The graph of the function f(x)= x^2 − 4x + 6 is shown here. What is its axis of symmetry? A. x = 0 B. x = 2 C. x = 6 D. x = -2

Could you take a shot of the full image so I can see the words above because I don't know which row like x or y the start value meant

Answer:

The area of the circle is 12.6 m2

DIVIDE the area of the circle by 2 to find area of the semicircle.

To find the area of the composite figure, ADD the area of the rectangle and the area of the semicircle.

Step-by-step explanation:

Hope this helps

Correct me if this is wrong

Answer:

12.6

Divide

Add

Step-by-step explanation:

Using the elimination method we got the value of x as 3 and the value of y as -4.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

-7x - 2y = -13

  x - 2y = 11  

(-)   (+)     (-)

-7x - x = = -13 - 11

-8x = -24

x = 3

Now,

x - 2y = 11

3 - 2y = 11

3 - 11 = 2y

2y = -8

y = -4

Thus,

The value of x is 3.

The value of y is -4.

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There will be $530.68 in the account at the end of 2 years, if Arianna deposits $500 in an account that pays 3% interest, compounded semiannually.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Principal P = $500

Compounded semi annually n = 2

Time t = 2 years

Interest rate r = 3%

Accrued amount A = ?

First, convert R as a percent to r as a decimal

r = R/100

r = 3/100

r = 0.03

Plug the values into the above formula:

A = P( 1 + r/n )^( n × t )

A = $500( 1 + 0.03/2 )^( 2 × 2 )

A = $500( 1 + 0.015 )^( 4 )

A = $530.68

Therefore, the accrued amount is $530.68.

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Answer:

1. The second number line, the third number line, the first number line.

2.

\(a) \: 1 \frac{7}{8} > \frac{7}{4} \)

\(b) \: \frac{21}{5} = 4 \frac{1}{5} \)

\(c) \frac{13}{4} < 3 \frac{5}{6} \)

Answer:

A . 496 ft²

Step-by-step explanation:

Area = ½ × base × height

= ½ × 62 × 16

=496 ft²

Creating a discussion question, evaluating prospective solutions, and brainstorming and evaluating possible solutions are steps in problem-solving.

What is problem-solving?

Problem-solving is the method of examining, analyzing, and then resolving a difficult issue or situation to reach an effective solution.

Problem-solving usually requires identifying and defining a problem, considering alternative solutions, and picking the best option based on certain criteria.

Below are the steps in problem-solving:

Step 1: Define the Problem

Step 2: Identify the Root Cause of the Problem

Step 3: Develop Alternative Solutions

Step 4: Evaluate and Choose Solutions

Step 5: Implement the Chosen Solution

Step 6: Monitor Progress and Follow-up on the Solution.

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The code of the puzzle is 75.5 which is the sum of all the sides of the missing triangles.

Pythagorean triples are a collection of three positive numbers that fit into the Pythagorean theorem formula, which is written as, a² + b² = c², where a, b, and c are positive integers.

1.

Substitute the known values in the Pythagorean theorem formula, and solve for a:

a² + 8² = 12²

a² + 64 = 144

a² = 144 - 64

a² = 80

a = √80

a = 8.9

Similarly, solve the length of the missing side of the other triangles.

2. The missing side b = 14.5

3. The missing side c = 10.3

4. The missing side a = 18.8

5. The missing side b = 8

6. The missing side c = 15

Now, the sum of all the sides of the missing triangles as:

8.9 + 14.5 + 10.3 + 18.8 + 8 + 15 = 75.5

Thus, the code of the puzzle is 75.5.

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Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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The random process Y(t) is not wide-sense stationary (WSS) because the phase term, ϕ, is uniformly distributed between 0 and π/4. In a WSS process, the statistical properties, such as mean and autocorrelation, should be independent of time.

To determine if the random process Y(t) is wide-sense stationary (WSS), we need to examine its statistical properties. A WSS process has two main characteristics: time-invariance and finite second-order moments.

Let's analyze the given process: Y(t) = A sin(wet + ϕ), where A is the amplitude, ω is the angular frequency, et is the time, and ϕ is uniformly distributed between 0 and π/4.

1. Time-Invariance: A WSS process should exhibit statistical properties that are independent of time. In this case, the phase term ϕ is uniformly distributed between 0 and π/4. As time progresses, the phase term ϕ changes randomly, leading to time-dependent variations in the process Y(t). Therefore, the process is not time-invariant and does not satisfy the first condition for WSS.

2. Finite Second-Order Moments: A WSS process should have finite mean and autocorrelation functions. Let's examine the mean and autocorrelation of Y(t):

Mean: E[Y(t)] = E[A sin(wet + ϕ)] = A E[sin(wet + ϕ)]

Since ϕ is uniformly distributed between 0 and π/4, its expected value is E[ϕ] = (0 + π/4) / 2 = π/8.

E[Y(t)] = A E[sin(wet + ϕ)] = A E[sin(wet + π/8)]

The expected value of sin(wet + π/8) is not zero, and it varies with time. Therefore, the mean of Y(t) is time-dependent, violating the WSS condition.

Autocorrelation: R_Y(t1, t2) = E[Y(t1)Y(t2)] = E[A sin(wet1 + ϕ)A sin(wet2 + ϕ)]

Expanding this expression and taking expectations, we have:

R_Y(t1, t2) = A^2 E[sin(wet1 + ϕ)sin(wet2 + ϕ)]

The product of two sine terms can be expanded using trigonometric identities. The resulting expression will involve cosines and sines of the sum and difference of the angles. Since ϕ is uniformly distributed, these trigonometric terms will also vary with time, making the autocorrelation function time-dependent.

Hence, we can conclude that the random process Y(t) is not wide-sense stationary (WSS) due to the time-dependent phase term ϕ, which violates the time-invariance property required for WSS processes.

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The diameter of a wire significantly impacts its strength, range, and stiffness.

1. Strength: As the diameter of a wire increases, its overall strength improves. A larger cross-sectional area allows the wire to withstand greater forces before breaking. This is because the increased material can distribute force more effectively, resulting in enhanced tensile strength.

2. Range: The diameter of a wire also influences its range or length. Thicker wires tend to have shorter range capabilities compared to thinner wires. As the diameter increases, the weight and stiffness of the wire rise as well, making it harder to extend or coil over long distances. Conversely, thinner wires are more flexible and lightweight, enabling them to cover greater lengths.

3. Stiffness: Lastly, the diameter of a wire impacts its stiffness, which is the resistance of the wire to bending or deformation. With a larger diameter, the stiffness of the wire increases due to the higher amount of material present. This means that it requires more force to bend or change the shape of the wire, resulting in greater rigidity. On the other hand, wires with smaller diameters are more pliable and can easily be bent or manipulated.

In summary, the diameter of a wire plays a crucial role in determining its strength, range, and stiffness. Thicker wires exhibit enhanced strength and stiffness but may have limited range capabilities, while thinner wires are more flexible and suitable for longer distances but may not be as strong or rigid.

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Answer:

(17, -13) (17, 8) --> In this problem, we use the y2-y1 over x2 - x1 formula.

Step-by-step explanation:

Step 1: Plug In--> 8-(-13)

                            17 - 17

Step 2: Simplify: 21

                             0

Answer: Undefined. Vertical line on graph.

Answer: 21

Step-by-step explanation: The first thing you should have noticed is that x is the same for both coordinates; in other words, x=17, which means there's no change and x, and it will therefore be a straight vertical line. From there, you can find the change in y to determine the slope (because slope is rise over run). Since 8-(-13)=21, the slope is 21.

Answer:

= 24.

Step-by-step explanation:

-(-5+(-8))-(-9-2)

= -(-5-8)-(-9-2)

= 5 + 8 + 9 + 2

= 13 + 11

= 24

Answer:

350 miles per week

Step-by-step explanation:

That'd be 70 miles each day for 5 days, or 350 miles per week.

2x2 matrices A and B such that AB = 0 but BA ≠ 0, we need to construct matrices that satisfy these conditions.

Let's consider the following matrices:

A = [1 0]

[0 0]

B = [0 1]

[0 0]

To verify that AB = 0, we multiply matrix A by matrix B:

AB = [1 0] [0 1] = [0 0]

[0 0] [0 0]

As we can see, the product of A and B is a zero matrix, meaning all elements of the resulting matrix are zero. Therefore, AB = 0.

Now, let's calculate BA to check if it is non-zero:

BA = [0 1] [1 0] = [0 1]

[0 0] [0 0]

As we can see, the product of B and A is not a zero matrix. In fact, it is equal to [0 1], which is a non-zero matrix.

Thus, we have found matrices A and B such that AB = 0 but BA ≠ 0. Matrix A has a non-zero entry in the top-left position and zeros elsewhere, while matrix B has a non-zero entry in the top-right position and zeros elsewhere. This arrangement ensures that the product AB results in a zero matrix, while the product BA yields a non-zero matrix.

It's worth noting that this specific example demonstrates the existence of matrices satisfying the given conditions. However, there are many other possible choices for matrices A and B that would fulfill the requirement AB = 0 but BA ≠ 0.

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Answer:

= 1.5 × 10 with the power of 10

Step-by-step explanation:

Answer:

2.9 per second

Step-by-step explanation:

Answer:

The price of rice per gram is 4.50 / 750 = 0.006 dollars per gram.

Step-by-step explanation:

David wants to make 10 servings, where each serving has 75 grams of rice. So, he needs a total of 10 * 75 = 750 grams of rice. the price of rice per gram is 4.50 / 750 = 0.006 dollars per gram.

Answer:

He only added Sundays run

Step-by-step explanation:

Answer:

Pay for 3 and get one off

Step-by-step explanation:

Because you would get more for your bargain. A 20% coupon would be for one. but to buy 3 and get one free, that's a better deal.

(Pls give brainliest)

Answer:

5/16

Step-by-step explanation:

Answer:

The probability that Janet will elect a green marble is that if she shake them up and down. When she puts her hand in she has the move her hand around giving her the chance that she might pick a green marble.

==================================================

Explanation:

Plug in n = 2

f(n) = 2*f(n-1)

f(2) = 2*f(2-1)

f(2) = 2*f(1)

f(2) = 2*1  ............. replace f(1) with 1, since f(1) = 1

f(2) = 2

Do so for n = 3

f(n) = 2*f(n-1)

f(3) = 2*f(3-1)

f(3) = 2*f(2)

f(3) = 2*2  ............. replace f(2) with 2, since f(2) = 2

f(3) = 4

Then replace every copy of n with 4.

f(n) = 2*f(n-1)

f(4) = 2*f(4-1)

f(4) = 2*f(3)

f(4) = 2*4  ............. replace f(3) with 4, since f(3) = 4

f(4) = 8

Repeat for n = 5

f(n) = 2*f(n-1)

f(5) = 2*f(5-1)

f(5) = 2*f(4)

f(5) = 2*8  ............. replace f(4) with 8, since f(4) = 8

f(5) = 16

Then finally n = 6

f(n) = 2*f(n-1)

f(6) = 2*f(6-1)

f(6) = 2*f(5)

f(6) = 2*16  ............. replace f(5) with 16, since f(5) = 16

f(6) = 32

The sequence is 1, 2, 4, 8, 16, 32, ...

This is the sequence of powers of 2. Each new term is found by doubling the previous term.

The closed form equation of this is \(a_n = 2^{n-1}\). Plugging n = 6 into that will lead to \(a_6 = 32\)

Answer:

Step-by-step explanation:

Right angled triangle. To find the missing side use Pythagorean theorem.

Base² + altitude² = hypotenuse²

7² + x² = 23.2²

49 + x² = 538.24

        x² = 538.24 - 49

        x² = 489.24

Take square root,

x =\(\sqrt{489.24}\)

x = 22.1 mm

Answer:

Step-by-step explanation:

(a) and (b) see diagram

(c) you can see from the graph, the purple line hits the parabola twice which is y=6   or k=6

(d)  Solving simultaneously can mean to set equal

6x - x² = k                        >subtract k from both sides

6x - x² - k = 0                  >put in standard form

- x² + 6x - k = 0               >divide both sides by a -1

x² - 6x + k = 0

(e) The new equation is the same as the original equation just flipped (see image)

(f)  The discriminant is the part of the quadratic equation that is under the root. (not sure if they wanted the discriminant of new equation or orginal.  I chose new)

discriminant formula = b² - 4ac

equation:   x² - 6x + 6 = 0            a = 1      b=-6    c = 6

discriminant = b² - 4ac

discriminant= (-6)² - 4(1)(6)

discriminant = 36-24

discriminant = 12

Because the discriminant is positive, if you put it back in to the quadratic equation, you will get 2 real solutions.

Answer:

264

Step-by-step explanation:

The answer is 264. Just add them up. 16+68+77+12+14+53+24.

You could also group them up like this: 16+24+68+12+77+53+14

That equals 264!

Answer:

56a+40b

Step-by-step explanation:

43a plus 13a is 56a, -12b + 52b is 40b, together it's 56a+40b

Answer:

x^1/8 y^8

Step-by-step explanation:

=   x^(1/4 * 1/2) y^(16 * 1/2)   =

Answer:

c=42

s=30

Step-by-step explanation: