give a coordinates of the Vertex y =(x + 2)
.
squared - 1
Given:
The equation of a parabola is:
[tex]y=(x+2)^2-1[/tex]
To find:
The coordinates of the vertex of the given equation.
Solution:
The vertex form of a quadratic function is:
[tex]y=a(x-h)^2+k[/tex] ...(i)
Where, a is a constant and (h,k) is the vertex.
We have,
[tex]y=(x+2)^2-1[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=1[/tex]
[tex]h=-2[/tex]
[tex]k=-1[/tex]
We know that the vertex of the parabola is (h,k).
Therefore, the vertex of the given equation is (-2,-1).
I need help ASAP thank you
Answer:
√9 × √6
√54
√27 × √2
Step-by-step explanation:
We can obtain the answer to the question given above as illustrated below:
3√6
Recall
a√b = √(a×a×b)
Thus,
3√6 = √(3×3×6)
3√6 = √(9 × 6)
Recall
√(a × b) = √a × √b
√(9 × 6) = √9 × √6
Therefore,
3√6 = √9 × √6
Recall
√9 × √6 = √(9 × 6)
√9 × √6 = √54
Thus,
3√6 = √54
Recall
√54 = √(27 × 2)
√54 = √27 × √2
Therefore,
3√6 = √27 × √2
Therefore,
3√6 = √9 × √6 = √54 = √27 × √2
Find the measure of each angle in the problem. TO contains point H.
Answer:
A. 45 and 135
Step-by-step explanation:
Recall: two angles on a straight line forms a linear pair. The pair sum up to 180°.
Thus:
✔️c° + 3c° = 180°
4c = 180
Divide both sides by 4
4c/4 = 180/4
c = 45°
✔️3c = 3(45) (substitution)
= 135°
An employee makes $11.20 per hour but is getting a 6.5% increase. What is his new wage per hour to the nearest cent? His new wage per hour is?
Answer:
11.93
Step-by-step explanation:
First find the amount of increase
11.20 *6.5%
11.20 *.065
0.728
Rounding to the nearest cent
.73
Add this to the original wage
11.20+.73
11.93
find the missing length indicated
Answer:
c = 175
Step-by-step explanation:
When the height of a right triangle is shown this way (at right angles with the hypotenuse, It can be found by using the way the hypotenuse is broken up. The following proportion works.
576/x = x / 49 Cross multiply
x^2 = 576 * 49
sqrt(x^2) = sqrt(576*49)
x = 24 * 7
x = 168
But that's not what you want (although it is close).
What you want is the hypotenuse to the small lower triangle
c = ?
a = 49
b = 168
c^2 = 49^2 + 168^2
c^2 = 2401 + 28224
c^2 = 30625
c = sqrt(30625)
c = 175
To calculate the volume of a chemical produced in a day a chemical manufacturing company uses the following formula below:
[tex]V(x)=[C_1(x)+C_2(x)](H(x))[/tex]
where represents the number of units produced. This means two chemicals are added together to make a new chemical and the resulting chemical is multiplied by the expression for the holding container with respect to the number of units produced. The equations for the two chemicals added together with respect to the number of unit produced are given below:
[tex]C_1(x)=\frac{x}{x+1} , C_2(x)=\frac{2}{x-3}[/tex]
The equation for the holding container with respect to the number of unit produced is given below:
[tex]H(x)=\frac{x^3-9x}{x}[/tex]
a. What rational expression do you get when you combine the two chemicals?
b. What is the simplified equation of ?
c. What would the volume be if 50, 100, or 1000 units are produced in a day?
d. The company needs a volume of 3000 How many units would need to be produced in a day?
Answer:
[tex]V(x) = [\frac{x}{x + 1} + \frac{2}{x-3}] * \frac{x^3 - 9x}{x}[/tex]
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
[tex]V(50) = 2548.17[/tex] [tex]V(100) = 10098.10[/tex] [tex]V(1000) = 999201.78[/tex]
[tex]x = 54.78[/tex]
Step-by-step explanation:
Given
[tex]V(x) = [C_1(x) + C_2(x)](H(x))[/tex]
[tex]C_1(x) = \frac{x}{x+1}[/tex]
[tex]C_1(x) = \frac{2}{x-3}[/tex]
[tex]H(x) = \frac{x^3 - 9x}{x}[/tex]
Solving (a): Expression for V(x)
We have:
[tex]V(x) = [C_1(x) + C_2(x)](H(x))[/tex]
Substitute known values
[tex]V(x) = [\frac{x}{x + 1} + \frac{2}{x-3}] * \frac{x^3 - 9x}{x}[/tex]
Solving (b): Simplify V(x)
We have:
[tex]V(x) = [\frac{x}{x + 1} + \frac{2}{x-3}] * \frac{x^3 - 9x}{x}[/tex]
Solve the expression in bracket
[tex]V(x) = [\frac{x*(x-3) + 2*(x+1)}{(x + 1)(x -3)}] * \frac{x^3 - 9x}{x}[/tex]
[tex]V(x) = [\frac{x^2-3x + 2x+2}{(x + 1)(x -3)}] * \frac{x^3 - 9x}{x}[/tex]
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * \frac{x^3 - 9x}{x}[/tex]
Factor out x
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * \frac{x(x^2 - 9)}{x}[/tex]
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * (x^2 - 9)[/tex]
Express as difference of two squares
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)(x -3)}] * (x- 3)(x + 3)[/tex]
Cancel out x - 3
[tex]V(x) = [\frac{x^2-x+2}{(x + 1)}] *(x + 3)[/tex]
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
Solving (c): V(50), V(100), V(1000)
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
Substitute 50 for x
[tex]V(50) = [\frac{(50^2-50+2)(50 + 3)}{(50 + 1)}][/tex]
[tex]V(50) = \frac{(2452)(53)}{(51)}][/tex]
[tex]V(50) = 2548.17[/tex]
Substitute 100 for x
[tex]V(100) = [\frac{(100^2-100+2)(100 + 3)}{(100 + 1)}][/tex]
[tex]V(100) = \frac{9902)(103)}{(101)}[/tex]
[tex]V(100) = 10098.10[/tex]
Substitute 1000 for x
[tex]V(1000) = [\frac{(1000^2-1000+2)(1000 + 3)}{(1000 + 1)}][/tex]
[tex]V(1000) = [\frac{(999002)(10003)}{(10001)}][/tex]
[tex]V(1000) = 999201.78[/tex]
Solving (d): V(x) = 3000, find x
[tex]V(x) = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
[tex]3000 = [\frac{(x^2-x+2)(x + 3)}{(x + 1)}][/tex]
Cross multiply
[tex]3000(x + 1) = (x^2-x+2)(x + 3)[/tex]
Equate to 0
[tex](x^2-x+2)(x + 3)-3000(x + 1)=0[/tex]
Open brackets
[tex]x^3 - x^2 + 2x + 3x^2 - 3x + 6 - 3000x - 3000 = 0[/tex]
Collect like terms
[tex]x^3 + 3x^2- x^2 + 2x - 3x - 3000x + 6 - 3000 = 0[/tex]
[tex]x^3 + x^2 -3001x -2994 = 0[/tex]
Solve using graphs (see attachment)
[tex]x = -54.783[/tex] or
[tex]x = -0.998[/tex] or
[tex]x = 54.78[/tex]
x can't be negative. So:
[tex]x = 54.78[/tex]
a. 6
b. 10
c. 7
d. 9
Answer:
6
Step-by-step explanation:
21-20 = 1
20-18 =2
18 -15 = 3
15-11 = 4
We are subtracting 1 more each time
11-5 = 6
how do i find the area of a cone when all i get is radius and theta? radius = 5 theta = 52°
Answer:
11.34464...
Step-by-step explanation:
it is not a 3-dimensional cone, it is a 2-dimensional segment of a circle. and you need to find its area.
which is also why you are asked to find the area, because for a 3-dimensional object you would have been asked about the volume of the surface.
now, about a circle and its segments.
you know how to get the area of a circle ?
it is pi×r²
that is for the full circle.
you know how many degrees it is to go "full circle" ?
360 degrees.
so, here we have only a segment of 52 degrees out of the full 360 degrees.
in other words we are dealing with 52/360 = 13/90 of the full circle.
all we have to do is therefore multiply the area of the full circle with that fraction, and we have our result.
pi×r²×13/90 = pi×5²×13/90 = pi×5×13/18 = 11.34464...
A survey showed that out of 600 surgery patients at ABC Medical Center, 8% of them had eye surgery. Find the number of patients that had eye surgery.
Answer:
48
Step-by-step explanation:
.08x600=48
Answer:
Step-by-step explanation:
total patients = 600
% of patients had eye surgery = 8%
Number of patients that had eye surgery ?= x
% of pt that had eye surgery = no. of pt that had surgery/ total number of pt
8/100= x/600
x=(8x600) /100
x= 4800/100
x= 48
Number of patients that had eye surgery were 48
Assume you have a ticket that will let you participate in a game of chance (a lottery) that will pay off $10 with a 45% chance (or a 55% chance of getting nothing). Your friend has a ticket to a different lottery that has a 20% chance of paying $25 (or an 80% chance of paying nothing). Your friend has offered to let you have his ticket if you will give him your ticket plus one dollar.
Required:
Build an influence diagram for this problem.
Solution :
I have a lottery ticket that will pay off $ 10 with a 45% chance and a friend of mine has a chance of 20% by paying off $ 25.
It is based on Double risk dilemma.
Individual --- trade ticket (-1) ----24 (win(25) (0.20))
----- -1 (lose ) (0.80)
----- keep trade -------10 (win 10) (0.45)
----- 0 (lose) (0.55)
Next, solve the decision tree using expected monetary value.
EVM (keep ticket) = 0.45 (10) + 0.55 (0) = $ 4.50
EVM (trade ticket) = 0.20 (24) + 0.80 (-1) = $ 4
Therefore, we keep the ticket and do not trade.
g Kristina Karganova invites 17 relatives to a party: her mother, aunts, uncles, brothers, 1 male cousin, and female cousins. If the chances of any one guest arriving first are equally likely, find the probabilities that the first guest to arrive is as follows. (a) A brother or an uncle (b) A brother or a cousin (c) A brother or her mother (a) The total number of outcomes is nothing and the number of outcomes in the event is nothing.
Answer:
7 / 17 ;
10 / 17 ;
5 / 17
Step-by-step explanation:
Guests :
Mother = 1
Aunts = 3
Uncles = 3
Brothers = 4
Male cousin = 1
Female cousin = 5
_________________
Total guests = 17
Since each of the guests have an equal probability of arrival :
Probability that first guest to arrive :
Brother or uncle :
Number of brothers =4
Number of uncles = 3
P(brother or uncle) = required outcome / Total possible outcomes
Required outcome (number of brothers + uncles) = (4 + 3) = 7
Total possible outcomes = total guests = 17
P(brother or uncle) = 7 / 17
2.)
P(brother or cousin) :
Required outcome = (number of brothers + cousins) = (4 + 1 + 5) = 10
Total possible outcomes = total guests = 17
P(brother or cousin) = 10/17
3.)
P(brother or mother) ;
Required outcome = (number of brothers + mother) = (4+1) = 5
Total possible outcomes = total guests = 17
P(brother or mother) = required outcome / Total possible outcomes = 5 / 17
In the statements below, V is a vector space. Mark each statement true or false. Justily each answer a. The set R is a two-dimensional subspace of R3.Choose the correct answer below O A. False, because R2 is not closed under vector addition. O B. True, because R2 is a plane in R3 Ос. False, because the set R2 is not even a subset of R3 OD. True, because every vector in R2 can be represented by a linear combination of vectors inR3 b. The number of variables in the equation Ax 0 equa's the dimension of Nul A. Choose the correct answer below O A. False, because the number of free variables is equal to the dimension of Nul A. O B. True, because the number of variables in the equation Ax 0 equals O C. True, because the dimension of Nul A equals the largest any solution to O D. False, because the number of plvot columns is equal to the dimension of Nud A. c. A vector space the number of columns in A and the number of columns in A equa's the dimension of Nul A. number of Os in any solution to the equation Ax -b, and the equation Ax- 0 always has the trivial solution, so the number of variables is infinite-dimensional if it is spanned by an infinite set Choose the correct answer below O A. True, because the dimension of a vector space is equal to the number of elements in a set that spans O B. Faise, because a basis for the vector space may O C. True, because the dimension of a vector space number of O D. Faise, because all vector spaces are finite-dimensional. d. If dim Van and it S spans V, then S is a basis of V. Choose the correct answer below. the vector space. have only finitely many elements, which would make the vector space finite-dimensional is the number of vectors in a basis for that vector space, and a vector space spanned by an infinite set has a basis with an infinite number of vect O A. False, because the set S must have less than n elements O B. True, because if a vector space is finite-dimensional, then a set that spans t is a basis of the vector space O C. False, in order for S to be a basis, it must also have n elements O D. True, because if a set spans a vector space, regardiess of the dimension of the vector space, then that setis a basis of the vector spaoe e. The only three-dimensional subspace of R3 is R3 itself. Choose the correct answer below Faise, because False, because any subspaces of R3 which contain three-element vectors are three-dimensional, but most of these most three-dimensional subspaces of R3 are spanned by a linearly dependent set of tree vectors, but R can only be sparned by thre Inearly independent vectors subspaces do not contain all of R
D. True, because any three linearly dependent vectors in R3 span all of R3, so there is no three-dmensional subspace of R' that is not R
Answer:
A. False
B. True
C. False
D. True
Step-by-step explanation:
Only three dimensional subspace for R3 is R3 itself. In a 3 d subspace there are 3 basis vectors which are all linearly independent vectors. Dimension of a vector is number of subspace in that vector. Finite set can generate infinite dimension vector space.
What is the volume of the cone below? radius is 10 and height is 81
Answer:
0.0000033cm^3
Step-by-step explanation:
V=1/3hπr²
r=10
h=81
V=1/3×81×(22÷7)×20^2
V=1/305,208
V=0.0000033cm^3
The temperature in Kansas City varies greatly some days. One day in January, the temperature was 16 degrees but then the temperature decreased by 23 degrees by midnight. What was the temperature at midnight?
Answer:
-7 degrees
Step-by-step explanation:
the temperature was 16 degrees then was the decrease by 23 degrees so subtract 23 from 16 and the answer is -7
Question 5 plz show steps
Answer:
C
Step-by-step explanation:
1 calculate the weight of a dog on the earth and on the moon if it has a mass of 28kg
To solve the problem.
W=m×g
W=28×10
W=280.
The weight of a dog on the surface of earth is 280N.
Answer:
274.68N and 45.36N respectively
Step-by-step explanation:
Weight of any object is the mass in kilograms(kg) multiplied by the gravity in meter per square second(m/s^2). The gravity on earth is 9.81m/s^2 and on moon is 1.62m/s^2...so since the gravity varies the weight of the dog will also vary. The wight on earth would be 28kg multiplied by 9.81m/s^2 which would be 274.68N and the weight on moon would be 28kg multiplied by 1.62m/s^2 which would be 45.36N.
at a basketball game, a vendor sold a combined total of 218 sodas and hotdogs. The number of hotdogs sold was 50 less than the number of soda sold. Find the number of soda sold and the number of hotdogs sold
9514 1404 393
Answer:
134 soda84 hot dogsStep-by-step explanation:
Let s represent the number of sodas sold. Then the number of hot dogs sold is (s-50) and the total is ...
s +(s -50) = 218
2s = 268 . . . . . . . . . add 50
s = 134 . . . . . . . divide by 2
134 sodas were sold; 84 hot dogs were sold.
on average, Jonny can pick 2/3 of the ripe apples on an apple tree in 1/2 an hour .At this rate, how long will it take him to pick all of the ripe apples on his 24 apple trees?
Answer:
18h
Step-by-step explanation:
let the number of ripe apples on a tree be x
2x/3 = 1/2
x = 1/2 ÷ 2/3 = 3/4
time taken for him to pick all the ripe apples from 1 tree = 3/4 h
total amount of time taken = 24 x 3/4 = 18h
One month Kaitlin rented 2 movies and 5 video games for total of $34. The next month she rented 8 movies and 3 video games for total of $51. Find the rental cost of each movie and each video game.
Answer:
A movie is $4.50 and a video game is $5
Step-by-step explanation:
Create a system of equations where m is the cost of each movie and v is the cost of each video game:
2m + 5v = 34
8m + 3v = 51
Solve by elimination by multiplying the top equation by -4:
-8m - 20v = -136
8m + 3v = 51
Add these together and solve for v:
-17v = -85
v = 5
So, a video game is $5. Plug in 5 as v into one of the equations, and solve for m:
2m + 5v = 34
2m + 5(5) = 34
2m + 25 = 34
2m = 9
m = 4.5
A movie is $4.50 and a video game is $5
For the function f(x)=-4•(0.3)^x+1, identify the y-intercept and asymptote.
Y-intercept:
Asymptote:
Answer:
-3; 1
Step-by-step explanation:
y-intercept is when x = 0
y = -4(0.3)^0 + 1
anything to the power of 0 is 1
y = -4(1) + 1
y = -4 + 1
y = -3
The asymptote of an exponential function is the vertical translation which in this case is 1
find the HCF of 20 and 25 by listing all possible factor
Answer:
Check Internet
Step-by-step explanation:
Switch on your laptop, Open the Internet and then type your question there.
Hope this Helped You :D
Two cards are drawn without replacement from a standard deck of 5252 playing cards. What is the probability of choosing a red card for the second card drawn, if the first card, drawn without replacement, was a club
Answer:
The probability is 0.51
Step-by-step explanation:
We want to find the of choosing a red card for the second card drawn, given that the first card drawn without replacement, was a club.
Then we need to assume that the first card drawn was a club, so now we have a deck of 51 cards with:
13 hearts
13 diamonds
13 spades
12 clubs.
Now with this deck, the probability of drawing a red card is equal to the quotient between the number of red cards and the total number of cards in the deck.
We have 26 red cards (13 hearts + 13 diamonds)
And there is a total of 51 cards in the deck, then the probability of drawing a red card now is:
P = 26/51 =0.51
The probability is 0.51
Write an expression for the baseball team’s Purchase.
If the white rod is 1/3, what color is the whole??
Answer:
brown
Step-by-step explanation:
it might be brown because it compelled
HELP ASAP!!
If the circle below is cut from the square of plywood below, how many square inches of plywood would be left over?
Use π = 3.14, and round your answer to the nearest hundredth.
Answer:
13.73 in^2 because the circle's area is 50.27 in^2
Calvin and Jamel each havr cats as pets. Calvin buys cat food in cylindrical can that are 6 centimeters in diameter and 12 centimeters high. Jamel buys cat food in cylindrical can that 12 centimeters in diameter and 6 centimeters high. What is the ratio of the volume of one of Calvin's cans of to the volume of one of Jamel's cans?
Answer:
see below
Step-by-step explanation:
CALVIN
v=[tex]\pi[/tex]× r ² × h
v=3.14 × 3² × 12
v=3.14×9 × 12
v=3.14 × 108
v = 339.12
JAMEL
v=[tex]\pi[/tex] × r ²×h
v=3.14× 6 ² × 6
v=3.14 × 36×6
v=3.14×216
v=678.24
PLEASE HELP NO ONE IS ANSWERING ANY QUESTION I ASK!!!!
Determine if the function f is an exponential function. If so, identify the base. If not, why not? f(x) = 3x + 1
A) This is a polynomial.
B) The base is x + 1.
C) The base is 3.
D) This is not an exponential function because the variable is in the exponent position.
Answer:
sorry in dont know the ans
a recent survey shows that 66% of college students have a cat and 37% have a HBO subscription. Assuming these two events are independent, what is the probability that a randomly selected student has neither a cat nor HBO
Answer:
[tex]P(C'\ and\ H') =0. 2178[/tex]
Step-by-step explanation:
Let
[tex]C \to[/tex] Student with cat
[tex]H \to[/tex] Student has HBO sub
[tex]P(C) = 66\% \\ P(H) = 37\%[/tex]
Required
[tex]P(C'\ and\ H')[/tex]
This is calculated as:
[tex]P(C'\ and\ H') = P(C') * P(H')[/tex]
Using complement rules, we have:
[tex]P(C'\ and\ H') = [1 - P(C)] * [1 - P(H)][/tex]
So, we have:
[tex]P(C'\ and\ H') = [1 - 66\%] * [1 - 37\%][/tex]
[tex]P(C'\ and\ H') = [33\%] * [66\%][/tex]
[tex]P(C'\ and\ H') =0. 2178[/tex]
Teddy wants to taste all of the flavors of ice cream at the mall, one by one. Tasting any one flavor will change the way the next flavor taste after it. The flavors are chocolate, vanilla, strawberry, birthday cake, Rocky Road, and butter pecan. In how many ways can he taste the ice cream.
A. 30
B.120
C. 360
D.720
Answer: (d)
Step-by-step explanation:
Given
There are six flavors of ice-cream that is chocolate, vanilla, strawberry, birthday cake, rocky road, and butter pecan
First ice-cream can be tasted in 6 different ways
Second can be in 5 ways
similarly, remaining in 4, 3, 2 and 1 ways
Total no of ways are [tex]6\times5\times 4\times 3\times 2\times 1=720\ \text{ways}[/tex]
Option (d) is correct.
Consider the functions f and g in the tables below. f(x) = 90x2 + 180x + 92 x y 0 92 1 362 2 812 3 1,442 4 2,252 5 3,242 g(x) = 6x x y 0 1 1 6 2 36 3 216 4 1,296 5 7,776 Which of the following statements is true? A. At approximately x = 4.39, the rate of change of f is equal to the rate of change of g. B. As x increases, the rate of change of g exceeds the rate of change of f. C. As x increases, the rate of change of f exceeds the rate of change of g. D. For every value of x, the rate of change of g exceeds the rate of change of f.
Answer:
As x increases, the rate of change of g exceeds the rate of change of f.
Step-by-step explanation:
Given
[tex]f(x) = 90x^2 + 180x + 92[/tex]
[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4} & {5} & f(x) & {92} & {362} & {812} & {1442} & {2252} & {3242} \ \end{array}[/tex]
[tex]g(x) = 6^x[/tex]
[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4} & {5} & g(x) & {1} & {6} & {36} & {216} & {1296} & {7776} \ \end{array}[/tex]
Required
Which of the options is true?
A. At [tex]x \approx 4.39[/tex], f(x) has the same rate of change as g(x)
Rate of change is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
For f(x)
[tex]f(x) = 90x^2 + 180x + 92[/tex]
[tex]f(4.39) = 90*4.39^2 + 180*4.39 + 92 = 2616.689[/tex]
So, the rate of change is:
[tex]m = \frac{2616.689}{4.39} = 596.06[/tex]
For g(x)
[tex]g(x) = 6^x[/tex]
[tex]g(4.39) = 6^{4.39} = 2606.66[/tex]
So, the rate of change is:
[tex]m = \frac{2606.66}{4.39} = 593.77[/tex]
The rate of change of both functions are not equal at x = 4.39. Hence, (a) is false.
B. Rate of change of g(x) is greater than f(x) with increment in x
Using the formula in (a), we have:
[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4} & {5} & f(x) & {92} & {362} & {812} & {1442} & {2252} & {3242} & m &\infty & 362 & 406 & 480 & 563 &648.4\ \end{array}[/tex]
[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4} & {5} & g(x) & {1} & {6} & {36} & {216} & {1296} & {7776} & m & \infty & 6 & 18 & 72 & 324 & 1555 \ \end{array}[/tex]
From x = 1 to 4, the rate of change of f is greater than the rate of g.
However, from x = 5, the rate of change of g is greater than the rate of f.
This means that (b) is true.
The above table further shows that (c) and (d) are false.
Answer:
Step-by-step explanation:
C
