graphing a parabola of the form y=ax squared 2
Answers
The graph of the parabola given by the equation:
[tex]y=\frac{1}{4}x^2[/tex]has a vertex when y=0 which happens iff
[tex]\begin{gathered} \frac{1}{4}x^2=0 \\ x^2=0 \\ x=0 \end{gathered}[/tex]Therefore the graph is:
The vertex has coordinates (0,0). Now, two points to the left of the vertex that are on the parabola have coordinates (-2,1) and (-4,4). Two points that are to the right of the parabola have coordinates
Related Questions
Given the equation y = 1.3* Growth a. Does this equation represent growth or decay? 1.3 b. What is the growth or decay factor? e. What is the rate of growth or decay? d. What is the initial value?
Answers
Answer:
a. Growth
b. 1.3
c. 30%
d. 1
Explanation:
The exponential equation given can be written in the form
[tex]y=1.3^x=1(1.3)^x[/tex]From this form, we see that
a. the function represents a growth since 1.3 > 1
b. the growth factor is 1.3
c. The rate of growth is (1.3 - 1) * 100% = 30%
d. the initial value is 1.
Hence, the answers
a. Growth
b. 1.3
c. 30%
d. 1
List the odd counting numbers between 4 and 14
Answers
ANSWER
[tex]5,7,9,11,13[/tex]EXPLANATION
We want to list the odd counting numbers between 4 and 14.
Odd numbers are numbers that are not divisible by 2 and counting numbers are natural numbers.
Therefore, odd counting numbers between 4 and 14 are:
[tex]5,7,9,11,13[/tex]That is the answer.
Find the area under the graph of f(x) = e-2ln(x) on the interval [1, 2]. (2 points)0.51.52.3331.75
Answers
Explanation:
To solve the question, we will need to re-express the given function as follow:
[tex]f(x)=e^{-2\ln (x)}[/tex]Will become
[tex]f(x)=e^{-2\ln (x)}=e^{\ln x^{-2}}[/tex]Thus
[tex]f(x)=e^{\ln x^{-2}}=x^{-2}[/tex]This simply means that we will find the area under the curve:
[tex]f(x)=x^{-2}\text{ within the interval \lbrack{}1,2\rbrack}[/tex]Thus
The area will be
[tex]\int ^2_1f(x)dx=\int ^2_1x^{-2}dx[/tex]This will then be
[tex]\lbrack\frac{x^{-2+1}}{-2+1}\rbrack^2_1=\lbrack\frac{x^{-1}}{-1}\rbrack^2_1[/tex]This will be simplified to give
[tex]-\lbrack\frac{1}{x}\rbrack^2_1=-\lbrack(\frac{1}{2})-(\frac{1}{1})\rbrack=-1\lbrack-\frac{1}{2}\rbrack=\frac{1}{2}[/tex]Therefore, the area under the curve will be
[tex]\frac{1}{2}=0.5[/tex]Thus, the answer is 0.5
Number of balls madeHow many games had 11 or fewer balls made?
Answers
The number of games that had 11 or fewer balls made = 6
Explanations:The number of games that have 11 or fewer balls made will be the number of games that have between 0 to 11 balls made.
Number of games that had 0-3 balls made = 0
Number of games that had 4 - 7 balls made = 1
Number of games that had 8-11 balls made = 5
The number of games that had 11 or fewer balls made = (Number of games that had 0-3 balls made) + (Number of games that had 4-7 balls made) + (Number of games that had 8-11 balls made)
The number of games that had 11 or fewer balls made = 0 + 1 + 5
The number of games that had 11 or fewer balls made = 6
Answer:
6
Step-by-step explanation:
Suppose a charity received a donation of $17.3 million. If this represents 41% of the charity's donated funds, what is the total amount of its donated funds? Round your answer to the nearest million dollars.
Answers
Using the concept of percentage, the total amount that was donated to charity is $42.195 million.
What is meant by percentage?A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics. The abbreviation used to represent percentages is the symbol "%". A% has neither a recognized unit of measurement nor any dimensions. Take this as an example: There will be 50 men in the class if there are 100 students total and there are 50 men in the class. There are 250 male students overall, or 250 out of 500.
According to the data, the charity got a donation of $17.3 million, or 41% of its total donations.
Let x serve as a symbol for the total sum.
This will be shown as follows:
41% × x = $17.3million
0.41x = $17.3 million
Divide by 0.41
x = $17.3million / 0.41
x = $42.195 million
The total amount that is donated to charity is $42.195 million
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How would you write the equation for the following sentence: 3 hot dogs and 4 sodas cost $20. * Do not put spaces or dollar signs in your answer. Your answer
Answers
3h + 4s = 20
1) Let's write an equation for that, calling hot dogs by h and sodas by s.
3h + 4s = 20
Note that in this equation we are relating prices, of hot dogs and sodas and the total cost of them. Similar reasoning is used to set a linear system of equations.
The function g is graphed below. At what numbers in the interval (-4,4) is g discontinuous?
Answers
The graph has discontinuity if the curve or the line is not continuous.
From the graph shown, The graph stopped at (-1, 0) and then starts again at (-1, 4), stopped again at (3, 2)
then gone with (3, 3) and continues up to (4, -2)
So graph g discontinuous at -1 and 3
The side lengths of a triangle are shownbelow. How many other triangles with thesemeasurements could be made?A. None just this unique triangleB. Two trianglesC. Many triangles84 mm96 mm60 mm
Answers
Given the side lengths of some triangle:
[tex]\begin{gathered} L_1=84 \\ L_2=96 \\ L_3=60 \end{gathered}[/tex]Let us suppose that there exists another triangle with these side lengths:
[tex]\begin{gathered} L_1^{\prime}=84 \\ L_2^{\prime}=96 \\ L_3^{\prime}=60 \end{gathered}[/tex]Based on these, we can say that:
[tex]\begin{gathered} L_1\cong L_1^{\prime} \\ L_2\cong L^{\prime}_2 \\ L_3\cong L^{\prime}_3 \end{gathered}[/tex]Then, using the Side-side-side theorem, we conclude that both triangles are congruent, so this triangle is unique
kenji mixes 1/5 clay soil with 1/8 bale of straw to make an Adobe brick how much soil will he need to use the whole bale of straw.
Answers
Clay soil = 1/5
bale of straw = 1/8
Clay soil needed = x
Bale of straw needed = 1
Clay soil : Bale of straw (rate)
1/5 : 1/8 = x : 1
1/5 ÷ 1/8 = x / 1
1/5 × 8/1 = x / 1
8/5 = x / 1
Cross product
8 * 1 = 5 * x
8 = 5x
Divide both sides by 5
x = 8/5
what is the volume of a sphere with a radius of 3.3m rounded to the nearest tenth in cubic meters
Answers
For this exercise you need to use the following formula for calculate the volume of a sphere:
[tex]V=\frac{4}{3}\pi r^3[/tex]Where "r" is the radius of the sphere.
In this case you can identify that:
[tex]r=3.3m[/tex]Then, you can substitute this value into the formula:
[tex]V=\frac{4}{3}\pi(3.3m)^3[/tex]Finally, evaluating, you get that the volume of the sphere (rounded to the nearest tenth in cubic meters) is:
[tex]V\approx150.5m^3[/tex]The answer is:
[tex]V\approx150.5m^3[/tex]were would he be at in 6 seconds
Answers
6 seconds later we can say that dwyane was running to the left of zero, because if he was running at 4 meters per second to the right when he passed the zero point, hence 6 seconds later he was on the left of the zero at the point -2.
6.Find the volume of the cone in terms of PiA cone with a radius of 10 in and a height of 12 in.a 800pi in ³b 2007pi in ³c 4007pi in^3d 600 in ³
Answers
Explanation
We are told to find the volume of a cone with a radius of 10 inches and a height of 12 inches
To do so, we will use the formula
[tex]Volume=\frac{1}{3}\times\pi\times r^2\times h[/tex][tex]\begin{gathered} where \\ radius=r=10inches \\ height=h=12inches \end{gathered}[/tex]Thus, the volume will be
[tex]Volume=\frac{1}{3}\times\pi\times10^2\times12=\frac{100\times12}{3}\times\pi=400\pi\text{ in}^3[/tex]use the information to answer the following questionsmr. ramirez purchased 20 concert tickets for a total of $225.the concert tickets cost $15 for adults and $10 for children under the age of 12 part A: write a system of equations to represent the given scenario. use the variables "a" for adults and "c" for children.
Answers
Answer:
a + c = 20
15a + 10c = 225
Explanation:
If 'a' is the number of tickets for adults and 'c' is the number of tickets for children, we can write the following equation:
a + c = 20
Because Mr. Ramirez purchased a total of 20 concert tickets.
In the same way, if the cost of the tickets is $15 for adults and $10 for children, we can write the following equation:
15a + 10c = 225
Because 15a is the total cost for adults, 10c is the total cost for children and 225 is the total cost in general.
Therefore, the system of equations that represents the given scenario is:
a + c = 20
15a + 10c = 225
Given the card is a club, what is the probability a card drawn at random will be a(n)…12.8?13.10 or ace?
Answers
A standard deck has 52 cards, there are four suits in the deck, "clubs", "diamonds", "hearts", and "spades". There are 13 ranks in each suit.
You know that the card drawn at random is a club. This means that there are 13 possible outcomes: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, and K.
→ You have to determine the probability of drawing an "8" given that the card is a club. There is only one 8 of clubs between the 13 cards of the suite, the probability is equal to the number of successes divided by the total number of outcomes:
[tex]P(8|Club)=\frac{1}{13}[/tex]→ You have to determine the probability of drawing a 10 or an ace, given that the card is a club. Once again, since you know that the card's suit is a club, you have to calculate the probability considering the 13 ranks that conform to the suit.
The events "drawing the 10 of clubs" and "drawing the ace of clubs" are mutually exclusive, which means that the probability of the union between both events is equal to the sum of their individual probabilities:
[tex]P((10|Club)\cup(Ace|Club))=P(10|Club)+P(Ace|Club)[/tex]There is only one 10 within the 13 ranks of the suit, the probability can be expressed as follows:
[tex]P(10|Club)=\frac{1}{13}[/tex]You can calculate the probability of drawing the Ace of Clubs using the same logic:
[tex]P(Ace|Club)=\frac{1}{13}[/tex]Now you can calculate the union between both events:
[tex]\begin{gathered} P((10|Club)\cup(Ace|Club))=P(10|Club)+P(Ace|Club) \\ P((10|Club)\cup(Ace|Club))=\frac{1}{13}+\frac{1}{13} \\ P((10|Club)\cup(Ace|Club))=\frac{2}{13} \end{gathered}[/tex]The period of a pendulum is the time the pendulum
Answers
The period of the pendulum is 11.11 seconds.
EXPLANATION
From the given equation,
L= 0.81t² -----------------------------------------(1)
But L= 100 feet
Substitute the value of L into equation (1)
That is;
100 = 0.81t²
Divide both-side of the equation by 0.81
[tex]\frac{\cancel{0.81}t^2}{\cancel{0.81}}=\frac{100}{0.81}[/tex][tex]t^2=123.45679[/tex]Take the square root of both-side of the equation.
[tex]t\approx11.11[/tex]T= 11.11 seconds.
Hence, the period of the pendulum is 11.11 seconds.
Can anyone help me pls this is my last grade for algebra and Ik failing the class right now I need this grade to be able to pass my class pls help
Answers
For every room added, the price increase is $50, therefore the slope is equal to 50.
Since the value for one room is $125 and we know that each room costs $50, then the y-intercept is the value for 1 room minus 50.
[tex]b=125-50=75[/tex]Now we can create the function for this situation:
[tex]f(x)=50\cdot x+75[/tex]Where f(x) is the price and x is the number of rooms to be cleaned. Since the function is linear, the unit rate is equal to the slope, so the unit rate is 50.
The amount charged to drive to the client's home is the fixed part of the price, so it is equal to the y-intercept. The price is $75.
To find the cost of 8 rooms we need to make x = 8 and calculate the value of the expression.
[tex]f(8)=50\cdot8+75=475[/tex]The value would be $475.
what is the maximum number of turns in the graph of this functuion f(x) x^4-x^3+3x+1
Answers
As given by the question
There are given that the function
[tex]f(x)=x^4-x^3+3x+1[/tex]Now,
By the defination, a polynomial of n degree, has a maximum turning points of:
[tex]n-1[/tex]Therefore, if you have the polynomial given in the problem, which is a polynomial of degree 4, that means (n=4).
The maximum number of turns can be obtained as following:
[tex]\begin{gathered} n-1=4-1 \\ =3 \end{gathered}[/tex]Hence, the maximum number of turns in the graph is 3.
Benchmark estimate of 6.34 + 3.95
Answers
The value of 6.34 + 3.95 using benchmarks estimating is 10.
BenchmarksBenchmarks to estimate means rounding to the nearest whole number
Step 1: If the value after decimal is 5 or more than round off it to successive whole number other wise round off it to preceding whole number
Step 2: We need to round 6.34 and 3.95 to the nearest whole number
6.34 will be rounded to 6.
3.95 will be rounded to 4.
Since we have gotten the rounded number to be 6 and 4 then;
Benchmark estimate = 6 + 4
= 10
Therefore, Benchmark estimate 6.34 + 3.95 =10.
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Find the height of the cone. Round to the nearest hundredth, if necessary. Show your work.
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The height of the cone is 6.16 inches
Explanation:Given:
diameter of the cone = 4 inches
Angle BAC = 72°
To find:
the height of the cone
To determine the height of the cone, we will use the right-angled triangle formed in the cone:
Diameter = 2(radius)
radius = diameter/2
radius = 4/2
radius = 2 inches
Height = BC
To get the height, we will apply the tan ratio (TOA):
[tex]tan\text{ 72\degree = }\frac{opposite}{adjacent}[/tex][tex]\begin{gathered} tan\text{ 72\degree = }\frac{BC}{2} \\ BC\text{ = 2\lparen tan 72\degree \rparen} \\ BC\text{ = 2\lparen3.0777\rparen} \end{gathered}[/tex][tex]\begin{gathered} BC\text{ = 6.1554} \\ \\ The\text{ height of the cone is 6.16 in} \end{gathered}[/tex]A 17-1b bag of Zollipops is $120.00. Connecticut 3 sales tax is 6.35% and Missouri's is 4.225%. How much more sales tax does a customer in Connecticut pay for the bag than one in Missouri?
Answers
step 1
Find out how much is the sales tax in Connecticut
we have
6.35%=6.35/100=0.0635
Multiply by $120.00
120.00*(0.0635)=$7.62
step 2
Find out how much is the sales tax in Missouri
we have
4.225%=4.225/100=0.04225
Multiply by $120.00
120.00*(0.04225)=$5.07
step 3
Find the difference
so
7.62-5.07=$2.55
therefore
the answer is $2.55Name two planes that intersect in VR in the figure to the right.
Answers
Answer:
(C)plane VWS and plane RQU.
Explanation:
Consider Rectangle RQUV and RVWS.
They share a common edge which is VR.
Therefore, the planes that intersect in VR are plane VWS and plane RQU.
The correct choice is C.
The Jordan family budgeted 16% of their disposable annual income of $44,000 for food, but found they needed $35 more per week. How much of their income should now beadded to their food budget?$1,587.00$1,820.00$1,924.00$2,042.00None of these choices are correct.
Answers
Given:
The percentage of income budgeted for food, R=16%.
The income of the family, I=$44,000.
The extra amount for food needed per week, x=$35.
The amount budgeted by the family for food in an year is,
[tex]\begin{gathered} A=\frac{R}{100}\times I \\ =\frac{16}{100}\times44000 \\ =7040 \end{gathered}[/tex]There are 365 days in an year and 7 days in a week.
The number of weeks per year is,
[tex]N=\frac{365}{7}[/tex]The extra amount added by the family for food is,
[tex]\begin{gathered} A_w=xN \\ =35\times\frac{365}{7} \\ =1825 \end{gathered}[/tex]Hence, the family should add $1825 to their food budget.
So, none of these choices are correct.
I need to find the solution to 5x-2 divided by 6
Answers
Given:
[tex](5x-2)\div6[/tex]To find:
Solve the given expression.
Explanation:
Rewrite the given expression,
[tex]\frac{5x-2}{6}[/tex]Expand the fraction into 2 simpler fractions with common denominator 6,
[tex]\frac{5x}{6}+\frac{-2}{6}[/tex]Simplify the expression, we will get:
[tex]\frac{5}{6}x-\frac{1}{3}[/tex]Final answer:
Hence, the required solution is:
[tex]\frac{5}{6}x-\frac{1}{3}[/tex]
Greatest common factor of 9 and 11
Answers
Answer:
1
Step-by-step explanation:
Since, 1 is the only common factor between 9 and 11. The Greatest Common Factor of 9 and 11 is 1.
Good morning can someone help me with my math
Answers
Part A
Angles 1 and 2 (<1 and <2 ) are alternate angles
Alternate angles are angles that are in opposite positions relative to a transversal intersecting two lines
Therefore < 1 and < 2 are equal
Part B
AC and BD are Arc angles
AC = 2 x < 1
BD = 2 x < 2
Since < 1 and < 2 are equal
Then AC = BD
Part C
Parallel lines AB and BC will intercept the AC and BD arcs
2. Noelle always leaves a tip of between 10% and 15% for the stylist when she gets her hair done. This can be represented by thesystem of inequalities shown below, where y is the amount of tip and x is the cost of the hair service. Which of the following isa true statement?y > 0.12y < 0.15%O When the cost of the hair service, x, is $75 the amount of tip, y, must be between $11.25 and $15.O When the cost of the hair service, x, is $50 the amount of tip, y, must be between $5 and $7.50.When the tip, y, is $15, the cost of the hair service, x, must be between $50 and $75.aWhen the tip, y, is $10, the cost of the hair service, x, must be between $100 and $150.
Answers
Substituting with x = 75 into the inequalities, we get:
y > 0.1*75
y > 7.5
y < 0.15*75
y < 11.25
Substituting with x = 50 into the inequalities, we get:
can someone help with algebra 2?
Answers
The given function is
[tex]f(x)=\begin{cases}\frac{1}{3}x+1\colon x<-2 \\ x-3\colon-1\leq x<2 \\ 3\colon x\ge2\end{cases}[/tex]A piecewise function is a function that behaves differently on each interval. In this case, we have three intervals with three different behaviors, so let's graph each of them.
First part. 1/3x + 1.We have to find coordinated points for the values x = -4 and x = -3. To do so, we have to evaluate the expression for each value.
[tex]\begin{gathered} \frac{1}{3}\cdot(-4)+1=-\frac{4}{3}+1=\frac{-4+3}{3}=-\frac{1}{3} \\ \frac{1}{3}\cdot(-3)+1=-1+1=0 \end{gathered}[/tex]So we have two points for the first expression: (-4, -1/3) and (-3, 0).
Second part. x - 3.Let's evaluate the expression for x = -1 and x = 0.
[tex]\begin{gathered} -1-3=-4 \\ 0-3=-3 \end{gathered}[/tex]The points are (-1, -4) and (0, -3).
For the third part, we don't have to evaluate any expression because the function, in that interval, is a horizontal line.
Now, we just have to graph all the points on the same coordinated plane, as the image below shows.
What are the domain and range of the function f of x is equal to the quantity x squared plus 6x plus 8 end quantity divided by the quantity x plus 4 end quantity?
A. D: {x ∊ ℝ | x ≠ 4}; R: {y ∊ ℝ | y ≠ 0}
B. D: {x ∊ ℝ | x ≠ −4}; R: {y ∊ ℝ | y ≠ −2}
C. D: {x ∊ ℝ | x ≠ 4}; R: {y ∊ ℝ | y ≠ 2}
D. D: {x ∊ ℝ | x ≠ −2}; R: {y ∊ ℝ | y ≠ 0}
Answers
The domain and range of [tex]f(x) = \frac{x^{2}+ 6x+8}{x+4}[/tex] is D: {x ∊ ℝ | x ≠ −4}; R: {y ∊ ℝ | y ≠ −2} .
The domain of a function f(x) is set of the value of x for which it is defied and Range of function is set of values f takes .
The rational number [tex]f(x) = \frac{p(x)}{q(x)}[/tex] where p(x) and q(x) are polynomial in terms of x and q(x) ≠ 0 . The domain of rational number is set of values that do not cause denominator equal to zero .
The given function is :
[tex]f(x) = \frac{x^{2}+ 6x+8}{x+4}[/tex]
we need to find domain and range of function,
For domain put denominator equals to zero
x+4 = 0
x = -4
so, domain is every real number except number making it zero
domain = (-∞,-4)∪(-4,∞) and x ≠ -4
For range ,factoring numerator
x²+6x+8 = x²+2x+4x+8
x(x+2)+4(x+2) = (x+4)(x+2)
Putting numerator back,
[tex]f(x) = \frac{(x+4)(x+2)}{x+4}[/tex]
Cancelling factor (x+4) from numerator and denominator
[tex]f(x) = x+2[/tex]
Putting x+2 = 0
[tex]x +2 = 0\\x = -2[/tex]
range = (-∞,-2)∪(-2,∞) and f(x) ≠ -2
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D: {x ∊ ℝ | x ≠ −4}; R: {y ∊ ℝ | y ≠ −2}
I took the test
Make use of structure. For rectangle ABCD, two vertices are A(-2, 3) and B(4, 6). Find the slopes of BC, CD, and DA. Explain your answer.
Answers
We are given a rectangle ABCD
A(-2, 3)
B(4, 6)
We are asked to find the slopes of sides BC, CD, and DA.
Let me first draw a rectangle to better understand the problem
Recall that the slope is given by
[tex]m=\frac{y_2−y_1}{ x_2−x_1}[/tex][tex]\text{where}(x_1,y_1)=(-2,3)\text{and}(x_2,y_2)=(4,6)[/tex]So the slope of side AB is
[tex]m_{AB}=\frac{6-3}{4-(-2)}=\frac{3}{4+2}=\frac{3}{6}=\frac{1}{2}=0.5[/tex]The sides BC and DA are perpenducluar to the side AB.
So their slopes will be
[tex]m_{BC}=m_{DA}=\frac{1}{-m_{AB}}[/tex]Substituting the value of slope of AB
[tex]m_{BC}=m_{DA}=\frac{1}{-0.5}=-2[/tex]The side CD is parallel to the side AB.
Parallel sides have equal slopes so
[tex]m_{CD}=m_{AB}=\frac{1}{2}[/tex]Therefore, the slopes of the rectangle ABCD are
[tex]\begin{gathered} m_{AB}=m_{CD}=\frac{1}{2} \\ m_{BC}=m_{DA}=-2 \end{gathered}[/tex]Each month a shopkeeper spends 5X + 14 dollars on rent and electricity . If he spends 3X -7 dollars on rent how much does he spend on electricity? use pencil and paper for each values of X is the amount the shopkeeper spends on electricity less than 100? explain how you found the values 
Answers
The values of x is x<39.5.
Given that the shopkeeper spends on rent and electricity is = 5x+14
Spending of shopkeeper on rent = 3x-7
So shopkeeper spends on electricity = (5x+14) - (3x-7) = 2x+21
Given that amount the shopkeeper spends on electricity less than 100.
So suitable inequality,
2x+21 < 100
2x < 100-21
2x < 79
x < 39.5
All the values of x<39.5.
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