Graphing exponential functions and logarithms involves understanding the key characteristics of these functions and how they are represented on a graph.
Asymptotes: The graph of an exponential function does not have any asymptotes.
Domain and range: The domain and range of an exponential function are all real numbers.
Increasing or decreasing: An exponential function is always increasing.
Shape: The graph of an exponential function is concave up.
y-intercept: The y-intercept is (0,1)
x-intercept: The x-intercept does not exist.
To graph an exponential function, you can start by plotting the y-intercept (0,1) on the graph. Then, you can use the information about the shape of the graph (concave up) and the increasing nature of the function to determine the general shape of the graph.
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Evaluate: Percents Benita answered 85% of the test questions correctly. If she answered 9 questions incorrectly, how many questions were on the test?
It is urgent.
Answer:
60
Step-by-step explanation:
the diffrence between the roots of the equation 2x^2-5x+c=0 is 0.25 find c
Answer:
c = 3.09375Step-by-step explanation:
Standard for of quadratic equation:
ax² + bx + c = 0We have
2x² - 5x + c = 0Sum of the roots
x₁ + x₂ = - b/a = -(-5)/2 = 2.5Product of the roots
x₁x₂ = c/a = c / 2We have:
x₁ - x₂ = 0.25The square of the above is:
(x₁ - x₂)² = (x₁ + x₂)² - 4x₁x₂Substitute known values and solve for c:
0.25² = (2.5)² - 4(c/2) 2c = 6.25 - 0.06252c = 6.1875c = 3.09375Answer:
c = 3.09375
Step-by-step explanation:
Factored form of a quadratic equation
[tex]y=a(x-r_1)(x-r_2)[/tex]
where:
a is the leading coefficient[tex]r_1[/tex] and [tex]r_2[/tex] are the rootsGiven quadratic:
[tex]2x^2-5x+c=0[/tex]
Therefore, the leading coefficient is:
[tex]\implies a=2[/tex]
Substitute the value of a into the formula:
[tex]\implies y=2(x-r_1)(x-r_2)[/tex]
Expand:
[tex]\implies y=2x^2-(2r_2+2r_1)x+2r_1r_2[/tex]
Compare the coefficients of x:
[tex]\implies -(2r_2+2r_1)=-5[/tex]
[tex]\implies 2r_2+2r_1=5[/tex]
[tex]\implies r_2+r_1=2.5[/tex]
If the difference between the roots is 0.25 then:
[tex]\implies r_2-r_1=0.25[/tex]
Add the two root equations to eliminate r₁:
[tex]\implies 2r_2=2.75[/tex]
[tex]\implies r_2=1.375[/tex]
Substitute the found value of r₂ into one of the root equations and solve for r₁:
[tex]\implies 1.375-r_1=0.25[/tex]
[tex]\implies r_1=1.375-0.25[/tex]
[tex]\implies r_1=1.125[/tex]
As c = 2r₁r₂ then:
[tex]\implies c=2(1.125)(1.375)[/tex]
[tex]\implies c=3.09375[/tex]
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What is the equation of the line in slope-intercept form that has a slope of 6 and a y-intercept of 1/2
- I have struggled with this for an hour
-I have been taking tutoring and still need help -it's just not clicking
The graphs of lines f an g are shown on the grid. Write a system of equations to represent this graph.
The Equation of line F is y= -9/2x + 59/2.
The Equation of line G is y = 1/10 x .
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
For Line F:
slope = -9 /2
and, Equation of line F as
y - (-2) = -9/2 (x -(7))
y + 2= -9/2( x- 7)
y = -9/2x + 63/2 -2
y= -9/2x + 59/2
For Line G:
Slope = (0 -(1))/ ( 0-(10))
slope = 1/10
and, Equation of line G as
y - (1) = 1/10 (x -10)
y-1 = 1/10 x - 1
y = 1/10 x
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cual es la raiz cuadrada de 94?
Answer:
9.7(aproximado)Step-by-step explanation:
Aquí,
[tex] \sqrt{94} [/tex]
= 9.69......
= 9.7(aproximado)
Jesse wanted a stamp collection his grandfather gave him 48 stamps to start it then his parents gave him 23 stamps and his aunt gave him 17 stamps how many stamps does Jesse have in his collection
Answer:88
Step-by-step explanation:
What is not a polynomial class 10?
A variable-containing expression that divides by a variable, contains fractional or negative exponents, or is enclosed in a radical is not a polynomial.
As long as the polynomial is specified over the real numbers, it is possible for it to have negative coefficients, fractional coefficients, or even radical coefficients.
There cannot be a negative exponent in a polynomial. The exponent of a variable in any term of a polynomial must, by definition, be a nonnegative integer, such as 0, 1, 2, 3, 4, etc. The exponents of variables do not contain fractions, decimals, or negative numbers. There cannot be a variable with a fractional exponent in a polynomial.
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help me please I’ll give BRAINLYIST. A person runs 1 mile in
in 1/2 hour. The
person's speed is miles per hour
Answer:
since speed is miles per hour it would be s=1/1/2 so it would be 2mph
The ratio of boys to girls at a local sports club is 3 to 1. If there are 45 girls, how many boys are
there?
Answer: 135 boys
Step-by-step explanation:
Multiply 3*45 since you know the number of boys is 3 times more than the number of girls.
MEDICINE: Ahmad took 200 mg of a medication. The
function f(t) = 200e 0. 4+ can be used to determine the amount of
medication, f(t), still in his system after t hours. To the nearest hundredth,
after how much time will Ahmad have only 50 mg of medication left in his
system?
A 4. 37 hours
B 7. 47 hours
C
3. 47 hours
D
3. 74 hours
A BH
BO
If Ahmad took 200 mg of medication and the function [tex]f(t) = 200e^{-0.4t}[/tex] can be used to determine the amount of medication, then He will have only 50 mg of medication left in his system after (c) 3.47 hours .
The Function that is used to determine the amount of medication, f(t), still in his system after t hours. is given as [tex]f(t) = 200e^{-0.4t}[/tex] ,
we have to find the after how many hours there will be only 50 mg of medication left ;
we need to substitute f(t) as 50 ;
we get ;
⇒ [tex]50 = 200e^{-0.4t}[/tex] ;
⇒ [tex]\frac{50}{200} =e^{-0.4t}[/tex] ;
⇒ [tex]\frac{1}{4} =e^{-0.4t}[/tex]
On solving further ,
we get ;
⇒ [tex]t=3.4657..[/tex] hours ;
So , t≈ 3.47 hours .
Therefore , After 3.47 hours there will be 50 mg of medication left .
The given question is incomplete , the complete question is
Ahmad took 200 mg of a medication. The function [tex]f(t) = 200e^{-0.4t}[/tex] can be used to determine the amount of medication, f(t), still in his system after t hours. To the nearest hundredth, after how much time will Ahmad have only 50 mg of medication left in his system ?
(a) 4.37 hours
(b) 7.47 hours
(c) 3.47 hours
(d) 3.74 hours
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62 less than j i need to know this answer immediately please
Answer:
62>j
Step-by-step explanation:
mrk me brainliest plz
danetta's dinner cost 5$ less than exwards dinner. write an equation to represent the comparison of the dinner bills
Answer:
alright, lets say danetta's dinner bill is 20 dollars, and she ordered 4 things, so the equation would be x times 5=20, and edwards would be 25 dollars, so that equation would be x times 5=25
Step-by-step explanation:
if the center of a circle is (-5, -8) and contains the point (16, 68) what is the equation ?
Answer:
[tex](x+5)^2+(y+8)^2=6217[/tex]
Step-by-step explanation:
Hi there!
Equation of a circle: [tex](x-h)^2+(y-k)^2=r^2[/tex] where the circle is centered at (h,k) and r is the radius
1) Plug the center of the circle into the equation
Center: (-5,-8)
[tex](x-h)^2+(y-k)^2=r^2\\(x-(-5))^2+(y-(-8))^2=r^2\\(x+5)^2+(y+8)^2=r^2[/tex]
2) Determine r²
Plug in the given point (16,68)
[tex](x+5)^2+(y+8)^2=r^2\\(16+5)^2+(68+8)^2=r^2\\(21)^2+(76)^2=r^2\\441+5776=r^2\\6217=r^2[/tex]
Therefore, r² is equal to 6217. Plug this back into [tex](x+5)^2+(y+8)^2=r^2[/tex]:
[tex](x+5)^2+(y+8)^2=6217[/tex]
I hope this helps!
Help please! I need to know if it’s a function or not!! Thank you!
Answer:
The table represents a function and the slope is -1/2
Step-by-step explanation:
Here, we want to know if the given table is a function
For a relation to be a function, no two y values have same x value
however, 2 x values can have same y value
Looking at the table, we can conclude that what we have is a function
To find the slope, we select any two points and apply the slope formula
m = (y2-y1)/(x2-x1)
(x1,y1) = (6,-2)
(x2,y2) = (-2,2)
m = (2 -(-2))/(-2-6) = 4/-8 = -1/2
Meri is making birdhouses. Each birdhouse uses 58 yard of wood. What is the total length of wood Meri will need to make 12 birdhouses? Drag each of the numbers from the box to complete and solve the equation. Each number will be used once
Meri will need 696 yards of wood to make 12 birdhouses, as each birdhouse requires 58 yards of wood.
Meri is making birdhouses and each birdhouse needs 58 yards of wood. To find out the total length of wood needed for making 12 birdhouses, we can use the formula:
length of wood per birdhouse x number of birdhouses = total length of wood
So, in this case, we can substitute the given values in the formula:
58 yards x 12 birdhouses = 696 yards
This means Meri needs 696 yards of wood to make 12 birdhouses.
This equation works because it uses the concept of the unitary method, where we find the total length of wood by multiplying the number of birdhouses by the length of wood used in each birdhouse, this way we are able to find the total amount of wood needed.
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Mark invests $1500 in an account that pays 5.7% interest compounded continuously. Assuming no deposits or withdrawals are made, how much money will be in the account after 10 years?
Answer:
$2,611.21
Step-by-step explanation:
A = P(1 + r/n)^nt
A = 1500(1 + 0.057/1)¹⁰
A = 1500(1.057)¹⁰
A = 1500(1.740803988528..)
A = 2611.205982792..
A ≈ $2,611.21
______________________
Where A is the total amount including interest, P is the initial amount or principle, r is the rate, n is how many times it is compounded per year, and t is the time in years.
A store has a sale for 15% off. You decide to buy a $45 jacket.
how much would u save? how much would u spend?
The degrees of freedom for a contingency table with 10 rows and 11 columns is
O 100 O 110 O 21 O 90
Essentially, a contingency table with 10 rows and 11 columns has (D) 90 degrees of freedom.
What is a contingency table?A contingency table is a matrix-form table that shows how often different combinations of variables appear.
It's really popular in survey research, business intelligence, engineering, and scientific research. Basically, a contingency table with 10 rows and 11 columns has 90 degrees of freedom.
They are also sometimes known as two-way frequency tables and are used to show how often different combinations of variables occur.
A contingency table gives you an idea of how two variables relate to each other.
It displays one categorical variable along the rows and another categorical variable along the columns. It can help point out any interactions between them.
Therefore, essentially, a table with 10 rows and 11 columns has (D) 90 degrees of freedom.
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Complete question:
The degrees of freedom for a contingency table with 10 rows and 11 columns are:
A. 100
B. 110
C. 21
D. 90
An iron paperweight has the shape of a cube with
side length 5 cm. Iron has a density of 7.874 grams
per cubic centimeter. What is the mass of the
paperweight?
Answer:
It's D
Step-by-step explanation:
984.25 g
•25 POINTS•
-A
-B
-C
Answer:
SaS
Step-by-step explanation:
What’s the gcf of 18 and 36
Answer: 18
Step-by-step explanation:
18*1=18
18*2=36
What is simple negation give 5 examples?
Negation means negative of something , in logical mathematics negation is an expression opposite to another operation .
Examples of negation are ,
The negation of P is ∼P.The negation of A ^ B^ C is ∼( A ^ B ^ C ).The negation of A is ∼( A ).The negation of Y ^ VB is ∼( Y ^ VB ).The negation of 6 ^ 7is ∼( 6 ^ 7).Logical operations are performed to check the trueness of an expression.
These are generally Boolean expressions or algebraic functions.
A negation of a basic assertion is made by inserting the word "not" into the original statement. The truth value of the negation will always be the inverse of the truth value of the original assertion.
Under negation, what was true becomes false and the vice - versa.
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a plane is traveling 9 miles per minute how much time is needed to travel 216 miles
Answer:
Step-by-step explanation:
so since it’s traveling 9mi/m you need to devide 216 by the rate of 9mi/m to find how long it takes.
216/9=24 so it will take 24 minutes!
Answer:1,944 minutes
Step-by-step explanation:
if the question is a plane is traveling 9 miles per minute how much time is needed to travel 216 miles you need it is clear that you are doing a multiplication problem so multiply that and you get 1,944 minutes
your welcome
Express the number in standard form
1.028×10^9
Answer:
1.028 × 10⁹
= 1028000000
which graph represents -12x-6y_>5
Answer:
l learnt it but I forgotten sorry
PLS HELP QUICKKKKK! Tap the photo to see the full problem. Answer all 3 questions please and I'll give brainliest if it is right.
4/5 + 3/4= asap PLEASEEE
What is the solution
Answer:
d
Step-by-step explanation:
Multiply.
Your answer should be a monomial in standard form.
{(4z^3)(-3z^3)}=(4z
3
)(−3z
3
)
The required simplified expression as a monomial is given as -12[z⁶].
What is a polynomial function?A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial and trinomial, etc. ax+b is a polynomial.
here,
Given an expression, the outcome of the multiplicative depression will be an expression of a monomial.
= [4z³][-3z³]
= 4 × 3 [-z ³⁺³]
= -12[z⁶]
Thus, the required simplified expression as a monomial is given as -12[z⁶].
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Find the domain and range of the function graphed below. PLEASE SHOW YOUR WORK!!
The domain and range of the function on the graph are:
D: [-2, 1)R: [0, 4]How to find the domain and range of the function below?Remember that for any function y = f(x), we define the domain as the set of possible inputs (possible values of x) and the range is the set of the possible outputs of the function (possible values of y).
To find the domain we need to look at the horizontal axis. The minimum is at x = -2 with a colored circle, so x = -2 belongs to the domain.
The largest value is at x = 1, now with an open circle, then this value does not belong to the domain. Thus the domain is:
D: [-2, 1)
For the range we need to look at the vertical axis, the minimum is at zero and the maximum at 4, then the range is:
R: [0, 4]
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