PLEASE HELP!!
i think it wants it in the form of
m = y2-y1
——————
x2-x1
but i could be wrong please please please help if you can it’s greatly appreciated
Answers
a) Two different ways.
x = ln(32)/ln(2)
2^x = 2^5
b) Only the natural logarithm way can be used.
c) x = 3.58
How to solve the equation?We want to solve:
2^x = 32
in two ways.
The first way is trivial, apply the natural logarithm to both sides:
ln(2^x) = ln(32)
x = ln(32)/ln(2)
The second way is the next one:
2^x = 32
The right number can be written as:
4*8 = 32
Now we can factorize the left side:
4*8 = (2*2)*(2*2*2) = 2^5
Replacing that we get:
2^x = 2^5
So we know that x = 5.
b) The second way can't be used to solve:
2^x = 12
Because 12 has a factor different than 2.
c) Using the natural logarithm way:
x = ln(12)/ln(2) = 3.58
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Related Questions
What is the image of (1, 0) after a dilation by a scale factor of 4 centered at the
origin?
Answers
Answer:
(4, 0)
Step-by-step explanation:
You want the image point coordinates of (1, 0) dilated by a factor of 4 centered at the origin.
DilationWhen the dilation is centered at the origin, all coordinate values are multiplied by the scale factor.
(1, 0) ⇒ 4(1, 0) = (4, 0)
The image of the point is (4, 0).
The lunch special at Rachel's Restaurant is a sandwich, a drink and a dessert. There are 2 sandwiches, 3 drinks, and 2 desserts to choose from. How many lunch specials are possible?
Answers
Answer:
3 lunch specials are possible.
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.
y=x-2
y=x-1
Answers
The system of equations are parallel lines and they do not intersect. Thus, the system has no solution.
What are parallel lines?Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.
No matter how far we extend a parallel line, it will never meet another parallel line.
Given that,
y=x-2
y=x-1
For x = 1:
y = x - 2 = 1 -2 = -1
y = x - 1 = 1 - 1 = 0
For x = 2:
y = 2- 2 = 0
y = 2 -1 = 1
Plot the graph using the points.
The two lines have the same slope hence they are parallel lines.
Since, the two lines are parallel the system has no solutions.
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Someone help me with this Quadratic function graph function question
Answers
The graph of the quadratic function y = -6x² + 1 is given by the image presented at the end of the answer.
How to obtain the graph of the quadratic function?The parent quadratic function is given as follows:
y = x².
The transformed quadratic function is given as follows:
y = -6x² + 1.
The transformations are given as follows:
Multiplication by the negative number: reflected over the x-axis, changing the concavity of the quadratic function.Multiplication of x by the number with an absolute value of 6: horizontal compression by a factor of 6.Addition by 1: translation up one unit.More can be learned about quadratic functions at https://brainly.com/question/1214333
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You are given the yearly interest earned from a total of $18,000 invested in two funds paying the given rates of simple interest. Write and solve a system of equations to find the amount invested at each rate. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.
Yearly Interest: $579
Rate 1: 2.75%
Rate 2: 4.75%
(dollars invested at 2.75%, dollars invested at 4.75%) =
Answers
The amount of investment at a rate of 2.75% and 4.75% will be $13,800 and $4,200m, respectively.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
The formula for interest is written as,
I = (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
Let 'x' be the amount of investment at a rate of 4.75%. Then the amount of investment at a rate of 2.75% is ($18,000 - x). Then the equation is given as,
(18,000 - x) × 0.0275 + 0.0475x = 579
495 - 0.0275x + 0.0475x = 579
0.02x = 84
x = $4,200
Then the value of ($18,000 - x) is given as,
$18,000 - x = $18,000 - $4,200
$18,000 - x = $13,800
The amount of investment at a rate of 2.75% and 4.75% will be $13,800 and $4,200m, respectively.
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Statesvilles population in 2010 was about 24800 and was growing about 1.2% each year. If this continues, what will statesvilles population be in 2015?
Answers
yearly multiplication growth factor is (1+0.011) = 1.011. the year 2017, seven years after 2010, the population will be [tex]24800*2A1.011^7 = 26,774[/tex]
what is multiply ?
Along with addition, subtraction, and division, multiplication is one of the four arithmetic operations. Multiplication in math refers to regularly adding groups of the same size. The formula for multiplication is multiplicand multiplier Equals product. Specifically, multiplicand: First number (factor). divider: Second number (factor). After multiplying the multiplicand and the multiplier, the result is known as the product. Multiple additions are made while adding numerals. as in 5 times 4 Equals 5 + 5 + 5 + 5 = 20. I multiplied 5 by 4 times. Multiplication is frequently referred to as "doubling" because of this.
yearly multiplication growth factor is (1+0.011) = 1.011.
the year 2017, seven years after 2010, the population will be [tex]24800*2A1.011^7 = 26,774[/tex]
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High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 21 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized? (Round your answer to 2 decimal places.)
Answers
A student would have to score approximately 0.84 standard deviations above the mean to be publicly recognized.
Is a high standard deviation desirable?The dispersion of asset prices from their average price, or market volatility, can be calculated with the use of standard deviation. A large standard deviation indicates a dangerous investment when prices move erratically. Low standard deviation indicates stable prices, which lowers the risk associated with investments.
The remaining 79 percent of pupils are not recognised if just the top 21% of students receive public recognition. Since a normal distribution is assumed, the conventional normal distribution and its corresponding z-scores can be used to provide the solution.
The percentage of scores that are higher than a certain z-score is shown by the area under the standard normal distribution to its right. Finding the z-score that represents the top 21% of scores is equivalent to locating the z-score that represents the bottom 79% of scores. By using a calculator or a table of the ordinary normal distribution, we can determine that the z-score for the bottom 79 percent of scores is roughly 0.84.
In order to be officially acknowledged, a student would need to get a score that is roughly 0.84 standard deviations above the mean.
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Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 4 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 111?
Answers
On solving the provided question, we can say that in the equation,Often, there is only one variable, which also serves as the symbol. An illustration would be , [tex]D = 4(82-D)+2[/tex]
What is equation?The equal sign (=), which denotes equality, is used to unite two statements in a mathematical equation. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions.
For instance, the equal sign separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14.The two sentences on either side of a letter are connected by a mathematical formula.
Each equation has a formula. Not every equation has a formula. Equations are created with the intention of being solved for a variable. If an equation meets the requirements for a function, it is a function. But not every equation is a function.
M+D = 82 marbles
[tex]M= 82- D[/tex]
[tex]D= 4M+2[/tex]
[tex]D= 4(82-D) +2[/tex]
[tex]D= 328 - 4D+2[/tex]
[tex]5D = 330[/tex]
[tex]D= 66[/tex]
Therefore, Don has 66 and Mark has 82-66 = 16
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Angela fully charged her laptop, then unplugged it and tracked the battery level at certain times under constant use. The table below shows her findings. The equation for the line of best
fit is below. Use the equation to estimate the battery level after two hours of constant use unplugged. Round to the nearest percent. (2:00 is an x-value of 0)
Answers
The battery level after two hours of constant use unplugged is found replacing the instance of x on the line of best fit by 2.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The variables for this problem are given as follows:
Variable x: time in hours.Variable y: battery percentage.Hence after a time of two hours the battery level is found as the numeric value at x = 2.
Missing InformationThe problem is incomplete, hence the general procedure to solve the problem is presented.
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Consider a function f(x) = x ^2 . A second function h(x) is the result of reflecting f(x) across the x axis and translating it 3 units in the positive y-direction (upward). Write the equation of h(x).
Answers
Answer:
So the equation of the transformed function h(x) is h(x) = -x^2 + 3.
Step-by-step explanation:
Since h(x) is the result of reflecting f(x) across the x axis and translating it 3 units in the positive y-direction, we know that:
The x-coordinates of f(x) and h(x) are the same, so x is unchanged.
The y-coordinates of f(x) and h(x) are reflected across the x axis, so we need to negate the y-coordinate.
The y-coordinate of h(x) is shifted up by 3 units, so we need to add 3 to the y-coordinate.
Given the equation of f(x) = x^2, the equation of h(x) can be written as:
h(x) = -x^2 + 3
So the equation of the transformed function h(x) is h(x) = -x^2 + 3.
rj and is 2 brother are given php2000 weekly allowance they have allocoted 60% for food 8% for fare 15% for school needs and the remaining 17% for savings how much is allocoted for the following
Answers
Answer:
RJ and his 2 brothers are given a weekly allowance of PHP 2,000. They have allocated 60% for food, 8% for fare, 15% for school needs, and 17% for savings.
For food, the allocation would be: PHP 2,000 x 60% = PHP 1,200.
For fare, the allocation would be: PHP 2,000 x 8% = PHP 160.
For school needs, the allocation would be: PHP 2,000 x 15% = PHP 300.
For savings, the allocation would be: PHP 2,000 x 17% = PHP 340.
So, for food, the allocation is PHP 1,200, for fare, it's PHP 160, for school needs, it's PHP 300, and for savings, it's PHP 340
The ratio of first- class, second- class and third-class passengers who survived the ship wreak is
101:59:89. How many passengers were saved if the total number of first-class passengers were 202?
Answers
Answer: If the ratio of first-class, second-class, and third-class passengers who survived the shipwreck is 101:59:89, then for every 101 first-class passengers who survived, there were 59 second-class and 89 third-class passengers who survived.
If the total number of first-class passengers was 202, then there were 202 * 59/101 = 118 second-class passengers who survived, and 202 * 89/101 = 180 third-class passengers who survived.
Therefore, the total number of passengers who survived the shipwreck is 202 + 118 + 180 = 500 passengers.
Step-by-step explanation:
-3x⁴+5x³+0x²+2x-1÷2x²-x
Answers
The quotient is -3x²/2 + 7x/4 + 7/8 and the remainder is 23x/8 - 1. The solution has been obtained by using polynomial long division method.
What is polynomial long division?
A formula for multiplying one polynomial by another of the same degree or lower is known as a long division polynomial. Like with long division of numbers, the components of long division of polynomials include the divisor, quotient, dividend, and remainder.
We are given dividend as -3x⁴+5x³+0x²+2x-1 and divisor as 2x²-x.
Using Polynomial Long Division,
Dividing : -3x⁴+5x³+0x²+2x-1 ("Dividend")
By : 2x²-x ("Divisor")
Dividend -3x⁴ + 5x³ + 0x² + 2x - 1
- divisor * -3x²/2 -3x⁴ + 3x³/2
Remainder + 7x³/2 + 0x² + 2x - 1
- divisor * 7x/4 + 7x³/2 - 7x²/4
Remainder 7x²/4 + 2x - 1
- divisor * 7/8 7x²/4 - 7x/8
Remainder 23x/8 - 1
Quotient : -3x²/2 + 7x/4 + 7/8
Remainder: 23x/8 - 1
Hence, the solution has been obtained.
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Jonathan is a single taxpayer. His taxable income before deductions was $63,110. He was able to reduce his taxable income by $10,312 when he filled out Schedule A and Schedule 1.
a. How much did he save in tax by using Schedule A?
Answers
In a linear equation. , $12,215 did he save in tax by using Schedule A .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Given,
Taxable income with out deductions = $63,110
total deductions = $10,312
the tax is given in the row 63.100 63,150 and in the column 'single' of the tax table is
tax = $12,215
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As a fundraiser for her soccer team, Leslie must raise at least $120 by selling keychains and t-shirts. Each keychain costs $4 and each t-shirt costs $10. She must sell at least 18 items in total.
Choose the correct system of linear inequalities that represents Leslie’s situations.
X = keychains, y = t-shirts
Answers
Answer: The correct system of linear inequalities that represents Leslie's situation is:
4x + 10y ≥ 120 (to represent the requirement to raise at least $120)
x + y ≥ 18 (to represent the requirement to sell at least 18 items in total)
x ≥ 0, y ≥ 0 (to represent that Leslie must sell a non-negative number of keychains and t-shirts)
Where x represents the number of keychains sold and y represents the number of t-shirts sold. The first inequality represents the minimum amount of money Leslie needs to raise, and the second inequality represents the minimum number of items she needs to sell. The last two inequalities represent that Leslie can only sell a non-negative number of items.
Step-by-step explanation:
Yoshi swam across a lake but did not know how far he swam. He found that it was 100sqrt(3) feet from point A to point C. Angle C was a right angle and angle A was 30°.
Find the distance he swam across the lake.
Hint: hypotenuse = 2shortleg )
Answers
The length of the lake is 100 ft
Finding the length of the lake:Form a right-angled triangle according to the given data in the problem. Chose which trigonometric ratio can be used to find the side that is considered as the side of the lake.
From the trigonometric ratio table,
Tan 30 = 1/√3Here we have
Yoshi swam across a lake but did not know how far he swam.
He found that it was 100√) feet from point A to point C.
Angle C was a right angle and angle A is 30°.
We represent the given scenario in the form of a right angle triangle as shown in the picture.
Let 'B' be the point where Yoshi swam started and BC be the length of the lake.
From the triangle,
Tan A = BC/AC
From the given data,
Tan 30° = BC/100√3
=> BC = Tan 30°(100√3)
=> BC = (1/√3)(100√3)
=> BC = 100 ft
Therefore,
The length of the lake is 100 ft
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Find an equation for the perpendicular bisector of the line segment whose endpoints are (−2 ,− 9) and (−6,7). PLSLLSLS
Answers
The equation of the perpendicular bisector of the line segment joining (-2, -9) and (-6, 7) is y = (-1/4)x - 2
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The midpoint of the line segment joining (-2, -9) and (-6, 7) can be found using the midpoint formula:
Midpoint = ( (x₁+x₁)/2 , (y₁+y₁)/2 )
Midpoint = ( (-2-6)/2 , (-9+7)/2 )
Midpoint = (-4,-1)
Next, we need to find the slope of the line joining the two points (-2, -9) and (-6, 7). We can do this using the slope formula:
Slope = (y₂ - y₁) / (x₂ - x₁)
Slope = (7 - (-9)) / (-6 - (-2))
Slope = 4
The slope of the line perpendicular to the line segment is the negative reciprocal of the slope of the line joining the two points. So the slope of the perpendicular line is -1/4.
Using the point-slope form of a line, the equation of the perpendicular bisector can be written as:
y - y₁ = m(x - x₁), where (x₁, y₁) is the midpoint and m is the slope of the line.
Plugging in the values we found, we get:
y - (-1) = (-1/4)(x - (-4))
y + 1 = (-1/4)(x + 4)
y + 1 = (-1/4)x - 1
y = (-1/4)x - 2
Therefore, the equation of the perpendicular bisector of the line segment joining (-2, -9) and (-6, 7) is y = (-1/4)x - 2.
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Solve the equation for the specified variable.
W = F(r + B), for r
Answers
The required equation in terms of r is r = (W - FB) / F
What is an equation?An equation is a mathematical statement given by connecting two expressions by equal sign.
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
For example: 3x=9y, 67x = 90+39y
Given that an equation W = F(r + B) we need to solve the equation for r,
Therefore, rearranging for r,
W = F(r + B)
Using the distributive law,
W = Fr+FB
Transposing FB to the LHS
Fr = W - FB
Diving the equation by F
r = (W - FB) / F
Hence, the equation in terms of r is r = (W - FB) / F
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The width of a table is 4 2/5
feet. The length of the table is 2 1/5
times as long as its width.
Which equation shows the length of the table?
Please answer ASAP
Answers
The equation that shows the length of the table is length = 11/5 × 22/5
What is a fraction?A fraction can be defined as the part of a whole number, variable or element.
The different types of fractions are;
Proper fractionsImproper fractionsMixed fractionsComplex fractionsSimple fractionsFrom the information given, we have that;
Length = 2 1/5 × Width
Width = 4 2/5 feet
Turn into improper fractions
Width = 22/5 feet
Then, length = 11/5 × 22/5
Hence, the equation is 11/5 × 22/5
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A boy contain 10 balls of which 6 are Red and the rest are White If a ball is pick at random find the probability of Either Red or White Not Red
Answers
Probability of white: 4/10
Write a equation with the slope of 3 and goes through the point (2,5)
Answers
The equation of the line with slope 3 that goes through the point (2, 5) is y = 3x - 1.
What is the slope-point form of the line?
The point-slope form of the equation of a line is given by:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is a point on the line.
Using the given slope of 3 and the point (2, 5), we can substitute into the point-slope form to get:
y - 5 = 3(x - 2)
Expanding the right-hand side:
y - 5 = 3x - 6
Adding 5 to both sides:
y = 3x - 1
Hence, the equation of the line with slope 3 that goes through the point (2, 5) is y = 3x - 1.
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Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 16. Complete parts (a) through (c) below.
Answers
a)The standard deviation is given by σ = sqrt(np(1-p)) = sqrt(24 × 0.75 × 0.25) = 2.12 . b)Significantly low: μ - 2σ = 18 - 2 × 2.12 ≈ 13.76 ,Significantly high: μ + 2σ = 18 + 2 × 2.12 ≈ 22.24 ,c)z = (x - μ) / σ = (3 - 18) / 2.12 ≈ -7.08.
How to calculate standard deviation?A group of 24 peas with green pods has a binomial distribution with n = 24 and p = 0.75. The mean is calculated as = np = 24 0.75 = 18, and the standard deviation is calculated as = sqrt(np(1-p)) = sqrt(24 0.75 0.25) = 2.12 (rounded to two decimal places).
b) The range rule of thumb states that results that deviate from the mean by more than two standard deviations are considered significantly low or significantly high. In this case, the values separating significantly low and significantly high results are:
Significantly reduced: - 2 = 18 - 2 2.12 13.76
Significantly greater: + 2 = 18 + 2 2.12 22.24
c) To see if a result of three peas with green pods is significantly low, we must calculate its z-score, which is given by:
z = (x - μ) / σ = (3 - 18) / 2.12 ≈ -7.08
Because the z-score is much lower than -2, the cutoff for significantly low results, we can conclude that a result of 3 peas with green pods is significantly low.
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Which of the following is an example of a continuous random variable?a. A Bernoulli trial
b. Binomial random variable
c. Normal random variable
d. Discrete uniform random variable
Answers
An example of a continuous random variable is a Normal random variable.
What is a normal random variable?
A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. A random variable can be either discrete (having definite values) or continuous (any value in a continuous range).
Here, we have
We have to determine the example of a continuous random variable.
We concluded that the example of a continuous random variable is a normal random variable.
Hence, an example of a continuous random variable is a Normal random variable.
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Find the indicated outputs for f(x) = 4x - 5x. f(2)=
Answers
Answer:
[tex] \sf \: f(2) = - 2[/tex]
Step-by-step explanation:
Given function,
→ f(x) = 4x - 5x
Now we have to,
→ Find the required value of f(2).
Then the value of f(2) will be,
→ f(x) = 4x - 5x
→ f(2) = 4(2) - 5(2)
→ f(2) = 8 - 10
→ [ f(2) = -2 ]
Hence, the value of f(2) is -2.
(c) 10:35 f the foll ing ratio
Answers
The ratio 10:35 can be simplified to 2:7.
What is a Ratio?
A ratio in mathematics demonstrates how many times one number is present in another.
For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.
Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
The ratio 10:35 can be simplified to 2:7.
To simplify a ratio, you can divide both values by the greatest common factor. In this case, the greatest common factor of 10 and 35 is 5, so 10 divided by 5 is 2, and 35 divided by 5 is 7.
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Simply the following ratio 10:35
Your friend begins to divide the numerator and denominator
12
by 4 and then gets stuck. Explain why your friend gets stuck.
Answers
Answer:
maybe your friend gets stuck because youre not supposed to divide the denominator, only make a common one by multiplying one or both untill they are the same. Least common multiples
Find the value of x that will make L||m
Answers
Answer:
x=-13
Step-by-step explanation:
Since the two angles given are equivalent, you set up the equation as 7x+205=114.
7x+205=114
7x=114-205
7x=-91
7x/7=-91/7
x=-13
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Suppose you bought ares company 4 years ago at a price of $63.00 per share sold it at $71.50 per share. How much money die you make? $37750 $382.50 $387.50 $392.50
Answers
The amount you made per share is $8.50.
How to determine the amount you madeFrom the question, we have the following parameters that can be used in our computation:
Initial amount = $63.00
Final amount = $71.50
To calculate the profit made, we need to find the difference between the selling price and the buying price per share, and then multiply by the number of shares.
The difference in price per share is:
Difference = $71.50 - $63.00
Evaluate the difference
Difference = $8.50
Hence, the profit per share is $8.50.
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Consider the graph of the function f(x)=log4(x-2)+2. What are the domain and the range of function f?
Answers
For the function f(x) = log4(x - 2) + 2, the domain is (2,∞) and range is (-∞,∞).
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The logarithmic function f(x) = log4(x - 2) + 2 is defined only for x-2 > 0, or equivalently, x > 2.
So, the domain of the function is all real numbers greater than 2, or -
Domain: x > 2
Now let's consider the range of the function.
The logarithmic function takes positive values for positive inputs, and it approaches negative infinity as x approaches zero from the right.
Since f(x) = log4(x-2) + 2, the function takes values greater than 2 when x is greater than 4, and it approaches 2 as x approaches 2 from the right.
So, the range of the function is -
Range: -∞ > f(x) > ∞
Therefore, the function has range and domain as (-∞,∞) and (2,∞) respectively.
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Solve the equations for x
Answers
Answer:
Step-by-step explanation:
5=cx-ax=x(c-a)
x(c-a)/5=1
(c-a)/5=1/x
x=5/(c-a)
