[tex]{\Large \begin{array}{llll} y = ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\ y = 10 \end{cases}\implies 10=ab^0\implies 10=a(1)\implies 10=a~\hfill \underline{y = 10b^x} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x = 3\\ y = 80 \end{cases}\implies 80=10b^3\implies \cfrac{80}{10}=b^3\implies 8=b^3 \\\\\\ \sqrt[3]{8}=b\implies 2=b~\hfill \underline{y = 10(2)^x}[/tex]
Austin has $100,000 in a savings account that earns 142% interest per year. The interest is
not compounded. How much will he have in total in 1 year?
The total amount received at the end of 1 year will be 242000
The amount available in Austin's saving account: $100,000
Rate of interest = 142% per year
Simple interest: Simple interest is a quick and simple formula for figuring out how much interest will be charged on loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
The formula for simple interest is given:
Simple Interest = P*R*T/100
where P = principal amount invested
R = rate of interest per year
T = time in years for which the amount is invested
Substituting the values in the formula we get:
Simple interest = 100000*142*1/100
= 142000
Total amount after 1 year = Principal invested + Simple interest earned
= 100000 + 142000
= 242000
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need help y’all pls ♀️
The value of x in the triangle extended through W to X is 39.5°.
What will be the value of x in the triangle?It should be noted that a triangle has a total angle of 180° and also has three sides. Based on the information given, the following can be deduced:
Angle 1 = 3x - 4.
Angle 2 = 6x + 6
Angle 3 = x + 20
Therefore, the value of x will be gotten by adding the values and equating to 180°. This will be:
3x - 4 + 6x + 6 + x + 20 = 180
4x + 22 = 180
Collect like terms
4x = 180 - 22
4x = 158°
Divide
x = 158/4
x = 39.5°
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Answer: 39.5°
Step-by-step explanation:
. TEST SCORES Benjamin's test scores for the quarter so far are 78, 82, 95, and 88. What does he need to score on the fifth test of the quarter in order to have an average test score of 87?
what is the value of x-y if y=4 and 3/5 / 1/2 = x/10
like
3/5
___
1/2
F.) 4
G.) 8
H.) 10
J.) 12
K.) 16
pls show work
Simplify.
16-8+5x-3x
08+8x
O 10 x
08+2x
O 16+ 2 x
Help please
Step-by-step explanation:
The answer is 8+2x . This is the correct answer .
Find each sim for 10,000+2,000+60+1 I tried searching it up
And I could not find it
The sum of the expression 10,000 + 2,000 + 60 + 1 is 12061
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the sum of the expression?The expression is given as
10,000 + 2,000 + 60 + 1
The sum of the expression can be calculated using a calculator
So, we have
10,000 + 2,000 + 60 + 1 = 12061
Hence, the value of the sum 10,000 + 2,000 + 60 + 1 is 12061
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What is the perimeter of the isosceles triangle?
Side A- 3x - 5
Side B- 2x
Side C- 19 - x
Answer:
perimeter of triangle = a + b + c
perimeter = 3x-5+2x+19-x
= 6x + 14
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Answer: P=2a + b which = A- 3x - 5
Step-by-step explanation:
9(4)^2 + 24(4) + 20 = 4
Answer:
Step-by-step explanation:
A rock is dropped from a height of 10 feet. The height of the rock is modeled by the graph shown.Part AWhat is the height of the rock 0.5 seconds after being dropped? The height of the rock 0.5 seconds after being dropped is ........... feet Part BTo the nearest tenth of a second, how many seconds after being dropped does the rock hit the ground? The rock hits the ground approximately ...............................seconds after being dropped.
SOLUTION:
Step 1:
In this question, we have the following question:
A rock is dropped from a height of 10 feet. The height of the rock is modeled by the graph shown.
Part A
What is the height of the rock 0.5 seconds after being dropped? The height of the rock 0.5 seconds after being dropped is ........... feet
6 .
Step 2:
Part B
To the nearest tenth of a second, how many seconds after being dropped does the rock hit the ground?The rock hits the ground approximately ...............................seconds after being dropped.
0.8
If you go to a restaurant and there are 4 choices for main dishes, 5 choices for sides, and 6 choices for drinks, how many possible meals can you order if you do or don't get one of each item?
Answer:
4 * 5 * 6 = 120 possible meals can we order.
Step-by-step explanation:
given that-
If you go to a restaurant and there are 4 choices for main dishes, 5 choices for sides, and 6 choices for drinks
4 * 5 * 6 = 120 combinations or Ways to Order
we can order the main dish in 4 different ways. Then, we can choices for sides in 5 different ways and the drinks in 6 different ways.
(The outcome of the selection of the first does not influence the second or third)
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f(x)=x-7; vertical stretch of 3 g(x)
The function that represents the vertical stretch by a factor of 3 of f(x) is given as follows:
g(x) = 3x - 21.
How are vertical stretches and compression applied to the graph of a function f(x)?Vertical stretches or compression to the graph of a function f(x) are applied by the multiplication of a constant a to the function, as follows:
g(x) = a x f(x).
Then the value of the constant determines if it is an stretch or a compression.
If the absolute value of the constant a is greater than 1, it is a stretch. If the absolute value of the constant a is less than 1, it is a compression.For this problem, we want a vertical stretch with a factor of 3, then the constant is given as follows:
a = 3.
Then the definition of function g(x) is given by:
g(x) = 3f(x)
g(x) = 3(x - 7)
g(x) = 3x - 21.
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-3a²+9a²-11a²-3x² simplify
Answer:
211a+9x
Step-by-step explanation:
first, calculate the exponents (the number times itself) of each number
9a +81a +121a+9x
the reason they are positive is that a negative times a negative equals a positive ex: -3 x -3 = 9
next, combine the coefficients
starting with the variable for a
9a+81a+121a= 211a
x has no other coefficients so it would remain 9x
so the simplified answer would be
211a+9x
5. 1 4/5 x 5/12 = ??????????
whats the answer
Answer:
Step-by-step explanation: the answer is .75. your welcome
the answer is 3/4 or 0.75
y is inversely proportional to a³
When a = 2, y = 10
a is directly proportional to x
When x = 4, a = 20
Find a formula for y in terms of x.
Give your answer in its simplest form.
The formula for y in terms of x is y = [tex]\frac{16}{25} x^{3}[/tex]
What is proportionality?Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.
Given that,
Y is inversely proportional to a³ When a = 2, y = 10
A is directly proportional to x when x = 4, a = 20
If y is inversely proportional to a³
[tex]\frac{y}{x^{3} }[/tex]∝1
y = [tex]\frac{k}{a^{3} }[/tex], where k is the proportionality constant
Given, a=2, y=10, then 10 = [tex]\frac{k}{2^{3} }[/tex]
k = 10 × 2³
k = 80
Substituting k = 80 back into the formula;
y = [tex]\frac{80}{a^{3} }[/tex]............. 1
Similarly, if a is directly proportional to x, then a ∝ x i.e a = kx
If x=4, a=20 then;
20 = 4k
k = [tex]\frac{20}{4}[/tex]
k = 5
Substituting k = 5 back into the formula;
a = 5x ....... 2
Substitute equation 2 into 1;
y = [tex]\frac{80}{a^{3} }[/tex]
y = [tex]\frac{80}{5x^{3} }[/tex]
y = [tex]\frac{80}{125x^{3} }[/tex]
y = [tex]\frac{16}{25x^{3} }[/tex]
Therefore, the formula for y in terms of x is y = [tex]\frac{16}{25} x^{3}[/tex]
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what is the value of m in the figure below? if necessary, round your answer to the nearest tenth of a unit.
The value of m in the right triangle to the nearest tenth is 7.2 units.
How to find the side of a right triangle?The figure above is a right triangle.
The right triangles are similar.
Therefore, right triangle ABC is similar to right triangle BDC.
Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Therefore, let's find the value of m using the similar triangle principle,
m / 13 = 4 / m
cross multiply
m × m = 13 × 4
m² = 52
square root both sides
√m² = √52
m = 7.21110255093
Therefore,
m = 7.2 units.
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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=8800(1.573)^x
y=8800(1.573)
x
The given exponential function represents the growth in function with a percentage increase as 57.3%.
Given we have the exponential function as :
y=8800(1.573)ˣ
it is in the form of: y=k.aˣ
therefore, if a>2 then the function represents growth.
and if a<1 then the function represents decay.
now, x=1.573
1.573 > 1
so, the function represents change in growth.
therefore, 1.573 - 1
= 0.573
= 57.3%
hence the change in growth of the function is increased by 57.3%.
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What is the distance between the following points
Choose 1 answer:
√63
√77
√79
√85
Check the picture below.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~7 - (-2)~~)^2 + (~~9 - 7~~)^2} \implies d=\sqrt{(7 +2)^2 + (9 -7)^2} \\\\\\ d=\sqrt{( 9 )^2 + ( 2 )^2} \implies d=\sqrt{ 81 + 4 } \implies d=\sqrt{ 85 }[/tex]
A car travels a distance of 2.6 kilometers.
What is this distance in meters?
10 millimeter (mm) =1 centimeter (cm)
100 cm =1 meter (m)
1000 m =1 kilometer (km)
CLEAR CHECK
meters
Answer:
2600 meters
Step-by-step explanation:
2.6x1000
Use the following information to find x: AB = 4x + 5; BC = 13; and B is the midpoint of AC
The numerical value of x is 2 as segment AB equals segment BC.
What is the numerical value of x ?A midpoint is simply a point that divides a line segment into two equal halves.
Given the data in the question;
B is the midpoint of ACSegment AB = 4x + 5Segment BC = 13Given that B is the midpoint of segment AC, this means that segment AB is equal to segment BC.
Hence
Segment AB = Segment BC
4x + 5 = 13
Solve for x
Subtract 5 from both sides
4x + 5 - 5 = 13 -5
4x = 8
Divide both sides by 4
4x/4 = 8/4
x = 8/4
x = 2
Therefore, the value of x is 2.
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Write the equation of the line that passes through the points (−8,−9) and (3,−4). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{(-9)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-8)}}} \implies \cfrac{-4 +9}{3 +8} \implies \cfrac{ 5 }{ 11 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-9)}=\stackrel{m}{ \cfrac{ 5 }{ 11 }}(x-\stackrel{x_1}{(-8)}) \implies {\large \begin{array}{llll} y +9= \cfrac{ 5 }{ 11 } (x +8) \end{array}}[/tex]
11.) Janiya plans on passing out Halloween candy
this year. She purchased 5 bags of Skittles TM for
$4.50 each. She purchased 3 bags of Nerd TM for
$3.75 each. Finally she purchased some full sized
Snickers TM bars for $1.25 each. How many full
sized bars did she purchase if her total bill was
$102.50? Define the variable.
Answer:
82 because 102.50/1.25=82
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Step-by-step explanation:
Keith has a shirt company that charges a delivery fee. The total charges are include the following
• $10 per short sleeve shirt
. $15 per long sleeve shirt
• The total of the charges must be at least $500 to get a discount.
Which inequality models the situation where x is the number of short sleeve shirts and y is the number of long sleeve shirts.
A
15x+10y≤ 500
B 15x+10y 2 500
C
10x + 15y ≤ 500
D 10x+15y 2 500
Please help!!!
Create an equivalent expression for 18^-7 • 18^5
1. -18^2
2. 18^2
3. 1/18^-2
3. 1/18^2
For an equivalent expression for [tex]18^{-7}\\[/tex] * [tex]18^5\\[/tex] it is option 4 that is correct that means the equivalent expression can be seen as [tex]\frac{1}{18} ^{2}[/tex].
What analogous expressions are there?Expressions that can be considered are equivalent do the same thing even when they have distinct appearances. When we get to enter the same value(s) for the same variable, two algebraic expressions that are equivalent have the same value (s).
Calculating the equivalent expression,
[tex]18^{-7}\\[/tex] * [tex]18^5\\[/tex]
= [tex]18^{-7+5}[/tex]
=[tex]18^{-2}[/tex]
= [tex]\frac{1}{18} ^{2}[/tex]
What is a good example of an equivalent expression?An expression that can be considered equivalent to another phrase but then differs in appearance is the one that has the same value or worth. In algebra, we can say 2(2x – 3y + 6) is equal to 4x -6y + 12 as an example of an equivalent expression.
Which two expressions are interchangeable?When two expressions can be reduced to a single thread expression or when one of the expressions can be written in the same way as the other, they are said to be equivalent. You can also determine whether two expressions are equivalent.
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2x+3y=13
4x-y=-2
Find x and y
Answer:
x = 1/2, y = 4
Step-by-step explanation:
2x + 3y = 13----------> 2x + 3y = 13
4x - y = -2------------> 12x - 3y = -6
-----------------
14x = 7
x = 1/2, y = 4
30 POINTS I need it quick with an explanation
The unit rate of the graph is is inches per hour
How to find unit rates of graphsA graph will hold as many information as the plotter will wish to give it. The information the graph has the more compicated wit will be
The graph plotted is a graph of snowfall in inches against time in hours. The input values of the graph is the time in hours while the snow fall in inches is the output values
The unit rate of graphs is gotten from the the units plotted against the other unit. Here it is inches against hours
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Please explain!!!
A clock face has a radius of 8 inches. What is the area of the clock face. Round your number to nearest hundredth.
Answer:
200.96 square inches
Step-by-step explanation:
it's asking for the area of a circle
we know that the radius is 8, so we can just plug it into the circle area formula which is
area = (pi) r^2
you plug in 8 for r (r stands for radius)
8^2 is 64
64 times pi is 200.96 (because pi=3.14)
Write an algebraic expression to represent each statement
50 added to half of a number, c
The expression represented by 50 added to half of a number, c is 50 + c/2
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to translate the algebraic expression?The expression is given as
50 added to half of a number, c
half of a number, c means divide c by 2
So, we have
50 added to half of a number, c => 50 added to c/2
Added to means +
So, we have
50 added to half of a number, c => 50 + c/2
Hence, the expression represented by the statement is 50 + c/2
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7,5,2,1,.......
tell the common difference of this sequence
There are 2 numbers between 7 and 5 and 3 numbers between 5 and 2
Which lines are parallel
FM and GB
MB and FG
MB and GB
FM AND FG
Answer:
FM and GB
Step-by-step explanation:
the angles are corresponding meaning that the lines must be parallel
14. Simplify - 17/0
0
17
undefined
-17
The simplification of number 17/0 gives the undefined form.
What is defined as the undefined form?Undefined in mathematics refers to a term that really is mathematically inexpressible or meaningless. The rules of mathematics consider whatever divided by zero to be undefined.A number multiplied by zero could result in any number (real or imaginary)A number divided by zero could represent an entity that has not yet been defined.Division of the a number by zero is illogical.If x=a/0, there is no solution!It may return a number that is not real or imaginary.For the given question;
The expression is 17/0
Let us say that 17/0 = x
Its means; 17 = x ×0
17 = 0
But , 17 ≠ 0
As, given expression 17/0 can not be defined by any number.
Thus, 17/0 is an undefined term.
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