Answers
An exponential function with an initial value of 2 can be represented as f(x) = 2e^x, where '2' is the coefficient and 'e^x' is the exponential term. The term 'initial value' in this context refers to the coefficient, which is the output of the function when the input is 0.
Explanation:An exponential function with an initial value of 2 can be represented as f(x) = 2e^x. Here, the initial value is referred to as a coefficient or base of the exponential function. This means that the output of the function is 2 when the input is 0. Squaring of exponentials involves multiplying the exponent of the exponential term by 2.
As another example, in the exponential arithmetic expression 5^2, you 'square' the base number 5 by using the exponent '2', resulting in 25. Similarly, in the exponential function 2e^x, '2' is the initial value, 'e' is the base of the natural logarithm, and 'x' is the exponent representing the rate of change.
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An exponential function with an initial value of 2 can be represented by the equation y = 2 × aˣ. The number 2 is the output of the function when x is 0 which represents its initial value. Exponential functions involve repeated multiplication, expressed as a base number raised to an exponent.
Explanation:An exponential function that has an initial value of 2 would be represented by the equation y = 2 × aˣ, where 'a' is the base of the exponent, and 'x' is the exponent itself. To understand this, it's crucial to understand how exponential functions work. They are mathematical expressions that involve an exponent or power, which is shorthand for repeated multiplications of the base number.
In this equation, the initial value is the number 2, which means when x = 0 in the function y = 2 × aˣ, the output will be 2. The 'a' in the equation represents the factor by which the function changes for each unit increase or decrease in 'x', and it can vary based on the specific function or problem context.
An example of such an equation would be y = 2 × 3ˣ, where the initial value y(0) = 2, and the base of the exponent is '3'. When dealing with Exponential Arithmetic, you're expressing very large or very small numbers as a product of two numbers, the first of which is usually a non-zero number between 1 and 10, and the second is 10 raised to an exponent.
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Related Questions
what is the answer to 10+7x
Answers
Answer:if u I simplified then 17x
Step-by-step explanation:
Like terms are 10+7=17+x=17x
in the rectangle below ac=48 units what is de
Answers
Answer:
24
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The diagonals of a rectangle are congruent, thus
DB = AC = 48
The diagonals also bisect each other, thus
DE = 0.5DB = 0.5 × 48 = 24 → B
Set up and solve a proportion 6/100=s/12
Answers
Amount of tax on the book (s) is $0.72
Step-by-step explanation:
Step 1: Given 6/100 = s/12Step 2: Cross multiply to solve for s⇒ 6 × 12 = 100 × s
⇒ 72 = 100s
⇒ s = 72/100 = 0.72
If PQR measures 75°, what is the measure of SQR?
Answers
Answer: the measure of SQR is 53°
how do you do number 5 please.
Answers
Answer:
2.4 kg
Step-by-step explanation:
Given
dog eats 0.3 kg of dog food each day
hence we can say that the unit rate is 0.3 kg per day
1 day ------> eats 0.3 kg
8 days -------> eats 0.3 kg x 8 = 2.4 kg
Answer:
2.4 kilogram
Step-by-step explanation:
If
1 day = 0.3kg
8day =
0.3 multiply by number of days
0.3kg * 8= 2.4kg
Equivalent expressions 3.7r - 1.5r =
Answers
Answer:
2.2r
Step-by-step explanation:
3.7r - 1.5r =
= r(3.7 - 1.5)
= r×2.2
= 2.2r
Yo sup??
given expression: 3.7r-1.5r
3.7r-1.5r
=3.7r+(-1.5r)
=2.2r
Hope this helps.
write a number with two decimal places that are bigger than 4 1/5 but smaller than 4.25
Answers
Answer:4.21,4.22,4.23, 4.24
Step-by-step explanation:
4 1/5 is 4.2 as a decimal and the numbers between 4.2 and 4.5 as numbers with 2 places past the decimal place are the ones above.
The number with two decimal places that are bigger than 4(1/5) and smaller than 4.25 is 4.22.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
4(1/5)
= 21/5
= 4.2
Now,
Two decimal numbers between 4.2 and 4.25.
4.21, 4.22, 4.23, and 4,24.
Thus,
The number is 4.22.
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IM KINDA SLOWWWWW sorry
Answers
For the square root of 48, you can simplify it by finding two numbers; one of them having a perfect square and whatever number you choose for the second one, you find numbers there with one number having a perfect square. So for example, I would do 4*12 since it’s the easiest one I know. 4 has a square root of 2. However, with twelve, you can find two numbers that multiply to it with one of them with a perfect square, which would be 4*3,(again 4 having a perfect square root). So you would multiply 2 from the first 4(when you square rooted it), and the second 2( from 4*3). You should get 4 √ 3. The little sign means square root by the way. And if u wanna make sure they are equivalent, you can find the square root of 48 and find the product of 4 times the square root of 3. They should give the same answer.
You cannot simplify the square root of 15 as there are no two numbers with one of them having a perfect square.
You can simplify the square root of 100, that gives you 10.
This may not have helped, but I tired to explain it the best I could. Let me know if u want another explanation :)
Can you please help me with the problem in the image below?
Answers
Given data:
m∠P = m∠R and TP = SR
To prove that ΔQTP ≅ ΔQSR:
Consider ΔQTP and ΔQSR,
m∠P = m∠R (given angle)
TP = SR (given side)
m∠Q = m∠Q (common angle)
∴ ΔQTP ≅ ΔQSR (by ASA congruence rule)
Hence ΔQTP and ΔQSR are congruence triangles by Angle - Side - Angle congruence rule.
20 business cards are placed in a hat, 10 belong to women, 10 belong yo men If 2 cards are drawn at once. what's the probability that the first is a Man's card and the Second, A woman's card?
5/19
14/19
1/4
9/10
Answers
Answer:
First choice:
[tex]\large\boxed{\large\boxed{5/19}}[/tex]
Explanation:
The probability that the first is a man's card and the second, a woman's card is calculated as the product of both probabilities, taking into account the fact that the second time the number of cards in the hat has changed.
In spite of it is said that the cards are drawn at once, since it is stated a specific order for the cards (first is a man's card and the second, a woman's card) you can model the procedure as if the cards were drawn consecutively, instead of at once.
1. Probability that the first is a man's card
Number of cards in the hat = 20 (the 20 business card)Number of man's card in the hat: 10Probability = favorable oucomes / possible outcomes = 10/20 = 1/2.2. Probability that the second is a woman's card
Number of cards in the hat = 19 (there is one less card in the hat)Number of wonan's card in the hat: 10Probability = favorable oucomes / possible outcomes = 10/19.3. Probability that the first is a man's card and the second, a woman's card
(1/2) × (10/19) = 5/19That is the first choice.
Answer:
5/19
Step-by-step explanation:
I know this isn't as good as the other persons answer but I wanted to reassure you that it was correct and my proof is that I took a test on this and got it right with this answer. I hope I helped! :>
What does x equal in
-0.4 (x+3)=4
Answers
Answer:
x=-13
Step-by-step explanation:
1. Divide both sides by -0.4
2. Subtract -3 on both sides.
3. -10-3=-13
I don’t understand how to get the answer
Answers
x = –5 or x = 3
Solution:
Given expression:
[tex]|-1-x|=4[/tex]
[tex]\Rightarrow |-x-1|=4[/tex]
⇒ –x – 1 = 4 or –x – 1 = 4
First take –x – 1 = 4.
Add 1 on both side of the equation.
⇒ –x – 1 + 1 = 4 + 1
⇒ –x = 5
Divide by –1 on both side of the equation, we get
⇒ x = –5
Now take –x – 1 = –4.
Add 1 on both side of the equation.
⇒ –x – 1 + 1 = –4 + 1
⇒ –x = –3
Divide by –1 on both side of the equation, we get
⇒ x = 3
x = –5 or x = 3
Hence the two values of x are –5 or 3.
Answer please! True or false!
Answers
Answer:
a. False
b. False
c. False
d. True
e. False. (any number above 14.5 is a solution).
Step-by-step explanation:
12 + 6y > 99
6y > 87
y > 14.5.
False
False (the answers are equal and therefore it’s not larger than 99)
True
False (there can be multiple answers but it needs to be above 14.5)
The graph at the right shows the relationship between distance and time for a car driven at a constant speed.
1. What is the speed?
2. Is this a function relationship?
3. If this is a function, write a rule to represent it.
Answers
Answer:
1. 60 miles per hour
2. Yes, linear
3. Y=60x
Step-by-step explanation:
1. Speed is 60 miles per hour.
2. A function relationship is a relationship between two variables.
3. The rule to represent the function is Distance = 60t.
1. What is the speed?
The speed of the car is the rate at which it is traveling. It is calculated by dividing the distance traveled by the time taken to travel that distance.
Speed = Distance / Time
From the graph, we can see that the car travels 120 miles in 2 hours. Therefore, the speed of the car is:
Speed = 120 miles / 2 hours = 60 miles per hour
2. Is this a function relationship?
A function relationship is a relationship between two variables where each input value has only one output value. In other words, for every value of the independent variable (in this case, time), there is only one corresponding value of the dependent variable (in this case, distance).
We can see from the graph that the distance traveled by the car increases linearly with time. This means that there is a one-to-one relationship between the two variables, and therefore the relationship is a function.
3. If this is a function, write a rule to represent it.
A rule for a function is a mathematical expression that shows how the dependent variable is related to the independent variable. In this case, the rule for the function would be:
Distance = Speed * Time
Substituting the speed of the car into the rule, we get:
Distance = 60 miles per hour * Time
Therefore, the rule to represent the function is:
Distance = 60t
where t is the time in hours.
Questions 32 help plz with explanation. 15 points!!
Answers
Answer:
The man's son
Step-by-step explanation:
"Brothers and sisters I have none, but that man's father is my father's son" the part where he says "that man's father is my father's son" implies that he is looking at his son.
What is 8x to the second power plus 10x
Answers
hope this helps!
The expression [tex]8x^2 + 10x[/tex] factors to [tex]2x(4x + 5)[/tex] and has solutions x = 0 and x = -5/4.
We first need to understand what it represents. In this expression, [tex]x[/tex] is the variable, and the terms [tex]8x^2[/tex] and [tex]10x[/tex] are polynomial terms where:
[tex]8x^2[/tex] indicates that the variable [tex]x[/tex] is raised to the power of 2, meaning it is multiplied by itself ([tex]x \times x[/tex]) and then scaled by a factor of 8.
[tex]10x[/tex] means that the variable [tex]x[/tex] is multiplied by 10.
The first term is [tex]8x^2[/tex].
The second term is [tex]10x[/tex].
In this case, the terms are not like terms because one is [tex]x^2[/tex] and the other is [tex]x[/tex]. Therefore, they cannot be combined further. The expression is simplest as it stands, which is: [tex]8x^2 + 10x[/tex]
Factoring out [tex]2x[/tex] gives us:
[tex]2x(4x + 5)[/tex]
Thus, [tex]8x^2 + 10x[/tex] can also be expressed as [tex]2x(4x + 5)[/tex]. This is useful if you are trying to find the roots of the equation (setting it equal to zero) since it can help identify the values of [tex]x[/tex] that satisfy the equation [tex]8x^2 + 10x = 0[/tex].
This gives two possible solutions for x:
2 * x = 0 which leads to x = 0
4 * x + 5 = 0 which leads to x = -5/4
What are all possible functions from 1 to 9
Answers
Answer:
In mathematics, a function (f) is a relationship between a given set X (called domain) and another set of elements Y (called codomain) so that each element x of the domain corresponds to a single element f (x) of the domain (the that form the route, also called scope ranking).
See: Relations and functions
In everyday or simpler language, we will say that mathematical functions are equivalent to the common logical process that is expressed as "dependent on."
Mathematical functions can refer to everyday situations, such as: the cost of a phone call that depends on its duration, or the cost of sending a parcel that depends on its weight.
As an example, what would be the rule that relates the numbers on the right with those on the left in the following list ?:
1 --------> 1
2 --------> 4
3 --------> 9
4 --------> 16
The numbers on the right are the squares of those on the left.
The rule is then to "square":
1 --------> 1
2 --------> 4
3 --------> 9
4 --------> 16
x --------> x 2.
To refer to this rule we can use a name, which is usually the letter f (of function). So, f is the rule "square the number".
Usually two notations are used:
x --------> x 2 or f (x) = x 2.
Thus, f (3) means applying the rule f to 3. Doing so results in 3 2 = 9.
Then f (3) = 9. Similarly f (2) = 4, f (4) = 16, f (a) = a 2, etc.
is 28 √6 rational or irrational
Answers
Answer:
68.58571279792898674952395409176495897504652945838676359611.....
Irrational
Step-by-step explanation:
Answer:
It is irrational
Step-by-step explanation:
28sqrt6=sqrt(28^2*6)=sqrt(784*6)=sqrt(4704)=68.5857128...
Since the decimals go on forever, 28sqrt6 is irrational
Hope this helped!
1/2 = 1/3 − |x−3/6 +x|
Answers
Answer:
No solution exist!
Step-by-step explanation:
Answer:
It is impossible to have an arithmetic answer. No Solutions, or ø
a teacher has 64 students to divide into small groups greater than 2 with no remaimder. how many ways can this be done?
Answers
To divide 64 students into small groups greater than 2 with no remainder, you would use the concept of combinations, specifically 62C3, resulting in 3,992 possible ways.
Explanation:A teacher has 64 students to divide into small groups greater than 2 with no remainder. To solve this, we can use the concept of combinations, denoted as nCr, where n is the total number of students and r is the size of each group. In this case, the calculation would be 62C3, which equals 3,992 ways of dividing the students into groups.
solve for x.
Brainlest for anyone who helps!!
thanks you
Answers
================================================
Explanation:
If points F and E are the midpoints of segment VU and segment ST respectively, then segment FE is the midsegment of the trapezoid. The midsegment is parallel to the bases, and the midsegment's length is found by adding up the bases VS and UT, then dividing by 2.
(VS + UT)/2 = FE
(29 + x+17)/2 = 23 ... plug in given info; isolate x
(x+46)/2 = 23
x+46 = 23*2 ... multiply both sides by 2
x+46 = 46
x = 46-46 ... subtract 46 from both sides
x = 0Louise completed the work shown below.
(5x3 + 3)2 = (5x3)2 + (3)2 = 25x6 + 9
Determine if Louise’s answer is correct. Explain.
Answers
Louise’s answer is not correct
Step-by-step explanation:
Let us revise how to solve (ax + b)²
Square the 1st term ⇒ (ax)²Multiply the 1st term, the 2nd term and 2 ⇒ 2(ax)(b)Square the 2nd term ⇒ (b)²(ax + b)² = (ax)² + 2(ax)(b) + (b)²The answer of square a binomial contains three terms: (1st)² + 2(1st)(2nd) + (2nd)²
∵ The bracket is (5x³ + 3)²
- Square the first term
∴ The first term of the answer = (5x³)² = (5)²(x³)² = [tex]25x^{6}[/tex]
- Multiply the 1st , the 2nd term and 2
∴ The second term of the answer = 2(5x³)(3) = 2(5)(3)x³ = 30x³
- Square the 2nd term
∴ The third term of the answer = (3)² = 9
∴ (5x³ + 3)² = [tex]25x^{6}[/tex] + 30x³ + 9
∵ Louise’s answer is (5x³)² + (3)² = [tex]25x^{6}[/tex] + 9
- By comparing the his answer with the answer above, he did
not find the middle term
∴ Louise’s answer is not correct
Learn more:
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Answer:
Sample Response: Louise’s answer is not correct. She is missing the term 30x3. When squaring a binomial, it is best to write the product of the binomial times itself. Then you can use the distributive property to multiply each term in the first binomial by each term in the second binomial. Louise also could have used the formula for a perfect square trinomial, which is found by squaring a binomial.
Step-by-step explanation:
Sample Response ^^^
The lines $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are parallel. If $\angle BAE=54^{\circ}$ and $\angle DCE=25^{\circ}$, what is the measure of $\angle AEC$?
Use an asymptote convertor if needed:
[asy]
size( 200 ) ;
pair A = (0,0) ;
pair B = (0,2) ;
pair C = (3,0.5) ;
pair D = (3,2.5) ;
pair ptE = extension( A , A+dir(90-54) , C , C+dir(90+25) ) ;
draw( (0,-0.5)--(0,3) , linewidth(1.3) ) ;
draw( (3,-0.5)--(3,3) , linewidth(1.3) ) ;
draw( A--ptE--C ) ;
dot(Label( "$A$" , A , W )) ;
dot(Label( "$B$" , B , W )) ;
dot(Label( "$C$" , C , E )) ;
dot(Label( "$D$" , D , E )) ;
dot(Label( "$E$" , ptE , N )) ;
label( "$54^{\circ}$" , A , 5dir(70) ) ;
label( "$25^{\circ}$" , C , 8dir(100) ) ;
[/asy]
Answers
Answer:
79°
Step-by-step explanation:
Label the intersection of AE and CD point F. Then angle CFE is an alternate interior angle with angle BAE, so is congruent. The angle of interest is an exterior angle to triangle CFE, so is the sum of remote interior angles CFE (54°) and DCE (25°). That sum is ...
m∠AEC = 54° +25° = 79°
Based on the definition of alternate interior angles, the measure of ∠AEC is: 79°
What are Alternate Interior Angles?Interior angles that are alternating each other on a transversal are congruent, and are called alternate interior angles.
Thus:
m∠AEC = m∠BAE + m∠FCE
Substitute
m∠AEC = 54° + 25°
m∠AEC = 79°
Therefore, based on the definition of alternate interior angles, the measure of ∠AEC is: 79°
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what is the solution ? Please help with this !!
Answers
Answer:
the answer is c
Step-by-step explanation:
see picture
Which of the following sets of numbers could be the side lengths of a right triangle? 5, 12, 13 5, 5, 9 14, 14, 14 2, 3, 5
Answers
Answer:
5,12,13
Step-by-step explanation:
i think thats what the other person meant to say, either way, these numbers are correct
Answer: 5, 12, 13
Step-by-step explanation:
what is 1% of 12.54?
Answers
Answer:
0.1254
Step-by-step explanation:
(Divide by 100 to get 1%)
Answer:
Step-by-step explanation:
0.1254
For all values of x, which expression is equivalent to x + 1 − x + 2x + x + 1?
Answers
Answer:
3x+2
Step-by-step explanation:
We want to find an expression that is equivalent to:
[tex]x+1-x+2x+x+1[/tex]
We regroup similar terms to get:
[tex]x-x+2x+x+1+1[/tex]
We now combine the similar terms to obtain:
[tex]3x+2[/tex]
Therefore the expression that is equivalent to: x + 1 − x + 2x + x + 1 is [tex]3x+2[/tex]
Answer:
3x + 2
Step-by-step explanation:
3x + 2
Solve by simplifying the given expression OR substitute 1 for x in each expression.
x + 1 − x + 2x + x + 1 → x − x + 2x + x + 2 → 3x + 2
OR
x + 1 − x + 2x + x + 1 → 1 + 1 − 1 + 2(1) + 1 + 1 = 5
3x + 2 → 3(1) + 2 = 5
help asap please!!!!!!!
Answers
Answer:
VW=30, WX=20, YW=30,ZX=20
Step-by-step explanation:
Which value of n makes the equation true? 6n − 2(4n + 7) + 4 = -2
Answers
Answer:
n = - 4
Step-by-step explanation:
Given
6n - 2(4n + 7) + 4 = - 2 ← distribute and simplify left side
6n - 8n - 14 + 4 = - 2
- 2n - 10 = - 2 ( add 10 to both sides )
- 2n = 8 ( divide both sides by - 2 )
n = - 4
To solve the equation 6n - 2(4n + 7) + 4 = -2, we apply the distributive property and combine like terms to simplify. The solution is n = -4.
To solve the equation 6n - 2(4n + 7) + 4 = -2, we need to apply the distributive property and combine like terms to simplify.
Distribute the -2 to both terms inside the parentheses: -2(4n + 7) = -8n - 14.Combine like terms: 6n - 8n - 14 + 4 = -2.Combine like terms again: -2n - 10 = -2.Next, we isolate the variable n by adding 10 to both sides: -2n - 10 + 10 = -2 + 10.Simplify: -2n = 8.Finally, solve for n by dividing both sides by -2: n = 8 / -2.Therefore, the value of n that makes the equation true is n = -4.
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If Greg but 10 pieces of candy for $5.20 How much will it be for one piece of
Answers
Answer:
One piece of candy costs $0.52.
Step-by-step explanation:
5.2/10=0.52