Answer:
[tex]\text{f)} \quad y=80(1.1)^x[/tex]
[tex]\text{g)} \quad y=225(0.8)^x[/tex]
[tex]\text{h)} \quad y=5(3)^x[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Part (f)Given points:
(-1, 72.73)(3, 106.48)Substitute the given (x, y) points into the exponential function formula to create two equations:
[tex]\implies 72.73=ab^{-1}[/tex]
[tex]\implies 106.48=ab^3[/tex]
Divide the second equation by the first equation to eliminate a:
[tex]\implies \dfrac{106.48}{72.73}=\dfrac{ab^3}{ab^{-1}}[/tex]
[tex]\implies \dfrac{106.48}{72.73}=\dfrac{b^3}{b^{-1}}[/tex]
Solve for b:
[tex]\implies \dfrac{106.48}{72.73}=b^3 \cdot b^{1}[/tex]
[tex]\implies \dfrac{106.48}{72.73}=b^{3+1}[/tex]
[tex]\implies \dfrac{106.48}{72.73}=b^4[/tex]
[tex]\implies b=1.09998968...[/tex]
[tex]\implies b=1.1[/tex]
Substitute the found value of b into one of the equations and solve for a:
[tex]\implies 72.73=a \cdot (1.09998968...)^{-1}[/tex]
[tex]\implies a=80.0022499...[/tex]
[tex]\implies a=80[/tex]
Substitute the found values of a and b into the exponential function formula:
[tex]\implies y=80(1.1)^x[/tex]
---------------------------------------------------------------------------------------
Part (g)Given points:
(-2, 351.56225)(3, 115.2)Substitute the given (x, y) points into the exponential function formula to create two equations:
[tex]\implies 351.56225=ab^{-2}[/tex]
[tex]\implies 115.2=ab^3[/tex]
Divide the second equation by the first equation to eliminate a:
[tex]\implies \dfrac{115.2}{351.56225}=\dfrac{ab^3}{ab^{-2}}[/tex]
[tex]\implies \dfrac{115.2}{351.56225}=\dfrac{b^3}{b^{-2}}[/tex]
Solve for b:
[tex]\implies\dfrac{115.2}{351.56225}=b^3 \cdot b^{2}[/tex]
[tex]\implies \dfrac{115.2}{351.56225}=b^{3+2}[/tex]
[tex]\implies \dfrac{115.2}{351.56225}=b^5[/tex]
[tex]\implies b=0.800000113...[/tex]
[tex]\implies b=0.8[/tex]
Substitute the found value of b into one of the equations and solve for a:
[tex]\implies 115.2=a(0.800000113...)^3[/tex]
[tex]\implies a=224.999904[/tex]
[tex]\implies a=225[/tex]
Substitute the found values of a and b into the exponential function formula:
[tex]\implies y=225(0.8)^x[/tex]
---------------------------------------------------------------------------------------
Part (h)Given points:
(4, 405)(9, 98415)Substitute the given (x, y) points into the exponential function formula to create two equations:
[tex]\implies 405=ab^4[/tex]
[tex]\implies 98415=ab^9[/tex]
Divide the second equation by the first equation to eliminate a:
[tex]\implies \dfrac{98415}{405}=\dfrac{ab^9}{ab^4}[/tex]
[tex]\implies 243=\dfrac{b^9}{b^4}[/tex]
Solve for b:
[tex]\implies 243=b^9 \cdot b^{-4}[/tex]
[tex]\implies 243=b^{9-4}[/tex]
[tex]\implies 243=b^{5}[/tex]
[tex]\implies b=3[/tex]
Substitute the found value of b into one of the equations and solve for a:
[tex]\implies 405=a \cdot 3^4[/tex]
[tex]\implies 81a=405[/tex]
[tex]\implies a=5[/tex]
Substitute the found values of a and b into the exponential function formula:
[tex]\implies y=5(3)^x[/tex]
Substitution Property of Equality
y=-5 and 7x + y =11
Answer:
x=2.28
Step-by-step explanation:
7x +y=11 we substitute y by ( -5)
7x +(-5)=11 (+)×(-)= --
7x-5=11
7x=11+5 when we move -5 to the opposite it become +5
7x =16
x=16 ÷7
x=2.28
the dot plot below shows the sizes for five classes with a mean of 44 and standard deviation of 8. the dynamic equation shows the mathematical conversion to z-scores in real-time. drag the vertical line to see the corresponding z-score for each possible class size.
The Z-Score associated on moving one standard devations to the right is equals to the 1.0, i.e., Z = 1.00. So, correct answer is option (c).
We have, The number of classes, n = 5
Mean of size of five classes,µ = 44
Standard deviations for five classes,σ = 8
The dynamic equation for conversion to z-scores in real-time is, Z = (Xᵢ - µ )/standard deviations (s)
Z-Score : A Z-Score is a metric that represents that how closely a value relates to mean of set of values. If Z score value is zero that means data point's scores are same as mean score.
Formula for Z- Score is Z = (X - µ)/σ
where, X ---> data values
µ --> mean of values
σ --> standard deviation
For 32, Z = (X - µ)/σ = (32 - 44)/8 = -1.50
For 42 , Z= (X- µ)/σ = (42 - 44)/8 = -0.25
For 48, Z = ( 48 - 44)/8 = 0.5
For 52, Z = ( 52 - 44)/8 = 1.0
For 54, Z = (54 - 44)/8 = 1.25
When we move One standard deviations to right , that means X = 44 + 8 = 52 , So the Z-Score for 52 is Z = 1.0. Hence, required value is 1.0.
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Complete question:
The dot plot below shows the sizes for five classes with a mean of 44 and standard deviation of 8. The dynamic equation shows the mathematical conversion to z-scores in real-time. Drag the vertical line to see the corresponding z-score for each possible class size,
Z =( Xᵢ - X)/s Created by Gary M. McClelland, Professor Emeritus | University of Colorado Boulder Cengage Learning. All Rights Reserved. 1. Make sure the green line is on the mean value of x= 44. Next, move the green line one standard deviation to the right. What Z-score is associated with this value?
a. ) Z-0.75
b) Z= 0.80
c) Z = 1.00
d) Z = 0.5
There are 18 streetlights evenly spaced on a 1.5-mile road. How many streetlights would you expect on a 4-mile road in which are spaced out the same?
If the streetlights are spaced in the same way, there will be 48 streetlights on the 4-mile road.
How many streetlights would you expect on a 4-mile road?First, we know that there are 18 streetlights evenly spaced on a 1.5 mile road.
Then the space between consecutive streetlights is:
1.5mi/18 = (3/36) mi = (1/12) mi
Now, the number of streetlights that we will have on a 4-mile road is given by the quotient between the length of the road and the distance between consecutive streetlights, it is:
N = 4mi/(1/12 mi) = 12*4 = 48
There will be 48 streetlights on a 4 mile road.
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what is the inverse f(x)=3x^3-4
Answer:
f^-1(x) = [tex]\sqrt[3]{(x + 4)/3}[/tex]
Step-by-step explanation:
y = 3x^3 - 4 ==> solve for x
y + 4 = 3x^3 ==> isolate x by adding 4 on both sides
(y + 4)/3 = x^3 ==> divide 3 into both sides
x = [tex]\sqrt[3]{(y + 4)/3}[/tex] ==> isolate x by taking the cube root on both sides
y = [tex]\sqrt[3]{(x + 4)/3}[/tex] ==> switch both x and y
f^-1(x) = [tex]\sqrt[3]{(x + 4)/3}[/tex]
the table and the scatter plot the total earning y(in dollars) of a food server who works x hours
Answer is B
y=16.9x+0.7
To Calculate line of best fit you can simply input the values into the stats function on your calculator and using the "Reg" function to get your values of the standard equation form of your line of best fit which is y=bx+a
b=16.9
a=0.7
Write an equivalent expression by distributing the "sign outside the parentheses:
4w (5.8x - 3.3)
Answer:
23.2wx - 13.2w
Step-by-step explanation:
4w (5.8x - 3.3) =
4w * 5.8x - 4w * 3.3 = distribute 4w to 5.8x and 3.3
4 * 5.8 *w * x - 4w * 3.3 =
23.2 * w * x - 13.2w ==> simplify
23.2wx - 13.2w
If there are 10 decimeters in a meter, explain why there are not 10 cubic decimeters in a cubic meter.
Choose the correct answer below.
OA. There are not 10 cubic decimeters in a cubic meter because a cubic meter is a meter squared. This means
that there are 10² cubic decimeters in a cubic meter.
OB. There are not 10 cubic decimeters in a cubic meter because a cubic meter is a meter cubed. This means
that there are 10 cubic decimeters in a cubic meter.
OC. There are not 10 cubic decimeters in a cubic meter because a cubic meter is a meter squared. This means
1
that there are cubic decimeters in a cubic meter.
10²
OD. There are not 10 cubic decimeters in a cubic meter because a cubic meter is a meter cubed. This means
that there are
1
cubic decimeters in a cubic meter.
10
Answer:
B. There are not 10 cubic decimeters in a cubic meter because a cubic meter is a meter cubed. This means that there are 10³ cubic decimeters in a cubic meter.
Step-by-step explanation:
When we cube a number, we multiply the number by itself twice.
Therefore a cubic meter is:
m × m × m = m³To calculate the number of cubic decimeters in a cubic meter, we need to cube the number of decimeters in a meter.
Given there are 10 decimeters in a meter, then there are 10³ cubic decimeters in a cubic meter:
10 × 10 × 10 = 10³vector <1,2,x> has magnitude of 3. find the value of x if x is a negative number
Answer:
x = - 2
Step-by-step explanation:
the magnitude of a vector < a, b, c > is
[tex]\sqrt{a^2+b^2+c^2}[/tex]
given vector < 1, 2, x > has magnitude of 3 , then
[tex]\sqrt{1^2+2^2+x^2}[/tex] = 3
[tex]\sqrt{1+4+x^2}[/tex] = 3
[tex]\sqrt{5+x^2}[/tex] = 3 ( square both sides to clear the radical )
5 + x² = 3² = 9 ( subtract 5 from both sides )
x² = 4 ( take square root of both sides )
x = ± [tex]\sqrt{4}[/tex] = ± 2
since x is negative then x = - 2
Which table has a constant of proportionality between yyy and xxx of 0.90.90, point, 9? Choose 1 answer: Choose 1 answer: (Choice A) A xxx yyy 101010 999 181818 171717 292929 282828 (Choice B) B xxx yyy 444 3.63.63, point, 6 666 5.45.45, point, 4 121212 10.810.810, point, 8 (Choice C) C xxx yyy 333 3.33.33, point, 3 999 9.99.99, point, 9 111111 12.112.112, point, 1Which table has a constant of proportionality between yyy and xxx of 0.90.90, point, 9? Choose 1 answer: Choose 1 answer: (Choice A) A xxx yyy 101010 999 181818 171717 292929 282828 (Choice B) B xxx yyy 444 3.63.63, point, 6 666 5.45.45, point, 4 121212 10.810.810, point, 8 (Choice C) C xxx yyy 333 3.33.33, point, 3 999 9.99.99, point, 9 111111 12.112.112, point, 1Which table has a constant of proportionality between yyy and xxx of 0.90.90, point, 9? Choose 1 answer: Choose 1 answer: (Choice A) A xxx yyy 101010 999 181818 171717 292929 282828 (Choice B) B xxx yyy 444 3.63.63, point, 6 666 5.45.45, point, 4 121212 10.810.810, point, 8 (Choice C) C xxx yyy 333 3.33.33, point, 3 999 9.99.99, point, 9 111111 12.112.112, point, 1
A table which has a constant of proportionality between y and x of 0.9 include the following: B. table B.
How to determine with a constant of proportionality of 0.9?In order to have a proportional relationship and equivalent ratios that is constant, the variables x and y must have the same constant of proportionality.
Next, we would determine the constant of proportionality (k) based on the given parameters in each table:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 17/18
Constant of proportionality (k) = 0.94 (False).
For the variables x and y in table B, the constant of proportionality (k) is given by;
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 3.6/4 = 5.4/6 = 10.8/12
Constant of proportionality (k) = 0.9 (True).
For the variables x and y in table C, the constant of proportionality (k) is given by;
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 3.3/3
Constant of proportionality (k) = 1.1 (False).
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Evaluate each geometric series described.
17) -2-4-8-16..., n=9
B) -1022
D) 2
A) -975
C) -947
The geometric series of the pattern is -512 for n = 9: -2, -4, 8-16,. is a geometric progression and .
What is the geometric series ?In mathematics, a geometric series is an infinite series with the formula a + ar + ar2 + ar3 +, where r is referred to as the common ratio. The geometric series for a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +, is a straightforward illustration and converges to a sum of 2. (or 1 if the first term is excluded).
is a geometric progression and r= 2.
is a geometric progression ai —2 and r= 2.
= —512
The place w Formulas are employed.
In this instance, we have and n=9. These values are added to the formula above to get the following results:
an
9—1
-2. (256)
= —512
The initial terms in this series are:
8, -16...
The total number of terms in a geometric sequence makes up a geometric series. Using the initial term and the common ratio r, it is possible to determine the nth partial sum of a geometric series as follows: .
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4) Match the polynomial with its factored form.
a. (a - b)(a - b)
b. (a + b)(a - b)
c. (a+b) (a²-ab+6²)
d. (a-b) (a² + ab +6²)
e. (a + b)(a + b)
a³ - 6³
a³ + b³
a²-6²
a² + 2ab + b²
a² - 2ab + b²
Calculations may be made for the polynomials (a - b)(a - b) = a2 - 2ab + b2, (a + b)(a - b) = a2-62, and (a+b)(a2-ab+62) = a3 - 63.
what is polynomial ?The only operations used in a polynomial are addition, subtraction, multiplication, and non-negative integer exponentiation of the variables. Polynomials are mathematical expressions made up of variables (also known as indeterminates) and coefficients. A mathematical expression known as a polynomial is made up of two or more algebraic terms that are added, subtracted, or multiplied (never divided!). In polynomial expressions, which often also have at least one variable, constants and positive exponents are frequently utilized. The equation x2 4x + 7 denotes a polynomial.
given
a) (a - b)(a - b) = a² - 2ab + b²
b. (a + b)(a - b) = a²-6²
c. (a+b) (a²-ab+6²) = a³ - 6³
d. (a-b) (a² + ab +6²) = a³ - 6³
e. (a + b)(a + b) = a² + 2ab + b²
Calculations may be made for the polynomials (a - b)(a - b) = a2 - 2ab + b2, (a + b)(a - b) = a2-62, and (a+b)(a2-ab+62) = a3 - 63.
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The complete question is :- Match the following polynomial by its factored form .
a. (a - b)(a - b)
b. (a + b)(a - b)
c. (a+b) (a²-ab+6²)
d. (a-b) (a² + ab +6²)
e. (a + b)(a + b)
Submarine A is 1200 feet underwater and has descended at a constant rate of 12 feet per minute. Submarine B is 1100 feet underwater but descends at a constant rate of 16 feet per minute. When will the two submarines be at the same depth?
The time when the two submarines will be at the same depth is 25 minutes.
How to calculate the value?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
In this case, Submarine A is 1200 feet underwater and has descended at a constant rate of 12 feet per minute. Submarine B is 1100 feet underwater but descends at a constant rate of 16 feet per minute
The equation will be:
1200 - 12m = 1100 - 16m
Collect the like terms
16m - 12m = 1200 - 1100
4m = 100
Divide
m = 100 / 4
= 25 minutes
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2 divided by 3xy raised to power 2 when x = negative 1 divided by 3, and y = one half
The value for expression 2/3xy² when x = -1/3 and y = 1/2 is 8.
What is an 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.
The given expression is 2/3xy².
The value of x is given as x = -1/3.
The value of y is given as y = 1/2.
To find the value of the expression, substitute the value of x and y in the expression -
= 2/3xy²
Expand using the power rule -
= [2/(3 × (-1/3) × (1/2)²)]
Use the arithmetic operation of multiplication -
= [2/(3 × (-1/3) × (1/4)]
= [-2/(-3/12)]
= -2/(-1/4)
The denominator will reciprocate -
= -2 × -4
= 8
Therefore, the final value is obtained as 8.
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What is the value of Y enter your answer in the box
Answer: y = 40
Step-by-step explanation:
we know 5x=40 so the 2 bottom angles combined are 80
so you have 2y+20=100
2y=80
y=40
Let G(x) = -2(3x+4)(x-1)(x-3)^2 be a polynomial function. make a rough sketch of polynomial, label, and name all the x-intercepts and y-intercepts
The intercepts of the graph are
x-intercepts are -4/3, 1, 3y-intercept is 72How to determine the intercepts of the graphThe polynomial is given as
G(x) = -2(3x+4)(x-1)(x-3)^2
Rewrite as
G(x) = -2(3x+4)(x-1)(x-3)²
The x-intercepts of a polynomial are the points at which the polynomial crosses the x-axis.
To find the x-intercepts, we need to set y = 0 and solve for x.
-2(3x+4)(x-1)(x-3)² = 0
Divide through by -1
(3x+4)(x-1)(x-3)² = 0
Now we can solve for each factor equal to zero:
3x+4 = 0, x = -1.33
x-1 = 0, x = 1
x-3 = 0, x = 3
So the x-intercepts are -4/3, 1, 3
The y-intercept of a polynomial is the point at which the polynomial crosses the y-axis.
For this polynomial, we have
G(0) = -2(30+4)(0-1)(0-3)² = -2(4)(-1)(9) = 72
So the y-intercept is (0, 72)
See attachment for the graph
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Point U is the midpoint of Find the value of x. Round to the nearest tenth if necessary.
Answer:
[tex]x=8.5[/tex]
Step-by-step explanation:
By the definition of a midpoint, [tex]TU=UV[/tex].
[tex]6=2x-11 \\ \\ 2x=17 \\ \\ x=8.5[/tex]
Consider a segment with endpoints S(-7,-6) and T(2,4). what is the length?
Answer:
Below
Step-by-step explanation:
Use the distance formula ( a modification of Pythagorean theorem)
d^2 = ( x1-x2)^2 + (y1-y2)^2
d^2 = (-7-2)^2 + (-6-4)^2
d = sqrt (181) =~ 13.454
If triangle ABC has the following measurements, find the measure of side c:
a = 17
b=23
C = 76°
O a
Ob
Od
37.56
7.69
31.74
25.08
If triangle ABC has the following measurements, than the measure of side c is 25.08
What is triangle ?
A triangle in which it contains three sides and three angles and the sum of three angles be 180 degrees.
Given ,
a = 17
b = 23
C = 76 degrees.
So,
we know that,
c = [tex]\sqrt{a^{2}+b^{2}-2abcosc }[/tex]
c = [tex]\sqrt{17^{2} + 23^{2} - 2*17*23*cos76 }[/tex]
c = [tex]\sqrt{289 + 529 - 884*cos76}[/tex]
c = [tex]\sqrt{818-189}[/tex]
c = [tex]\sqrt{629}[/tex]
c = 25.08
hence , If triangle ABC has the following measurements, than the measure of side c is 25.08
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What are the solutions of x² - 5x+7=0?
Answer:
x = 5/2 + (i sqrt(3))/2 or x = 5/2 - (i sqrt(3))/2
Step-by-step explanation:
Solve for x:
x^2 - 5 x + 7 = 0
Subtract 7 from both sides:
x^2 - 5 x = -7
Add 25/4 to both sides:
x^2 - 5 x + 25/4 = -3/4
Write the left hand side as a square:
(x - 5/2)^2 = -3/4
Take the square root of both sides:
x - 5/2 = (i sqrt(3))/2 or x - 5/2 = -(i sqrt(3))/2
Add 5/2 to both sides:
x = 5/2 + (i sqrt(3))/2 or x - 5/2 = -(i sqrt(3))/2
Add 5/2 to both sides:
Answer: x = 5/2 + (i sqrt(3))/2 or x = 5/2 - (i sqrt(3))/2
Use what you know about scientific notation to write the number - 8,000 with a power of 10.
- 8,000
- 8,000 = 0
Therefore , the solution to the given problem of expression comes out to be -8 * 10³.
How do you determine an expression?A number must be substituted for each variable and arithmetic operations must be carried out in order to verify an algebraic expression. The response variable is equivalent to 6 in the illustration above because 6 + 6 equals 12. The variables can be replaced with their values if we know what they are, and the expression can then be evaluated.
Here,
Given : - 8,000
To write -8000 with a power of 10
Thus,
-8000 written into
=> -8 * 10³
So, we get -8 * 10³ as the scientific notation for the given expression
Therefore , the solution to the given problem of expression comes out to be -8 * 10³.
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This table shows the amount of commission
earned for a broker receiving 3% commission
on sales. How much would this agent earn in
commission for $680,000 in sales?
Commission Earned
Sales (in thousands of $)
Commission (in thousands of $)
140
4.2
280
8.4
420
12.6
560 680
16.8
?
Answer:
$20,400
Step-by-step explanation:
You just have to multiply 680,000 by 0.03 (since 3% is equivalent to 0.03)
pls help with a easy problem miles and kilometers ansewer
Answer:
Step-by-step explanation:
Since 5 miles is approximately 8 kilometers, and Sawyer lives 12.7 kilometers from the soccer field, Sawyer lives farther than Jabar from the soccer field.
So Sawyer lives about 4.7 kilometers farther from the soccer fields.
how to solve 3(x-12)=15
Answer:
Below
Step-by-step explanation:
3 (x-12) = 15 divide both sides of the equation b y 3 to get :
x-12 = 5 now add 12 to both sides
x = 17 Done.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Solving for x or simplify this equation}[/tex]
[tex]\mathsf{3(x - 12) = 15}[/tex]
[tex]\huge\textbf{DISTRIBUTE 3 within PARENTHESES}[/tex]
[tex]\mathsf{3(x) + 3(-12) = 15}[/tex]
[tex]\mathsf{3x - 36 = 15}[/tex]
[tex]\huge\textbf{ADD 36 to BOTH SIDES}[/tex]
[tex]\mathsf{3x - 36 + 36 = 15 + 36}[/tex]
[tex]\huge\textbf{SIMPLIFY IT}[/tex]
[tex]\mathsf{3x = 15 + 36}[/tex]
[tex]\mathsf{3x = 51}[/tex]
[tex]\huge\textbf{DIVIDE 3 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{3x}{3} = \dfrac{51}{3}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT}[/tex]
[tex]\mathsf{x = \dfrac{51}{3}}[/tex]
[tex]\mathsf{x = 17}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = 17}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Nick has $20. He wants to buy as
many toy cars as he can. Each car
costs $3. How many toy cars can
Nick buy?
Answer:
6
Step-by-step explanation:
20 divided by 3 without any remainders, fractions, or decimals is 6.
Hope I helped!
I NEED HELP PLEASE I WILL GIVE BRAINLYIES
Answer: b
Step-by-step explanation:
The difference between eleven and the number d
For f(x), the transformation of the function is stated in the first column. Determine the type of transformation
The first column of the transformation of the function contains information on the transformation of the functions f(x) - f(x) -2.
What is functions ?The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
transformation of functions
f(x) - f(x) -2
translate 2 units down
f(x) - f(x - 2)
translate 2 units right
f(x) - f(x) + 2
translate 2 units up
The first column of the transformation of the function contains information on the transformation of the functions f(x) - f(x) -2.
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which value of w makes the equation true
2w+4=28
Answer:
12
Step-by-step explanation:
2w + 4 = 28
2w = 24
w = 12
w = 12.
Step-by-step explanation:1. Write the expression.[tex]2w+4=28[/tex]
2. Subtract 4 from both sides of the equation.[tex]2w+4-4=28-4\\ \\2w=24[/tex]
3. Divide by 2 in both sides of the equation.[tex]\frac{2w}{2} =\frac{24}{2} \\ \\w=12[/tex]
4. Verify your answer.To verify the answer, write the original expresion and substitute variable "w" by the calculated value (12). If the calculations equal the same number of both sides of the equal sign (=) then the answer is correct.
[tex]2(12)+4=28\\ \\24+4=28\\ \\28=28[/tex]
The same number appears on both sides of the equal sign. Hence, the answer is correct!
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help. i don’t understand this
Answer:
the answer is 1
Step-by-step explanation:
b(n) = -4 so b(n) is 2-4 then n is -1
b(n) = -2
n = -1
Answer:
Step-by-step explanation:
b(n) = -4 -2(n -1)
Find the 12th term in the sequence.
Put 12 where n is and evaluate.
The 12th term of the sequence is -2052.
A person invests 1000 dollars in a bank. The bank pays 5.75% interest compounded
monthly. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 2900 dollars?
The person must leave the money for 18.6 .
How long must the person leave the money ?The amount deposited in the bank,[tex]A= P (1 +\frac{r}{n} )^{nt}[/tex]
Here ,A =Amount = 2900
P = Principal = 1000
r = ratio = 5.75%
2900 = 1000[tex](1 +\frac{5.75}{12} )^{12x[/tex]
Converting decimals to integers,2900 = 1000 [tex](1 +\frac{575}{120000} )^{12x[/tex]
Reducing the fractions,2900 = 1000[tex](1 +\frac{23}{4800} )^{12x\\\\[/tex]
2900 = 1000[tex](1 +\frac{4823}{4800} )^{12x\\\\[/tex]
Dividing both sides of the equation by the coefficient of variable,2900/1000 = 1000[tex](\frac{4823}{4800} )^{12x\\\\[/tex]
29/ 10 = [tex](\frac{4823}{4800} )^{12x\\\\[/tex]
Converting exponential to logarithm form,12x = [tex]log _{\frac{4823}{4800} }\frac{29}{10}[/tex]
[tex]x = \frac{log _{\frac{4823}{4800} }\frac{29}{10}}{12}[/tex]
Rounding to the required place , x = 18.6What are fractions?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.The numerator of a proper fraction is less than the denominator.A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated. A number that represents a rational number is called a common fraction. A decimal, percent, or negative exponent can all be used to represent the same number.To learn more about fractions, refer :
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