The input value x when the output value f( x ) = 4 in the function f( x ) = 5x - 7 is 11/5.
What is the value of x when the output value f(x) = 4?A function is simply a relationship that maps one input to one output, each x-value can only have one y-value.
Given the data in the question;
f( x ) = 5x - 7f(x) = 4x = ?To determine the input value x when the output value f( x ) = 4, replace f( x ) by 4 in the function and solve for x.
f( x ) = 5x - 7
4 = 5x - 7
Collect like terms
4 + 7 = 5x
5x = 11
Divide both sides by 5
5x/5 = 11/5
x = 11/5
Therefore, the input value x is 11/5, this forms an ordered pair of ( 11/5, 4 ).
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4va olleckpoiniDiscrete Mathematics OL v1 A - Koscianski, Megan / Chapter 2: Set TheoryRD 2. Use the accompanying Venn diagram that shows the number of elements in regions I through IV to answer the question.10MHow many elements belong to neither set A nor set B?BU Font FamilyAAIFEEOOOE•"'NE
The elements that are neither in set A nor set B are: {10}
Answer: 10
Find the zeros of the function and state the multiplicities.
k(x)=15x³-48x²-48x
If there is more than one answer, separate them with commas. Select "None" if applicable.
Part: 0/2
Part 1 of 2
Zero(s) of k:
The zeroes of the function k(x)=15x³-48x²-48x are 0, 4 and -4/5.
The function provided is a cubic polynomial.
There will be three zeroes in total for the function k(x).
K(x) = 15x³-48x²-48x
If we put x = 0,
We can see that k(x) becomes zero,
So we can say that 0 is a solutions for this function,
Now,
K(x) = x(15x²-48x-48)
Solving 15x²-48x-48 seperately using quadratic formula,
a = 15
b = -48
c = -48
x = (-b+√D)/D and (-b-√D)/D
D = b²-4ac.
D = (-48)²-4(15)(-48)
D= 5184.
√D = 72
putting all the values to find x,
x = (-(-48)+72)/30 and (-(-48)+72)/30
x = 4 and -4/5.
our function becomes,
k(x) = x(x-4)(x+4/5)
so the zeroes are 0, 4, -4/5.
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the membership for a local zoo is $135. Members do not pay admissions, but they are charged $3 to park. Non-member admission is $25 for the zoo and $5 for the parking. After how many visits have members and non-members paid the same amount?
The members and non-members who pay the equal cost after 5 visits for the local zoo.
What is defined as the term equations?When one variable is determined to be equal to the other, the equation formula method is used to calculate the value of the a second variable.This second variable's value is the value that the others have same value.For the given question;
The cost of membership of local zoo is $135 for members.
The parking cost is $3 for members.
Non-member admission cost is $25 for the zoo and $5 for the parking.
Let the number of number of visits paid the same amount be 'x'.
Then, the equation becomes.
Members: m = 135 + 3x
Non-Members: n = 25x + 5x
As, members and non-members are equal.
m = n
Put the values;
135 + 3x = 25x + 5x
135 + 3x = 30x
27x = 135
x = 5
Thus, members and non-members who pay the equal cost after 5 visits.
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w(x)=0.6x + 2 graph the linear function please I need to answer it soon
The graph of the linear function w(x) = 0.6x+2 has been plotted
The given linear function is
w(x) = 0.6x+2
The domain is the set of all possible inputs of the functions.
The range is the set of all possible outputs of the functions
Here we will substitute some values of x that is the domain of the function and the result will be the range of the function
w(-3) = 0.6×-3+2
= 0.2
w(-2) = 0.6×-2+2
= 0.8
w(-1) = 0.6×-1+2
= 1.4
w(0) = 0.6×0+2
= 2
w(1) = 0.6×1+2
= 2.6
w(2) = 0.6×2+2
= 3.2
w(3) = 0.6×3+2
= 3.8
Plot the graph using the domain and range
Hence, the graph of the linear function w(x) = 0.6x+2 has been plotted
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which point most closely approximates the difference of B and A, that is (B -A) ?
Point (C) C closely approximates the given mathematical operation that is the difference between B and A (B - A).
What are mathematical operations?An operation, also known as an "operand" or "argument," is a function in mathematics that converts zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the operations that are most frequently studied. A constant is an operation of arity zero, also known as a nullary operation. An example of an operation of arity 3, also known as a ternary operation, is the mixed product.So, when we add up 2 numbers let's say A and B, the result is always a 3rd number which is C.
A + B = CSimilarly, when we subtract a number from another number (B - A), the result is always a third number C.
B - A = CSo, (C) C closely approximates the difference between B and A (B - A).
Therefore, point (C) C closely approximates the given mathematical operation that is the difference between B and A (B - A).
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Roger Laut, who lives in Territory 5, carries 10/20/5 compulsory liability insurance along with optional collision that has a $1,000 deductible. Roger was at fault in an accident that caused $4,800 damage to the other car and $8,800 damage to his own car. Also, the courts awarded $19,000 and $9,000, respectively, to the two passengers in the other car for personal injuries. How much does the insurance company pay, and what is Roger’s share of the responsibility?
The insurance company will pay $10000 while Roger's share will be $4800 and therefore he must pay $4,800 in the insurance claim.
How to illustrate the information?From the information, Roger Laut, who lives in Territory 5, carries 10/20/5 compulsory liability insurance along with optional collision that has a $1,000 deductible.
An insurance claim is a formal request for payment for losses protected by your insurance policy. A contract between you and your insurer is known as an insurance policy. You must pay a predetermined premium. With a $5,000 maximum limit on property damage, the insurance provider will pay losses up to $10,000 for one injured or killed person and up to $20,000 for several persons. This slab is for any accident.
Roger's share will be $4800 because the cost of repairing the other car is only expected to be around $4800. He's got $4,800 to pay.
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Which percent is larger 5 , 15 or 20?
Dados los vectores: a = -2i + 2j -k ; b = 3i - j + 2k y c = (-2,3, -1) . a) Determine: (b x a). (a x c) b) Halle el angulo que forman los vectores a y c.
From the given vectors, we have that:
a) The vectorial products are given as follows:
(b x a) = -3i - j + 4z.(a x c) = a x c = 1i - 2z.b) The angle between vectors a and c is of 6.84º.
How to find a vectorial product?A vectorial product between two vectors A and B is found from the determinant of a matrix, in which:
The first line is composed by the coordinates i, j and k.The second line is composed by the elements of vector a.The third line is composed by the elements of vector b.Then for the vectorial product b x a, the matrix is:
[tex]\left[\begin{array}{ccc}i&j&k\\3&-1&2\\-2&2&1\end{array}\right][/tex]
Using a calculator, the determinant, which is the vectorial product, is given by:
b x a = -3i - j + 4z.
For the vectorial product a x c, the matrix is:
[tex]\left[\begin{array}{ccc}i&j&k\\-2&2&-1\\-2&3&-1\end{array}\right][/tex]
a x c = 1i - 2z.
The angle is found as follows:
sin(θ) = |a x c|/(|a| x |c|)
The norms are given as follows:
[tex]|a \times c| = \sqrt{1^2 + (-2)^2} = \sqrt{5}[/tex]. [tex]|a| = \sqrt{(-2)^2 + (2)^2 + (-1)^2} = 3[/tex]. [tex]|c| = \sqrt{(-2)^2 + (3)^2 + (-1)^2} = \sqrt{14}[/tex].Hence:
[tex]\sin{\theta} = \frac{\sqrt{5}}{3\sqrt{14}}[/tex]
[tex]\theta = \sin^{-1}{\left(\frac{\sqrt{5}}{3\sqrt{14}}\right)}[/tex]
θ = 6.84º.
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The difference of three times a number and eight is two more than the number.
Answer:
The number is 5.
Step-by-step explanation:
Let x be the number.
[tex]3x - 8 = x + 2[/tex]
[tex]2x = 10[/tex]
[tex]x = 5[/tex]
Hayden recorded his speed while walking and determined he walked 120 feet in 30 seconds . At this rate how many feet will Hayden walk in 45 seconds
Answer:
180
Step-by-step explanation:
120ft/30sec=4sec per ft
45-30=15
4(15)=60
120+60=180
9583cm=9hm+5dam+8m+3cm
Answer:
a=(9580c-8-9h)/5d
Step-by-step explanation:
9hm+5dam+8m+3cm=9583cm
Subtract (9hm+8m+3cm) from both sides
5dam=9580mc-8m-9mh simplify
then divide both sides by 5dm
a=(9580c-8-9h)/5d
THIS QUESTION IS VERY UNCLEAR SO I JUST SOLVED FOR A
NEED THIS DONE ASAP!!
The ratios of y/x are the same for the graph of y = 3x
and the ratios of y/x are NOT the same for the graph of y = 3x + 4
In this question, we have been given the graphs of lines y = 3x and y = 3x + 4.
Consider the ratios of y/x for the graph y = 3x
6/2 = 3
3/1 = 3
(-6)/(-2) = 3
Consider the ratios of y/x for the graph y = 3x + 4.
7/1 = 7
(1)/(-1) = -1
(-2)/(-2) = 1
We can observe that the ratios of y/x are the same for the graph of y = 3x
and the ratios of y/x are different for the graph of y = 3x + 4.
Therefore, the ratios of y/x are the same for the graph of y = 3x
and the ratios of y/x are NOT the same for the graph of y = 3x + 4
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Luke is driving from Hillwood to Springfield, 926 miles apart from each other. If Luke drives at a constant speed of 57 miles per hour,what equation can we make to find out how much time will like take to get to Springfield? Represent the time in hours as the variable x.
The equation that calculates the time taken to get to Springfield is x = 926/57
What is rate?Rate is used to establish the relationship between two quantities of different units. one of the quantity is usually expressed to unity in order to estimate the change in the other quantity.
If Hillwood and Springfield are 926 mile apart, and the speed taken to get to Springfield is 57miles per hour.
Let the time taken to get to Spring field be x.
Then if 57 miles is covered in an hour and it takes x hours to get to the destination
It means total distance covered is 57 × x
This distance is equal to the distance from Hillwood to Springfield which is 926 miles.
Equating both equations.
57x = 926
In conclusion, 57x = 926 is the equation that can be used to find out the time taken.
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-3(3+ p) <-66=
A) p >1
B) p> -19
C) p< 19
D) p >19
Answer:
D
Step-by-step explanation:
[tex]-3(3+p)<-66 \\ \\ 3+p>22 \\ \\ p>19[/tex]
A local hamburger shop sold a combined total of 449 hamburgers and cheeseburgers on Thursday. There were 51 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Thursday?
Taking into account the definition of a system of linear equations, the local hamburger shop sold 199 hamburgers on Thursday.
System of linear equationsA system of linear equations is a set of equations in which every equation is linear., in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.
This caseIn this case, a system of linear equations must be proposed taking into account that:
"c" is the number of cheeseburgers sold on Thursday."h" is the number of hamburgers sold on Thursday.You know:
A local hamburger shop sold a combined total of 449 hamburgers and cheeseburgers on Thursday. There were 51 fewer cheeseburgers sold than hamburgers.The system of equations to be solved is
h + c= 449
h= c - 51
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, substituting the second equation in the first you get:
c - 51 + c= 449
c+ c= 449 + 51
2c= 500
c= 500÷2
c= 250
Remembering that h= c - 51, you get:
h= 250 - 51
h= 199
Finally, 199 hamburgers were sold on Thursday.
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Solve k over negative 1.6 is greater than negative 5.3 for k.
k > −8.48
k < −6.9
k > −6.9
k < 8.48
The required inequality is k > -8.48. Option A is correct.
Given that,
To determine the equivalent expression to the k / -1.6 > -5.3
What is inequality?
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
As per the given condition, we have to simplify the given expression to get the equivalent expression,
k / -1.6 > -5.3
k > -1.6 (-5.3)
k >- 8.48.
Thus, the required inequality is k > -8.48. Option A is correct.
Let t(x) = gof (x). where g (12) = 6. g(6) =-8, and f(x) = 4x - 6.
What is the value of t(3)?
The composition of functions evaluated in x = 3 is equal to -8.
t(3) = -8.
How to evaluate the composition of functions?Here we have the two functions g(x) and f(x), and the composition:
(g°f)(x) = t(x).
This is equal to:
t(x) = g(f(x))
Then:
t(3) = g( f(3) )
Evaluating f(x) in 3 we get:
f(3) = 4*3- 6 = 12 - 6 = 6
Then:
t(3) = g( f(3)) =g(6)
And we know that g(6) = -8, then:
t(3) = -8.
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Find the equation of a line parallel to 2x-2y=-4 that passes through the
point (3,9).
The line which is parallel to 2x-2y=-4 that passes through the
point (3,9) is x-y = -6.
Given that, 2x-2y = -4 passes through the point (3,9) then we have to find the equation of a line which is parallel to the given equation of line.
Let's proceed to find the equation of the line.
The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).
Using the slope-intercept formula, the equation of the line is:
y = mx + b
where,
m = the slope of the line
b = y-intercept of the line
(x, y) represent every point on the line
x and y have to be kept as the variables while applying the above formula.
2x-2y = -4
-2y = -4-2x
y = -4/-2 - 2x/-2
y = 2+x
y = x+2
On comparing with y = mx+b
m = 1 and b = 2
As the lines are parallel then the slope of other line will also be same i.e., m = 1
The point from which it is passes is (3,9)
⇒ x₁ = 3 and y₁ = 9
y-y₁ = m(x-x₁)
⇒ y-9 = 1(x-3)
⇒ y-9 = x-3
⇒ y = x-3+9
⇒ y = x+6
⇒ x-y = -6
Therefore, the line which is parallel to 2x-2y=-4 that passes through the
point (3,9) is x-y = -6.
Hence, x-y = -6 is the required answer.
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Trigonometric functions using the ratio of two sides of a triangle can be used to solve ______ triangles.
A. acute
B.obtuse
C.oblique
D.right
Trigonometric functions using the ratio of two sides of a triangle can be used to solve D.right triangles.
How to solve right triangles?To solve for a missing side of a right angle, one can use trigonometric functions that will use the ratio of the other two known sides of the triangle in question.
For instance, using the trigonometric function of Sin can allow for the use of the opposite side and the hypotenuse to find the adjacent side. The Cos and Tan can also be used for the other sides.
This means that either of two sides (including the hypotenuse) can be used to find the other.
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I need help on this one:)
iven: ²
equired:
xplanation:
Since the graph is translated vertically downwards by 3 units, so the function f(x) is
[tex]\begin{gathered} f(x)=h(x)-3 \\ f(x)=3x^2-6-3 \end{gathered}[/tex]Hence, the function is
[tex]f(x)=3x^2-9[/tex]inal Answer
[tex]f(x)=3x^2-9[/tex]Which of the following quantities are directly proportional? (Answer if they are directly proportional or not) PLS HELP ASAP
A) distance and time traveled if speed is a constant 77 mph
B) speed and time if the distance traveled is 110 miles
C) the price per item and the number of items bought if the amount of money spent is constant
The only quantities that will be directly proportional are; A) distance and time traveled if speed is a constant 77 mph
Which Quantities are Directly Proportional?
Direct proportionality means the change of a similar kind.
For example, as pressure increases, density also increases, which means both the parameters (pressure and density) are experiencing a similar kind of change i.e. increment in their magnitude.
Looking at the given options;
A) Distance and time traveled if speed is a constant 77 mph.
Now, formula for speed is;
Speed = Distance/Time
Thus, if speed is constant, then it means that distance varies directly with the time because as distance increases, then time also increases.
B) We are told that the distance traveled is 110 miles.
Distance = Speed * time.
Thus, speed and time vary indirectly with the time because as one increases, the other decreases
C) Since the amount of money spent is constant, then it means that;
Amount spent = Price per item * number of items
The price per item and the number of items bought will vary indirectly
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A die is a rolled. the set of equally likely outcomes is {1,2,3,4,5,6} find the probability of getting a 3
Answer:
1/6th chance
Step-by-step explanation:
Since there are 6 possible outcomes that will be the denominator, now count the number you want to roll, in this case 1 since you only want to find the probably of getting a 3. So the probably is 1/6
A company is going to make a water tank in the shape of a cylinder. As shown below, the tank will have a height of 3ft and a diameter of 8ft. The tank will be made from metal (including its top and bottom). If the metal costs $29 for each square foot, how much will the metal cost in total?
The total cost of the metal needed to cover the tank shaped like a metal is $5,099.36.
What is the total cost?In order to determine the total metal cost, we are to first calculate the total surface area of the tank. Since the tank is a closed cylinder, we are to determine the total surface area of a cylinder.
The total surface area of a closed cylinder can be determined by adding the area of all its faces.
Total surface area of the closed cylinder = 2πr(r + h)
Where:
r = radius = diameter / 2 = 8/2 = 4ft
h = height
π = pi = 3.14
(2 x 3.14 x 4)(4 + 3)
25.12 x 7 = 175.84 ft²
Total cost of the metal = $29 x 175.84 = $5,099.36
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Triangle side splitter theorem question
Applying the side splitter theorem
we have that
PT/TS=PQ/QR
so
substitute the given values
7/21=PQ/27
solve for PQ
PQ=27*7/21
PQ=9
Find the value of PR
PR=PQ+QR
PR=9+27
PR=364. Leila just graduated from college and is comparing a few different cities to move to. Which of these factors is the LEAST important thing for her to consider right now?
The factor that is the least important thing for Lelia to consider right now is D. Average cost of Uber, Lyft, or taxi fare.
How to illustrate the information?It should be noted that Leila just graduated from college and is comparing a few different cities to move to.
It's important for her to consider the average rent for an apartment, food and grocery store options in the area, and employment opportunities.
In this case, the. oat of Uber isn't necessary. The correct option is D.
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Leila just graduated from college and is comparing a few different cities to move to. Which of these factors is the LEAST important thing for her to consider right now?
Average rent for an apartment
Food and grocery store options in the area
Employment opportunities
Average cost of Uber, Lyft, or taxi fare
2 3/16 divided by 3 3/4
The answer to your question is =
0.583333333
I believe the answer is 0.58333333333. I think it would be 0.583 if you rounded it up. Hope this helps:)
Graph the function y= |x| +3 Use a table of values giving some values for x like -4,-3,-2,-1,0,1,2,3,4 . Then graph the points and complete the graph. Use arrowheads when applicable. Is it a function? Find domain and range.
The function y =|x|+3 has been plotted in the graph and
Domain = {-4, -3, -2, -1, 0, 1, 2, 3, 4}
Range = {7,6,5,4,3}
The function y =|x|+3
The some values of x = -4, -3, -2, -1, 0, 1, 2, 3 and 4
Substitute the values in the function
y=|-4|+3 =7
y=|-3|+3 = 6
y=|-2|+3 = 5
y=|-1|+3 = 4
y=|0|+3 = 3
y=|1|+3 = 4
y=|2|+3 =5
y=|3|+3 = 6
y=|4|+3 = 7
Using the values complete the graph
The domain is the set of all possible inputs of the function
Domain = {-4, -3, -2, -1, 0, 1, 2, 3, 4}
The range is the set of all possible outputs of the function
Range = {7,6,5,4,3}
Hence, the function y =|x|+3 has been plotted in the graph and, the Domain = {-4, -3, -2, -1, 0, 1, 2, 3, 4}
Range = {7,6,5,4,3}
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a national caterer determined that 87% of the people who sampled their food said it was delicious. A random sample of 144 people is obtained from a population of 5,000. The 144 people are asked to sample the caterer's food. Will the distribution of p hat, the sample proportion saying that the food is delicious, be approximately normal?
The sample proportion saying that the food is delicious will be approximately normal.
In this question, we have been given that 87% of the people who sampled their food said that it was delicious
so, the Population proportion = 87%
A random sample of 144 people is obtained from a population of 5,000. The 144 people are asked to sample the caterer's food.
The sample size of 144 from 5000 will have proportion p cap which will follow a normal distribution with mean= p = 87%
and variance = npq
Since the mean of the sampling distribution of p hat, mean is 0.87 the sample proportion saying that the food is delicious will be approximately normal.
Therefore, the sample proportion saying that the food is delicious will be approximately normal.
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hi i have a question
Given the sample table below:
Total number of teenagers that get less than 8 hours of sleep each school night
Sample #1:
The number of teenagers that get less than 8 hours of sleep each night include the sum of teenagers that get less than 4 hours, teenagers that get between 4 and 6 hours, teenagers that get between 6 and 8 hours.
Thus, we have
[tex]2+9+39=50\text{ t}eenagers[/tex]Sample #2:
Thus, we have
[tex]1+12+34=47\text{ te}enagers[/tex]Percentage of teenagers that get between 4 and 10 hours of sleep each school night
ample #1:
The total number of teenagers that get between 4 and 10 hours of sleep is evaluated to be
[tex]9+39+44=92\text{ te}enagers[/tex]Thus, the percentage becomes
[tex]\frac{92}{100}\times100\text{ = 90\%}[/tex]Sample #2:
[tex]12+34+48=94\text{ te}enagers[/tex][tex]\frac{94}{100}\times100=94\text{ \%}[/tex]Hence, based on the result of the survey,
About half of the teenagers get less than 8 hours of sleep each school night,
More than 90% of teenagers get between 4 and 10 hours of sleep each school night.
Write the slope intercept form for the points through (-4,-5) and (0,2)
Answer:
y = (7/4)x + 2
Step-by-step explanation:
(-4, -5) and (0, 2)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 2 - (-5) 2 + 5 7
m = ------------- = ------------- = ------------- = --------
x₂ - x₁ 0 - (-4) 0 + 4 4
(it doesn't matter which points you put)
y - y₁ = m(x - x₁)
y - 2 = (7/4)(x - 0)
y - 2 = (7/4)x - 0
+2 +2
----------------------------
y = (7/4)x + 2
I hope this helps!