An equation for a linear function is, [tex]h(x)[/tex] = 56[tex]x[/tex] - 63 where h(7)=329 and h(11)=553.
Given that,
h(7)=329 and h(11)=553
Linear function, y = [tex]mx + c[/tex]
Let, h = y and [tex]x =x[/tex]
Define Linear function :A function whose graph is a straight line and which is represented by an equation of the form y = mx + c where a and b are constants, m does not equal zero, and x is any real number.
The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y).
So,
[tex]h(x)[/tex] = [tex]mx + c[/tex]
When,
[tex]x[/tex] = 7 , [tex]h(x)[/tex] = 329
( [tex]x_{1}[/tex] , [tex]h(x_{1} )[/tex] ) = ( 7 , 329 ) (Equation-1)
When,
[tex]x[/tex] = 11 , [tex]h(x)[/tex] = 553
( [tex]x_{2}[/tex] , [tex]h(x_{2} )[/tex] ) = ( 11 , 553 ) (Equation-2)
Linear function,
[tex]\frac{h(x)-h(x_{1} )}{x-x_{1} }[/tex] = [tex]\frac{h(x_{2} )-h(x_{1} )}{x_{2} -x_{1} }[/tex]
We can substitute equation -1 and 2
[tex]\frac{h(x)-329}{x-7}[/tex] = [tex]\frac{553-329}{11-7}[/tex]
[tex]\frac{h(x)-329}{x-7}[/tex] = 224/4
[tex]\frac{h(x)-329}{x-7}[/tex] = 56
[tex]h(x)[/tex] - 329 = 56 ( [tex]x-7[/tex] )
[tex]h(x)[/tex] - 329 = 56[tex]x[/tex] - 392
[tex]h(x)[/tex] = 56[tex]x[/tex] - 392 + 329
[tex]h(x)[/tex] = 56[tex]x[/tex] - 63
Therefore,
An equation for a linear function is, [tex]h(x)[/tex] = 56[tex]x[/tex] - 63 where h(7)=329 and h(11)=553.
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(3,b) is the midpoint of (a,1) and (b,-a) find a and b
Answer:
Step-by-step explanation:
MidpointofAB=x1+x22,y1+y22
Midpoint=5−32,−1+52=(1,2)
Write an
graph:
equation for the following
Answer:
y=-(2/3)x-1
Step-by-step explanation:
y=kx+n
n= -1
k = (y2-y1)/(x2-x1) = -2 / 3 = -2/3
y=-(2/3)x-1
Consider the function
f(x) = (a^T.x)(b^T.x).
where a b and x are n dimensional vectors
a. find f(x),
b. find the hessian H(x)
c. is the function f(x) a quadratic from x^T.Qx? if yes, what is the symmetric Q?
The value of f(x) = ∑_{i=1}ⁿ ∑_{j=1}ⁿ a_ib_jx_ix_j, the hessian H(x) is [tex]a.b^{T}[/tex], and f(x) is a quadratic form, and the symmetric matrix Q is [tex]a.b^{T}[/tex].
a. The function f(x) is defined as the product of two dot products,
f(x) = ([tex]a^{T}[/tex].x)([tex]b^{T}[/tex].x) = (∑_{i=1}ⁿ a_ix_i)(∑_{j=1}ⁿ b_jx_j) = ∑_{i=1}ⁿ ∑_{j=1}ⁿ a_ib_jx_ix_j
b. To find the Hessian H(x), we need to find the second partial derivative of f(x) with respect to x. Let's define H(x) as
H(x) = [∂^2f(x)/∂x_i∂x_j] = [∂/∂x_i(∂f(x)/∂x_j)]
Since f(x) = ∑_{i=1}ⁿ ∑_{j=1}ⁿ a_ib_jx_ix_j, the first partial derivative of f(x) with respect to x_j is
∂f(x)/∂x_j = ∑_{i=1}ⁿ a_ib_jx_i = [tex]b_{j}^{T}[/tex].a.x
The second partial derivative of f(x) with respect to x_i and x_j is
∂^2f(x)/∂x_i∂x_j = ∂/∂x_i([tex]b_{j}^{T}[/tex].a.x) = a_ib_j
So, the Hessian H(x) is
H(x) = [a_ib_j] = [tex]a.b^{T}[/tex]
c. To determine if f(x) is a quadratic form, we need to find the symmetric matrix Q such that f(x) = [tex]x^{T}[/tex].Qx.
Let's define Q = [tex]a.b^{T}[/tex].
Then, f(x) can be written as
f(x) = [tex]x^{T}[/tex].Qx = ([tex]a.b^{T}[/tex]).x.[tex]x^{T}[/tex] = [tex]x^{T}[/tex].([tex]a.b^{T}[/tex]).x = [tex]x^{T}[/tex].([tex]a.b^{T}[/tex]).x = [tex]x^{T}[/tex].Qx
So, f(x) is a quadratic form, and the symmetric matrix Q is [tex]a.b^{T}[/tex].
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Please help thank you
Answer:x=4 y=6.66666666667
Step-by-step explanation:
5. 3x = 6. 40x how many time do I need to multiply thee number for them to be the ame
The equation 3x = 6.4 can be solved for x by dividing both sides of the equation by 3: 3x/3 = 6.4/3; x = 2.13
So, for 3x and 6.4x to be equal, x must be equal to 2.13. This means that you need to multiply the number 6.4 by 2.13 to equal 3. The equation 3x = 6.4 represents the relationship between two variables, x and 3x. We are trying to find the value of x that would make 3x equal to 6.4. To do this, we divide both sides of the equation by 3. Dividing both sides of an equation by the same number does not change the relationship between the variables; it only scales down the variable's value by the same factor.
So, by dividing both sides of the equation by 3, we get:
3x/3 = 6.4/3
x = 2.13
Finally, to make 6.4x equal to 3, we need to divide 6.4 by 2.13: 6.4 / 2.13 = 3. So, we need to multiply 6.4 by 2.13 to equal 3.
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Points (1,-1), (3,2), and (7,-3) are three vertices of a parellelogram. How many parallelograms can be created using these three vertices?
One
Two
Three
Four
Answer:
One
Step-by-step explanation:
You can see this easily if you plot the three points on a graph and plot the fourth point using the fact that the sides of a parallelogram are of equal length.
Figure provided
fourth vertex D has coordinates (9,0)
We obtain this by noting that the x and y distances between A and B are
(3-1, 2-(-1) = 3, 2
= (2, 3)
Add these same dimensions to C to get point D
D = (7 +2, -3 + 3) = (9 , 0)
Only one such vertex exists which will cover the other three points
Help solve this as SIMPLY as you can, please. There are two parts.
16 A and 16 B.
Answer:
16A.) C
16B.) x=6; the students each paid $6 for their concert tickets.
Step-by-step explanation:
[Note: I know that this answer is lengthy, but the explanation is very simple and is worth reading]
16A.)
First, let's "figure out" the amount of money spent by the students. Each student paid $x for a ticket and $4 on parking. That means that the cost for one student would be $x + $4. To figure out how much it would cost 12 students, we can take the amount it costs 1 student and multiply it by 12. Again, since x + 4 is the cost for 1 student, 12( x + 4 ) would be the cost of 12 students. Next, let's figure out how much the adults paid for their tickets.
Now, let's find the cost the adults paid for the ticket. If the students paid $x and the adults paid four times as much for each of their tickets, then the cost of the ticket for the adults must have been $4x. Now, we know each adult paid $4x for a ticket and $6 on parking. That means that the cost for one adult would be $4x + $6. To figure out how much it would cost 4 adult , we can take the amount it costs 1 adult and multiply it by 4. Again, since 4x + 6 is the cost for 1 adult, 4( 4x + 6 ) would be the cost of 4 adults.
Since the 12 students paid 12(x+4) dollars for the concert and the 4 adults paid 4(4x+6) and since we know they spent the same amount of money, we can set 12(x+4) and 4(4x+6) equal to each other. This gives us the answer 12(x+4)=4(4x+6), or C, for question 16A.
16B.)
To solve the equation 12(x+4)=4(4x+6) means to solve for x. So, let's solve for x:
12 ( x + 4 ) = 4 ( 4x + 6 ) [Distribute the 12 on the left side]
12x + 48 = 4 ( 4x + 6 ) [Distribute the 4 on the right side]
12x + 48 = 16x + 24 [Subtract 12x from both sides]
48 = 4x + 24 [Subtract 24 from both sides]
24 = 4x [Divide both sides by 4 to get the value of x]
6 = x
Now, for the second half of the question, what does x=6 mean? Well, if we look at the previous problem, x was the amount of money spent by the students for the concert ticket. So, the answer x=6 tells us that the students paid $6 for their concert tickets.
[Note: They didn't ask for the price of the adults' tickets, but if they did, we would have plugged in x=6 into the equation 4x to find that the cost of the adults' tickets were $24.]
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The intruction booklet for a cd player ay that the player ue about 0. 2 of electricity per hour if electricity cot 0. 30 per hour hour how much doe it cot to run a player for an hour
If the instruction booklet for a CD player says that player uses 0.2 kilowatt of electricity per hour and electricity costs $0.30 per kilowatt hour, then the cost to run the player for an hour is $0.06 .
The cost of running a CD player for an hour can be calculated by multiplying (the amount of electricity it uses) by (the cost per kilowatt hour) .
According to the instruction booklet, the player uses 0.2 kilowatt of electricity per hour.
So, if electricity costs $0.30 per kilowatt hour, then
it would cost ⇒ 0.2 × $0.30 = $0.06 .
Therefore , it will take $0.06 to run the player for an hour.
The instruction booklet for a CD player says that player uses 0.2 kilowatt of electricity per hour. If electricity costs $0.30 per kilowatt hour, how much does it cost to run the player for an hour ?
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GEOMETRY!!!!!!
Triangles ACD and BCD are isosceles. Angle BAC has a measure of 18 degrees and angle BDC has a measure of 48 degrees. Find the measure of Angle ABD.
What is the measure of angle ABD?
_______
a 2016 national public radio report described a study comparing patients who had their first ever traumatic brain injury 18 months earlier with similar healthy individuals with no prior brain trauma. The news report states that, 18 months after their traumatic brain injury, the patients "were still getting, on average, an hour more sleep each night than similar healthy people were getting. And despite the extra sleep, 67 percent showed signs of excessive daytime sleepiness. Only 19% of healthy people had that problem.
a) Identify the individuals in the study.
b) identify the variables recorded and whether they are categorical or quantitative.
The individuals in the study are those who had their first ever traumatic brain injury 18 months earlier and similar healthy individuals with no prior brain trauma. The variables recorded are sleep duration (quantitative) and signs of excessive daytime sleepiness (categorical).
a) The individuals in the study are patients who had their first ever traumatic brain injury 18 months earlier and similar healthy individuals with no prior brain trauma.
b) The variables recorded are sleep duration (quantitative) and signs of excessive daytime sleepiness (categorical).
a) The individuals in the study are those who had their first ever traumatic brain injury 18 months earlier and similar healthy individuals with no prior brain trauma.
b) The variables recorded are sleep duration (quantitative) and signs of excessive daytime sleepiness (categorical). Quantitative variables are those that measure a numerical value, such as sleep duration, while categorical variables are those that measure a characteristic or attribute, such as signs of excessive daytime sleepiness.
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In 1980, the population of Kentucky wa 3. 7 million. If the population grow 23% every decade, what i the population in 2010?
The population of Kentucky in 2010 is 6.3 millions
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
1st data = 19802nd data = 20101st data population = 3.7 million% growth = 23%2nd data population = ?Calculating how many decades have been passed from 1980 to 2010:
1 decade is equal to 10 year
Decades = (2010 - 1980)years * 1 decade / 10 years
Decades = 30/10
Decades = 3 decades
Calculating how much the population have grown:
Growth = 3.7 million * 23/100 * 3 decades
Growth = 2.6 million
Calculating the population in 2010:
2010 population = 3.7 + 2.6
2010 population = 6.3 millions
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ulia examines the two triangles below and determines that Triangle F G H is similar to triangle L N M. Triangle F G H. Angle F is 98.6 degrees and angle G is 61.1 degrees. Triangle L N M. Angle M is 18.3 degrees and angle L is 98.6 degrees. Which best describes the accuracy of Julia’s solution? Accurate. The triangles are similar and the congruent angles are listed in corresponding order. Inaccurate. The triangles are not similar because the sum of the angles in each triangle is not 180º. Inaccurate. The triangles are similar, but the triangles are named incorrectly. The vertices are listed out of corresponding order. Inaccurate. The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G. Mark this and return
The solution is Option D.
The triangles are not similar because angle M is not congruent to angle H, and angle N is not congruent to angle G
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ΔFGH
Now , the measure of ∠F = 98.6
The measure of ∠G = 61.1
So , the measure of ∠H = 180° - ( ∠F + ∠G ) ( sum of internal angles = 180° )
On simplifying the equation , we get
The measure of ∠H = 20.3
And ,
Let the second triangle be represented as ΔLMN
Now , the measure of ∠L = 98.6
The measure of ∠M = 18.3
So , the measure of ∠N = 180° - ( ∠L + ∠M ) ( sum of internal angles = 180° )
On simplifying the equation , we get
The measure of ∠N = 63.1
So , from the similar triangle theorem ,
The angle M is not congruent to angle H, and angle N is not congruent to angle G
Hence , the triangles are not similar
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If x and y are in direct proportion and y is 15 when x is 5, find y when x is 4.
Answer: 25
Step-by-step explanation:
y:x = 15:3 = 5:1
If x is 5, then y = 25
i really do need help with this
On applying the supplementary angle rule, the value for x is obtained as 10°, and the angle 7x° is obtained as 70°.
What is a supplementary angle?
The definition of "supplementary" in mathematics relates to angles that combine to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles.
The line segment is given which has a ray diving the line segment.
Since it is a straight line, the total angle on it will be 180°.
The two angles given are 110° and 7x°.
Apply the supplementary angle rule =
On a straight line sum of two angles = 180°
Substitute the values in the equation -
110° + 7x° = 180°
Collect the like terms -
7x° = 180° - 110°
Apply the arithmetic operation of subtraction -
7x° = 70°
Apply the arithmetic operation of division -
x = 70/7
x = 10°
Now the angle 7x° = 7(10°) = 70°
Therefore, the angle value is obtained as 70°.
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katherine spent of her hike going uphill. if she spent hour and minutes hiking uphill, how many hours long was her hike?
Katherine spent 1 hour and 42 minutes hiking uphill, so her hike would be approximately 2.3 hours long.
To calculate how many hours Katherine spent on her hike going uphill, we can use the following steps:
Calculate the total number of minutes Katherine spent hiking uphill by multiplying the number of hours (1) by the number of minutes in an hour (60): 1 * 60 = 60 minutes.Divide the total number of minutes (60) by the number of minutes in an hour (60) to calculate the total number of hours: 60 / 60 = 1 hour.Add the number of hours spent hiking uphill (1) to the total number of hours Katherine spent on her hike (1) to get the total number of hours her hike was: 1 + 1 = 2 hours.Learn more about mathematics:
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assuming you have the following data values (6, 1, 3, 7, 2), what is the min-max normalized value for 4.
The min-max normalization formula, the normalized value for 4 is (4-1)/(7-1) = 0.5.
The min-max normalization formula is (x-min)/(max-min). To calculate the min-max normalized value for 4 we need to first calculate the min and max of the given datavalues. The min is 1 and the max is 7. Therefore, using the min-max normalization formula, the normalized value for 4 is (4-1)/(7-1) = 0.5. Min-max normalization is used to scale values in a dataset to a range between 0 and 1. Min-max normalization is a technique used to scale numeric values between 0 and 1. It is useful for data normalization, which helps to bring all the values within a given range. For example, if the data set contains values ranging from 0 to 10, min-max normalization can be used to scale the values between 0 and 1. The formula for min-max normalization is (x - min) / (max - min), where x is the value to be normalized, min is the minimum value in the data set, and max is the maximum value in the data set.This technique ensures that all values in a dataset are scaled to the same range. It is useful when comparing values from different datasets that have different scales.
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Answer pls! Limited time! Lots of points for the correct answer! Question down below.
The possible pair of a and b are; (-2, 2)
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
Given that 2.(2x+a) (3x+b) is the same as the product of polynomials 3.(x-1)-(4x+1)
2.(2x+a) (3x+b) = 3.(x-1)(4x+1)
(4x + 2a)(6x + 2b) = (3x-3)(12x+ 3)
Let multiply by 3 then
3(4x + 2a)(6x + 2b)
= (12x + 6a)(18x + 6b)
Multilpy by 4 on left side;
(12x- 12)(48x+ 12)
So, (12x + 6a) = (12x- 12)
6a = -12
a = -2
Now, (18x + 6b) = (48x+ 12)
b = 2
The pair of a and b could be (-2, 2)
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how many sheets of 8.5 * 11 digital cover stock will it take to print 5000 postcards that are 4 1/4 * 5 1/2
Answer:
hhhjhj
Step-by-step explanation:
Write an equation of the altitude from vertex A.
Answer:
Below
Step-by-step explanation:
Not sure this is the easiest way
line BC equation is y = - 2/9x + 3 7/9
perpindicular line that includes point A (2,1) has slope 9/2
point slope form would be
y-1 = 9/2(x-2) re-arranged to y = mx+b form
y = 9/2 x -8
to find the actual altitude , these two lines intersect.....equate them
-2/9x + 3 7/9 = 9/2 x- 8
11 7/9 = 4 13/18 x
x = 2 42/85 then y = 3 19/85
altitude then (using distance formula)
a^2 = (2 42/85 -2)^2 + (1- 3 19/85)^2
a = 2.278 units
I hope this answered the question....I am not sure what 'the equation of the altitude' means
The equation of the altitude of the triangle is y = ( 9/2 )x - 8
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be B ( -1 , 4 )
Let the second point be C ( 8 , 2 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope m = ( 4 - 2 ) / ( -1 - 8 )
m = -2/9
Now , the slope of the altitude is m₂ = 9/2 ( perpendicular lines have negative reciprocal slope )
And , the altitude passes through the point A ( 2 , 1 )
So , the equation of line is y - y₁ = m ( x - x₁ )
y - 1 = ( 9/2 ) ( x - 2 )
y - 1 = ( 9/2 )x - 9
Adding 1 on both sides , we get
y = ( 9/2 )x - 8
Hence , the equation of line is y = ( 9/2 )x - 8
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Ms. Wu runs a house cleaning business. To save money, she bought a 1-gallon container of concentrated cleaner. She mixed the cleaner with 10 gallons of water. Then, she filled as many 1-pint spray bottles as she could. How many spray bottles did she fill?
She had filled 88 spray pint bottles.
What are algebraic expressions?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.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Ms. Wu runs a house cleaning business. To save money, she bought a 1 gallon container of concentrated cleaner. She mixed the cleaner with 10 gallons of water. Then, she filled as many 1 - pint spray bottles as she could.
1 pint = 0.125 gallons
Total amount = 11 gallons.
The total number of bottles that can be filled are -
n = 11/0.125
n = 88
Therefore, she had filled 88 spray pint bottles.
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40% of an hour
pls helpppp
Answer:
24 Minuets
Step-by-step explanation:
Answer:
24 minutes
Step-by-step explanation:
What do I put in the boxes
The function f(x) = x^5 + (x + 3)^2 is used to create this table. Which value completes the table?
If the function f(x) = x⁵ + (x + 3)² will be 3 then x = -1.
What is meant by function?The graph is a function if any vertical line drawn through it can cross it at most one point. The graph is not a function if it has any locations where a vertical line can pass through the graph at two or more different places.
A mathematical function from a set X to a set Y assigns exactly one element of Y to each element of X. The function's domain and codomain, respectively, are the sets X and Y as a whole. Initially, functions represented the desired relationship between two fluctuating values.
A function is a relation that specifically links members of one set to those of another set. Formally speaking, a function from to is an object such that each is specifically connected with an object. Therefore, a function is a many-to-one (or occasionally, a one-to-one) relation.
Let the given function be f(x) = x⁵ + (x + 3)²
When x = -1 then f(-1) = (-1)⁵ + (-1+3)² = -1 + 4 = 3.
Therefore, the function f(x) = x⁵ + (x + 3)² will be 3 then x = -1.
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students who had a low level of mathematical anxiety were taught using the traditional expository method. these students obtained a mean score of 450 with a standard deviation of 30 on a standardized test. the test scores follow a normal distribution. a. what percentage of scores would you expect to be less than 390?
If the test scores follow a normal distribution, then you would expect approximately 16 percent of the scores to be less than 390. This can be calculated using the cumulative normal distribution formula.
Calculating the percentage of scores that would be less than 390 using the cumulative normal distribution formula involves determining the area under the normal curve for the desired range.
In this case, the area under the normal curve from minus infinity to 390 would need to be calculated. This can be done using a scientific calculator or a statistical software program. The result will be the proportion of the scores that are less than 390. This proportion can then be converted to a percentage to determine what percentage of scores would be expected to be less than 390.
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Mark's model train can go 1/3 laps around its track in 2 mins. If it runs at the same speed,
1. How many laps can the train go in 9 mins?
2. Rate needed?
3. Unit rate?
4 Interpretation of unit rate?
In 9 mins Mark's model train can go 1.5 laps and unit rate is 1/6 laps per minute.
What is the average rate of change?It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
Given, Mark's model train can go 1/3 laps around its track in 2 mins. If it runs at the same speed,
Since,
In 2 mins Mark's model train can go = 1/3 laps
Thus,
In 1 min Mark's model train can go = 1/3/2 laps
In 1 min Mark's model train can go = 1/6 laps
In 9 mins Mark's model train can go = 9/6 laps
In 9 mins Mark's model train can go = 1.5 laps
Therefore, In 9 mins Mark's model train can go 1.5 laps and unit rate is 1/6 laps per minute.
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cual es el área bajo la curva normal entre 840 y 1200
The area under the normal curve between 840 and 1200 is calculated by subtracting the cumulative distribution function (CDF) at 840 and 1200.
The area under the normal curve between 840 and 1200 is calculated using the cumulative distribution function (CDF). The formula for the CDF is
F(x) = 1/2[1 + erf((x-μ)/σ(2)^1/2)]
where μ is the mean and σ is the standard deviation.
To calculate the area between 840 and 1200, we first calculate the CDF at 840 and 1200.
F(840) = 1/2[1 + erf((840-μ)/σ(2)^1/2)]
F(1200) = 1/2[1 + erf((1200-μ)/σ(2)^1/2)]
We then subtract the two values to get the area between 840 and 1200. Area = F(1200) - F(840)
This gives us the area under the normal curve between 840 and 1200.
The area under the normal curve between 840 and 1200 is calculated by subtracting the cumulative distribution function (CDF) at 840 and 1200.
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Solving the following Logarithmic Equation:-
[tex]\mathrm{log_2(x+5)=log_2(1-5x)}[/tex]
The solution to the logarithmic equation log₂( x + 5 ) = log₂( 1 - 5x ) is x = -2/3.
What is the solution to the given Logarithmic Equation?Given the equation in the question;
log₂( x + 5 ) = log₂( 1 - 5x )
Note that, for the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.
Hence,
x + 5 = 1 - 5x
Solve for x
Move all terms containing x to the left side of the equation.
x + 5 + 5x = 1 - 5x + 5x
x + 5 + 5x = 1
Subtract 5 from both sides
x + 5 - 5 + 5x = 1 - 5
x + 5x = 1 - 5
6x = -4
x = -4/6
x = -2/3
Therefore, the value of x is -2/3.
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Is (-2, 1) a solution of the following system of equations?
2x + y = -3
y = 2x + 5
A) yes
B
no
Answer: A; Yes
Step-by-step explanation:
Plug in the ordered pair into the equation: 2(-2) + (1) = -3
Solve: -4 + 1 = -3
-3 = 3 ; (-2, 1) is a solution for 2x + y = -3
Now, repeat the same process for the second equation:
(1) = 2(-2) + 5
1 = -4 + 5
1 = 1 ; (-2, 1) is a solution for y = 2x + 5
a deck of cards contains 52 different cards. for each of the following situations, give the number of equally likely outcomes (note: not probabilities.)
A deck of cards contains 52 different cards is 52 = 52 P1
What is Probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
a) as there are 52 cards ; and selecting one card from 52 = 52P1 equally likely outcome
b)for order matters ; number of ways =52 P2
=52*51
=2652
c) for order not matter ; number of ways =52 C3
=22100
d) this is similar to problem 2 of having 2 cards from deck ; number of ways =52 P2
=52*51
=2652
e) if order matters ;number of ways =52*52
=2704
52 distinct cards make to a deck of cards, hence 52 = 52 P1
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Use the figure. 8 ft Find the area. Use Enter the correct answer in the boxes.for T. ft 2
The area of the circle is 201 1 / 7 ft square.
How to find the area of a circle?The figure above is a circle. The radius of the circle is 8 feet. The area of the circle can be found as follows:
area of the circle = πr²
where
r = radius of the circleπ = 22 / 7Therefore, let's find the area of the circle as follows:
area of the circle = πr²
π = 22 / 7
r = 8 ft
Hence,
area of the circle = 22 / 7 × 8²
area of the circle = 22 / 7 × 64
area of the circle = 1408 / 7
Therefore,
area of the circle = 201 1 / 7 ft²
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