The values for a and b in the given exponential function are a = 4 and b = 1/2
What is an exponential function?An exponential function is a mathematical function used to calculate the exponential growth or decay of a given set of data.
For example, exponential functions can be used to calculate changes in population, loan interest charges, bacterial growth, radioactive decay or the spread of disease.
Given that,
The exponential function is given as, y = abˣ, we need to find the value of a and b,
When x = 0, ab⁰ = 4
a=4 (since, b⁰ = 1)
When x = 1, ab¹ = 2
4b = 2
b = 1/2
Hence, The values of a and b are a = 4 and b = 1/2
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Triangle
A
′
B
′
C
′
is the image of
Triangle
A
B
C
under a rotation about point
Q
Determine the angle of rotation
A:-165 degrees
B:-120 degrees
C:165 degrees
D:120 degrees
Answer:
The correct answer is 120. Thank me later.
Step-by-step explanation:
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Answer:
1 % decrease
Step-by-step explanation:
The percent of decrease time can be written as the expression [tex]\frac{200}{200}-\frac{198}{200} = \frac{2}{200}.[/tex] Now, we convert the fraction into a decimal: [tex]\frac{2}{200} = \frac{1}{100} = 0.01.[/tex] We can convert this decimal into a percentage: 0.01*100 = 1%.
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A science teacher collects 18 pints of lake water for a lab she is teaching. The lab requires each student to use 4 fluid ounces of lake water. If 52 students are participating, how many pints of lake water will the teacher have left over?
Answer:
The teacher will have 5 pints left.
Step-by-step explanation:
One pint has 16 fluid ounces, therefore if the teacher got 18 pints he has a total of:
lake water = 18*16 = 288 fluid ounces
If each student use 4 fluid ounces, and there are 52 students the class will use:
used = 52*4 = 208 fluid ounces
And the remainder will be:
remainder = 288 - 208 = 80 fluid ounces
remainder = 80/16 = 5 pints
The teacher will have 5 pints left.
Which solid figure has a base that is a polygon and triangular faces that meet
at a vertex?
A. Cone
B. Cylinder
O C. Prism
D. Pyramid
Answer:
D. Pyramid
Step-by-step explanation:
A. cone does not have any triangular faces
B. does not have any triangular faces either
C. Prism may have triangular faces if it is a triangular prism but they do not meet at a vertex
Therefore it must be D.
A pyramid is a solid has a base that is a polygon and triangular faces that meet at a vertex.
What is a pyramid?A pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex. A pyramid is formed by connecting the bases to an apex.
Pyramids :-
A pyramid is defined as a three-dimensional structure encompassing a polygon as its base. The Great Pyramid of Giza, which is structured in the same concept. Every corner of this structure is linked to a single apex which makes it appear as a distinct shape.
A pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex. A pyramid is formed by connecting the bases to an apex. Each edge of the base is connected to the apex, and forms the triangular face, called the lateral face. If a pyramid has an n-sided base, then it has n+1 faces, n+1 vertices, and 2n edges.
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Round your answer to the nearest hundredth
Any help will be appreciated thank you
I need help with maths
Answer:
what's your question?
Step-by-step explanation:
You have to solve for y
Answer:
[tex]y = 2 \sqrt{5} [/tex]
Step-by-step explanation:
[tex]y^{2} = ef = 5 \times 4 = 20[/tex]
[tex]y^{2} = 20[/tex]
[tex] \sqrt{y} = \sqrt{20} [/tex]
[tex]y = 2 \sqrt{5} [/tex]
An exterior angle of a regular polygon is 72°.
(i) what is the size of each interior angle of the polygon?
(ii) Find the number of sides of the polygon.
Answer:
Exterior angle = 72⁰
As polygon is regular , each interior angle = 180⁰ - 72⁰ = 108⁰
Number of sides :
As the sum of exterior angles is 360⁰ :
n × 72⁰ = 360⁰
n = 360/72 = 5
If a aquadrilateral is equiangular, then it coul be a .....
Multiple choice. A. square
B.rectangle
C.rhombus
D.parallelogram
Answer:
Square
Answer A is correct
Answer:
A- square is the answer
state whether -4^{2} and (-4)^{-2} represent the same quantity. Explain.
Answer:
No
Step-by-step explanation:
-4^2 is -4 * 4 = -16
(-4)^2 = (-4) * (-4) = 16
A school took £1584 selling tickets.
Each ticket was sold for £8.
How many tickets were sold?
Answer: 198 tickets
Step-by-step explanation: 1584/8 = 198
Value of x ?
X/2=8.5
Answer:
x=17
Step-by-step explanation:
to find x use this
[tex]\frac{x}{2} =8.5[/tex]
x=8.5*2=17
Answer:
x=17
Step-by-step explanation:
To solve the equation, we want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.
x/2=8.5
x is being divided by 2. The opposite of division is multiplication. Multiply both sides by 2.
2*x/2=8.5*2
x=8.5*2
x=17
To check the solution, substitute 17 in for x in the original equation.
Original equation: x/2=8.5
Substitute 17 in for x: 17/2=8.5
17/2=8.5
8.5=8.5
This is true, so we know that x is equal to 17.
4 tens and 3 hundredths as a decimal
Answer:
This would be 40.03. The 4 is in the tens place and the 3 is in the hundredths place.
Step-by-step explanation:
Answer:
0.43
Step-by-step explanation:
I need help fast please I need help:)
Answer:
35 degrees
Step-by-step explanation:
a triangle has 180 degrees so 70 + 75 + x = 180
solve for it and you get 35 degrees.
Answer:
x = 35
Step-by-step explanation:
We know that the sum of all the angles inside a triangle is 180°. We can solve for x by setting up the simple equation x + 70° + 75° = 180°
You would then use subtraction to get x by itself by subtracting 70° and 75° from the left and right side of the equation.
This would leave you with the answer, x = 35°
What is the surface area of the rectangular prism below?
15
A. 525 units2
B. 432 units2
C. 490 units2
D. 496 units2
Answer:
B ( 432 units^2)
Step-by-step explanation:
Total surface area= 2*(6*6)+ 4*(15*6)
There are 2 squares at each end of the same size so total area will be 2*(6*6)
If we look at the rectangles( bottom, top and the sides), we can see that all are of same dimensions and there are 4 of them so it's 4*(15*6)
In short, total surface area= 2*(6*6)+ 4*(15*6) = 432 units^2
___sides of equal length
___acute angel(s)
___right angle(s)
___obtuse angle(s)
The triangle is _____and_____.
Answer:
__2_sides of equal length
__2_acute angels
__0_right angle(s)
_1__obtuse angle
The triangle is _isosceles____and_obtuse____.
Step-by-step explanation:
if this is the right triangle the longest side will be √162≈ 12.7
the longest side is 15 so the vertex angle is obtuse
Which two transformations can be used to
obtain the graph of y = 3(x - 5)2 from the
graph of y = x2?
F. A vertical compression and a translation
5 units left.
G. A vertical stretch and a translation
5 units left.
H. A vertical compression and a translation
5 units right.
J. A vertical stretch and a translation
5 units right.
We have been given that that function [tex]y=3(x-5)^2[/tex] is obtained from the graph of [tex]y=x^2[/tex]. We are asked to find the two transformations that can be used to obtain the transformed function.
We will use transformation rules to solve our given problem.
[tex]f(x-a)\Rightarrow\text{Graph shifted to the right by a units}[/tex], where a is any positive number.
We can see that the value of a is 5 for our given function, therefore, graph is shifted to right by 5 units.
Now we will use scaling rules.
[tex]f(x)\Rightarrow a\cdot f(x)[/tex]
If [tex]a>1[/tex], then function is stretched vertically by a factor of 'a'.
If [tex]a<1[/tex], then function is compressed vertically by a factor of 'a'.
We can see that value of a is 3. Since 3 is greater than, so function will be stretched vertically by a factor of 3.
Therefore, the function can be obtained by a vertical stretch and translation of 5 units to right and option J is the correct choice.
why is the slope unidentified for vertical lines
Answer:
see below
Step-by-step explanation:
Vertical lines have the same x coordinates
The slope is given by
m = (y2-y1)/(x2-x1)
The x values are the same
m = (y2-y1)/(x-x)
m = (y2-y1)/ 0
Any number, except 0, divided by 0 is undefined
I need to find the value of X.
Answer:
44
Step-by-step explanation:
because it looks like a square tilted
The product of two rational numbers is (-28/81). If one of them is (-2/3), the find the other.
Answer:
The other rational number is [tex]\dfrac{14}{27}[/tex].
Step-by-step explanation:
First rational number is [tex]\dfrac{-2}{3}[/tex]
Let other rational number is [tex]\dfrac{x}{y}[/tex]
The product of two rational numbers is [tex]\dfrac{-28}{81}[/tex]
According to question,
[tex]\dfrac{x}{y}\times \dfrac{-2}{3}=\dfrac{-28}{81}[/tex]
Multiplying both sides by (-3/2) such that,
[tex]\dfrac{x}{y}\times \dfrac{-2}{3}\times \dfrac{-3}{2}=\dfrac{-28}{81}\times \dfrac{-3}{2}\\\\\dfrac{x}{y}=\dfrac{14}{27}[/tex]
So, the other rational number is [tex]\dfrac{14}{27}[/tex].
Answer:
The other rational number is . 14
Step-by-step explanation:
To qualify for the postcard rate for postage, a postcard must be less than 4 1/2 inches high. Elayne has a postcard that is 4 7/8 inches high. How much is her postcard over the height limit?
Answer:
3/8 inches
Step-by-step explanation:
The postcard must be less than 4 1/2 inches high.
Elayne's postcard is 4 7/8 inches high.
We need to subtract the limit from the height of her postcard to know how high it is above the limit:
4 7/8 - 4 1/2 = 3/8
Her postcard is higher than the limit by 3/8 inches.
The answer is 3/4 or 1 1/2 inches.
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Drag each tile to the correct box.
Amy, Catherine, and Herb sell Internet advertising. The dot plots show how many companies they sell advertising to per day. Each data set is for 20 days randomly selected from a full year. Arrange the data sets in order from the data that is most spread out to the data that is least spread out.
TILES:
Amy
Herb
Catherine
SEQUENCE:
____>_____>_____
Answer:
Herb-Catherine-Amy
Step-by-step explanation:
Answer:
Herb-Catherine-Amy
Step-by-step explanation:
How do you answer the question in the picture below?
The graph of quadratic parent function f was transformed to create the graph of
g(x) = f(x + 2) - 5. Which graph best represents g?
Answer:H
Step-by-step explanation:
Y= (x+2)^2-5
2 to the left x+2=0 x=-2
5 dpwn
Answer:
h
Step-by-step explanation:
The volume of a cube is 125 in.cubed. How long is each side?
Answer:
each side is by 5
a square blanket has an area of 64 square feet. find the length of one side of the blanket
Answer:
The length of one side of the blanket is [tex]8ft[/tex]
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, a square shape.In this problem we are expected to find the side of the square shape.
we know that the area of the square is expressed as
[tex]area= length * width[/tex]
but a square shape has all sides equal hence
[tex]area= length* length\\[/tex]
[tex]area= l^{2}[/tex]
substituting our area and squaring both side to find l we have
[tex]64= l^{2} \\l= \sqrt{64} \\l= 8 ft[/tex]
The low temperatures for the week in Carrollton, in degrees Fahrenheit (°F), were 17, 41, 11, 14, 11, 13, and 15. What is the mean of the temperatures without the outlier?
Answer:
The mean of the temperatures is 13.5 without the outlier.
Step-by-step explanation:
To find the mean, you add all of the numbers in your data set and divide that by how many numbers you added.
Before we do this, we must first identify the outlier and remove it from our calculations since it is asking us to find the mean without it. 41 is the outlier because it is a considerably larger number than the other numbers in the data set.
Equations: 11 + 11 + 13 + 14 + 15 + 17 = 81
81 ÷ 6 = 13.5
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A: (2, -6) B: (5, -6) C: (5, -2) D: (2, -2). What is the perimeter of ABCD.
Answer:
14
Step-by-step explanation:
Graph all the points on a coordinate grid. Two sides are 4 units each and the other two sides are 3 unites each.
P = 2(l + w)
P = 2(3 + 4)
P = 6 + 8 ← (The distributive property) OR 2(7) ← (Normal way to solve)
P = 14 units and 14 units.
You could also do addition.
P = 3 + 3 + 4 + 4
P = 6 + 8
P = 14 units
Hope this helped!
Bob Tina and Hadley went running. Bob ran for 3/8 hour, Tina ran for 3 4/9 hours, and Hadley ran for 4 19/29 hours. Which running times can be written as improper fractions
Answer: 3 4/9 and 4 19/29
Step-by-step explanation: Mixed fractions can be converted into improper fractions. Example: 3 1/2=
3×2+1= 7/2
So, 3 4/9= 3×9+4= 31/9
4 19/29= 4×29+19= 135/29
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An improper fraction is one in which the numerator is bigger than the denominator, which means the value of the fraction is more than ' 1 ' .
Bob petered out after only 3/8 of an hour. This number is less than ' 1 ', so if it's left in the form of hours, it can't be an improper fraction. If Bob wants his effort to look more impressive, he might try to describe his performance as 22.5 minutes. THAT number could be written as an improper fraction, (45/2 minutes), but somebody would be sure to notice his trick, and they would laugh at him.
Tina and Hadley both ran longer than 1 hour, so both of them could write their times directly as improper fractions, without any deceptive monkey business.
Tina . . . 3-4/9 hours . . . 31/9 hours
Hadley . . . 4-19/29 hours . . . 135/29 hours
the answer to the question
Answer:
All of the choices.
Step-by-step explanation:
A rational number is one that can be represented by the ratio of two integers. In other words, if you can write the number as a fraction of two whole numbers, then it is a rational number.
All of these numbers can be written this way. Therefore, all of the numbers seen are rational.