9. Select values of an exponential function are given in the table. X -2 0 4 5
Answers
The form of the exponential function is
\(y=a(b)^x\)Where a is the value of y at x = 0
b is the base of the exponential function
Let us use 2 points from the table to find a and b
∵ At x = 0, y = 4
∵ a is the value of y at x = 0
∴ a = 4
Substitute it in the form of the function
\(f(x)=4(b)^x\)Now let us use the point (-1, 4/3)
\(\because f(-1)=\frac{4}{3};x=-1\text{and y = }\frac{4}{3}\)\(\frac{4}{3}=4(b)^{-1}\)Divide both sides by 4
\(\begin{gathered} \frac{\frac{4}{3}}{4}=\frac{4b^{-1}}{4} \\ \frac{1}{3}=b^{-1} \end{gathered}\)To change the power of b to +1, reciprocal 1/3
\(\begin{gathered} \because\frac{1}{3}=\frac{1}{b} \\ \therefore b=3 \end{gathered}\)The function of the table is
\(f(x)=4(3)^x\)The answer is D
Related Questions
Find all points (x,y) on the graph of f(x) = 2x ^ 2 - 5x with tangent lines parallel to the line y = 3x + 1
Answers
Answer:
Step-by-step explanation:
Diberi 1 ½s = ⅗t² + ⅓u², hitung (ii) nilai t apabila u = -6 dan s = 28
Answers
Answer:
√2' = t
Step-by-step explanation:
1 1/2s = 3/5t^2 + 1/3u^2; substitute known values
1 1/2 • 28 = 3/5 • t^2 + 1/3 • -6^2; simplify
42 = 3 • t^2 ÷ 5 + 1/3 • 36
42 = 3 • t^2 ÷ 5 + 12; apply property of subtraction of equality
42 – 12 = 3t^2 ÷ 5 + 12 – 12; simplify
30 = 3t^2 ÷ 5; apply property of multiplication of equality
30 • 5 = 3t^2 ÷ 5 • 5; simplify
6 = 3t^2; apply property of division of equality
6 ÷ 3 = 3t^2 ÷ 3; simplify
2 = t^2
√2' = t
The length of each side of triangle LMN is shown below.
LM = 18 cm
MN = 29 cm
LN = 20 cm
Which list shows the angles of triangle LMN in order from least measure to greatest measure?
Answers
The angles of triangle LMN in order from least measure to the greatest measure as angle ∠ N < angle ∠ M < angle ∠ L which is determined by the triangle inequality theorem.
What are the vertical angles?When two lines intersect at a location, vertical angles are generated. They are always equal to each other.
The length of each side of the given triangle LMN is shown below.
LM = 18 cm
MN = 29 cm
LN = 20 cm
According to the triangle inequality theorem, in a triangle, the largest angle is the one opposite to the longest side of the triangle.
Therefore, in triangle LMN, we have the greatest angle as angle ∠ L
And the smallest angle is ∠ N
Arrange the angles in ascending order,
angle ∠ N < angle ∠ M < angle ∠ L
Thus, the angles of triangle LMN in order from least measure to the greatest measure as angle ∠ N < angle ∠ M < angle ∠ L.
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Three pizzas and four sandwiches cost $34. Three pizzas and seven sandwiches cost $41.50. How much does a pizza,
p, and a sandwich, s, cost?
Answers
Answer: p= $8 s= $2.50
Step-by-step explanation:
3p + 4s = 34 and 3p + 7s= 41.50
Since the number of pizzas DIDNT change between these two equations, we can use the total of the second equation to help us find the price of one sandwich.
41.50 - 34 = $7.5 for 3 sandwiches (7s-4s)
So how much is one sandwich? 7.50/3 = $2.50 for each sandwich
now that we know s, it’ll be much easier finding p. We can use one equation to find p.
3p + 4(2.5) = 34 (Solve algebraically)
3p + 10 = 34
- 10 | -10
3p = 24
3p/3 = 24/3
p = $8. Now you can check by substituting the variables!
Find the area bounded by the graphs of the indicated equations over the given interval.
y = x² + 17; y = 0, -3 ≤ x ≤ 3
Answers
The area bounded by the graphs of y = x² + 17 and y = 0 over the interval -3 ≤ x ≤ 3 is 120 square units.
To find the area bounded by the two graphs, we need to calculate the definite integral of the difference between the upper function (y = x² + 17) and the lower function (y = 0) over the given interval.
Integrating the difference of the two functions, we have:
∫[from -3 to 3] (x² + 17 - 0) dx
Simplifying, the integral becomes:
∫[from -3 to 3] (x² + 17) dx
To evaluate this integral, we can use the power rule of integration. Integrating x² gives us (1/3)x³, and integrating the constant term 17 gives us 17x.
Applying the limits of integration, the integral becomes:
[(1/3)x³ + 17x] from -3 to 3
Evaluating the expression at the upper limit (x = 3) and subtracting the expression at the lower limit (x = -3), we get:
[(1/3)(3)³ + 17(3)] - [(1/3)(-3)³ + 17(-3)]
Simplifying further:
[(1/3)(27) + 51] - [(1/3)(-27) - 51]
= [9 + 51] - [-9 - 51]
= 60 + 60
= 120
Therefore, the area bounded by the two graphs is 120 square units.
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evaluate 2^-4
a. -8
b.-16
c.1/8
d.1/16
Answers
Answer:
DD
Step-by-step explanation:
hope this helps ^-^
Evaluate the expression when a=6 and b=4. b - 3a
Answers
-14 is the value of the expression b - 3a at a =6 and b = 4.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given an expression b - 3a
For this expression given,
a = 6 and b = 4
Thus the value of expression at given values
=> b - 3a
=> 4 - 3 * 6
=>4 - 18
=> -14
Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.
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Write an inequality to represent the following sentence:
“Six is at least four more than a number.”
Answers
Answer:6 < 4+n
Step-by-step explanation:at least symbol is < . and more than means add .
Determine if the expression 9y5 – 10y3 is a polynomial or not. If it is a polynomial,
state the type and degree of the polynomial.
Answers
I am going to assume that the equation was supposed to be \(9y^{5}\)\(-10y^{3}\)
Answer:
It is a polynomial. It is a binomial and it has a degree of 5.
Step-by-step explanation:
A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables so \(9y^{5}\)\(-10y^{3}\) will be considered a polynomial.
A binomial is a polynomial with 2 terms.
The degree of a polynomial is the highest exponent in it which in this equation is 5.
A certain type of bacteria doubles each day. On day 3, there is 100
bacteria. On day 4 there is 200 bacteria. How much bacteria was there on
day 3.5?
Answers
Answer:
150
Step-by-step explanation:
Answer: 150
Step-by-step explanation:
find a unit vector n normal to the surface represented by the equation x2-8y2 z~0 at the point (4, 2, 4).
Answers
A unit vector normal to the surface represented by the equation \(x^2 - 8y^2 + z = 0\) at the point (4, 2, 4) is approximately:
n ≈ <0.738, -0.295, 0.606>
To find a unit vector normal to the surface x^2 - 8y^2 + z = 0 at the point (4, 2, 4), we can first find the gradient vector of the surface at that point, which will be normal to the surface.
The gradient vector of a surface is a vector that points in the direction of the maximum rate of change of the surface at a given point. It is given by the partial derivatives of the surface with respect to each variable, evaluated at that point, and is denoted by the symbol ∇.
So, we need to find the gradient vector ∇f(x,y,z) of the surface \(f(x,y,z) = x^2 - 8y^2 + z\) at the point (4,2,4):
∂f/∂x = 2x = 8
∂f/∂y = -16y = -32
∂f/∂z = 1
Therefore, the gradient vector at the point (4,2,4) is:
∇f(4,2,4) = <8, -32, 1>
To obtain a unit vector normal to the surface, we need to divide this vector by its magnitude:
|∇f(4,2,4)| = \(\sqrt{(8^2 + (-32)^2 + 1^2)} = \sqrt{(1057)\)
So, a unit vector normal to the surface at the point (4,2,4) is:
n = ∇f(4,2,4) / |∇f(4,2,4)| = <8, -32, 1> / \(\sqrt{(1057)\)
Therefore, a unit vector normal to the surface represented by the equation \(x^2 - 8y^2 + z = 0\) at the point (4, 2, 4) is approximately:
n ≈ <0.738, -0.295, 0.606>
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I have many questions.
Answer them ALL please
What number is 72% of 15?
42% of 18 is what number?
12 is what percent of 24?
What number is 118% of 206?
200% of 40 is what number?
What number is 50% of 36?
88% of 60 is what number?
Answers
Answer:
1. 10.8
2. 7.56
3. 243.08
4. 40
5. 18
6. 52.8
Step-by-step explanation:
Question 1:
Covert the percent to a decimal: 72% / 100 = 0.72
Multiply that by the number to get the percent.
0.72 x 15 = 10.8
So, 72% of 15 is 10.8
Question 2:
The same concept applies for the rest of the questions.
0.42 x 18 = 7.56
Question 3:
1.18 x 206 = 243.08
Question 4:
2.00 x 40 = 80
Question 5:
0.50 x 36 = 18
Question 6:
0.88 x 60 = 52.8
suppose 48 out of every 120 people like baseball/softball. of the people who like baseball/softball, 3 out of 5 play the game. if you ask 500 people, how many would you expect play baseball/softball?
Answers
out of 500 people 200 like baseball and 120 people like to play game baseball/softball
suppose 48 out of every 120 people like baseball/softball.
of the people who like baseball/softball, 3 out of 5 play the game.
if you ask 500 people,
how many would you expect play baseball/softball
it means 40% like baseball and 60% like to play game
if there are 500 people
then 500 *(40/100)=200
thus 200 people like baseball
and 200*(60/100)=120
Hence 120 people to play game
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What is multiplicative property of equality?
Answers
According to this property, when both sides of an equation are multiplied by the same real number, both sides of the equation always remain the same. The formula for this property can be expressed in real numbers a, b and c. If a × c = b × c.
Property of Equality:
The equivalence property describes the relationship between two equal quantities. If you apply a math operation to one side of the equation, you must also apply it to the other side of the equation to maintain balance.
That is, a property that does not change the truth value of an equation or does not affect the equivalence of two or more quantities is called an equality property. These equality properties help solve various algebraic equations and define equivalence or equilibrium relationships.
Multiplicative Property of Equality:
According to this property, when both sides of an equation are multiplied by the same real number, both sides of the equation always remain the same.
The formula for this property can be expressed as for the real numbers a, b, and c.
If a × b, then, a × c = b × c.
In algebra, the multiplicative property of an equation helps extract unknown terms from an equation. Because multiplication and division are opposites of each other.
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For a statistics question, I'm given a probability (which is 1/8) of flipping three coins and getting three heads and I'm asked to interpret this probability. What does it mean to interpret a probability?
Answers
Answer:
probabilty is the chance for you to get something
Answer:
This is the likelihood of getting 3 heads
I need a answer fast thanks!
Answers
Answer:
Chart:
x y
-6 11
3 5
15 -3
-12 15
Step-by-step explanation:
The only things you can plug in are the domain {-12, -6, 3, 15}
Plug in the domain into equation to find y.
-6 :
y = -2/3 (-6) +7
y = +47
y=11
(-6,11)
3:
y = -2/3 (3) +7
y = -2 +7
y = 5
(3, 5)
15:
y = -2/3 (15) +7
y = -10 +7
y = -3
(15 , -3)
-12:
y = -2/3 (-12) +7
y = 8 + 7
y= 15
(-12,15)
Answer:
1) 11
2) 3
3) -3
4) -12
Step-by-step explanation:
eq(1):
\(y = \frac{-2}{3} x + 7\\\\y - 7 = \frac{-2}{3} x\\\\x = (y - 7)\frac{-3}{2} \\\\x = (7-y)\frac{3}{2} ---eq(2)\)
1) x = -6
sub in eq(1)
\(y = \frac{-2}{3} (-6) + 7\\\\y = \frac{12}{3} + 7\\\\y = 4+7\\\\y = 11\)
2) y = 5
sub in eq(2)
\(x = (7-5)\frac{3}{2} \\\\x = 3\)
3) x = 15
sub in eq(1)
\(y = \frac{-2}{3} 15 + 7\\\\y = \frac{-30}{3} +7\\\\y = -10 + 7\\\\y = -3\)
4)
sub in eq(2)
\(x = (7-15)\frac{3}{2} \\\\x = -8\frac{3}{2}\\ \\x = -12\)
5713065981 if your this guy text me
Answers
Answer:
imagine she doesn't find him
*grins with werid intantions*
Angela works 18 hours a week for 12 weeks in the summer at the local swimming pool as a life guard. she earns $13 per hour. her employer takes 15 percent out of her check for federal income tax withholding and 6.2 percent for social security and 1.45 percent for medicare. she will receive 12 paychecks, one for each week she works. calculate angela’s weekly gross pay: calculate the amount taken out of angela’s check for federal income tax withholding: calculate the amount taken out of angela’s check for social security taxes: calculate the amount taken out of angela’s check for medicare taxes: calculate angela’s net paycheck using the calculations above: calculate angela’s total gross pay for all 12 weeks: calculate angela’s total net pay for all 12 weeks:
Answers
Answer:
Gross pay per week = $234
Federal income tax = $421.2
Social security = $174.96
Medicare =$40.71
net pay per week = $181
Total gross pay = $2,808
Total net pay = $2172
Step-by-step explanation:
Hi, to answer this question, first, we have to calculate Angela gross income per week:
18 hours per week x $13 per hour = $234 per week (gross)
234 x 12 =2,808
Amount taken ; multiply weekly gross pay by each percentage discount in decimal form (divided by 100)
Federal income tax = 234 x (15/100) = $35.1 (in 12 weeks = 35.1 x 12 = $421.2)
Social security = 234 x (6.2/100)= $14.508 (in 12 weeks = 14.5 x 12 = $174.96)
Medicare = 234 x (1.45/100)=$3.393 (in 12 weeks = 3.39x 12 = $40.71)
Total amount taken (per week)= 35.1+14.508+3.393=$53.001
Net pay per week = 234-53 = $181
For the total gross pay we have to multiply the weekly gross pay by the number of weeks (12)
Total gross pay = 234 x 12 =$2,808
Total net pay = 181 x 12 = 181 per week x 12 = $2172
-5y+15=3x i really need help on this question! 10 points! please explain.
Answers
Answer:
Step-by-step explanation:
-5y +15 = 3x
divide both sides by 3 to find x
-5y/3 + 5 = x
to find Y you have to isolate it so you add 5y to both sides and subtract 3x from both sides to get
-3x + 15 = 5y
then to find y divide both sides by 5
-3x/5 + 5 = y
The ones in bold are your answers and they are in their simplest form.
The plane with equation r= (1, 2, 3) + m(1, 2, 5) + n(1, 1, 3), m, n e R, intersects the x- and z-axes at the points A and B respectively. Determine the Cartesian equation of the line that contains these two points.
Answers
The Cartesian equation of the line that contains the points A and B, where A is the intersection point of the given plane with the x-axis and B is the intersection point with the z-axis, is x = 1 and z = 3.
To find the Cartesian equation of the line, we need to determine the values of x and z while allowing y to vary freely. Since point A lies on the x-axis, its y-coordinate is 0, so we have x = 1 and y = 0 for point A. Similarly, since point B lies on the z-axis, its y-coordinate is also 0, so we have z = 3 and y = 0 for point B.
Thus, the equation x = 1 represents the line that contains point A, and the equation z = 3 represents the line that contains point B. Since y can vary freely, we do not include it in the equations. Therefore, the Cartesian equation of the line that contains points A and B is x = 1 and z = 3.
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What is the area of this figure? Enter your answer in the box. units2
Answers
Answer:
42 un^2
Step-by-step explanation:
You can split the hexagon into 2 triangles and a rectangle. For this, I will use the triangle that goes from (-5, 2) to (2, 2) to (-1, 4), the triangle that goes from (-5, -2) to (2, -2) to (-2, -4), and the rectangle that goes from (-5, 2) to (-5, -2) to (2, -2) to (2, 2). The top triangle is 7 units by 2 units, so using triangle formula, you get 7*2/2 = 7. The rectangle is 4 by 7, so you get 4*7=28, and the bottom triangle is 7 units by 2 units (identical to top triangle) so you get 7. 28+7+7=42 units^2
If PQR is congruent TSR what are the congruent corresponding parts?
Answers
The congruent corresponding parts are PQ & TS, QR & SR and PR & TR
What are the congruent corresponding parts?From the question, we have the following parameters that can be used in our computation:
PQR is congruent TSR
using the above as a guide, we have the following:
P corresponds to TQ corresponds to SR corresponds to RWhen two points are combined, we have the congruent corresponding parts to be:
PQ corresponds to TSQR corresponds to SRPR corresponds to TRRead more about similar shapes at
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PLEASE HELP!!!!!!! What is the slope of the line?
−53
−35
35
53
Answers
Answer:
Slope = 1
Step-by-step explanation:
Help ASAP due tomorrow! Will mark brainliest!
Answers
#1
You solved already
#2
\(\\ \sf\longmapsto tan\Theta=\dfrac{p}{b}\)
\(\\ \sf\longmapsto tan\Theta=\dfrac{10}{7}\)
Noah is correct#3
\(\\ \sf\longmapsto tan\Theta=\dfrac{9}{7}\)
\(\\ \sf\longmapsto tan\Theta=1.2\)
\(\\ \sf\longmapsto \Theta=tan^{-1}(1.2)\)
\(\\ \sf\longmapsto \Theta=50.1°\)
ms. crawford bought a large bag of plastic shapes that her students can use to build 3d figures. she was curious what color shapes she received, so she randomly selected some shapes from the bag. here are the colors of the shapes she selected: blue, green, yellow, green, blue, blue, orange, green, yellow, blue, green, blue based on the data, what is the probability of selecting a blue shape? write your answer as a fraction or whole number.
Answers
To find the probability of selecting a blue shape, the probability of selecting a blue shape from the bag of plastic shapes is 5/12 or 0.4167 (rounded to four decimal places).
To find the probability of selecting a blue shape, we need to determine the number of blue shapes selected and divide it by the total number of shapes selected. From the given data, we can see that out of the 12 shapes selected, 5 of them are blue.
Therefore, the probability of selecting a blue shape is 5/12.
In probability, the probability of an event occurring is calculated by dividing the number of favorable outcomes by the number of possible outcomes. In this case, the favorable outcome is selecting a blue shape, and the possible outcomes are the total number of shapes selected. By dividing the number of blue shapes (5) by the total number of shapes selected (12), we obtain the probability of 5/12. This means that there is approximately a 41.67% chance of selecting a blue shape from the bag of plastic shapes.
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Which number is the closest approximation to the value of \(\sqrt{83}\)?
A) 9.1
B) 9.2
C) 41.5
D) 41.6
Answers
At 6:00 A.M., the temperature was 10º below zero. During the day, the temperature rose an average of 2º per hour. If h represents the number of hours since 6:00 A.M., which equation represents the temperature T?
Answers
Answer:
t=-10+2h
Step-by-step explanation:
Please tell me the answer I have been struggling. PS this is middle school math
Answers
Answer:8
Step-by-step explanation
Answer:
\(\frac{4}{8}\)=\(\frac{50}{100}\)
Step-by-step explanation:
Help me on this please.
I don’t know how to read the graphhhhhhhh.
Answers
Answer:
Graphs have two axes, the lines that run across the bottom and up the side. The line along the bottom is called the horizontal or X-axis, and the line up the side is called the vertical or Y-axis. The X-axis may contain. categories or numbers, you read it from the bottom left of the graph.
Calculate the measure of ∠AEC.
A. m∠AEC=105∘
B. m∠AEC=115∘
C. m∠AEC=125∘
D. m∠AEC=135∘
