Answer:add 341 more cubes and that shall be your answer
1,2, 3 and 4 are the consecutive perfect cubes which added to obtain a sum of 100.
What is Number system?A number system is defined as a system of writing to express numbers.
Consecutive perfect cubes which added to obtain a sum of 100
Perfect cubes are the numbers that are the triple product of the same number.
1³+2³+3³+4³
One cube plus two ube plus three cube plus four cube
1+8+27+64
One plus eight plus twenty seven plus sixty four.
100
1,2, 3 and 4 are the consecutive perfect cubes which added to obtain a sum of 100.
Hence, 1,2, 3 and 4 are the consecutive perfect cubes which added to obtain a sum of 100.
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Find the probability of X less than or equal to 2X 0 1 2 3P(x) 0.12 0.67 0.19 0.020.980.790.020.19
Step 1:
Probability of x less than or equal to 2.
[tex]\begin{gathered} \text{Probability of x less than or equal to 2 = 0.12 + 0.67 + 0.19} \\ =\text{ 0.98} \end{gathered}[/tex]Step 2:
Final answer
= 0.98
Please finish the following proof using the "prove steps" and write the two-column statements.
Based on the AAS congruence theorem, ΔADB ≅ ΔCDB. The two-column proof for this is explained below.
What is the AAS Congruence Theorem?The AAS congruence theorem states that two triangles are equal or congruent to each other if they have two pairs of congruent angles and a pair of non-included congruent sides.
We are given that ∠ADB and ∠CDB are right angles, therefore, they are congruent to each other. We are also given that ∠A ≅ ∠C.
Also, BD ≅ BD based on the reflexive property of congruency.
Therefore, according to the AAS congruence theorem, ΔADB ≅ ΔCDB.
The two-column proof would be stated as shown below:
Statement Reasons
1. ∠ADB and ∠CDB are right angles 1. Given
2. ∠A ≅ ∠C 2. Given
3. BD ≅ BD 3. Reflexive property
4. ΔADB ≅ ΔCDB 4. AAS congruence theorem
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bailey buys new winter clothes for $136 she has to pay 8.25% sales tax on her purchase. how much is the sales tax for her new clothes?
Given :
The cost of the new winter clothes = $136
The sales tax = 8.25%
So, the sales tax = 8.25% of 136 =
[tex]\frac{8.25}{100}\cdot136=11.22[/tex]So, the answer is : the sales tax = $11.22
solve for the indicated Variable 5t+r=s for tt=
Given the following equation:
[tex]5t+r=s[/tex]You can solve for the variable "t" by following the steps shown below:
1. You can apply the Subtraction Property of Equality by subtracting "r" from both sides of the equation:
[tex]\begin{gathered} 5t+r-(r)=s-(r) \\ 5t=s-r \end{gathered}[/tex]2. Finally, you can apply the Division Property of Equality by dividing both sides of the equation by 5. Then, you get:
[tex]\begin{gathered} \frac{5t}{5}=\frac{s-r}{5} \\ \\ t=\frac{s-r}{5} \end{gathered}[/tex]Therefore, the answer is:
[tex]t=\frac{s-r}{5}[/tex]A rocket is fired from the ground at an angle of 1.12 radians. Suppose the rocket has traveled 440 yards since it was launched. Draw a diagram and label the values that you know.How many yards has the rocket traveled horizontally from where it was launched?____ yards What is the rocket's height above the ground? ____yards
ANSWER
• Horizontal distance it traveled: ,191.7 yards
,• Height above ground: ,396 yards
EXPLANATION
Diagram:
The height, the horizontal distance and the distance traveled form a right triangle.
Since we know the angle, we can find both x and y. The distance traveled is the hypotenuse of the triangle, y is the opposite side to the known angle and x is the adjacent side:
[tex]\sin (1.12)=\frac{y}{440}\Rightarrow y=440\cdot\sin (1.12)=440\cdot0.9=396[/tex][tex]\cos (1.12)=\frac{x}{440}\Rightarrow x=440\cdot\cos (1.12)=191.7[/tex]What is the volume of the solid?8 cm12 cm12 cm16 cm2 cmWe talenteΟ Α112 cubic cmОв192 cubic cmОс224 cubic cmOD304 cubic cm
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
diagram:
solid
Step 02:
geometry:
volume:
we must analyze the figure to find the solution.
volume solid 1:
rectangle:
V = l * w * h
V1 = 12 cm * (16 cm - 12 cm) * 2 cm = 12 cm * 4 cm * 2 cm = 96 cm³
volume solid 2:
rectangle:
V = l * w * h
V2 = 12 cm * 2 cm * (16 cm - 8 cm) = 12 cm * 2 cm * 8 cm = 192 cm³
Total volume:
VT = V1 + V2 = "96 cm + ³192 cm = ³
For each ordered pair, determine whether it is a solution to the system of equations -5x+4y=2. 3x-5y=4 solution? (x, y) (6,8) it is a solution yes or no. (-4,-4) it is a solutions yes or no. (-7,0) it is a solution yes or no. (3,1) it is a solution yes or no
Check the solutions
(6,8)
(-4,-4)
(-7,0)
(3,1)
To check if the pair is a solution to teh system of equations you must replace x and y on both of the equations and see if the equation is fulfilled
(6,8) Is not a solution to the system of a solutions
[tex]\begin{gathered} \begin{aligned}-5(6)+4(8)=2 \\ 3(6)-5(8)=4\end{aligned} \\ \\ -30+32=2\longrightarrow2=2 \\ 18-40=4\longrightarrow-22\ne4 \end{gathered}[/tex](-4,-4) is not a solution to the system of equations
[tex]\begin{gathered} \begin{aligned}-5(-4)+4(-4)=2 \\ 3(-4)-5(-4)=4\end{aligned} \\ \\ 20-16=2\longrightarrow4\ne2 \\ -12+16=4\longrightarrow4=4 \end{gathered}[/tex](-7,0) is not a solution to the system of equations
[tex]\begin{gathered} \begin{aligned}-5(-7)+4(0)=2 \\ 3(-7)-5(0)=4\end{aligned} \\ \\ 35+0=2\longrightarrow35\ne2 \\ -21-0=4-21\ne4 \end{gathered}[/tex](3,1) is not a solution to the system of equations
[tex]\begin{gathered} \begin{aligned}-5(3)+4(1)=2 \\ 3(3)-5(1)=4\end{aligned} \\ \\ -15+4=2\longrightarrow-11\ne2 \\ 9-5=4\longrightarrow4=4 \end{gathered}[/tex]Write the series using sigma notation to find the sum of the termsDrag the tiles to the correct location is not a tiles will be used
The number over the sigma sign is 5
Explanation:
5 represent the finale value
A store had 896 swimsuits that were marked to sell at $40.99. Each suit was marked down $17.90. Find the reduced price using the formula M=S-N, where M is the markdown, S is the original selling price, and N is the reduced price. The reduced price is?
Let us assumed that each of the swimsuit is marked to sell at $40.99, and each suit was marked down $17.90 (given).
With the given formula below, we solve for the reduced price
[tex]M=S-N[/tex][tex]\begin{gathered} M=\text{ \$17.90(given)} \\ S=\text{ \$40.99(given)} \\ N=\text{reduced price} \end{gathered}[/tex]Substitute the value of M and S in the given formula to solve for N as shown below:
[tex]\begin{gathered} 17.90=40.99-N \\ 17.90+N=40.99-N+N \\ 17.90+N=40.99 \\ 17.90+N-17.90=40.99-17.90 \\ N=23.09 \end{gathered}[/tex]Hence, the reduce price is $23.09
Sketch the graph of the equation Y=2x^2-10x+9
Solution:
The equation is given below as
[tex]y=2x^2-10x+9[/tex]Step 1:
We will figure out the y-intercept by putting x=0
[tex]\begin{gathered} y=2x^{2}-10x+9 \\ y=2(0)^2-10(0)+9 \\ y=9 \\ (0,9) \end{gathered}[/tex]Step 2:
Calculate the vertex of the graph using the formula below
[tex]\begin{gathered} y=2x^2-10x+9 \\ x=-\frac{b}{2a},b=-10,a=2,c=9 \\ x=\frac{-(-10)}{2(2)}=\frac{10}{4}=\frac{5}{2} \\ \\ y=2(\frac{5}{2})^2-10(\frac{5}{2})+9 \\ y=2(\frac{25}{4})-25+9 \\ y=\frac{25}{2}-16 \\ y\frac{=25-32}{2} \\ y=-\frac{7}{2} \end{gathered}[/tex]Hence,
The vertex of the equation is
[tex](\frac{5}{2},-\frac{7}{2})[/tex]Using a graphing calculator, we will have the graph be
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. A flashlight is projecting a triangle onto a wall, as shown below. A The original triangle and its projection are similar. What is the missing length n on the projection? O 35 0224 10 40
We can see that the scale factor from the smaller triangle to the projected triangle is 2.
Multiply each length of the original triangle by the scale factor, to obtain the side lengths of the second triangle:
15 x 2 = 30
15x 2 = 30
20 x 2 = 40
answer : 40
Sally invested $1,200 in an account where interest compounded quarterly. After two years, she had $1,351.79 in her account. What was her interest rate?
use the formula
[tex]A=P(1+\frac{r}{t})^{n\cdot t}[/tex]clear the formula for the rate
[tex]A=P(1+\frac{r}{t})^{n\cdot t}[/tex].
Use the specified row transformation to change the given matrix.6R_1+R_2
ANSWER:
[tex]6\cdot R_1+R_2=\begin{bmatrix}{0} & 39 & {23} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix}[/tex]STEP-BY-STEP EXPLANATION:
We have the following matrix:
[tex]\begin{bmatrix}{1} & 5 & {4} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix}=\begin{cases}R_1 \\ R_2 \\ R_3\end{cases}[/tex]Now, we apply the following changes
[tex]\begin{gathered} 6\cdot R_1+R_2 \\ 6\cdot R_1=\begin{bmatrix}{6\cdot1} & 6\cdot5 & 6\cdot{4} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix}=\begin{bmatrix}{6} & 30 & {24} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix} \\ 6\cdot R_1+R_2=\begin{bmatrix}{6+(-6)} & 30+9 & {24+(-1)} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix}=\begin{bmatrix}{0} & 39 & {23} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix} \\ 6\cdot R_1+R_2=\begin{bmatrix}{0} & 39 & {23} \\ {-6} & {9} & {-1} \\ {3} & {7} & {0}\end{bmatrix} \end{gathered}[/tex]a recent poll contacted 230 people who own a car and live in the California and asked whether or not they were a homeowner. Idenify the population of this poll
Population in statistics is the total collection of data being considered.
This could be in a survey.
In our question we are told 230 people were contacted if they were homeowner.
SInce we are dealing with a particular sample of people, the population poll will be 230 people who own a car and live in the California
An ordinary ( fair) die is a cube with the numbers. 1 through 6 on the sides ( represented by painted spots.) imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events.Event A: The sum is greater than 7 Event B: The sum is an even numberWrite your answer as fractions
EVENT A.
We have to count in how many possible ways does the sum of the two rolls of the die add up to more than 7. The possibilities are:
6+2
6+3
6+4
6+5
6+6
5+3
5+4
5+5
5+6
4+4
4+5
4+6
3+5
3+6
2+6
Then, there is 15 ways that the sum os greater than 7. Now we have to calculate how many combinations there is in total, which is 6 possible outcomes for the first roll and other 6 for the second roll, then there is 6x6=36 possible outcomes.
The probability for event A is then 15/36 or 5/12
EVENT B:
In a similar way, we have to count how many ways there is such that the sum is even:
1+1
1+3
1+5
2+2
2+4
2+6
3+1
3+3
3+5
....
We notice that there is 3 ways for each number from the first roll. Then the total is 6*3=18 ways such that the sum is even. The total possible outomes is 6x6=36.
Hence the probability for Evenet B is 18/36 or 1/2
Ms. Chen can run 5 miles in 2 hours andMs. Assis can run 6.3 miles in 3 hours.Who can run faster? Explain.
Ms. Assis
1) The way to find out who's faster, is to find their unit rates.
2) So, assuming their speed was at a constant rate, throughout the track we can write:
Chen hours
5 miles ------------------2
1 -------------------x
Cross Multiplying those ratios:
5x = 2 Divide both sides by 5
x=2/5
x=0.4 miles per hour
Assis
miles hours
6.3 ----------------- 3
1 -------------------- y
3 =6.3y Divide both sides by 6.3
y=0.47 miles per hour
3) Comparing those unit rates as
0.47 > 0.4
Then we can say that Ms. Assis runs faster than Ms. Chen
I need help with this. Find the value ( s ) of x and y.
Answer:
x = 10
y = 71 degrees
Explanation:
Let's go ahead and find x as shown below;
[tex]\begin{gathered} 38+(7x+1)=(10x+9)\text{ (external angle is equal sum of opposite interior angles)} \\ 7x-10x=9-38-1 \\ -3x=-30 \\ x=\frac{-30}{-3} \\ \therefore x=10 \end{gathered}[/tex]To find y, we need to know that;
[tex]\text{Angle}(7x+1)=7(10)+1=^{}71^{\circ}[/tex]So let's call the third angle z. Let's go ahead and find z;
[tex]\begin{gathered} 38+71+z=180\text{ (sum of angles in a triangle)} \\ z=180-71-38 \\ \therefore z=71 \end{gathered}[/tex]Therefore y = 71 degrees (vertically opposite angles and equal)
how do I find out whether an infinite geometric series converges and how do I find its sum. for example:6+3+3/2+3/4+...
We are given the following infinite geometric series
[tex]6+3+\frac{3}{2}+\frac{3}{4}+\cdots[/tex]The general form of an infinite geometric series is given by
[tex]a_1+a_1r+a_1r^2+a_1r^3+\cdots[/tex]Where a1 is the first term and r is the common ratio.
The first term is equal to 6
The common ratio is the division of any two consecutive numbers in the infinite geometric series.
[tex]\frac{3}{6}=\frac{1}{2}[/tex]You can also take any other two consecutive numbers in the series and you will get the same common ratio.
[tex]\frac{\frac{3}{2}}{3}=\frac{3}{2}\cdot\frac{1}{3}=\frac{3}{6}=\frac{1}{2}[/tex]As expected, we still got the same common ratio as before.
How do I find out whether an infinite geometric series converges?
An infinite geometric series converges if the absolute value of the common ratio is less than 1.
[tex]\begin{gathered} |r|<1 \\ \frac{1}{2}<1 \\ 0.5<1 \end{gathered}[/tex]Since the absolute value of the common ratio is less than 1, the infinite geometric series converges.
How do I find its sum?
The sum of this infinite geometric series is given by
[tex]S=\frac{a_1}{1-r}[/tex]Substitute the values of first term a1 and common ratio r.
[tex]S=\frac{6}{1-\frac{1}{2}}=\frac{6}{\frac{1}{2}}=6\cdot\frac{2}{1}=12[/tex]Therefore, the sum of this infinite geometric series is 12.
What is the M and B forX = 5M=B=
ANSWER
m = undefined
b = doesn't exist
EXPLANATION
x = 5 is a vertical line where in all points x is 5. Therefore, if we use the formula for the slope:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]The denominator will always be 0. Since we can't divide by 0, the slope is undefined.
Since it's a vertical line, there's no y-intercept. This is because the y-intercept is the value of y when x = 0 and in a vertical line x has always the same value: in this case, 5.
ARITHMETIC AND ALCEBRA REVIEWWord problem on optimizing an area or perimeter
region 1 will require the most paint
Explanation:length of tape = 24 ft
perimeter of the region to be painted = 24 ft
The region is rectangular, so we will apply the area of rectangle and perimeter to find the width.
perimeter = 2(length + width)
Area = length × width
We have 3 different regions with different lengths
For region 1:
length = 6 ft
from the formula for perimter, we can find the width:
perimeter = 2(length + width)
perimeter/2 = length + width
[tex]\text{width = }\frac{perimeter\text{ }}{2}-\text{ length}[/tex]width for region 1 = 24/2 - 6 = 12 - 6
width = 6
Area = 6 × 6 = 36 ft²
For region 2:
length = 7 ft
width = 24/2 - 7 = 12 - 7
width = 5 ft
Area = 7 × 5 = 35 ft²
For region 3:
length = 8 ft
width = 24/2 - 8 = 12 - 8
width = 4 ft
Area = 8 × 4 = 32 ft²
b) The region that will require the most paint is the one that has the highest area. The higher the area, the larger the amount of paint that will be needed.
From calculations above, the highest area is 36 ft²
Hence, the region that will require the most paint is region 1
Use substitution to solve.Solve the first equation for y and substitute it into the second equation. The resulting equati
The first equation is given as,
[tex]\begin{gathered} 2X^2\text{ = 5 +Y} \\ Y\text{ = }2X^2\text{ - 5\_\_\_\_\_\_\_(1)} \end{gathered}[/tex]The second equation is given as,
[tex]4Y\text{ = }-20\text{ }+8X^2_{_{_{_{}}}}\text{ \_\_\_\_\_\_\_\_\_(2)}[/tex]Substituting equation ( 1 ) in equation (2),
[tex]4(\text{ }2X^2\text{ - 5) = }-20\text{ }+8X^2_{_{_{_{}}}}\text{ }[/tex]Simplifying further,
[tex]8X^2-20\text{ = -20 + }8X^2[/tex]Thus the required answer is
[tex]8X^2-20\text{ = -20 + }8X^2[/tex]Determine which of the value(s), if any, must be excluded from the domain of the variable in the expression x^2/x^2+25Options:x=3,x=5,x=0,x=-5None
Given:
The expression is,
[tex]\frac{x^2}{x^2+25}[/tex]The domain of the function is values of independent variable for which expression is defined. Since expression is not defined when,
[tex]x^2+25=0[/tex]Sinece there is no real value of x for which denominator of expression,
[tex]x^2+25[/tex]is zero. So domain of the expression is,
[tex](-\infty,\infty)[/tex]So all values of x is included in the domain of the function. Thus answer is None.
P(E') = P(F) = 0.6 and P(E n F) = 0.24:a. Write down P(E).b. Explain how you know E and F:i are independentii are not mutually exclusivec Find P(E u F').
Answer:
Explanations:
Given the following probability values:
P(E') = 0.6
P(F) = 0.6
P(E n F) = 0.24
a) The probability of E [P(E)] is expressed according to the formula;
[tex]\begin{gathered} P(E)=1-P(E^{\prime}) \\ P(E)=1-0.6 \\ P(E)=0.4 \end{gathered}[/tex]b) For the events E and F to be independent, the product of their individual proban
Bob grew 1,102 plants with 29 seed packets. With 94 seed packets, how many total plants can Bob have in his backyard? Assume the relationship is directly proportional.
If the relation between number of plants and the number of seed packets is directly proportional and x is the number of plants can Bob have for 94 seed packets, you can write;
[tex]\frac{x}{94}=\frac{1102}{29}[/tex]By solving for x in the previous expression and simplifying, you get:
[tex]\begin{gathered} x=\frac{1102}{29}\cdot94 \\ x=3572 \end{gathered}[/tex]Hence, Bob could have 3572 plants if he uses 29 seed packets.
In the figure below, find each of the following.A right triangle has a vertical side labeled "3.00", a horizontal side labeled "4.00" that goes rightwards from the bottom of the vertical side, and a hypotenuse labeled "5.00" that goes down and right from the top of the vertical side to the right of the horizontal side. The top left interior angle of the triangle is an acute angle and the bottom right interior angle is an acute angle .(a) the length of the side opposite (b) the length of the side adjacent to (c) cos()(d) sin()(e) tan()
Given
To find:
a) The length of the side opposite
(b) The length of the side adjacent to
(c) cos()
(d) sin()
(e) tan()
Explanation:
It is given that,
That implies,
(a) The length of the side opposite is 3.00.
(b) The length of the side adjacent to is 3.00.
(c) cos()
[tex]\begin{gathered} \cos(\theta)=\frac{adjacen\text{t }side}{hypotenuse} \\ =\frac{4.00}{5.00} \\ =\frac{4}{5} \\ =0.8 \end{gathered}[/tex](d) sin()
[tex]\begin{gathered} \sin(\varphi)=\frac{opposite\text{ }side}{hypotenuse} \\ =\frac{4.00}{5.00} \\ =\frac{4}{5} \\ =0.8 \end{gathered}[/tex](e) tan()
[tex]\begin{gathered} \tan(\varphi)=\frac{opposite\text{ }side}{adjacent\text{ }side} \\ =\frac{4.00}{3.00} \\ =\frac{4}{3} \\ =1.33 \end{gathered}[/tex]Which expression is equivalent to 9(7 +5) by the Distributive Property?
we have
9(7 +5)
apply distributive property
9*(7)+9*(5)
63+45
combine like terms
108
Find the greatest common factor of the following monomials46b^5 16b^3
Factors of 46: 1, 2, 23 and 46
Factors of 16: 1, 2, 4, 8 and 16.
With respect to variable b, the GCF has the variable raised to the lowest power of the monomials, which in this case is 3. Then, the greatest common factor of the given monomials is: 2b³
A.bMicah used the wrong sign for b in the formula x = -2aO B. Micah should have evaluated the function with x = 0 to find they-coordinate.O C. Micah did not use the correct order-of-operations dividing 47.5 by21 -9.5)OD. Micah should have found a positive value when he simplified the-9.5(2.5)2 term.The correct vertex is(Type an ordered pair.)
Answer
- Micah's mistake in calculating the vertex is that he used the wrong sign for b in using (-b/2a) to calculate the x-coordinate of the vertex.
The correct vertex is (-2.5, 122.375).
Explanation
The quadratic equation is
y = -9.5x² - 47.5x + 63
It is evident that Micah's mistake in calculating the vertex is that he used the wrong sign for b in using (-b/2a) to calculate the x-coordinate of the vertex.
To no calculate the correct vertex,
a = -9.5
b = -47.5
c = 63
x = (-b/2a)
[tex]\begin{gathered} x=-\frac{b}{2a} \\ x=-\frac{-47.5}{2\times-9.5} \\ x=-\frac{-47.5}{-19} \\ x=-2.5 \end{gathered}[/tex]We can hen substitute this for x in the quadratic equation to get the corresponding y-coordinate for the vertex.
y = -9.5x² - 47.5x + 63
y = -9.5(-2.5)² - 47.5(-2.5) + 63
y = -9.5 (6.25) + 118.75 + 63
y = -59.375 + 118.75 + 63
y = 122.375
Hence, the vertex is (-2.5, 122.375)
Hope this Helps!!!
what is 6cos square theta+cos theta -2=0 what the theta in degrees
Given:
[tex]6\cos^2\theta+\cos\theta-2=0[/tex]Let
[tex]\cos\theta=t[/tex]Then
[tex]\begin{gathered} 6t^2+t-2=0 \\ (2t-1)(3t+2)=0 \\ 2t-1=0 \\ \Rightarrow t=\frac{1}{2} \\ \\ 3t+2=0 \\ \Rightarrow t=-\frac{2}{3} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \cos\theta=\frac{1}{2} \\ \\ \Rightarrow\theta=60^o \\ \\ \cos\theta=-\frac{2}{3} \\ \Rightarrow\theta=131.8^o \end{gathered}[/tex] Exponential Transformations: Identify if they represent growth or decay, range, horizontal move, vertical move, flip, stretch or shrink Y = 3(1/2) ^x+3 Y = 4^x-3 + 6Y = -2^x - 5 Y = (2/3)^x-2 +1
If b > 1 then it's an exponential growth
If b < 1 then it's an exponential decay
Y = 3(1/2)^(x+3) decay
Y = 4^(x-3) + 6 growth
Y = -2^x - 5 decay
Y = (2/3)^(x-2) +1 decay
The y-intercept is found replacing x = 0 into the equation.
Y = 3(1/2)^(0+3)
Y = 3(1/2)^3
Y = 3(1/8)
Y = 3/8
Y = 4^(0-3) + 6
Y = 4^(-3) + 6
Y = 1/64 + 6
Y = 385/64
Y = -2^0 - 5
Y = -1 - 5
Y = -6
Y = (2/3)^(0-2) +1
Y = (2/3)^(-2) +1
Y = (3/2)^(2) +1
Y = 9/4 +1
Y = 13/4
The vertical movement is found identifying k in the equations.
Y = 3(1/2)^(x+3) k = 0 no vertical move
Y = 4^(x-3) + 6 k = 6 vertical move 6 units up
Y = -2^x - 5 k = -5 vertical move 5 units down
Y = (2/3)^(x-2) +1 k = 1 vertical move 1 unit up
If the equation is flipped or not is seen in the a parameter. If a < 0, it's flipped, if a > 0, it isn't flipped
Y = 3(1/2)^(x+3) a > 0 not flipped
Y = 4^(x-3) + 6 a > 0 not flipped
Y = -2^x - 5 a < 0 flipped
Y = (2/3)^(x-2) +1 a > 0 not flipped
The range is found with help of the vertical move and the flip
Y = 3(1/2)^(x+3) no vertical move, not flipped range: [0, ∞]
Y = 4^(x-3) + 6 vertical move 6 units up, not flipped range: [6, ∞]
Y = -2^x - 5 vertical move 5 units down range: [-5, -∞]
Y = (2/3)^(x-2) +1 vertical move 1 unit up, not flipped range: [1, ∞]
The horizontal movement is found identifying h in the equations.
Y = 3(1/2)^(x+3) h = 3 horizontal move 3 units left
Y = 4^(x-3) + 6 h = -3 horizontal move 3 units right
Y = -2^x - 5 h = 0 no vertical move
Y = (2/3)^(x-2) +1 h = -2 horizontal move 2 units right
If the equation is stretched or shrunk is seen in the a parameter. If a > 1, the function stretches, if 0 < a < 1, 1, the function shrinks
Y = 3(1/2)^(x+3) a = 3 stretches
Y = 4^(x-3) + 6 a = 1 doesn't stretch nor shrink
Y = -2^x - 5 a = -1 doesn't stretch nor shrink
Y = (2/3)^(x-2) +1 a = 2/3 shrinks