Answer:
G = 6(2)^n
Step-by-step explanation:
a) At 1 month he will have 12 guppies, at 2 months he will have 24 guppies and at 3 months he will have 48 guppies.
b) G = 6(2)^n
This is following the exponential formula.
c) G = 6(2)^6.5 = 543 guppies
d) At this rate, there will be no room for the guppies to continue growing.
Solve the following linear systems of equations using substitution. y = 3x + 5 y = 2x + 4
Solve each equation. Check for extraneous solutions.√x+6 +2=x+6
The solution for the equation √x + 6 + 2 = x + 6 is 4.
An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.
A formula known as an equation uses the equals sign (=) to express how two expressions are equal.
Consider the equation,
√x + 6 + 2 = x + 6
Subtracting 6 from each side of the equation.
√x + 6 + 2 - 6 = x + 6 - 6
√x + 2 = x
Subtracting 2 from each side.
√x + 2 - 2 = x - 2
√x = x - 2
Squaring the above equation.
( √x )² = ( x - 2 )²
x = x² - 4x + 4
x² - 5x + 4 = 0
x² - x - 4x + 4 = 0
x( x - 1 ) - 4( x - 1 ) = 0
( x - 1 )( x - 4) = 0
x = 1, 4
Checking for extraneous solutions,
x = 1
√x + 6 + 2 = x + 6
√1 + 6 + 2 = 1 + 6
9 ≠ 7
Hence, x = 1 is not a solution.
For, x = 4
√x + 6 + 2 = x + 6
√4 + 6 + 2 = 4 + 6
2 + 6 + 2 = 4 + 6
10 = 10
The solution of equation √x + 6 + 2 = x + 6 is x = 4.
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Leah has five older brothers and one identical twin sister.
Identify all the logical conclusions regarding Leah's siblings.
There are two girls in Leah's family.
There is one girl in Leah's family.
The firstborn child in Leah's family is a boy.
There are seven children in Leah's family.
Leah is the firstborn child in her family.
Leah and her sister look alike.
There are five boys in Leah's family.
There are six children in Leah's family.
PLEASE HELP!!!
Find the value of x.
3, 6, X.
x = [ ? ]
Give your answer in simplest form
The value of x is 12.
What is triangle proportion?
According to the Triangle proportion rule, When a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
In the diagram;
The side with x is a reflexive side of both triangles and as such from triangle proportionality theorem we can say that;
⇒6/x = 3/6
⇒ 36 = 3x
⇒ x = 12
Hence, The value of x is 12.
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Sketch the graph of the function by first making a table of
values.
[tex]f(x)=-x+3, -3\leq x\leq 3[/tex]
A pictorial representation or a diagram that represents data or values in an organized manner. For function f(x)=-x+3, -3≤x≤3 the graph is in attachment.
What is Graph?A pictorial representation or a diagram that represents data or values in an organized manner.
Given f(x)=-x+3, -3≤x≤3
It means x values lies from -3 to 3
x -3 -2 -1 0 1 2 3
f(x) 6 5 4 3 2 1 0
By taking the table values we can draw a graph.
Therefore the attached graph is the graph for f(x)=-x+3.-3≤x≤3.
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What is the next number in this pattern? 1, 2, 4, 5, 8, 9, 13, 14, ... A) 15 B) 18 C) 19 D) 20
A store is offering a 15% discount on all items. Also, employees get a 20 % employee discount. Write composite functions
a. to model taking the 15 % discount and then the 20 % discount.
The composite discount = 32%
The store offers 15% which on all items and employees get a 20% discount.
The composite discount formula is:
-x - y + ( x ×y / 100)
Here x = 15% and y = 20%
So by putting the value of x and y we get
- 15 - 20 + ( 15 × 20 /100)
- 15 -20 + 3
- 35+ 3
-32
Therefore we get the composite discount i.e., 32%
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HELP BRAINLEIST TO FIRST PERSON TO GET IT CORRRECT
The unknown angle in the triangle is as follows:
m∠A = 52°
How to find the angle in a triangle?External angle theorem states that If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
Therefore,
m∠D = m∠A + m∠B
m∠D = 116°
m∠A = (2x)°
m∠B = (x + 38)°
Hence,
116 = 2x + x + 38
116 = 3x + 38
3x = 116 - 38
3x = 78
divide both sides by 3
x = 78 / 3
x = 26
Therefore,
m∠A = 2(26)
m∠A = 52°
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96x+23=265 solve for x
ANSWER- X is 2.52083333 or 2.52083 rounded
265-23 is 242. 242 divided into 96 is 2.52083333
(96 x 2.52083333)+23 = 265
This means our X is 2.52083...
HOPE THIS HELPS & GOOD LUCK
Answer:
[tex]\displaystyle \frac{121}{48}[/tex]
or
[tex]2.5208\bar3[/tex]
SolveTo begin, subtract 23 from both sides of the equation. This will move the constants to the right side.
[tex]96x=242[/tex]
Then, divide both sides of the equation by 96. This will isolate the unknown, x, and allow you to solve the equation.
[tex]\displaystyle \frac{96x}{96}=\frac{242}{96}[/tex]
[tex]\displaystyle x=\frac{121}{48}[/tex]
There are two different answers that are equivalent but will depend on what you are looking for.
For a fraction answer, your final answer is [tex]\displaystyle \frac{121}{48}[/tex].
For a decimal answer, your final answer is [tex]2.5208\bar3[/tex].
The length of a rectangle is 4 meters less than twice the width. If the area of the rectangle is 286 square meters, find the Dimensions.
Answer:
The dimensions of the rectangle are length = 22 meters and width = 13 meters.
Step-by-step explanation:
It is given that the length of a rectangle is 4 meters less than twice the width and if the area of the rectangle is 286 square meters we need to calculate the dimensions.
Firstly, let us look at the dimensions of the rectangle;
=> Let 'l' be the length and 'b' be the width of the rectangle.
Now, let us look at the area of a rectangle;
=> l × b
So, we get an equation from the above condition;
=> l = 2b - 4
Now, the area of the rectangle is given that is 286 square meters;
=> A = 286 sq. m.
Using the above-mentioned formula for the area of the rectangle we get;
=> A = l × b
=> 286 = (2b - 4) × b
=> 286 = 2b² - 4b
=> 2b² - 4b - 286 = 0
After solving it further we get;
=> 2b² - 4b - 286 = 0
=> b² - 2b - 143 = 0
=> b² - 13b + 11b - 143 = 0
=> (b - 13) + (b + 11) = 0
Now, after equating both the sides we get;
=> (b - 13) = 0
=> b = 13
and
=> (b + 11) = 0
=> b = -11
But, b = -11 is not possible so, the width of the rectangle is 13 meters.
And the length of the rectangle would be,
=> l = 2b - 4
=> l = 2 × 13 - 4
=> l = 22
Therefore, the dimensions of the rectangle are length = 22 meters and width = 13 meters.
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What is the slope of the line that passes through the points (8, 0) and (-4, -8)
The slope of the line that passes through (8, 0) and (-4, -8) is calculated as: m = 2/3.
How to Calculate the Slope of a Line that Passes through two Points?The slope (m) formula is given as:
Slope (m) = change in y/change in x = y2 - y1/x2 - x1.
Given the following points on the line:
(8, 0) = (x1, y1)
(-4, -8) = (x2, y2)
Plug in the values into the slope formula, x = y2 - y1/x2 - x1:
Slope (m) of the line = (-8 - 0) / (-4 - 8)
Slope (m) of the line = (-8) / (-12)
Slope (m) of the line = 2/3
Thus, the slope of the line that passes through (8, 0) and (-4, -8) is calculated as: m = 2/3.
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Help with basic algebra problem! Show the steps please!!!! Will give brainliest!!
Answer:
-18k
Step-by-step explanation:
-> -8k+ 10k
-> minus and plus is = minus
-> 8k+10k
-> -18k(ans)
5.450×10-4 x 3.550×10-7 in scientific notation
Answer:
[tex]1.93475*10^{-10}[/tex]
Step-by-step explanation:
To multiply the decimal numbers in scientific notation, multiply the decimals and add the powers of the 10.
[tex]\sf 5.45 * 10^{-4}* 3.55*10^{-7}=5.45*3.55 * 10^{(-4)+(-7)}[/tex]
[tex]\sf = 19.3475*10^{-11}[/tex]
Now, write the decimal 19.3475 in scientific notation.
As we have to move the decimal one count towards left, add 1 to the power.
[tex]\sf = 1.93475*10^{-11+1}\\\\ = 1.93475*10^{-10}[/tex]
Nautica is making a scaled copy of a square using a scale factor of 2. which of the following is NOT true?
A. each angle is multiplied by 2
B. the corresponding side lengths are multiplied by 2
C. The perimeter is multiplied by 2
D. The corresponding angles in each figure are equivalent
When Nautica is making a scaled copy of a square using a scale factor of 2, the option that isn't true is D. The corresponding angles in each figure are equivalent.
How to illustrate the information?It should be noted that based on the information given, we've to multiply the given figures by 2
Therefore, each angle is multiplied by 2, the corresponding side lengths are multiplied by 2, and the perimeter is multiplied by 2
Therefore, the correct option is D.
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A piece of stained glass in the shape of a parallelogram LMNO is such that the diagonal LN is at a right angle to LM. Given that LM= 12 cm and MN = 15 cm, find the area of the piece of stained glass.
The area of stained glass with a parallelogram shape is 108cm².
What are parallelograms?A parallelogram in Euclidean geometry is a simple quadrilateral with two pairs of parallel sides. A parallelogram's opposite or facing sides are equal in length, and its opposite angles are equal in size.So, Area of parallelogram = Base × Height
Area of parallelogram = 2 × (area of triangle LMN)(as LON triangle corresponding to LMN)Now, in △LMN use the Pythagorean theorem:
LM² + LN² = MN²12² + LN² = 15²LN² = 225 - 144LN = √81LN = 9cmUsing the parallelogram area formula:
Area = Base × HeightBase = LM = 12 cmAltitude = LN = 9 cmArea of LMNO parallelogram = (12 × 9) cm²Area of LMNO parallelogram = 108 cm²Then,
Area of Triangle LMN = 1/2 × LM × LNArea of Triangle LMN = 1/2 × 12 × 9Area of Triangle LMN = ( 6×9 )cm²Area of Triangle LMN = 54 cm²Area of parallelogram LMNO = Twice of area of triangle LMNArea of parallelogram LMNO = (2 × 54) cm²Area of parallelogram LMNO = 108 cm²Therefore, the area of stained glass with a parallelogram shape is 108cm².
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There are 36,102 bags filled with coins. There are 21 coins in each bag. How many coins are
there in all?
Use the following information to fill in the blanks. On earth, there are about 1 quadrillion ants and about 8 billion people
The number of ants that are more than people will be 9800000.
How to illustrate the information?It should be noted that based on the information, it was stated that on earth, there are about 1 quadrillion ants and about 8 billion people.
Therefore, the difference between the values illustrated will be:
= 1 quadrillion - 8 billion
= 1 × 10^15 - 8 × 10^9.
= 9.2 × 10^5
Therefore, the number of ants that are more than people will be 9800000
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Use the following information to fill in the blanks. On earth, there are about 1 quadrillion ants and about 8 billion people.
On Earth, there are about ...... more ants than people.
A quadrilateral has four angles each angle is 90° Write down a mathematical name
Answer: A quadrilateral that has 4 sides is known as a rectangle.
Answer:
Step-by-step explanation:
This is either a rectangle or a square.
(A square is a special type of rectangle, with 4 equal sides).
Very confused how to do this please help
What is the x equivalent to for x/5=10 ?
Answer:
50
Step-by-step explanation:
because 10 × 5 is 50
- to check 50 ÷ 4 is infact equal to 10 (make sure u always double check ur answers)
PLEASE HELP ME!!!!
ALGEBRA 1.
4 QUESTIONS PLEASE LOOK AT THE PHOTOS
The equation that shows the different and incorrect relationship is C. b = ✓(a² + c²)
How to illustrate the information?It should be noted that from the information the Pythagoras theorem was illustrated and given as c² = a² + b²
Therefore, the equations that can be gotten from it include b² = c² - a².
It should be noted that the equation that shows the different and incorrect relationship is b = ✓(a² + c²)
In conclusion, the correct option is C.
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suppose we have collected the weights of 100 main subjects as a part of a nutrition study. for your weight data we have values ranging from a low of 121 pounds to a high of 263 pounds determine reasonable class intervals for a frequency table
The reasonable class intervals for a frequency table in between 120-269 with 14 class interval in between is shown .
What is frequency in a table?
Frequency refers to the number of times an event or a value occurs. A frequency table is a table that lists items and shows the number of times the items occur.
Given:
The weights of 100 main subjects as a part of a nutrition study.
The values ranging from a low of 121 pounds to a high of 263 pounds.
According to given question we have
Total span =263 pounds- 121 pounds
=142 pounds
Interval frequency
120-134 4
135-149 14
150-164 16
165-179 28
180-194 17
195-209 8
210-224 7
225-239 6
240-254 2
255-269 3
Therefore, the reasonable class intervals for a frequency table in between 120-269 with 14 class interval in between is shown .
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What is each expression written as a single natural logarithm?
(a) ln 7+2 ln 5
According to the question, the given expression is a single natural logarithm and the expression is as follows:
Expression: [tex]ln7+2ln5[/tex]
Using logarithmic formulas, the above expression can be written as:
Expression: [tex]ln7+2ln5 = ln7+ln5^{2} =ln7+ln25[/tex]
Using multiplication logarithmic formula that is [tex]log(ab)=log(a)+log(b)[/tex]
Now the above expression can be written as:
Expression: [tex]ln7+ln25 = ln(7X25) = ln(175)[/tex]
The solution for the given expression is: [tex]ln(175)[/tex].
What is logarithmic function?
In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.
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From 100 yards away, a marksman hit 9/10 of the targets last year.
From 100 yards away, a marksman hit probability of It means 90% of the targets were hit .
What is the probability?
Probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula.Total no of targets = 10
number of targets hit = 9
= 100/10 = 10
= 10 * 9 ⇒ 90
It means 90% of the targets were hit .
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ANSWEE ASAPP !!! i’ll mark u brainliest
what point do the equations y=2x+1 , y=3x+1 and 5x+1 have in common?
a) 2,0
b) 0,3
c) the origin
d) they have no point in common
e) 0,1
Answer:
E) (0, 1)
Step-by-step explanation:
We can equalize the first two equations to find a certain point they share. We can then check if the third line also passes through this point if substituting that point's x coordinate into the third line's equation returns the point's correct y value.
[tex]2x + 1 = 3x + 1 \\\to 0 = x[/tex]
Therefore, the point is (0, 1) as substituting [tex]x = 0[/tex] into the first equation returns [tex]y = 1[/tex].
Substituting [tex]x = 0[/tex] into the third equation does also return [tex]y = 1[/tex], therefore, that line passes through the shared point (0, 1).
An earthquake of magnitude 9.1 occurred in 2004 in the Indian Ocean near Indonesia. It was about 74,900 times as strong as the greatest earthquake ever to hit Texas. Find the magnitude of the Texas earthquake. (Remember that an increase of 1.0 on the Richter scale means an earthquake is 30 times stronger.)
b. How does the solution of your equation help you find the magnitude?
The Magnitude of earthquake that hit Texas is 5.8; With the help of the logarithmic equation so found, we can get the value of M, with which we can get the magnitude of the Texas earthquake.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given:
Magnitude of earthquake that hit Indian Ocean = 9.1 [tex]I_1[/tex] = Intensity of weaker earthquake[tex]I_2[/tex] = Intensity of greater earthquake.To find: Magnitude of earthquake that hit Texas.
Finding:
From the given, [tex]\frac{I_2}{I_1}[/tex] gives the ratio of the greater earthquake's intensity to the weaker earthquake's intensity.This ratio, when written as an exponential equation, equals [tex]30^M[/tex] where M is the increase in magnitude difference:=> [tex]\frac{I_2}{I_1}[/tex] = [tex]30^M[/tex]
For [tex]\frac{I_2}{I_1}[/tex] = 74900, the above expression becomes:
=> 74900 = [tex]30^M[/tex]
Taking logarithm on both sides, with base 10 gives:
=> log (74900) = log ([tex]30^M[/tex])
As [tex]log_b(a)^m = m(log_b(a))[/tex],
=> log (74900) = M ( log (30))
=> [tex]\frac{log(74900)}{log (30)}[/tex] = M
=> M ≈ 3.3, i.e., the increase in magnitude difference is approximately 3.3.
Thus, the magnitude of the earthquake that hit Texas = 9.1 - 3.3 = 5.8.
The logarithmic equation, in terms of exponents, so formed is: 74900 = [tex]30^M[/tex]. By finding the solution of this equation, we get the value of M, which gives us the value of the increase in the magnitude of the earthquakes.With the help of this value so found, we can find the required value of the magnitude of earthquake in Texas, as we already know that of Indian Ocean, by basic algebra.To learn more about logarithms, refer to the link: brainly.com/question/25710806
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Sam evaluated the expression x2y for x = 7 and y = 9. He got a value of 49. Which of the following statements is correct?
Hey there!
x^2 * y
= 7^2 * 9
= 7 * 7 * 9
= 49 * 9
= 441
Thus, the answer should be:
441
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Will give Branliest ASAP PLEASE
Answer: Evaluate x[tex]\frac{8}{3}[/tex]
DIFFERENTIATE W.R.T. X
[tex]\frac{8x\frac{5}{3} }{3}[/tex]
Step-by-step explanation:
Find the value of x so that line m is parallel to line l.
Based on the given parameters, the value of x such that the lines are parallel is 20
What are parallel lines?Parallel lines are lines that extend indefinitely and do not meet
How to determine the value of x?The given parameter is the lines in the figure
From the figure, we have the following angles:
3x + 20 and 2x + 40
The angles are corresponding angles
Corresponding angles are congruent
So, we have
3x + 20 = 2x + 40
Collect the like terms
3x - 2x = 40 - 20
Evaluate the like terms
x = 20
Hence, the value of x such that the lines are parallel is 20
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Part F
PLEASE HELP!!!
Complete the table to find the rule for the reflection, the coordinates of trapezoid PQRS, and the coordinates of the reflected image, trapezoid P′Q′R′S′.
The new coordinates after transformation of the original coordinates using the transformation rule (x, y) → (x, -y) are;
P(6, -4) → P'(6, 4)
Q(2, -2) → Q(2, 2)
R(2, -6) → R(2, 6)
S(6, -6) → S(6, 6)
What are the coordinates of the reflection transformation?The given reflection transformation of (x, y) → (x, -y) simply means a reflection across the x-axis.
Thus, the new coordinates after undergoing the above transformation are;
P(6, -4) → P'(6, 4)
Q(2, -2) → Q(2, 2)
R(2, -6) → R(2, 6)
S(6, -6) → S(6, 6)
Thus, we conclude that the new coordinates after transformation of the original coordinates using the transformation rule (x, y) → (x, -y) are;
P(6, -4) → P'(6, 4)
Q(2, -2) → Q(2, 2)
R(2, -6) → R(2, 6)
S(6, -6) → S(6, 6)
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