What is the value of a for the exponential function in the
graph represented in the form of f(x) = a(b)?
O -4
O -3
O 3
O 4
Answers
Answer:
Option (4)
Step-by-step explanation:
If the given exponential function is in the form of f(x) = [tex]a(b)^x[/tex]
From the graph we find that two points (0, 3) and (0.5, 6) lie on the graph.
For (0, 3),
f(0) = [tex]a(b)^0[/tex]
3 = a
For (0.5, 6),
f(0.5) = [tex]3(b)^{0.5}[/tex]
6 = [tex]3\sqrt{b}[/tex]
[tex]\sqrt{b}=2[/tex]
b = 4
Therefore, value of b in the given function 'f' is 4.
Option (4) will be the answer.
Answer:
(D) 4
Step-by-step explanation:
♥☺
Related Questions
Marta is solving the equation x2+x=3 by completing the square what number should be added to both sides of the equation to complete the square?
Answers
Answer:
C = 1/4
Step-by-step explanation:
When solving a quadratic equation, there are steps to follow and I'll highlight them here.
Assuming we have an equation
ax² + bx + c = 0
Step 1
If a is not equal to 1, divide all through by a
x² + bx + c = 0
Take c to the other side of the equation
x² + bx = c
Step 2
Add (b/2)² to both sides of the equation
x² + bx + (b/2)² = c + (b/2)²
In our original question,
We had x² + x = 3
a = 1 , b = 1 c = 3
Using step two, we would have
(b / 2)² = (½)² = ¼ (which is the answer)
Now back to the steps
Step 3
We factor our left side of the equation so as to have a perfect square
[x + (b/2)]² = c + (b/2)²
Step 4
Take the square root of both sides of the equation and solve for x
x + b/2 = ±√[c + (b/2)²]
The answer to the question is ¼
Answer:
1/4
Step-by-step explanation:
Wolfrich lived in Portugal and Brazil for a total period of 141414 months in order to learn Portuguese. He learned an average of 130130130 new words per month when he lived in Portugal and an average of 150 new words per month when he lived in Brazil. In total, he learned 1920 new words. How long did Wolfrich live in Portugal, and how long did he live in Brazil
Answers
Answer:
Wolfrich lived in Brazil for 5 months and 9 months in Portugal
Step-by-step explanation:
Given;
Total Months = 14
Total Words = 1920
Required
Find the time spent in Portugal and time spent in Brazil
Let P represent Portugal and B represent Brazil; This implies that
[tex]P + B = 14[/tex] ---- Equation 1
Considering that he learnt 130 words per month in Portugal and 150 per month in Brazil; This implies that
[tex]130P + 150B = 1920[/tex] --- Equation 2
Make P the subject of formula in equation 1
[tex]P = 14 - B[/tex]
Substitute 14 - B for P in equation 2
[tex]130(14 - B) + 150B = 1920[/tex]
Open Bracket
[tex]1820 - 130B + 150B = 1920[/tex]
[tex]1820 + 20B = 1920[/tex]
Subtract 1820 from both sides
[tex]1820 - 1820 + 20B = 1920 - 1820[/tex]
[tex]20B = 100[/tex]
Divide both sides by 20
[tex]\frac{20B}{20} = \frac{100}{20}[/tex]
[tex]B = 5[/tex]
Substitute 5 for B in [tex]P = 14 - B[/tex]
[tex]P = 14 - 5[/tex]
[tex]P = 9[/tex]
Wolfrich lived in Brazil for 5 months and 9 months in Portugal
An inverse variation includes the point (4,17). Which point would also belong in this inverse variation?
Answers
Answer:
(2, 34 )
Step-by-step explanation:
Since the points vary inversely then half the x, means double the y, thus
(2, 34) or (1, 68 ) would also belong in this inverse variation
A group of students were given a spelling test the table shows their mark Mark: 6,7,8,9,10 frequency:5,4,7,10,4 a) work out the range of the marks. B)how many students are in a group C) work out the mean mark of the group
Answers
Answer:
Step-by-step explanation:
From the information given,
Mark: 6,7,8,9,10
frequency:5,4,7,10,4
a) Range = highest mark - lowest mark
Range = 10 - 6 = 4
b) The number of students in the group is the sum of the frequency. Therefore,
Number of students = 5 + 4 + 7 + 10 + 4 = 30 students
c) Mean mark = (mark × frequency)/total frequency
[(6 × 5) + (7 × 4) + (8 × 7) + (9 × 10) + 10 × 4)]/ 30
Mean mark = (30 + 28 + 56 + 90 + 40)/30 = 244/30
Mean mark = 8.1
Answer: From the information given, Mark: 6,7,8,9,10 frequency:5,4,7,10,4 a) Range = highest mark - lowest markRange = 10 - 6 = 4b) The number of students in the group is the sum of the frequency. Therefore, Number of students = 5 + 4 + 7 + 10 + 4 = 30 studentsc) Mean mark = (mark × frequency)/total frequency[(6 × 5) + (7 × 4) + (8 × 7) + (9 × 10) + 10 × 4)]/ 30Mean mark = (30 + 28 + 56 + 90 + 40)/30 = 244/30Mean mark = 8.1
Step-by-step explanation:
"Use what you know about zeros of a function and end behavior of a graph that matches the function f(x)=(x-3)(x-2)(x+1)." Choices below:
Answers
Explanation:
The x intercepts here are -1, 2 and 3. This is where the graph crosses the x axis. We can determine these three values by solving f(x) = 0.
In other words, set (x-3)(x-2)(x+1) equal to zero and solve for x.
(x-3)(x-2)(x+1) = 0
x-3 = 0 or x-2 = 0 or x+1 = 0
x = 3 or x = 2 or x = -1
x = -1 or x = 2 or x = 3
When we expand out (x-3)(x-2)(x+1), there will only be one x^3 term and the coefficient for this term is positive 1. The positive leading coefficient indicates that the graph goes up forever as we move to the right. In other words, the graph grows forever after passing that dip between x = 2 and x = 3.
Another way you could phrase it is that "as x goes to infinity, y also goes to infinity". An informal way is to say "the graph rises to the right" to describe the end behavior.
There are 18cans on a shelf a customer bought 7 cans then jake pu 6cans on the shelf how many cans are on the shelf
Answers
Answer:
17 cans
Step-by-step explanation:
18 cans
7 are taken away
18-7 =11
Then we put 6 back on
11+6 = 17
There are now 17 cans
Please help! "Create a real-life scenario involving an angle of elevation or depression. Draw an appropriate diagram and explain how to solve your example."
Answers
Answer:
Height of the kite = 86.60 meter (Approx)
Step-by-step explanation:
The angle of elevation to see a kite from a stone lying to the ground is 60 degrees. If a thread is tied with a kite and a stone, then that thread is 100 meters long, find the height of the kite.
Given:
Length of thread = 100 meter
Angle of elevation = 60°
Find:
Height of the kite.
Computation:
Using trigonometry application:
Height of the kite / Length of thread = Sin 60°
Height of the kite / 100 = √3 / 2
Height of the kite = [√3 / 2]100
Height of the kite = 50√3
Height of the kite = 86.60 meter (Approx)
how high does the ball roll on its 3rd time up the cylinder's side
( d is 1/8 )
Answers
Step-by-step explanation:
aₙ = 2 (¼)ⁿ⁻¹
a₃ = 2 (¼)³⁻¹
a₃ = 2 (¼)²
a₃ = ⅛
Answer:
1/8 inches
Step-by-step explanation:
Using the given function
d(n) = 2(1/4)^(n-1)
the initial value is 2, which is the height of the ball after the first roll.
For the third roll, n = 3
d(n) = 2 (1/4)^(3-1)
d(n) = 2 (1/4)^2
d(n) = 2/16
d(n) = 1/8
Eric completed 1/3 of his homework before dinner and then 2/7 after dinner. How much homework did Eric complete?
Answers
To add fractions, you first have to set the denominators equal to each other. To do this, you find the LCD (least common denominator) of the two fractions until you find a shared number.
To do this, list out the multiples of each number (3x1=3,3x2=6,3x3=9, and so on. Do this also with 7) The LCD for 3 and 7 is 21. 3x7=21, and 7x3=21. You want to set each fraction’s denominator equal to 21.
You want to multiply each side of 1/3 by 7. 1/3 would become 7/21. You’d do this because 3x7=21, and what you multiply the bottom by you need to multiply the top by. 7x3=21 so you multiply both sides by 3 to get 6/21.
Now you have 7/21 and 6/21 and can add them. Now that they are equal, you can ignore the denominator and just add the numerators. 7+6=13 so Eric completed 13/21 of his homework.
Hope this helps!
The homework completed by Eric will be equal to 13/21.
What is the fraction?
The fraction is defined as the division of the whole part into an equal number of parts.
To add fractions, you first have to set the denominators equal to each other. To do this, you find the LCD (least common denominator) of the two fractions until you find a shared number.
To do this, list out the multiples of each number (3x1=3,3x2=6,3x3=9, and so on. Do this also with 7) The LCD for 3 and 7 is 21. 3x7=21, and 7x3=21. You want to set each fraction’s denominator equal to 21.
You want to multiply each side of 1/3 by 7. 1/3 would become 7/21. You’d do this because 3x7=21, and if you multiply the bottom by you need to multiply the top by. 7x3=21 so you multiply both sides by 3 to get 6/21.
Now you have 7/21 and 6/21 and can add them. Now that they are equal, you can ignore the denominator and just add the numerators. 7+6=13 so Eric completed 13/21 of his homework.
To know more about fractions follow
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(05.02 LC)What is the area, in square inches, of the figure shown here? A parallelogram with a height of 4inches is shown. The height of the parallelogram is used to divide the side of the parallelogram into 5 inches, which is the length (or side) of the rectangle, and into 4 inches, which is the base of the triangle formed by the division. 20 in2 24 in2 32 in2 36 in2
Answers
Answer:
36 in²
Step-by-step explanation:
The figure that is been described is a Parallelogram.
The area of a Parallelogram is = Base × Height
From the question, the Height of the Parallelogram = 4 inches
The Base of the Parallelogram is calculated as the Length or base of the rectangle + base of the triangle
= 5 inches + 4 inches
= 9 inches
Area of the Parallelogram = 9 inches × 4 inches
= 36 square inches or 36 in²
Answer:
20 INCHES SQUARED
Step-by-step explanation:
Which one of the following would most likely have a negative linear correlation coefficient?
A. the value of a car compared to its age
B. the points scored by a basketball player compared to his minutes played
C. the height of a woman compared to her age
D. the hours of daylight in a city throughout the year
Answers
Answer:
D. the hours of daylight in a city throughout the year
Step-by-step explanation:
The hours of daylight in a city throughout the year represent the negative linear correlation coefficient. Then the correct option is D.
What is a negative linear correlation coefficient?Independent quantities with an inverse relationship tend to move in different directions.
In essence, any figure between 0 and -1 denotes an opposing movement of the equity stocks.
When the correlation coefficient becomes less than 0, there is a negative (opposite) correlation. This suggests that both parameters are moving in the obverse direction.
The hours of daylight in a city throughout the year represent the negative linear correlation coefficient
Then the correct option is D.
More about the negative linear correlation coefficient link is given below.
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Which of the following statements is true about the relation represented in the table? The data in the table is linear. The data in the table is nonlinear.
Answers
Answer:
Sacramento
Step-by-step explanation:
S 11+9+14+12+8=54
SF 11+8+8+9+12=48
The statement that is true about the information in the table is that the data is non-linear.
Which statement is true about the given table?
The easier way to study the table is by graphing it. Here we have the points:
(11, 11), (12, 9), (9, 8), (8, 8), and (14, 12).
The graph of these points can be seen below, there you can see that the data in the table is clearly non-linear, as we can't draw a line that contains the points on the table.
So the correct option is non-linear.
If you want to learn more about tables, you can read:
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Find f. f '''(x) = cos(x), f(0) = 8, f '(0) = 4, f ''(0) = 9 f(x) =
Answers
======================================================
Work Shown:
f ''' (x) = cos(x) .... third derivative
f '' (x) = sin(x)+C ... integrate both sides to get second derivative. Don't forget the +C at the end
We are given f '' (0) = 9, so we'll make use of this to find C
f '' (x) = sin(x)+C
f '' (0) = sin(0)+C
9 = sin(0) + C
9 = 0 + C
9 = C
C = 9
Therefore, f '' (x) = sin(x)+C turns into f '' (x) = sin(x)+9
------------
Integrate both sides of the second derivative to get the first derivative function
f '' (x) = sin(x)+9
f ' (x) = -cos(x)+9x+D ... D is some constant
Make use of f ' (0) = 4 to find D
f ' (x) = -cos(x)+9x+D
f ' (0) = -cos(0)+9(0)+D
4 = -1 + 0 + D
D = 5
So we have f ' (x) = -cos(x)+9x+D turn into f ' (x) = -cos(x)+9x+5
------------
Lastly, apply another round of integrals and substitutions to find the f(x) function. We'll use f(0) = 8.
f ' (x) = -cos(x)+9x+5
f(x) = -sin(x) + (9/2)x^2 + 5x + E .... E is some constant
f(0) = -sin(0) + (9/2)(0)^2 + 5(0) + E
8 = 0 + 0 + 0 = E
E = 8
------------
We have
f(x) = -sin(x) + (9/2)x^2 + 5x + E
turn into
f(x) = -sin(x) + (9/2)x^2 + 5x + 8
Solve the following question
The difference of two numbers is 12 and their sum is 20 find the numbers
Answers
Answer:
they are 16 and 4
Step-by-step explanation:
We can call the numbers x and y and we can write:
x - y = 12
x + y = 20
Adding these equations gives us 2x = 32 which means x = 16 and substituting this value into the first equation gives us y = 4.
Answer:
The numbers are 16 and 4
Step-by-step explanation:
Let the two numbers be x and y
x-y = 12
x+y = 20
Add the two equations together
x-y = 12
x+y = 20
-------------------
2x = 32
Divide by 2
2x/2 =32/2
x = 16
Now find y
x+y =20
16+y =20
Subtract 16
y = 20-16
y = 4
The angle of elevation from a sailboat in a lake to the top of a vertical cliff is 60∘60∘. The sailboat is 210 feet from the foot of the cliff. How high is the cliff?
Answers
Answer:
363.741 feet
Step-by-step explanation:
Let the height of the cliff be represented by x. Applying the appropriate trigonometric function, we have;
Tan θ = [tex]\frac{opposite side}{adjacent side}[/tex]
Tan [tex]60^{0}[/tex] = [tex]\frac{x}{210}[/tex]
cross multiply to have;
x = 210 × Tan [tex]60^{0}[/tex]
= 210 × 1.7321
= 363.741
The cliff is 363.741 feet high.
find answer is fast friends
Answers
Answer:
see explanation
Step-by-step explanation:
The restriction a ≠ 0 and b ≠ 0 is applied since division by zero would make
[tex]\frac{a}{b}[/tex] and its reciprocal [tex]\frac{b}{a}[/tex] undefined, thus meaningless
If f (x) = StartRoot x minus 3 EndRoot, which inequality can be used to find the domain of f(x)?
Answers
Answer:
[tex]x\geq 3[/tex] is the inequality to find the Domain of f(x)
Step-by-step explanation:
When we have a function where the variable "x" is inside a square root, we find its Domain by looking for all those values x for which the function is defined for the root, which means all the x-values that make the expression inside the root larger than or equal to zero, avoiding the values smaller for which the square root is not defined.
Therefore, in this case , for
[tex]f(x)=\sqrt{x-3}[/tex]
we ask for the x-values that verify:
[tex]x-3\geq 0\\x\geq 3[/tex]
where we have isolated x on one side of the equal sign.
This would be the definition of the Domain of the function.
Answer:
The answer is C
Step-by-step explanation:
A rectangular playground has an area of 180 square yards. The length of the playground is 3 yards longer than the width. Find the length of the playground.
A)15 yards
B)18 yards
C)12 yards
D)13 yards
Answers
Answer: The length is 15 yards so the answer is A.
Step-by-step explanation:
If the length is 3 more than the width the we will represent it by the equation L = w+3 where w is the width and to find the area of a rectangle, we need to multiply the length by the width. so the length is w+3 and the width is w so
w(w+3) = 180 solve for the w
w^2 + 3w = 180 subtract 180 from both sides
w^2 + 3w -180 = 0 find two numbers that their product is -180 and add to 3.
the number 12 and -15 works out because -12*15= -180 and -15+ 12 =3
We will now have a new quadratic equation as
w^2 - 12w + 15w - 180 = 0 factor by grouping
w(w-12) 15(w-12)= 0 factor out w-12
(w-12)(w+15) = 0 set them both equal zero.
w -12 = 0 or w+15= 0
w = 12 or w = -15
Since we know that -15 can't represent a distance, then 12 is the width .
So if we are to find the length and it gives us the information that the length is 3 yards more that the width then we will add 3 to the width to equal the length.
L= 12 +3
L = 15
The length of the rectangular playground is 15 yards. The correct answer would be an option (A).
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
Since the length is 3 more than the width
So, we will represent it by the equation L = W+3 ...(i)
A rectangular playground has an area of 180 square yards
So, L × W = 180
Substitute the value of equation (i), and we get
W(W+3) = 180
W² + 3W = 180
W² + 3W -180 = 0 ...(i)
Solving the above quadratic equation, we get the values of W :
W = 12 and W = -15
Take positive value because dimensions can't be negative.
Substitute the value of W = 12 in equation (i), and we get
L = 12 + 3 = 15
Therefore, the length of the playground is 15 yards.
Learn more about the Area of the rectangle here:
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AYOOO PLZ HELP ASAP!!!
Answers
Answer:
B.
Step-by-step explanation:
Well we know that
[tex]224=2^{5} *7[/tex]
so we can get the 2 outside of the radical
[tex]x^{11} =(x^{5} )^{2} *x[/tex]
and we can get the x^2 outside too.
[tex]y^8=y^5*y^3[/tex]
and we also can get y outside.
so we have:
[tex]2x^{2}y\sqrt[5]{7xy^3}[/tex]
DatGuy! Sekkrit! Wishing! Anyone? Find the discriminant of 3x²+5x-2 = 0
Answers
Answer:
49
Step-by-step explanation:
[tex]3x^2+5x-2 = 0[/tex]
Apply discriminant formula : [tex]D = b^2- 4ac[/tex]
[tex]D=discriminant\\b=5\\a=3\\c=-2[/tex]
[tex]D = b^2- 4ac[/tex]
Plug in the values for a, b, and c.
[tex]D = 5^2- 4(3)(-2)[/tex]
Evaluate.
[tex]D = 25- 12(-2)[/tex]
[tex]D = 25- - 24[/tex]
[tex]D=25+24[/tex]
[tex]D=49[/tex]
Answer:
49
Step-by-step explanation:
3x²+5x-2 = 0
This is in the form
ax^2 + bx + c=0
a=3 b=5 c = -2
The discriminant is
b^2 -4ac
5^2 -4(3) (-2)
25 + 24
49
The discriminant is 49
Please hel- I really need this it’s not a test I’m not cheating please help
Answers
Answer:
x = 45
Step-by-step explanation:
Since ray IK║EH and IG is a transverse,
∠GIK ≅ ∠IGF [Corresponding angles]
Therefore, m∠IGF = x
Since, m∠JIF + m∠GIF = 180° [Supplementary angles]
2x + m∠GIF = 180°
m∠GIF = (180 - 2x)
Similarly, m∠IFE + m∠IFG = 180°
3x + m∠IFG = 180°
m∠IFG = (180 - 3x)
By the property of a triangle,
"Sum of all interior angles of a triangle is 180°"
m∠IGF + m∠GFI + m∠FIG = 180°
x° + (180 - 2x)° + (180 - 3x)° = 180°
(x - 2x - 3x) + 360 = 180
-4x + 360 = 180
4x = 360 - 180
4x = 180
x = 45
a student answered 44 questions correctly on a test with 55 questions. what percent of the test was answered correctly?
(plz tell me how to figure it out)
Answers
Answer:
80%
Step-by-step explanation:
The basic idea of this problem is to convert [tex]\frac{44}{55}[/tex] into a percentage. [tex]\frac{44}{55}[/tex] can be simplified to [tex]\frac{4}{5}[/tex] which is also 80%.
Answer:
Step-by-step explanation:
44 out of 55
divide :44/55=0.8
to convert it to decimal you multiply by 100 and put percentage next to it
0.8*100=80
%80
A college student team won 20% of the games it played this year. If the team won 11 games, how many games did it play?
Answers
Answer:
55 games
Step-by-step explanation:
What we have to figure out is the total amount of games they played the whole year. We know they won 20% of their games, which equates to 11 games won in total. In order to find the total amount of games we will need to set up the equation [tex]g = 11/20[/tex]%. We solve this accordingly: [tex]g = (11/20) *100[/tex]; [tex]g = (.55)*100[/tex]; [tex]g = 55[/tex].
Please Help me ni️️as
Answers
Answer: see below
Step-by-step explanation:
Multiply the coefficient by the exponent and reduce the coefficient by 1.
1) f'(x) = 10
2) f'(x) = 12x³ + 4x - 5
3) f'(x) = 6x² + 7
4) f'(x) = 20x + 20
5) f'(x) = 20x + 23
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answers
Answer:
w²-30w+210=0
Step-by-step explanation:
2w + 2l = 60 , w + l = 30, l = 30 - w
wl = 210
w(30-w) -210 = 0
30w - w²-210 = 0
w²-30w+210=0
Please answer this fast in two minutes now
Answers
Answer:
18.3Step-by-step explanation:
from cosines theorem:
t² = 11² + 14² - 2•11•14•cos87°
t² = 121 + 196 + 308•0.05236
t² = 333.12688
t = √333.12688
t = 18.2517... ≈ 18.3
what is the equation of 7/12=blank×1/2
Answers
Answer: x = [tex]1\frac{1}{6}[/tex]
Step-by-step explanation:
7/12 = 1/2x
Multiply by 2
14/12=x
x = 1 1/6
Hope it helps <3
2.
Solve the equation.
2
3 x - 2 = 7
Answers
Answer:
4/ 3 = 7
Step-by-step explanation:
Answer: x=3
Step-by-step explanation:
first add two to each side
Simplify 7+2 to 9
3x=9
divide both sides by 3.
x=9/3
simplify 9/3 to 3
Where L is the length, in feet, of the pendulum, and π is approximately 22 7 . How long must the pendulum be if one complete cycle takes 8 seconds?
Answers
Answer:
Length L = 51.88 feet
Step-by-step explanation:
From the given information,
The length of the pendulum can be determined by using the Formula for the period T which is the time of one full oscillation of a simple pendulum.
[tex]T = 2 \pi \sqrt {\dfrac{L}{g}}[/tex]
where;
T = period of the time of one full oscillation = 8 seconds
L = length in feet
g = acceleration due to gravity in feet = 32 ft/s²
π = 22/7
[tex]8 = 2 \times \dfrac{22}{7} \times \sqrt {\dfrac{L}{32}}[/tex]
[tex]8 = 6.2857 \times \sqrt {\dfrac{L}{32}}[/tex]
[tex]\dfrac{8}{6.2857} =\sqrt {\dfrac{L}{32}}[/tex]
[tex]1.273=\sqrt {\dfrac{L}{32}}[/tex]
[tex]1.273= {\dfrac{\sqrt L}{ \sqrt {32}}}[/tex]
[tex]1.273 \times { \sqrt {32}}}= {\sqrt L}[/tex]
[tex]7.2012= {\sqrt L}[/tex]
L = 7.2012²
L = 51.88 feet
Find: ∠a ∠b ∠c Plaese help
Answers
Answer:
i believe a=105, b=29, and c=45
