We need to know about natural exponential function to solve the problem. The given function is a natural base exponential function.
An exponential function is a function in which x is an exponent. An exponential function has an exponential graph that keeps growing. A natural base exponential function is one where the base of the function is e which is a mathematical constant and is approximately equal to 2.71828. The inverse of a natural exponential function is a logarithmic function. An exponential function is of the form y=[tex]b^{x}[/tex] where b is the base, in a natural base exponential function, the b is replaced by e which means y=[tex]e^{x}[/tex]. In the given question y=[tex]e^{x+7}[/tex] is a natural base exponential function since the base is the natural base.
Therefore we found that the given function is a natural base exponential function.
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Which Of the expressions below means same as w/5
The expression that means the same as the given expression is w ÷ 5
Evaluating an expressionFrom the question, we are to determine which of the given expressions means the same as w/5
To do this, we will simplify each of the given expressions if possible
w + 5This expression cannot be simplified further
w -5This expression cannot be simplified further
w ÷ 5This expression can be written as w/5
5 × wThis expression can be written as 5w
5 - wThis expression cannot be simplified further
5 ÷ wThis expression can be written as 5/w
Hence, the expression is w ÷ 5
Here is the complete question:
Which Of the expressions below means same as w/5
w + 5
w - 5
w ÷ 5
5 × w
5 - w
5 ÷ w
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Let u = (-1,3), v=(2,4) , and w= ( 2,-5) . Find the component forms of the following vectors. 2u
Given u = (-1,3), v=(2,4) , and w= ( 2,-5), then, by applying scalar multiplication on vector, 2u = (–2, 6)
In the two-dimensional coordinate system, vectors can be split into x-component and y-component.
We can write, for example, a vector q = (1,–5), which means:
x-component = 1
y-component = –5
Operations on vectors:
Addition / subtraction of vectors: Just add or subtract the corresponding components.In the given problem:
u = (-1,3), v = ( 2,4) , and w = (2,-5)
Then,
2u = 2 (-1,3)
= (2 . (-1), 2. 3) = (–2, 6)
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Four different linear functions are represented below.
HELP!
Answer:
Step-by-step explanation:
A: Function 2 only; at the point where x = 0, the value of the function is 5, which is greater than 3.
B: Function 3; the coefficient of x is the greatest out of all of them.
C: Function 4; the y-intercept of -1 only deviates from 0 by 1.
There are approximately 9.3 x 106 dairy cows in the United States, with each cow producing approximately 2.5 x 10 gallons
of milk each year. How much milk do United States dairy cows produce each year? Write the answer in scientific notation
2.4645×10⁴ gallons of milk do United States dairy cows produce each year.
Why we need scientific notation ?We need scientific notation reason is large number can be written in compact form.
According to the given question There are approximately 9.3 x 106 dairy cows in the United States.
Which is 985.8 cows in the united states.
Also given each cow produces 2.5×10 = 25 gallons of milk per year.
∴ United state cows will produce (985.8×25) gallons of milk each year which is = 24645 gallons of milk per year.
Now 24645 can be represented as 2.4645×10⁴ gallons of milk.
We have raised it to the 4th power of 10 because we have moved the decimal 4 digits before to balance the number and we know that in scientific notation base should be greater than 1 and less than 4 so moving the decimal to some other place is not valid.
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Use the properties of logarithms to write log 18 in four different ways. Name each property you use.
The logarithmic properties used are Quotient property, Product property, Power property and Product and Power Property.
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log a × b = log a + log blog a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression is,
log 18
now, log 18 can be written in following four ways :
1. Using Quotient Property of logarithms
[tex]log 18 = log \frac{36}{2} = log 36 - log 2[/tex]
2. Using Product Property of logarithms
[tex]log 18 = log (9.2) = log 9+ log2[/tex]
3. Using Power Property of logarithms
[tex]log 18 = log (324)^\frac{1}{2} = \frac{1}{2} log (324 )[/tex]
4. Using Product and Power Property of logarithms
[tex]log 18 =l og 2.3^2 = log 2 +2log3[/tex]
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what is the distance (2,-2) and (-3,-1) points
The distance between two points (2,-2) and (-3,-1) is √26 units.
Given points are (2,-2) and (-3,-1)
Let A(2,-2), B(-3,-1)
We need to calculate the distance between two points.
We know that distance between two points means the length of the line segment that connects two points in the 2D plane.
The formula for finding the distance between the two points A(x₁, y₁),
B(x₂, y₂) in a plane is given by
D = √((x₂ - x₁)² + (y₂ - y₁)²)
Now we have two points A(2,-2), B(-3,-1)
By using the above formula we get the distance as
D = √((-3 - 2)² + (-1 - (-2))²)
D = √((-5)² + (-1+2)²)
D = √(25 + (1)²
D = √(25+1)
D = √26 units
∴ The distance between two points (2,-2) and (-3,-1) is √26 units.
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(please help) a couple with 32 children want to save for college. They invest 50,000 in two different corporate bonds for 1 year One bond pays 5% simple interest while the other pays 6.5% simple interest. The total interest they received from the bonds was $3000. Find the amount they invested in each bond
The amount invested in the bond with 5% simple interest is $16,666.67
The amount invested in the bond with 6.5% simple interest is $33,333.33
What is simple interest?
The interest earned under a simple interest arrangement is determined as the amount invested multiplied by the interest rate and the time the investment lasts
I=PRT
let us assume that x was invested in the bond with 5%
interest on x=5%*x=0.05x
amount invested in other bond=50000-x
interest earned on 6.5%=(50000-x)*6.5%
interest earned on 6.5%=3250-0.065x
total interest=0.05x+3250-0.065x
total interest=3250-0.015x
total interest=3000
3000=3250-0.015x
0.015x=3250-3000
0.015x=250
x=250/0.015
x=$16,666.67
amount invested at 6.5%=$50,000-$16,666.67
amount invested at 6.5%=$33,333.33
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Simplify each expression. (-27)²/₃
The simplification of the expression (-27)²/₃ is 9.
We are given, (-27)²/₃ and we are required to simplify
What (-27)²/₃ means is that (-27) is to the power of 2 and 1/3
Let's start by finding out [tex](-27)^{2}[/tex] .The result is, 729
Then, [tex]729^{1/3}[/tex]
= 9
The final result is 9
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How do I do this ???
Answer:
(-1,4)
(0,0)
(1,-4)
(1,-8)
Step-by-step explanation:
Substitute the value of x in the equation and find the corresponding y value.
y = -4x
When x = -1 ; y = -4*(-1) = 4.
When x = 0 ; y = 0
When x = 1 ; y = -4*1 = -4
When x = 2 ; y = -4*2 = -8
Look at the following conditionals:
If Vivian is eating pizza, then she is at Big Slice Pizza.
If Vivian is at Big Slice Pizza, then she is eating pizza.
Is the second conditional the contrapositive, converse, or inverse of the first cond
contrapositive
converse
inverse of the first conditional
Answer:
inverse I believe because it is the same statement but opposite
A person invests 9000 dollars in a bank. The bank pays 4.25% interest compounded
semi-annually. To the nearest tenth of a year, how long must the person leave the
money in the bank until it reaches 14200 dollars?
The time taken to reach $14200 in the bank with 4.25% interest compounded is 50 years
The time taken to reach 14200 with interest compounded semi-annually can be calculated by
[tex]A = P (1 +\frac{R}{100n})^{nT}[/tex]
where A is the total amount at the end of the period
P is the principal amount
R is the rate of interest
n is the no. of interest compounded per year
T is the time period
We know that A = 14200
P = 9000
R = 4.25%
n = 2
By substituting these values, we get
14200 = 9000 [1 + (4.25 /200[tex]]^{2T}[/tex]
14200/9000 = [tex](1+0.02125)^{2T}[/tex]
1.5778 = [tex](1+0.02125)^{2T}[/tex]
1.5778 = [tex](1+0.02125)^{2T}[/tex]
1.5778 =[tex](1 +0.02125)^{2T}[/tex]
Taking logs on both sides,
log (1.5778) = log [tex](1+0.02125)^{2T}[/tex]
log (1.5778) = 2T log(1 +0.02125)
0.198 = 2T log(1.02125)
0.198 = 2T (0.00913)
0.918 = 0.01826 T
T = 0.918 / 0.01826
T = 50.27 yrs
T ≅ 50 years
Therefore, the time taken to reach $14200 in the bank with 4.25% interest compounded is 50 years
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The force F of gravity on a rocket varies directly with its mass m and inversely with the square of its distance d from Earth. Write a model for this combined variation. Write an equation to find the mass of the rocket in terms of F and d .
Model for the Combined variation is [tex]F = \frac{km}{d^{2} }[/tex]
Equation to find the mass of the rocket in terms of F and d is :
[tex]m=\frac{F d^{2} }{k}[/tex]
What is Force ?A force is the quantity that change the motion of the object. Force is that influence which can cause any object having some mass, to change it's position or to accelerate from it's original position.
Force (F) and mass (m) of any object are directly proportional to each other. More the mass of the object , more the force will require to accelerate it.
Mathematically, we can write the equation of force as :
F = m . a
where , m = mass of the object
a = constant value
In the statement given,
As, force of gravity varies directly with its mass
Therefore, F= k m , where k is a constant
Also force is inversely varies with square of distance d
Thus, F = k / d²
Combining both equations :
[tex]F = \frac{km}{d^{2} }[/tex]
and the equation of mass in terms of F and d can be written as :
[tex]m=\frac{F d^{2} }{k}[/tex]
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Can someone please help me with this i been working so long with this
Answer:
12
Step-by-step explanation:
since both are square it is 12
Which of the following is the slope-intercept form of 9x + 3y – 15 = 0?
Answer:
y = -3x + 5
Step-by-step explanation:
slope-intercept form means it should look like
y = mx + b
9x + 3y – 15 = 0
3y = -9x + 15
y = -3x + 5
can anyone help fast please
The rate at which Riya is applying mulch in m³/m² is 0.25m³/m²
From the question, we are to determine the rate at which Riya is applying mulch in m³/m²
From the given information, we have that
Riya is applying mulch to her garden at a rate of 250,000 cm³ of mulch for every m² of the garden space
That is,
The rate at which she is applying mulch is 250,000 cm³/m²
Now, to determine the rate in m³/m², we will convert 250,000 cm³ to m³
Converting 250,000 cm³ to m³
250,000 cm³ = 250000 × (10⁻²)³ m³
= 250000 × 10⁻⁶ m³
= 0.25 m³
Hence, the rate at which Riya is applying mulch in m³/m² is 0.25m³/m²
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g(t)=−9t−4g, left parenthesis, t, right parenthesis, equals, minus, 9, t, minus, 4
g\Big(g(g, left parenthesis
\Big)=23)=23
The resulting expression if the value of t is 23 is g(23) = -4g - 207
Function and valuesA function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given the function below;
g(t)=−9t−4g
We are to determine the value of g(23). Substitute t = 23;
g(t)=−9t−4g
g(23) = -9(23) - 4g
g(23) = -207 - 4g
g(23) = -4g - 207
Hence the resulting expression if the value of t is 23 is g(23) = -4g - 207
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photo.
Write in standard notation.
1. 2.3 x 102
2. 4.67 x 107
3. 9.1 x 10-5
4. 1.2 x 10⁰
5. 5x10
The standard notation for the given terms is (1). 234.6; (2). 499.69; (3). 86; (4). 1.2; (5). 50.
What is standard notation?A standard notation is a set of rules for writing a given number, equation, or expression.To represent large or small numbers, a standard form of a number is used. In standard notation, exponents are used to represent such numbers.As a result, to represent very large or very small numbers in a concise manner, we use standard notation.Depending on the mathematical concept, the standard notation will differ.Conversion of the different notation into standard notations is given below:
1. 2.3 x 102 = 234.6
2. 4.67 x 107 = 499.69
3. 9.1 x 10-5 = 86
4. 1.2 x 10⁰ = 1.2
5. 5x10 = 50
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Simplify (-6b)(-18b) please!!!
Answer:
108b^2
Step-by-step explanation:
(-6)(-18)=108
(b)(b)=b^2
108b^2
8. Find y
7yº
(5y+36)
Answer:
35ºy^2+252yº
Step-by-step explanation:
Please help me with these questions!
Since slopes m₁ and m₂ are equal to 5, it shows that these two lines are parallel.
What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
The condition for two parallel lines.In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts. This ultimately implies that, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m is the slope.
Mathematically, the standard form of the equation of a straight line is given by;
y = mx + b
Given the following equations:
y = 5x + 1
2y - 10x + 3 = 0 ⇒ y = 5x - 3/2
m₁ = m₂ = 5.
In this context, we can reasonably infer and logically deduce that these two lines are parallel.
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Complete Question:
The equation line L₁ is y = 5x + 1
The equation line L₂ is 2y - 10x + 3 = 0
Show that these two lines are parallel.
9x +8y=40 written in slope-intercept form.
Answer: Slope = 2.250/2.000 = 1.125
x-intercept = 40/9 = 4.44444
y-intercept = 40/-8 = 5/-1 = -5.00000
Step-by-step explanation:
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -5.000 and for x=2.000, the value of y is -2.750. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -2.750 - (-5.000) = 2.250 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
ttttttgyygyyAnswer:
Step-by-step explanation:
gtgtggtgyyyhhyhyy
What is the center of dilation?
Answer:
Point Y
Step-by-step explanation:
This dilation is an expansion, so in order for it to expand, the center of dilation need to be in the middle or near the middle of the pre-image.
What is a pre-image?
Noun. preimage (plural preimages) (mathematics) For a given function, the set of all elements of the domain that are mapped into a given subset of the codomain; (formally) given a function ƒ : X → Y and a subset B ⊆ Y, the set ƒ−1(B) = {x ∈ X : ƒ(x) ∈ B}.
What is an Image?
The new position of a point, a line, a line segment, or a figure after a transformation is called its image.
Center of Dilation:
The center of a dilation is a fixed point in the plane about which all points are expanded or contracted. The center is the only invariant (not changing) point under a dilation (k ≠1), and may be located inside, outside, or on a figure.
I hope this helps! :)
Find the least integer greater than each number. Do not use a calculator.
log₅1/47
The least integer greater than each number for log₅1/47 = -3
All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.
Let y = log₅1/47
We know, logₐ x = y, only if a^y= x
Therefore, 5^y = 1/47
So, we must find an integer y such that 5 > 1/47
5^y > 1/47
5^{-3} > 1/47
(As, 5² = 25; 5³ = 125) (Since, 5² < 47, the answer will be 5³ as 5³ > 47)In this case, y = -3 will be the least integer to satisfy this inequality.
Therefore, the ultimate answer to the equation is log₅1/47 = -3
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E is the midpoint of segment DF. if DE = 3x and EF = 18, find the value of x.
The value of x is 6 if E is the midpoint of the segment.
Given,
E is the midpoint, so DE = EF
DE = 3x
EF = 18
Since DE = EF,
3x = 18
x =18/3
x = 6
If x = 6 , then
DE = 3x
DE = 3(6)
DE = 18
therefore, DE = EF since E is the mid point.
EF = 18
hence we get the value of x as 6.
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What is the slope of the line that passes through the points (2, 3) and (0, 11)? Write
your answer in simplest form.
Answer:
-4
Step-by-step explanation:
If you graph the two coordinates the line is going down, so the answer is going to be negative. The slope is -4/1 but simplified is -4. Hope this helps. Have a great night.
The scale on a map is 1:500000
Two towns are 7cm apart on the map
Work out the actual distance between the towns. Give your answer in kilometres
Answer:
Step-by-step explanation:
1: 500,000 cm
500,000cm can also be written as 5000m or 5 km
So it becomes 1:5km
the 1 represents 1cm on the map so every centimeter in the map is 5 kilometers in real life
If we want to get what 7 cm would be in kilometers then we have to multiply both sides by 7.
So it would be 1 x 7 and 5x 7
it would end up being 7 : 35 km
The answer is: 35km
help me
please show your solution
Answer:
[tex] a_{1} = 5[/tex]
Step-by-step explanation:
check the attached image for explanation
I am a 5-digit number between 52,000 and 53,000. The sum of my digits is 21. My ones digit is a multiple of 3. My tens digit is equal to my hundreds digit.
Read the clues. Find the number
Step-by-step explanation:
5 digit number
5abcd
a = 2 or a = 3. but a = 3 means the upper limit of 53,000. and the sum of digits is 8 and not 21.
so, a = 2.
d = 3n
c = b
5 + a + b + c + d = 21
5 + a + 2b + 3n = 21
a + 2b + 3n = 16
2 + 2b + 3n = 16
2b + 3n = 14
so, n must be an even number to allow an even result (14). therefore, n = 0 or n = 2 (any larger even number n like 4 would not create a single digit result)
if n = 0, then 2b = 14, b = 7
if n = 2, then 2b + 6 = 14, 2b = 8, b = 4
so, we have the options
52770
52446
I suspect that 0 as 0×3 is not considered a multiple of 3 by your teacher, so only n = 2 (or d = 6) is a desired solution.
therefore, I would use
52446
as answer.
What is the value of 1742 divided by 4.16
Answer:
1742 is divided by 2.16 than answer is 418.75
I need to find the mean of -2, 20, -200, 2,000
Answer: 454.5
Step-by-step explanation:
-2, 20, -200, 2,000 ==> 4 numbers
Mean: (-2+20+(-200)+2000)/4=
(18-200+2000)/4=
(-182+2000)/4
1818/4=454.5