Write the standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point. Use a graphing utility to verify your result.
Vertex: (3, 1); Point: (5, −7)

Option D and E are equivalent to the given expression.

First we find the x and y values of the equation -2y+3/2x+7/4.

For example x= 0, substitute:

-2y+3/2x+7/4=0

-2y=-7/4

y=7/8

For example y=0, substitute:

-2y+3/2x+7/4=0

3/2x=-7/4

x=-7/6

Then we look for choices A, B, C, D and E, which one produces x=-7/6 and y=7/8 if for example x=0 and y=0.

And those that have the same value are equations D and E.

Equivalent equations are systems of equations that have the same solutions. Identifying and solving equivalent equations is a valuable skill, not only in algebra class, but also in everyday life.

The simplest example of an equivalent equation doesn't have any variables.

For example, these three equations are equivalent to each other:

3 + 2 = 5

4 + 1 = 5 5 + 0 = 5

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The value of a geometric sequence can not be zero, because for that we have to include 0 as a term in it and that will turn the sequence into zero.

A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

In geometric sequences, the terms given by the ratio of every two successive terms is a constant. they can be either negative or positive but not zero, because if any term will be zero it will directly make the common ratio equal to 0, that will make the sequence turning to  0, and it won't be a geometric progression anymore, therefore, the successive values of a geometric sequence could become infinitesimally small but never be equal to 0.

An example of a Geometric sequence is 2, 4, 8, 16, 32, 64, …, where the common ratio is 2.

If suppose 2nd term is 0, then common ratio = 0/2 = 0, that will disturb the pattern and the sequence will not be a GP

Hence, the successive values of a geometric sequence could become infinitesimally small but never be equal to 0.

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Answer:

Step-by-step explanation:

1/10 = 0.1

4/5 = 0.8

What's halfway between 1 and 8?

Let's show it on a number line:

             ¬                                                                                        ¬

_0____1____2_____3______4_____5____6_____7_____8__________

It's 4 and 5, therefore it's 4.5

0.45 comes halfway through 1/10 and 4/5

Expressed as a fraction: 45/100 = 9/20

Hope that helps! Please make me brainliest!

Answer: 0.45

Step-by-step explanation:

Answer:

multiply the big number

Step-by-step explanation:

multiply it theres ur answer sub to Lil-Jrplayz for more help

The sides h of the similar triangle is 2√6 units.

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.

The triangles are similar. Therefore, the side h can be found using the proportion of the sides.

using proportion,

6 / h = h / 4

cross multiply

6 × 4 = h²

h² = 24

square root both sides of the equation

h = √24

h = 2√6

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The value of x from the given figure is 10.

According to the theorem, the product of the measurements of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment if two secant segments are drawn to a circle from an exterior point.

Applying the rule to the given diagram:

3(3+x-5) = 4(4+x-8)

Simplify

3(x-2) = 4(x-4)

3x - 6 = 4x - 16

3x - 4x = -16 + 6

-x = -10

x = 10

Hence the value of x from the diagram is 10

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Answer: Given that a, b, and c form an arithmetic sequence, so they are equally spaced, meaning the difference between each of them is constant. Let's denote the common difference between a, b, and c as d.

So, we have:

a = b - d

c = b + d

Using these two equations, we can prove that 2^a, 2^b, and 2^c form a geometric sequence.

We have:

2^a = 2^b / 2^d

2^c = 2^b * 2^d

Since the product of two powers of the same base is equivalent to the power of the base with the sum of the exponents, we have:

2^a * 2^c = 2^b * 2^b * 2^d * 2^d = 2^(b+b+d+d) = 2^(2b+2d)

So, we have:

2^a * 2^c = 2^(2b+2d) = 2^(2b) * 2^(2d) = 2^b * 2^b * 2^d * 2^d = 2^b * 2^c

This means that 2^a, 2^b, and 2^c form a geometric sequence, with the common ratio of 2^d.

Step-by-step explanation:

The partial fraction decomposition of 2x-5 over x(x-4) is 2/x + 5/x-4. This separates the fraction into two simple fractions with a common denominator.

2x-5 = (2/x) + (5/x-4)

By breaking down the expression into two simpler fractions, we can more easily manipulate the equation and solve for the unknowns. It is an important tool when it comes to solving complex polynomials and equations.

Partial fraction decomposition is a technique used to break down a complex fraction into simpler fractions with a common denominator. This makes the equation easier to manipulate, and can be used to solve polynomials and equations.

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Anwser:

Its B

Explanation

A/x + B/x+4

Answer:

y=4,x= -1

Step-by-step explanation:

2y-3 =y+1

2y-y=1+3

y=4

∆CBD

2x+7=2y-3

2x+7=5

2x= 5-7

2x= -2

x= -1

Answer: Let's call the rainfall in the second half of the month "x".

From the first half of the month, we know that the total rainfall was 1/5 inch.

At the end of the month, we know that the total rainfall was 1/2 inch:

1/5 + x = 1/2

Subtracting 1/5 from both sides:

x = 1/2 - 1/5

x = 3/10

So the rainfall in the second half of the month was 3/10 of an inch.

Step-by-step explanation:

The number of observations will always be the same as the sample size. Therefore, the answer is A.

What is permutation ?

In mathematics and statistics, a permutation refers to a way of arranging a set of objects in a particular order. More specifically, a permutation is an arrangement of a set of distinct objects in a specific order. For example, if we have the set {1, 2, 3}, there are six possible permutations: {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, and {3, 2, 1}.

In permutations, the order of elements matters, which means that changing the order of any of the elements will result in a different permutation. Permutations are used in many areas of mathematics and statistics, including combinatorics, probability theory, and group theory. They are also used in computer science and cryptography for generating random sequences and encryption keys.

According to given conditions:

The number of observations refers to the number of data points or cases that you have in your dataset. For example, if you're collecting data on the heights of people in a certain population, each person's height measurement would be considered one observation.

A sample size, on the other hand, refers to the number of observations that you have included in your sample from the larger population. For example, if you're taking a random sample of 100 people from a population of 10,000, your sample size would be 100.

The number of elements typically refers to the number of individual items or units that you're measuring or counting. For example, if you're counting the number of cars in a parking lot, the number of elements would be the total number of cars.

The number of variables refers to the number of characteristics or attributes that you're measuring for each observation. For example, if you're collecting data on people's heights, weights, and ages, you would have three variables.

Finally, the population size refers to the total number of individuals or units in the population that you're interested in studying. This may or may not be relevant depending on the type of analysis you're doing. If you're conducting a sample survey, for example, the population size would be important to determine the appropriate sample size.

The number of observations will always be the same as the sample size. Therefore, the answer is A.

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The volume of the cylinder with a diameter of 14 mm and a height of 8 mm is approximately 1230.88 mm³.

The volume of a cylinder can be calculated using the formula:

V = πr²h

where r is the radius of the cylinder and h is its height. To find the volume, we first need to find the radius, which is half of the diameter:

r = 14 mm / 2

= 7 mm

Now that we have the radius, we can plug it into the formula along with the height to find the volume:

V = π * (7 mm)² * 8 mm

= 3.14 * 49 * 8 mm³

= 1230.88 mm³

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Answer:

Explanation:

A function has each x input go to exactly one and only one y output. This means something like (3,7) and (3,6) leads to "not a function". The input x = 3 leads to multiple outputs.

So all we have to do is look at the x coordinates of the points. If we see any repeats, then the answer is "not a function". Otherwise, we have a function.

Answer:

1.not function

2. function

3.not function

4.function

The number Joe is thinking of is -36.

To find the number Joe is thinking of, use algebraic expression and equation.

Let x be the number Joe is thinking of

According to the problem, "Eleven more than one third of the number is -1". We can translate this into an algebraic expression such as:

x/3 + 11 = -1

To find the value of x, we'll isolate it on one side of the equation:

x/3 = -12

Next, we'll multiply both sides of the equation by 3 to cancel out the fraction:

x = -36

Therefore, the number Joe is thinking of is -36.

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Answer: figure 1 is 9

figure 2 is 81

figure 3 is 72

= 162

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

2 multiplied by 2 is 4. You have 2 of the 2's so it becomes 4.

Answer:4

Step-by-step explanation:

have a good day :)

Answer:

Just use reflection, rotation, and translation.

Step-by-step explanation:

Reflection is when something is reflected in an opposite direction.

Rotation is when motion rotates in either a 90 or 180 degree flip.

Lastly is translation in which an object can move up or down.

Simply apply these rules with the purpose of making the objects slide into each other and unite as one or 'coincide'. Hope this helps!

u^3 + 8 factors as (u + 2)(u^2 + 2u + 4) is explained by kuta software infinite algebra as

x^3 + 125

To factor this expression, we can use the formula for the difference of cubes:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

We can set a = x and b = 5:

x^3 + 125 = (x + 5)(x^2 - 5x + 25)

So x^3 + 125 factors as (x + 5)(x^2 - 5x + 25).

a^3 + 64

To factor this expression, we can use the formula for the sum of cubes:

a^3 + b^3 = (a + b)(a^2 + ab + b^2)

We can set a = a and b = 4:

a^3 + 64 = (a + 4)(a^2 + 4a + 16)

So a^3 + 64 factors as (a + 4)(a^2 + 4a + 16).

x^3 - 64

To factor this expression, we can use the formula for the difference of cubes:

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

We can set a = x and b = 4:

x^3 - 64 = (x - 4)(x^2 + 4x + 16)

So x^3 - 64 factors as (x - 4)(x^2 + 4x + 16).

u^3 + 8

To factor this expression, we can use the formula for the sum of cubes:

a^3 + b^3 = (a + b)(a^2 + ab + b^2)

We can set a = u and b = 2:

u^3 + 8 = (u + 2)(u^2 + 2u + 4)

So u^3 + 8 factors as (u + 2)(u^2 + 2u + 4).

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Since the length of the string is not specified, we cannot find the Y value (fret position) exactly.

Given in this word problem:

Length of the string: Not specified

Number of notes higher than the root note: 3 (G note is 3 notes higher than the E string's root note)

Scale: Not specified

The equation for the fret position can be represented as follows:

fret position = length of string * 2^(-12 * n)

where n is the number of notes higher than the root note.

To find the X value, we need to know the length of the string, which is not specified in the problem.

To find the Y value, we need to calculate the fret position using the equation:

fret position = length of string * 2^(-12 * n)

fret position = length of string * 2^(-12 * 3)

fret position = length of string * 2^-36

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The correct option regarding the final solution in the Second World War is given as follows:

Germany's plan to exterminate all the Jewish people in Europe.

The final solution in the Second World War was Germany's plan to exterminate all the Jewish people in Europe.

Initially, when Hitler took power in 1933, Jewish people lost their possessions and were sent to concentration camps in following years, initially to work as slaves. However, in 1941, the decision was made to exterminate Europe's Jewish Population, which was called the final solution.

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Lauren spent a total of 10 hours on the duties if he spent 1 3/8 hour cleaning, 7/8 hour doing laundry, and 1 5/8 cooking dinner.

A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.

Here,

To find the total time Lauren spent on the tasks, we need to add the time she spent cleaning the house, doing the laundry, and preparing food.

Cleaning the house: 1 3/8 hours

Doing the laundry: 7/8 hours

Preparing food: 1 5/8 hours

Adding these three quantities, we get:

1 3/8 + 7/8 + 1 5/8 = 1 3/8 + 7/8 + (2 3/8)

Next, we simplify each fraction by finding a common denominator of 8:

(18/8) + (7/8) + (28/8) = 1 + 7 + 2 = 10

So, Lauren spent a total of 10 hours on the tasks if he spent 1 3/8 hour cleaning the house, 7/8 hour doing the laundry, and 1 5/8 preparing food.

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Answer:

E

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

note that n! = n(n - 1)(n - 2) ..... × 3 × 2 × 1

using n = 8 and r = 3 in the combination formula

[tex]\frac{8!}{3!(8-3)!}[/tex]

= [tex]\frac{8(7)(6)(5)(4)(3)(2)(1)}{3(2)(1)5!}[/tex] ← cancel 5! on denominator with 5(4)(3)(2)(1) on numerator

= [tex]\frac{8(7)(6)}{3(2)(1)}[/tex]

= [tex]\frac{56(6)}{6}[/tex] ← cancel 6 on numerator/ denominator

= 56

Answer:

$27/month

Step-by-step explanation:

300-220=80

100%= 300

1%= 300÷100

= 3

10%= 3×10

= 30

300-30=270

270÷10= $27

The distribution was skewed or had other non-normal characteristics, it would be more difficult to make a definitive statement about the probability of paying less than $7,700 without additional information.

The probability distribution of a variable that is normally distributed is bell-shaped, with the majority of observations centred around the mean and decreasingly more observations as you travel away from the mean. The mean and standard deviation of the variable influence the shape of the distribution.

We may use the characteristics of the normal distribution to calculate the likelihood that a person would pay less than $7700 in taxes if we assume that the variable in question is normally distributed. To perform this computation, we would need to know the variable's mean and standard deviation.

For instance, if we were aware that the average tax paid by individuals was $10,000 with a $2,000 standard deviation, we could use a calculator or table of the standard normal distribution to estimate the likelihood that a person would pay less than $7,700. As $7,700 is more than two standard deviations below the mean, if the distribution were totally normal, we could argue that it would be exceedingly unusual for an individual to pay less than that amount. Without more information, it would be more challenging to make a firm determination regarding the likelihood of paying less than $7,700 if the distribution was skewed or had other non-normal characteristics.

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By substituting the linear equations, we know that the value of x and y are -2 and -8 respectively.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Ax+By=C is the usual form for two-variable linear equations.

A standard form linear equation is, for instance, 2x+3y=5.

When an equation is given in this format, finding both intercepts is rather simple (x and y).

So, we have the equation:

y=4x ...(1)

x+y=-10 ...(2)

Now, substitute y = 4x in equation (2):

x+y=-10

x+4x=-10

5x = -10

x = -10/5

x = -2

Then, substitute x = -2 in equation (1):
y = 4x

y = 4(-2)

y = -8

Therefore, by substituting the linear equations, we know that the value of x and y are -2 and -8 respectively.

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Answer:

The missing measure is: 71

Step-by-step explanation:

Hope it helps! =D