Answers
Explanation:
We have the equation of a quadratic function:
[tex]f(x)=(x-2)^2+2[/tex]And we need to find and plot the vertex of the equation.
We start by remembering that a quadratic equation is represented by a parabola and that the vertex is the point where the parabola changes direction, usually represented by (h, k) as shown in the following example:
• How do we find the vertex using the given equation?
We find it by comparing our equation with the general vertex form of the quadratic equation:
[tex]f(x)=a(x-h)^2+k[/tex]where
[tex](h,k)[/tex]is the vertex, and a is a constant.
Using the given equation, we find the h and k values:
[tex]\begin{gathered} f(x)=(x-2)^{2}+2 \\ \downarrow \\ h=2 \\ k=2 \end{gathered}[/tex]Therefore, the vertex is at (2, 2).
Answer:
The point (2,2) representing the vertex is shown in the image:
Related Questions
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()
Answers
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]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
Answers
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]Which tree is growing faster?Tree 2Tree 1 is growing 2 week 2 4 6 8 10inches every week. inches5 10 15 20 25tallHint: First calculate the unit rate for Tree 2.Enter the number that belongs in the numerator.Unit Rate[?]=inches/week
Answers
Calculating the unit rate for Tree 2 we have the following
[tex]\text{Unit Rate }=\frac{5\text{ inches}}{2\text{ week}}\text{ }=\frac{10\text{ inches}}{4\text{ week}}\text{ }=\frac{15\text{ inches}}{6\text{ week}}[/tex]When simplified the unit rate is
[tex]\frac{5}{2}\text{ inches/week}[/tex]This is 2.5 inches per week. Compared to Tree 1,
Simplify.
Radical sign 45x
9
Answers
Answer:
20.12461179
Step-by-step explanation
The temperature of a solution in a science experiment is -6.2°C. Jesse wants to raise the temperature so that it is positive. (a) Give an example of a number of degrees Celsius by which Jesse could raise the temperature. (b) Write a equation to represent the solution.
Answers
Hello!
First, the temperature is -6.2ºC, and Jesse wants to raise it until be positive.
(a) Give an example of a number of degrees Celsius by which Jesse could raise the temperature.If we add 6.2ºC, we will obtain a temperature equal to 0ºC, right? So, to the temperature be positive you can choose any temperature greater than 6.2º.
For example, I'll choose 15ºC.
(b) Write an equation to represent the solution. We will write the current temperature plus the temperature that we will add, then we obtain the new temperature, look:
-6.2ºC + 15ºC = 8.8ºC
A clothing store is donating socks to various charities. The store gave 6 regular packs and 5 value packs to a homeless shelter, which contained a total of 163 pairs of socks. For foster children, the store donated 6 regular packs and 4 value packs, which equaled 146 pairs. How many pairs of socks are in each pack?
Answers
Let r and v be the number of socks ina regular pack and value pack, respectively. Since the store gave 6 regular packs and 5 value packs which contained 163 pair of socks, we can write
[tex]6r+5v=163[/tex]Similarly, since the store donated 6 regular packs and 4 value pack which add 146 pair of socks, we can write
[tex]6r+4v=146[/tex]Then, we have the following system of equations:
[tex]\begin{gathered} 6r+5v=163\ldots(a) \\ 6r+4v=146\ldots(b) \end{gathered}[/tex]Solving by elimilation method.
By multiplying equation (b) by -1, we have an equivalent system of equations:
[tex]\begin{gathered} 6r+5v=163 \\ -6r-4v=-146 \end{gathered}[/tex]Then, by adding both equations, we have
[tex]v=17[/tex]Now, in order to obtain the number of socks in a regular pack, we must substitute the last result into equation (a). It yields,
[tex]6r+5(17)=163[/tex]which gives
[tex]6r+85=163[/tex]By subtracting 85 to both sides, we have
[tex]6r=78[/tex]Then, r is given by
[tex]\begin{gathered} r=\frac{78}{6} \\ r=13 \end{gathered}[/tex]Therefore, the answer is: There are 13 pairs of socks in each regular pack and 17 pairs in each value pack.
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.
Answers
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.
A card is chosen from a standard deck, thena month of the year is chosen. Find theprobability of getting a face card and June. use the counting principle to find each probability
Answers
1) Gathering the data
1 face card out of one deck: 12 /52
1 month of the year: 1/12
2) In Probability, The counting principle says we can multiply two
events
The question, says the probability of getting a face card
We have 12 face cards in a deck so, using the counting principle:
P( face card and June) = 12/52 *1/12 =1/52
Determine the equation of the straight line that passes through the point (-2, -4)and is perpendicular to the line y +2x=1
Answers
If the line is perpendicular to:
[tex]y=-2x+1[/tex]the we know that the slope will be the negative reciproc of the slope so the new slope is:
[tex]m=\frac{1}{2}[/tex]So the equation is:
[tex]y=\frac{1}{2}x+b[/tex]So we can replace the coordinate (-2,-4) and solve for b so:
[tex]\begin{gathered} -4=\frac{1}{2}(-2)+b \\ -4+1=b \\ -3=b \end{gathered}[/tex]So the final equation is:
[tex]y=\frac{1}{2}x-3[/tex]what value of c would complete the square for the following trinomials?
Answers
To find the value of c that will make the given expression a perfect square, we simply;
Step 1: Take the coefficient of x : that is, 6
Step 2: Divide the coefficient obtained in step 1 by 2: That is, 6/2 = 3
Step 3: Square the result in step 2: That is, 3^2 = 9
Hence, c = 9
The value of c in the first expression is 9.
Second Expression:
[tex]x^2-10x+c[/tex]Step 1: 10 ( Do not bother yourself with the negative sign, just pick the number 10)
Step 2: 10/2 = 5
Step 3: 5^2 = 25
so, c = 25
Third expression:
[tex]x^2+32x+c[/tex]Step 1: 32
Step 2: 32/2 = 16
Step 3: 16^2 = 256
So, c = 256
Fourth expression:
[tex]x^2-12x+c[/tex]Step 1: 12
Step 2: 12/2 = 6
Step 3: 6^2 = 36
So, c = 36
Last expression:
[tex]x^2+8x+c[/tex]Step 1: 8
Step 2: 8/2 = 4
Step 3: 4^2 = 16
so, c = 16
Determine the equation of the line that goes through the point (4, 4) with -1/4 slope. Enter your answer in slope-intercept form.Enter EquationPls see picture
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
From the information given,
m = - 1/4
the line passes through the point (4, 4). This means that
x = 4, y = 4
We would find c by substituting m = - 1/4, x = 4 and y = 4 into the slope intercept equation. We have
4 = - 1/4 * 4 + c
4 = - 1 + c
Adding 1 to both sides of the equation,
4 + 1 = - 1 + 1 + c
c = 5
By substituting m = - 1/4 and c = 5 into the slope intercept equation, the equation of the line is
y = - x/4 + 5
On June 10, Trudy Polanski deposited $1260 in a savings account that pays 5.5% interest compounded daily. How much interest will the money earn in 60 days?
Answers
The answer will be $32,893.43 compound interest will the money earn in 60 days.
What is compound interest?
The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is computed by multiplying the starting principal amount by one and the annual interest rate raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.
When the amount compounds quarterly, it means that the amount compounds 2 times, n=12. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:
A = P (1 + r/12)^12t
A = 1260(1+5.5/12) ^12
A = $32,893.43
Hence the interest will be $32,893.43.
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Solve fort.-t = 9(t – 10)t=Stuck? Watch a video or us
Answers
We are to solve for t in the equation given
To do this, we have to expand the bracket
Expanding, we have
-t = 9(t-10)
-t = 9t - 90
Collecting the like terms, we have
90 = 9t + t
90 = 10t
Dividing both sides by 10 to get t, we have
[tex]\begin{gathered} t=\frac{90}{10} \\ t=9 \end{gathered}[/tex]Therefore the value of t is 9.
Complete the following equation. Your answers will be algebraic expressions. (a+bi)^2= _____ + 2abiHint: think of i as an ordinary variable and then replace i^2 with -1.
Answers
The given expression is:
[tex](a+ib)^2[/tex]Expand to get:
[tex]\begin{gathered} (a+ib)^2=a^2+i^2b^2+2abi \\ =a^2-b^2+2abi \end{gathered}[/tex]The value is as above since it is given that i^2=-1.
So the expansion is:
[tex](a+ib)^2=a^2-b^2+2abi[/tex]The blank should be:
[tex]a^2-b^2[/tex]using the graph below wich graphs shows the mapping of ABCD to A'B'C'D for a dilation with center (0,0) and a scale factor of 3
Answers
The rule for a dilation with center at (0,0) and scale factor k is:
[tex](x,y)\rightarrow(kx,ky)[/tex]Find the transformed vertices A'. B', C' and D' using this rule:
[tex]A(-2,3)\rightarrow A^{\prime}(3\times-2,3\times3)=A^{\prime}(-6,9)[/tex]Similarly, the coordinates of B', C' and D' wil be:
[tex]\begin{gathered} B^{\prime}(6,12) \\ C^{\prime}(6,-3) \\ D^{\prime}(-9,3) \end{gathered}[/tex]Plot A', B', C' and D' along with A, B, C and D:
A grocery store surveys its customers and asks them to indicate (a) how many times they go to the grocerystore in a typical month, (b) their age (in years), (c) whether or not they have ever had to wait in line at thegrocery store more than 10 minutes, (d) the product they purchase most often at the grocery store, and (e)how long (in years) they have shopped at this particular grocery store. We would consider the customer'sage in years to be aand whether or not the customer has had to wait in linemore than 10 minutes to be aO numerical variable; categorical variableO categorical variable; categorical variableO numerical variable; numerical variableO explanatory variable; response variableO categorical variable; numerical variable
Answers
The age in years is a numerical variable because it can be listed in ascending or descending order. while whether or not the customer has had to wait in line more than 10 minutes is a categorica
select all of the trips that would take 5 hours 1. Drive 40 miles per hour between Bend and Portland, which are 200 miles apart 2. Take a train going 50 miles per hour from Martinez to Dunsmuir, which are 259 miles apart 3. Walk 4 miles per hour to school, wh6is 1.75 miles apart
Answers
Answer:
1. Yes
2. No
3. No.
Explanation:
The amount of time taken on a trip is equal to the distance travelled divided by the speed.
[tex]\text{time taken = }\frac{dist\text{ travelled }}{\text{speed}}[/tex]1. The drive from Bend to Portland is 200 miles and the speed is 40 miles per hour; therefore, the time taken is
[tex]\text{time taken = }\frac{200}{40}=5\text{ hours.}[/tex]2. The drive from Martinez to Dunsmuir is 259 and the speed is 50 miles per hour; therefore, the time taken is
[tex]\text{time taken = }\frac{259\text{ miles}}{50\text{ mile per hour}}\text{ = 5.18 hours}[/tex]3.
The distance to the school is 1.75 miles and the speed is 4 miles per hour; therefore, the time taken is
[tex]\text{time taken = }\frac{1.75\text{ miles}}{4\text{ miles per hour }}=0.4375\text{ hours. }[/tex]Hence, the only trip that takes 5 hours is trip 1.
Find the area of 11.4 and 7.4
Answers
let,
lenght (l)=11.4 , and width (b)=7.4
so,
[tex]\begin{gathered} \text{area}=l\times b \\ =11.4\times7.4 \\ =84.36 \end{gathered}[/tex]area=84.36
The ratio of the amount of money Rachel saved to the amount of money Timothy saved was12 : 13. After Timothy spent $27, Rachel had 3 times as much as Timothy,A. How much did Rachel save?b How much did they save altogether at first?
Answers
For a)
Before
Rachel : Timothy
12 : 13
After
Rachel : Timothy
3 : 1
In order to have the same amount for Rachel
12: 4
Timothy
13units -4 units =9 units
9units=$27
1 unit=27/9
1unit = $3
For Rachel
Rachel saved $36
b)
Total units at first =12+13=25
If 1units is $3
25 units is 3x25
25 units is $75
They saved together 75
ANSWER
Rachel saved $36
They saved together 75
12 Stefanie is painting her bedroom. She can paint 12 1/3 square feet in 1/5 of an hour. How many square feet can she paint in one hour?
Answers
stephanie can paint 12 1/3 square feet in 1/5 of an hour. So,
[tex]undefined[/tex]How many ways can we award a 1st, 2nd, and 3rd place prize among eight contestants?
Answers
We have:
- There are 8 choices for awarding first prize.
- Then there are 7 choices for awarding second prize.
- And there are 6 choices for awarding third prize.
Therefore, there are:
[tex]8\cdot7\cdot6=336\text{ ways}[/tex]Answer: 336 ways
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
Answers
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
Jamie cut a rope into thirds.He used two of the pieces to make a swing
Answers
The complete length of the rope would be represented by 1
If he cut the rope into thirds, it means that each length woiuld be 1/3.
Given that he used two of the pieces to make a swing, it means that the length used in making the swing is
1/3 + 1/3 = 2/3
The left over rope is 1/3
Also, he used equal lengths of the left over rope on four picture frames. It means that the length used on each picture frame is
1/3 divided by 4
= 1/3 * 1/4 = 1/12
Thus, the fraction of the original rope that he used for each picture frame is 1/12. Option B is correct
Name the quadrant in which each of the point lies. (-2,5)
Answers
The quadrants have the following division.
Since the points (-2, 5) is located on the negative side of the x-axis, and in the positive side of the y axis, it belongs to the second quadrant.
The answer is quadrant II
which expression can be used to find the length of the side of the triangle represented by the vertices (5,5) and (7,-3) on the graph?
Answers
In order to determine the correct expression for the length of the side, consider that the distance in between two points (x1,y1) and (x2,y2) is given by the following formula:
d = √((x2 - x1)² + (y2 - y1)²)
if (x1,y1) = (5,5) and (x2,y2) = (7,-3) you have for d:
d = √((7 - 5)²+(5 - (-3))²)
Determine whether the function is linear. If it is, State the rate of change.Question 8
Answers
Question 8.
Given the table:
x -7 -5 -3 -1 0
y 11 14 17 20 23
To determine if the function is linear, let's calculate to see if the rate of change is constant.
The x-values need to have a constant rate of change and the y-values need to have a constant rate of change.
If the function has a constant rate of change, then the functioncan be said to be linear.
To calculate the rate of change, we have:
[tex]\begin{gathered} x2-x1=-5\text{ - (-7) = -5 + 7 = 2} \\ \\ x3-x2=-3-(-5)=-3+5=2 \\ \\ x4-x3=-1-(-3)=-1+3=2 \\ \\ x5-x4=0-(-1)=0+1=1 \\ \\ We\text{ can se}e\text{ the x-values do not have a constant rate of change} \end{gathered}[/tex][tex]\begin{gathered} y2-y1=14-11=3 \\ \\ y3-y2=17-14=3 \\ \\ y4-y3=20-17=3 \\ \\ y5-y4=23-20=3 \\ \\ \text{The y-values have a constant rate of change} \end{gathered}[/tex]Since the x-values do not have a constant rate of change that means the function is not linear.
ANSWER:
The table does not represent a linear function
can u help solve problem
Answers
To multiply the matixes, we'll look at their elements
[tex]A=\begin{bmatrix}{A_1} & {A_2} & {A_3} \\ {} & {} & {} \\ {} & {} & \end{bmatrix},\text{ B=}\begin{bmatrix}{B_1} & {} & {} \\ {B_2} & {} & \\ {B_3} & {} & {}\end{bmatrix}[/tex]In order to get AB, we simply use the following formula
[tex]AB=A_1\cdot B_1+A_2\cdot B_2+A_3\cdot B_3[/tex]In this case
[tex]AB=3\cdot1+4\cdot2+5\cdot3+6\cdot4=3+8+15+24=50[/tex]Since both matrixes have 4 elements. Thus
[tex]AB=50[/tex]Filling in Table (decreasing)Dependent QuantityA Helicopter flying at 3509 feet begins its descent. Itdescends at a rate of 41 feet per minuteIndependent Quantity0Complete the missing part of the tables, and make afunction that describes the Helicopter's decent133222Your answer: Not there yet, keep working3140Share with Class
Answers
(0,3509)
(1,3468)
(3,3386)
(7,3222)
(9,3140)
h=3509-41x
Explanation
Step 1
as we can see, the independent quantity is the time , and the dependent quantity is the heigth because it depends on the time.
then when time = o, t=o
[tex]0\Rightarrow3509\text{ ft}[/tex]after 1 minute the helicopter has descended 41 ft, then
when time = 1, t=1
[tex]\begin{gathered} heigth_1=3509-(1\cdot41) \\ heigth_1=3509-41 \\ heigth_1=3468 \\ (1,3468) \end{gathered}[/tex]when t=3
[tex]\begin{gathered} heigth_3=3509-(3\cdot41) \\ heigth_3=3509-123 \\ heigth_3=3386 \end{gathered}[/tex]when heigth=3222
[tex]\begin{gathered} \text{heigth}_x=3509-(x\cdot41) \\ 3222=3509-41x \\ \text{subtract 3509 in both sides} \\ 3222-3509=3509-41x-3509 \\ -287=-41x \\ \text{divide both sides by -41} \\ \frac{-287}{-41}=\frac{-41x}{-41} \\ 7=x \\ \text{hence}(7,3222) \end{gathered}[/tex]when heigth=3140
[tex]\begin{gathered} \text{heigth}_x=3509-(x\cdot41) \\ \text{3140}=3509-41x \\ subtract\text{ 3509 in both sides} \\ \text{3140-3509}=3509-41x-3509 \\ -369=-41x \\ \text{divide both sides by -41} \\ \frac{-369}{-41}=\frac{-41x}{-41} \\ 9=x \\ x=9,\text{then} \\ (9,3140) \end{gathered}[/tex]Step 2
now, the equation is
[tex]\begin{gathered} \text{Heigth}=3509-41x \\ h=3509-41x \\ \text{where} \\ h\text{ is the heigth in ft and t is the time in minutes} \end{gathered}[/tex]I hope this helps you
Solve the system of equations:3x+y=6 2x+3y=11
Answers
Answer:
(1,3)
Explanation:
Given the system of equations:
[tex]f(x)=\begin{cases}3x+y=6 \\ 2x+3y=11\end{cases}[/tex]To solve the system using the elimination method, multiply the first equation by 3.
[tex]\begin{gathered} f(x)=\begin{cases}9x+3y=18 \\ 2x+3y=11\end{cases} \\ \text{Subtract} \\ 7x=7 \\ \text{Divide both sides by 7} \\ \frac{7x}{7}=\frac{7}{7} \\ x=1 \end{gathered}[/tex]Next, substitute x=1 into any of the equations to solve for y.
[tex]\begin{gathered} 3x+y=6 \\ 3(1)+y=6 \\ y=6-3 \\ y=3 \end{gathered}[/tex]The solution to the system of equations is (x,y)=(1, 3).
InequalitiesEvaluate. Show your work or explain how you arrived at your answer.-|-34|
Answers
The value of -|-34| is -34
-|-34|
Apply absolute rule: |-a|=a, a>0 =-34
The absolute value (or modulus)| x | of a real number x is its non-negative value regardless of its sign. For example, 5 has an absolute value of 5, and 5 has an absolute value of 5. A number's absolute value can be conceived of as its distance from zero along the real number line.
Absolute values for real numbers occur in a wide range of mathematical contexts. Absolute values, for example, are defined for complex numbers, quaternions, ordered rings, fields, and vector spaces. In numerous mathematical and physical contexts, the absolute value is intimately related to the concepts of magnitude, distance, and norm.
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