what are the y values of the equation y = 3x + 4 at x values -1, 0, 1, 2​

The vertex of the parabola of the given quadratic equation is (-5, 1).

The given quadratic equation is y²+4x-2y+21=0.

Rewrite in vertex form and use this form to find the vertex (h,k).

Here, y²-2y=-4x-21

Add 1 to both the sides of an equation, we get

y²-2y+1=-4x-21+1

(y-1)²=-4x-20

(y-1)²= -4(x+5)

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

So, the vertex (-5,1)

Therefore, vertex of the parabola of the given quadratic equation is (-5, 1).

To learn more about the quadratic function visit:

https://brainly.com/question/27918223.

#SPJ1

"Your question is incomplete, probably the complete question/missing part is:"

Complete the square to find the vertex of this parabola.

y²+4x-2y+21=0.

The solution of the given algebraic expression is: ⁷/₁₂ + ⁴/₆q

We are given the algebraic expression as:

¹¹/₁₂ - ¹/₆q + ⁵/₆q - ¹/₃

Combining Like terms gives us:

(¹¹/₁₂ - ¹/₃) + (⁵/₆q - ¹/₆q)

Solving both brackets individually gives us:

((11 - 4)/12) + ⁴/₆q

= ⁷/₁₂ + ⁴/₆q

Thus, we conclude that is the solution of the given algebraic expression problem

Read more about Algebraic Expressions at: https://brainly.com/question/4344214

#SPJ1

This transformation of the polygon ABCD to A'B'C'D' is a by a factor of 2√5.

The coordinates are given as:

First polygon: A (-3, 7), B (-4, 9), C (-7, 9), and D (-4, 5).

Second polygon: A' (3, -4), B'(3, 6), C'(8, 2.8), and D'(7.2, -1.9)

Calculate the distance AB and A'B' using:

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ AB = √ (-4 + 3)² + (9 - 7)²

⇒ AB = √1 + 4

⇒ AB = √5

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ A'B' = √ (3 - 3)² + (6 + 4)²

⇒ A'B' = 10

This gives, Divide A'B' by AB to determine the scale factor (k)

k = 10 / √5

k = 2√5

Hence, this transformation is a by a factor of 2√5

Read more about transformation at:

brainly.com/question/4289712

#SPJ1

Answer:

Reflection and 2

Step-by-step explanation:

for plato

The probability that she will make a basket on or before her last attempt within her average waiting time are 1/8 and 2/8

Probability of an event is a measurement of how likely an event can occur as an outcome of a random experiment;

Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively);

When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%;

Given:

Hannah makes 5 out of 8 attempted free-throws.

Now,

The average waiting time of hannah to make her first basket is 5/8

The probability of hannah making basket at her last attempt is 1/8

The probability of hannah making basket before her last attempt is 2/8

Hence, the probabilty will be 1/8 and 2/8;

Learn more about interpretation of probability here;

https://brainly.com/question/23024246

#SPJ1

The remainder must be 7 when z(x) is divided by x + 4

The equation is given as

z(-4) = 7

The function is represented as

z(x)

This means that

x = -4

So, we add 4 to both sides of the equation

This gives

x + 4 = 0

So, when the equation in interpreted, it means

The remainder when z(x) is divided by x + 4 is  7

Read more about remainder theorem at

https://brainly.com/question/11854141

#SPJ1

The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.

Let's denote the missing terms as A and B.

The given sequence is: 3/k, A, B, 9/2k.

The common difference can be found by subtracting 3/k from A or B. Therefore:

A - 3/k = B - A = 9/2k - B.

To simplify, we can equate the two expressions for the                     common difference:

A - 3/k = 9/2k - B.

Next, we can solve for A and B using this equation.

Adding 3/k to both sides gives:

A = 3/k + 9/2k - B.

Now, we can substitute the value of A into the equation:

3/k + 9/2k - B - 3/k = 9/2k - B.

Simplifying further, we have:

9/2k - 3/k = 9/2k - B.

Cancelling out the common terms, we find:

-3/k = -B.

Multiplying both sides by -1, we get:

3/k = B.

For more such questions on Adjacent numbers:

https://brainly.com/question/28207765

#SPJ8

Answer: The measure of the supplement is 150 degrees. The other angle is 30 degrees.

Step-by-step explanation:

angle: x/5

x+x/5=180

5x+x/5=180

6x/5=180

x=180(5/6)

x=150

Other angle: 150/5=30

or 180-150=30

Answer: plant → grasshopper → spider → frog → lizard → fox → hawk.

This is just one food chain that shows the sider and the lizard in the same foodchain. The frog eats the spider, and the lizard eats the frog.

Step-by-step explanation:

Answer:

x = 41

Step-by-step explanation:

Thus, we can find x by setting (x + 22)°, (2x - 6)°, and x° equal to 180:

(x + 22) + (2x - 6) + x = 180

(x + 2x + x) + (22 - 6) = 180

4x + 16 = 180

4x = 164

x = 41

Thus, x = 41

Check the validity of the answer:

We can check that x = 41 is the correct answer by pluggin in 41 for x in (x + 22)°, (2x - 6)° and x° and seeing whether the sum is 180:

(41 + 22) + (2(41) - 6) + 41 = 180

63 + (82 - 6) + 41 = 180

63 + 76 + 41 = 180

139 + 41 = 180

180 = 180

Thus, our answer is correct.

Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) \(\times\)(x + 1/2)

(y - 6) = -1/4 \(\times\)(x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

For more such answers on coordinates

https://brainly.com/question/30227780

#SPJ8

Answer:

So the greatest common factor 44 and 220 is 44.

Step-by-step explanation:

Answer:

525 foot is the answer

A' - (-1,4)

B' - (-1,8)

C' - (-5,4)

hope this helps

The bolt with diameter 0.47 inch should not go into the package .

In the question ,

it is given that ,

the diameter if the bolt that is on the label of the package = 0.45 inch .

the percent of error that is allowed for the diameter = 4%  

the diameter of the bolt on the production line = 0.47 inch

the diameter of the bot that is allowed = 4% of 0.45 + .45

= 0.04 × 0.45 + 0.45

= 0.018 + 0.45

= 0.468 inch

and the diameter of the bolt given is 0.470 which is greater than 0.468 .

So , the bolt will not go into the package .

Therefore , The bolt with diameter 0.47 inch should not go into the package .

Learn more about Percent here

https://brainly.com/question/22264138

#SPJ1

Answer:

1617.5mm^3

Step-by-step explanation:

The square base with a side length of 10 mm and an overall height of 17.25 mm.

Based on your question, it seems that you have a figure with a square base and a height.

The extent or potential of a rectangular pyramid can be calculated the usage of the formula:

V = (1/3)abH

Where "a" and "b" are the size and width of the rectangular base, and "H" is the top of the pyramid.

Similarly, the floor vicinity of a rectangular pyramid can be calculated the use of the formula:

A = ab + (1/2)P(lateral)

where "P(lateral)" is the perimeter of the lateral face, which can be calculated as the sum of the slant heights of the 4 triangular faces.

The slant top can be calculated the use of the Pythagorean theorem, the place the base of the triangle is one facet of the rectangular base, the top is the top of the pyramid, and the hypotenuse is the slant height.

To provide a relevant answer,

I need to know the type of figure you are referring to (e.g., pyramid, prism). Once you provide that information.

For similar question on square base:

https://brainly.com/question/29918849

#SPJ11

The amount of water tank  with water after 10 minutes will be 4950 liters.

To solve this problem, we need to keep track of the net flow of water into the tank over the course of 10 minutes. The tap filling water adds water to the tank, while the tap emptying water removes water from the tank.

Let's calculate the net flow rate of water per minute:

Flow rate = (filling tap flow rate) - (emptying tap flow rate)

Flow rate = 40 L/min - 25 L/min

Flow rate = 15 L/min

Now, we can calculate the net flow of water over 10 minutes:

Net flow of water = (flow rate) * (time)

Net flow of water = 15 L/min * 10 min

Net flow of water = 150 L

Therefore, over the course of 10 minutes, the net flow of water into the tank is 150 liters.

Initially, the tank had 4800 liters of water. Adding the net flow of water, we can determine the final amount of water in the tank:

Final amount of water = (initial amount of water) + (net flow of water)

Final amount of water = 4800 L + 150 L

Final amount of water = 4950 L

After 10 minutes, there will be 4950 liters of water in the tank.

for similar questions on water tank.

https://brainly.com/question/30723760

#SPJ8

Answer:

133 m^2

Step-by-step explanation:

to find are of a circle it’s r^2 times pi

6^2 x pi

36 pi

113 m^2

Hopes this helps please mark brainliest

Answer:

Answer C is correct

Step-by-step explanation:

The formula to find the area of a circle is:

A = πr²

Here,

r => radius = 6m

Let us find the area of the circle.

A = πr²

A = 3.14 × 6 × 6

A = 113.04 m²

Approx. = 113m²

The statements supported by the data in the table are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

To determine which statements are supported by the data in the table, let's analyze the given information:

The mean number of cars sold in a month is the same at both dealerships.

To calculate the mean, we need to find the average number of cars sold each month at each dealership.

For Admiral Autos:

(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13

For Countywide Cars:

(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13

Since both dealerships have an average of 13 cars sold per month, the statement is supported.

The median number of cars sold in a month is the same at both dealerships.

To find the median, we arrange the numbers in ascending order and select the middle value.

For Admiral Autos: 4, 10, 15, 17, 19

Median = 15

For Countywide Cars: 9, 10, 14, 15, 17

Median = 14

Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.

The total number of cars sold is the same at both dealerships.

To find the total number of cars sold, we sum up the values for each dealership.

For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65

For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65

Since both dealerships sold a total of 65 cars, the statement is supported.

The range of the number of cars sold is the same for both dealerships.

The range is determined by subtracting the lowest value from the highest value.

For Admiral Autos: 19 - 4 = 15

For Countywide Cars: 17 - 9 = 8

Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.

The data for Admiral Autos shows greater variability.

To determine the variability, we can look at the range or consider the differences between each data point and the mean.

As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.

Based on the analysis, the statements supported by the data are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

for such more question on mean

https://brainly.com/question/14532771

#SPJ8

Answer:

The probability of choosing an even number greater than or equal to 4 is;

Explanation:

Given the tiles with the number 1 through 9 are placed in a bag.

The number even numbers that are greater than or equal to 4 is;

The total number from 1 to 9 is;

The probability of choosing an even number greater than or equal to 4 is;

Therefore, the probability of choosing an even number greater than or equal to 4 is;

Answer:

Step-by-step explanation:

-x + 2 = 3x + 6

3x + 6 = -x + 2

4x + 6 =  2

4x = -4

x = -1

y = 1 + 2 = 3

(-1, 3)

The intersection points of lines y = -x + 2 and y = 3x + 6  is (-1, 3). The graph is shown below.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

The given equations of line are,

y = -x + 2              (1)

And y = 3x + 6      (2)

The Slope of the equation (1) is -1.

And to find y intercept substitute x = 0,

y = 2.

The slop of the equation (2) is 3,

And to find y intercept substitute x= 0,

y = 6.

To find the points of intersections, solve equation (1) and (2),

x = -1 and y = 3

The points of intersections are (-1, 3).

The graph of the equations y = -x + 2 and y = 3x + 6 are shown below.

To know more about Equation of line on:

https://brainly.com/question/21511618

#SPJ5

Answer:

What are the number to find the amount I thin you're missing information

Step-by-step explanation:

Answer:

2,315.25

Step-by-step explanation:

9514 1404 393

Answer:

  the correct answer is marked

Step-by-step explanation:

The circle with center (h, k) and radius r has equation ...

  (x -h)² +(y-k)² = r²

For the given center, that is ...

  (x -1)² +(y +1)² = r²

The value of r² can be found by using the given point for x and y, and seeing what value of r² makes the equation true.

  (5 -1)² +(7 +1)² = 4² +8² = 16 +64 = 80

So, r² = 80 makes the equation true, and that equation is ...

  (x -1)² +(y +1)² = 80

The obtained quadratic function has the same stretch factor as the given function and contains the given point is  y = 3x² + 6x - 12

A quadratic function is one of the following: f(x) = ax² + bx + c, where a, b, and c are positive integers and an is not equal to zero. A parabola is a curve that represents the graph of a quadratic function.

Because a quadratic function is indeed a parabolic curve, we use the standard parabola equation.

y = a(x - h)² + k

where a = stretch factor,

h = x-coordinate of vertex and

k = y-coordinate of vertex.

The quadratic function incorporates the point (1, -3) and has the vertex x-coordinate at x = -1. h = -1 is the answer.

It also has the stretch factor of f(x) = 3x². So, a = 3.

Thus, y = a(x - h)² + k

y = 3(x - (-1))² + k

y = 3(x + 1)² + k

Now, because the quadratic function proceeds through (1, -3), we have

y = 3(x + 1)² + k

-3 = 3(1 + 1)² + k

-3 = 3(2)² + k

-3 = 3(4) + k

-3 = 12 + k

k = -3 - 12

k = -15

Similarly, find the value for y.

y = 3(x + 1)² + k

y = 3(x + 1)² - 15

y = 3(x² + 2x + 1) - 15

y = 3x² + 6x + 3 - 15

y = 3x² + 6x - 12

Therefore, the equation of the quadratic function that contains the given point and has the same stretch factor as the given function is y = 3x² + 6x - 12.

To learn more about quadratic functions, here:

brainly.com/question/10606041

#SPJ9

The complete question is-

Write the equation of the quadratic function that contains the given point and has the same stretch factor as the given function.

Contains (1, −3) and has the same stretch factor as

f(x) = 3x².

Vertex has x-coordinate of −1.

Answer:

3.75 lt or 3750 mlts

Step-by-step explanation:

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

0.50n+25=27.50

Step-by-step explanation:

you can ride 5 rides, aka n=5

Step-by-step explanation:

To determine the constant of proportionality (k) in a proportional relationship, we need to compare corresponding values of x and y and calculate the ratio between them.

Let's examine the given values:

2. UX: x 6 15 9 y 42 200

To find the constant of proportionality (k), we can take any pair of corresponding values and calculate their ratio. Let's choose the first pair: (6, 42).

k = y / x

k = 42 / 6

k = 7

So, the constant of proportionality (k) is 7.

Now, let's find the missing values for the second set of values:

d. X: 14 y: 21 6 15 3 7 8

Since we know the constant of proportionality is 7, we can calculate the missing values of y by multiplying each corresponding x value by 7.

Missing values for y:

- For x = 21, y = 21 * 7 = 147

- For x = 6, y = 6 * 7 = 42

- For x = 15, y = 15 * 7 = 105

- For x = 3, y = 3 * 7 = 21

- For x = 7, y = 7 * 7 = 49

- For x = 8, y = 8 * 7 = 56

Therefore, the missing values of y are: 147, 42, 105, 21, 49, and 56.

There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

for such more question on combinations

https://brainly.com/question/28065038

#SPJ8