The value of ex = e2x + 5 is -5.
What is mean by exponential function ?The mathematical expression f(x)=exp or ex denotes the exponential function. Unless otherwise stated, the term typically refers to the positive-valued function of a real variable. it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.
A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.
Given ,
[tex]e^x=e^{2 x}+5[/tex]
By simplifying the exponential rule we get
x= -5
Therefore the value of [tex]e^x=e^{2 x}+5[/tex] is -5
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Find dy/dx =(1+x/1-x)^1/3
The solution to the differentiation dy/dx =(1+x/1-x)^1/3 is [tex]\frac{dy}{dx} = 1^\frac{1}{3}[/tex]
What is differentiation?
Differentiation is a method of finding the derivative of a function.
To find the derivation of the function Simplify
[tex]\frac{dy}{dx} = ( 1+ \frac{x}{1} - x)^ \frac{1}{3}[/tex]
Any expression divided by one remains the same
[tex]\frac{dy}{dx}= ( 1+ x-x) ^\frac{1}{3}[/tex]
Eliminate x
[tex]\frac{dy}{dx} =[/tex] 1 [tex]\frac{1}{3}[/tex]
Therefore, the solution to the differentiation is [tex]\frac{dy}{dx} =[/tex] 1 [tex]\frac{1}{3}[/tex]
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(2-3i)+(-2+7i)= (2+ (− 2) ) + (−3+7)i
Answer:
is 121.004 I hope I've helped!
4x3x2=4x3x2 find the product
Answer:
- 4x3=12
12x2=24
so, 24 = 24
A person standing on the ground outside a building throws a set of keys directly upward to a person standing on a second-floor balcony. The person on the ground releases the keys with an initial vertical velocity of 28 ft/s from a height of 4 ft. The function h(t) = 16t^2 + 28t +4 models the height (in feet) of the keys at time t (in seconds) after the keys are thrown. The person standing on the balcony can catch the keys once they reach a height of 12 ft. For what period of time are the keys high enough to be caught?
a [0,1.88]
b[0.36,1.39]
c[0,0.36] U [1.39,1.88]
d(-∞,0.36] U [1.39,∞)
Answer:
Step-by-step explanation:
The center of a circle is (4, -11) and a point on the circle is (4, -3). Determine the
equation of the circle.
(x+12)² + (y + 6)² = 64
(x-4)² + (y +11)² = 64
(x-4)² + (y +11)² = 4096
(x-3)² + (y-13)² = 64
The equation of circle (x-4)² + (y+11)² = 64
What is a Circle?
All points in a plane that are at a specific distance from a specific point, the center, form a circle. Alternatively, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
Here we know that (h,k)=(4,-11) but we are not given the radius.
However, we can find the radius by using the distance formula.
Therefore,
r = √[(x2 - x1)² + (y2 - y1)²]
r = √[(4 - 4)² + (-3 + 11)²]
r = √[(0)² + (8)²]
r = √(8²)
r = 64
An equation of the circle with center (h,k) and radius r is
(x−h)^2 +(y−k)^2=r^2
Substitute the values in the equation of circle as follows:
(x-4)² + (y+11)² = 8²
(x-4)² + (y+11)² = 64
Therefore, the equation of the circle is (x-4)² + (y+11)² = 64
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The function f(x) is graphed below. How many points represent a relative maximum?
The polynomial graph has only one relative maximum at point b.
What are relative maxima and minima?A function's graph can be used to determine the relative peaks and minima of the function. A relative maximum or minimum is a point that is higher than the points directly adjacent to it on both sides. The opposite is true for a relative maximum or minimum. When drawing a curve, relative maxima and minima are crucial spots that can be discovered using either the first or second derivative test.
Given, a polynomial function by observing the graph itself we conclude that the graph has no absolute maxima as it is going towards negative and positive infinity but it has a relative maximum a point b.
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Use implicit differentiation to find dy/dx at the given point. Show steps
The value of dy/dx is -27/8 for 1=5x³+2y²+4xy at (-1,3).
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
Given,
The equation is 1=5x³+2y²+4xy
We need to differentiate the given equation
5.3x²+4ydy/dx+4(xdy/dx+y)=0
15x²+4ydy/dx+4(xdy/dx+y)=0
15x²+4ydy/dx+4xdy/dx+4y=0
15x²+dy/dx(4y+4x)+4y=0
dy/dx(4y+4x)=-15x²-4y
dy/dx=-15x²-4y/4y+4x
Now plug in x =-1 and y=3
dy/dx=-15(-1)²-4(3)/4(3)+4(-1)
=-15-12/12-4
=-27/8
Hence, the value of dy/dx is -27/8 for 1=5x³+2y²+4xy at (-1,3).
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a baseball player averages 2 hits per game. The player already has 18 hits this season. another player has 22 hits so far this season and averages 1 hit per game. After how many games will both players have the same number of hits?
They needed 4 more games to have same number of hits which is 26 hits
The answer to the common factor is?
Factors that are shared by two or more numbers are referred to as common factors in mathematics. To put it another way, a common factor is a number that will divide a group of two or more numbers exactly.
Given That:
Player 1 average hits = 2 hit per game
Player 1 Total hits this season = 18
Player 1 total game this season = 18/2 = 9
Player 2 average hits = 1 hit per game
Player 2 Total hits this season = 22
Player 2 total game this season = 22/1 = 22
If we add 4 game for each player than
Player 1 total hits = 18 + 4(2) = 26
Player 2 total hits = 22 + 4 = 26
Hence they needed 4 more games to have same number of hits which is 26 hits
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please help
1. Draw a triangle.
2. Plot a midsegment of the triangle in the image with number 11. Include work to verify that the segment drawn is the midsegment. Make sure to include the midsegment in the image.
1. Triangle ABC with the vertices, A(0, 2), B(6, 4), and C(4, -2) is drawn and attached below.
2. The midsegment is EF. This is verified using the triangle midsegment theorem which states that EF = 1/2(AC).
What is the Midsegment of a Triangle?The midsegment of a triangle is the line segment that joins the midpoints of two sides of a triangle together. Every triangle typically has three midsegments.
According to the triangle midsegment theorem, the length of the midsegment is half the length of the third side of the triangle that it is parallel to.
What is the Midpoint of a Line?The midpoint of a line is its middle, which can be calculate using the formula:
M(x, y) = [tex](\frac{x_2 - x_1}{2}, \frac{y_2 - y_1}{2})[/tex].
1. The coordinate of the three vertices that is used to draw a triangle are:
A(0, 2), B(6, 4), and C(4, -2).
The triangle is in the attachment below.
2. To plot the midsegment of the triangle, determine the midpoints of AB and BC, then plot the coordinate where both midpoints would be joined.
Midpoint of AB = (x, y) = (0+6)/2, (2+4)/2
= (6/2, 6/2)
= (3, 3) (let this be point E)
Midpoint of AB = (x, y) = (4+6)/2, (−2+4)/2
F = (5, 1)
The midsegment will have the endpoints, E(3, 3) and F(5, 1).
To verify the segment draw is the midsegment according to the triangle midsegment theorem, find the length of the midsegment, EF, and the length of the third side, AC using the distance formula, d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
EF = √[(5−3)² + (1−3)²]
EF = √8 units
AC = √[(4−0)² + (−2−2)²]
AC = √32 units
Based on the triangle midsegment theorem:
EF = 1/2(AC)
Plug in the values:
√8 = 1/2(√32)
√8 = 1/2(4√2)
√8 = 2√2
2√2 = 2√2 (true)
This means that EF is a midsegment of triangle ABC.
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Find the missing values in the ratio table.
2,_,_
3,1,8
The missing values in the ratios are 2/3 and 16/3 in the set of 1, _ , _.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given are two sets of ratios 2, _, _ and 3, 1, 8.
If we observe the first value of the first and second ratio we see that
The second set of ratios is (3/2) or 1.5 times larger than the first set of ratios.
So the second and the third value of the first set of ratios are (1/3/2) = 2/3 and 8/(3/2) = 16/3.
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Complete the table: (Enter your answers as a whole dollar amount.) Units Unit Cost Dollar Cost Beg. Inventory Jan. 1 8 $ 6.00 A Apr. 11 24 $ 11.00 B May 17 30 $ 14.00 C Dec. 5 19 $ 16.00 D 21 units sold
The completion of the inventory table is as follows:
A = $48
B = $264
C = $420
D = $304.
What methods are used for inventory?
Utilizing some of the inventory procedures, the aforementioned inventory table is finished.
The First-in, First-out (FIFO) principle presupposes that the physical flow of products sold corresponds to the order in which they were acquired.
The Last-in, First-out method (LIFO) bases the cost of products sold on the most recent inventory acquisitions.
The weighted-average technique calculates the ending inventory and cost of goods sold using the average cost of goods.
Allocating the expenses of products sold and ending inventory are not based on any presumptions in Specification Identification. It substitutes specified expenses instead.
Inventory Table:
Units Unit Cost Total Cost
Jan. 1 Beg. Inventory 8 $6.00 $48 ($6 x 8)
April 11 Purchases 24 $11.00 $264 ($11 x 24)
May 17 Purchases 30 $14.00 $420 ($14 x 30)
Dec. 5 Purchases 19 $16.00 $304 ($16 x 19)
Total 81 $1,036
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Fill in the blanks to create an equation that has infinite solutions
7x+3x+10=-2(_x + _)
Fill in the blanks to create an equation that has no solutions
7x+3x+10=-2(_x + _)
An equation 7x+3x+10= -2[-5x +(-5)] has infinite solutions and an equation 7x+3x+10= -2[-5x + (-4)] has no solution.
Given that:
7x+3x+10 = -2 (_x + _)
=> 10x + 10 = -2 (_x + _)
Putting in the blank -5 so as to satisfy the equation that has an infinite solution.
=> 10x + 10 = -2(-5x + -5)
This is the equation that shows that it has infinite solutions and they are in the same line.
For no solutions
7x+3x+10 = -2 (_x + _)
In no solution, the value of b is not equal to -5.
For equation:
7x+3x+10 = -2 (-5x + b) [If putting value in first blank = -5]
Therefore, -2 (-5x + b) is parallel to 10x+10 for any value of b not equal to -5. Parallel lines never intersect. So solutions are no solution.
Putting the value of b = -4
7x+3x+10 = -2 [-5x + (-4)]
This is the equation that shows that it has infinite solutions and they are in the same line.
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Part D ? Question Suppose the cylindrical water tank has a radius of 12 feet. Use this information and the equation modeling the radius of the tank to complete these statements
The volume of the water tank is about _____ cubic feet.
a. 2,880
b. 400
c. 754
d. 9,048
The volume of the cylindrical water tank that has a length of 20 feet and a radius of 12 feet is about 9,048 cubic feet.
The correct option is option d;
d. 9,048
What is the volume of a solid?The volume of a solid indicates the amount of space the solid takes at a location.
The formula for finding the volume of the cylindrical tank is presented as follows;
V = π·r²·L
Where;
r = The radius of the tank
L = The length of the tank
From a similar question on the website, we have;
The length of the tank, L = 20 feet
Therefore;
The volume of the tank, V = π × 12² × 20 ≈ 9048
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answer:
Step-by-step explanation:
x= a. 60
y = I. 15
angle c = b. 45
angle DBC = h. 105
angle CBA = g. 75
Answer:
x=60° y=15° m∠c=45° ∠DBC=105° ∠CBA=75°
Step-by-step explanation:
Since it shows that 7y and 5y make 180 degrees, 12y=180 and y=15
So m∠c=45 degrees and ∠CBA is 75 degrees.
180-(45+75)=60 degrees.
So ∠DBC is 105 degrees. :D
integral of 2x^3 * (x^2 + 4)^ (1/2) dx
Please answer I need to turn it in asap morning when please help
Answer:
-7/3
Step-by-step explanation:
(-2-5)/(5-2)
-7/3
Answer:
C.
Step-by-step explanation:
Using Slope formula (y2-y1/x2-x1), we can plug these 2 coordinates in. -2-5/5-2= -7/3.
Or even by simply using rise over run, we can get the slope. Up 7 over 3, and we know that the slope is negative, so we add a negative sign in front.
-Hope this helped
AD is a median in AABC, if BD = 5x - 8, CD = 3x + 12, and AC = 7x -14. Find the length of all three segments.
According to the give triangle ABC, the length of the line segments
BD is 5.5
CD is 13.5
AC is 10.5
Triangle:
Triangle refers a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees.
Given,
AD is a median in ΔABC, if BD = 5x - 8, CD = 3x + 12, and AC = 7x -14.
Here we need to find the length of the all three segments.
We know that, the length of BC is the sum of BD and CD.
Thus can be written as,
BC = BD + CD
Now, we have to apply the values on the equation, then we get,
Length of BC is x.
=> 5x - 8 + 3x + 12
=> 8x - 4
=> 8x = 4
=> x = 1/2
Now, we have to apply the value of x as 1/2, on the line segments, then we get,
BC = 5(1/2) - 8
BC = 5/2 - 8
BC = 11/2 = 5.5
So, the value of CD is,
CD = 3(1/2) + 12
CD = 3/2 + 12
CD = 27/2
CD = 13.5
Then the value of AC is,
AC = 7(1/2) - 14
AC = 7/2 - 14
AC = 21/2
AC = 10.5
Therefore, the line segments BC is 5.5, CD is 13.5 and AC is 10.5.
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Question 23
Springfield's population in 2019 was 202628 people and is projected to grow at a rate of 0.81 % each year. If the growth continues at this annual rate, what will the population be in 2046?
Round to the nearest person.
The population of Springfield in 2046, given the growth rate, can be found to be 251, 940 people
How to find the population in 2046?When given the starting population, and the population growth rate, the growth in population can be found by the formula:
= Starting population x ( 1 + population growth rate ) ^ number of years
The number of years would be:
= 2046 - 2019
= 27 years
The population in 2046 would be:
= 202, 628 x ( 1 + 0.81 % ) ²⁷
= 251, 940 people
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What is m∠DBC? a 58° b 52° c 44° d 38°
The measure of the ∠DBC is 52°.
Because in this (∠DBC ) type of the situation we always consider the center alphabet for the angle.
In this the center alphabet is B, and there are some values given in the equation for a, b, c, d angles.
So, we can find the value of angle B which is 52°.
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3 over one thirds minus one foruth
The value of 3 over one thirds minus one forth is 8 3/4.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, 3 over one thirds minus one forth. This will be:
= 3 /(1/3) - 1/4
= (3 × 3) - 1/4
= 9 - 1/4
= 8 3/4
The value is 8 3/4.
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The Lakeview Toy Factory produced 180 stuffed animals. After donating 25 of the stuffed animals to a local e
Lakeview shipped the rest to 5 stores. Each of the stores received the same number of stuffed animals
Use the drop-down menus to select the response to make each statement true.
The expression
store.
180-25/5 Y
Each of the stores received
Q Revie
can be used to find the number of stuffed animals Lakeview shipped to each
stuffed animals.
The number of stuffed animals Lakeview shipped to each store is 31
The Lakeview Toy Factory produced 180 stuffed animal
It donated 25 of the stuffed animals to a local e
After donation the number of stuffed toys left = 180 - 25 = 155
Lakeview shipped the rest to 5 store
Each of the stores received the same number of stuffed animals
Number of stuffed animals each store recieved = total toys/ number of store
= 155/ 5 = 31
Therefore, the number of stuffed animals Lakeview shipped to each store is 31
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Square the binomial: (12y - 5)²
1. 144y² - 60y + 25
2. 144y² + 25
3. 144y² + 120y - 25
4. 144² - 120y + 25
Answer:
144y²-120y+25
Step-by-step explanation:
(12y-5)²
(12y-5)(12y-5)
12y(12y-5)-5(12y-5)
144y²-60y-60y+25
144y²-120y+25
The rate of change for linear function A is 1/3. It’s graph has a y intercept of 1. The graph below represents function B. What do the graphs of these two functions have in common?
Answer:
The [tex]x[/tex]-intercept
Step-by-step explanation:
The equation of line A is [tex]y=\frac{1}{3}x+1[/tex].
The equation of line B is [tex]y=x+3[/tex].
The lines share the same [tex]x[/tex] intercept, since when [tex]x=-3[/tex], [tex]y=0[/tex] for both lines.
Multiply and then simplify, if needed: 3x/ x² - 25 . x²+6x+5/6x²+6x Divide and then simplify, if needed: x²-2x-3/x²+2x+1 ÷ x³ -5x² +6x /x²-3x -4
The simplified form of the expression will be 1 / [2(x - 5)] and [(x - 4) / [x (x - 2)].
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The expression is given below.
⇒ [(3x) / (x² - 25)] · [(x² + 6x + 5) / (6x² + 6x)]
Simplify the expression, then we have
⇒ [(3x) / (x² - 25)] · [(x² + 6x + 5) / (6x² + 6x)]
⇒ [(3x) / (x² - 5²)] · [(x² + 5x + x + 5) / (6x² + 6x)]
⇒ {3x / [(x - 5)(x + 5)]} · {[(x + 5)(x + 1)] / [(6x)(x + 1)]}
⇒ 1 / [2(x - 5)]
The expression is given below.
⇒ [(x² - 2x - 3) / (x² + 2x + 1)] ÷ [(x³ - 5x² + 6x ) / (x² - 3x - 4)]
Simplify the expression, then we have
⇒ [(x² - 2x - 3) / (x² + 2x + 1)] ÷ [(x³ - 5x² + 6x ) / (x² - 3x - 4)]
⇒ {[(x - 3)(x + 1)] / [(x + 2)(x + 1)]} · {[(x - 4)(x + 1)] / [x(x - 3)(x - 2)]}
⇒ [(x - 4) / [x (x - 2)]
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a2- 3x -10 please solve this what will be the factor of it
Step-by-step explanation:
a² - 3x - 10
a(a -3) (x - 10)
The expression gives the same value as (3x-2x) + 2(2x-x)+4
3x + 4 is the expression that gives the same value as (3x-2x) + 2(2x-x) + 4
The Given Expression is : (3x-2x) + 2(2x-x) + 4
⇒ 1(x) + 2(x) + 4
⇒ x + 2x + 4
⇒ 3x + 4
Hence, the equivalent expression for the given expression is 3x + 4.
An Expression is composed only of variables, operators (or) symbols, and numbers. There will be no equality(=) sign in an expression.
If there is an equality(=) sign, then it is called an equation.
The value of given expression at x = 2 is :
(3(2) - 2(2)) + 2(2(2) - 2) + 4
= (6 - 4) + 2(4 - 2) + 4
= 2 + 2(2) + 4
= 2 + 4 + 4
= 10
The value of the equivalent expression is :
3(2) + 4
= 6 + 4
= 10
Both the expressions gave the same value.
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A polygon with an area of (4x^2 + 2x - 16) square units is combined with a rectangle that has a width of (6x + 2) units and a length of (x - 5) units. Then, a polygon with an area of (2x^2 - 30x - 10) square units is removed. What is the area of the final polygon?
The area of the final polygon is 8x² + 4x - 16
Calculating the area of a polygonFrom the question, we are to determine the area of the final polygon.
From the given information,
"A polygon with an area of (4x^2 + 2x - 16) square units is combined with a rectangle that has a width of (6x + 2) units and a length of (x - 5) units."
First, we will determine the area of the rectangle.
Area of the rectangle = (6x + 2)(x - 5)
Area of the rectangle = 6x² - 30x + 2x - 10
Area of the rectangle = 6x² - 28x - 10
Now, we will add it to the area of the polygon
4x² + 2x - 16 + 6x² - 28x - 10
= 4x² + 6x² - 28x + 2x - 10 - 16
= 10x² - 26x -26
Also,
From the given information,
"a polygon with an area of (2x^2 - 30x - 10) square units is removed"
Then,
The area of the final polygon = 10x² - 26x - 26 - (2x² - 30x - 10)
Area of the final polygon = 10x² - 26x - 26 - 2x² + 30x + 10
Area of the final polygon = 10x² - 2x² + 30x - 26x + 10 - 26
Area of the final polygon = 8x² + 4x - 16
Hence, the area is 8x² + 4x - 16
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8 more than s stripes
8 more than s stripes:
equation: s + 8
Cameron bought 9 bananas for $18. What was the cost of the bananas in bananas per dollar?
Answer:
2 dollars
Step-by-step explanation:
You divide 18 by 9 and get 2. That is the unit rate. :)
The annual profits for a company are given in the following table, where x represents the number of years since 1997, and y represents the profit in thousands of dollars. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected profit (in thousands of dollars) for 2006, rounded to the nearest thousand dollars.
Years since 1997 (x) Profits (y)
(in thousands of dollars)
00 131131
11 168168
22 202202
33 193193
44 221221
Regression Equation:
Final Answer:
The linear regression equation for the profit in x years after 1997 is of:
y = 20.5x + 142.
Using this equation, the estimate for the profit in 2006, is of: $326,500.
How to obtain the linear regression equation?The linear regression equation is obtained inserting the points of the data, represented either in a table or in a scatter plot, into a linear regression calculator.
In the context of this problem, these points are given as follows:
(0, 131), (1, 168), (2, 202), (3, 193), (4, 221).
Inserting these points into a calculator, the equation is:
y = 20.5x + 142.
The estimate for the profit in 2006, that is, 9 years after 1997, is of:
y = 20.5(9) + 142 = 326.5 thousand dollars = $326,500.
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