what is the next pattern? 1, 8, 27, 64? explain your answer.

A function f(x) = -(x+4)^2 + 2 has vertex (-4,2) which is a maximum point and a function g(x) = (x-2)^2 - 2 has vertex (2,-2) which is a minimum point.

In this question we have been given two functions  f(x) = −(x + 4)2 + 2 and g(x) = (x − 2)2 − 2which  have been rewritten using the completing-the-square method.

We need to determine if the vertex for each function is a minimum or a maximum.

We know that, the vertex form of a quadratic function is f(x) = a(x – h)2 + k, where a, h, and k are constants.

The graph of parabola is at (h, k).

So, the vertex of the quadratic function f(x)=-(x+4)^2+2 is (-4,2)

The vertex of quadratic function g(x) =(x-2)^2-2 is vertex (2,-2)

The graph of both the functions is shown below.

A vertex (-4,2) is a maximum point of function f(x) = −(x + 4)2 + 2  and a vertex (2,-2) is a minimum point of function g(x) = (x − 2)2 − 2

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The vertex of the equation is (x, y) = (2, 0). This also makes sense since the equation is a parabola that opens downward, meaning the lowest point is at the vertex.

The function f(x) = −(x + 4)2 + 2 is in vertex form and can be written as:

f(x) = −(x + 4)2 + 2 = −(x + 4)2 + 4 − 2

Using the completing-the-square method, the equation can be rewritten as:

f(x) = −(x + 4)2 + 4 − 2 = −(x + 4)2 + 4 − 4 + 2 = −(x + 4)2 + 4 = −(x + 4 + 2)(x + 4 − 2)

Now, we can determine the vertex of the equation. To do this, we can set the equation equal to 0.

0 = −(x + 4 + 2)(x + 4 − 2)

From this equation, we can solve for x to get the x-coordinate of the vertex.

x = −2

Now, we can plug this x-coordinate into the equation to get the y-coordinate of the vertex.

f(−2) = −(−2 + 4)2 + 4 = 0

Therefore, the vertex of the equation is (x, y) = (−2, 0). Since the y-coordinate of the vertex is 0, this means that the vertex is a minimum. This makes sense since the equation is a parabola that opens downward, meaning the lowest point is at the vertex.

We can use the same method for the function g(x) = (x − 2)2 − 2. First, we can rewrite the equation using the completing-the-square method.

g(x) = (x − 2)2 − 2 = (x − 2)2 − 4 + 2 = (x − 2)2 − 4 = (x − 2 + 2)(x − 2 − 2)

Set the equation equal to 0 and solve for x to get the x-coordinate of the vertex.

0 = (x − 2 + 2)(x − 2 − 2)

x = 2

Plug this x-coordinate into the equation to get the y-coordinate of the vertex.

g(2) = (2 − 2)2 − 4 = 0

Therefore, the vertex of the equation is (x, y) = (2, 0). Since the y-coordinate of the vertex is 0, this means that the vertex is a minimum. This also makes sense since the equation is a parabola that opens downward, meaning the lowest point is at the vertex.

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Step-by-step explanation:

everything can be found in the picture

Answer:

D

Step-by-step explanation:

the hypotenuse is 10 cm one leg is 8 cm and the other leg is 6 cm

Answer:

- 4 hope this helps i think its correct

Step-by-step explanation:

The specific gravity of the combined product is 1.22

Specific gravity is the ratio of the density of a substance to the density of some substance (such as pure water) taken as a standard when both densities are obtained by weighing in air.

Given,

The total quantity of portion= 50 ml

Specific gravities of the three syrups = 1.10,1.25 and 1.32

Then,

The specific gravity of the combined product= \(\frac{1.10+1.25+1.32}{3}\)

= 1.22

Hence, the specific gravity of the combined product is 1.22.

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Answer:

Step-by-step explanation:

1). 17 and 2

17 × 2 = 34 and 17 + 2 = 19

2). 7 and 4

3). 24 and 1

4). ( - 11) and ( - 3)

5). ( - 15) and ( - 2)

6). 22 and 3

Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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Answer:

A=270 in^2

Step-by-step explanation:

A=d1*d2/2 formula for A using the diagonals

A=45*12/2

A=540/2

A=270 in^2

A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line).

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                         Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations whose variables have a power of one are called linear equations. A single variable example with real values for a and b and x as the variable is ax+b = 0.

A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line).

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There is a 6.7 percent probability that you are making a mistake by failing to reject the null hypothesis. Hence, option C is the correct answer to this question.

The p-value is a measure of the evidence against a null hypothesis. A smaller p-value means that there is stronger evidence against the null hypothesis. A common threshold for rejecting the null hypothesis is a p-value of less than 0.05, which corresponds to a confidence level of 95%. In this case, the p-value of 0.067 is greater than 0.05, meaning that there is not enough evidence to reject the null hypothesis and conclude that there is a statistically significant difference between the two experimental groups. Therefore, there is a 6.7% probability that you are making a mistake by failing to reject the null hypothesis, which means that the two experimental groups may be statistically identical.

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The complete question is -

As a statistician, you conducted an experiment and obtained a t-test value for the two experimental groups. At a confidence level of 5 percent, the corresponding statistical p-value of 0.067 would suggest that:

a. The inherent error of the experiment is calculated to be 6.7 percent.

b. There is probably a statistically significant difference between the two groups of interest.

c. There is a 6.7 percent probability that you are making a mistake by failing to reject the null hypothesis.

d. There is a 6.7 percent probability that you are making a mistake in accepting the experimental hypothesis.

e. The two experimental groups are statistically identical.

Answer:

262

Step-by-step explanation:

Answer:

CGF=262

Step-by-step explanation:

it’s A

Answer:

7-(-12)/10-10

19

I hope this is correct.

Answer:

slope is undefined

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (10, - 12) and (x₂, y₂ ) = (10, 7)

m = \(\frac{7+12}{10-10}\) = \(\frac{19}{0}\)

Since division by zero is undefined then the slope of the line is undefined

Answer:well by using the point slope form the answer for the x intercept is 1 and the y intercept is -2 point slope is y-4=2(x-1)

Step-by-step explanation: then you solve for x and y I hope I’m correct

Answer:

Step-by-step explanation:

45/11 miles per day or ~4.091 miles per day

Step-by-step explanation:

3 inches per second

24 hours in a day

60 minutes in 1 hour

60 seconds in 1 minute

Amount of inches per minute: 3 x 60 = 180 inches

Amount of inches per hour: 180 x 60 = 10,800 inches

Amount of inches per day 10,800 x 24 = 259,200 inches

To find the number of feet that 259,200 inches is, divide by 12.

259,200/12 = 21,600 feet per day

To find the number of miles that 21,600 feet is, divide by 5280.

21,600/5280 = 45/11 = 4.09090909091 = ~ 4.091

So, an ant could walk 45/11 miles per day or ~4.091 miles per day if it walked without taking a break.

Answer:

63 miles

Step-by-step explanation:

Bonnie ran a total of 18 miles over the course of 2 track practices. How many miles would Bonnie have run after 7 track practices?

2 track practices = 18 miles

7 track practices = y miles

Cross Multiply

2 track practices × y miles = 18 miles × 7 track practices

y miles = 18 miles × 7 track practices/ 2 track practices

y miles = 63 miles.

Therefore, Bonnie will have run 63 miles after 7 track practices

Answer:

answer is 7.66666 so the answer is between 7 and 8

Step-by-step explanation:

Answer:

\( \frac{7}{15} \)

Step-by-step explanation:

The question is asking us to find the difference between 4/5 and 1/3.

\( \frac{4}{5} - \frac{1}{3} \)

First we have to determine the LCM which is 15.

LCM is obtained by multiplying 5 and 3 from the denominators.

Then proceed as follows

\( \frac{4}{5} - \frac{1}{3} = \frac{12 - 5}{15} \\ = \frac{7}{15} \)

The solution is therefore

\( \frac{7}{15} \)

Answer:

1

Step-by-step explanation:

theyre all even

Answer:

Step-by-step explanation:

Answer: D) subtract one x block from the left side and subtract two numbered blocks from the right side

Step-by-step explanation:

The blood pressure after 40 seconds is approximately 120. The maximum blood pressure is approximately 135, and the minimum blood pressure is approximately -85.

The equation P = 25 sin (2nt) + 110 represents the blood pressure, where P is the blood pressure and t is the time in seconds. To find the blood pressure after 40 seconds, we substitute t = 40 into the equation:

P = 25 sin (2n * 40) + 110

Since the sine function oscillates between -1 and 1, the maximum value for sin (2n * 40) is 1, and the minimum value is -1. Plugging these values into the equation, we have:

P = 25 * 1 + 110

P = 135

Therefore, the blood pressure after 40 seconds is 135.

The maximum and minimum blood pressures can be determined by analyzing the equation. The amplitude of the sine function determines the range of oscillation, which represents the difference between the maximum and minimum values of the blood pressure. In this case, the amplitude is 25.

The maximum blood pressure is found by adding the amplitude to the average blood pressure (110):

Maximum blood pressure = 110 + 25 = 135.

Similarly, the minimum blood pressure is found by subtracting the amplitude from the average blood pressure:

Minimum blood pressure = 110 - 25 = 85.

Therefore, the maximum blood pressure is 135, and the minimum blood pressure is 85.

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Victor met 32 ants on his way back.

To determine how many ants (walking to the tree) does Victor meet on his way back, he must perform the following calculation:

Therefore, Victor met 32 ants on his way back.

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Answer:

32 ants

Step-by-step explanation:

Answer:

06 + 10

Step-by-step explanation:

a2 + b2

(3x2) + (5 x 2)

6 + 10

therefore option A is the correct answer

Answer:

245.04 cm

Step-by-step explanation:

The criteria that we could use to prove the congruency that ΔABC ≅ ΔDEC is;

Vertical Angles are Congruent. We could then use AAS to prove that ΔABC ≅ ΔDEC

There are different triangle congruency postulates namely:

SSS: Side Side Side Congruency Postulate

SAS: Side Angle Side Congruency Postulate

ASA: Angle Side Angle Congruency Postulate

AAS: Angle Angle Side Congruency Postulate

HL: Hypotenuse Leg Congruency Postulate

We want to prove that ΔABC ≅ ΔDEC

Now, from the given image, we see that we are given 2 congruent sides.

However, angle ECD is congruent to angle DCA because they are vertically opposite angles and vertical angles are congruent.

Thus, the triangles are congruent by AAS Congruency postulate.

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In my opinion the answer it either A or C because they make the most sense if you calculate.

Answer:

no

Step-by-step explanation: