Which exponential function has an initial value of 2?
Of(x) = 2(3)
Of(x) = 3(2)
X
-2
-1
TY
f(x)
18
Answers
f(x) =2(3ˣ) is an exponential function which has an initial value of 2.
What is an exponential function?Another word for "involving an exponent" in mathematics is exponential. For instance, an exponential rise in a number occurs when you raise it to the tenth power.
A mathematical function with the formula f(x) = aˣ 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 seen. A variable is used as the exponent in exponential functions.
The exponential function that has an initial value of 2 is f(x) = 2ˣ.
f(x) = 2(3ˣ) can be written as f(x) = 2 × 3ˣ, so it starts at 2 × 3⁰ = 2 × 1 = 2.
f(x) = 3(2ˣ) can be written as f(x) = 3 × 2ˣ, so it starts at 3 × 2⁰ = 3 × 1 = 3
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Related Questions
what is the coefficient of x8y9 in the expansion of (3x + 2y)17?
Answers
The coefficient of x⁸y⁹ is 81662929920.
What is binomial expansion?A binomial is a two-term algebraic expression. Examples of binomials include a + b, x - y, and more.
The binomial expansion formulae are used to find the powers of the binomials that cannot be extended using the algebraic identities.
Given expansion (3x + 2y)¹⁷
to find the coefficient of x⁸y⁹
this is found by binomial expansion,
(x + y)ⁿ = ∑ₙˣ⁻⁰ ⁿCₓxⁿ⁻ˣyˣ
here n = 17 and x = 9
(3x + 2y)¹⁷ = ¹⁷C₉ (3x)¹⁷⁻⁹ (2y)⁹
¹⁷C₉ = 24310
(3x + 2y)¹⁷ = 24310 (6561) (x)⁸ (512) (y⁹)
(3x + 2y)¹⁷ = 81662929920x⁸y⁹
Hence the coefficient is 81662929920.
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Two numbers have a sum of 21 and a difference of 6. What are these two numbers?
Answers
If the sum of 21 and a difference of 6 then the numbers are 27/2 and 15/2.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let, The two numbers be a and b.
Therefore, (a + b) = 21 and (a - b) = 6.
Adding these two equations, The variable 'b' will cancel out and we'll have
2a = 27.
a = 27/2.
And, 27/2 + b = 21.
b = 21 - 27/2.
b = (42 - 27)/2.
b = 15/2.
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During a particularly dry growing season in a southern state, farmers noticed that there is a delicate balance between the number of seeds that are planted per square foot and the yield of the crop in pounds per square foot. The yields were the smallest when the number of seeds per square foot was either very small or very large. What is the explanatory variable for this relationship
Answers
The number of seeds per square foot is the variable that explains the variation in the yield of the crop in pounds per square foot.
The explanatory variable for this relationship is the number of seeds per square foot. The number of seeds per square foot is the variable that is being manipulated or changed by the farmers in order to observe the effect on the yield of the crop in pounds per square foot.
The farmers observed that the yields were the smallest when the number of seeds per square foot was either very small or very large, this means that there is an optimal number of seeds per square foot that yields the highest crop.
So, the number of seeds per square foot is the variable that explains the variation in the yield of the crop in pounds per square foot.
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How do you find Y1 and y2 on a graph?
Answers
The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁).
Now, According to the question:
Finding Slope From Two Points Formula
The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁). Here,
m = slope of the line
x₁ = the x-coordinate of the first point
y₁ = the y-coordinate of the first point
x₂ = the x-coordinate of the second point
y₂ = the x-coordinate of the second point
Then rise from A to B = y₂ - y₁
Run from A to B = x₂ - x₁
Then the slope, m = rise/run = (y₂ - y₁) / (x₂ - x₁)
Hence, we derived the slope formula.
Here are the steps to find the slope of a line given two points on it.
In the first point, denote the x coordinate with x₁ and denote the y-coordinate with y₁.In the second point, denote the x coordinate with x₂ and denote the y-coordinate with y₂.Find the differences y₂ - y₁ and x₂ - x₁.Divide the difference of y-coordinates by the difference of x-coordinates to find the slope (m). i.e., m = (y₂ - y₁) / (x₂ - x₁).Learn more about Slope at:
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Suppose $P(x)$ is a polynomial of smallest possible degree such that: $\bullet$ $P(x)$ has rational coefficients $\bullet$ $P(-3)
Answers
The value of polynomial p(x) when x=0 is 35.
What is a polynomial?
An expression made up of indeterminates and coefficients and utilising solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables is referred to as a polynomial.
The complete question is as follows:
Suppose p(x) is a polynomial of smallest possible degree such that: bullet p(x) has rational coefficients bullet p(-3) = p(\sqrt 7) = p(1-\sqrt 6) = 0 bullet p(-1) = 8 determine the value of p(0).
Given,
p(x) is a polynomial of smallest degree where
p(-3) = p(√7) = p( 1-√6) = 0
p(-1) = 8
So the factors of p are (x+3),(x-√7) and (x - 1+√6)
Given p has rational coeffecients. So we should remove √7 and √6. This can be done by multiplying with conjugates.
(x-√7)*(x+√7) = x²-7
(x-1+√6) * (x-1-√6) = (x-1)² - √6² = x²-2x+1-6 = x²-2x-5
Now the polynomial can be written as
p(x) = c (x+3)(x²-7) (x²-2x-5 )
Here c is a constant and can be determined using p(-1) = 8
p(-1) = c ( -1+3)(-1² - 7 )(-1²-2*(-1) -5)
8 = c(2)(-6)(-2)
c = 1/3
Now the polynomial p(x) = 1/3(x+3)(x²-7) (x²-2x-5 )
Therefore p(0) = 1/3 (3) (-7)(-5) = 35
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A university just acquired more land which is shown by the triangle in the diagram. What is the area of the land that the university just aquired?
Answers
Therefore , the solution of the given problem of area comes out to be the land acquired by university is of 3 miles square area.
Define area.The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.
Area = length x breadth.
Here,
Given : A triangle land which has
height = 2miles
and base = 1.5+ 1.5 = 3 miles
Thus,
To find the area of triangle :
=> Area = 1/2*b*h
=>Area = 3*2/2
=> Area = 3 miles square
Therefore , the solution of the given problem of area comes out to be the land acquired by university is of 3 miles square area.
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If the ratio of the model car was 2:35 then what would be the actual length of the car??
PLEASE HELP AND SHOW WORK
Answers
The actual length of the car based on the model will be 350 inches.
How to calculate the ratio?Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
Since the ratio of the model car was 2:35. If the model is 20 inches long, the actual length of the car will be:
= 20 ÷ 2/35
= 20 × 35/2
= 350 inches.
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Complete question
The ratio of the model car was 2:35. If the model is 20 inches long. then what would be the actual length of the car??
Marcelle and Megan realized that they could express their ages more specifically if they used fractions. Doing this will allow them to calculate their difference in their ages. Marcelle is $15\frac{1}{2}$ years old, and Megan is $7\frac{7}{12}$. What is the difference in their ages? Express your answer as a simplified mixed number.
Answers
The difference in ages of Marcelle and Megan is 95/12 as an improper fraction and as a mixed number is 7 whole number and the fraction 11/12.
How to evaluate the difference in the fraction of the agesWe shall convert the fractions to have similar denominators and simply apply subtraction for the numerators as follows:
Marcelle's age = 15 whole number, 1/2
Marcelle's age = 31/2
Megan's age = 7 whole number, 7/12
Megan's age = 91/12
LCM of 2 and 12 is 12 so;
Marcelle's age = 31/2 × 12/12
Marcelle's age = 186/12
difference in their age (186 - 91)/12
difference in their age = 95/12
Therefore, the difference in the ages of Marcelle and Megan is the fraction 95/12 or as a mixed number is 7 whole number and the fraction 11/12
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Don’t know need help
Answers
I think that the answer would be 14
Charlie reads quickly. He reads 1 3/7 pages every 2/3 minutes. Charlie reads at a constant rate: How many pages foes he read per minute?
Answers
In one min Charlie can read is [tex]2\frac{1}{7}[/tex] pages at a constant rate.
What is Unitary Method ?A single unit's value may be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. We typically utilize this technique for math computations.
In the unitary technique, the value of a unit or one quantity is always counted first, and the values of additional or less quantities are subsequently determined. This approach is known as the unitary method for this reason. Due to the fact that they generate two distinct sorts of variations, there are two different types of unitary approaches.
Direct VariationIndirect VariationIn [tex]\frac{2}{3}[/tex] min Charlie can read [tex]1\frac{3}{7} = \frac{10}{7}[/tex] pages
In one min Charlie can read is: [tex]\frac{10}{7}*\frac{3}{2} = \frac{30}{14} = 2\frac{2}{14} =2\frac{1}{7}[/tex]
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PLEASE PLEASE HELP I WILL MARK THE BRAINIEST (the little crown thingy)
Answers
Answer: A
Step-by-step explanation: They both go up but they have diffrent patterns
hopes this helps any
Answer:
A.
Step-by-step explanation:
the 'x' slot is going up two and the 'y' slot is going up one every change.
what is 2.38 correct to 2 significant figures
Answers
Answer: 2.4
Step-by-step explanation:
we start from the right most digit, that is 8. Since 8 is greater than 5, we add 1 in the number before 8, that is 3. When we add 3 and 1 we get 4. This way, we get our answer 2.4 , which is correct to 2 significant figures.
hope that helps...
PLEASE HELP. I'LL DO ANYTHING THAT'LL BENEFIT YOU.
Answers
If you double the amount of fluid ounces, the amount of cups also double
There is a proportional relationship between the number of fluid ounces and the number of cups. So, the number of cups would change by the same factor as the number of fluid ounces.
The cost of renting equipment is sometimes proportional; because, it depends on whether the equipment has a rental fee and charge per hour or just a charge per hour. Option A.The cost of mailing a letter is proportional to the weight. The cost of mailing a 6-ounce letter is $2.82. Option BThe donation is proportional to the dinner bill
The donation for a dinner bill of $50 is $9
How to determine proportional relationship?If there are 8 fluid ounces in one cup
8 : 1 = 16 : x
8/1 = 16/x
8 × x = 16 × 1
8x = 16
x = 16/8
x = 2
The difference between weight = 1
The difference between cost = $0.68 - $0.47
= $0.21
$0.89 - $0.68
= $0.21
$1.10 - $0.89
= $0.21
Cost of mailing 6-ounce letter
1 : 0.47 = 6 : x
1/0.47 = 6/x
1 × x = 6 × 0.47
x = $2.82
The donation for a dinner bill $50 is
Dinner bill : donation
25 : 4.50 = 50 : x
25/4.50 = 50/x
25 × x = 50 × 4.50
25x = 225
x = 225/25
x =$ 9
Therefore, there is a proportional relationship between two quantities if there is an equal change in the values of both quantities.
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A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limits, until it reaches its destination 200 miles away. Letting x represent the amount of time in hours that the car is going 55 miles per hour, and y being the time in hours that the car is going 35 miles per hour, an equation describing the relationship is: 55x+35y=200
A: If the car spends 2.5 hours going 35 miles per hour on the trip, how long does it spend going 55 miles per hour?
B: If the car spends 3 hours going 55 miles per hour on the trip, how long does it spend going 35 miles per hour?
C: If the car spends no time going 35 miles per hour, how long would the trip take? Explain your reasoning.
Answers
Answer:
A. The car spends 2.05 hours going 55 miles per hour
B. The car spends 1 hour going 35 miles per hour
C. The trip takes 3.6 hour
Step-by-step explanation:
The equation is
55x+35y=200
Let's solve A
We know the car spends 2.5 hours going 35 miles per hour on the trip, so we put 2.5 in for y and solve for x
55x+35(2.5) = 200
55x + 87.5 = 200
55x = 112.8
x = 2.05 hours going 55 miles per hour
So, the car spends 2.05 hours going 55 miles per hour
Let's solve B
55(3)+35y=200
165 + 35y = 200
35y = 35
y = 1 hour
So, the car spends 1 hour going 35 miles per hour
Let's solve C
We know the car spends no time going 35 miles per hour, so we put 0 in for y and solve for x
55x+35(0)=200
55x = 200
x = 3.6 hours
So, the trip takes 3.6 hour
You work at an oil refinery and are in charge of draining a tank until the
are 635 gallons left inside. The tank starts with 827 gallons, and you c
drain it at a rate of 48 gallons per minute. How many minutes do you
need to drain the tank to the right level?
You need
minutes.
Answers
Explanation below
at a local cafeteria there are 10 vegetable selections available how many three vegetable plates maybe made
Answers
The number of vegetable plates can be made = 120
We know that a combination is nothing but a way of selecting items from a collection. In combination the order of selection does not matter.
We know that a formula for a combination is,
^nC_r = n! / r!(n - r)!
where, ^nC_r = number of combinations
n = total number of items in the collection
r = number of choosing items from the collection
and n! = n × (n - 1) × (n - 2) × . . . × 1
Here, we have n = 10 and r = 3
Using combination formula, the total number of plates made:
^10_C_3
= 10! / (3! × (10 - 3)!)
= 10! / (3! × 7!)
= (10 × 9 × 8 × 7!) /( 3! ×7!)
= (10 × 9 × 8) / (3 × 2 × 1)
= (90 × 8) / 6
= 720/6
= 120
Therefore, 120 vegetable plates maybe made
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Eight packages of paper weigh a total of 38 pounds. What is the weight of 40 packages of the same kind of paper?
Answers
Answer:
1,520 pounds
Step-by-step explanation:
40x 38 = 1520
3 1/2 x 1 1/2 as a mixed number in simplest form
Answers
Answer: 8 3/4 because first find your common denominator, then solve the math and you will get 8 3/4
An aircraft hangar is semi-cylindrical with
diameter 40 m and length 50 m. A helicopter
places a cable across the top of the hangar, and
one end is pinned to the corner at A. The cable
is then pulled tight and pinned at the opposite
corner B. Determine the length of the cable.
Answers
On solving the provided question, we can say that - the volume of the cylinder will be V = 3.14 * 20*20*50 = 62800
what is radius?The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle. Diameter
volume of the cylinder -
V = [tex]\pi r^2h[/tex]
r = 40/2 = 20
h = 50
V = 3.14 * 20*20*50 = 62800
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Which equation can be used to determine the line that passes through the points (-1, -2) and (3, 10)?Justify your reasoning using new and prior concepts. Use math vocabulary to explain your thinking.
Answers
The equation the line is, y-3x=1
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
Here, we have to points (-1,-2) and, (3,10)
So, by using the formula of equation of straight line of two-point form, we get,
(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )
=>(y+2)/(x+1)=(10+2)/(3+1)
=>y+2=3x+3
=>y-3x=1
Hence, the required equation is, y-3x=1
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How many solutions does 5x 2y =- 7?
Answers
There is no single answer to this question. It depends on what values are chosen for x and y , equation has an infinite
The equation 5x + 2y = -7 is an indeterminate equation with two unknowns, x and y. This means that the equation has an infinite number of solutions, depending on the values of x and y. For example, if x = 3 and y = -2, then the equation would be satisfied. If x = 2 and y = -3, then the equation would also be satisfied. Therefore, the number of solutions for this equation is infinite.There is no single answer to this question. It depends on what values are chosen for x and y.
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A train moving at a constant speed travels 325 mi in 8 hr. At this rate, how many miles does the train travel in 12 hr?
ANSWER ASAP!!!
Answers
Answer:
Step-by-step explanation:
In 12 hours, the train will travel 487.5 miles
8/325=40.625
40.625 x 12 = 487.5
A company makes chocolate candies in the shape of a solid sphere. Each piece of candy has a diameter of 6cm. If a box contains 15 pieces of candy, how much chocolate does the box contain? Use 3. 14 for π, and do not round your answer
Answers
The total amount of solid sphere chocolate in the box is 1695.6 cubic centimeters.
What is volume?The space occupied within an object's borders in three dimensions is referred to as its volume.
What is the volume of sphere?The volume or the space inside the borders of the sphere is given by the formula:
[tex]V = \frac{4\pi r^3}{3}[/tex]
Given that the diameter is 6cm, the radius r = 3cm.
Substituting the value of radius in volume we have:
[tex]V = \frac{4 (3.14)(3)^3}{3}[/tex]
[tex]V= 113.04[/tex]
The box contains 15 candies hence the total volume will be:
V = 15 * 113.04
V = 1695.6 cubic centimeters.
Hence the total amount of chocolate in the box is 1695.6 [tex]cm^3[/tex].
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What is the discriminant of 3x^2 2x 1 0?
Answers
The discriminant of quadratic equation 3x^2 + 2x + 1 =0 is -8
We know that the standard form of quadratic equation is ax^2 + bx + c = 0, with a ≠ 0
The discriminant of quadratic equation ax^2 + bx + c = 0 is:
D = b^2 - 4ac
Comparing given quadratic equation 3x^2 + 2x + 1 =0 with ax^2 +bx + c = 0 we get,
a = 3, b = 2 and c = 1
So, the discriminant of given equation would be,
D = b^2 - 4ac
D = 2^2 - 4(3)(1)
D = 4 - 12
D = -8
Therefore, the discriminant is D = -8
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ou have $54.75. You earn additional money by mowing lawns. Then you purchase a new pair of shoes for $79.99 and have $34.76 left. How much money do you earn mowing lawns
Answers
Answer: 60
Step-by-step explanation:
If you subtract how much money you already had(54.75) from what you spent(79.99) you get 25.24. You then add 25.24 to the koney you had left(34.76) to get you answer of 60
Please help
Find the value of x
Find the measure of the two marked angles
PLEASE ALSO FIND X
Answers
The value of x is 8 and the measure of the two marked angles is 60°.
Which angles are corresponding and adjacent?When an angle's vertex and side are shared by another angle, the two angles are said to be neighboring angles. The vertex of an angle is the point where the rays come to a halt and create the sides of the angle. When two adjacent angles share a vertex and a side, they can be either complimentary or supplementary angles.
we know that ,
10x-20=7x+4 (it is corresponding opposite angle)
3x=24
x=8
the value of x is 8.
the measure of the two marked angles is 10*8-20= 80°-20°= 60°.
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Given the answer for part D, write an expression that will tell you the direction the robot is going if, in the course of its journey, it turns left 21 times and turns right 22 times. Does the order the robot makes the turns in matter for the purpose of knowing the direction it is finally facing?
The answer to part D is in the picture...
Answers
The robot is moving in the direction indicated by the formula ((i)²¹*(-i)²²)d, or in the beginning direction.
What is complex plain?
When a line is rotated in the complex plane either clockwise or anticlockwise, it is multiplied by -i or I depending on which direction the line is rotated. The direction vector is rotated 90 degrees in the clockwise direction to make a right turn. It is the same as increasing the complex number by -i.
A left turn is represented as a 90° anticlockwise rotation of the direction vector. It is comparable to increasing the complex number by i.
There are 21 left turns of the robot. The direction vector will now be di21. Once it has been rotated 22 times to the right, the direction vector will now be (di²¹)*(-i)²²=d((i)²¹*(-i)²²).
Consequently, the robot's current direction is:
d((i)²¹*(-i)²²)= di²¹⁺²²=di⁴³= d(-i)= -di
No matter what, the direction will always be the same, hence the sequence is irrelevant.
Hence, the equation that will indicate where the robot is moving is ((i)²¹*(-i)²²)d, or in the starting direction. Furthermore, the final direction it faces does not depend on the order.
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Mario has 3/4 cups of chocolate chips needs 1/3 cup to make a batch of cookies how many batches can Mario make if he uses all of his chocolate chips
Answers
In the given equation, Mario can make 2.25 batches of cookies using all of his chocolate chips.
How to find the given equation?First, you can find out how many total cups of chocolate chips Mario has by multiplying the number of cups per unit (3/4) by the number of units (1).
[tex]3/4 cups * 1 = 3/4 cups\\[/tex]
Then you can divide the total amount of chocolate chips Mario has by the amount of chocolate chips needed per batch:
[tex]3/4 cups / 1/3 cup/batch = 3/4 cups * 3/1 cup/batch = 9/4 cups/batch[/tex]
Finally, you can convert this to a whole number by dividing both the numerator and denominator by their greatest common factor, which is 1:
[tex]9/4 cups/batch = (9/1) / (4/1) = 9/4 = 2.25 batches[/tex]
Mario can make 2.25 batches of cookies using all of his chocolate chips.
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Find the length of the third side. If necessary, round to the nearest tenth
Answers
Answer:
I'm pretty sure the answer for this is 28 :))
REALY HELP ME PLEASE!!!!!!
Answers
The equation of line in slope intercept form is,
⇒ y = x - 2
When the graph is shift down 9 units.
Then, Equation of line become,
⇒ y = x - 11
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (2, 0) and (0, -2).
Now,
Since, The equation of line passes through the points (2, 0) and (0, -2).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 2 - 0) / (0 - 2)
m = - 2 / -2
m = 1
Thus, The equation of line with slope 1 is,
⇒ y - 0 = 1 (x - 2)
⇒ y = x - 2
And, When the graph is shift down 9 units.
Then, Equation of line become,
⇒ y = x - 2 - 9
⇒ y = x - 11
Therefore, The equation of line in slope intercept form is,
⇒ y = x - 2
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