All exponential functions go through the point (0,1) because the value of x when it equals to 0, in the general form of exponential function f(x) = [tex]a^x[/tex], results in [tex]a^0[/tex] = 1, which is why all exponential functions have the point (0,1) on their graph.
All exponential functions go through the point (0,1) because of the properties of exponential functions. The general form of an exponential function is f(x) = [tex]a^x[/tex], where a is a positive constant. When x = 0, the function evaluates to [tex]a^0[/tex] = 1, which is why all exponential functions have the point (0,1) on their graph.
Another way to understand this is that the exponential function is defined as the function that describes how a quantity grows or decays at a fixed percentage rate over time. The function f(x) = [tex]a^x[/tex], where a is a constant greater than 0 and less than 1, describes the decay of a quantity over time. For example, if the interest rate is 10%, the value of a = 0.1 and the function f(x) = [tex]0.1^x[/tex]. When x = 0, the function evaluates to [tex]0.1^0[/tex] = 1, which means that the initial value of the quantity is 1.
It's important to note that the point (0,1) is called the y-intercept, and it is a special point in the graph of exponential functions, and it's always present in the graph of exponential functions.
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The complete Question is:
Why do all exponential functions go through point(0,1)?
What is ¾ divided by 4?
The solution to this ¾ divided by 4 is 0.1875.
To visualize the question we are trying to solve, let's put 3/4 and 4 side-by-side so it's easier to see:
3/4÷4
The numbers in 3/4 divided by 4 are labeled below:
3 = numerator
4 = denominator
4 = whole number
All we need to do here is keep the numerator exactly the same (3) and multiply the denominator by the whole number:
3/4 x4= 3/16.
Once you have your final fraction, just divide the numerator by the denominator to get your answer in decimal form:
3/16=0.1875
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What is the value of x? there are two triangles, triangle abc and triangle def. Side ab is congruent to side de, side ac is congruent to side df. Angle cab is congruent to angle fde. The length of the side bc is (x-4).
There are two triangles, triangle abc and triangle def. Side ab is congruent to side de, side ac is congruent to side df. Angle cab is congruent to angle fde. The length of the side bc is (x-4). The value of x is 23.
The value of x can be calculate as follows:
Given that the triangles are congruent and moreover
Considering that
AB = DE
AC = DF
so,
The third will be compatible as well.
so,
BC = AE
x - 4 = 19
x = 19 + 4
x = 23
Therefore , the value of x is 23. When there are two triangles, triangle abc and triangle def. Side ab is congruent to side de, side ac is congruent to side df. Angle cab is congruent to angle fde. The length of the side bc is (x-4).
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What is the total area of the three triangle?
Answer: triangle 1's 1/2 length* triangle 1's width+triangle 2's 1/2 length* triangle 2's width+triangle 3's 1/2 length* triangle 3's width
Step-by-step explanation: triangle 1/2 length* triangle width=triangle area.
Pablo shares his birthday cake with a friend. Pablo eats 3/8 and his friend eats 1/4. How much of the cake was left over? (Represent your answer as a fraction)
Answer:3/8 was left over
Step-by-step explanation: 3/8 plus 1/4 x 2 equals 5/8... remainder 3/8
Answer:
3/8 (this is the answer)
What vertical translation is applied to y = x2 if the transformed graph passes through the point (5, 18)?
Step-by-step explanation:
well,
y = x²
would give us
y = 5² = 25
(5, 25)
but we have
(5, 18) so, what is the difference ?
we see that y is reduced by 7 units.
so,
y = x² - 7
the whole curve is moved down by 7 units.
Give the first five terms of the sequence:
2/5,A₂ =4/5; ªn‚ = ª,-2 (for n ≥ 3)
Answer: 2/5, 4/5, -4/5, 8/5, -16/5
I dunno that's what I got I could be wrong
What causes eye dilation?
Light and emotional variables are affected by eye dilation. Under typical conditions, pupils are meant to dilate as a result of changes in lighting and psychological factors.
Why do your pupils continue to dilate?A physical or psychological condition, certain substances or prescriptions, or an injury could be the cause of this. The term "blown pupil" is occasionally used by doctors to describe more severe mydriasis when the pupils are fixed and dilated. This disorder may be a sign of brain damage brought on by a stroke or other physical trauma.Light and emotional variables are affected by eye dilation. Under typical conditions, pupils are meant to dilate as a result of changes in lighting and psychological factors.Under typical conditions, pupils are meant to dilate as a result of changes in lighting and psychological factors. A dilated pupil will typically return to its normal size on its own.To learn more about eye dilation refer to:
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A line pae through the point (–6,5) and (8,–2). What i it equation in point-lope form?
The equation of the line passing through the point (-6, 5) and (8, -2) in point-slope form is y - 5 = -0.5(x + 6).
The point-slope form of a line is
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line.
To find the equation of a line given two points, we can use either point and find the slope of the line using the formula:
m = (y2 - y1) / (x2 - x1)
So, we can use the point (-6, 5) and (8, -2)
m = (y2 - y1) / (x2 - x1) = (-2 - 5) / (8 - (-6))
m = -7/14
m = -1/2
Now we can use this slope and the point (–6,5) to find the equation of the line in point-slope form:
y - 5 = -1/2(x - (-6))
y - 5 = -0.5(x + 6)
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Please answer this question and I will give you a brainlist!
Answer:
I think it's (4,4) but I could be wrong
Step-by-step explanation:
Non -examples of the property 0
When we multiply any number by zero, the outcome is always a zero, according to the definition of the zero property of multiplication, examples as 8 x 0 = 0.
What is zero property?When we multiply any number by zero, the end result is always a zero, according to the definition of the zero property of multiplication. Zero need not always be the first or second number. When multiplied by another number, it could be anywhere. This indicates that the outcome of the multiplication is unaffected by the placement of the digit zero.
All different kinds of numbers fall under the umbrella of this property. They could be fractional, decimal, or integer numbers. Thus, the results of some such numbers will be as follows:
10 x 0 = 0 6.4 x 0 = 0
½ x 0 = 0 1 x 2 x 3 = 0
A non-example of property 0 is: 5 × 1 = 5, the number is not multiplied by 0, therefore, it does not denote the zero property of multiplication.
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Compete question is: Give non-example of the property 0.
Use the distributive
property to write an
expression
that is
equivalent
to 32 + 4r.
Answer:
4 (8+r)
Step-by-step explanation:
Maisie knows that she needs 3 kg of grass seed to make a rectangular lawn 5 m by 9m.
Grass seed is sold in 2 kg boxes
Maisie wants to make a rectangular lawn 10 m by 14m.
She has 5 boxes of grass seed.
(a) Has Maisie got enough grass seed to make a lawn 10 m by 14m!
You must show all
your working
(4)
Total Seeds required 9.33 kg and she has 10 kg.so, she has enough grass seed to make a lawn 10m by 14 m.
If you're fortunate enough to have a rectangular lawn, determining the size is straightforward. Multiply the length and breadth measurements together to get the total. You now have your region/area.
So, Maisie knows that she needs 3 kg of grass seed to make a rectangular lawn 5 m by 9m.
Grass seed is sold in 2 kg boxes,
Maisie wants to make a rectangular lawn 10 m by 14 m,
She has 5 boxes of grass seed
To Find, Has Maisie got enough grass seed to make a lawn 10m by 14 m
Solution:
3 kg of grass seed to make a rectangular lawn 5 m by 9m.
=> 3 kg of grass seed needed for 5 x 9 = 45 m²
=> 1 m² required = 3/45 kg seed
a rectangular lawn 10 m by 14 m,
area = 10 x 14 = 140 m²
Hence 140 m² required = 140 x 3/45 = 9.33 kg
Grass seed is sold in 2 kg boxes,
She has 5 boxes of grass seed
Hence total seeds = 5 x 2 = 10 kg
Therefore, total seeds required 9.33 kg and she has 10 kg.so, she has enough grass seed to make a lawn 10m by 14 m.
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Four glasses of milk and 2 snack bars have a total of 86 carbohydrates (carbs), and 2 glasses of milk and 3 snack bars have a total of 69 carbs. Determine how many carbs are in one glass of milk and in one snack bar.
Answer:
One glass of milk: 15 carbs
One snack bar: 13 carbs
Step-by-step explanation:
This problem is an example of systems of linear equations. We can set this problem up by defining variable. I used [tex]m[/tex] for the glass of milk and [tex]b[/tex] for the snack bar.
First, we have: 4 glasses of milk and 2 snacks bar have a total of 86 carbs. We can write this as
[tex]4m+2b=86[/tex]
Next: 2 glasses of milk and 3 snack bars have a total of 69 carbs.
We can write this as
[tex]2m+3b=69[/tex]
Now we set it up.
[tex]4m+2b=86[/tex]
[tex]2m+3b=69[/tex]
By dividing both sides of the first equation by 2, we can use the subtraction method to get rid of the variable [tex]m[/tex]. Now we have
[tex]2m+b=43[/tex]
[tex]2m+3b=69[/tex]
Subtract like terms and solve for [tex]b[/tex]
[tex]-2b=-26[/tex]
[tex]b=13[/tex]
Now we substitute [tex]b[/tex] back into the original equation to find [tex]m[/tex].
[tex]2m+(13)=43[/tex]
[tex]2m=30[/tex]
[tex]m=15[/tex]
There you have it. I hope this helps!
How many types of images are there in class 8?
There are 2 types of images namely virtual and real image
The point where light rays from an object meet or appear to contact after reflection or refraction is sometimes referred to as the image. In this concept, a "object" might be anything that light rays are emanating from.
Real images and virtual images are the two types of images. The method by which they are created distinguishes a genuine image from a virtual image. Light beams must converge to create an actual image, whereas they must diverge to create a virtual image.
Real images are those that are created when light rays collide at a specific location after being reflected or refracted by a mirror or lens.
Virtual pictures are those that only seem to form when viewed from behind a mirror. Behind the mirror, the picture is not actually there. When light beams are refracted or reflected, a virtual picture is created.
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help asap please math hw
Answer:
First question:
y intercept = 3
slope = -1/3
y = -1/3x+3
Second Question:
y intercept = -3
slope = -3/2
y = -3/2x=3
Third Question:
y intercept = -1
slope = 3
y = 3x-1
youre welcome buddy :)
the perimeter of a rectangle is 70 cm. if its length is decreased by 5 cm and its width is increased by 5 cm,its area will increase by 50 cm^2.find the length and the width of the original rectangle
The length of the rectangle is 25 cm and the width is 10 cm.
How to evaluate for the length and width of the original rectangleWe shall represent the length and width of the original rectangle with x and y respectively so that the perimeter is;
2(x + y) = 70 {divide through by 2}
x + y = 35...(1)
length of new rectangle = x - 5
width of new rectangle = y + 5
area of new rectangle:
(x - 5)(y + 5) = xy + 50
xy + 5x - 5y - 25 = xy + 50
xy - xy + 5x - 5y = 50 + 25
5x - 5y = 75 {divide through by 5}
x - y = 15...(2)
add equations (1) and (2) we have;
x + y + x - y = 35 + 15
2x = 50 {divide through by 2}
x = 25
substitute 25 for x in equation (1), we have;
25 + y = 35
y = 35 - 25 {subtract 25 from both sides}
y = 10
Therefore, have the length and width of the original rectangle to be x = 25 cm and y = 10 cm respectively.
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Sue ha 20 bicuit in a tin. There are: 12 plain bicuit
5 chocolate bicuit
3 currant bicuit
Sue take two random bicuit from the tin. Work out the probability that the two bicuit are not the ame type
So, the probability that the two biscuits are not the same type is 0.15 or 15%.
To find the probability that the two biscuits are not the same type, we need to calculate the probability that Sue takes one biscuit of each type.
First, we will calculate the probability that Sue takes one plain biscuit, one chocolate biscuit, and one currant biscuit.
The probability of Sue taking one plain biscuit is 12/20, since there are 12 plain biscuits out of a total of 20.
The probability of Sue taking one chocolate biscuit after taking a plain biscuit is 5/19, since there are now 5 chocolate biscuits out of 19 remaining.
The probability of Sue taking one currant biscuit after taking a plain and chocolate biscuit is 3/18, since there are now 3 currant biscuits out of 18 remaining.
To find the overall probability that Sue takes one biscuit of each type, we multiply the individual probabilities together:
P = (12/20) * (5/19) * (3/18) = 0.15
So, the probability that the two biscuits are not the same type is 0.15 or 15%.
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Brayden i earning money for a charity by walking lap around a track. He walk 2 1/2 lap each day for 7 day for 7 day. Hi goal i 16 lap. If he walk 16 lap or more, he earn $2 per lap. If he walk le than 16 lap, he earn $1 per lap
Brayden's total earning by walking lap around a track is $35, if he walks 2+1/2 = 5/2 laps per day for 7 days.
Per day walking of brayden = 5/2 laps
7 days walking of brayden = 5/2 × 7 = 35/2 laps
As per the question statement he earns $1 per lap if he walk less than 16 laps and $2 per lap if hi walks 16 or more lap. Since the total walking of brayden is more than 16 laps, so he will earn at the rate of $2 per lap. So total earning will be,
= 2× 35/2
= $35
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For a given recipe, 3 cups of flour are mixed with 9 cups of sugar. How many cups of flour should be used if 63 cups of sugar are used?
Assuming a constant ratio, fill out the table of equivalent ratios until you have found the value of x.
Answer:
Use direct variation method of mathematics
What is the value of x in X² 9?
The value of x in the given equation x² = 9 is x = ± 3.
In x² = 9, we need to remove the power of 2 in order to separate just x.
This implies finding the square root √x² which is equal to x.
However, there are 2 possible answers to any square root, a positive or a negative answer.
x = √9
x = ± 3
0r we can solve this equation by the splitting method.
Rearrange the equation
x² = 9
(x - 3)(x + 3) = 0
On solving, we get
x = +3 and x = -3
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If 750ml of paint covers an area of 12 m2, what area (in m2) will 1.6 litres of paint cover?
Answer: To find the area that 1.6 litres of paint will cover, we can use the unit rate. The unit rate is a way to compare different quantities by finding how much of one quantity corresponds to one unit of another quantity.
We know that 750ml of paint covers an area of 12 m2, this means that the unit rate of paint:area is 750ml:12m^2
We can use this to find the area that 1.6 litres of paint will cover.
First we should convert the 1.6 litres of paint to milliliters, since we have the unit rate in ml:
1.6 litres = 1.6*1000 ml = 1600 ml
Now we can use the unit rate to find the area that 1.6 litres of paint will cover:
Area = (1600 ml paint) * (12 m2/750ml paint) = 21.333 m2
So, 1.6 litres of paint will cover approximately 21.333 m^2
Note that you could also use the proportion (750ml/12m^2) = (1600ml/x) to find the value of x.
Step-by-step explanation:
What are the 4 quadrants in order?
The 4 (four) quadrants in order are: Quadrant I, Quadrant II, Quadrant III, and Quadrant IV.
A coordinate plane is divided into four sections called quadrants. These quadrants are numbered I, II, III, and IV in a counterclockwise direction, starting with the top right.
Quadrant I is the top right section of the coordinate plane, and it contains all the points where the x-coordinate and y-coordinate are positive.
Quadrant II is the top left section of the coordinate plane, and it contains all the points where the x-coordinate is negative and the y-coordinate is positive.
Quadrant III is the bottom left section of the coordinate plane, and it contains all the points where the x-coordinate and y-coordinate are negative.
Quadrant IV is the bottom right section of the coordinate plane, and it contains all the points where the x-coordinate is positive and the y-coordinate is negative.
Understanding this concept is important for solving mathematical problems, especially in algebra and geometry.
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What does range () function returns Mcq?
The range is found by finding the vertex and noting that it is the minimum or maximum (depending on direction) of the function. You can find the vertex by using -b/2a for the x value and then plugging in to get y value.
What is a function?
A mathematical phrase, rule, or rule that establishes the link between explanatory variables or a dependent variable In mathematics, curves exist everywhere, and they are crucial for constructing physical links in the sciences.
A Method can be defined by a module, an object, or another function. An internal feature of a class is called a method. Methods are listed inside a base class to make the connections between it class and thus the method clear. A method can be called or invoked using different syntax. We can convert a type into an object before being able to access its methods.
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What is the solution for [tex]x^{2} + 4x\ \textgreater \ 77[/tex]?
x < –7 or x > 11
x < –11 or x > 7
–7 < x < 11
–11 < x < 7
The solutions of x² + 4x > 77 is x < –11 or x > 7
Solutions of an equation:An equation is a mathematical expression that states that two algebraic expressions must be equal in nature. Finding the value of a variable in an equation indicates the process of solving an equation. The solution of the equation is the value that was determined while solving the equation.
Here we have
x² + 4x > 77
Subtract -77 from both sides
=> x² + 4x - 77 > 77 - 77
=> x² + 4x - 77 > 0
The above expression can be factorized as follows
=> x² + 11x - 7x - 77 > 0 [ Split middle term ]
=> x(x + 11) - 7(x + 11) > 0
=> (x + 11) (x - 7) > 0
=> (x + 11) > 0 (x - 7) > 0
=> x < -11 x > 0
Therefore,
The solutions of x² + 4x > 77 is x < –11 or x > 7
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braylon had 75% of all baseball cards ever made bob's publishing company. if he has 960 cards, how many had bob's publishing company made?
Answer:1280
Step-by-step explanation:
75% of something is 960 you can use trial and error to find the amount by just doing 75% of a number a little higher than what you got
What is the additive inverse of 8 /- 13?
The additive inverse of 8 /- 13 is -8 /+ 13. This means that when you add 8 /- 13 to its additive inverse, the result is 0.
The additive inverse of 8 /- 13 is its opposite number. This means that the sign of the number must be flipped. The inverse of 8 /- 13 is -8 /+ 13. To find the inverse of a number, you must switch the sign of the number from positive to negative or from negative to positive.
When two numbers are added together, the result will be zero if the numbers are opposites. This means that 8 /- 13 and its inverse, -8 /+ 13, when added together, will equal 0. This is because the two numbers have the same value but opposite signs. The positive 8 is cancelled out by the negative 8, and the negative 13 is cancelled out by the positive 13, leaving 0.
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The range of the function f(x)=[x+3]-5 is
A) [-5,∞)
B) (-5,∞)
C) [3,∞)
D) (3,∞)
The range of a function is the set of all possible outputs (y-values) for a given input (x-value).
Given the function f(x) = [x+3]-5, we can see that the function first adds 3 to x and then subtracts 5. The square bracket notation around (x+3) indicates that the function is taking the greatest integer less than or equal to (x+3).
For any input x, the output of the function will always be the greatest integer less than or equal to (x+3) - 5. Therefore, the output of the function is always an integer less than or equal to -2.
So the range of the function is [-5, -2] U (-2, ∞)
Option A) [-5,∞) is incorrect as the range starts with -5 but the function output is always less than or equal to -2.
Option B) (-5,∞) is incorrect as the function output is always less than or equal to -2.
Option C) [3,∞) is incorrect as the function output is always less than or equal to -2.
Option D) (3,∞) is incorrect as the function output is always less than or equal to -2.
The correct answer is (-2, ∞)
The volume of a sphere is given by the equation $V=\frac{1}{6\sqrt{\pi}}S^{3/2}$V=
1
6√πS3/2 , where cap s$S$S is the surface area of the sphere. Find the volume of a sphere, to the nearest cubic meter, that has a surface area of 60 square meters. Use 3.14 for pi$\pi$π .
The volume of a sphere, to the nearest cubic meter is; 44 cubic meter
How to find the Volume of a sphere?
We are given that the formula for the volume of a sphere is;
V = [1/(6√π)]S^(3/2)
where;
V is volume
S is the surface area of the sphere
π = 3.14
We are given that surface area is 60 square meters. Thus, we will now have;
V = [1/(6√3.14)]60^(3/2)
V = 43.713 m³
Approximating to the nearest cubic meter gives;
V = 44 cubic meter
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A newsletter publisher believes that more than 31% of their readers own a personal computer. Is there sufficient evidence at the 0.02 level to substantiate the publisher's claim?
State the null and alternative hypotheses for the above scenario
The null hypothesis is: H0: p ≤ 0.31
The alternative hypothesis is : H1: p > 0.31
What is a null hypothesis?A common statistical theory called the null hypothesis asserts that there is no statistical link or significance between two sets of observed data and measurable events for a given single observed variable.
The null states that the probability of the readers have the personal computers have to be lower than or equal to 31 percent.
What is the alternative hypothesis?
An alternate hypothesis is a claim that the two variables have some kind of statistical relationship.
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Suppose a ball was dropped from a TV tower 2120 feet high. The time it takes an object to free-fall from the top of this tower to the ground can be represented by the equation s = -16t^2 + 2120, where s is the distance from the ground in feet and t is the time in seconds. Approximately how long will it take the object to reach the ground?
If a ball is dropped from 2120 feet, it will take approximately_________ seconds to reach the ground.
The time taken by the ball to reach the ground is 11.5 seconds.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Suppose a ball was dropped from a TV tower 2120 feet high. The time it takes an object to free-fall from the top of this tower to the ground can be represented by the equation s = -16t² + 2120.
The time will be calculated as,
s = -16t² + 2120
Equate with zero as the ball reaches the ground the height s becomes zero.
-16t² + 2120 = 0
-16t² = -2120
t² = 2120 / 16
t² = 132.5
t = √132.5
t = 11.5 seconds
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