11. rewrite the function in the form y=a (1+r)*
or y=a (1-r) ² then state the growth or decay
rate. y = a (6) t/a
Please help!!
Answers
Problem 10
The two functions are inverses of each other. Why? Because we can think of f(x) = (x-7)/(-2) as y = (x-7)/(-2).
Swap x and y to get x = (y-7)/(-2). Solving for y leads to y = -2x+7 showing that g(x) = -2x+7 is the inverse of f(x) = (x-7)/(-2). This process can be done in reverse to get the same result.
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Problem 11
y = a(6)^(t/2)
y = a( 6^(1/2) )^t
y = a(2.4494897)^t
y = a( b )^t
where b = 6^(1/2) = 2.4494897 approximately
Set b equal to 1+r and solve for r
1+r = 2.4494897
r = 2.4494897-1
r = 1.4494897
This rounds to about r = 1.45
The r value is the decimal form of the percentage, which means we move the decimal point over two spots to the right to get 145% approximately
Answers:
The equation is roughly y = a(1 + 1.4494897)^t
The growth rate is approximately 145%
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Problem 12
You have the correct answer. Nice work.
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Problem 13
You are very close to the correct answer. However, you're missing the base of the log.
The answer should be [tex]\log_{49}(343) = \frac{3}{2}[/tex]. So you'll need to write in a small "49" under the log.
The general rule is that exponential equations in the form [tex]b^x = y[/tex] are equivalent to the log version of [tex]\log_{b}(y) = x[/tex]. For each equation, b is the base. The idea of logs is to isolate the exponent.
Related Questions
Given that y varies directly as x², find the percentage increase in y when x doubles.
Answers
Answer:400%
Step-by-step explanation: by the commutativity of multiplication we find (2x)^2=4(x^2)=4(y)
can u give the direct answer of 1 and 2
Answers
[tex] {a}^{3} . \\ \\ {a}^{5}. \\ \\ {a}^{9} . \\ \\ {a}^{m + n}. \\ \\ {x}^{1} = x.\\ \\ {x}^{3}. \\ \\ {x}^{3}. \\ \\ {x}^{m - n} . \\ \\ {y}^{6} . \\ \\ {y}^{12} . \\ \\ {y}^{18} . \\ \\ {y}^{ab}. \\ \\ 1. \\ \\ 1. \\ \\ {px}^{1} = px.[/tex]
••••••••••••••••••••••••••••••••••••••[tex]343 .\\ \\ 16 .\\ \\ 3125 .\\ \\ \frac{ - 8}{27} .[/tex]
Calculate the unpaid balance, finance charge, and new balance using the unpaid balance method. Note: Interest rate is given as a monthly rate
Previous balance:$179.32
Payments/credits:$85.00
Unpaid balance:$
Monthly rate:1.25%
Finance charge:$
New purchases=$117.42
New balance=$
Answers
The Unpaid balance is $94.32, Finance charge is $1.179 and new balance is $148.079.
Finance charge
Unpaid balance:
Unpaid balance=Previous balance-Payments/credits
Unpaid balance=$179.32-$85.00
Unpaid balance= $94.32
Finance charge:
Finance charge =Finance charge×Monthly rate
Finance charge=$94.32×1.25%
Finance charge=$1.179
New balance:
New balance =Previous balance-(New purchases-Payments/credits)+Finance charges
New balance=$179.32-($117.42-$85.00)+$1.179
New balance=$179.32-$32.42+$1.179
New balance=$148.079
Therefore the Unpaid balance is $94.32, Finance charge is $1.179 and new balance is $148.079.
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Answer:
94.32
1.18
212.92
in order
Step-by-step explanation:
13 7in 7in 7in volume and surface area pyramid
Answers
The Volume and Surface Area of Prism is 294 in² and 114.33 in³.
What is pyramid?A large structure built especially in ancient Egypt that usually has a square base and four triangular sides meeting at a point and that contains tombs.
Surface rea of rectangular prism,
= 2( lb +bh +lh)
= 2 ( 7*7 + 7*7+ 7*7)
= 2 ( 49+49+49)
= 2*3*49
= 294 in²
Now, Volume,
= bhl/3
= 7*7*7/3
= 114.33 in³
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Suzy invests $2,600 in an account that earns 2.3% annual interest, compounded continuously. What is the value of the account after 10 years? Round to the nearest dollar
Answers
Answer:
$3,272
Step-by-step explanation:
Continuous Compounding Formula
[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]
where:
A = Final amountP = Principal amounte = Euler's number (constant)r = annual interest rate (in decimal form)t = time (in years)Given:
P = $2,600r = 2.3% = 0.023t = 10 yearsSubstitute the given values into the formula and solve for A:
[tex]\sf \implies A=2600e^{(0.023 \times 10)}[/tex]
[tex]\sf \implies A=2600e^{0.23}[/tex]
[tex]\implies \sf A=3272.360026...[/tex]
Therefore, the value of the account after 10 years is $3,272 to the nearest dollar.
In ABC, CT is a median. What is the measure of AB?
Fill in the blank by enter in just a number for your answer.
Answers
Answer:
AB = 102
Step-by-step explanation:
the median CT bisects the side AB at T , then
BT = AT , that is
7x + 9 = 5x + 21 ( subtract 5x from both sides )
2x + 9 = 21 ( subtract 9 from both sides )
2x = 12 ( divide both sides by 2 )
x = 6
then
AB = 5x + 21 + 7x + 9 = 12x + 30 = 12(6) + 30 = 72 + 30 = 102
The measure of AB is 102.
How to estimate the measure of AB?
The median CT bisects the side AB at T, then
BT = AT
7x + 9 = 5x + 21
subtracting 5x from both sides of the equation, we get
2x + 9 = 21
subtract 9 from both sides, and we get
2x = 12
Divide both sides by 2, we get
x = 6
then, AB = 5x + 21 + 7x + 9
AB = 12x + 30
Substituting the value of x,
12x + 30 = 12(6) + 30
= 72 + 30
AB = 102
Therefore, the measure of AB is 102.
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I need help with dis math problem (img included)
Answers
Answer:
4500 sec
Step-by-step explanation:
1hr 15min= 75 min
75 x 60=4500
Please help due tomorrow
What transformations could have been used to map ABCE onto A’B’C’D’E?
Answers
Answer: This looks like it is a reflection of the y-axis and then an enlarging dilation.
You are walking directly away from your house.
You are 5 miles away from your house when
you start walking, so you can determine your
distance from your house by adding 5 to the
number of miles you have walked. In the
equation below, a represents the number of
miles you have walked, and y represents your
distance from home in miles.
The relationship between these two variables
can be expressed by the following equation:
y = x + 5
Identify the dependent and independent
variables.
Your distance
from home
Number of
miles you
walk
Dependent
variable
Independent
variable
Answers
Answer:
dependent: your distance from home
independent: number of miles you walk
Step-by-step explanation:
lmk if you want an explanation
i would appreciate your help
Answers
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[tex]\text{\textbf{Hello!} In this question, we are trying to figure out the \underline{equation} of the line}\\\text{with the given information.}[/tex]
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[tex]\textbf{Explanation:}\\\quad{}\\\text{In the question, we were given our \emph{slope} (gradient) and a \emph{point}. This will help}\\\text{us solve our problem.}\quad{}\\\\\text{Slope: 2 }\\\\\text{Point: (1, 4)}\\\quad{}\\\text{In order to find the equation, we will be using the \underline{point-slope formula:}}\\\quad{}\\y - y1 = m(x - x1)\\\quad{}\\\text{With this equation, we would plug in our given values to its}\\\text{correct variable and solve.}[/tex]
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[tex]\textbf{Solve:}\\\\\text{Use the point-slope formula to solve.}\\\\y - y1 = m(x - x1)\quad{}\\\\\text{Plug in 2 to m, 1 to x1, 4 to y1 and then solve.}\\\\y - 4 = 2(x - 1)\\\\\text{Use the \underline{distributive property} to distribute the 2.}\\\\y - 4 = 2x - 2\\\\\text{Add 4 to both sides to cancel the 4 on the left and move the remainder}\\\text{to the right side of the equal sign.}\\\\y = 2x + 2\\\\\text{Since we can't simplify any further, our answer is: \fbox{y = 2x + 2}}[/tex]
__________________________________________________________
[tex]\textbf{Answer:}\\\\\text{Therefore, the equation of the line (our final answer) would be \fbox{y = 2x + 2}}[/tex]
__________________________________________________________
Picture shown PLEASE HELP
Answers
Answer:
m= –4
So, you only need to of the points to find the slope, why not choosing the first two:
[tex]m = \frac{y2 - y1}{x2 - x1} = = = > \\ m = \frac{12 - 8}{ - 3 - ( - 2)} = = = > \\ m = \frac{4}{ - 1} = - 4[/tex]
so basically, this is the slope your looking for
G E Which of the following segments is tangent to the circle ? 1) overline HL 2 ) overline DE 3 overline FG 4 ) overline AC
Answers
Answer:
DE
Step-by-step explanation:
........................
show that 8/15 plus 3/10 equals 5/6
Answers
Step-by-step explanation:
find the Lcm of 15 and 10 which is 30
multiply the 2fractions by the LCM
8/15*30=16
3/10*30=9
add the products and put them all over the Lcm
(16+9)/30
=25/30 which is equivalent to 5/6 when you divide both the numerator and the denominator by 5
The function a(b) relates the area of a trapezoid with a given height of 14 and one base length of 5 with the length of its other base. It takes as input the other base value, and returns as output the area of the trapezoid. a(b)=14 x b+5/2
Answers
A function assigns the values. The inverse of the function in terms of the area will be b=(a/7)-5.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The complete question is,
The function a(b) relates the area of a trapezoid with a given height of 14 and one base length of 5 with the length of its other base. It takes as input the other base value, and returns as output the area of the trapezoid. a(b)=14 x b+5/2. Write a function in terms of area to find the length of the other side.
The given is the function of the area of the trapezoid, a(b)=14 x b+5/2.
The area of a trapezoid is given as,
Area = Height × [(Sum of parallel sides)/2]
The given function can be written in terms of area as,
[tex]a = 14\times \dfrac{(b+5)}{2}\\\\\dfrac{2(a)}{14} = b+5\\\\\dfrac{2(a)}{14} -5= b\\\\\dfrac{(a)}{7} -5= b[/tex]
Hence, the inverse of the function in terms of the area will be b=(a/7)-5.
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Find the length of side BC.
Give your answer to 3 significant figures.
C
A
71°
B
Answers
Answer:
BC ≈ 19.4 cm
Step-by-step explanation:
using the cosine ratio in the right triangle
cos71° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{6.3}{BC}[/tex] ( multiply both sides by BC )
BC × cos71° = 6.3 ( divide both sides by cos71° )
BC = [tex]\frac{6.3}{cos71}[/tex] ≈ 19.4 cm ( to 3 sig. figs )
Answer:
19.4°
Step-by-step explanation:
I put the image of how I did it if you don't understand let me know
What’s the answer? How do I find the opposite
Answers
Answer:
I think the answer is 4
Step-by-step explanation:
PLEASE HELP ASAP
If "x" varies directly with "y," and
x = -19 when y = 14, what is
"x" when y = 2?
Enter the number that belongs in the green box.
Reduce to simplest form.
X = -
Notice that the negative sign has already been entered.
Answers
The value of x when y = 2 is -19/7
How to solve for x?A direct variation from x to y is represented as:
x = ky
Where k represents the variation constant.
x = -19 when y = 14.
So, we have:
-19 = 14k
Make k the subject
k = -19/14
Substitute k = -19/14 in x = ky
x = -19y/14
When y = 2, we have:
x = -19 * 2/14
Evaluate
x = -19/7
Hence, the value of x when y = 2 is -19/7
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Helppp! Which linear inequality is represented by the graph
Answers
A circle inside of a square. The square has side lengths of 5 meters.
Tariq also designs hot tubs. The diameter of the hot tub is 3 meters. What is the area of the deck that surrounds the hot tub? If necessary, round to the nearest tenth.
Answers
Answer:
the area is 25/4 π
Step-by-step explanation:
diameter is 5 m
area will be 25/4π
Answer:
17.9 m²
Step-by-step explanation:
The area of the deck is the difference between the area of the square and the area of the circular hot tub.
__
square areaThe area of the square is given by the formula ...
A = s² . . . . where s is the side length
For a side length of 5 m, the area is ...
A = (5 m)² = 25 m²
circle areaThe area of a circle is found from the formula ...
A = (π/4)d² . . . . where d is the diameter
For a diameter of 3 m, the area is ...
A = (π/4)(3 m)² = 9/4π m² ≈ 7.069 m²
deck areaThe area of the deck is the difference between the square area and the circle area:
deck area = 25 m² -7.069 m² ≈ 17.9 m²
The area of the deck surrounding the hot tub is about 17.9 m².
state one example of 2 numbers where the LCM of the 2 numbers is the product of those numbers. explain your answers
Answers
Answer:
See below
Step-by-step explanation:
3 and 5 have a LCM of 15 which is 3 * 5
30.
10 cm
O
7 cm
10 cm
4 cm
How many triangles are needed to draw the net of this object?
Answers
There are two triangles in the figure(triangular prism) option third is correct.
What is a triangular prism?When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.
The complete question is:
How many triangles are needed to draw the net of this object?
4321For the figure please refer to the attached picture.
As we can see in the figure we have given a triangular prism:
The triangular prism has two triangles.
A triangle for the base of the prism and a triangle for the top of the prism.
The lateral faces of the prism are rectangular.
Thus, there are two triangles in the figure(triangular prism) option third is correct.
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PLS HELP I DONT KNOWWW!!
Answers
Answer:
3rd option
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (4, - 1) ← 2 points on the line
m = [tex]\frac{-1-(-2)}{4-0}[/tex] = [tex]\frac{-1+2}{4}[/tex] = [tex]\frac{1}{4}[/tex]
the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2
y = [tex]\frac{1}{4}[/tex] x - 2 ← equation of line
y = mx + c
where,
m is the gradient, and
c is the y-intercept (where the line crosses the y-axis)
Gradient can be calculated using the following formula, or rise/run:
m = (y2 - y1)/(x2 - x1)
= (-1 - - 2)/(4 - 0)
= 1/4
Therefore, using the gradient-intercept form:
y = mx + c
y = (1/4)x + (-2) (-2 is the point where the line crosses the y-axis)
Therefore, y = (1/4)x - 2 or Option C is the answer
Find the value of x. Round the length to the nearest tenth.
Answers
Answer:
5.1 yd
Step-by-step explanation:
tan(25°) = x/11
x = 11tan(25°)=5.1 yd
The steps for multiplying the linear expressions –2n and three-fourths n are shown. A 2-column table with 4 rows. First column is labeled Reason with entries Given, Step 1, Step 2, Step 3. Second column is labeled Step with entries (negative 2 n) (three-fourths n), negative 2 times three-fourths times n times n, (negative 2 times three-fourths) times (n times n), negative three-halves n squared. What is the mathematical reasoning for Step 1? associative property commutative property distributive property simplify
Answers
The mathematical reasoning for the first step is; Distributive Property
How to use Algebra Properties?We want to multiply the linear expressions; -2n and ³/₄n.
The first step will be to express them with the multiplication sign to get and factorize;
-2n × ³/₄n
Now, since n is common to both terms, we will factorize it out to get;
n(-2 × ³/₄)
Now, that operation above is termed as a distributive property because we know that the algebra distributive property is;
a(b + c) = ab + ac
Or a(b × c) = ab × ac
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Answer:
communitave property i think
Step-by-step explanation:
Dilate the figure by the scale factor. Then enter the new coordinates.
K= 2
Answers
Answer:
A(2, 8)
B(4, 4)
C(-4, 2)
Step-by-step explanation:
Multiply all the coordinates by 2
Angela is an electrical engineer who is testing the voltage of a circuit given a certain current and resistance. she uses the following formula to calculate voltage:
the circuit she tests has a current of 3 + j 4 amps and a resistance of 4 - j 6 ohms.
what is the voltage of the circuit?
Answers
The Voltage of the given Circuit is gotten as; V = 36 - 2j Volts
How to multiply Vectors?We are given;
Current; I = 3 + 4j amps
Resistance; R = 4 - 6j ohms
From ohms law, we know that;
V = IR
Thus;
V = (3 + 4j) * (4 - 6j)
V = 12 + 16j - 18j - 24j²
Now, in vector notation; j² = -1. Thus;
V = 12 - 2j + 24
V = 36 - 2j Volts
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The function y = f(x) is graphed below. What is the average rate of change of the
function f(x) on the interval -3 ≤ x ≤-1?
Answers
The average rate of change of the function in the given interval -3 ≤ x ≤-1 is 10.
What is the average rate of change?The average Rate of Change of the function f(x) can be calculated as;
[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}[/tex]
Interval -3 ≤ x ≤-1
a = -3, b = -1
f(a) = f(-3) = -20
f(b) = f(-1) = 0
Step 2: Find Average
[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}\\\\\\f(x) = \dfrac{f(-1) - f(-3)}{-1-(-3)}\\\\\\f(x) = \dfrac{0 - (-20)}{2}\\\\f(x) = 10[/tex]
Therefore, the average rate of change of the function in the given interval -3 ≤ x ≤-1 is 10.
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Find the value of x ??
A. 31
B. 5
C. 11
D. 25
Answers
Answer: 11
Step-by-step explanation:
By the trapezoid midsegment theorem, x = (9+13)/2 = 11
how to solved theses question (4.2×7)-10.4÷2²+2.9×3-6 explain
Answers
Answer:
29.5
Step-by-step explanation:
Use PEDMAS
P - Paraenthesis
E -Exponents
D - Divsion
M - Multiplication
A and S - Addition and subtraction respectively.
First multiply 4.2 and 7 as they are inside the parenthesis
Then find 2² which 4
(4.2 *7) - 10.4 *2² + 2.9*3 - 6 = 29.4 - 10.4 ÷2² + 2.9*3 - 6 {Parenthesis}
= 29.4 - 10.4÷4 + 2.9*3 - 6 {Exponents}
= 29.4 - 2.6 + 2.9*3 - 6 {Division}
= 29.4 - 2.6 + 8.7 - 6 {Multiplication}
= 29.5
What is the range of f(x) = 3x + 9?
Answers
Answer:
The range is all real numbers.
Step-by-step explanation:
The function shown is a line (and not a horizontal line).
The range is all the y's on the graph or all the y's that can be generated by the equation of the function.
f(x) = 3x + 9
You could put ANY, literally any, number in place of the f(x) and be able to calculate an x for it. Looking at the graph of this line, you could go up and down the y-axis to infinity in either direction, and the graph of the line would be there.
The range is All Real Numbers.
