Answers
Step-by-step explanation:
exponential decay functions are written in the form :
[tex]y=ab^{x}[/tex]
where b is less than 1
if we look at the 3rd choice and consider the term on the right.
[tex](8/7)^{-x}[/tex]
= [tex](7/8)^{x}[/tex]
If we compare this to the general form above,
b = 7/8 (which is less than 1)
hence the 3rd choice is correct.
The function which is an exponential decay function is:
[tex]f(x)=\dfrac{3}{2}(\dfrac{8}{7})^{-x}[/tex]
Step-by-step explanation:We know that an exponential function is in the form of:
[tex]f(x)=ab^x[/tex]
where a>0 and if 0<b<1 then the function is a exponential decay function.
and if b>1 then the function is a exponential growth function.
a)
[tex]f(x)=\dfrac{3}{4}(\dfrac{7}{4})^x[/tex]
Here
[tex]b=\dfrac{7}{4}>1[/tex]
Hence, the function is a exponential growth function.
b)
[tex]f(x)=\dfrac{2}{3}(\dfrac{4}{5})^{-x}[/tex]
We know that:
[tex]a^{-x}=(\dfrac{1}{a})^x[/tex]
Hence, we have the function f(x) as:
[tex]f(x)=\dfrac{2}{3}(\dfrac{5}{4})^x[/tex]
Here
[tex]b=\dfrac{5}{4}>1[/tex]
Hence, the function is a exponential growth function.
c)
[tex]f(x)=\dfrac{3}{2}(\dfrac{8}{7})^{-x}[/tex]
We know that:
[tex]a^{-x}=(\dfrac{1}{a})^x[/tex]
Hence, we have the function f(x) as:
[tex]f(x)=\dfrac{3}{2}(\dfrac{7}{8})^x[/tex]
Here
[tex]b=\dfrac{7}{8}<1[/tex]
Hence, the function is a exponential decay function.
d)
[tex]f(x)=\dfrac{1}{3}(\dfrac{9}{2})^x[/tex]
Here
[tex]b=\dfrac{9}{2}>1[/tex]
Hence, the function is a exponential growth function.
Related Questions
what is the middle term in the simplified product( x+3) (x-4)
Answers
Answer:
The middle term, once simplified is -x
Step-by-step explanation:
( x+3) (x-4)
FOIL
first
x*x = x^2
outer: -4*x = -4x
inner: 3*x = 3x
last: -4*3 = -12
Add them together x^2 -4x+3x-12
x^2 -x +12
Find the length of KB¯¯¯¯¯¯¯¯+AK¯¯¯¯¯¯¯¯.
A. 28
B. 33
C. 21
D. 35
Answers
Intersecting chord rule:
DK x KB = AK x CK
12 x 4x+1 = 14 x 3+3x
Simplify:
48x +12 = 42x +42
Subtract 12 from each side:
48x = 42x + 30
Subtract 42x from each side:
6x = 30
Divide both sides by 6:
x = 5
Now find the length of KB: 4x +1 = 4(5) +1 = 20 +1 = 21
Now add KB and AK:
21 + 14 = 35
The answer is D. 35
The required length of KB(21) + AK(14) is 35. Option D is correct.
The figure is given,
where AK = 14. DK = 12, KB = 4x+1 and KC =3+3x.
KB + AK to be determined.
The ratio can be defined as the relativeness of the fraction of one quantity towards others.
Here,
The ratio of AK: DK = KB:KC
[tex]14/12= 4x+1/3+3x\\14*(3+3x) = 12*(4x+1)\\2+42x = 48x+12\\42-12=48x-42x\\6x= 30\\x = 5[/tex]
Now,
= KA + KB
= 14 + 4x+1
= 14+ 4(5)+1
= 35
Thus, the required length of KB + AK is 35.
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Mischa wrote the quadratic equation 0 = –x2 + 4x – 7 in standard form. What is the value of c in her equation?
Answers
Answer:
-7
Step-by-step explanation:
Mischa's equation is -x² + 4x - 7 = 0
The standard form is ax² + bx + c = 0
c is the constant term in the quadratic equation.
If we compare terms, we find that c = -7.
Which of the following represents the set of possible rational roots for the
polynomial shown below?
2x^3+ 5x^ 2– 8x-10=0
Answers
Answer:
is there an option for no solution? because when I solved there were no possible rational solutions
Step-by-step explanation:
Answer:
This was the correct answer choice in my case.
Step-by-step explanation:
Hope this helps!
On a baseball field, the pitcher’s mound is 60.5 feet from home plate. During practice, a batter hits a ball 257 feet at an angle of 31° to the right of the pitcher’s mound. An outfielder catches the ball and throws it to the pitcher. Approximately how far does the outfielder throw the ball?
A. 174.2 ft
B. 183.0 ft
C. 207.5 ft
D. 147.2 ft
Answers
Answer:
Option C (207.5 feet)
Step-by-step explanation:
The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the two sides that are given are adjacent to each other the given angle is the included angle. This means that the angle is formed by the intersection of the lines. Therefore, cosine rule will be used to calculate the length of b. The cosine rule is:
x^2 = y^2 + z^2 - 2*y*z*cos(X).
Let x be the distance covered by the outfielder's throw, let y be the distance between the pitcher's mound and the home plate, let z be the distance covered by the batter's shot, and let X be the mentioned angle.
The question specifies that y=60.5 feet, X=31°, and z=257 feet. Plugging in the values:
x^2 = 60.5^2 + 257^2 - 2(60.5)(257)*cos(31°).
Simplifying gives:
x^2 = 43053.9184501 feet.
Taking square root on the both sides gives x = 207.5 feet (rounded to the one decimal place).
This means that the Option C is the correct choice!!!
When studying the population of flying squirrels, only a sample of flying squirrels population was measured. Why would just a sample be measured? Explain how this sample can be used to make an inference about the entire population of flying squirrels.
Answers
Answer:
When studying a random sample of the population, you are studying one of many (generally the same) flying squirrels that live. This small selection represents the whole population, (because as said before, they are generally the same). In this way, you can assume that the small section that you picked is going to represent the entire flying squirrel population.
(-6,5)
(-3,3)
(0,1)
what are the intercepts
Answers
Answer:
(0, 1)Step-by-step explanation:
y-intercept: (0, y)
x-intercept: (x, 0)
Therefore the y-intercept is only (0, 1).
Angles 4 and 5 form what type of angles?
complementary angles
supplementary angles
vertical angles
obtuse angles
Answers
Answer:
the answer will be verticle angles
Step-by-step explanation:
∠4 and ∠5 form vertical angles.
What is vertical angles?When two lines intersect each other, then non-adjacent opposite angles are called vertical angles.
Vertical angles are always equal in measurement.
If line AB and CD intersect each other at point O, ∠AOC and ∠BOD are vertical angles, similarly, ∠AOD and ∠BOC are also vertical angles.
Here lines 1 and 2 intersect each other.
So ∠4 and ∠5 are formed which are non-adjacent and opposite also.
Therefore ∠4 and ∠5 form vertical angles.
Learn more about vertical angles
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The length of a rectangle is three times its width. The perimeter is 160 cm. What is the number of square centimeters in the area of the rectangle?
Answers
Answer:
1200 cm²
Step-by-step explanation:
width = x cm
length = 3x cm
perimeter = 160 cm
2(x + 3x) = 160
4x = 160/2
4x = 80
x = 80/4
x = 20 cm - width
length = 3x = 3 · 20 = 60 cm
Area = length · width = 60 · 20 = 1200 cm²
The rectangle's width is 20 cm and its length is 60 cm. Thus, the area of the rectangle is 1200 square centimeters.
Explanation:We are given that the length of a rectangle is three times its width. Let's denote the width as 'w'. Consequently, the length would be '3w'.
The perimeter of a rectangle is given by the formula: 2*(length + width). Given that the perimeter is 160 cm, we can substitute our variables into the formula: 2*(w + 3w) = 160. This simplifies to 8w = 160. Therefore, the width (w) equals 20 cm, and the length is 60 cm (3w).
The area of a rectangle is calculated by multiplying its length and width. Hence, the area of our rectangle is: 60 cm * 20 cm = 1200 square centimeters.
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Solve for x
(x-4)(x - 4) = 0
Answers
Answer:
x=4
Step-by-step explanation:
Answer:
X=4
Step-by-step explanation:
(x-4)(x-4)=0
if x=4 then 4-4=0
0^(x-4)=
x-4=0
0^0=0
5(2x-3) in distributive property
Answers
5 times 2x is 10x and 5 times -3 is -15
Thus, 10x-15
Answer:
The answer is (5*2x) - (5*3)
Step-by-step explanation:
You just have to multiply the coefficient by the individual numbers and variables inside the parentheses. :)
Should it be facing left or right ?
Answers
Answer:
Facing Right
Step-by-step explanation:
Given inequalities are:
4-x≤-1
Subtracting 4 from both sides
4-x-4≤-1-4
-x≤-5
Multiplying both sides with -1. Multiplying with a negative number changes the sign of the inequality
So,
x≥5
Second Inequality:
2+3x≥17
Subtracting 2 from both sides
2+3x-2≥17-2
3x≥15
Dividing both sides by 3
x≥5
Union of both solutions:
x≥5 ∩ x≥5
=> x≥5
Hence the solution will be facing right on the number line towards all numbers greater than or equals to 5 ..
241,389.613 which digit is in the hundred millons place
Answers
Answer:
241,389.613
Step-by-step explanation:
The first 1 is in the hundred millons place.
Answer:
3
Step-by-step explanation:
the algebraic expression for "the quotient of 51 and x" is?
Answers
Answer:
51/x
The first number/ variable always goes on top
Find the value when x=2and y=3 x^-3y^-3
Answers
Answer:
4/27
Step-by-step explanation:
x^-3y^-3
Let x=2 and y=3
2^ (2) (3)^-3
2^2 * 1/3^3
4/27
given the two Fibonacci numbers below, which number would follow? F(14) = 377 and F(15) = 610
Answers
Answer:
987.
Step-by-step explanation:
The terms in a Fibonacci series are obtained form the sum of the previous 2 terms. So the next number F(16) = 377 + 610 = 987.
APEX ANSWER: 987
Step-by-step explanation:
377 + 610 = 987
Find the area of the image.
Answers
See the attached picture:
Which expression is equivalent to 6x2– 19x – 55?
Answers
Answer:
( 6x + 11 ) ( x - 5 )
Step-by-step explanation:
Let
6x2 - 19x - 55 = 0
6x2 - (30-11)x - 55 = 0
6x2 - 30x + 11x - 55 = 0
6x ( x - 5 ) + 11 ( x - 5 ) = 0
( 6x + 11 ) ( x - 5 ) = 0
Therefore, ( 6x + 11 ) ( x - 5 ) = 6x2 - 19x - 55
I need help!!!!
Which represents the inverse of the function f(x)=4x?
Answers
Answer:
[tex]h(x)=\frac{1}{4}x[/tex].
Step-by-step explanation:
The inverse is basically you just swapping x and y. People want to solve it for y to make it a function of x.
[tex]y=4x[/tex]
Swap x and y:
[tex]x=4y[/tex]
Now solve for y by dividing y on both sides:
[tex]\frac{x}{4}=y[/tex]
[tex]\frac{1}{4}x=y[/tex]
[tex]y=\frac{1}{4}x[/tex].
Points C, D, and G lie on plane X. Points E and F lie on plane Y.Which statements are true? Select three options.
Answers
Answer:
2nd , 3rd, & 4th
Step-by-step explanation:
What is the first step in solving the inequality 2x + 3 ≥ 17?
Answers
The first step of solving this inequality is subtracting 3 to both sides. This will cancel 3 from the left side to start isolating x.
2x + 3 - 3 ≥ 17 - 3
2x ≥ 14
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
x≥7
Step-by-step explanatio
To solve this problem, subtract 3 from both sides and divide by 2 from both sides.
2x+3-3≥17-3
17-3=14
2x≥14
2x/2≥14/2
14/2=7
x≥7 is the correct answer.
1. If a, b, c, d, and e are whole numbers and a(b(c
+ d) + e) is odd, then which of the following
CANNOT be even?
(A) a
(B) b
(C)c
(D) d
Answers
Answer:
a CANNOT be even ⇒ answer A
Step-by-step explanation:
* Lets revise the rules of even and odd numbers
- Even numbers any number its unit digit is (0 , 2 , 4 , 6 , 8)
- Odd numbers any number its unit digit is (1 , 3 , 5 , 7 , 9)
# even + even = even ⇒ 2 + 4 = 6
# odd + odd = even ⇒ 1 + 3 = 4
# odd + even = odd ⇒ 1 + 2 = 3
# even × even = even ⇒ 2 × 4 = 8
# odd × odd = odd
⇒ 3 × 5 = 15
# odd × even = even ⇒ 5 × 6 = 30
∵ a[b(c + d) + e] = odd
∵ odd × odd = odd
∴ a must be odd and [b(c + d) + e] must be odd
∵ odd + even = odd
∵ odd × even = even
# Case 1
∴ b(c + d) must be odd if e even
∵ b(c + d) is odd
∴ b must be odd and (c + d) must be odd
∵ c + d must be odd
∵ odd + even = odd
∴ c or d can be even
- We now now that e , c and d can be even
# case 2
∴ b(c + d) must be even if e odd
∵ b(c + d) is even
∵ even × even = even
∴ b and (c + d) both can be even
∵ c + d can be even
∴ c or d can be even or odd
- We now now that e , c , d and b can be even
∴ Only a can not be even
* a CANNOT be even
PLEASE HURRY
WILL GIVE BRAINLIEST
Answers
This is because to solve for the semicircle the equation is:
1/2*pi*r^2 1/2*pi*16
And the equation for the triangle is:
1/2*hb*h 1/2*8*3
(Plz mark Brainliest have a nice day)
The system of equations y=-1/2x+4 and y = 2x – 1 is shown on the graph below. According to the graph, what is the solution to this system of equations?
A. (2, 3)
B. (3, 2)
C. (–1, 4)
D. (4, –1)
Answers
Answer: You can use a graphing calculator in the future
(2,3)
A
Answer: A(2,3)
Step-by-step explanation:
To solve the system of equations;
y=-1/2x+4 and y = 2x – 1
y=-1/2x+4 ----------(1)
y = 2x – 1 -----------(2)
Lets substitute equation 2 in equation 1
2x - 1 = -1/2x+4
Collect like term
(We move the x variables from the right -hand side of the equation to the right-hand side of the equation to the right-hand-side of the equation and then move the constants to the right-hand side of the equation)
2x + 1/2x = 4 + 1
5x/2 = 5
To get the value of x, we will multiply both-side of the equation by 2/5
5x/2 × 2/5 = 5 × 2/5
(On the left-hand side of the equation, the 5/2 will cancel out the 2/5 leaving us with x and on the right-hand side of the equation 5 will cancel out 5 leaving us with 2)
x = 2
Substitute x =2 in equation (2)
y = 2x - 1
y = 2(2) - 1
y = 4 -1
y =3
The solution to the system of the equations is x=2 and y=3
Therefore the answer is A(2,3)
What is the slope of the line represented by the equation y = x – 3? –3 3
Answers
Answer:
None of then, the slope is 1
Step-by-step explanation:
We have to use the general equation for lines, that is:
[tex]y=mx+b[/tex]
where 'm' is the slope (by comparison)
So, we only need to compare your equation ([tex]y=x-3[/tex]) with the general one.
We can see that m=1, b=-3
So our slope turns out to be equals to 1
The axis of symmetry for the graph of the function is f(x) = 1/4 x2 +
bx 10 is x = 6. what is the value of b?
Answers
Answer:
Step-by-step explanation:
f(x) = 1/4 x²+bx+10
the derivate is : f'(x) = 1/2 x +b
you have : f'(6)=0
1/2 (6)+b=0
3+b =0
b = -3
so f(x) = 1/4 x²-3x+10.......f(6) =1/4(6)² -3(6)+10 =9-18+10 =1
f(x) = 1/4(x-6)²+1... the vertex form
Value of 'b' from the quadratic function will be (-3).
Axis of symmetry of a parabola,If the quadratic equation for the parabolic path has been given as,
f(x) = ax² + bx + cAxis of symmetry of the parabola will be given by,
Axis of symmetry = [tex]-\frac{b}{2a}[/tex]
Quadratic function given in the question → [tex]f(x)=\frac{1}{4}x^2+bx+10[/tex]
Compare this equation by [tex]f(x)=ax^2+bx+c[/tex]
[tex]a=\frac{1}{4},b=b,c=10[/tex]
Axis of symmetry of the parabola will be,
Axis of symmetry = [tex]-\frac{b}{2(0.25)}[/tex]
= [tex]-2b[/tex]
Axis of symmetry has been given as x = 6,
[tex]6=-2b[/tex]
[tex]b=-3[/tex]
Therefore, value of b will be (-3).
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What is the quotient of -13/8 divided by -1/4
Answers
Answer:
0.40625
Step-by-step explanation:
Answer:
The answer is 13/2
Step-by-step explanation:
At East Middle School, there are 58 left-handed students and 609 right-handed students. The numbers of left- and right-handed students at West Junior High are proportional to the numbers at East Middle School. Which of the following could be the numbers of left-handed and right-handed students at West Junior High?
Choose 2 answers:
A= left-handed: 42
Right-handed: 483
B= lef-handed: 28
Right-handed: 378
C= left-handed: 48
Right-handed: 504
D= left-handed: 56
Right-handed: 560
E: left-handed: 30
Right-handed: 315
Answers
Answer:
C. Left-handed: 48, Right-handed: 504
D. Left-handed: 30, Right-handed: 315
Step-by-step explanation:
We are given that there are 58 left-handed students and 609 right-handed students at East Middle School and these numbers of students are proportional to the number of left and right handed students at East Middle School.
Given the above information, we are are to determine which two options could be the the numbers of left-handed and right-handed students at West Junior High.
Ratio of right handed to left handed students at East Middle School = [tex]\frac{609}{58} = 10.5[/tex]
Checking for ratios of the given options:
A. [tex]\frac{483}{42} =11.5[/tex]
B. [tex]\frac{378}{28} =13.5[/tex]
C. [tex]\frac{504}{48} =10.5[/tex]
D. [tex]\frac{560}{56} =10[/tex]
E. [tex]\frac{315}{30} =10.5[/tex]
Therefore, the possible numbers of left-handed and right-handed students at West Junior High could be C. Left-handed: 48, Right-handed: 504 and D. Left-handed: 30, Right-handed: 315.
Answer:
OPTION C.
OPTION E.
Step-by-step explanation:
A relationship is proportional if the ratio between the variables is always the same.
In this case we know that the numbers of left- and right-handed students at West Junior High are proportional to the numbers at East Middle School and there are 58 left-handed students and 609 right-handed students at East Middle School. Therefore, the ratio is:
[tex]ratio=\frac{58}{609}=\frac{2}{21}[/tex]
So, we can check the ratio in each option to know which has ratio [tex]\frac{2}{21}[/tex]:
OPTION A:
[tex]\frac{42}{483}=\frac{2}{23}[/tex]
OPTION B:
[tex]\frac{28}{378}=\frac{2}{27}[/tex]
OPTION C:
[tex]\frac{48}{504}=\frac{2}{21}[/tex]
OPTION D:
[tex]\frac{56}{560}=\frac{1}{10}[/tex]
OPTION E:
[tex]\frac{30}{315}=\frac{2}{21}[/tex]
Therefore, you can observe that the numbers of left-handed and right-handed students at West Junior High could be:
[tex]Left-handed: 48\\Right-handed: 504\\\\\\Left-handed: 30\\Right-handed: 315[/tex]
Hello
I will mark you as a brainliest
Please answer my question.....
Solve the following equation:-
6+5 (a-1) = 30
Answers
6+5a-5=30
1+5a=30
5a=30-1
5a=29
a=29/5
Answer:
29/5 or 5.8
Step-by-step explanation:
6+5(a−1)=30
first it would be good to distribute:
6+5(a-1)=30 -> 6+(5)(a)+(5)(−1)=30 which simplifies to 6+5a+−5=30
at this point it is best to rearrange:
(5a)+(6+−5)=30 which simplifies to 5a+1=30
from then on its a matter of doing opposite operation. at my school we would call this the "equality" method. what you do to one side you do the other.
Observe:
5a+1=30
-1 -1
5a=29
5a/5=29/5
a=29/5 (in decimal it would be like 5.8)
I hope this is helpful!
Gabe swam 2 hours each day, 5 days each week, for 5 weeks. In that time,gabe swam 1,500 laps. What was his average rate in laps per hour?
Answers
Answer:
30 laps per hour
Step-by-step explanation:
The first thing you do is calculate the amount of hours he swam for. Since he swam 2 hours each day, 5 days each week, for 5 weeks we use the equation 2*5*5. The answer is 50. After that what we do is take the amount of laps and divide it by 50. We do 1500 divided by 50 and we get a total of 30 laps per hour.