The distance the submarine needs to travel to get to the destination is 15 feet.
Describe Distance?Distance is a numerical measurement of how far apart two points or objects are in space. In mathematics, distance is typically measured using the Euclidean distance formula, which applies to points in two- or three-dimensional space.
The Euclidean distance between two points, (x1, y1) and (x2, y2), in a two-dimensional plane is given by the formula:
d = √[tex][(x2 - x1)^2 + (y2 - y1)^2][/tex]
where the symbol √ represents the square root function.
Similarly, the Euclidean distance between two points, (x1, y1, z1) and (x2, y2, z2), in a three-dimensional space is given by the formula:
d = √[[tex](x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2][/tex]
The distance between two points can be positive or zero, but it cannot be negative. Distance is an important concept in many areas of mathematics and science, such as geometry, physics, and engineering. It is also used in real-life applications, such as navigation, transportation, and sports.
There are other measures of distance used in different contexts, such as Manhattan distance or taxicab distance, which measure the distance between two points by the sum of the absolute differences of their coordinates, rather than the square of the differences as in Euclidean distance. Additionally, distance can be defined in different ways for objects other than points, such as for the distance between two lines or two planes in geometry.
To determine the distance the submarine needs to travel to get to the destination, we need to calculate the vertical distance between the submarine and the destination point.
The vertical distance is the difference between the destination point and the submarine's current position:
Distance = Destination Point - Submarine's Position
Distance = (-10.5 ft) - (4.5 ft)
Distance = -15 ft
Therefore, the distance the submarine needs to travel to get to the destination is 15 feet.
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if the sum of the measures of the interior angles of a polygon is 1980°, how many sides does the polygon have?
Answer:
The polygon has 13 sides.
Step-by-step explanation:
The sum of the interior angles of a polygon is (n - 2) * 180, where n is the number of sides. This formula can be set equal to the sum of the interior angles to determine how many sides it has.
(n - 2) * 180 = 1980
180n - 360 = 1980
180n = 2340
n = 13
The Banks family would like to borrow $120,000 to purchase a home. They qualified for an annual interest of 4.8%.
Algebraically determine the fewest number of whole years the Banks family would need to include in the mortgage
agreement in order to have a monthly payment of no more than $720.
The fewest number of whole years the Banks family would need to include in the mortgage agreement in order to have a monthly payment of no more than $720 is 25 years.
How can we have a monthly payment of no more than $720Let's denote the number of years by y. Then the total number of monthly payments will be 12y.
The formula to calculate the monthly payment for a mortgage loan is:
M = P * (r/12) * (1 + r/12)^(12y) / ((1 + r/12)^(12y) - 1)
where:
M = monthly payment
P = principal (the amount borrowed)
r = annual interest rate
Plugging in the given values, we get:
720 = 120000 * (0.048/12) * (1 + 0.048/12)^(12y) / ((1 + 0.048/12)^(12y) - 1)
To solve for y, we can use trial and error or a numerical solver. Using trial and error, we can start with a few values of y and check if the monthly payment is less than or equal to $720.
Trying y = 20, we get:
720 = 120000 * (0.048/12) * (1 + 0.048/12)^(1220) / ((1 + 0.048/12)^(1220) - 1)
This results in a monthly payment of $753.81, which is higher than $720.
Trying y = 25, we get:
720 = 120000 * (0.048/12) * (1 + 0.048/12)^(1225) / ((1 + 0.048/12)^(1225) - 1)
This results in a monthly payment of $715.48, which is lower than $720.
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Decide which of the following are true statements. Provide a short justification for those that are valid and a counterexample for those that are not:
(a) Two real numbers satisfy a0 . (b) Two real numbers satisfy a0 . (c) Two real numbers satisfy a≤b if and only if a0 .
All the three statements given in the question are valid.
(a) Two real numbers satisfy a^2 < b^2 if and only if |a| < |b|. This is a valid statement, and the justification follows from the fact that the square of any real number is non-negative, i.e., a^2 ≥ 0 and b^2 ≥ 0, and if a^2 < b^2, then taking square roots of both sides yields |a| < |b|.
(b) Two real numbers satisfy a^2 > b^2 if and only if |a| > |b|. This is also a valid statement, and the justification follows from the fact that the square of any non-zero real number is positive, i.e., a^2 > 0 and b^2 > 0, and if a^2 > b^2, then taking square roots of both sides yields |a| > |b|.
(c) Two real numbers satisfy if and only if |a| ≤ |b|. This statement is also valid, and the justification follows from the fact that the square of any real number is non-negative, i.e., a^2 ≥ 0 and b^2 ≥ 0, and if a^2 ≤ b^2, then taking square roots of both sides yields |a| ≤ |b|.
Therefore, all three statements are valid.
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what is p value significance
In statistics, p-value significance is the measure of the strength of evidence against the null hypothesis.
P-value significance is used to determine whether or not a result is statistically significant. The p-value is the probability of obtaining the observed results or more extreme results if the null hypothesis is true. If the p-value is below the chosen significance level, usually 0.05, the null hypothesis is rejected, indicating that the results are statistically significant.
This means that the observed data is unlikely to have occurred by chance alone and that there is strong evidence to support the alternative hypothesis. P-value significance is an essential concept in hypothesis testing, and it is widely used in scientific research, medical trials, and other statistical analyses.
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renata is a 5-year-old girl from a poor family in the united states, who is about to enter kindergarten. according to recent statistics, the chances of renata being ready to complete kindergarten tasks when she enters school are about:
The chances of Renata being ready to complete kindergarten tasks when she enters school are about 1/2. The solution has been obtained by using the concept of probability.
What is probability?
To calculate the chance of an event, use the mathematical notion of probability. It only enables us to estimate the likelihood that an event will take place. On a scale of 0 to 1, where 0 represents impossible and 1 represents a certain event.
We are given that Renata is a 5-year-old girl from a poor family in the united states, who is about to enter kindergarten.
The chances of Renata being ready to complete kindergarten tasks when she enters school are about 1/2 because it is not necessary that she will be able to do all the tasks. She might be able to do and she might not be able to do.
So, there are equal chances of both.
Hence, chances of Renata being ready to complete kindergarten tasks are 1/2.
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how to convert 200 mph in km?
200 mph is approximately equal to 321.86 km per hour ( rounded to two decimal places )
The conversion factor to convert mph to km per hour is 1.6093
1 mph = 1.6093 km per hour
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
The speed in km per hour = The speed in mph × conversion factor
Substitute the values in the equation
1 mph = 1.6093 km per hour
200 mph = 1.6093 × 200
Multiply the numbers
= 321.86 km per hour ( rounded to two decimal places )
Therefore, 200 mph is 321.86 km
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FIND THE LENGTH OF SEGMENT AB HELP
Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = €* and the line * = 8 about the line x = 8.
The volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^-x and the line x = 8 about the line x = 8 is approximately 1483.6 cubic units.
To find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^-x and the line x = 8 about the line x = 8, we can use the method of cylindrical shells.
To find the volume of the solid, we need to integrate the area of each cylindrical shell over the height of the solid. Let r be the radius of a cylindrical shell at height y, and let h be the thickness of the shell. Then the volume of the shell is given by:
dV = 2πrh × h
where the factor of 2 comes from the fact that there are two cylindrical shells (one on either side of the line x = 8).
We can express r and h in terms of y:
r = 8 - y
h = e^8 - e^-x
Substituting these expressions into the formula for dV and integrating from y = 0 to y = 1, we get,
V = ∫(0 to 1) 2π(8 - y)(e^8 - e^-x) dy
= 2π ∫(0 to 1) (8e^8 - 8e^-x - ye^8 + ye^-x) dy
= 2π [8e^8 - 8e^-1 - (1/2)e^8 + (1/2)e^-1]
= 2π [15e^8 - 4e^-1]
≈ 1483.6 cubic units
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The given question is incomplete, the complete question is:
Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^-x and the line x = 8 about the line x = 8.
What is a two sample t test used for?
A two-sample t-test is a statistical test used to determine if there is a significant difference between the means of two independent groups or populations.
In research and experimental investigations, the two-sample t-test is frequently used to assess if there is a statistically significant difference between the mean values of two samples or groups.
The average test results of two separate student groups, for instance, may be compared by a researcher to see if one group performs noticeably better than the other.
The two-sample t-test makes the assumption that the two samples are independent, have nearly normal distributions, and have identical variances.
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Find the common ratio of the geometric sequence -10, 20, -40,
The common ratio of the geometric sequence -10, 20, -40 is -2.A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a fixed number called the common ratio.
To find the common ratio of the sequence -10, 20, -40, we can divide each term by the previous term.
The second term divided by the first term gives:
20 / (-10) = -2
The third term divided by the second term gives:
(-40) / 20 = -2
We can see that the quotient is the same in both cases, which means that the common ratio of the sequence is -2.
This tells us that to find the next term in the sequence, we multiply the previous term by -2. For example, to find the fourth term, we would multiply -40 by -2 to get 80, which would be the next term in the sequence.
In summary, the common ratio of the geometric sequence -10, 20, -40 is -2.
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Which of the following regressions represents the weakest linear relationship
between x and y?
Regression 1
y = ax + b
a = -5.8
b=-6.5
r = -0.7621
Regression 2
y = ax + b
a = 2.4
b = -14.7
T= = 0.809
Regression 3
y = ax + b
= -7.4
b=-17.4
a=
r=-0.233
Regression 4.
yax+b
a = -3.4
b= -8.5
T= -0.6121
Please send help
Answer:
Step-by-step explanation:
The strength of a linear relationship between two variables is typically measured by the correlation coefficient (r) or the coefficient of determination (r^2). A value of r or r^2 closer to 1 indicates a stronger positive linear relationship, whereas a value closer to -1 indicates a stronger negative linear relationship. A value of r or r^2 closer to 0 indicates a weaker or no linear relationship.
Looking at the given regression equations and their correlation coefficients, the regression with the weakest linear relationship between x and y is Regression 3:
Regression 1: y = -5.8x - 6.5, r = -0.7621
Regression 2: y = 2.4x - 14.7, r = 0.809
Regression 3: y = -7.4x - 17.4, r = -0.233
Regression 4: y = -3.4x - 8.5, r = -0.6121
Regression 3 has the lowest absolute value of r (0.233), indicating the weakest or no linear relationship between x and y. Therefore, Regression 3 represents the weakest linear relationship between x and y among the given options.
10 is what percentage of 50 
Answer:
20%
Step-by-step explanation:
10 of 50 can be written as:1050To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 1001050 × 100100= (10 × 10050) × 1100 = 20100 Therefore, the answer is 20%
Question 10 (4 points)
The following statements describe triangles ABC and PQR-
For A ABC AC-2, AB-4, and BC= 5.
For A POR: QR-7.5, PR-3, and PQ-6.
Which statement explains why A ABC and A POR are either similar or not similar?
AABC and
A
B.
C.
D.
AABC and
AABC and
4430 and
APQR
APQR
APQR
APQR
are not similar because AC
QR
are similar because c PQ
PR
AB
=
#
are similar because AB BC
PQ
QR
=
are similar because AC BC
PR
QR
=
AB
PR
=
BC
QR
AB.
PQ
Answer:
aabc
Step-by-step explanation:
Its asking to solve and substitue, what do i substitue and solve?
The solutions of the given equation are 3.16, 1, and - 1.
Solutions of equations:All numbers that make an equation true when the unknowns are eliminated from the equation are considered the solution of the equation.
For the given equation, we can find the solutions by factorizing as shown below.
Here finding the factors of the given polynomial is known as Factorizing. In other words, writing the given equation as a product of its factors.
Here we have
x⁴ - 11x² + 10 = 0
We can solve the above equation as follows
x⁴ - 11x² + 10 = 0
x⁴ - 10x² - x² + 10 = 0
Group out the like terms
x²(x² - 10) - (x² - 10) = 0
(x² - 10) (x² - 1) = 0
(x² - 10) (x - 1)(x + 1) = 0 [ ∵ (x² - 1²) = (x - 1)(x + 1) ]
x² - 10 = 0 => x = √10 = 3.16
x - 1 = 0 => x = 1
x + 1 = 0 => x = -1
Therefore,
The solutions of the given equation are 3.16, 1, and - 1.
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how to convert 0.9375 as a fraction?
The value 0.9375 as a fraction is 15/16 .
In mathematics, fractions are defined as part of a whole. A whole can be an object or a group of objects. In real life, if you cut a pie out of the whole pie, that piece becomes part of the pie. Fractions are words of Latin origin. "Fractus" means "broken" in Latin. In ancient times, rest was expressed in words. Later it was introduced in numerical form.
Fractions are also called parts or sections of any quantity. Represented by the symbol '/'. Bachelor/Bachelor For example, 2/4 is the numerator above and the fraction below the denominator. In this article, you will learn the definition of fractions in mathematics, types of fractions, how to convert fractions to decimals, and many solved examples and full explanations
to convert in fraction we will muliply and devide by 100.
0.9375*100/100 = 15/16
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Which expressions are equivalent to
35
+
30
�
−
45
�
35+30s−45t35, plus, 30, s, minus, 45, t?
The expressions which are equivalent to 35 + 30s - 45t are:
5(7+6s−9t)
(−35−30s+45t)×(−1)
The correct answer options are options B and C
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
We have to determine equivalent expression:
35 + 30s - 45t
Check all options
A. 7⋅(5+30s−45t)
= 35 + 210s - 315t
False
B. 5(7+6s−9t)
= 35 + 30s - 45t
True
C. (−35−30s+45t)×(−1)
= 35 + 30s - 45t
True
D. 10×(3.5+3s−4.5)
= 35 + 30s - 45
False
E. ( 35/2 - 15s + 45/2t) ⋅ (-2)
= (17.5 - 15s + 22.5t) (-2)
= -35 + 30s - 45t
False
Therefore, the equivalent expression is an expression which has an equal value to each other.
Complete question:
Which expressions are equivalent to 35 + 30s - 45t?
A. 7⋅(5+30s−45t)
B. 5(7+6s−9t)
C. (−35−30s+45t)×(−1)
D. 10×(3.5+3s−4.5)
E. ( 35/2 - 15s + 45/2t) ⋅ (-2)
choose 2 answers
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How to convert 750 ml to cup?
The value of volume 750 ml after converting to cups is 3.17 cups.
The conversion is useful when you need to measure liquids in cups instead of milliliters, especially if you are following a recipe that is written in cups instead of milliliters.
To convert 750ml to cups, you need to know that one cup is equal to 236.6ml. Knowing how to make the conversion can help you get the right measurements and produce accurate results in your cooking or baking. To do the conversion, divide 750 by 236.6 to get the answer in cups.
So, 750ml / 236.6ml per cup = 3.17 cups (rounded to the nearest hundredth).
Therefore, volume of 750ml is equivalent to 3.17 cups.
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A geometric sequence has first term 14 and common ratio 2. Which term of the sequence is 64?
The required, fourth term of the geometric sequence is 64.
What is geometric progression?Geometric progression is a sequence of series whose ratio with adjacent values remains the same.
Here,
We can use the formula for the nth term of a geometric sequence to solve the problem. The nth term of a geometric sequence with first term a and common ratio r is given by:
[tex]an = ar^(n-1)[/tex]
In this case, the first term is 14 and the common ratio is 2. So the nth term is:
[tex]an = 14*2^{n-1}\\[/tex]
So
[tex]14(2^{n-1}) = 64\\2^{n-1} = 64/14 = 32/7[/tex]
To solve for n, we can take the logarithm of both sides of the equation. We can use any base for the logarithm, but it's usually convenient to use base 2 since the equation involves powers of 2. So
[tex]log_2(2^{n-1}) = log_2(32/7)\\(n-1) = log_2(32/7)\\n = log_2(32/7) + 1[/tex]
Using a calculator, we can approximate log_2(32/7) as 2.665. So:
n = 2.665 + 1
n ≈ 3.665
Since n must be a whole number (we're looking for a specific term of the sequence), we can round up to the nearest integer to get:
n = 4
Therefore, the fourth term of the sequence is 64.
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Find the perimeter of the composite heart shape, round to two decimal places. pls help
Answer:
18.00 cm
Step-by-step explanation:
This composite heart shape consists of two semi-circles and a rectangle.
[tex]r_{ssc}[/tex] = radius of small semi-circle
= [tex]\frac{3 cm}{2}[/tex] = 1.5 cm
[tex]r_{bsc}[/tex] = radius of big semi-circle
= [tex]\frac{4 cm}{2}[/tex] = 2 cm
Perimeter of this composite shape
= Perimeter of big semi-circle + Perimeter of small semi-circle + 2 outer sides of the rectangle
= [tex](\frac{2}{2} \pi r_{bsc} + \frac{2}{2} \pi r_{ssc} + 3 + 4)[/tex] cm
= [tex](\pi r_{bsc} + \pi r_{ssc} + 3 + 4)[/tex] cm
= [tex][\pi (2) + \pi (1.5) + 3 + 4][/tex] cm
= [tex](2\pi + 1.5\pi + 7)[/tex] cm
= [tex](3.5\pi + 7)[/tex] cm
= 17.995 cm
= 18.00 cm (Rounded to two decimal places)
What is the conversion of 72 into feet?
After converting 72 inches into inches, we will get it as: 72 inches equal to 6 feet.
Length conversion is the process of converting length measurements between different units.
The metric system uses length units like kilometres (km), metres (m), centimetres (cm), and so on.
As we know,
1 Foot equal to 12.000005 Inches.
But actually, we can consider it as:
The 12 inches is equal to 1 foot.
We have to convert the 72 inches into feet,
So, We will simply divide the value of given inches by 12
Thus, we will get it as:
72 inches = (72/12) feet = 6 feet
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The complete question may be:
What is the conversion of 72 inches into feet?
what is 10 feet to meters?
10 feet to meters can be find out by simply dividing the 10 feet by 3.081 so the value will be 3.048 meters.
Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.
One foot is equal to 0.3048 metres, or 3048/10000 metres. So, you multiply 10 by either 0.3048 or 3048/10000 to convert 10 feet to metres.
For the decimal answer, we use 0.3048, and for the fractional answer, we use 3048/10000. The math, formulas, and conversions from 10 feet to metres are shown below.
0.3048 metres divided by feet
10 feet = 3.048 metres, or 10 divided by 0.3048.
metres equal 3048/10000 feet.
10 × (3048/10000) = 3 6/125
10 feet equals 36/125 metres.
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What is the domain of the following function? {-3, 1} {-4, -3, 1, 2, 6, 9} All Real Numbers {-4, 2, 6, 9}
Answer:
{-4, 2, 6, 9}
Step-by-step explanation:
I took the quiz lol
16. A farmer wants to build a rectangular pasture that has an area represented by 20x6y5. He has
enough room for the length to be 5x³y4. How wide would he need to make the pasture?
The width he need to make the pasture with the given rectangle is 4x³y⁶.
How does area of a rectangle, and its length and width are related?
Area of a rectangle is the product of its length and width.
If a rectangle has length L units and width of W units, then
Area = L × W squared units.
We are given that;
Area= 20x6y5
Length= 5x³y4
We can start by using the formula for the area of a rectangle:
Area = length x width
We know that the area of the rectangular pasture is 20x6y5, and we know the length is 5x³y4. So we can plug in these values and solve for the width:
20x6y5 = (5x³y4) x width
To solve for width, we can divide both sides by 5x³y4:
width = 20x6y5 / (5x³y4)
Simplifying the expression on the right-hand side, we can divide each term in the numerator by 5x³y4:
width = (4x³y¹) x (4y5)
Simplifying further, we can add the exponents of the common factor y:
width = 4x³y⁶
Therefore, the farmer would need to make the width of the rectangular pasture will be 4x³y⁶.
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What is the conversion of 30 celsius to fahrenheit ?
The conversion value of Celsius to Fahrenheit for the value 30 Celsius is equal to 86 Fahrenheit.
Standard units used for measuring the temperature is named as Celsius and Fahrenheit.Relation to convert the temperature from Celsius to Fahrenheit is equal to :
°F = 9 /5 ( ° C ) + 32.
Convert 30 Celsius to Fahrenheit by substituting the value in the formula :
= 9 /5 ( 30° ) + 32
= 9 (6° ) + 32
= 54° + 32
= 86°F
Therefore, the converted values for the 30Celsius to Fahrenheit is given by 86 Fahrenheit.
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50% of the machines at Bud's Suds are washing machines. If there are 10 washing machines, how many machines are at Bud's Suds in all?
Answer:
20
Step-by-step explanation:
If 50% of machines are washing machines and there are 10, then add 10 again to get 100% of the total machines
What is a 8-sided shape called?
Answer:
Octagon.
Octa comes from the Greek word "okto", which means eight.
The width of the rectangle is the length minus 5 units. The area of the rectangle is 6 square units. What is the width, in units, if the rectangle?
Answer:The width of the rectangle is 1 unit
Step-by-step explanation:Let the length of the rectangle be x
let the breadth be x-5
Since ,area of rectangle=length*breadth
area = x*(x-5)
6=x^2-5x
x^2-5x-6=0
solving the above equation,
x^2-(6x-x)-6=0
x^2-6x+x-6=0
x(x-6)+1(x-6)=0
(x-6)(x+1)=0
x=6 and x=-1
since the breadth cannot have negative value
Hence ,the breadth of rectangle is 1 unit
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What is the conversion of 2000 pounds to dollars ?
The conversion of 2000 pound sterling to dollars is 2,740 US dollars.
The conversion of 2000 pounds sterling to dollars depends on the current exchange rate between the two currencies.
The exchange rate was approximately 1.37 US dollars per 1 British pound.
Using this exchange rate, we can convert 2000 pounds sterling to US dollars as follows:
2000 pounds * 1.37 dollars/pound = 2,740 US dollars
Therefore, 2000 pounds sterling is equivalent to approximately 2,740 US dollars using the exchange rate mentioned above. However, please note that exchange rates can fluctuate over time, so the exact conversion may be different depending on the current exchange rate.
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Correct Question :
What is the conversion of 2000 pound sterling to dollars ?
f(x)
A
6
X
-8
6
8
Which of the given functions could this graph represent?
OA. f(t) = (x - 1)(x - 2)(x + 1)(x + 2)
O B. f(x) = x(x - 1)(1 + 1)
Oc. /(x) = x(x - 1)(x - 2)(x + 1)(x + 2)
OD. (r) = x(x - 1)(x - 2)
The correct answer is option C. f(x) = x(x - 1)(x - 2)(x + 1)(x + 2)
Explanation:
To determine the correct answer, we need to look at the zeros of the given functions and compare them to the zeros shown on the graph. The zeros of a function are the values of x that make the function equal to zero. These are also the points where the graph of the function crosses the x-axis.
Option A: f(t) = (x - 1)(x - 2)(x + 1)(x + 2)
The zeros of this function are x = 1, x = 2, x = -1, and x = -2.
Option B: f(x) = x(x - 1)(x + 1)
The zeros of this function are x = 0, x = 1, and x = -1.
Option C: f(x) = x(x - 1)(x - 2)(x + 1)(x + 2)
The zeros of this function are x = 0, x = 1, x = 2, x = -1, and x = -2.
Option D: f(r) = x(x - 1)(x - 2)
The zeros of this function are x = 0, x = 1, and x = 2.
Comparing the zeros of these functions to the zeros shown on the graph, we can see that option C is the correct answer. The graph shows zeros at x = 0, x = 1, x = 2, x = -1, and x = -2, which are the same zeros as the function f(x) = x(x - 1)(x - 2)(x + 1)(x + 2).
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Nakeisha is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Nakeisha will earn $30 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Nakeisha's songs were played on 2 more commercials than movies, and her total earnings on the royalties from all commercials and movies was $760. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Nakeisha's songs were played. Define the variables that you use to write the system.
hese two equations can be used to solve for the values of c and m.
Let's define:
c = the number of commercials on which Nakeisha's songs were played
m = the number of movies on which Nakeisha's songs were played
Based on the problem statement, we can set up the following system of equations:
Nakeisha's songs were played on 2 more commercials than movies:
c = m + 2
Nakeisha's total earnings on the royalties from all commercials and movies was $760:
30c + 110m = 760
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