Answer:
Both the equation and its inverse are functions.
Step-by-step explanation:
A function is relation in which one input gives one and only one output.
Here, the given function,
[tex]f(x)=5x+1[/tex]
Which is a polynomial,
A polynomial is a function because for each input value it gives only one output value.
⇒ f(x) is a function.
Now, For finding the inverse of f(x),
Replace f(x) by y,
y = 5x + 1
Switch x and y,
x = 5y + 1
Isolate y on the left side,
-5y = 1 - x
[tex]y = \frac{1-x}{-5}=\frac{x-1}{5}[/tex]
Replace y by [tex]f^{-1}(x)[/tex],
[tex]f^{-1}(x)=\frac{x-1}{5}[/tex]
Which is also a polynomial,
Hence, the inverse of f(x) is also a function,
Last option is correct.
A store is having a sale on chocolate chips and walnuts. For
5
pounds of chocolate chips and
2
pounds of walnuts, the total cost is
$10
. For
3
pounds of chocolate chips and
8
pounds of walnuts, the total cost is
$23
. Find the cost for each pound of chocolate chips and each pound of walnuts.
Represent the following sentence as an algebraic expression, where "a number" is the letter x.
You do not need to simplify. The quotient of 2 and the sum of a number and 1.
The sentence 'The quotient of 2 and the sum of a number and 1' can be represented as an algebraic expression 2 / (x + 1).
Explanation:To convert the given statement into an algebraic expression, let's first identify the components of the statement. 'A number' is represented as x. 'The sum of a number and 1' can be written as (x + 1). 'The quotient of 2 and...' signifies division by 2.
Therefore, based on the above definitions, we can represent 'The quotient of 2 and the sum of a number and 1' as 2 / (x + 1).
Learn more about Algebraic expression here:https://brainly.com/question/953809
#SPJ12
Figure TQRS ~ BCDE. What are the pairs of congruent angles?
Answer:
R ~ D,
S ~ E,
T ~ B, and
Q ~ C
Partway through the season, a basketball coach promises his team that he will take them to a water park if they reach 1,000 points as a team by the end of the season. So far, they have scored 424 points. There are 9 games left in the season. Fill in the values for a, b, and c to create an equation that can be used to find the average number of points, x, the team needs to score in each of the remaining games to meet their goal.
Greta is opening a savings account. She starts with $100 and plans to add $59 each week. Write an equation she can use to calculate the amount of money she will have after any number of weeks. How much money will she have after 1 year?
if f(4)=183.07 when r=0.04 for the function f(t)=Pe* then what is the appropriate value of P?
Show work please
What is 31/8 as a decimal
Find the slope of each of the lines below:
simplify 3+4p to the second power -5p - 3p to the second power + 4p - 8
ANSWER CHOICES:
A - p to the second power - 7p - 11
B p to the second power + p - 11
C p to the second power - p - 5
D 7p to the second power - p - 5
The simplified version of the polynomial 3+4p to the second power -5p - 3p to the second power + 4p - 8 is p to the second power - p - 5 which corresponds to answer choice C.
Explanation:The problem you're asking about is a simplification of a polynomial. We can combine like terms in the polynomial which is a basic skill in algebra. The polynomial you provided is 3+4p to the second power -5p - 3p to the second power + 4p - 8
To solve this, we combine similar variables and constant separately. So, we add 4p to the second power and - 3p to the second power which will give us p to the second power. Next, we add -5p to +4p which results in -p. Finally, adding the constants 3 and -8 gives us -5. Therefore, the simplified polynomial becomes p to the second power - p - 5. Thus, the correct answer is option C.
Learn more about Polynomial Simplification here:
https://brainly.com/question/16495370
#SPJ12
Whats 5(-2/3) and 3(1/4)?
solve the system of equations solve for x
y=6x+12
solve for y
y=x+47
To solve the system of equations xy = 6x + 12 and yy = x + 47, we can rearrange the equations, isolate one variable, and substitute it into the other equation. Then, solve for the variables. The solution is x = 282 / (270 - y) and y = (270 - xy) / 6.
Explanation:To solve the given system of equations,
xy = 6x + 12
yy = x + 47
We can start by rearranging the equations:
xy - 6x = 12
yy - x = 47
Next, we can isolate one variable in terms of the other variable and substitute it into the other equation:
x = (yy - 47)
xy - 6(yy - 47) = 12
Simplifying the equation:
xy - 6yy + 282 = 12
Combining like terms:
-6yy + xy = -270
Now, we can solve this equation for y in terms of x:
y = (270 - xy) / 6
Re-substituting the value of y back into one of the original equations:
(270 - xy) / 6 * x = 47
Simplifying and solving for x:
270x - xy = 282
x(270 - y) = 282
x = 282 / (270 - y)
So, the solution to the system of equations is:
x = 282 / (270 - y)
y = (270 - xy) / 6
Andy ran 436.8 meters in 62.08 seconds. Use place value, multiplication with powers of 10, or equivalent fractions to explain what is happening mathematically to the decimal points in the divisor and dividend before dividing!!
IM GIVING AWAY ALL MY POINTS FOR THIS!!
Answer:
If you round, he runs 7 meters in a second.
436.8 m 62.08 s
x m 1 s
(436.8 X 1) / 62.08 = 7.03 m/s
7.03 m 1 s
y m 1/10 s
(7.03 X 0,1 ) /1 = 0,703 m
Step-by-step explanation:
To find Andy's running speed, divide distance by time, adjusting for decimals by multiplying both the divisor and dividend by powers of 10, shifting the decimal point to simplify division.
To calculate Andy's running speed, you would divide the distance he ran (436.8 meters) by the time it took (62.08 seconds). When you divide or multiply decimals by powers of 10, the decimal point is shifted. For instance, if we multiply or divide a number like 1.9436 by 10, 100, or 1000, our decimal point moves to the right or left accordingly. If dividing by 10, it moves one place to the left; by 100, two places; by 1000, three places, turning our number into 0.19436, 0.019436, and 0.0019436 respectively. The same principle applies to Andy's calculation, where the numbers would be easier to handle if we removed the decimal points by multiplying both the divisor and dividend by the same power of 10. Consequently, when dividing 436.8 by 62.08, we can multiply both by 100 to remove the decimal and divide 43680 by 6208, ultimately giving the same answer but with much simpler arithmetic.
The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′. Which statement correctly describes the relationship between △DEF and △D′E′F′ ?
A. The triangles are congruent because △D′E′F′ is a rotation of △DEF , and a rotation is a rigid motion.
B. The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
C. The triangles are not congruent because △D′E′F′ is a translation of △DEF , and a translation is not a rigid motion.
D. The triangles are congruent because △D′E′F′ is a reflection of △DEF , and a reflection is a rigid motion.
Answer: B. The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
Step-by-step explanation:
Given : The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.
We can see that a scale factor (2) is used in the above rule.
Rigid motions do not use any scale factor.
The transformation that uses scale factor to transforms figure is dilation.
And Dilation is not rigid motion because it does not produce congruent images.
Hence, The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
Simplify. 7/3+3(2/3−1/3)^2
All of these are fractions except the three and the exponent
7/3 +3(2/3 -1/3)^2 =
2/3 -1/3 = 1/3 now you have
7/3 +3(1/3)^2
1/3^2 = 1/9
7/3 +3(1/9)
3*1/9 = 1/3
7/3 + 1/3 = 8/3, which can be changed to 2 2/3
Calculate the area of the regular pentagon below:
A.164.025 square inches
B.238.95 square inches
C.351.78 square inches
D.477.9 square inches
Answer:
B. 238.95 is correct
Step-by-step explanation:
Find the distance between the points 1,4 and (-2,-1
How much pasta will each person get if 6 people share 2/3 lb of pasta equally?
Each person would get 1/9 lb of pasta if 6 people were to share 2/3 lb of pasta equally.
Explanation:In the given question, 6 people are sharing 2/3 lb of pasta equally. This implies that we are performing an operation of division. You would divide 2/3 by 6 to find out how much each person gets. Here's how you can do it:
First, write the fraction 2/3 as the division of two numbers 2 divided by 3. Now divide 2 by 6 which equals 1/3. Now, divide 1/3 by 3. Therefore, each person will get 1/9 lb of pasta. Learn more about division here:
https://brainly.com/question/33969335
#SPJ2
Which line is a line of symmetry for this regular polygon?
line g
line h
line i
Line g is a line of symmetry of this regular polygon.
We have regular polygon as shown in the figure.
We have to determine which line is a line of symmetry for this regular polygon.
What do you understand by the Symmetry of any plane figure?A plane figure is symmetric about a line if it is its own image when flipped across the line. The reflection line is the line of symmetry.
According to the question, we have a Regular Polygon.
According to the concept of Symmetry of any plane figure -
if we fold this polygon about the line g then both the sides will overlap.
The lines i and h do not fulfill this condition.
Hence, line g is a line of symmetry of this regular polygon.
To solve more questions on Symmetry of plane figures, visit the link below -
https://brainly.com/question/4179607
#SPJ2
In the inverse variation function, what happens to the output when the function's inputvalue is multiplied by 4?
f (x)=4x-7 when f (x)=8
If you rotate a right triangle, what feature of the triangle changes?
You are sending your friend a coded message by rearranging the letters in the word “STRIKE.” That is, your code can be any arrangement of the letters in the word “STRIKE” except one, “S-T-R-I-K-E.”
How many different ways can you code your message?
A) 720
B) 719
C) 120
D) 119
Answer:
Option B) 719 ways
Step-by-step explanation:
Given that you are sending your friend a coded message by rearranging the letters in the word “STRIKE.” That is, your code can be any arrangement of the letters in the word “STRIKE” except one, “S-T-R-I-K-E.”
This means any code we can send using the given letters without strike.
There are 6 different letters and order matters for coding i.e. st is different from ts
Hence no of ways of arranging strike in different ways
[tex]= 6!= 6*5*4*3*2*1\\= 720[/tex]
We must subtract the arrangement strike from this as strike is not allowed.
Hence total number of different ways we code this message
=720-1 =719 ways
Carlotta is constructing an equilateral triangle. She has already constructed the line segment and arc shown. What should Carlotta do for her next step?
Use the straightedge to draw a line that passes through point Q and intersects the arc.
Place the point of the compass on point Q and draw an arc that intersects the first arc, using the same width for the opening of the compass as the first arc.
Use the straightedge to draw a line that passes through point P and intersects the arc.
Place the point of the compass on point Q and draw an arc that intersects the first arc, using a width for the opening of the compass that is less than 1/2 PQ.
someone help asap !! is this the right answer?
Can someone please help me with this? Preferably ASAP
The folding chair can be set in different positions that change the angles formed by its parts. As angle 1 increases, how does the relationship change between the back of the chair and the front leg of the chair?
A. As the measure of increases, the distance between the back of the chair and the front leg of the chair increases.
B. As the measure of increases, the distance between the back of the chair and the front leg of the chair decreases.
C. As the measure of increases, the distance between the back of the chair and the front leg of the chair remains constant.
Final answer:
In the context of a folding chair, as angle 1 (between the backrest and the seat) increases, the distance between the back of the chair and the front leg correspondingly increases due to the lever-like movement of the backrest.
Explanation:
When considering the geometry of a folding chair and the angles formed by its parts, it's important to visualize the chair as a system of linked levers. As angle 1 increases, which is the angle between the backrest of the chair and the seat, the relationship between the back of the chair and the front leg changes. If we assume that the front leg stays still and the back of the chair moves backward to increase the angle, the distance between the back of the chair and the front leg increases. This movement can be seen as the backrest acting like a lever, where increasing the angle effectively moves the lever away from the pivot point at the front leg.
Therefore, the correct answer in the context of a folding chair is: A. As the measure of angle 1 increases, the distance between the back of the chair and the front leg of the chair increases.
Mark shoots arrows at a target and hits the bull's-eye about 40% of the time. find the probability that he hits the bull's-eye on the fourth shot
The probability of Mark hitting the bull's-eye on the fourth shot, assuming he misses the first three times, is 8.64%. This is calculated as the product of the probabilities of each event occurring independently.
Explanation:This is indeed a problem related to probability, particularly, this pertains to the concept of an independent event in statistics. Mark's success in shooting an arrow accurately to the target is an independent event because the outcome of one shot doesn't affect the outcome of other shots.
In Mark's case, he hits the bull's-eye about 40% of the time, i.e. his success rate P(Success) is 0.40 and his failure rate P(Failure) is 0.60. Since the question asked about the probability of him hitting the bull's-eye on the fourth shot, we should look at the first three shots being failures and only the fourth being a success.
This leads us to the calculation: P(FFFH) = P(F) x P(F) x P(F) x P(H) = (0.60)*(0.60)*(0.60)*(0.40) = 0.0864 or 8.64% chance.
So, there's an 8.64% chance that Mark will hit the bull's-eye on the fourth shot given that he misses the first three.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ12
The probability that Mark hits the bull's-eye on his fourth shot, given he typically hits the bull's-eye 40% of the time, is 0.0864 or 8.64%
Explanation:The problem is about the probability that Mark hits the bull's-eye on the fourth shot given that he hits the bull's-eye about 40% of the time. In these cases, for the first three shots, he should not hit the bull's-eye (probabilty of 60%) and on the fourth trial, he should hit the bull's-eye (probability of 40%). Therefore, we multiply the individual probabilities together to find the answer.
Step 1: Find the probability that he does not hit the bull's-eye in the first three trials. This is (0.6)*(0.6)*(0.6) = 0.216.
Step 2: Find the probability that he hits the bull's-eye on the fourth trial. This is simply 0.4.
Step 3: Multiply the two probabilities together to find the final answer. This gives us 0.216*0.4 = 0.0864.
So, the probability that Mark hits the bull's-eye on the fourth shot is 0.0864, or 8.64%.
Learn more about probability here:https://brainly.com/question/32117953
#SPJ12
What are the dimensions of the rectangle of greatest area that can be formed with 200 feet of fence?
Dimensions are 50 feet by 50 feet.
Let the length = x
the width = y
So the perimeter = 2(x+y)=200
or, x+y=100
or, y=100-x
So the area is = A = xy = x(100-x).
For greatest area A' = 0 and A" < 0.
[tex]A= x(100-x)\\A=100x-x^2\\A'=100-2x\\A''=-2[/tex]
We set A'=0 to find x.
[tex]100-2x=0\\2x=100\\x=50[/tex]
For x=50, A"=2 < 0
It means for x=50, y=100-50=50 the rectangle will have the greatest area.
Learn more: https://brainly.com/question/14324158
At the city museum, child admission is $5.20 and adult admission is $9.10. on saturday, three times as many adult tickets as child tickets were sold, for a total sales of $975.00. how many child tickets were sold that day?
Finding slope from an equation
Answer:
[tex]\frac 15[/tex]
Step-by-step explanation:
Hello!
We can convert it into slope intercept form: [tex]y = mx + b[/tex]
m = slopeb = y-interceptConvert:[tex]-15 - x = -5y[/tex][tex](-15 - x)\div(-5) = y[/tex][tex]3 + \frac15x = y[/tex][tex]y = \frac15x + 3[/tex]The slope is [tex]\frac15[/tex].
Finding the slope of a line from its equation depends on the equation's form. If it's already in slope-intercept form (y = mx + b), the coefficient of x (m) is the slope. If not, rewrite it to that form by isolating y. Alternatively, use the point-slope form (y - y1 = m(x - x1)) with a known point on the line and solve for m. Remember, the slope tells you how much the line rises/falls per unit move to the right. For the equation in the image, the slope is 1/5.
• Using the slope-intercept form: This is the most straightforward way to find the slope if the equation is already in slope-intercept form, which is y = mx + b. In this form, the slope (m) is the coefficient of the x term. For example, if the equation is y = 2x + 3, the slope is 2.
• Using the standard form: If the equation is not in slope-intercept form, you can first rewrite it in slope-intercept form. To do this, you need to isolate the y term. For example, if the equation is 3x + 2y = 6, you would first subtract 3x from both sides to get 2y = -3x + 6. Then, you would divide both sides by 2 to get y = -3/2x + 3. Once the equation is in slope-intercept form, you can find the slope as described in the first method.
• Using the point-slope form: The point-slope form of the equation of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. To find the slope using this form, you need to plug in the coordinates of a point on the line. For example, if the equation is y - 2 = 3(x - 1), and you know that the point (3, 7) is on the line, you can plug in x = 3 and y = 7 to get 5 = 3(2). Solving for m, you get m = 5/3.
The slope of a line tells you rise over run, or how much the line goes up or down for every unit it goes to the right. A positive slope means the line goes up as you move to the right, a negative slope means the line goes down as you move to the right, and a zero slope means the line is horizontal.
In the image, the equation is -15 - x = -5y. To find the slope using the slope-intercept form, we need to rewrite the equation so that y is isolated on one side. We can do this by adding x and dividing both sides by -5:
y = (1/5)x + 3
Therefore, the slope of the line is 1/5.