GRAPH the parabola.y=-x^2+6Plot 5 points on the parabola: the vertex, two points on the left of the vertex, and two points in the right of the vertex
Answers
Given: The function below
[tex]y=-x^2+6[/tex]To Determine: The graph of the parabola and the vertex
Solution
Determine the vertex
The vertex form of a parabola is
[tex]\begin{gathered} y=a(x-h)^2+k \\ vertex=(h,k) \end{gathered}[/tex][tex]\begin{gathered} h=-\frac{b}{2a} \\ k=f(-\frac{b}{2a}) \end{gathered}[/tex]Note:
[tex]\begin{gathered} If \\ ax^2+bx+c=0 \\ y=-x^2+6 \\ a=-1,b=0,c=6 \end{gathered}[/tex][tex]\begin{gathered} Therefore \\ h=\frac{-(0)}{2\times-1}=0 \\ y=-x^2+6 \\ when,x=0 \\ y=-0^2+6 \\ y=0+6 \\ y=6 \end{gathered}[/tex]The coordinate of the vertex is (0, 6)
Let us take two points on the left
[tex]\begin{gathered} x=-2 \\ y=-(-2)^2+6 \\ y=-4+6 \\ y=2,(-2,2) \\ x=-1 \\ y=-(-1)^2+6 \\ y=-1+6 \\ y=5(-1,5) \end{gathered}[/tex]Let us take two points on the right
[tex]\begin{gathered} x=1 \\ y=-(1)^2+6 \\ y=-1+6 \\ y=5,(1,5) \\ x=2 \\ y=-(2)^2+6 \\ y=-4+6 \\ y=2,(2,2) \end{gathered}[/tex]Let us plot the 5 points as a graph as shown below
Hence, the vertex is (0, 6) and two points on the left of the vertex are (-1,5) and (-2, 2), and two points to the right of the vertex are (1, 5) and (2, 2)
Related Questions
y = -x, where x is the amount of gummy candy in lbs?
Answers
The given equation : y = 5/2 x
For the table we need four set of x & y values:
Substitute x = 0,1,2,3,4 and then solve for y:
Use the value of x and y as a coordinates :
(x,y) = (0,0), (1,2.5), (2,5), (3,7.5), (4,10)
The graph will be :
what's 3 ÷4 [tex]3 \div 4[/tex]what's 3 divided by 4
Answers
put a 0 and a coma since there aint a possible answer
use 4 times 7 and substract it from 30
put another 0 in the factor
use 4 times 5 as the new mulple and see that the residue is equal to 0
PLEASE HELP ME SOLVE THIS PROBLEM,I’ve been trying all morning
Answers
Answer:
Explanation:
Patricia built a shelf to hold her trophies. The shelf can support a maximum of 15 lbs, and her trophies weigh 1.25 lbs each. How many trophies can Patricia place on her shelf? _________
Answers
Let's use a rule of three to solve this:
Thereby,
[tex]\begin{gathered} x=\frac{15}{1.25} \\ \rightarrow x=12 \end{gathered}[/tex]She can place 12 trophies on her shelf
6/x = 7/13Round your answer to the nearest 10th
Answers
Answer:
x = 11.1
Explanation:
We were given that:
[tex]\frac{6}{x}=\frac{7}{13}[/tex]We will solve this simple proportion as shown below:
[tex]\begin{gathered} \frac{6}{x}=\frac{7}{13} \\ \text{Cross multiply, we have:} \\ x\times7=6\times13 \\ 7x=78 \\ \text{Divide both sides by ''7'', we have:} \\ x=\frac{78}{7} \\ x=11.143\approx11.1 \\ x=11.1 \\ \\ \therefore x=11.1(to\text{ the nearest tenth)} \end{gathered}[/tex]Therefore, x equals 11.1
The sum of the ages of nick and Diana is 119 years. 12 years ago nicks age was 4 times Diana’s age. How old is nick now?
Answers
let
Nick age = x
Diana age= y
x + y = 119
12 years ago their age can be represented below
[tex]\begin{gathered} 4(y-12)=x-12 \\ 4y-48=x-12 \\ x-4y=-36 \end{gathered}[/tex][tex]\begin{gathered} x+y=119\ldots\ldots\ldots\ldots...(1) \\ x-4y=-36\ldots\ldots\ldots\ldots......\mathrm{}(2) \\ x=119-y \\ 119-y-4y=-36 \\ -5y=-36-119 \\ -5y=-155 \\ y=\frac{-155}{-5} \\ y=31 \\ x+31=119 \\ x=119-31 \\ x=88 \end{gathered}[/tex]Nick's age= 88
Find the domain of the graphed function. M B. xis all real numbers. C. -9 sxs 5
Answers
Remember the domain of a function is the values of x for which the function is defined (exists)
Notice that if x is less than 0, there's no graph. (Function isn´t defined for x<0)
That little filled ball in the begining of the graph is telling us that the function is defined for 0. If it wasn't, the ball would be empty.
With this info, we can conclude that the function is defined for x equal or greater than 0
Therefore, the domain of the function is:
[tex]x\ge0[/tex](Option A)
B. Find the surface area of the triangular prism. Remember that the surface area includes the areas of all surfaces – the sides and the bases. Carefully organize your work and verify your solution with your teammates. C. Find the volume of the triangular prism. D. Does your method for finding surface area and volume work for other prisms? Find the surface area and volume of a hexagonal prism. Assume that the bases are regular hexagons with side length of 4 inches.
Answers
Answer:
hi
Step-by-step explanation:
bye
Graph the solution set for the inequality in problem 5. Describe what the solution means andhow the number of balloons bought will affect the amount in the budget.
Answers
We have the following information
The cost of each ballon is 0.8
The total cost of ballons =0.8x, This means that the total number of ballons is x
For the inequality below
[tex]0.8x+18.60\le25[/tex]It means that there is a fixed cost of 18.60, and the total cost including the fixed cost shouldn't be more than
sum of sq of -2 and -18
Answers
We have to solve an addition of two numbers. The first one seems to be the square of -2, an the number -18 is the other one.
So we have: (-2)^2 - 18 = 4 -18 = -14
FOR SUM WE ADD
[tex] { (- 2)}^{2} + ( - 18) \\ = 4 - 18 \\ = - 14[/tex]
ATTACHED IS THE SOLUTION
P(A) = 0.65 P(B) = 0.25 P(A or B) = ? *
Answers
0.9
1) Assuming that these Probabilities refer to mutually exclusive events, i.e. there are no common elements from A and B.
2) We can write out:
P(A or B) = P(AUB)
P(AUB) = P(A) + P(B) Plugging into that the given data:
P(AUB) = 0.65 + 0.25
P(AUB) = 0.9
3) Hence, the answer is 0.9
use unit rates to determine the better buy and provide the unit price for your answer. round to the nearest hundredth, if necessary. $17.49 for 20 AA batteries or $42.58 for 48 AA batteries
Answers
Given the cost of some batteries as;
[tex]\begin{gathered} \text{ \$17.49 for 20 AA batteries} \\ \text{or \$42.58 for 48 AA batteries} \end{gathered}[/tex]We can find out which one of the two would be the better buy, using the formula below.
[tex]\text{Unit price =}\frac{Total\text{ cost}}{\text{Number of batteries}}[/tex]For Option A,
[tex]\text{Unit Price = }\frac{17.49}{20}=\text{ \$0.875}[/tex]For Option B
[tex]\text{Unit price =}\frac{42.58}{48}=\text{ \$0.887}[/tex]Answer:
If we compare both options, Option A is the better buy, because the unit price is lower than option B. The unit price for option A is $0.875
two cars leave town at the same time going in opposite directions. One travels at 70 miles per hour in the other travels at 55 miles per hour. And how many hours will they be 250 miles apart?
Answers
Given:
Speed of car A = 70 miles per hour
Speed of car B = 55 miles per hour
Given that they are going in opposite directions, let's find the time it will take them to be 250 miles apart.
Let T represent the number of hours.
Thus, we hae the equation:
70T + 55T = 250
Let's solve for T:
70T + 55T = 250
125T = 250
Divide both sides by 125:
[tex]\begin{gathered} \frac{125T}{125}=\frac{250}{125} \\ \\ T=2 \end{gathered}[/tex]Therefore, it will take both cars 2 hours to be 250 miles apart
ANSWER:
2 hours
Jack conducted a blind taste test on some of his friends in order to determine if organic fruits tasted different than non-organic fruits. Each friend ate one type of fruit. Organic Non-organic 8 9 Apples Peaches 11 9 Blueberries 6 6 What is the probability that a randomly selected friend tasted blueberries or preferred organic? Simplify any fractions.
Answers
Adding up both columns, we can conclude that Jack conducted the blind test with:
[tex]8+11+6+9+9+6=49[/tex]49 friends.
Out of these 49 friends, 12 tasted blueberries and 25 preferred organic. This way, the probability that a randomly selected friend tasted blueberries or preferred organic is:
[tex]\frac{12+25}{49}=\frac{37}{49}\rightarrow0.76[/tex]Or 76%
I need help on this I need to find the restrictions and the rest
Answers
Solution
For this case we have the following:
[tex]\frac{5}{xy}+\frac{7}{2x^2}[/tex]And we can do the following:
[tex]\frac{1}{x}(\frac{5}{y}+\frac{7}{2x})=\frac{1}{x}(\frac{10x+7y}{2xy})=\frac{10x+7y}{2x^2y}[/tex]Then the conditions are:
[tex]x_{}\ne0,y\ne0[/tex]since we cant divide by 0 and for this reason thats the restriction
A sound wave is modeled with the equation y= 1/4 cos 2π/3 θa. Find the period. Explain your method.b. Find the amplitude. Explain your method
Answers
The cosine function is expressed as:
[tex]y=Acos(w\theta)[/tex]Where A is the amplitude and w is the angular frequency.
The period of a wave is given by:
[tex]T=\frac{2\pi}{w}[/tex]We are given the equation:
[tex]y=\frac{1}{4}cos\left(\frac{2\pi}{3}\theta\right?\text{ }[/tex]By comparison, we have:
[tex]A=\frac{1}{4},\text{ }w=\frac{2\pi}{3}[/tex]Calculate the period:
[tex]T=\frac{2\pi}{\frac{2\pi}{3}}=3[/tex]a. The period is T = 3
b. The amplitude is 1/4
A poker hand consisting of 9 cards is dealt from a standard deck of 52 cardsFind the probability that the hand contains exactly 7 face cards. Leave your answer as a reducedfractionThe probability is
Answers
A face card is a card that is a King, a Queen or a Jack. In a standard deck, there is a total of 12 face cards.
Suppose that the first 7 cards we take are faces and the remaining two are not.
The probability of taking a face on the first withdrawal, is 12/52, since there are 12 faces and there is a total of 52 cards.
On the second withdrawal, there are 11 faces remaining, and a total of 51 cards remain. Therefore, the probability of the second card also being a face is 11/51.
On the third withdrawal, the probability of taking a face will be 10/50, and so on:
On the fourth withdrawal, the probability will be 9/49.
On the fifth, 8/48.
On the sixth, 7/47.
On the seventh, 6/46.
The next two withdrawals must not be faces. On the eight withdrawal, a total of 45 cards remain, 5 of them are faces. So, the probability of not taking a face, is 40/45.
On the nineth withdrawal, the probability of not taking a face is 39/44.
The combined probability of all this events happening one after another is the product of the individual probabilities. Therefore, the probability of the hand containing exactly 7 face cards, is:
[tex]\frac{12}{52}\cdot\frac{11}{51}\cdot\frac{10}{50}\cdot\frac{9}{49}\cdot\frac{8}{48}\cdot\frac{7}{47}\cdot\frac{6}{46}\cdot\frac{40}{45}\cdot\frac{39}{44}[/tex]Write each factor as a product of powers of prime numbers:
[tex]=\frac{2^2\cdot3}{2^2\cdot13}\cdot\frac{11}{3\cdot17}\cdot\frac{2\cdot5}{2\cdot5^2}\cdot\frac{3^2}{7^2}\cdot\frac{2^3}{2^4\cdot3}\cdot\frac{7}{47}\cdot\frac{2\cdot3}{2\cdot23}\cdot\frac{2^3\cdot5}{3^2\cdot5}\cdot\frac{3\cdot13}{2^2\cdot11}[/tex]Use the laws of exponents to reduce this expression:
[tex]\begin{gathered} =\frac{2^{10}\cdot3^5\cdot5^2\cdot7\cdot11\cdot13}{2^{10}\cdot3^4\cdot5^3\cdot7^2\cdot11\cdot13\cdot17\cdot23\cdot47} \\ =\frac{3}{5\cdot7\cdot17\cdot23\cdot47} \\ =\frac{3}{643195} \end{gathered}[/tex]Therefore, the probability is:
[tex]\frac{3}{643195}[/tex]If a 50% horizontal scale factor decrease and a 75% vertical scale factor increase were applied to the rectangle above, what would be the new horizontal and vertical measurements? A) horizontal 8 inches; vertical 35 inches B) horizontal 8 inches, vertical 30 inches horizontal 10 inches; vertical 16 inches D) horizontal 12 inches: vertical 28 inches
Answers
We have the following rectangle
We want to calculate the new dimensions by applying the corresponding factors.
First we start with the horizontal side. The initial length of this side is 16. Since we are decreasing by a factor of 50% we must subtract 50% to the original length. We can calculate the 50% by multiplying 16 by 50/100. So we get
[tex]16\text{ - }\frac{50}{100}\cdot16=16\cdot(1\text{ -0.5)=16}\cdot0.5=8[/tex]So the horizontal dimension after scaling is 8.
Now, for the vertical dimension, we are applying a 75% increasing scale factor. So we should add to the original length an 75% extra. To calculate the 75%w e multiply the original length by 75/100. So we get
[tex]20+20\cdot\frac{75}{100}=20\cdot(1+0.75)=20\cdot(1.75)=35[/tex]so the vertical dimension after scaling is 35.
This leads that the correct answer is A.
The area, A, of a square is a function of the length, x, of a side of the square. Which of the following expresses the function, A(x), and the value at x = 2.5?a. A(x)=2x; 5cm^2b.A(x)=4x; 10cm^2c.A(x)=x^2; 6.25cm^2d.A(x)=4x^2; 25cm^2
Answers
We will have that the solution is the following:
[tex]A(x)=x^2;A(2.5)=6.25[/tex]So, the solution would be option C.
Explain why 1 13/7 does not represent a ratio and 1 3/7 : 3/7 does represent a ratio. Then tell how you express 1 3/7 as a ratio.
Answers
It is not a ratio because it should not be expressed as a mixed number
so you can express the mixed number like a fraction
[tex]\begin{gathered} 1\frac{13}{7} \\ \frac{(7\times1)+13}{7} \\ \frac{7+13}{7} \\ \\ =\frac{20}{7} \end{gathered}[/tex]20/7 is a ratio because is a fraction, the division between two numbers
Electric utility poles in the form of right cylinders are made out of wood that costs $29.07 per cubic foot. Calculate the cost of a utility pole with a radius of 0.75 ft and a height of 45 ft. Round your answer to the nearest cent.
Answers
To answer this question we will use the following formula to compute the volume of a cylinder:
[tex]Volume=\pi\times radius^2\times height.[/tex]Substituting radius=0.75ft and height=45ft in the above formula we get:
[tex]Volume=\pi\times(0.75ft)^2\times45ft.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} Volume=\pi\times0.5625ft^2\times45ft \\ =23.3125\pi ft^3\approx79.52156ft^3. \end{gathered}[/tex]Since the wood costs $29.07 per cubic foot, then each utility pole costs:
[tex]\text{\$}29.07\times79.52156.[/tex]Simplifying the above result we get:
[tex]\text{ \$}29.07\times79.52156\approx\text{\$}2311.69.[/tex]Anwer: $2,311.69.
se lanza una moneda y se hace girar una ruleta con tres sesiones iguales etiquetadas como A coma B y C Cuál es la probabilidad de que la moneda salga cara Y y la ruleta caiga C?
Answers
Given a coin and spinner with three equal sections
For the coin, there are head and tail
So, the total outcomes = 2
So, The probability of the coin will come up heads = 1/2
For the spinner , there are 3 equal sections A, B and C
So, the probability of the spinner land on C = 1/3
So, the total probability =
[tex]\frac{1}{2}\cdot\frac{1}{3}=\frac{1}{6}[/tex]So, the answer is : 1/6
For the given parent function, write the equation for g(x), the transformed function of f(x)=|x|, stretched vertically by a factor of 4 and translated up three units Answer Choices A.|4x+3|B.4|x|+3C.4|x+3|
Answers
Explanation
Step 1
Let
x represent the independent variable
stretched vertically by a factor of 4, then
[tex]\begin{gathered} f(x)=\mleft|x\mright| \\ f^{\prime}(x)=4\mleft|x\mright| \end{gathered}[/tex]Step 2
translated up three units
[tex]\begin{gathered} f^{\prime}(x)=4\mleft|x\mright| \\ f^{\doubleprime}(x)=g(x)=4|x|+3 \end{gathered}[/tex]so,the answer is B
(8i)(-3i)(-4i)write the expression as a complex number in standard form
Answers
The given expression is
[tex](8i)(-3i)(-4i)[/tex]Let's multiply
[tex]96i^3=96i[/tex]Hence, the expression is equal to 96i.On the coordinate grid, the graph of y = √√-x - 1 isshown. It is a reflection and translation of y = 3√x.-7-6-5-4-3-2-15 6 7 XF(3)6-LE4لی32--7 ? 1 ?-62 3 4What is the range of the graphed function?O {x 1-2
Answers
ANSWER
C
EXPLANATION
From the given function;
From this graph, you can observe that for everry value of x there will be a corresponding value of y, so that the domain of the graph function is all the real values of X
The outcome X of an experiment has only two possible values, X=4 and X=5. Given that the expected outcome E(X)=4.2, find P(X=5). Give your answer as a decimal.
Answers
Expected Value - is the probability of an event multiplied by the amount of times the event. Therefore,
E(x) = ∑XP(X) and we know that E(x)=4.2
Let's consider
P(X=4)= f and P(X=5)= g
f+g=1 as the sum of the probabilities of all possibilities must equal 1
E=4f + 5g= 4.2 (1)
f +g= 1 (2)
f=1-g - Replacing in equation 2, we have
[tex]\begin{gathered} 4\cdot(1-g)+5g=4.2 \\ 4-4g+5g=4.2 \\ g=0.2 \end{gathered}[/tex]Answer: P(X=5) = 0.2
Assume the pattern continues for the following sequence of tile figures; that is, each tile divided into four tiles in the subsequent figure. Let S(n) be the function giving the total number of tiles in the nth figure. Find a formula for S(n) in terms of n.
Answers
The sequence given can be seen as:
1, 4, 16, .......
From this three terms we notice that the terms of this sequence are obtain by multiplying the previous term by 4, this means that this a geometric sequence.
We know that a geometric series is given by:
[tex]a_n=ar^{n-1}[/tex]where a is the first term and r is the common ratio. In this case the common ratio is 4, then the sequence is:
[tex]a_n=4^{n-1}[/tex]This gives the total number of tiles in the nth figure, then we can rewrite as:
[tex]S(n)=4^{n-1}[/tex]Are 7:3 and 28:12 proportional?
Answers
To find out, you can write the ratios as a fraction and simplify, like this
[tex]\begin{gathered} 7\colon3\text{ }\Leftrightarrow\frac{7}{3} \\ 28\colon12\Leftrightarrow\frac{28}{12} \\ \text{Now simplifying the second ratio} \\ \frac{28}{12}=\frac{4\cdot7}{4\cdot3}=\frac{7}{3} \\ \end{gathered}[/tex]scale factor of 5:2.is the ratio an enlargement or a reduction ?
Answers
If we divide we get
[tex]\frac{5}{2}=2.5[/tex]So, the scale factor is 2.5 which will enlarge the figure since its greater than 1.Natasha is seeding her backyard. the backyard is square in shape and has an area of 4,096 square feet. what is the length of one side of natasha's backyard?
Answers
Natasha's backyard is in the shape of a square and that means the length and the width are the same measurement. The area of a square shape is given as
Area = L x W
OR
Area = L² (since the L is the same as the W, it can as well be writen as L x L which is L²)
If the area of her backyard is given as 4096, then
Area = L²
4096 = L²
Add the square root sign to both sides of the equation
√4096 = L
64 = L
Therefore, one side of Natasha's backyard is 64 feet long
