Answer:
[tex]\mathsf e^{t-1}[/tex]
Step-by-step explanation:
Definition of an inverse function
[tex]\textsf {A\:function\:g\:is\:the\:inverse\:of\:function\:f\:if\:for}\:y=f\left(x\right),\:\:x=g\left(y\right)\:[/tex]
In order to find the inverse of p(t) = 1 + ln(t)...
Set y = 1 + ln(t)Replace t with yJane and jill want their mom to ride the roller coaster with them, but she thinks it will be too fast. she asks the girls to find out how fast the roller coaster will be traveling. they find out that the speed of the roller coaster, in miles per hour, is modeled by the function g(x) = x4 − 4x2 7x − 8, where x is time measured in seconds. how fast is the roller coaster traveling at 2 seconds? 6 miles per hour 22 miles per hour 26 miles per hour 54 miles per hour
Answer:
6 miles per hour!
Step-by-step explanation:
solve the following simultaneous equations
y=x^2
y= x+6
The solution of the simultaneous equations are x = 2, 3 and y = 3,9.
What are simultaneous equation?In mathematics; a set of simultaneous equations, also known as a system of equations or an equation system, it is a finite set of equations for which common solutions are sought.
WE have given simultaneous equations as;
y = x^2 ...(i)
y = x + 6 .....(ii)
Now Equating (i) and (ii) we get,
x^2 = x + 6
or, x^2 - x - 6 = 0
Then Solving we get;
x^2 - 3x - 2x - 6 = 0
x(x - 3) -2(x - 3) = 0
(x - 2)(x - 3) = 0
So, x = 2, 3
Now Putting x = 2, 3 in equation (i) we get;
y = 2^2
y = 4
and,
y = 3^2
y = 9
Thus, y = 3,9
Hence the solution of the simultaneous equations are x = 2, 3 and y = 3,9.
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A 9-foot piece of ribbon costs $20.07. What is the price per yard?
The price per yard of the ribbon is $6.69
Conversion of foot to yardFirst, we will need to convert 9 foot to yards as shown;
9 foot = 3 yards
This shows that a 3 yard piece of ribbon costs $20.07, the price per yard is expressed as;
Price per yard = 20.07/Total yard
Price per yard = 20.07/3
Price per yard = 6.69
Hence the price per yard of the ribbon is $6.69
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Quadrilateral ABCD undergoes a reflection across the x-axis to form quadrilateral A'B'C'D'. The coordinates of A' are (
,
).
The reflected quadrilateral A'B'C'D' is then translated 3 units right and 2 units up to form quadrilateral A"B"C"D". The coordinates of A" are (
,
).
The coordinates of A'' will be ( -2, 5).
We are given that:
Quadrilateral ABCD is reflected across the x - axis.
We know that, when a refection is done about x-axis, the values of the abscissa x remain identical & the value of ordinate just change their signs:
A(-5,-3) will become A'(-5,+3)
B(-6,-1) will become B'(-6,+1)
C(-3,-1) will become C'(-3,+1)
D(-2,-3) will become D'(-2,+3)
Now, the reflected quadrilateral A'B'C'D' is then translated 3 units right and 2 units up to form quadrilateral A"B"C"D".
So, the coordinates of A'' will become:
( - 5 + 3, 3 + 2)
( -2, 5)
Therefore, we get that, the coordinates of A'' will be ( -2, 5).
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two positive integers have a product of 176. one integer is 5 less than the other integer. which equation can be used to find the value of x, the greater integer? x2 5
x(x – 5) = 176 is the correct equation to find the greater integer.
As the question mentions, the greater integer is x. So, the smaller integer will be (x - 5). Also, we are informed that their product is 176.
Now, representing the given information as mathematical expression -
x(x – 5) = 176
On further multiplication on Left Hand Side, we get the equation -
x² - 5x = 176
Rewriting the equation -
x² - 5x - 176 = 0
Further solving the equation to validate it.
x² - 16x + 11x - 176 = 0
x (x - 16) + 11 (x - 16) = 0
(x - 16) (x + 11) = 0
x = 16, -11
As stated, the integers are positive. So, the value of x and hence greater integer is 16.
Value of small integer = 16 - 5
Value of small integer = 11
So, the two integers are 16 and 11. Their product is 176 hence, our formed equation is correct.
Therefore, the equation that can be used to find x is : x(x – 5) = 176.
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The complete question is -
Two positive integers have a product of 176. One integer is 5 less than the other integer. Which equation can be used to find the value of x, the greater integer?
x² + 5 = 176
x(x + 5) = 176
x(x – 5) = 176
x² – 5 = 176
2 Shape 1 and Shape 2 are congruent pentagons.
Shape 1
Shape 2
Shape 2 is congruent to Shape 1 because -
Shape 2 is a translation of Shape 1.
Shape 2 is a reflection of Shape 1.
Shape 2 is a rotation of Shape 1.
D. Shape 2 and Shape 1 are both pentagons.
A.
B
C.
The shape 1 and shape 2 are congruent pentagons becuase shape 2 is a reflection of shape 1.
Given that shape 1 and shape 2 are congruent pentagons.
We are required to choose the option which is correct according to the given statemment that shape 1 and shape 2 are congruent pentagons.
Pentagons are the shape which have 5 sides and 5 angles.
Two shapes are congruent if they are copy of each other means all the corresponding sides are equal to each other.
The shape 1 and shape 2 are congruent pentagons becuase shape 2 is a reflection of shape 1.
Hence the shape 1 and shape 2 are congruent pentagons becuase shape 2 is a reflection of shape 1.
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A strategy for 8,429 x 7
Answer: 59,003
Step-by-step explanation:
8,429 x 7=
8,429 x (5+2)=
8,429 x 5 + 8,429 x 2=
4,214.5*10+16,858= ==> n*5=n/2 * 10
42,145+16,858=59,003
Point M is the midpoint of AB. The coordinates of point A are (−8, 2) and the coordinates of M are (−2, 2). What are the coordinates of point B?
Hailey must make at least $200 in sales each week. So far this week, she has already made $60 in sales. How much more does she need in sales this week (x) in order to meet her goal?
Answer:
Step-by-step explanation:
If she made 60$ she only needs 140$ more to get to 200$
Find the exponential form of the complex number \[ e^{17\pi i/60} e^{27\pi i/60} e^{37\pi i /60} e^{47 \pi i /60} e^{57 \pi i/60}\]with proof
the exponential form of the complex number \[ e^{17\pi i/60} e^{27\pi i/60} e^{37\pi i /60} e^{47 \pi i /60} e^{57 \pi i/60}\]
= (2+[tex]\sqrt{3}[/tex]) [tex]e^3^7^\pi^ i^/^6^0.[/tex]
How is the exponential form calculated?[tex]e^1^7^\pi ^i/^6^0[/tex] + [tex]e^2^7^\pi^ i^/^6^0[/tex]+⋯+[tex]e^5^7^\pi ^i^/^6^0[/tex]
=[tex]e^1^7^\pi ^i^/^6^0[/tex](1+[tex]e^\pi^ i^/^6[/tex]+....+[tex]e^4^\pi ^i^/^6[/tex])
=[tex]e^1^7^\pi ^i^/^6^0[/tex] (1−[tex]e^5^\pi ^i^/^6[/tex]) ÷ (1−[tex]e^\pi ^i^/^6[/tex])
=[tex]e^1^7^\pi ^i/^6^0[/tex] ([tex]\frac{1}{2}[/tex](2+[tex]\sqrt{3}[/tex]) + [tex]\frac{1}{2}[/tex](3+2[tex]\sqrt{3}[/tex])i)
=(2+[tex]\sqrt{3}[/tex])e17πi/60(12+([tex]\sqrt{3}[/tex]/ [tex]2[/tex]) i )
=(2+[tex]\sqrt{3}[/tex])[tex]e^1^7^\pi ^i^/^6^0[/tex] [tex]e^\pi ^i^/^3[/tex]
=(2+[tex]\sqrt{3}[/tex]) [tex]e^3^7^\pi^ i^/^6^0.[/tex]
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Help would be EXTREMELY appreciated I really need this tomorrow
The value of csc x=-13/5.
Given that the sin x=-5/13 and x∈[3π/2 , 2π).
A trigonometric function is a real function that relates the angle of a right triangle to the ratio of the lengths of the two sides. The basic functions are sin, cos, tan, cot, sec, csc.
The given function is sin x=-5/13.
As we all know that sin x=1/csc x or csc x=1/sin x.
As it is given that x∈[3π/2 , 2π) that means x lies in fourth quadrant and in fourth quadrant sin and csc is negative in it.
So, we will apply this identity csc x=1/sin x, we get
csc x=1/(-5/13)
csc x=-13/5
And it also lies in x∈[3π/2 , 2π).
Hence, the value of csc x when sin x=-5/13 and x∈[3π/2 , 2π) is csc x=-13/5.
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I thought of a number, added 21, and then added twice my
original number and got 84. What is my number?
Answer:
31.5
Because if you Subtract 21 from 84 you get 63
then if you divide 63 by 2 you get 31.5 so your Answer would be 31.5.
three zebras are chilling in the desert. suddenly a lion attacks. each zebra is sitting on a corner of an equally length triangle. each zebra randomly picks a direction and only runs along the outline of the triangle to either edge of the triangle. what is the probability that none of the zebras collide?
Probability that no zebras collide is 0.25
The zebras are represented as z1, z2 and z3.
Z1 to B, Z2 to C, and Z3 to A come first [tex]= (\frac{1}{2})^3[/tex]
Following that, z1 to C, z2 to A, and z3 to B = [tex](\frac{1}{2})^3[/tex]
Consequently, the likelihood of no collision is 2×1/8 = 0.25.
What are the types of probability distributions ?Discrete and continuous probability distributions are the two main categories in which probability distributions fall. There are numerous varieties of probability distributions within each category.
The number of favorable outcomes of an event divided by the total number of possible outcomes of an event can be used to calculate the probability of an event.The likelihood of a sure or certain event is one.The likelihood of an impossibility is 0 (0).Every event has a probability between 0 and 1.To learn more about Probability, visit
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a highway has an optional toll lane that drivers may take to reduce the time they spend driving. drivers pay a small fee to enter the toll lane ($0.25) . then, once they leave the toll lane, they pay a fee based on the number of miles they have traveled on the toll lane. assume that the driver may leave the lane after any whole number of miles and pays for exactly that number, without rounding up. note that there is a linear relationship between the number of miles a vehicle has traveled and the price of the toll. a. if frank is on the toll road for 4.00 miles and then leaves the lane, how much will he have to pay total for the trip?
He have to pay $3.25.
Let the number of miles traveled by a driver be x
The toll paid by the driver is then represented as y. (in dollar)
Linear equation : an equation in which there is only one variable present. It is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution.
Since there is a linear relation between the two, we can assume the equation can be written as:
y = mx + c
From the given data, we get
0.24 = m(0) + c
c = 0.25
Using the second point:
1 = m(1) + 0.25
m = 1 − 0.25 = 0.75
Hence, the equation is y = 0.75x + 0.25.
If x = 4, then:
y = 0.75 × 4 + 0.25
y = 5.50
Hence, He have to pay $3.25.
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find an equation for the line that passes through the points (6,-5) and (-2,5)
Answer: I think ok not sure but yet positive but i think it is y= -7
Step-by-step explanation:
for the following exercise, consider the following scenario: a town has an intial population of 50000 . it grows at a constant rate of 5000 per year. find the linear function that model's the town's population p as a function of the year, t , where t is the number of years since the model began.
The required function is P(t)=50000 + 5000t.
In this problem we need to form the function of the population in a town.
Here it is given that the initial population of the town is 50000.
the rate at which the population increases is 5000 per year.
So, the increase for the first year will be 5000. And the population will be 55000.
Then again for the next year the growth will be 5000 and the population will be 50000 + (5000×2)
= 60000
So we can see clearly that the population is varying with time and we can write the function as P(t)=50000 + 5000t where t is the time in years.
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in a game of poker, what is the probability that a five-card hand will contain (b) four of a kind, and (c) a full house (three cards of one value and two cards of another value)?
(b) We have 13 possibilities that a five-card hand will contain four of a kind.
(c) We have 12 possibilities that a five-card hand will contain a full house.
What do you mean by 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.
The probability of an occurrence is a number between 0 and 1, with 1 representing certainty and 0 representing impossibility.
Since there are no other conceivable outcomes and the coin is fair, the odds of both the possibilities, "heads" and "tails," are equally likely to occur. As a result, the probability of either occurrence is half (which could also be written as 0.5)
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translate the following verbal statement into an algebraic equation and then solve: use x for your variable. the quotient of two more than a number and five is eight.
The algebraic equation of the verbal statement is (x + 2) / 5 = 8 and the value of x is 38.
Algebraic Equation
An algebraic equation means the statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root.
Given,
The quotient of two more than a number and five is eight.
Here we need to translate the given verbal statement into an algebraic expression and solve it.
The quotient of two more than a number and five is eight.
Let, the number be x.
According to the question, the equation is
=> (x + 2) / 5 =8
=> x + 2 = 8 x 5
=> x + 2 = 40
=> x = 40 - 2
=> x = 38
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Solve the system of equations : 5x - 2y = -1 and -15x + 6y = 3
Equation are defined by equating two or more expressions. The solution to the system of equation is (k, (1+5k)/2)
Solving system of equationSystem of equations are equations are equations that contains several variables and expression.
Given the system of equations
5x - 2y = -1
-15x + 6y = 3
Divide equation 2 through by -3 to have:
-15x/-3 + 6y/-3 = 3/-3
5x - 2y = -1
You can see that both equations are equal. Let x = k so that;
5k - 2y = -1
-2y = -1 - 5k
2y = 1 + 5k
y = (1+5k)/2
Hence the solution to the system of equation is (k, (1+5k)/2)
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Suppose a meal consists of one sandwich, one side order and one beverage. What is the most
expensive meal you can purchase? How much does it cost?
Hamburger $3.25
Bacon Cheeseburger $4.75
Chicken Fajita Taco $3.50
French Fries, Small $1.55
French Fries, Large $1.90
Onion Rings $2.40
Cole Slaw $1.45
Soft Drink, Small $1.30
Soft Drink, Large $1.65
Milkshake $3.25
Juice $1.80
$26.8 is the total cost and Chicken Fajita Taco is the most
expensive meal .
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.Hamburger + Bacon Cheeseburger + Chicken Fajita Taco + French Fries, Small + French Fries, Large + Onion Rings + Cole Slaw + Soft Drink, Small + Soft Drink, Large + Milkshake + Juice
= $3.25 + $4.75 + $3.50 + $1.55 + $1.90 + $2.40 + $1.45 + $1.30 + $1.65 + $3.25 + $1.80
= $26.8
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4. Gilbert needs his work double-checked. Choose the best answer for Gilbert's total estimate. Estimate to the nearest dollar amount. Show each step.
Answer: D $30
Step-by-step explanation:
$12.79 rounds to $13
$2.33 round to $2
$14.65 rounds to $15
Add the estimates: 13+2+15= $30
A store had 4 packs of paper for 7.44.how much would it cost if you were to buy 5 packs
Answer: $9.30
Step-by-step explanation:
7.44/4 = 1.86
1.89 x 5 = $9.30
then calculate the area and perimeter of each shape, assuming that all corners are right angles..
Answer:
a. A = 647
P = 120
b. A = 192
P = 70
Step-by-step explanation:
a. A = (16 x 12) + (13 x 35) = 192 + 455 = 647
P = 16 + 12 + 19 + 13 + 35 + 25 = 120
b. A = (12 x 8) + (8 x 12) = 96 + 96 = 192
P = 12 + 8 + 7 + 8 + 12 + 8 + 7 + 8 = 70
WILL GIVE YOU EXTRA POINT BY BRAINLIEST (need help asap THANKS)
Answer:
7: #3. 8: #2
Step-by-step explanation:
in the first question the format is simply (x, y) and because it is a translation, we are basically just moving the point by these numbers, with this information, it is simply moving x to the left(negative) 8 times, and y(up/positive) 4 times. The next question is simply moving the point across the x axis by the same amount that it is above the x axis, so it would be one down from the x-axis' bold line, or in this case moved 2 y-units down. Hope this helps mate :)
Helpppppp
Question 2 (Essay Worth 2 points)
(01.02 MC)
Answer:
x⅔
Step-by-step explanation:
1. we understand the concept that x÷x is a subtraction as an instance, x³/x² = x¹ so we can apply this knowledge in this question
2. x⅚ / x⅙ --> x⅚-⅙
--> x^4/6 [simplify this]
--> x^4/6 [ divide 2 at the numerator and also the denominator]
--> x⅔
Last but not least, you got your 2 points
it takes an air pump 5 minutes to fill a twin sized air mattress (39 by 8.75 by 75 inches). how long will it take to fill a queen sized mattress (60 by 8.75 by 80 inches)?
It take 8.205 minutes to fill a queen sized mattress.
What is volume?'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
Given dimensions:
Twin sized air mattress (39 by 8.75 by 75 inches).
Queen sized mattress (60 by 8.75 by 80 inches)
Now, Volume of twin sized mattress
=39* 8.75* 75
= 25593.35 cubic inch
Volume of queen sized mattress,
=60* 8.75* 80
= 42000 cubic inch
as, To fill 25593.35 cubic inch it takes 5 minutes
so, to fill 1 cubic inch = 5/25593.35
and, So to fill 42000 cubic inch it will take = 42000* 5/25593.35
=8.205 minutes
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What is the valur of expression 6 3/4 (-11.5) ?
77 5/8
69 3/4
- 77 5/8
- 69 3/4
I need help
Step-by-step explanation:
so, this is a multiplication ?
6 3/4 × (-11.5)
let's bring the mixed numbers to full fractions, and then we can easily multiply.
6 3/4 = (6×4 + 3)/4 = (24 + 3)/4 = 27/4
-11.5 = -11 1/2 = (-11×2 - 1)/2 = (-22 - 1)/2 = -23/2
so, the multiplication is
27/4 × -23/2 = 27×-23 / 4×2 = -621/8 =
= (-616 - 5)/8 = (-77×8 - 5)/8 = -77 5/8
Answer:
-77 5/8
Step-by-step explanation:
6 3/4 can be turned into 6.75.
6.75 * -11.5 is -77.625
-77.625 can be simplified into 5/8
Brainliest pls?
you will get 30 points if you solve this
Answer:
41
Step-by-step explanation:
5y+x
Evaluate the expression
Let x=6 and y=7
5*7 +6
Multiply first
35 +6
Then add
41
Answer:
it 41
Step-by-step explanation:5(7)+6=41
A box contains 20 balls: 10 are yellow, 6 are red, and 4 are grey. What is the probability of picking a yellow and then a red ball? (the first ball will be replaced)
probability of picking a yellow ball: 10/20 (1/2)
probability of picking a red ball: 6/20 (3/10)
1/2 times 3/10 =
3/20
Given m//n, find the value of x
In
135*
M
x*
N
The value of x that makes the lines m and n to be parallel lines is 45 degrees
How to determine the value of x that makes the line parallel?The figure that completes the question is added as an attachment
From the figure, we have the following angles
Angle = x and 3x
The angles are interior of parallel lines
This means that they add up to 180 degrees
So, we have the following equation
Angle 1 + Angle 2 = 180 degrees
Substitute the known values in the above equation
So, we have
x + 3x = 180
Evaluate the like terms in the above equation
So, we have:
4x = 180
Divide both sides of the above equation by 4
So, we have
x = 45
Hence, the value of x that makes the lines m and n to be parallel lines is 45 degrees
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