Yes, three equations are needed to find the values of three variables. Then only it will have a unique solution. The solution of three variable equation is also known as the ordered triple.
There must be 3 equations, If there are 3 variables.
Lets consider A,B,C as our equations and x, y, and z as the variables.
We will now follow these following steps:
1) By using C, first write z in terms of x and y. Then, Replace z with its equivalent in B.
2) Then write y in terms of x.
3) In A, replace y with its equivalent and replace z with its equivalent then solve A for x. Now you should know the value of x. You should have written y in terms of x so plug x and you will find y.
4)Finally, you should have written z in terms of x and y so you can find the value of z.
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What is the sum of 2/8+3/9?????
Answer:42/72 simplify =7/ 12
Step-by-step explanation:
PLEASE HELPPPPP Determine the type of correlation represented in the scatter plot below.
The graph shows:
A. A perfect positive correlation
B A strong positive correlation
C. A weak postitive correlation
D. No correlation
E. A weak negative correlation
F. A strong negative correlation
G. A perfect negative correlation
The answer is weak negative correlation.
What is meant by correlation?Positive correlation: An increase or decrease in one variable causes an increase or decrease in the other when the values of the two variables move in the same direction.A drop or increase in one variable causes a decrease or increase in the other when the values of the two variables move in the opposite direction.No linear dependency or correlation exists.An illustration of how these connections appear in a graph is shown below:As a result, we can see from the provided image that there is a negative correlation between x and y, i.e., as x increases, y lowers. Additionally, the dispersion of the dots indicates a poor association.The degree to which two variables are linearly connected is expressed by the statistical concept of correlation (meaning they change together at a constant rate). It is a typical technique for outlining straightforward connections without stating cause and consequence.A statistical term known as correlation indicates the strength and direction of a relationship between two or more variables. It is expressed as a number. However, just because two variables are correlated does not necessarily imply that the change in one of the variables is what changed the values of the other.To learn more about correlation refer to:
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What is the rule about splitting infinitives How would you rewrite the quote above?
The rule about splitting infinitives is avoid using a word between TO and the verb if at all possible. The correct quote is "To go boldly where no one has gone before."
In the given question, we have to explain the rule about splitting infinitives and how we rewrite the quote based on this rule
The given quote is
"To boldly go where no one has gone before."
Splitting infinitives is prohibited according to grammar rules. Avoid using a word between TO and the verb if at all possible. Split infinitives are improper grammatically, therefore avoid using them.
So, in order to change this quote, you should:
"To go boldly where no one has gone before."
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The right question is:
What is the rule about splitting infinitives? How would you rewrite the quote above based on this rule?
read this quote that comes from a popular television and movie franchise:
"To boldly go where no one has gone before."
which is more 2,005 pounds or 1 ton
Answer: 2005 pounds
Step-by-step explanation:
1 ton is 2000 pounds
Answer:
2,005 pounds
Step-by-step explanation:
Hope it helps!
Consider the function y = 3 | x - 1 | +3 under the restricted domain 0 ≤ x ≤ 3. The range is a ≤ y ≤b.
The range of the given function y = 3 | x - 1 | +3 for the domain 0 ≤ x ≤ 3 will be [3,9].
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
The given function has been drawn below.
The minimum value of the function in interval 0 ≤ x ≤ 3 is 3 while the maximum value is 9.
The range will be [3,9].
Hence "For the domain 0 x 3, the provided function, y = 3 | x - 1 | +3, will have a range of [3,9].".
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Rewrite the expression 12m(m-3n) using the Distributive Property.
O A. 12m² - 36mn
OB. 12m² - 12mn
O C. 12m² - 9mn
O D. 12m² - 3mn
The expression equivalent to 12m(m-3n) using distributive property is 12m² - 36mn.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 12m(m-3n) .
Twelve m times m minus three times n.
12m(m-3n).
12m is to multiplied to m minus three n.
12m²-35mn.
Twelve m square minus thirty five times of m and n.
Hence, 12m²-35mn is the expression equivalent to 12m(m-3n) .
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Monica would like to save up $10,000. She is going to make monthly deposits for 5 years into an account that will get 2.05% compounded monthly. How much does she need to deposit in the account to reach her goal?
The amount of money that Monica needs to deposit each month in order to save up $10,000 in 5 years is; $91017.17865
How to solve compound interest problems?The formula for compound interest is;
A = P (1 + r/n)^(nt)
where;
A is the total amount of money in the account after the interest has been compounded.
P is the initial deposit.
r is the interest rate.
n is the number of times the interest is compounded in a year
t is the number of years the money is deposited.
We are told that Monica would like to save up $10,000. Thus;
The initial deposit = $10,000.
The interest rate = 2.05%.
The number of times the interest is compounded per year; n = 12 (because the interest is compounded monthly),
The number of years the money is deposited; t = 5.
Plugging these values into the compound interest formula, we get:
A = 10000 (1 + (0.0205 / 12))^(12 * 5)
A = 10000 (1.001708333)^60
A = 10000 (1.101717865)
A = $101017.17865
Thus, the total amount of money in the account after 5 years will be $101017.17865.
Since Monica wants to save up $10,000, we can subtract this amount from the total amount in the account to find out how much she needs to deposit each month in order to reach her goal:
101017.17865 - 10000 = 91017.17865
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formula for area and perimeter of a circle
Answer:a=pi*r^2
Step-by-step explanation:
area=pi*radius squared
Solve the system
x+y=6
5x-y=3
by graphing and by substitution. Compare the
methods. Which method is more accurate? Explain
We can solve the given linear equations using graphing and substitution method. Substitution is more accurate, since it provides an exact answer.(x,y)=(1.5,4.5) is the answer for the given linear equation.
What is Substitution and Graphing method ?As Math Planet correctly notes, to solve a system of linear equations by graphing, we simply graph both equations in the same coordinate plane and locate the intersection of the two lines. Substitution-Based Graphing of Linear Equations. By substituting values for x, we may obtain the appropriate y values and display the points on a line with the equation y = ax + b. (x, y). Two points must be produced by replacement in order to create a line between them.
Calculation:x + y = 6 → y = 6 − x
5x − y = 3
⇒5x − (6 − x) = 3
⇒5x + x − 6 = 3
⇒6x = 9
⇒x = 1.5
⇒1.5 + y = 6
⇒y = 4.5
(x,y)=(1.5,4.5)
We can solve the given linear equations using graphing and substitution method. Substitution is more accurate, since it provides an exact answer.(x,y)=(1.5,4.5) is the answer for the given linear equation.
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A rectangular storage container without a lid is to have a volume of 10 m3. The length of its base is twice the width. Material for the base costs $5 per square meter. Material for the sides costs $3 per square meter. Let w denote the width of the base. Find a function in the variable w giving the cost C (in dollars) of constructing the box.
A function in the variable w giving the cost C is 81.77 dollars.
What is meant by volume?Volume is a unit of measurement for the area occupied in three dimensions. It is widely quantified and measured using SI-derived units, alternative imperial units, or US standard units (such as the gallon, quart, cubic inch). Volume and length (cubed) have a similar meaning.
First, volume was calculated using naturally occurring vessels with a similar shape, and then using standardized containers.
Surface area of an open lid container is:
A=2×sides+Base
So,
A=2(lh+wh)+lw
Cost of the base is $5 per square meter and the cost of the sides is $3 per square meter.
Now, the cost function is:
C=3×2(lh+wh)+5×lw
C=6(lh+wh)+51w
Here, the length is twice the width then,
l=2w
C=6(2wh+wh)+5×2w²
C=6(3wh)+10w²
C=18wh+10w²
And we know that the volume is,
V= lwh
2w²h=10
h=5/w²
C=18wh+10w²
C=18w×(5/w²)+10w²
C=(90/w)+w²
C'=(-90/w²)+20w
0=(-90/w)+20w
20w=(90/w²)
20w³=90
w³=45
w=1.65
C=(90/1.65)+10×1.65²
C=81.77
Therefore, a function in the variable w giving the cost C is 81.77 dollars.
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three people A, B, C, are to share 44,000usd among themselves in the ration a:b:c: respectively .if a = ½b c=⅓b how much will B receive more than C
There are B receives an amount of $35,733.33 more than C.
What is Ratio?A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
Let "b" be the amount that B receives.
A receives 1/2 × b, and C receives 1/3 × b.
The total amount that A and C receive is 1/2 × b + 1/3 × b = 5/6 × b.
Since A, B, and C are to share $44,000 in the ratio a:b:c, the total amount that A and C receive is 5/6 × b = $44,000.
Solving this equation for b, we get:
b = $44,000 / (5/6)
b = $44,000 x (6/5)
Apply the multiplication operation, and we get
b = $53,600
Therefore, B receives $53,600, and C receives 1/3 x $53,600 = $17,866.67.
B receives $53,600 - $17,866.67 = $35,733.33 more than C.
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if you subtract 12 from my number and multiply the difference by -3, the result is -27. what is my number
Answer:
21
Step-by-step explanation:
27/3 + 12
i need help asap pls help im on a time limit so pls help me
Answer:
What is even the question?
Step-by-step explanation:
75 POINTS!!
Write a system of equations to model Monica's savings and Shanna's savings. Let x represent the number of weeks and y represent savings.
Type your response in the box
The system of equations to model Monica's and Shanna's savings is y = 10x + 50 for Monica and y = 15x + 100 for Shanna.
To model Monica's savings and Shanna's savings using a system of equations, we can use the variables x and y, where x represents the number of weeks and y represents the savings.
Let's start by defining the equation for Monica's savings. We'll use the equation y = mx + b, where m represents the savings per week and b represents the initial savings.
Next, let's define the equation for Shanna's savings. We'll use the same equation, y = mx + b, but with different values for m and b.
For example, let's say Monica saves $10 per week and initially has $50 in savings. The equation for Monica's savings would be y = 10x + 50.
Now, let's say Shanna saves $15 per week and initially has $100 in savings. The equation for Shanna's savings would be y = 15x + 100.
So, the system of equations to model Monica's and Shanna's savings would be:
Monica: y = 10x + 50
Shanna: y = 15x + 100
By using this system of equations, we can determine Monica's and Shanna's savings at any given number of weeks, x. Simply substitute the value of x into the equations and solve for y.
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8 ≤ -4(x - 1)
Please help me.
Answer: x ≤ -1
Step-by-step explanation:
8 ≤ -4x+4
4x+8 ≤4
4x ≤-4
x ≤ -1
Answer:
Step-by-step explanation:
first open the bracket by multiplying -4 through
8 ≤ -4x + 4
then group like terms and unlike terms
therefore; 8 - 1 ≤ -4x or -4x ≤ 8-4
-4x ≤ 7 then divide both side by -4
so, ⇒ x ≤ -4/4
x≤-1
What are the vertex and range of y = |x − 5| 4? (5, 4); −[infinity] < y < [infinity] (5, 4); 4 ≤ y < [infinity] (−5, 4); −[infinity] < y < [infinity] (−5, 4); 4 ≤ y < [infinity]
The range and the vertex is 4 ≤ y < [infinity] and (5, 4).
To find the vertex, we can take the derivative of the function and set it equal to 0:
y' = |x − 5|' = 0
=> x − 5 = 0
=> x = 5
Then, we can plug x = 5 into the original equation to find the y-value at the vertex:
y = |x − 5| = |5 − 5| = |0| = 0
So, the vertex of y = |x − 5| is (5, 4).
To find the range, we need to consider the range of the absolute value function. The range of the absolute value function is:
−[infinity] < y < [infinity]. So, the range of y = |x − 5| is also −[infinity] < y < [infinity] (or 4 ≤ y < [infinity]).
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In the diagram, /\ABC \cong≅ /\DEF, write an equation and find the value of y, then write another question to find the value of x.
The values of x and y of the corresponding sides of the congruent triangles are;
y = 3.8
x = 4.6
How to solve congruent triangles?There are 5 main congruence postulates pertaining to congruent triangles and they are;
SSS - Side Side Side congruence postulate
SAS - Side Angle Side congruence postulate
ASA - Angle Side Angle congruence postulate
AAS - Angle Angle Side congruence postulate
HL - Hypotenuse Leg Congruence Postulate
Now, we are given the three sides of both triangles that are said to be congruent and this means that the three corresponding sides are congruent. Thus;
AB = DE;
10 = 3x - y ------(1)
Similarly;
BC = EF
18.8 = 6y - 4 -----(2)
Add 4 to both sides in equation 2 to get;
22.8 = 6y
y = 22.8/6
y = 3.8
Thus;
10 = 3x - 3.8
3x = 13.8
x = 13.8/3
x = 4.6
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half of the quantity of 6 less than a number f is 4. how do u put in the algebraic form
Wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww
-0.47x+0.27x = 5.8 Solve for X
Answer:
-29
Step-by-step explanation:
you add both decimals together you get -.2x=5.8 you divide both sides by -.2x and you get x=-29
Find the slope of the line that passes through (1, 12) and (5, 5).
Answer: -7/4
Step-by-step explanation: see attached
w(t)-2t +3; Find w(0)
Answer:
3
Step-by-step explanation:
w(0) = 2(0) + 3
w(0) = 0 + 3
w(0) = 3
A box of cereal weighs 14 ounces and costs $2. 66. What is the price per ounce of the cereal?.
Find the measure of angle 1
Answer:
∠1 = 47°
Step-by-step explanation:
angles in a triangle add up to 180°
∠1 + 63 + 70 = 180
∠1 + 133 = 180
∠1 = 180 - 133
∠1 = 47°
the mean of a distribution of data is 3.56 . if the distribution is symmetric , what is the median ?
Since, the mean of distribution of data is 3.56 then the median is also 3.56 because the distribution is symmetric.
Symmetric Distribution:
A symmetric distribution is when the values of a variable occur with regular frequency, often the mean, median, and mode all occurring at the same point. A line in the middle of the chart indicates that the two planes are mirror images of each other.
In graphical form, a symmetric distribution is displayed as a normal distribution (that is, a bell curve). Symmetric distribution is a central concept in technical trading as it assumes that the price movements of an asset over time follow a symmetric distribution curve. A symmetric distribution can be contrasted with an asymmetric distribution.
Relation between Median and Mean
A distribution always has a median and a mode, but not always a mean. Consider the Cauchy distribution. No average exists. Modes are always present, but may not be unique. This means that you can get a distribution that is not unimodal (that is, multimodal).
So, if we have a symmetric distribution with a mean and the distribution is unimodal, we can say:
Mean = Median = Mode
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the sum of a number x and 4, all divided by 3
The value of l such that the rectangle and trapezium have the same area will be 18 feet.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
The perimeter of the rectangle = 2( length + width).
As per the given,
Area of rectangle = area of a trapezoid
9 x l = (1/2)(24 + 12)9
9l = 162
l = 18 feet
Hence "The amount of l that must be present for the rectangle and trapezium to share the same area is 18 feet.".
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Annie was given two pieces of information and must write the equation of a line. She knows the line crosses the y-axis at the point(0,6)and has a slope of7. What is the equation of the line?
A.y=7x+6
B.y=7x−6
C.y=6x+7
D.y=−6x+7
At the theatre, there are six seats in a row. Eliot and Doug have three people between them. Chuck sits next to Eliot, but not next to Bob: Andy is on the end: but Eliot isn't. Frank is between
From the arrangement given, it can be concluded that-
Frank is between Chuck and Bob
What is arrangement?
The way of putting up a particular thing in order for a particular purpose or activity is called arrangement.
From the seating arrangement given,
Andy is on the end: but Eliot isn't
Andy ___ ___ ___ ___ ___
Eliot is not on the end and Eliot and Doug have three people between them
Andy Elliot ___ ___ ___ Doug
Chuck sits next to Eliot, but not next to Bob
Andy Elliot Chuck ___ Bob Doug
Only Frank is left
Andy Elliot Chuck Frank Bob Doug
So Frank is between Chuck and Bob
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Can we use two infinitives in a sentence?
Yes, one can use more than one infinitives in the same sentence. For example : I have to wash my hand to keep myself clean.
Reason for the given statement:
To use two or more infinitives in the same sentence:
Multiple of infinitives can be used in the same sentence.For example : I want to purchase new clothes to attend marriage belongs to my family members.Here we have used three infinitives which are to purchase , to attend and to my.Mostly when two or more infinitives are used the last one ends with and.Therefore, it is perfectively alright to use more than one infinitives in the same sentence.
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given that about 25% of the mammalian genome is associated with genes, including introns and regulatory sequence, what would be the approximate average length of dna per gene if the genome contained 20,000 genes?
According to the question,
Given data in the question.
If the genome contained 20,000 genes, the average length of DNA per gene will be 40,000 base pairs.
What is the average length of DNA per gene?
Only 2.5% of the human genome is protein-coding. Introns make up the remaining 97.5%. The male nuclear diploid genome is 6.27 Giga base pairs (G b p), 205.00 cm (cm) long, and 6.41 picograms in weight (p g). Female measurements are 6.37 G b p, 208.23 cm, and 6.51 p g
For a 25% mammalian genome with 20,000 genes, the total number of base pairs, which is the length of DNA per gene, will be approximately double the payment of genes contained in the genome, in this case 40,000.
The average length of DNA per gene, assuming 20,000 genes in the genome, is 40,000 base pairs.
How long does DNA typically be per gene?
Only 2.5% of the human genome codes for proteins. The remaining 97.5% is made up of introns. The size and weight of the male nuclear diploid genome are 6.27 Giga base pairs (G bp), 205.00 centimetres (cm), and 6.41 picograms (p g). 6.37 G bp, 208.23 cm, and 6.51 p g are the female measurements.
The total number of base pairs, which is 20,000 for a 25% mammalian genome with 20,000 genes,
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The average length of DNA per gene would be 40,000 base pairs if the genome had 20,000 genes.
What is the average length of DNA per gene?The human genome only codes for proteins in 2.5% of it. The remaining 97.5% are introns. The male nuclear diploid genome measures 205.00 centimeters (cm), is 6.27 Gigabase pairs (Gbp), and weighs 6.41 picograms (pg). 208.23 cm, 6.51 pg, and 6.37 Gbp are the female measurements.
Is genetics a lot of math?Although there may be some hereditary component to math aptitude, this probably only accounts for a small portion of it. Even in the current study, genetics alone could only account for 20% of math prowess. According to Libertus, "this leaves more than 80% of the variety in children's math aptitude unexplained."
The overall number of base pairs, which is the length of DNA per gene, will be roughly twice the number of genes present in the genome, in this example 40,000, for a 25% mammalian genome with 20,000 genes.
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Which function represents the exponential graph given that (0, 1) and (4, 81/16) are points that lie on the graph?
A ƒ(x) = (23)xƒ(x) = ( 2/3 ) x
B ƒ(x) = (4)xƒ(x) = ( 4 ) x
C ƒ(x) = (1)xƒ(x) = ( 1 ) x
D ƒ(x) = (3/2)x
Answer:
Step-by-step explanation:
A......