Identify the vertex and the axis of symmetry of the graph of the function y=3(x+2)^2-3
we know that
The equation in vertex form of a vertical parabola is of the form
[tex]y=a(x-h)^{2}+k[/tex]
where
[tex](h,k)[/tex] is the vertex of the parabola
and
[tex]x=h[/tex] is the axis of symmetry
if [tex]a > 0[/tex] -----> open upward
if [tex]a < 0[/tex] -----> open downward
In this problem we have
[tex]y=3(x+2)^{2}-3[/tex]
[tex]a=3[/tex]
This is a vertical parabola open upward
The vertex is a minimum
therefore
the answer is
the vertex is the point [tex](-2,-3)[/tex]
the axis of symmetry is [tex]x=-2[/tex]
see the attached figure to better understand the problem
The vertex of the function [tex]y=3{\left({x+2}\right)^2}-3[/tex] is [tex]\boxed{\left({-2,-3}\right)}[/tex].
Further Explanation:
The standard form of the parabola is shown below.
[tex]\boxed{y=a{{\left({x-h}\right)}^2}+k}[/tex]
Here, the parabola has vertex at [tex]\left({h,k}\right)[/tex] and has the symmetry parallel to x-axis and it opens left.
Given:
The quadratic function is [tex]y=3{\left({x+2}\right)^2}-3[/tex].
Calculation:
Compare the [tex]y=3{\left({x+2}\right)^2}-3[/tex] with the general equation of the parabola [tex]\boxed{y=a{{\left({x-h}\right)}^2}+k}[/tex]
.
The value [tex]a[/tex] is [tex]3[/tex], the value of [tex]h[/tex] is [tex]-2[/tex] and the value of [tex]k[/tex] is [tex]-3[/tex].
Therefore, the vertex of the parabola is [tex]\left({-2,-3}\right)[/tex].
The function is symmetric about [tex]x=-2[/tex].
The vertex of the function [tex]y=3{\left({x+2}\right)^2}-3[/tex] is [tex]\boxed{\left({-2,-3}\right)}[/tex].
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Conic sections
Keywords: vertex, symmetry, symmetric, axis, y-axis, x-axis, function, graph, parabola, focus, vertical parabola, upward parabola, downward parabola,
What is 0.3 * 1.3 = ?
Please help me!
Joe wants to saw a wooden plank into 3/4 meter prices the lenght of the wooden plank is 3 3/4 meter how many 3/4 meter prices pieces can joe saw from the wooden plank
3/4xy What are the factors of the expression?
The factors of the given expressions are [tex]\dfrac{3}{4},x,y[/tex].
Given:
The given expression is [tex]\dfrac{3}{4}xy[/tex].
To find:
The factors of the given expression.
Explanation:
Factors of an expression are the terms or expressions whose product is equal to that expression.
We have,
[tex]\dfrac{3}{4}xy[/tex]
Therefore, the factors of the given expressions are [tex]\dfrac{3}{4},x,y[/tex].
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Assume that you select two 3-digit numbers at random from the set of consecutive integers from 000 through 999. The selections are made with replacement and are independent of one another. If the two numbers are the same, you make $700. If they are different, you lose $2. A random variable XX is defined as your gain or loss.
How many different values are possible for the random variable XX
Answer:
the answer is: 2
Step-by-step explanation:
from 000 to 999 makes a total of 1000 numbers from which we are selecting two numbers with replacement. This means that the possible combinations will be double of 1000.
1000 * 1000 = 1000000
to have the same number twice means that the possible combinations will be only 1000. (As there are only 1000 numbers).
But whether they are same or not there will be only two possible values of XX , 2 dollars or 700 dollars which will be the loss or gain for one trial, as the numbers picked will either be same or different.
Tuiton at a certain college recently increased from $4000 to $5000. Find the ratio of the increase in price to the original price.
What is the intersection of plane TUYX and plane VUYZ?
I have attached an image with the diagram and answers.
Answer:
A) UY
Step-by-step explanation:
From the given figure, TUYX is one of the side of the rectangular prism and UVYZ is another side of the rectangular prism.
The both sides are intersecting perpendicular in one edge, that is the line segment UY.
You can see it on the figure.
Therefore, the intersecting line is UY.
Order these numbers from least to greatest.
14325
,
5.753
,
534
,
5.34
What is 200 times 180
Answer:
36000
Step-by-step explanation:
If you multiply 200x180 it equals 36000
A way you can find this out is by writing it down
200
x
180
________
36000
Will the first digit of the quotient of 2589 divided by 4 be in the hundreds or thousands place? Explain how you can decide without finding the quotient.
Actually we can directly check if the quotient has equal or one less amount of places than the given number. This can be checked by looking at the number on the biggest place of the dividend, if it is less than the divisor, the answer will have one less digits place. So in this case since the divisor is 4 and the greatest place of the dividend is thousands and the number is 2, so the quotient will be in the hundreds place.
Hundreds place
Answer:
Step-by-step explanation:Actually we can directly check if the quotient has equal or one less amount of places than the given number. This can be checked by looking at the number on the biggest place of the dividend, if it is less than the divisor, the answer will have one less digits place. So in this case since the divisor is 4 and the greatest place of the dividend is thousands and the number is 2, so the quotient will be in the hundreds place.
Suppose bob uses the rsa cryptosystem with a very large modulus n for which the factorization cannot be found in a reasonable amount of time. suppose alice sends a message to bob by representing each alphabetic character as an integer between 0 and 25 (a s 0, . . . , z s 25), and then encrypting each number separately using rsa with large e and large n. is this method secure? if not, describe the most efficient attack against this encryption method.
The answer is this method is not secure but a frequency attack can be applied. Knowing the public key in this case is, nonetheless, adequate for an attacker to calculate a table, on behalf of one-to-one communication between the plaintext and the cipher text. Computed table allows him/her to decrypt any ciphertext, encoded using RSA Cryptosystem in such a means.
Encrypting each character separately in RSA is insecure due to the limited set of characters and can be compromised by frequency analysis. RSA's security typically relies on the difficulty of factorizing large numbers, but with only 26 character possibilities, patterns can emerge that allow decryption.
When Alice sends a message to Bob using the RSA cryptosystem, each alphabetic character is represented as an integer between 0 and 25 and then encrypted using RSA with a large exponent e and a large modulus n. Although this method uses a robust encryption algorithm, encrypting each character separately can be insecure due to the limited number of possible characters (26 in this case). An efficient attack against this method is a frequency analysis attack, where the attacker could exploit the fact that some letters appear more frequently in a language than others. The attacker could potentially guess the encrypted values of these common characters and use patterns to decrypt the rest of the message.
RSA encryption is one of the oldest and widely used public key encryption algorithms and relies on the difficulty of factoring very large numbers. This difficulty provides the security in RSA; however, when the encryption is done on a small set of possibilities—as is the case with single alphabetic characters—the security can be compromised, making RSA vulnerable in such a scenario.
Break apart and distribute to solve 56/8
Steve is taller than Jon, but Elijah is taller than Steve. Is Elijah taller than Jon?
Find the z-scores that delineate the middle 96% of all values from the others. enter your answers to 2 or 3 decimal places. from to
You have a well-shuffled 52-card deck. on average, how many pairs of adjacent cards are there such that both cards are red?
The average number of pairs of adjacent cards in a well-shuffled 52-card deck that are both red is about 12 or 13 pairs. This is calculated based on the probability of drawing red cards.
Explanation:In a well-shuffled 52-card deck, there are 26 red cards out of the total 52 cards. Thus, the probability of drawing a red card is 26/52 = 0.5.
Now, let's consider two neighboring cards as an ordered pair. There are 51 such pairs in a 52-card deck. We are looking for pairs where both cards are red. The probability that the first card of any given pair is red is 0.5, as already noted. The probability that the next card (in that pair) is also red, assuming the first one is red, is now 25/51 (since one red card is assumed as taken already).
Thus, the probability that a given pair of adjacent cards are both red is 0.5 * (25/51) = 25/102 ≈ 0.245.
Given that we have 51 possible pairs, the expected number of red pairs is 51 * (probability of red pair) which equals about 12.48.
Therefore, on average, you can expect about 12 or 13 pairs of adjacent cards to be both red.
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which sets of numbers represent geometric sequences check all that apply
Given a normal distribution with mu equals 100μ=100 and sigma equals 10 commaσ=10, complete parts (a) through (d). loading... click here to view page 1 of the cumulative standardized normal distribution table. loading... click here to view page 2 of the cumulative standardized normal distribution table.
a. what is the probability that upper x greater than 85x>85? the probability that upper x greater than 85x>85 is nothing.
I believe the parts are:
A. What is the probability that Upper X greater than 95X>95?
B. What is the probability that Upper X less than 75X<75?
C.What is the probability that Upper X less than 85X<85 and Upper X greater than 125X>125?
D. 95% of the values are between what two X-values (symmetrically distributed around the mean)?
Solution:
We use the equation for z score:
z = (X – μ) / σ
Then use the standard normal probability tables to locate for the value of P at indicated z score value.
A. Z = (95 – 100) / 10 = - 0.5
Using the tables, the probability at z = -0.5 using right tailed test is:
P = 0.6915
B. Z = (75 – 100) / 10 = - 2.5
Using the tables, the probability at z = -2.5 using left tailed test is:
P = 0.0062
C. Z = (85 – 100) / 10 = - 1.5
Using the tables, the probability at z = -2.5 using left tailed test is:
P = 0.0668
Z = (125 – 100) / 10 = 2.5
Using the tables, the probability at z = 2.5 using right tailed test is:
P = 0.0062
So the probability that 85<X and X>125 is:
P(total) = 0.0668 + 0.0062
P(total) = 0.073
D. P(left) = 0.025, Z = -1.96
P(right) = 0.975, Z = 1.96
The X’s are calculated using the formula:
X = σz + μ
At Z = -1.96
X = 10 (-1.96) + 100 = 80.4
At Z = 1.96
X = 10 (1.96) + 100 = 119.6
So 95% of the values are between 80.4 and 119.6 (80.4< X <119.6).
find the measure of each marked angle (2x-21) and (x+3)
How many proper subsets are there for each set? {a,b,c}
what is scatterplot ?
A scatter plot is a graph in which the data is plotted on a coordinate grid. The horizontal axis will be the x-axis and the vertical axis will be the y-axis.
how many triangles exist with the given angle measures? 55°, 45°, 90° ?
No Euclidean triangles can have angles that sum to more than 180°, so there are zero triangles with the given measures in Euclidean space; however, exactly one right-angled spherical triangle with these angles exists on a curved surface like a sphere.
The question asks how many triangles exist with the given angle measures of 55°, 45°, and 90°. In Euclidean geometry, the sum of the interior angles of a triangle must equal exactly 180°. Since 55° + 45° + 90° = 190°, which is greater than 180°, no Euclidean triangle can have those angle measures. Therefore, there are zero triangles that can exist with the given angle measures in a flat, two-dimensional Euclidean space.
However, in the context of spherical geometry, triangles can have angles that sum to more than 180°. The provided angles actually describe a right-angled spherical triangle, of which exactly one exists with these measures. This is because on a spherical surface, the sum of the angles of a triangle can be greater than 180° due to the curvature of the space.
A hospital has three independent fire alarm systems, with reliabilities of 0.95, 0.97, and 0.99. in the event of a fire, what is the probability that a warning would be given?
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
The probability that a warning would be given is 0.97.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
A hospital has three independent fire alarm systems, with reliabilities of 0.95, 0.97, and 0.99.
This means,
The probability that one alarm will give a warning = 0.95
The probability that one alarm will give a warning = 0.97
The probability that one alarm will give a warning = 0.99
Combining each of them we get,
0.95 + 0.97 + 0.99 = 2.91
Divide by 3.
= 2.91 / 3
= 0.97
This means,
The probability that a warning would be given is 0.97.
Thus,
The probability that a warning would be given is 0.97.
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how do I solve (7-6i)(-8+3i)?
There are approximately 3.5 million deaths per year in a country express this quantity as deaths per minute
E xex2 + y2 + z2 dv, where e is the portion of the unit ball x2 + y2 + z2 ≤ 1 that lies in the first octant.
The question is asking to evaluate the triple integral of a function over a portion of the unit sphere lying in the first octant. It involves the use of multivariable calculus and spherical coordinates
Explanation:This question is asking to evaluate the triple integral of E xex2 + y2 + z2 dv over the region e, which is the section of the unit sphere x2 + y2 + z2 ≤ 1 within the first octant. Here, dV is the differential volume element, and x, y, and z are the Cartesian coordinates. As the first octant is defined by x ≥ 0, y ≥ 0, and z ≥ 0, we will only need to consider positive values for these variables.
To evaluate the integral, the formula for the volume of the unit sphere in three dimensions x2 + y2 + z2 should be used. Furthermore, as the integral is taken over the first octant, each variable would be bound between 0 and 1.
It is important to note that this is a multivariable calculus problem and involves the concept of integration in spherical coordinates. This topic is typically covered in a college-level calculus course.
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For homework, a student had to complete 54 problems total. If she finished 9 problems in class, what is the ratio of problems she still needs to complete the problems that she already finished?
Answer:
29
Step-by-step explanation:
The perimeter of a rectangle is 16 inches. The equation that represents the perimeter of the rectangle is 2l + 2w = 16, where l represents the length of the rectangle and w represents the width of the rectangle. Which value is possible for the length of the rectangle?
Tyra wants to arrange 32 tiles in equal rows and columns. How many ways could she organize the tiles? List the factors
Choose the equation that represents the graph below: Graph of a line passing through points 0 comma 4 and 3 comma 0 y = −three fourthsx + 4 y = −four thirdsx + 4 y = three fourthsx − 4 y = 4 thirdsx − 4
A music school has budgeted to purchase 3 musical instruments. they plan to purchase a piano costing $4,000, a guitar costing $600, and a drum set costing $750. the mean cost for a piano is $5,000 with a standard deviation of $2,000. the mean cost for a guitar is $550 with a standard deviation of $250. the mean cost for drums is $950 with a standard deviation of $100. (enter your answers to two decimal places.) how many standard deviations above or below the average piano cost is the piano
To solve this, we can use the z statistic. The formula for z score is given as:
z = (x – u) / s
where x is the actual cost = 4000, u is the mean cost = 5000, and s is the standard deviation = 2000
Solving for z:
z = (4000 – 5000) / 2000
z = - 0.5
Therefore the piano cost is only 0.5 standard deviations below the average cost.