Marques played songs in Number of movies = 5 and Number of commercials = 10
A mathematical statement proving the equality of two mathematical expressions is the essence of an equation. For example, 8x + 3 = 12 is an equation in which the expressions 8x + 3 and 12 are separated by a 'equal' sign.
The system of equations that could be used to determine the number of commercials and the number of movies on which Marques songs were played is illustrated as 30(x + 5) + 120(x) = 900.
The variable x represents the number of times the song has been played in movies.
According to the information, Marques is a songwriter who collects royalties on his songs whenever they are used in a commercial or a movie, and she will earn $30 every time one of his songs is used in a commercial, while he will earn $120 every time one of his songs is used in a movie.
Let x be the number of times the song was heard in movies.
Marques' songs were heard in five times more commercials than in movies. x+5 will be the answer.
As a result, the equation to solve the problem will be:
30(x + 5) + 120(x) = 900
30x + 150 + 120x = 900
150x + 150 = 900
150x = 900 -150
150x = 750
x = 750/150
x = 5
Number of movies = 5
Number of commercial = x + 5
5 + 5 = 10
Therefore Marques played songs in Number of movies = 5 and Number of commercials = 10
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A 9-inch candle burns down in 12 hours. At what rate does the candle burn, in inches per hour?
Answer:
0.75
Step-by-step explanation:
because 9/12 is 0.75
Let's establish what this rate indicates through an equation:
inches burned
hour
Now, plug in the information you have:
inches burned = 9
hour 12
9/12 = 0.75
0.75 inches of the candle is burned per hour
one antifreeze solution is 26% alcohol and another is 20% alcohol. how much of each mixture should be added to make 45 l of a solution that is 24% alcohol?
30 L of 26% and 15L of 20% of each mixture should be added to make 45 l of a solution that is 24% alcohol.
What is concentration?The quantity of a substance, like salt, that is present in a specific volume of tissue or liquid, like blood, according to science. When there is less water present, the substance becomes more concentrated. You can determine how much solute has been dissolved in the solvent by looking at the concentration of the solution.
Here,
26x + 20(45-x) = 45(24)
26x -20x = 45(24) -(20(45)
6x = 4(45) = 180 x = 180/6 = 30 L of 26%
45-x = 45-30 = 15L of 20%
To make 45 l of a 24% alcohol solution, combine 30 l of 26% and 15 l of each mixture.
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2^30 ? 30^2 which is bigger
Answer:
2³⁰ > 30²
Step-by-step explanation:
Now the values of,
→ 2³⁰ = 1073741824
→ 30² = 900
Then the expression will be,
→ 2³⁰ ? 30²
→ 1073741824 > 900
→ 2³⁰ > 30²
Hence, answer is 2³⁰ > 30².
principle is ___ ??????????????????????
- the original amount invested
- the total amount earned
- interest plus original amount invested
- interest on a loan
Is this relation a function?
(14, 9), (15, 8), (8, 7), (1, 9), (15, 2)
The given relation is not function, because 15 is repeating twice. In domain 15 is with 8 and 2.
What is a Function in math ?Function is a mathematical phrase, rule, or law that establishes the connection between two variables. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.Most frequently, the letters f, g, and h are used to represent functions. The value of a function f at an element x in its domain is represented by the symbol f. (x)The collection of all pairings (x, f (x)), also known as the function graph, serves as the sole representation of a function.To learn more about Function refer :
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5(6x+2),x=8 what is the answer
Answer:250
Step-by-step explanation:5((6(8))+2)=250 using pemdas start with parenthesis so 6*8=48 this puts the equation at 5(48+2) then do the parenthesis again so 48+2=50 this puts the equation at 5*50 then do your last step which will give you your answer of 250
For what value of x is line m parallel to line n?
Answer:
x = 42
Step-by-step explanation:
You want to know the value of x that makes alternate interior angles 105° and (3x-21)° congruent.
Congruent anglesWhen alternate interior angles are congruent, the lines forming them are parallel. Congruent angles have the same measure, so we want ...
3x -21 = 105
3x = 126 . . . . . . add 21
x = 42 . . . . . . . divide by 3
The value of x is 42 when the lines are parallel.
What is the 3 geometric means between 5 and 3125?.
The 3 geometric means between 5 and 3125 is 5, 25, 125, 625, 3125 using Geometric progression.
What is geometric mean?The geometric mean is a mean or average used in mathematics that uses the product of the values of a collection of numbers to show the central tendency of that set of numbers. The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values. An average that multiplies all values and determines the number's root is known as the geometric mean. You locate the nth root of their product for a collection of n integers. This descriptive statistic can be used to sum up your data.
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In the video about the construction of the insect phylogeny, the researchers faced the problem that there was not enough computational power in all of the world to construct every possible tree. What was the researchers’ solution?.
In the video about the construction of the insect phylogeny, the researchers faced the problem that there was not enough computational power in all of the world to construct every possible tree.
The use of computing algorithms, tools, and programmes to phylogenetic analysis is known as computational phylogenetics. The purpose is to create a phylogenetic tree that represents a hypothesis about a set of genes, species, or other taxa's evolutionary ancestry.
There was not enough computational power to construct every possible tree in all of the world. So the probable solution for this problem will be:
Use math to avoid constructing improbable trees
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y - 3x = 7 What is the y-intercept of the equation above?
a.7
b.9
c.-7
d.-7/3
Answer:
A: 7
Since the slope is 3 and passes down (1, 10), the answer will be 7
y=2(x+1)^2 has how many real roots
The answer will be:
The equation has one real root. And the root is -1/2.
The equation y= 2[tex](x+1)^2[/tex] has one real root and that is x=-1.
What is real roots of the equation?
We are aware that when we resolve a linear or quadratic equation, we always arrive at the value variable of the equation, or, to put it another way, we always locate the equation's solution. This "solution" is what we refer to as the real roots. For instance, when the equation [tex]X^2[/tex]-7x+12=0 is solved, the actual roots are 3 and 4.
Here given,
=> y = 2[tex](x+1)^2[/tex]
Take y=0 then,
=> 2[tex](x+1)^2[/tex]=0
=> [tex](x+1)^2[/tex]=0
=>(x+1)=0
=> x=-1
Hence the given equation has one real root and that is x=-1.
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what is 18.92 divided by 11 equal explain your answer?
The decimal division of 18.92 by 11 gives us; 1.72
How to divide decimal numbers?
When dividing decimals we first of all have to convert the divisor to a whole number by moving the decimal point to the right. Thereafter, we now carry the dividend's decimal point up to the exact same number of places to the right and then divide the resultant numbers in the normal way like in regular long division.
We want to divide 18.92 by 11. Thus, let us apply that rule described above to get;
18.92/11 = 1892/1100
= 1 + (1892 - 1100)/1100
= 1 + (792/1100)
= 1 + 0.72
= 1.72
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re Stock Market Alexander is a stockbroker. He earns 14% commission each week. Last week. he sold $5.300 worth of Locks. How much did he make last week in commission? If he averages that me amount each week, how much did he make in commission in 2011?
Help meee
Alexander made $742 last week in commission. He made $40068 in commission in 2011.
Sold = $5300
Commission percent = 14%
Commission = 14% of 5300
= (14/100)*5300
= 14*53
= 742
No. of weeks in 2011 = 54
Commission = 54 * 742
= 40068
Hence, he makes $742 in weeks and $40068 in year 2011.
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Which expression is equivalent to 3 log2 x – 4 log2 y + 2 log2 z?
log base 2 of the quantity x cubed y to the fourth all divided by z squared end log
log base 2 of the quantity x times z to the fifth all divided by y end log
log base 2 of the quantity x cubed z squared all divided by y to the fourth end log
log base 2 of the quantity xy divided by z end quantity raised to the fourth end log
Answer:log base 2 of the quantity x cubed z squared all divided by y to the fourth end log
Step-by-step explanation:
HELP ASAP PLEASE PLEASE ILL DO THE BRAINLIST PLS PLS PLS
Oliver borrowed $1,500 to purchase a riding lawn mower for his lawn care business. The bank offered him an interest rate of 12% for 6 months. Calculate
the simple interest using /= prt.
O $69
O $90
O $420
O$1,080
Answer:
$90
Step-by-step explanation:
The amount Oliver borrowed = 1,500
The interest rate applied to the loan = 12%
Required: To calculate the simple interest using the formula, I = P•R•T
Where;
I = The simple interest
P = The principal borrowed = $1,500
T = The time or loan duration = 6 months = 1/2 year
R = The rate at which the loan is applied = 12% = 0.12
Therefore;
I = $1,500 × 0.12/year × 6/12 year = $90
The correct option for the interest paid on the loan is therefore;
$90
You are in an elevator in a mine shaft preparing to descend into the mine. As you begin, you are nine feet above ground level. You then begin to descend. Your elevation changes at the rate of negative one foot per second. Treat elevations above ground level as positive and elevations below ground level as negative.
What will your elevation be in five minutes?
The elevation is represented by y = -t + 9, and after 5 minutes would be 4 feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the height of the elevator above the ground after t seconds.
As you begin, you are nine feet above ground level. Your elevation changes at the rate of negative one foot per second. Hence:
y = -t + 9
In 5 minutes:
y = -(5) + 9 = 4
The elevation in 5 minutes would be 4 feet.
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find 3x+4y when x is 6 and y is -3
Answer:
Step-by-step explanation:
3x + 4y when x = 6 and y = -3
Put in values of x and y:
3(6) + 4(-3) = 18 + (-12) = 6
a automobile race contains 15 racecars. in how many ways can the racecars finish in first, second, and third place?
There are 2730 ways in which 15 race cars can finish in first, second, and third place.
Let's examine this logically now. Any one of the 15 runners can cross the finish line in first place. You can still have any one of the 14 race cars who are still running finish in second place. Any one of the 13 race cars who haven't crossed the finish line yet can take third place.
As a result, multiplying all the possibilities will give us the number of ways ;
Number of ways =15*14*13
=2730
So, the total number of ways in which the race cars finish in first, second, and third place is 2730.
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if you can help you get 30 points I need help
The measure of angles ∠1 = 60 degrees, ∠2=120 degrees, ∠3 = 60 degrees, ∠4=60 degrees, ∠5 = 120 degrees, ∠6= 120degreesa and ∠7 = 60 degrees
The measure of angle 3 = 180 - 120
= 60 degrees
Because the sum of angles on a straight line will be 180 degrees
The measure of angle 6 = 120 degrees
The measure of angle 3 = The measure of angle 7 = 60 degrees
Because the corresponding angle will be equal
The measure of angle 1 = 180-120
= 60 degrees
The measure of angle 2 = 180 - 60
= 120 degrees
Because the sum of angles on a straight line will be 180 degrees
The measure of angle 2 = The measure of angle 5 = 120 degrees
The measure of angle 1 = The measure of angle 4 = 60 degrees
Because the corresponding angles will be equal
Hence, the measure of angles ∠1 = 60 degrees, ∠2=120 degrees, ∠3 = 60 degrees, ∠4=60 degrees, ∠5 = 120 degrees, ∠6= 120degrees and ∠7 = 60 degrees
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A new company wants to offer a line queuing service where customers book someone to wait in line on their behalf through a smart phone app. What concept is represented by the possibility that no one wants to pay someone else to wait in line ?.
A new company wants to offer a line queuing service where customers book someone to wait in line on their behalf through a smart phone app.
The possibility that no one wants to pay someone else to wait in line can be represented by the concept of probability.
The probability of an event occurring is defined by probability.
The outcome of an event may be known to us or unknown to us. When this happens we say that there is a chance that the event will happen or not.
We can identify probability by simply dividing the favorable number of possibilities by the entire number of possible outcomes.
Hence, probability is a numerical representation of the chance that a specific event will take place.
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Select the correct answer. What are the solutions to the equation x2 − 1 = 399? A. B. C. D.
Answer:
x=20
x= -20
Step-by-step explanation:
The volume of a sphere is decreasing at a constant rate of 55 cubic feet per minute. At the instant when the radius of the sphere is 11 feet, what is the rate of change of the radius? The volume of a sphere can be found with the equation V=\frac{4}{3}\pi r^3.V= 3 4 πr 3 . Round your answer to three decimal places.
If the volume of a sphere is decreasing at a constant rate of 55 cubic feet per minute. The volume of a sphere is 0.036.
How to find the volume of a sphere?Using this formula to find the volume of a sphere
V = 4/3 π r³
Taking the derivative with respect to time:
dV/dt = 4π r² dr/dt
Let plug in the formula
55 = 4π (11)² dr/dt
dr/dt = 55/ (484π)
dr/dt = 55/1,520.5308
dr/dt = 0.036
Therefore the volume of a sphere is 0.036.
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The points (0, –10) and (15, 6) fall on a particular line. What is its equation in slope-intercept form?
Answer:
slope: (6+10)/(15-0)
M: 16/15
B = -10
y = 16/15x -10
Use the parabola to graph the quadratic function f(x)=-2(x+4)^2-3
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
*i’ve been trying to understand this question for so long and when i try to find the answer they don’t make sense!!*
Given that the directrix is -2 and the vertex is (-4,-3), the graph will be the parabola plotted in the negative quadrant.
What is parabola?Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. Three crucial components make up a parabola: a focus, a directrix, and a vertex. This upward-opening parabola illustrates how all points along its curve will be equally distant from the directrix and the focus.
Here,
The equation of the parabola is,
f(x)=-2(x+4)²-3
a=-2
(h,k)=(-4,-3)
The graph will be the parabola plotted in the negative quadrant as the directrix is -2. and the vertex is (-4,-3).
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The equation x^2-6x=72 ha a olution between 4 and 5
Ue a trial and improvement method to find thi olution
Give your anwer correct to 1 decimal place
The solution of the quadratic equation [tex]x^2 - 6x = 72[/tex] is
x = 12 or x = -6
What is a quadratic equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
The given quadratic equation is
[tex]x^2 - 6x = 72[/tex]
Now,
[tex]x^2 - 6x = 72\\x^2 - 6x - 72 = 0\\x^2 - 12x + 6x -72 = 0\\x(x -12)+6(x -12)=0\\(x-12)(x+6)=0\\x-12=0 \ or \ x+6 = 0\\x = 12 \ or \ x = -6[/tex]
The solution of the quadratic equation [tex]x^2 - 6x = 72[/tex] is
x = 12 or x = -6
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the mixed number 1 2/5 and the decimal number 1.4 can be used to represent the same data. true or false
Answer:
True
Step-by-step explanation:
True.
1 and 2/5 can be rewritten as 1 and 4/10, and thus is equal to 1.4.
Mrs. Becker wants to get family portraits taken and is comparing prices between two different photography studios. Murray Photography charges $25 per portrait sheet, plus $30 for the session fee. Lasting Memories Company charges $50 for the session fee and $15 per portrait sheet. If Mrs. Becker plans to purchase a certain number of portrait sheets, the cost will be the same at either studio. What would the total cost be?
Write a system of equations, graph them, and type the solution.
A system of equations to describe this situation is:
c(n) = 25n + 30
c(n) = 15n + 50
The total cost is equal to $80.
The solution to this system of equations is 2.
How to write a system of equations?In order to write a system of equations to describe this situation, we would assign variables to the number of portrait sheets and cost of a photography session respectively, and then translate the word problem into algebraic equation as follows:
Let the variable n represent the number of portrait sheets.Let the variable c represent the cost of a photography session.The cost for Murray Photography is given by:
c(n) = 25n + 30
The cost for Lasting Memories Company is given by:
c(n) = 15n + 50
Next, we would solve the system of equations as follows:
25n + 30 = 15n + 50
25n - 15n = 50 - 30
10n = 20
n = 20/10
n = 2.
Now, we can calculate the total cost:
c(n) = 25n + 30
c(2) = 25(2) + 30
c(2) = $80.
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What is the solution?
Answer:
x = - 1/2
Step-by-step explanation:
3x - 6 = -7.5
3x = -7.5 + 6
3x = - 1.5
3/3 x = -1.5 / 3
x = - 0.5
x = - 1/2
Answer:
x = -1/2
Step-by-step explanation:
Given equation,
→ 3(x - 2) = -7 1/2
Now the value of x will be,
→ 3(x - 2) = -7 1/2
→ 3x - 6 = -15/2
→ 3x = -7.5 + 6
→ x = -1.5/3
→ [ x = -1/2 ]
Hence, value of x is -1/2.
STRUCTURE Find the slope of the line that passes through the pair of points.
ty
O
(0, 1)
(1,-2)
X
The slope of the line that passes through the pair of points (0, 1) and (1, -2) will be -3.
First, let us understand the slope of a line:
A slope of a line is defined in mathematics as the change in the y coordinate with regard to the change in the x coordinate.
We are given the points:
(0, 1) and (1, -2)
We will calculate the slope of the line using the following formula:
m = (y_2 - y_1) / (x_2 - x_1)
Let x_1 = 0, x_2 = 1, y_1 = 1 and y_2 = -2.
Substitute the given values in the above formula, we will get:
m = (-2 - 1) / (1 - 0) = -3 / 1 = -3
So, the slope of the line is -3.
Thus, the slope of the line that passes through the pair of points (0, 1) and (1, -2) will be -3.
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14.5 divided by 17.5
answer must be rounded 2 decimal places
Answer: 0.83
Step-by-step explanation:
14.5/17.5 = 0.828571429
We stop at the 2nd decimal placement after 0.82 but because the following number 8 > 0 we round up the hundredths place which gives us 0.83
