Answers
Exponential functions are given by:
f(x)=a(b)^x
when:
a is negative, the graph will be reflected along y-axis
b>1 the graph will be an exponential growth
b<1 the graph will be an exponential decay
1] a]
y=3(2)^x
y-intercept:
at y-intercept x=0 thus
y=3(2)^0
y=3(1)=3
thus y intercept is at y=3
c] since there is no asymptote
d] Domain:
All real numbers
e] Range:
[0,∞)
That all positive real numbers.
2]
a] f(x)=2(0.25)^x
a=2
b=0.25
b<1
thus the function is exponential decay
b] The horizontal axis is at y=0.
c] Domain:
The domain is all real numbers.
d] Range:
The range are all positive values.
e] y-intercept
f(x)=2(0.25)^x
at y-intercept , x=0 thus
y=2(0.25)^0
y=2(1)
y=2
3] y=-5(2)^x
a] This is a decay function since a=-5
b] y-intercept
f(x)=-5(2)^x
f(x)=-5(2)^0
f(x)=-5
C] the asymptote is y=0
d] Domain are all real numbers
e] Range
Range are all negative real numbers
Related Questions
PLS HELP ME ASAP WITH 1 AND 2, THANK YOU!! SM!!
(Brainliest will be given hopefully!)
(Random answers gets moderated.)
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(3) The graph represents a function. The table has a domain of [0, 7] and a range of [170, 240].
The function might reasonably be used over a domain of [0, 24] and a range of [0, 240].
What is the minimum value of the graph of y=sin x assumes
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The first thing you should do is draw this or get a program to do it. I use desmos. It is included. The graph shows one complete cycle every 2*pi intervals (or 360 degrees.)
You will find no lower value that y = - 1 (nor any value greater than y = 1)
Answer:
the answer is
negative one
- 1
Step-by-step explanation:
Write an equation in intercept form of the parabola that Passes through (-1,40) and x=-5, 4
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If this is the case, then the equation of the parabola is found as follows:
y=ax^2 + bx + c for the point (-5, 0) is 0=a(-5)^2 + b(-5) + c
for the point (4,0) is 0 = a(4)^2 +b(4) + c
for the point (-1,40) is 40 = a(-1)^2 + b(-1) + c
Here we have 3 equations in 3 unknowns, which is enough to solve for {a,b,c}. Using matrix algebra, I found that a= -2, b= -2, c= 40.
Then one equation for this parabola would be:
y = -2x^2 - 2x + 40
Check this by substitution. Does the point (-5,0) satisfy y = -2x^2 - 2x + 40?
Yes. So y = -2x^2 - 2x + 40 is the general form of the equation of this parabola. To express it in intercept form, factor y = -2x^2 - 2x + 40.
A family of four (two kids and two parents) spend the day at an amusement park. At the end of the day, the family adds up all of the receipts from their meals: $16.25, $17.96, $3.58, $4.61, $5.23. What is the mean and median cost spent? What does the mean cost represent? Why is the mean cost significantly different from the median cost? Which measurement of central tendency is a better representation of the amount of money that the family spent at the amusement park?
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A family of four spent the following for their meals $16.25, $17.96, $3.58, $4.61, $5.23.
Mean cost spent is calculated by:
Total Cost/Number of Meals
(16.25+17.96+3.58+4.61+5.23)/5
47.63/5
$9.53
Mean Cost represents the average amount per meal the family has spent.
Median cost is the cost that in the middle of the five costs which is $5.23.
The mean cost is significantly different from the median cost because it is higher.
Median cost is a better representation of the amount of money that the family spent because, with regard to meal costs, this means that exactly half of the meals in the amusement park are above this price ($5.23) and exactly half are below.
The sum of two numbers is 25, and the difference of their squares is 75. what are the two numbers?
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14*14=196
11*11=121
196-121=75
the answer is x=14 and y=11
David wants to rent a movie. He wants to watch either a comedy or a drama. The movie rental store has 18 comedies and dramas available for rent. Seven of the movies are comedies, and eleven of the movies are dramas. David has not seen two of the comedies, and he has not seen four of the dramas. If David selects a movie randomly, what is the probability the movie will be a comedy or a movie that he has not seen?
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A = number of ways to pick a movie David wants (either a comedy or a movie he hasn't seen)
B = number of movies total
There are 7 comedies and 4 dramas that David hasn't seen (note: the comedy movies that he hasn't seen are part of the "comedy movie" count, so there's no need to double count these). So there are 7+4 = 11 movies that David would want to rent. Therefore, A = 11.
There are 18 movies total for rent, so B = 18
Dividing the two values
A/B = 11/18 = 0.6111 approximately
The answer as a fraction is exactly 11/18
The answer in decimal form is roughly 0.6111
The answer in percent form is approximately 61.11%
[tex] |\Omega|=18\\
|A|=7+4=11\\\\
P(A)=\dfrac{11}{18}\approx61\% [/tex]
find the point slope equation for (-2,-20) and (9,79)
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x1: -2
x2: 9
y1: -20
y2: 79
The general form for writing a point slope equation is y-y1 = m(x-x1)
M is your slope.
To find the slope, plug the values you just identified into the equation y2-y1/x2-x1
This leaves you with 79+20/9+2
Which equals 9, so your slope (m) equals nine.
you can now plug everything into the general form which gives you:
y+20 = 9(x+2)
The point-slope equation for the points (-2,-20) and (9,79) is y + 20 = 9(x + 2).
Explanation:To find the point-slope equation, we can use the formula: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Firstly, we calculate the slope using the formula: m = (y2 - y1)/(x2 - x1). Given the points (-2, -20) and (9, 79), the slope is (79 - (-20))/(9 - (-2)). Simplifying the expression, we get m = 99/11 = 9.
Next, we substitute one of the points and the calculated slope into the point-slope formula. Let's choose (-2, -20). So the equation becomes: y - (-20) = 9(x - (-2)). Simplifying further, we have: y + 20 = 9(x + 2).
This is the point-slope equation for the given points: y + 20 = 9(x + 2).
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A. 0
B. 4
C. 2
D. -2
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Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. x - 2; 4x2 - 3x + 22
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Answer:
[tex]x-2[/tex] is not a factor of [tex]p(x)=4x^2-3x+22[/tex].
Step-by-step explanation:
According to the factor theorem, if [tex]x-a[/tex] is a factor of [tex]p(x)[/tex], then [tex]p(a)=0[/tex].
Let [tex]p(x)=4x^2-3x+22[/tex]. If [tex]x-2[/tex] is a factor of [tex]p(x)=4x^2-3x+22[/tex], then [tex]p(2)=0[/tex].
Let us plug in [tex]x=2[/tex] in to the function to see if it will give us zero.
[tex]p(2)=4(2)^2-3(2)+22[/tex]
We simplify to obtain,
[tex]p(2)=4(4)-3(2)+22[/tex]
[tex]p(2)=16-6+22[/tex]
[tex]p(2)=10+22[/tex]
[tex]p(2)=32[/tex]
Since [tex]p(2)\ne0[/tex], [tex]x-2[/tex] is not a factor of [tex]p(x)=4x^2-3x+22[/tex].
According to the Factor Theorem, 'x - 2' is not a factor of the polynomial '4x^2 - 3x + 22'. This determination was made by plugging '2' into the second polynomial and finding that it does not result in zero.
Explanation:For a polynomial P(x), the Factor Theorem states that if you plug a value 'a' into the polynomial and get zero (P(a) = 0), then x-a is a factor of that polynomial. In this case, you are asked to determine whether 'x - 2' is a factor of the quadratic function '4x^2 - 3x + 22'.
To do so, according to the Factor Theorem, plug the value '2' into the second polynomial function, so we have 4*(2)^2 - 3*(2) + 22 = 16 - 6 + 22 = 32. Because this does not equal zero, we can conclude that 'x - 2' is not a factor of the second polynomial '4x^2 - 3x + 22' based on the Factor Theorem.
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What are the minimum, first quartile, median, third quartile, and maximum of the data set?
12, 6, 8, 3, 10, 15, 18, 7
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[tex]3,\:6,\:7,\:8,\:10,\:12,\:15,\:18[/tex]
The minimum is 3.
The first quartile is the average of 6 and 7, which is 6.5
The median is the average of 8 and 10 which is 9.
The third quartile is the average of 12 and 15 which is 13.5.
The maximum is 18.
evaluate a = log(0.1) and b = ln(e^3)
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A set of n = 15 pairs of scores (X and Y values) has SSX = 4, SSY = 25, and SP = 6. What is the Pearson correlation for these data
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[tex]r = \frac{SP}{ \sqrt{SS_{x}SS_{y} } } [/tex]
Therefore:
r = 6 / √(4·25)
= 6 / √100
= 6 / 10
= 0.60
Hence, the Pearson correlation for this set is 0.60
your mom is looking at he amount of sugar in two different drinks the apple juice has 216 grams sugar for every 8 serving the sprite 234 grams of sugar for every 9 serving which drink has more sugar
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The area of a rectangular garden is given by the trinomial x2 + x – 42. What are the possible dimensions of the rectangle? Use factoring.
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= x^2 + 1x - 42
^ ^
| |
| you need two numbers that multiply to -42
|
and add to 1
Find two numbers whose product is -42 and whose sum is 1.
The numbers are -6 and 7.
x^2 + x - 42 = (x - 6)(x + 7)
The dimensions of the rectangle given by the trinomial (x² + x – 42) are 7 and 6, which are derived by factoring the trinomial and applying the quadratic formula.
Explanation:To find the possible dimensions of the rectangle, we start by factoring the trinomial that represents the area of the rectangle, namely x² + x – 42.
This can be factored as (x + 7)(x - 6), which are the roots of the quadratic equation when set to equal zero.
The roots, or solutions to this equation, can be calculated using the quadratic formula, -b ± √b² - 4ac 2a, which includes squaring the coefficient of the x-term, subtracting four times the product of the remaining coefficients, and dividing the result by twice the leading coefficient.
In this case, the dimensions that correspond to these roots, namely length and width, are 7 and -6. However, since dimensions cannot be negative, we disregard -6. Therefore, the possible dimensions of the rectangle are 7 and 6.
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If nine people are in a room and every person shakes hands exactly once with each of the other people, how many handshakes will occur
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Answer: 36 handshakes
A quiz consists of two multiple-choice questions. the first question has a total of 7 possible answers followed by the second question which has a total of 3 possible answers. if both questions are answered with random guesses,
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Select all that are undefined. sec (45°) csc (0°) sec (90°)
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csc(0°) = 1/sin(0°) = 1/0 /undefined/
sec(90°) = 1/cos(90°) = 1/0 /undefined/
Final answer:
The sec(45°) and sec(90°) are defined, but csc(0°) is undefined.
Explanation:
To determine which of the given trigonometric functions are undefined, we need to understand the domains of these functions. In trigonometry, the secant and cosecant functions are undefined for angles where the cosine and sine functions are equal to zero, respectively.
For sec(45°), the cosine of 45° is equal to √2/2, which is not zero. Therefore, sec(45°) is defined.For csc(0°), the sine of 0° is equal to 0, which results in division by zero. Hence, csc(0°) is undefined.For sec(90°), the cosine of 90° is equal to 0, which again leads to division by zero. Thus, sec(90°) is undefined.Find the value of n such that x2-10x+n is a perfect square trinomial.
A. -5
B. 50
C. 100
D. 25
Answers
D. 25
The explanation is shown below:
1. You have that:
(a ± b)^2=a^2 ± 2ab + b^2
2. The expression given in the problem is:
x^2-10x+n
Where x^2=a and 2ab=10x
2b=10
b=10/2
b=5
3. Therefore, you have:
b^2=5
b^2=25
b^2=n
n=25
Answer:
the answer is 25!!
Step-by-step explanation:
I hope this is helpful to sum of y'all!!
is it always true that trapezoids height is the distance between the 2 bases?
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Help
A survey was taken of 36 people to see if they owned a car and/or a truck. The results are shown in the Venn diagram.
Enter your answers in the boxes to complete the two-way table based on the given data.
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Answer: The table should look like this
4 9 13
15 8 23
19 17 36
Step-by-step explanation:Happy to help
Based on the complete table, 19 people own a car, 13 people own a truck while 8 people neither own a car nor a truck.
How to complete the table
A survey was taken of 36 people to see if they owned a car and/or a truck. The results are shown in the Venn diagram.
own a car Dont own a car Total
Own a trcuk 4 9 13
Dont own a trcuk 15 8 23
Total 19 17 36
Those that own car 15 + 4 =19
those that own truck 9 + 4 = 13
Those that own car and truck 4 (Given)
Those that owns none = 36-15-9 - 4 = 8
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Using sin^2x+ cos^2 x=1 and other trig properties, simplify the following: (cos^2Ø*tan^2Ø)/(1-cos^2 Ø.
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[tex]Used:\\\\\sin^2\O+\cos^2\O=1\to1-\cos^2\O=\sin^2\O\\\\\tan\O=\dfrac{\sin\O}{\cos\O}[/tex]
JK, KL, and LJ are all tangent to circle O. The diagram is not drawn to scale. If JA = 10, AL = 23, and CK = 9, what is the perimeter of ∆JKL
A.84
B.66
C.42
D.38
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Answer: the perimeter of JKL is 84
ik this is rlly late but to help anyone else who gets this question:
This is an equilateral triangle, so the adjacent length is gonna be the same value as its corresponding length that was listed
JA = 10
JB = JA, JB is also 10
JA + JB (10+10) = 20
AL = 23
LC = AL, LC is also 23
AL + LC (23+23) = 46
CK = 9
KB = CK, KB is also 9
CK + KB (9+9) = 18
add all those up:
20 + 46 + 18 = 84
please help. there is a picture below
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A two digit number with two different digits has a special property when th sum of its digits is added to the product of its digits the result is the number itself
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PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE HELP!! WILL GET BRAINIEST IF YOU SHOW WORK
1. Simplify the radical
2. Simplify the radical
3. Simplify the radical
4. Simplify the radical
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The simplification of the radical is c/3
What are radicals in math?Radicals in math refer to expressions containing square roots or higher-order roots.
Represented by the radical symbol (√), they involve finding the root of a number. For example, √9 equals 3, as 3 * 3 equals 9.
Simplifying the surd;
√3c²)/√27
= √3 × √c²)/√9 × √3
= √3c/3√3
= c/3
Therefore the simplification of √3c²)/√27 is c/3.
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how many times greater is the value of the 2 in 204,936 than the value of the 2 in 124,936
A. 1/100
B. 1/10
C. 10
D. 100
E. 1,000
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How many Liters of a liquid can be held in a barrel
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Maria needs to mail 3 letters. Each letter costs $0.41 to mail. How much change will she get back if she gives the clerk $2.00?
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I found this by using the expression x = 2.00 - 3(0.41) and solving for x.
Maria has to mail 3 letters, each costing $0.41, totaling to $1.23. She gives the clerk $2.00, so the change she will get back is $2.00 - $1.23 = $0.77.
Explanation:This problem is about simple arithmetic and money management. Maria has to mail 3 letters, each costing $0.41. This means that the total expense that Maria has to pay is $0.41 * 3, which equals $1.23. Maria gives the clerk $2.00, so to find out the change, subtract the total cost of the letters ($1.23) from the amount she gave to the clerk ($2.00). So, the change Maria will get back is $2.00 - $1.23 = $0.77.
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Find the probability of drawing a heart or a black card from a standard deck of cards
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Hearts and black cards make up 3 of the 4 suits of cards. You could count the amount of them and then divide by 52 cards, or you can divide 3 by 4 since there are the same amount in every suit.
The probability of drawing a heart or a black card from a standard deck of cards is 3/4.
Explanation:In a standard deck of cards, there are 52 cards in total. However, since we are interested in finding the probability of drawing a heart or a black card, we need to determine how many cards satisfy this condition.
There are 13 hearts in a deck, so the probability of drawing a heart is 13/52 or 1/4. Additionally, there are 26 black cards (13 spades and 13 clubs) in a deck, so the probability of drawing a black card is 26/52 or 1/2.
To find the probability of drawing a heart or a black card, we can add the probabilities together: 1/4 + 1/2 = 3/4.
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Which function represents a reflection of f(x) = 5(0.8)x across the x-axis? A. g(x) = 5(0.8)–x B. g(x) = –5(0.8)x C. g(x) = 1/5(0.8)x D. g(x) = 5(–0.8)x
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So f(x) = 5(0.8)^x turns into g(x) = -5(0.8)^x
Answer: Choice B
Answer:
2nd option
Step-by-step explanation: