more complex and closer in form to a cylinder. For example, a prism with two identical polygonal bases, such as a rectangular prism or a triangular prism, will have a more blocky or pyramidal shape. However, as the number of sides of the base increases, the shape of the prism becomes more cylindrical and less pyramidal in appearance. This is because the more sides a polygon has, the more closely it approximates a circle, and the cross-section of the prism becomes more circular in shape.
When the number of sides of the base of a prism increases, the prism becomes more like a cylinder.
What is the opposite of 12 written in simplest terms?
Answers
Answer:
Step-by-step explanation:
It is -12.
The opposite of a positive number would be its negative.
what is the answer (x+80)(x-20)
Answers
Answer:
Using the FOIL method to multiply (x + 80)(x - 20), we get:
(x + 80)(x - 20) = x^2 - 20x + 80x - 1600
Simplifying the expression, we get:
(x + 80)(x - 20) = x^2 + 60x - 1600
Therefore, the answer is x^2 + 60x - 1600.
I need help solving this question
Answers
Answer:
C. y = 3/2x + 4
Step-by-step explanation:
C. y = 3/2x + 4
A car is purchased for $19,500. After each year, the resale value decreases by 20%. What will the resale value be after 3 years? Use the calculator provided and round your answer to the nearest dollar.
Answers
The resale value of the car after 3 years is $9,984.
How to find the resale value after 3 years?Since the resale value decreases by 20%. Thus, the resale value of the car will be 80% of its original value.
After the first year, the resale value of the car will be 80% of its original value:
Resale value after 1 year = 80/100 * $19,500 = $15,600
After the second year, the resale value of the car will be 80% of its value after the first year:
Resale value after 2 years = 80/100 * $15,600 = $12,480
After the third year, the resale value of the car will be 80% of its value after the second year:
Resale value after 3 years = 80/100 * $12,480 = $9,984
Therefore, the resale value of the car after 3 years will be $9,984.
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9. The Donut Shoppe sells "day old" donuts at 40% off original price. If a customer buys three "day old" donuts for $2.75, what is the cost after the discount?
Answers
the cost of day old donuts after the discount is $4.95.
what is discount?A discount is a decrease in the cost of a good or service. Discount is the reduction in the price of goods or services offered by shopkeepers at the marked price.
Discounts are offers or rebates made to customers on the marked-down prices of goods. We come across phrases like cost price, tagged price, discount, and selling price when making a purchase. Shop owners give discounts to customers to encourage product sales. Let's examine the connections between these concepts.
The formula to calculate the discount is:
Discount = List Price - Selling Price
Discount (%) = (Discount/List Price) × 100
the discount is 40% ⇒0.4
customer buys 3 donuts.
price of 1 donut = $2.75
total cost for 3 donuts= $2.75 x 3 = $8.25
discount for 1 donut= [tex]\frac{0.4}{100}* 2.75[/tex]=$1.1
so, for 3 donuts discount = $1.1 x 3 = $3.3
therefore the final price to be paid by customer is
=$8.25-$3.3
=$4.95
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Choose the scatterplot(s) that DO NOT suggest a linear relationship between x and y.
O a
Ob
Oc
Od
y
y
*
y
LOVE
y
X
Answers
The scatter plots that do not show a linear relationship are B and C
How can a scatter plot show a linear relationship?The distribution of points on a scatter plot's graph can show a linear relationship between two variables. A linear relationship exists between two variables when there is a consistent change in one variable for every change in the other.
The horizontal axis and the vertical axis of a scatter plot each indicate a separate variable. Each data point is plotted on the graph based on its values for the two variables. If the variables are related to one another linearly, the points will often fall in a straight line.
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HELLLLLLP!!! I WILL GIVE BRAINLIEST!!!
Answers
The expression that is equivalent to 6x2y + 2xy^5 include:
2(3x²y + xy^5).
2xy(3x + y⁴)
xy(6x + 2y⁴)
What is an expression?An expression can refer to a variety of things depending on the context in which it is used.
In mathematics and computer programming, an expression typically refers to a combination of numbers, variables, operators, and/or functions that are evaluated to produce a value. For example, "2 + 3" is an expression that evaluates to "5"
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The value of y is directly proportional to the value
of x. If x = 8, then y = 12. What is the value of x when y = 30?
Answers
Answer:
If the value of y is directly proportional to the value of x, we can use the formula for direct variation to find the value of x when y = 30. The formula for direct variation is:
y = kx
where k is the constant of proportionality.
To find the value of k, we can use the values given in the problem:
y = kx
12 = k(8)
Solving for k, we get:
k = 12/8 = 3/2
Now that we know k, we can use the formula for direct variation to find the value of x when y = 30:
y = kx
30 = (3/2)x
Solving for x, we get:
x = (30)/(3/2) = 20
Therefore, when y = 30, x = 20
The piecewise function g(x) is shown in the graph.
Graph with three pieces. The first piece is a horizontal line from the left with an open right endpoint at negative 2 comma negative 1. The second piece is curved with a solid point at negative 1 comma 0, which ends at 1 comma 1. The last piece starts with a solid circle at 0 comma 1 and increases to the right as it passes through 4 comma 5.
Which of the following represents g(x)?
g of x is a piecewise function, which equals negative 2, when x is less than negative 1, and it equals the quantity x plus 1 end quantity squared, when negative 1 is less than or equal to x is less than 0, and it equals x plus 1, when x is greater than or equal to 0.
g of x is a piecewise function, which equals negative 2, when x is less than or equal to negative 1, and it equals the quantity x minus 1 end quantity squared, when negative 1 is less than x is less than 0, and it equals negative x plus 1, when x is greater than 0.
g of x is a piecewise function, which equals negative 2, when x is less than negative 1, and it equals the quantity x minus 1 end quantity squared, when negative 1 is less than or equal to x is less than or equal to 0, and it equals negative x plus 1, when x is greater than 0.
g of x is a piecewise function, which equals negative 2, when x is less than or equal to negative 1, and it equals the quantity x plus 1 end quantity squared, when negative 1 is less than x is less than 0, and it equals x plus 1, when x is greater than or equal to 0.
Answers
The description that correctly represents g(x) is g of x is a piecewise function, which equals negative 2, when x is less than or equal to negative 1, and it equals the quantity x minus 1 end quantity squared, when negative 1 is less than x is less than or equal to 0, and it equals negative x plus 1, when x is greater than 0 (third option).
What represents g (x)?Looking at the graph, we can see that:
g(x) is equal to -2 for x ≤ -1.g(x) is a quadratic function that passes through the point (-1,0) and (1,1), with a vertex at (0,1), for -1 < x ≤ 0.g(x) is a linear function that passes through the point (0,1) and (4,5), for x > 0.Thus, the correct piecewise function that represents g(x) is:
g(x) = {-2 if x ≤ -1
{ (x-1)^2 if -1 < x ≤ 0
{ -x+1 if x > 0
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4/7 of the length of a car ride is 8 miles. How many miles is the whole car ride ?
Answers
hi
4/7 = 8
7/7 = ?
so ? = 7/7 * 8 /4/7 = 8/4/7 = 8 *7/4 = 4*2*7 /4 = 2*7 = 14
so whole thing is 14
let's check : 14 * 4/7 = 56/7 = 8
Match initial data. answer is correct.
I need help with this please
Answers
The line plot representing the values on the number line can be presented as follows;
[tex]{}[/tex] ×
[tex]{}[/tex] × ×
[tex]{}[/tex] × × × ×
<-|------|------|------|------|------|------|------|------|->
[tex]{}[/tex]0 1/8 1/4 1/2 5/8 3/4 1
What is line plot?A line plot is a graph displaying data as points above a number, which indicates the frequency of the data.
The values in the fraction can be expressed as follows;
5/8, 5/8, 1/4, 1/8, 1/8, 3/4, 1/8
The values that are repeated can be excluded to get;
Values to be represented are; 5/8, 1/4, 1/8, 3/4
The above fractions can be expressed as fractions with a denominator of 8 as follows;
5/8, 1/4, 1/8, 3/4 = 5/8, 2/8, 1/8, 6/8
The fractions can be arranged in increasing order as follows;
5/8, 2/8, 1/8, 6/8; 1/8, 2/8, 5/8, 6/8
The fractions 1/8, 2/8, 5/8, 6/8, can therefore, be entered into the number line as follows;
<-|------|------|------|------|------|------|------|------|->
0[tex]{}[/tex] 1/8 2/8 1/2 5/8 6/8 1
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The concentration C of a drug in a patient's bloodstream t hours after injection is given by C(t) = 100t/2 t^2 + 85.
Use a calculator to approximate the time when the concentration is highest. (Round your answer to two decimal places.)
Answers
Approximately 1.18 hours the concentration is highest.
The given function is c(t)=100t/t² +85.
When the concentration is highest, the function becomes
100t/t² +85 =0
100/t +85=0
100+85t=0
85t=100
t=100/85
t=1.18 hours
Therefore, approximately 1.18 hours the concentration is highest.
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What is 6 5/6-5 1/2
6 5
6
-
5 1
2
Answers
The difference between 6 5/6 and 5 1/2 is 4/3 .
How to subtract these mixed numbers?To subtract these mixed numbers, we need to first convert them into improper fractions:
6 5/6 = (6 x 6 + 5)/6 = 41/6
5 1/2 = (5 x 2 + 1)/2 = 11/2
Now we can subtract:
41/6 - 11/2
To deduct divisions with various denominators, we really want to track down a shared factor. 6 is the smallest common multiple of 6 and 2 in this instance. Therefore, we can use denominator 6 to convert 11/2 into an equivalent fraction:
11/2 = (11 x 3)/(2 x 3) = 33/6
Now we can subtract the fractions with the same denominator:
41/6 - 33/6 = 8/6
Working on the portion by partitioning both the numerator and denominator by their most prominent normal component, we get:
8/6 = 4/3
As a result, in mixed numbers, the difference between 6 5/6 and 5 1/2 is 4/3, or 1 1/3..
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The complete question is:
What is the rule for the sequence
5/6, 1 1/2, 2 1/6, 2 5/6.....
Lauren works at a reception hall and is setting tables for a retirement party. She takes a basket of 98 soup spoons, and she places 8 soup spoons on every table she sets.
Write an equation that shows how the number of soup spoons remaining, y, depends on the number of tables Lauren sets, x.
y=
Answers
The equation that shows how the number of soup spoons remaining, y, depends on the number of tables Lauren sets, x, is:
y = 98 - 8x
The initial number of soup spoons, 98, is reduced by 8 for each table Lauren sets. Therefore, the number of soup spoons remaining after x tables have been set is 98 - 8x.
What expression is equivalent to 4- 1/3-7/8+1/6?
A. 6/24-8/24-21/24+4/24?
Answer for brainliest. Don't care if its wrong.
Answers
The simplified form of the expression is 71/24.
What is the simplified form?
To simplify the expression 4 - 1/3 - 7/8 + 1/6, we can follow the order of operations, which dictates that we perform multiplication and division before addition and subtraction.
Here's the step-by-step solution:
Find a common denominator for the fractions involved. In this case, the least common denominator (LCD) is 24, which is the least common multiple of 3, 8, and 6.
Convert the fractions to have the same denominator, which is 24:
4 - 1/3 - 7/8 + 1/6
= 4 * 24/24 - 1/3 * 8/8 - 7/8 * 3/3 + 1/6 * 4/4 (Multiplying each fraction by the appropriate form of 1 to get the common denominator)
= 96/24 - 8/24 - 21/24 + 4/24 (Performing the multiplication)
Combine the numerators over the common denominator:
= (96 - 8 - 21 + 4)/24 (Combining numerators)
= 71/24 (Performing the subtraction)
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1 1 Jemima has three boxes with a total weight of 51 kg. Box B weighs 5 kg more than box A and box C weighs 3 kg more than box B. Ch the correct statement. Select one: a. Box C weighs 21 O b. O c. kg. 30 1 Box A weighs 42 kg. 1 Box B weighs 12 kg. O d. 5 Box A weighs 17 kg.
Answers
On solving the question, we can say that Therefore, none of the answers to the question's assertions are true.
What is equation?A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.
Let's use "x" to symbolise box A's weight. Then, we could type:
Given that box B weighs 5 kg more than box A, its weight is "x + 5".
Given that box C weighs 3 kg more than box B, its weight is calculated as "x + 5 + 3" = "x + 8".
We can write: Since we are aware that the combined weight of the three boxes is 51 kg:
[tex]x + (x + 5) + (x + 8) = 51\\3x + 13 = 51\\3x = 38\\x = 12.67\\[/tex]
Therefore, box A weights around 12.67 kg. The weights of boxes B and C may also be ascertained using the equations we discovered earlier:
17.67 kg (x + 5) is the estimated weight of Box B.
The approximate weight of Box C is 25.67 kg (x + 8).
Therefore, none of the answers to the question's assertions are true.
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What is the area of a rectangular picture frame with twenty inches in length, and a width of fifteen inches?
Answers
The area of the rectangular picture frame with twenty inches in length, and a width of fifteen inches is 180inches.
Given length of the rectangular picture frame = 20inches
Given width of the rectangular picture frame = 15inches
The formula for finding the area of a rectangular frame is the multiplication of both length and width = Length x Width
So, the area of the given rectangular picture frame = 20 x 15 = 180 inches
From the above explanation, we can conclude that the area of the given rectangular frame with length of 20 inches and the width of 15 inches is 180 inches.
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Valerie bought a clownfish for $47 at the pet store. She planned to spend her remaining money on smaller fish that cost $9 each. If Valerie began with $120, which inequality could be used to find f, the number of smaller fish she can buy?
A 9 +47f≤ 120
B 47 +9f≤ 120
C 56+9f≤ 120
D 38 + 47f≤ 120
Answers
Answer:
Step-by-step explanation:
b
Answer:
47 + 9f [tex]\leq[/tex] 120
Step-by-step explanation:
B is the correct answer.
Write an equation of the line below.
Answers
Select all the expressions that have the same value. a \large 3^3 b \large 3^4 c \large 6^2 d \large 6^3 e \large 9^2 f \large 9^3
Answers
The expressions that have the same value are: b) 3^4 = 81 and e) 9^2 = 81
Selecting all expressions that have the same value.To compare the expressions, we can simplify them using the rules of exponents:
a) 3^3 = 27
b) 3^4 = 81
c) 6^2 = 36
d) 6^3 = 216
e) 9^2 = 81
f) 9^3 = 729
Using the above as a guide, we have the following:
Therefore, the expressions that have the same value are: b) 3^4 = 81 and e) 9^2 = 81
So, options b and e have the same value.
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The segmented bar graph shows the relative frequencies regarding your arrival time to school using three different routes. How many times more likely are you to be on time than be late to school if you take Route C?
Answers
Therefore, you are three times more likely to be on time than be late if you take Route C to school.
What is relative frequency?Relative frequency is a statistical term that refers to the proportion or percentage of times an event or a particular value occurs within a larger set of data. It is calculated by dividing the number of times the event or value occurs by the total number of observations in the data set.
Here,
To determine how many times more likely you are to be on time than late if you take Route C, we need to compare the heights of the green and red bars for Route C. From the graph, we can see that the green bar (representing on-time arrivals) is approximately three times taller than the red bar (representing late arrivals) for Route C.
To calculate how many times more likely you are to be on time than late if you take Route C, we need to find the ratio of the heights of the green and red bars:
Ratio = height of green bar / height of red bar
Looking at the segmented bar graph, we can see that the height of the green bar for Route C is approximately 0.45, and the height of the red bar is approximately 0.15.
Ratio = 0.45 / 0.15
= 3
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if k(x) = 3x, then f'(x)=? A. x³Ln3 B. 3xLn3 C. 3x/Lnx D. 3/3xLn3
Answers
The correct answer is not listed among the options. The correct answer is E. 1/x.
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.
To find f'(x), we need to differentiate the function f(x) with respect to x. Since we are given k(x) = 3x, we can use the chain rule to differentiate f(x) = ln(k(x)) = ln(3x) as follows:
f'(x) = d/dx [ln(3x)]
= 1/(3x) * d/dx [3x] (applying the chain rule)
= 1/(3x) * 3
= 1/x
Therefore, the correct answer is not listed among the options. The correct answer is E. 1/x.
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Is the figure line symmetric?
If yes, how many lines of symmetry does the figure have?
a picture of a snow flake
Answers
Answer:
Yes, the figure is line symmetric.
A snowflake has six lines of symmetry. Therefore, the correct answer is: 6.
The distance of 15 miles on a map is represented by 2 inches.
If the distance between two cities on the map is 8 inches, what is the actual distance
between them?
A 60 miles
B 75 miles
C 90 miles
D 120 miles
awing of an airplane. The airplane has a 100-foot wings
Answers
Answer:
A. 60 miles
Step-by-step explanation:
2 in. = 15mi or like 2in+2in+2in+2in = 8in
15mi+15mi+15mi+15mi = 60mi
2×4 =8
/
/
v
4 × 15mi = 60mi
NO LINKS!! URGENT HELP PLEASE!!
For what value of c is the number "a" a solution of the equation? (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, enter INFINITELY MANY.)
4x + 1 + 7c = 8c - 3x + 6; a = -5
c = ________
Answers
Answer:
To find the value of "c" for which the number "a" (-5 in this case) is a solution of the equation, we can substitute "a" into the equation and solve for "c".
Given equation: 4x + 1 + 7c = 8c - 3x + 6
Substituting x with "a": 4(-5) + 1 + 7c = 8c - 3(-5) + 6
Simplifying the equation: -20 + 1 + 7c = 8c + 15 + 6
Combining like terms: -19 + 7c = 8c + 21
Moving all "c" terms to one side: 7c - 8c = 21 + 19
Simplifying: -c = 40
Dividing both sides by -1 to isolate "c": -c/-1 = 40/-1
Flipping the sign when dividing by a negative number: c = -40
So, the value of "c" for which the number "a" (-5) is a solution of the equation is c = -40.
Answer:
[tex]c=-40[/tex]
Step-by-step explanation:
Since a is a Solution to the Equation , then it satisfies the Equation
Substitute by [tex]x=a=-5[/tex] into the Equation [tex]4x+1+7c=8c-3x+6[/tex]
Then [tex]4(-5)+1+7c=8c-3(-5)+6[/tex]
Then [tex]-20+1+7c=8c+15+6[/tex]
By adding like-terms
Then [tex]-19+7c=8c+21[/tex]
Then [tex]8c-7c=-19-21[/tex]
Then [tex]c=-40[/tex]
If (x -1) is a factor of the polynomial f(x) = 4x²- 4x² - x - K, where K is a Constant.
1. What is the Value of K?
2. What are the roots of the equation
Answers
Answer:
If (x-1) is a factor of the polynomial f(x) = 4x² - 4x² - x - K, then we know that (x-1) divides evenly into the polynomial, which means that the polynomial can be written as:
f(x) = (x-1)(ax + b)
where a and b are constants that we need to determine. We can use the distributive property to expand this expression and equate it with the original polynomial:
f(x) = (x-1)(ax + b) = 4x² - 4x - K
Expanding the left side of the equation, we get:
ax² + bx - ax - b = ax² - (a-b)x - b = 4x² - 4x - K
Now we can equate the coefficients of the like terms on both sides of the equation.
The coefficient of x^2 on the left side is a, and on the right side it is 4. Therefore, we have:
a = 4
The coefficient of x on the left side is b - a, and on the right side it is -4. Therefore, we have:
b - a = -4
Substituting a=4, we get:
b - 4 = -4
Solving for b, we get:
b = 0
So the polynomial can be written as:
f(x) = (x-1)(4x + 0) = 4x² - 4x
Therefore, K = 0.
To find the roots of the equation, we need to set f(x) = 0 and solve for x:
4x² - 4x = 0
Factor out 4x:
4x(x - 1) = 0
So the roots of the equation are x = 0 and x = 1.
Which equation is correct for the circle shown on the graph?
(x+3)²+ (y-6)² = 4
(x-3)² + (y+6)² = 4
(x+3)² + (y-6)² = 2
(x-3)² + (y-6)² = 4
Answers
Option 2 is the correct answer, that is, the equation of the given circle is (x+3)² + (y - 6)² = 4 with center at (-3,6) and radius 2.
What is a distance formula?The distance formula is a mathematical formula used to determine the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem as:
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
where (x₁, y₁) and (x₂, y₂) are the x and y coordinates of the said two points. This formula works for any two points in a two-dimensional space with a Cartesian coordinate system.
To answer this we need to know the equation of a circle.
Let (a,b) be the center of a circle with radius r, then the equation of the circle can be written as:
(x - a)² + (y - b)² = r²
We see that from the given graph center of the circle is the point (-3,6) and radius will be 2.
We can now substitute these information in the circle equation,
(x - -3)² + (y - 6)² = 2²
(x+3)² + (y - 6)² = 4
That is the equation of the given circle is (x+3)² + (y - 6)² = 4.
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Hi I need help finding the degree measure of Radian on a triangle with hypotenuse =7 and opposite =3
Answers
Answer:
24.6 degrees.
Step-by-step explanation:
To find the degree measure of the radians in a right triangle with hypotenuse = 7 and opposite = 3, we need to use trigonometric ratios. Since the opposite and hypotenuse are given, we can use the sine ratio.
sin(θ) = opposite/hypotenuse
sin(θ) = 3/7
Now we need to find the angle measure θ. We need to use the inverse sine or arcsine function to do this.
θ = sin^-1(3/7)
θ ≈ 0.429 radians
To find the degree measure, we must convert radians to degrees by multiplying by 180/π.
θ ≈ 0.429 x 180/π
θ ≈ 24.6 degrees
Therefore, the degree measure of the radians in the given triangle is approximately 24.6 degrees.