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A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.
A vertex example is what?f(x)=3(x−1)2
Find the given parabola's characteristics.
Lessen the steps you tap...
Vertex form is to be used, y=a(x−h)2+k,
to calculate the values of a, h, and k.
a=3
h=1
k=0
The parabola widens because the value of an is positive.
opens up
Find the (h,k) vertex. ( 1 , 0 )
Calculate p, the distance between the focus and the vertex.
To continue, tap...
1/ 12
Locate your focus.
To continue, tap... ( 1 , 1/ 12 )
By identifying the line that connects the vertex with the focus, you may determine the axis of symmetry.
x = 1
The horizontal line that results from deducting p from the vertex's y-coordinate k depends on whether the parabola opens up or down. This line is known as the directrix.
y = k − p
Simplify the formula after substituting the known p and k values.
y = − 1 /12
Analyze and graph the parabola using its characteristics.
Direction: opens up
vertices: ( 1, 0 )
Focus: ( 1 , 1 /12 )
x = 1 is the symmetry axis.
Direction: y = /1 12.
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Related Questions
Katherine bought à sandwich for 5 1/2 dollar and a adrink for $2.60.If she paid for her meal with a $ 10 bill how much money did she have left?
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To find out how much Katherin have left we need to substrac the amount she spent:
[tex]10-5\frac{1}{2}-2.6=10-5.5-2.6=1.9[/tex]Therefore she has $1.9 left.
To do this same problem in fraction form we need to convert the 2.6 in fraction, to do this we multiply the number by 10 and divided by ten. Then:
[tex]2.6\cdot\frac{10}{10}=\frac{26}{10}=\frac{13}{5}[/tex]then we have:
[tex]\begin{gathered} 10-5\frac{1}{2}-\frac{13}{5}=10-\frac{11}{2}-\frac{13}{5} \\ =\frac{100-55-26}{10} \\ =\frac{19}{10} \end{gathered}[/tex]Therefore, the answer in decimal form is 19/10 dollars.
questionSuppose $24,000 is deposited into an account paying 7.25% interest, which is compoundedcontinuouslyHow much money will be in the account after ten years if no withdrawals or additional depositsare made?
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This is a compound interest question and we have been given:
Principal (P) = $24000
Rate (r) = 7.25%
Years (t) = 10
However, we are told this value is compounded continuously. This means that for every infinitesimal time period, the value keeps being compounded.
The formula for finding the compound interest is:
[tex]\text{Amount}=P(1+\frac{r}{n})^{nt}[/tex]But because the compounding period is continuous and therefore, infinitesimal,
[tex]\begin{gathered} Amount=P(1+\frac{r}{n})^{nt} \\ But, \\ n\to\infty \\ \\ \therefore Amount=\lim _{n\to\infty}P(1+\frac{r}{n})^{nt} \end{gathered}[/tex]This is similar to the general formula for Euler's number (e) which is:
[tex]e=\lim _{n\to\infty}(1+\frac{1}{n})^n[/tex]Thus, we can re-write the Amount formula in terms of e:
[tex]\begin{gathered} \text{Amount}=\lim _{n\to\infty}P(1+\frac{r}{n})^{nt} \\ \text{This can be re-written as:} \\ \\ Amount=\lim _{n\to\infty}P(1+\frac{r}{n})^{\frac{n}{r}\times r\times t}\text{ (move P out of the limit because it is a constant)} \\ \\ \text{Amount}=P\lim _{n\to\infty}((1+\frac{r}{n})^{\frac{n}{r}})^{r\times t} \\ \\ \text{Amount}=P(\lim _{n\to\infty}(1+\frac{r}{n})^{\frac{n}{5}})^{rt} \\ \\ \text{but,} \\ e=(\lim _{n\to\infty}(1+\frac{r}{n})^{\frac{n}{r}} \\ \\ \therefore\text{Amount}=Pe^{rt} \end{gathered}[/tex]Therefore, we can find the amount of money in the account after 10 years:
[tex]\begin{gathered} \text{Amount}=Pe^{rt} \\ P=24000 \\ r=7.25\text{ \%=}\frac{7.25}{100}=0.0725 \\ t=10\text{ years} \\ \\ \therefore\text{Amount}=24000\times e^{10\times0.0725} \\ \\ \text{Amount}=24000\times2.06473 \\ \\ \therefore\text{Amount}=49553.546\approx49553.55 \end{gathered}[/tex]Therefore the amount after compounding continuously for 10 years is:
$49553.55
c. Where would the line y = - 2x + 1 lie? Again, justify your prediction and add the graph of this lineto your graph from part (b).
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Given:
b) First the two lines are graphed,
[tex]\begin{gathered} y=2x+3 \\ y=2x-2 \end{gathered}[/tex]Now, yoshi wants to add one more equation,
[tex]y=2x+1[/tex]The graph is represented as,
In the above graph the green line represents the y=2x+1 and it lies between the line y= 2x+3 and y= 2x-2.
c) The graph of the line y = -2x +1
It is observed that the green line y= -2x+1 intersects both the lines y= 2x+3 and y= 2x-2.
Ms. Bell's mathematics class consists of 6 sophomores, 13 juniors, and 10 seniors.
How many different ways can Ms. Bell create a 3-member committee of sophomores
if each sophomore has an equal chance of being selected?
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The number of different ways in which Ms. Bell's can select 3-member committee of sophomores is 20 ways.
What is termed as the combination?Selections are another name for combinations. Combinations are the selection of items from a given collection of items. We need not aim to arrange anything here. Combinations do seem to be selections made by having taken some or all of a set of objects, regardless of how they are arranged. The amount of combinations of n things taken r at a time is denoted by nCr and can be calculated as nCr=n!/r!(nr)!, where 0 r n.0 ≤ r ≤ n.For the given question;
Ms. Bell's mathematics class consists -
6 sophomores, 13 juniors, and 10 seniors.Ms. Bell create a 3-member committee of sophomores with unbiased outcomes.
The section of 3 sophomores can be done as;
⁶C₃ = 6!/3!(6-3)!
⁶C₃ = 6/3!.3!
⁶C₃ = 20 ways.
Thus, the number of different ways in which Ms. Bell's can select 3-member committee of sophomores is 20 ways.
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Mr. and Mrs. Hill hope to send their son to college in fourteen years. How much money should they invest now at an interest rate of 9.5% per year, compounded continuously, in order to be able to contribute $8500 to his education?Round your answer to the nearest cent.
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continuouslyUsing the formula for a compounded continously
[tex]P=P_0\cdot e^{r\cdot t}[/tex]where P is the amount on the account after t years compounded at an interest rate r when Po is invested in an account.
then,
[tex]\begin{gathered} 8500=P_0\cdot e^{0.095\cdot14} \\ 8500=P_{0^{}}\cdot e^{1.33} \\ P_0=\frac{8500}{e^{1.33}} \\ P_0=2248.056\approx2248.06 \end{gathered}[/tex]2) From an elevation of 38 feet below sea level, Devin climbed to an elevation of 92 feet abovesea level. How much higher was Devin at the end of his climb than at the beginning?
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Ok, so he started at 38 feet below and ended at 92 feet above. 38 below = -38.
The difference in the height is given by
92-(-38) =
92+38 =
130 feet
Devin was 130 feet higher at the end of climbing.
hello and thank you for helping me and this is a trigonometry question bit for the question has give exact value and it won't accept decimals as an answer and thank you for your time.
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1) In this question let's calculate the sin(θ) and cos(θ)
Given that
[tex]\begin{gathered} \text{If }\sin (\theta)=\frac{5\pi}{4} \\ \sin (\theta)\text{ }\Rightarrow\sin (\frac{5\pi}{4})\text{ }=-\frac{\sqrt[]{2}}{2} \\ \cos (\frac{5\pi}{4})=-\frac{\sqrt[]{2}}{2} \end{gathered}[/tex]2) In this question, we're calculating the value of the sine and the cosine in radians.
We must remember that 5π/4 ⇒ to 225º, and that it's in the Quadrant III
If we subtract
225 -180 =45 So the sine of 5π/4 is -√2/2 and the cosine (5π/4 ) = -√2/2
2.3) The sign of the Quadrant
Since 225º is in Quadrant III both results are negative ones.
Rewrite the equation in Ax+By=C form.Use integers for A, B, and C.y-4=-5(x+1)
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The given equation is
[tex]y-4=5(x+1)[/tex]To write the equation in standard form, first, we have to use the distributive property.
[tex]y-4=5x+5[/tex]Now, we subtract 5x and 5 on both sides.
[tex]\begin{gathered} y-4-5x-5=5x+5-5x-5 \\ -5x+y-9=0 \end{gathered}[/tex]Now, we add 9 on each side
[tex]\begin{gathered} -5x+y-9+9=0+9 \\ -5x+y=9 \end{gathered}[/tex]Therefore, the standard form of the given equation is[tex]-5x+y=9[/tex]Where A = -5, B = 1, and C = 9.5 cm5 cmThe surface area of the above figure isA. 208.1 cm2B. 225.6 cm2C. 314.2 cm2D. none of the above
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It is a cylinder.
1.- Calculate the area of the base and the top
Area = 2*pi*r^2
Area = 2*3.14*5^2
Area = 157 cm^2
Total area of the base and top = 2 x 157 = 314 cm^2
2.- Calculate the perimeter of the circle.
Perimeter = 2*pi*r
Perimeter = 2*3.14*5
Perimeter = 31.4 cm
3.- Calculate the lateral area
Lateral area = 5 x 31.4
Lateral area = 157 cm^2
4.- Calculate the total area = 157 + 314
= 471 cm^2
5.- Result
D. None of the above
the top ten medal winning nations in a in a particular year are shown in the table. use the given information and calculate the median number of bronze medals for all nations round to the nearest tenth as needed
Answers
We have the following:
We know that to calculate the average we must add the corresponding values of bronze medals of each nation and then divide by the number of nations like this
[tex]\begin{gathered} m=\frac{11+7+9+5+5+3+8+4+6+0}{10} \\ m=\frac{58}{10} \\ m=5.8 \end{gathered}[/tex]the median number of bronze medals for all nations is 5.8
8x - 3x + 4x = -36x = ?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
8x - 3x + 4x = -36
x = ?
Step 02:
We must apply the algebraic rules to find the solution.
8x - 3x + 4x = -36
12x - 3x = - 36
9x = - 36
x = - 36 / 9
x = - 4
The answer is:
x = - 4
Let log, A = 3; log, C = 2; log, D=5 D? what is the value of
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Evaluate the value of expression.
[tex]\begin{gathered} \log _b\frac{D^2}{C^3A}=\log _bD^2-\log _bC^3-\log _bA \\ =2\log _bD-3\log _bC-\log _bA \\ =2\cdot5-3\cdot2-3 \\ =10-6-3 \\ =1 \end{gathered}[/tex]So answer is 1.
I need help please. I don’t know what to do.Number 6
Answers
By definition, a relation is a function if each input value (x-value) has one and only one output value (y-value).
In this case, you have the following relation:
[tex]\mleft(1,5\mright)\mleft(3,1\mright)\mleft(5,0\mright)\mleft(-2,6\mright)[/tex]Notice that each ordered pair has this form:
[tex](x,y)[/tex]Where "x" is the input value and "y" is the output value.
You can identify that each input value has one and only output value. Therefore, you can conclude that this relation is a function.
Hence, the answer is: It is a function.
Select the correct product of (x + 3)(x - 5). CX - 15 X5 + 3x - 5x2 - 15 X - 15 C x + 3x - 5x - 15
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Distributive property:
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]Multiplication of powers with the same base:
[tex]a^m\cdot a^n=a^{m+n}[/tex]For the given expression:
[tex]\begin{gathered} (x^2+3)(x^3-5)=x^2\cdot x^3+x^2\cdot(-5)+3\cdot x^3+3\cdot(-5) \\ \\ =x^{2+3}-5x^2+3x^3-15 \\ =x^5-5x^2+3x^3-15 \\ =x^5+3x^3-5x^2-15 \end{gathered}[/tex]Answer is the second option
New York City mayor Michael made it his mission to reduce smoking in New York City. New York city’s adult smoking rate is 13.2%. In a random sample of 3932 New York City residents, how many of those people smoke? Round to the nearest integer
Answers
519 people smoked
Explanation
to figure out this we need to find teh 13.2 % of 3932
so
Step 1
Convert 13.2% to a decimal by removing the percent sign and dividing by 100
then
[tex]13.2\text{ \%}\rightarrow\frac{13.2}{100}\rightarrow0.132[/tex]Step 2
now, multyply the number by the percentage ( in decimal form),so
[tex]\begin{gathered} 13.2\text{ \% of 3932=0.132}\cdot3932=519.04 \\ \text{rounded} \\ 519 \end{gathered}[/tex]therefore, the answer is
519 people smoked
I hope this helps you
Which number can be inserted into the parentheses to make a true statement?-10°C<( )A. -12° CB. -18° CC. -3°CD. -10° C
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Answer:
[tex]-3\degree C[/tex]Explanation:
Here, we want to get the number that could be inserted into the parentheses to make it true
From the logical operator given, we can see that we need a number greater than -10
From the options given, only -3 is greater than -10, which makes it the correct answer choice
Complete a two-column algebraic proof.Given: x – 4 = (8x+6) + 4xProve: x = -1
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To perform a two column proof, we should give a statement and give a reason of it.
So we start with the initial statement.
1. Statement: x-4 =(1/2)(8x+6)+4x. Reason: Given
Next, we distribute the multiplication (1/2) with(8x+6). If we do so, we get the following statement.
2. Statement x-4 = (4x+3) + 4x. Reason: Distributive property of addition and multiplication.
Now, on the right we can add 4x with 4x, due to the associative property of additon, we get
3. Statement: x-4 = (4x+4x)+3 = 8x+3. Reason: Associative property of addition.
Now, we can subtract x on both sides, so we get
4. Statement: -4 = 7x+3. Reason: Subtraction property of equality.
By the same reason, we should subtract 3 on both sides. We get
5. Statement: -7 = 7x. Reason: Subtraction property of equality.
Finally, we divide by 7 on both sides, so we get
6. Statement: -1=x. Reason: Division property of equality.
7. Statement: x=-1. Reason: Symmetric property of equality.
What is the volume of this sphere? Use a ~ 3.14 and round your answer to the nearest! hundredth. 5 m cubic meters
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We will have the following:
[tex]V=\frac{4}{3}\pi r^3[/tex]Now, we replace the values and solve:
[tex]V=\frac{4}{3}(3.14)(5)^3\Rightarrow V\approx523.33[/tex]So, the volume of the sphere is approximately 523.33 cubic meters.
***Example with an 8 m radius***
If the radius of the sphere were of 8 meters, we would have:
[tex]V=\frac{4}{3}(3.14)(8)^3\Rightarrow V\approx2143.57[/tex]So, the volume of such a sphere would be approximately 2143.57 cubic meters.
Which quadrant has ordered pairs (-x,-y)?
Answers
ANSWER
Quadrant III
STEP-BY-STEP EXPLANATION:
Firstly, we need to draw the cardinal points and label each quadrant on it
Looking at the ordered pair (-x, -y), you will see that the x and y-values both fall on the negative side of the x-ais and y-axis
Hence, it falls on the quadrant III
Convert the fraction to a decimal. Round the quotient to hundredths when necessary70 over 45
Answers
Given:
[tex]\frac{70}{45}[/tex]Required:
We need to convert the given fraction to a decimal.
Explanation:
Divide the number 70 by 45.
[tex]\frac{70}{45}=1.555...[/tex]Round off to the nearest hundredth.
[tex]\frac{70}{45}=1.56[/tex]Final answer:
[tex]\frac{70}{45}=1.56[/tex]Given:
[tex]\frac{70}{45}[/tex]Required:
We need to convert the given fraction to a decimal.
Explanation:
Divide the number 70 by 45.
[tex]\frac{70}{45}=1.555...[/tex]Round off to the nearest hundredth.
[tex]\frac{70}{45}=1.56[/tex]Final answer:
[tex]\frac{70}{45}=1.56[/tex]A wheel is rotating 600 times per minute. Through how many degrees does a point in the edge of the wheel move in 1/2 seconds.
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The wheel is rotating 600 times per minute, find how many times rotate in 1 second:
1 minute = 60 seconds
[tex]600\frac{times}{\min}\cdot\frac{1\min}{60s}=10\frac{times}{s}[/tex]Then, if in 1 second it rotates 10 times in 1/2 seconds it rotates:
[tex]\frac{10\frac{times}{s}}{2}=5\text{times}[/tex]Multiply the number of times it rotates (5 times) by 360 (a wheel has 360º)
[tex]5\text{times}\cdot\frac{360º}{1\text{time}}=1800º[/tex]Then, a point moves 1800º in 1/2 secondsIs this a right triangle?Use the Pythagorean Theorem to find out!20 cm12 cm16 cmYesNo
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If this is a right triangle, then the Pythagorean theorem has to be valid.
This means that the sum of the squares of the legs has to be equal to the square of the hypotenuse (NOTE: we can identify the potential hypotenuse by finding the side with the most length).
Then, we calculate:
[tex]\begin{gathered} 12^2+16^2=20^2 \\ 144+256=400 \\ 400=400\longrightarrow\text{True} \end{gathered}[/tex]As the Pythagorean theorem is valid for this side's lengths, we know that this triangle is a right triangle.
Answer: Yes.
A 65 ft tree casts a 13 ft shadow. At the same time of day, how long would the shadow of a 20 ft building be? (Draw a diagram to help you set up a proportion)
Answers
height of tree = 65 ft
length of shadow = 13 ft
Let draw a diagram to illustrate the question effectively
The proportion can be set up below
[tex]\begin{gathered} \frac{65}{20}=\frac{13}{x} \\ \text{cross multiply} \\ 65x=260 \\ x=\frac{260}{65} \\ x=4\text{ ft} \end{gathered}[/tex]Th shadow will be 4 ft. do you
hey i need help giving 10 points
Answers
Answer:
B(2) = -1
Step-by-step explanation:
Assuming each division on the grid is 1 unit
Locate 2 on the x-axis. That is two divisions to the right of the origin. The y value corresponding to this is -1
Find the coordinates of the center, vertices, covertices, foci, length of transverse and conjugate axis and the equation of the asymptotes. Then graph the hyperbola.
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The given equation is,
[tex]\frac{x^2}{36}-\frac{y^2}{16}=1\text{ ---(1)}[/tex]It can be rewritten as,
[tex]\frac{x^2}{6^2}-\frac{y^2}{4^2}=1\text{ ---(2)}[/tex]The above equation is similar to the standard equation of left-right facing a hyperbola given by,
distribute and simply 5(3x+1)-6x
Answers
Find (w∘s)(x) and (s∘w)(x) for w(x)=7x−2 and s(x)=x^2−7x+5
(w∘s)(x)=
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The two composite functions have their values to be (w o s)(x) = 7x² - 49x + 33 and (s o w)(x) = (7x - 2)² - 7(7x - 2) + 5
How to determine the composite functions?Composite function 1
The given parameters are
w(x) = 7x - 2
s(x) = x² - 7x + 5
To calculate (w o s)(x), we make use of
(w o s)(x) = w(s(x))
So, we have
(w o s)(x) = 7s(x) - 2
Substitute s(x) = x² - 7x + 5
(w o s)(x) = 7(x² - 7x + 5) - 2
Expand
(w o s)(x) = 7x² - 49x + 35 - 2
Simplify
(w o s)(x) = 7x² - 49x + 33
Composite function 2
Here, we have
w(x) = 7x - 2
s(x) = x² - 7x + 5
To calculate (s o w)(x), we make use of
(s o w)(x) = s(w(x))
So, we have:
(s o w)(x) = w(x)² - 7w(x) + 5
Substitute w(x) = 7x - 2
(s o w)(x) = (7x - 2)² - 7(7x - 2) + 5
So, the composite functions are (w o s)(x) = 7x² - 49x + 33 and (s o w)(x) = (7x - 2)² - 7(7x - 2) + 5
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Create a table of values to represent the equation y = x - 9
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Answer:
Explanation:
Here, we want to create a table of values to represent the given equation
To do this, we need to select a range of values for x
This can be a range of any set of numbers
With respect to this question, we shall be choosing -2 to +2 with an increment of 1
The values of x are thus: -2,-1 , 0, +1 and +2
So, now let us get the corresponding y-values using the equation rule
Now, let us get the y-values
when x = -2
y = -2-9 = -11
when x = -1
y = -1-9 = -10
when x = 0
y = 0-9 = -9
when x = 1
y = 1-9 = -8
when x = 2
y = 2-9 = -7
Thus,we have the table of values as follows:
Solve this system of linear equations. Separatethe x- and y-values with a comma.6x + 20y = -623x - 9y = -12Enter the correct answerDONE
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Given the following systems of linear equations,
6x + 20y = -62 (Equation 1)
3x - 9y = -12 (Equation 2)
Step 1 : Solve 6x+20y=−62 for x:
6x + 20y + (−20y) = −62 + (−20y) (Add -20y to both sides)
6x = −20y −62
6x/6 = (−20y −62)/6 (Divide both sides by 6)
x = (-10y/3) + (-31/3)
Substitute to Equation 2:
3x−9y=−12
3[(-10y/3) + (-31/3)] - 9y = -12
−19y−31=−12 (Simplify both sides of the equation)
−19y−31+31=−12+31 (Add 31 to both sides)
−19y=19
-19y/-19 = 19/-19 (Divide both sides by -19)
y= −1
Step 2: Substitute −1 for y in x =(-10y/3) + (-31/3)
x =(-10(-1)/3) + (-31/3)
x = -7
Answer:
x=−7 and y=−1
Find an equation of the circle having the given center and radius.Center (-3, 3), radius 16
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The equation of a circle is given by the next formula:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where the center is the point (h, k) and r means the radios. Therefore:
[tex]\begin{gathered} (x-(-3))^2+(y-3)^2=(\sqrt[]{6}_{})^2 \\ (x+3)^2+(y-3)^2=6^{} \end{gathered}[/tex]Answer is letter C