The values of P and a such that [tex]f(x) = Pa^x[/tex] is an exponential growth function are given as follows:
C. P = 2; a = 3.
How to define an exponential function?An exponential function has the definition presented according to the equation as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The conditions for an exponential growth function are given as follows:
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A quadratic equation has solutions of (4+i) and (4−i). Which could represent the quadratic equation?
The quadratic equation with solutions of (4 + i) and (4- i) is,
⇒ x² - 8x + 17 = 0
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The solutions of the quadratic equation are,
⇒ (4 + i) and (4- i)
Now, We know that;
A quadratic equation with roots a and b is,
⇒ x² - (a + b)x + a × b = 0
Hence, A quadratic equation with roots (4 + i) and (4 - i) is,
⇒ x² - (4 + i + 4 - i)x + (4 + i) (4 - i) = 0
⇒ x² - 8x + (4² - i²) = 0
⇒ x² - 8x + 16 + 1 = 0
⇒ x² - 8x + 17 = 0
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Brianna has a loyalty card good for a 10% discount at her local hardware store. If the
total cost, before tax and discount, of all the items she wants to buy is c, which
expression represents the cost after the discount?
(1-0.2)C expression represents the cost after the discount
How to find discounted price?Discount pricing' refers to a range of strategies where the price of a product or service is decreased in the interest of generating interest, unloading excess inventory, or boosting sales. The effectiveness of discount pricing rests on consumers' perception that they're 'getting a good deal' for an offering.The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product. It is mostly used in consumer transactions, where people are provided with discounts on various products. The discount rate is given in percentage.The discount rate is the interest rate used to determine the present value of future cash flows in a discounted cash flow (DCF) analysis. This helps determine if the future cash flows from a project or investment will be worth more than the capital outlay needed to fund the project or investment in the presentTo learn more about discounted price refers to:
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the sum of three numbers is 75 the First number is 9 less than the third the second number is 2 times the third what are the numbers
The value of the third number is 25.5
What is an algebraic expression?An algebraic expression can be defined as an expression can be defined as an expression that consists of variables, coefficients, terms, constants and factors.
From the information given as;
First number = x - 9second number = 2(x - 9)third number = xNow, substitute the values, we get;
x - 9 + 2(x-9) + x = 75
expand the bracket
x - 9 + 2x - 18 + x = 75
collect like terms
x +2x + x = 75 +27
add or subtract the like terms
4x = 102
Make 'x' the subject of formula by dividing both sides by 4
x = 102/4
x = 25.5
Hence, the third number is 25.5
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Complete question
the sum of three numbers is 75 the First number is 9 less than the third the second number is 2 times the third what are the numbers. Find the third number
The three numbers are 19, 28 and 56
What is word problem?Word problem in mathematics is expressing mathematical problems in words. In other words, a word problem is a verbal description of a problem situation wherein one or more questions are posed, the answers to which can be obtained by the application of mathematical operations to information available in the text.
Represent the three numbers with x, y, z
x = z-9
y = 2z
x+y+z = 75
substitute 2z for y in x+y+z
2z+x+z = 75
substitute z-9 for x
2z+z-9 = 75
3z- 9 = 75
3z = 75+9
3z = 84
z = 28
y = 2z
y = 2× 28
y = 56
to find the value of x;
x = 28-9
x = 19
therefore the value of the three numbers (x,y,z) is 19, 28, 56
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Select all the expressions that are equal to 89.7 divided by 10 (/=divide)
1. 897.5/100
2. 8.975/100
3.8.975/1
4.8,975/1000
5.89,750/1000
The expression that is equal to 89.7 ÷ 10 is 897.5/100
What are expressions?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that an expression 89.7 ÷ 10
89.7 ÷ 10 = 8.97
1. 897.5/100
= 8.97
2. 8.975/100
= 0.08975
3. 8.975/1
= 8.975
4. 8.975/1000
= 0.008975
5. 89.750/1000
= 0.08975
Hence, the expression that is equal to 89.7 ÷ 10 is 897.5/100
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for the frame and loading shown, determine the force acting on member abc (a) at b, (b) at c.
The force of the thrust loaded and supported as 12KN
By taking into account the equilibrium of the entire truss, it is possible to predict the reaction at the supports. Only the vertical component of the reaction at the ends A needs to be taken into account since both external loads are vertical. Given that the angle of the triangle AEC is 90 degrees, it has a right angle.
AE = AC cos 60º = 5 X 0.5 = 2.5m
CE = AC sin60º = 5 X 0.866 = 4.33m
Due to the fact that triangle ABE is an equilateral triangle,
AB = BC = AE = 2.5m
A right-angle triangle with an angle, the triangle BDC is once again
BDC = 90º
Also, BC = AC – AB = 5 – 2.5 = 2.5m BD = BC cos 60º = 2.5 X 0.5 = 1.25m
path of action of 12 KN force away from joint A,
AG = AB + BG
= AB + BD cos 60º = 2.5 + 1.25 X 0.5 = 3.125m
RC X 5 = 12 X 3.125 + 10 X 1.25 = 50 RC = 10KN ...(i) ∑V = 0, RC + RA = 10 + 12 = 22KN RA
= 12KN
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The question is incomplete, The question is:
Determine the force of the thrust loaded and supported as shown in fig
A passenger jet flies from one airport to another 1,213 miles away in 2.7 h. Find its average speed.
Answer:m/s
Step-by-step explanation:
Answer:
To find the average speed of the passenger jet, we need to divide the distance traveled by the time it took to travel that distance.
Average speed = distance / time
In this case, the distance is 1,213 miles and the time is 2.7 h.
Average speed = 1213 miles / 2.7 h = 449.6 miles/h
So the average speed of the passenger jet is 449.6 miles per hour.
HELP ME PLEASE!!!!!! I NEED IT ASAP.
Answer:
14. x = 9.7 cos(17) = 9.28
15. x = cos^-1 (10/16) = 51.32
16. x = 41/tan(35) = 58.55
The first term in a sequence is 5 and the fifth term 17.what is the common difference ?
Using the concept of arithmetic progression , We have t(n) = a +(n-1)d formula, The answer is 3.
What do you mean by sequence?A number sequence is a series of numbers that are listed in a particular order. The numbers in a sequence may follow a specific pattern or rule. Examples of number sequences include the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, etc.), the Fibonacci sequence (1, 2, 4, 8, 16, 32, etc.), and the triangular number sequence (1, 3, 6, 10, 15, etc.). Number sequences are often studied in mathematics and have many applications in fields such as computer science, engineering, and physics.
What is arithmetic progression?An arithmetic progression (AP) is a type of number sequence in which the difference between any two consecutive terms is always the same. This common difference is known as the "common ratio" of the sequence. For example, the sequence 2, 5, 8, 11, 14 is an arithmetic progression because the common difference is 3.
t(n) = a + (n-1)d
n=5
t(5)=17
a=5
17 = 5 +(5-1)d
12=4d
d=12/4 = 3
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Please help me with this question
The solution to the equation cosh(t) = t does not exist
How to determine the solution to the equationThe equation is given as
cosh(t) = t
To solve the equation cosh(t) = t, we can start by expressing the equation in terms of e^t and e^-t.
So, we have"
cosh(t) = (e^t + e^-t)/2 = t.
Rewrite the above equation as
e^t + e^-t = 2t.
Using a graphing calculator, the curve of e^t + e^-t and the line of 2t do not intersect
Hence, the equation has no solution
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Just a quick question!
Solve using substitution.
–3x − 4y = 17
x − y = –1
Help please!
Answer:
(-3, -2)
Step-by-step explanation:
-3x -4y = 17
x -y = -1 Can be rewritten x = y - 1
Substitute y -1 for x into the first equation
-3(y - 1) - 4y = 17 Distribute the -3
-3y + 3 -4y = 17 Combine like terms
-7y + 3 = 17 Subtract 3 from both sides
-7y = 14 Divide both sides by -7
y = -2
Substitute -2 for y in x = y -1 to solve for x
x = -2 -1
x = -3
Check
-3x -4y = 17
-3(-3) - 4(-2) = 17
9 + 8 = 17
17 = 17 checks
x -y = -1
-3 -(-2) = -1
-3 + 2 = -1
-1 = -1 checks
I need help on this question I have attached it on this assignment. THX
Answer:
I) 5575
ii) 312.50
b) 345
Step-by-step explanation:
I)11.15(500)=5575
ii) 1.25(250)=312.50
b) 407.10/1.18 = 345
Solve the system of equations using substitution. 3x + 2y = 7 x = 3y + 6 (0, −2) (1, 2) (3, −1) (6, 0)
Answer:
(3, −1)
Step-by-step explanation:
I did the test
Create a problem in which you subtract two five digit numbers to get a difference of 66827
?-?=66,827
Answer:
96,100-29273=66,827
Step-by-step explanation:
Make up a number higher than 66,827
I chose 96,100
find the difference between the number made up (EX. 96,100)
EX. 96,100- 66,827 = 29273
Then double check your answer as it is easy to make mistakes
96,100-29273=66,827
Question
Evaluate the expression when a=14 and b=6.
−8ab=
Answer:
Step-by-step explanation:
-672 would be your answer
Please answer with a step-by-step explanation!
The probability of the first number being divided by the second number is greater than zero is 1/2.
What is probability?Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. Probability that an event will occur P(E) is equal to the ratio of favourable outcomes to total outcomes. Because the favourable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Additionally, the proportion of positive outcomes cannot be negative.
Given four tiles in a bag with numbers -2, -1, 1, 2
one tile selected at random the probability is 1/4
tile return to bag and another tile selected,
the probability of the second tile is 1/4
total outcome for both is 4 x 4 = 16
the ratio of both numbers should be positive
outcomes are (-2, -1)(-2, -2)(-1, -1)(-1, -2)(2, 1)(2, 2)(1, 1)(1, 2)
favourable outcome are 8
probability is 8/16 = 1/2
Hence the probability is 1/2
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a flooring tile has a shape of a parallelogram Hight is 10cm and base is 24cm how many tiles do you need to fill a room with area 1080 msq
45000 tiles we need to fill a room with area 1080 m²
What is Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides.
Area of floor =1080m²
Base of parallelogram shaped tile (b) =24 cm
and corresponding height (h)=10 cm
Area of one tile=b×h
=24×10
=240 cm²
=240/10000=24/1000 m²
Number of tiles required=1080/(24/1000)
=1080×1000/24
=45000 tiles
Hence, 45000 tiles we need to fill a room with area 1080 m²
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PLEASEEEEEEEEEEEEEEEEEEEEEEEEEE HELP MEEE. Which statement best describes a graph of paired points that form a proportional relationship? Responses A straight line cannot be drawn through all the points, and the line passes through the origin. A straight line cannot be drawn through all the points, and the line passes through the origin. A straight line can be drawn through all the points, and the line passes through the point (3, 0). A straight line can be drawn through all the points, and the line passes through the point , begin ordered pair 3 comma 0 end ordered pair, . A straight line can be drawn through all the points, and the line passes through the point where x = 0 and y = 0. A straight line can be drawn through all the points, and the line passes through the point where , x, = 0 and , y, = 0. A straight line can be drawn through all of the the points, but the line does not pass through the origin.
A graph of paired points that form a proportional relationship is a straight line that can be drawn through all the points, and the line passes through
the point where, x, = 0 and, y, = 0.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The equation of a line on a graph that forms a straight line and forms a proportional relationship will have to pass through the origin.
origin = (x, y) = (0, 0)
Thus,
The graph of paired points that form a proportional relationship is a straight line that can be drawn through all the points, and the line passes through the origin.
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Find m∠ABD and m∠DBC
Answer:
m∠ABD=116°
m∠DBC=64°
Step-by-step explanation:
The sum of the two angles given equals 180°. To find the two angle measures, use the following equation:
m∠ABD+m∠DBC=180°
For this problem, m∠ABD=(7x+67)° and m∠DBC=(8x+8)°. So,
(7x+67)°+(8x+8)°=180°
15x+75=180
15x=105
x=7
Next, substitute x=7 into the original expressions for the angle measures.
m∠ABD=(7(7)+67)°
m∠ABD=(49+67)°
m∠ABD=116°
and
m∠DBC=(8(7)+8)°
m∠DBC=(56+8)°
m∠DBC=64°
Find the missing side of each triangle. Leave your answers in the simplest radical form.
On solving the provided question, we can say that it is a right angle triangle x = [tex]\sqrt{5}[/tex]
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
here
it is a right angle triangle
so by trigonometry
Sin 90 = [tex]\sqrt{5} / x[/tex]
x = [tex]\sqrt{5}[/tex]
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If you vertically compress the absolute value parent function, f(x) = |x|, by a
factor of 5, what is the equation of the new function?
O A. g(x) = x
OB. g(x) = 5|x|
OC. g(x) = 15x1
OD. g(x)= x - 51
The image of absolute value function f(x) = |x| by rigid transformation is g(x) = 5 · |x|. (Correct choice: B)
How to apply compressions on functions
In this case we must derive the image of a absolute value function by means of a rigid transformation known as vertical compression, defined as:
f(x) = |x| → g(x) = k · |x|, where k > 0, k ≠ 1
There is enlargement for k > 1 and contraction for 0 < k < 1. Herein we find an enlargement case (k = 5), then the image of function f(x) = |x| is equal to:
g(x) = 5 · |x|
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Two random number generators each generate a number from 1 to 10. What is the probability that both number generators generated the number 5? (Give your answer as a percentage, decimal or fraction in simplest form.)
The probability that both numbers generated the number '5' is 1/100
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
The probability is expressed as : sample space/ total outcome
Two number generators can generate number from 1 to 10. This means that the total outcome is 10.
The number 5 has a sample space of 1 in the generated numbers.
Therefore the probability to generate 5 in the first machine = 1/10
The probability to generate 5 in the second machine = 1/10
The probability to generate 5 in both machines = 1/10 × 1/10 = 1/100.
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Please help its geometry
Answer: B
Step-by-step explanation:
b is 64 because exterior angles are congruent
Question content area top left
Part 1
Find the slope of the line.
Question content area bottom left
Part 1
The slope of the line is 22.
(Type an integer or a simplified fraction.)
.
.
.
Question content area right
Part 1
-10
-8
-6
-4
-2
2
4
6
8
10
-10
-8
-6
-4
-2
2
4
6
8
10
x
y
The slope of the line is -5/6 in the graph.
What is slope?The slope of a line is how steep it is going from LEFT to RIGHT. Slope is the proportion of a line's rise, or vertical change, to its run, or horizontal change.
No matter which two points you choose for the line's starting and ending points, the slope is always constant (it never changes).
From the given picture we can verify that
x₁ and y₁ is (-4, 6) and x₂ and y₂ is (2, 1).
We know the slope formula is y₂ - y₁ = m(x₂ - x₁)
Substituting the given details in formula we get
1 - 6 = m(2 - (-4))
-5 = m(6)
m = -5/6
Thus, the slope of the line is -5/6.
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I have no idea how to figure this out. I've been stuck on it for a while
Answer:
Step-by-step explanation:
x=-1/2,1/2
Step-by-step explanation:
4x^2 - 1 = 0
(2x - 1)(2x + 1)= 0
x = 1/2
x = -1/2
write an equation in slope-intercept form of the line given the slope- 1/4 pass through (-2,1).
On solving the question we can say that slope intercept form of the equation is y = -1/4x +1/2
What is Slope Intercept form ?One of the most popular ways to describe a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula may be used to get the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills.
The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. Any point's coordinates on a straight line must fulfill a certain relation, which is known as the equation of a straight line.
Any location that is not on the line will not fulfill the coordinates.
This equation's solution is simple to find. A straight line's slope, or angle of inclination from the x-axis, and the intercept it makes with the y-axis are both necessary to determine the slope intercept form of the line.
The line passes through (-2,1)
slope = -1/4
The equation of the line
y = mx + c
here m is the slope and c is the intercept.
putting the point and slope in the equation
1 = -1/4 *(-2) + c
⇒ c = 1/2
So the slope intercept form of the equation is
y = -1/4x +1/2
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Consider points R, S, and T. Point S is in the middle. Point R is below and to the left of point S. Point T is below and to the right of point S. Which statement is true about the geometric figure that can contain these points? No line can be drawn through any pair of the points. One line can be drawn through all three points. One plane can be drawn so it contains all three points. Two planes can be drawn so that each one contains all three points. Mark this and return
One plane can be drawn, so it contains all three points.
What is spherical coordinates?
The coordinate system that is most frequently employed in three-dimensional systems is called spherical coordinates of the system, represented as (r,Ф,∅ ). The surface area in three dimensions is calculated using the spherical coordinate system. Radial distance, polar angles, and azimuthal angle are the three numbers that these coordinates indicate. Additionally known as spherical polar coordinates.
Consider points R, S, and T. Point S is in the middle. Point R is below and to the left of point S.
Suppose that the S coordinate is at the origin, that is (0, 0)
The coordinates of R and T with respect to S will then be (-x, -y) and (x, -y).
Hence One plane can be drawn, so it contains all three points.
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Name the following function.
Answer: it is not a function
Step-by-step explanation: occurs when there was an attempt to call a value from a function, but the value is not actually a function.
Answer the question.
Answer:
16 boys and 8 girls
Step-by-step:
24 / 3 = 8
so 8 girls
24 - 8 = 16
and 16 boys
The general equation for depreciation is given by y = A(1 – r)t, where y = current value,
A = original cost, r = rate of depreciation, and t = time, in years.
The original value of a car is $24,000. It depreciates 15% annually. What is its value in 4 years?
Using the general equation for depreciation which is y = A(1 – r)^t, The value of the car in 4 years is $12528.15
How to find the value of the car in 4 yearsThe value of the car is solved by using the formula for depreciation which is y = A(1 – r)t
definition of variables
where
y = current value, = ?
A = original cost, = $24,000
r = rate of depreciation, = 15% and
t = time, in years. = 4 years
substituting the variables
current value, y = A(1 – r)t
current value, y = 24000 * (1 - 0.15)⁴
current value, y = 12528.15
the depreciation is $12528.15
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Don Richie goes bowling. • He has $25.00 to spend. • He spends $5.00 to rent shoes • He spends $2.50 for each game he bowls
Write and solve an equation to show how many games Don Richie can bowl.
Answer:
Let x be the number of games Don can bowl.
We can write the equation as:
25 - 5 - 2.5x = 0
This equation represents the total amount of money Don has, minus the cost of renting shoes, minus the cost of each game he bowls, which should equal zero if he wants to spend all of his money.
Solving for x, we get:
25 - 5 - 2.5x = 0
2.5x = 20
x = 8
Don can bowl 8 games.
Step-by-step explanation:
Hope this helps (: