Identify the vertex, the axis of symmetry, the maximum or minimum value, and the domain and range of each function.

y= (1/2)(x-3)²-2

The solutions for the given system of equations are:

(3, 0), (-4, 7).

Here we have the system:

x + y = 3

y = x² - 9

To solve this, we can replace the second equation into the first one, so we get:

x + (x² - 9) = 3

Now we can solve this quadratic equation for x, we need to solve:

x² + x - 12 = 0.

The solutions are given by Bhaskara's formula:

\(x = \frac{-1 \pm \sqrt{1^2 - 4*1*(-12)} }{2*1} \\\\x = \frac{-1 \pm 7 }{2}\)

Then the two solutions are:

x = (-1 + 7)/2 = 3

x = (-1 - 7)/2 = -4

To get the y-values correspondent, we can evaluate the linear equation in these two values:

y = 3 - x.

For x = 3:

y = 3 - 3 = 0

For x = -4:

y = 3 + 4 = 7

Then the two solutions are: (3, 0), (-4, 7).

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The capacitance does not depend on the potential difference, the capacitance of the capacitor is the same at t = 0s and all other times. The charge on the capacitor is zero at t = 0s.

When the switch is closed at t = 0s, the capacitor is initially uncharged. The current through the capacitor is zero since there is no voltage difference across it. Consequently, the charge on the capacitor is also zero. This is because, when a capacitor is connected to a circuit, the presence of an electric field causes electrons to move from one plate to the other, resulting in a build of charge on the capacitor. Since the current is zero at t = 0s, electrons do not move, preventing the buildup of charge on the capacitor. Mathematically, this can be explained by considering the electric field inside a capacitor: E = V/d where V is the potential difference between the plates and d is the distance between the plates. Since V = 0 at t = 0s, the electric field is also zero, meaning that no electrons move and the charge on the capacitor is zero.

Furthermore, the capacitance of a capacitor is determined by the equation C = εA/d where ε is the permittivity of the material between the plates, A is the area of the plates, and d is the distance between the plates. Since the capacitance does not depend on the potential difference, the capacitance of the capacitor is the same at t = 0s and all other times. Therefore, the charge on the capacitor is zero at t = 0s.

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Inequality shows a relationship between two numbers or two expressions.

The solution for the inequality is x ≤ -2.

The graph is given below.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

Example:

2x > 4

We have,

x + 7 ≤ 5

Subtract 7 on both sides we get,

x + 7 - 7 ≤ 5 - 7

x ≤ -2

This inequality can be graphed as given below:

x is equal and less than -2.

Thus,

The solution for the inequality is x ≤ -2.

The graph is given below.

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(5x^2-21x-20)/(5x^2-16x-16)

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

(x-5)/(x-4)

x² - 3 x - 54 = x² + 6 x - 9 x - 54 = x ( x + 6 ) - 9 ( x + 6 ) = ( x + 6 ) ( x - 9 )

x² - 18 x + 81 = ( x - 9 )²

x² + 12 x + 36 = ( x + 6 )²

... = ( x + 6 ) · ( x - 9 ) / ( x - 9 )²  * ( x + 6 )² / ( x + 6 ) = ( after cancellation )

=  ( x + 6 )² / ( x - 9 )

After solving the given problem, I’ve been able to get 3(x-2) / 2(x-3) as the simplified form of the given equation. I am hoping that this answer has satisfied your query and it will be able to help you, and if you would like, feel free to ask another question.

If I understand clearly, the expression is

(18st^4/52s^3t)(16s^3/9s^2t)

To simply the expression, we simply have to multiply the constants and reduce the product to the lowest terms and apply the laws on exponents to simplify the variables. So, the answer would be:

8t^2/13s

(40v^2)/(35v^4) / (20v^3)/(5v)

(8)/(7v^2) / (4v^2/1)

(8)/(7v^2) * (1 / 4v^2)

2/(7v^4)

Answer:

1) m= 2

2)a=3

3) t =7

this are the first 3

Answer:

a.  L = 0.5d + 34, and

b.  "Never," or "can't be determined with the information provided."

Step-by-step explanation:

a.  Write an equation for the water level, L, after d days.

L is water level, in feet.  It is rising at a rate of 0.5 ft/day.  The slope of an equation of a straight line (we know it is straight, since the rate of increase is a constant, 0.5 ft/day) would be:

y = mx + b

y = 0.5x + b

x is the number of days, which are set to "d," as per the instructions., and b is the water height at day 0, the start.  In this case, the initial height is 34 feet.  So the equation for predicting future water levels, L, is:

L = 0.5d + 34                                [L = 0.5(ft/day)d + 34(ft)]

b. In how many days will the water level be 26 feet?

The question is asking how many days it will take for the water level to reach 26 feet.  This is odd, since we are only told that the river is rising.  No information was given about timing when the river may begin falling, not the rate at which that will occur.  Based only on the way the question is written, the answer is "Never," or "can't be determined with the information provided."

If the question was phrased "In how many days will the water level reach 42 feet, we can use the equation to find d:

L = 0.5d + 34

42 = 0.5d + 34

0.5d = 8

d = 16 days  

Answer:

she

Step-by-step explanation:

Answer:

A - she

pronounced shee

hope this helps

Answer + Step-by-step explanation:

2x – y + 1 = 0

We know that the graph of a linear equation is a line.

So ,in order to draw it we need to find two points A and B of the line

Afterward, we join A and B to get the graph.

2x – y + 1 = 0

If x = 0 → y = 1 ⇒ A(0 , 1) lie on the line AB (the graph)

If x = 1 → y = 3 ⇒ B(1 , 3) lie on the line AB

Now ,all we have to do is plotting A and B

on the coordinates plane ,then connecting then with a line.

According to the graph (check the attached image) :

If (h,4) ∈ line AB ⇒ h = 3/2

If (1/2 , k) ∈ line AB ⇒ k = 2

Answer:

Step-by-step explanation:

If I found the mean, the answer would be:

3+ 4+4+4+5+6+7+23= 56

56/ 8 = 7

If I found the average value using the median, the answer would be 4.5.

In this set of data, the anomaly is 23 as it is much higher than the other numbers.

The median is more accurate because it find the more ‘central’ number and is not affected as greatly with anomalies whereas the mean is affected greatly with anomalies as it raises the value significantly.

Therefore, the median is better to work out the average in this set of data.

:)

Answer:

slope = - \(\frac{1}{2}\)

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - \(\frac{1}{2}\) x + 3 ← is in slope- intercept form

with slope m = - \(\frac{1}{2}\)

Given : A linear equation in two variables is given to us , which is y = -½ + 3 .

To Find : The slope of the line .

Solution : The given equation to us is y = -½ + 3 . This equation is also similar to form of a equation in slope - intercept form , which is ,

\(\large\boxed{\red{\bf y = mx + c }}\)

Where , m is the slope of the line and c is the y - intercept of the line .

Now , on comparing the equation with the standard form , we have :

Hence the slope of the line is -½.

Answer:

13

Step-by-step explanation:

count across and then down

Using the definition of slope, the points (-2 , 6), (0 , 2), and (1 , 0) are collinear.

Three or more points are said to be collinear if they lie on a single straight line.

To determine whether the given points are collinear, use the definition of slope. The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points.

m = (y2 - y1)/(x2 - x1)

Getting the slope of each pair of points:

(-2 , 6) and (0 , 2)

m = (y2 - y1)/(x2 - x1)

m = (2 - 6)/(0 - -2)

m = -4/2

m = -2

(0 , 2), and (1 , 0)

m = (y2 - y1)/(x2 - x1)

m = (0 - 2)/(1 - 0)

m = -2/1

m = -2

(-2 , 6) and (1 , 0)

m = (y2 - y1)/(x2 - x1)

m = (0 - 6)/(1 - -2)

m = -6/3

m = -2

Since collinear points lies on the same line, the slope of any pair of points should be the same. Since the slopes of each pair of points is equal with each other, then they are collinear.

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Answer:

\(\frac{1}{12}\) Km

Step-by-step explanation:

the area (A) of a square is calculated as

A = s² ( s is the side length )

here A = \(\frac{1}{144}\) , then

s² = \(\frac{1}{144}\) ( take square root of both sides )

s = \(\sqrt{\frac{1}{144} }\) = \(\frac{1}{\sqrt{144} }\) = \(\frac{1}{12}\)

Answer:

side= 1/12 km = 0.083km

Step-by-step explanation:

The formula of area of a square is: A=side²

To get the length of each side, square root each side of the formula as shown below:

√A=√(side)²

√(1/144)=side

side= √(1/144) = 1/12 = 0.083km

A Pentagon

A Dodecagon

A Decagon

Sure hope this helps you

The probability that atleast one students is taking a language class is 0.7

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Let :

Spanish = S ; French = F ; German = G

SnFnG = 3

(SnF) only = 9 - 3 = 6

(SnG) only = 5 - 3 = 2

(FnG) only = 5 - 3 = 2

S only = 28 - (6+3+2) = 17

F only = 21 - (2+3+2) = 14

G only = 12 - (6+3+2) = 1

Student not taking any of the classes are;

(100 - (17+14+1+2+2+6+3))

100 - 45 = 55

Atleast 1 is taking a language class out of 2 selected

The probability that atleast one students is taking a language class :

(45/100 * 55/99) + (55/100 * 45/99) + (45/100 * 44/99)

= 0.7

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Answer:

16 months

Step-by-step explanation:

40k-16.5k=23.5k. 23.5k/1450= A little bit more than 16 months.

Answer: 9 1/8x

Step-by-step explanation:

Answer:

Down below :#

Step-by-step explanation:

The first one is False: reason \(\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\)

\(b^9b^2=b^{9+2}\)

\(=b^{9+2}\)

And then its b^11

Second one is false

Third one is  True

Fourth false

Reason: \(\mathrm{Apply\:exponent\:rule:\:}\left(a^b\right)^c=a^{bc},\:\quad \mathrm{\:assuming\:}a\ge 0\)

\(=b^{6\cdot \:5}\)

fifth one is False

\(\mathrm{Apply\:exponent\:rule:\:}a^0=1,\:\quad \mathrm{\:assuming\:}a\ne \:0\)

That equals 1

:) hope this helps  

The group you wish to generalize your results to is called the population (option b).

In statistical terms, the population refers to the entire set of individuals, items, or elements that possess certain characteristics of interest and from which a sample is drawn.

When conducting research or experiments, it is often not feasible or practical to collect data from the entire population due to factors such as time, cost, and accessibility.

Instead, a smaller subset known as a sample is selected to represent the larger population.

The purpose of sampling is to obtain information about the population by studying a more manageable and representative subset.

The goal is to make inferences and draw conclusions about the population based on the characteristics observed in the sample.

Generalizing the results from a sample to the population involves assuming that the sample is representative and accurately reflects the larger population.

Statistical techniques and methods are used to estimate population parameters, such as means, proportions, or relationships between variables, based on the data collected from the sample.

It is important to recognize that the accuracy of generalizations depends on the quality of the sample and the sampling methods employed. Additionally, sampling error (option c) refers to the variability or discrepancy between sample statistics and population parameters, which is inherent in the process of sampling.

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Answer:

3600

Step-by-step explanation:

125%=4500

5*25%=4500

25%=900

125%-25%=100%

4500-900=3600

The height of the cable is 0.15 meters and 1.35 meters at a point 200 meters and -200.

The given details are: Height of twin towers above road surface = h = 160 meters. Distance between twin towers = d = 800 meters. At the center of the bridge, the cables touch the road surface so the maximum height of the cable will be h. Using the formula for the parabolic cable we get: h(x) = a(x - d/2)(x + d/2). Let's find the value of "a" using the maximum height of the cable at the center of the bridge .i.e., h = a(0 - d/2)(0 + d/2) => h = a(d/2)^2 => a = (4h/d^2)Therefore, h(x) = (4h/d^2)(x - d/2)(x + d/2)We need to find the height of the cables at a point x meters from the center. Therefore, we need to find the value of h(x) when x = ±200 meters from the center of the bridge. h(x) = (4h/d^2)(x - d/2)(x + d/2) => h(x) = (4 × 160)/(800 × 800) (x - 800/2)(x + 800/2)When x = -200,h(-200) = (4 × 160)/(800 × 800) (-200 - 800/2)(-200 + 800/2)= (4 × 160)/(800 × 800) (-1200)(200)h(-200) = 0.15 meters. When x = 200,h(200) = (4 × 160)/(800 × 800) (200 - 800/2)(200 + 800/2)= (4 × 160)/(800 × 800) (-400)(1200)h(200) = 1.35 meters. Hence, the height of the cable is 0.15 meters and 1.35 meters at a point 200 meters and -200 meters from the center of the bridge respectively.

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For this problem, we are given the mean and standard deviation for the height of men. We need to calculate the minimum height to be considered in the top 10% of tallest men, and the maximum height to be considered in the shortest 15% of men.

The first step we need to solve this problem is to calculate the z-score. The z-score can be found by using the following expression:

For the first situation, we want a z-score for the top 10% of tallest men. This means that we need to go on the z-table and find the z-score that represents 90% of probability to the left because this will give us the minimum height to be at the 10% tallest. From the z-table we have:

Now we can use the z-score expression to find the value of x. We have:

The man should be at least 71.85 inches tall to be considered among the 10% of tallest men.

For the second situation, we have something similar. We need to find the maximum height for a man to be considered between the 15% of men. We need to go into the z-table and find the z-score that produces a result close to 0.15. We have:

Now we need to use the z-score expression to determine the height:

In order to be considered among the smallest men, someone needs to be 64.88 inches tall.

Answer: 36x + 68

Step-by-step explanation:

Expanding it, you get:

36x + 72 - 4

= 36x + 68

STEP - BY - STEP EXPLANATION

What to find?

• Surface area of the cylinder.

• Volume of the cylinder.

Given:

Radius = 3.5

Height =14

π is a constant = 3.14

The surface area can be determined using the formula below:

Substitute the values into the formula and simplify.

Hence, the surface area is 384.7 ft²

The volume of the cylinder can be obtained using the formula below:

Substitute the values into the formula and simplify.

Simplify the above.

ANSWER

• Surface area = 384.7 ft²

• Volume = 538.5 ft,³

Answer:

15.56

Step-by-step explanation:

mark brainliest k ty

Step-by-step explanation:

50 - ( 1.95+ 7.50+ 24.99) =

50 - 34.44 = 15.56

Answer:

Greater than.

Step-by-step explanation:

Let the original value be x.

A 50% increase in x is given by

x + 50%x

=> x + 0.5x

=> 1.5x

Followed by a 33 \(\frac{1}{3}\) % decrease in the value gives:

1.5x - 33 \(\frac{1}{3}\) %(1.5x)

=> 1.5x - 0.33(1.5x)

=> 1.5x - 0.495x

=> 1.005x

Since 1.005x is greater than the original value, x, then:

A 50% increase followed by a 33 \(\frac{1}{3}\) % decrease gives a value that is greater than the original.

If lidocaine is injected intra-arterially, it can quickly lead to systemic toxicity. The first signs of toxicity may include circumoral numbness and tongue paresthesia, but these symptoms may be followed by more severe manifestations such as dizziness, seizures, and cardiac arrest.

The systemic effects of lidocaine are dose-dependent, meaning that the higher the dose, the more severe the symptoms.

Lidocaine is a local anesthetic that is commonly used for minor surgical procedures or dental work. It works by blocking the nerve signals that transmit pain to the brain. However, if it is injected into an artery, it can rapidly spread throughout the body and affect other organs, leading to potentially life-threatening complications.

If you suspect that a patient has been injected with lidocaine intra-arterially, it is important to act quickly. The first step is to stop the injection and monitor the patient closely for signs of toxicity. If the patient is experiencing severe symptoms, such as seizures or cardiac arrest, emergency treatment should be initiated immediately. Treatment may include administering medications to counteract the effects of the lidocaine or performing cardio-pulmonary resuscitation (CPR) if necessary.

In conclusion, the first signs of lidocaine toxicity may include circumoral numbness and tongue paresthesia, but more severe symptoms may follow, such as dizziness, seizures, and cardiac arrest. If you suspect that a patient has been injected with lidocaine intra-arterially, it is important to act quickly to prevent potentially life-threatening complications.

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Elements in set A is 7.

Consider the following example: If set A includes the elements, A = a, b, then the correct subset of the provided subset is, a, and b. The set has two components in this case. The formula for calculating the number of appropriate subsets is 2n – 1.

RECALL: The number of proper subsets of a set with nn elements is 2^n-12

N

−1.

Let n = number of elements of the set.$

Then,Then, 2^n-1 = 127

2^n = 127+1

2^n=128

2^n = 2^7

N=7

$The set has 7 elements.

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According to the given information in the question the element in set A is  7.

Consider the following example: If set A includes the elements, A = a, b, then the correct subset of the provided subset is, a, and b. The set has two components in this case. The formula for calculating the number of appropriate subsets is 2n – 1.

RECALL: The number of proper subsets of a set with nn elements is 2^n-12

N

−1.

Let n = number of elements of the set.$

Then, Then, 2^n-1 = 127

2^n = 127+1

2^n=128

2^n = 2^7

N=7

$The set has 7 elements.

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The company's profit if there are no price increases is $120.

We have,

The problem provides a function P(x) that models the profit of a natural sponge company.

The function takes as input the number of $0.15 increases in the price of each sponge, denoted by x.

When the value of x is 0, it means that there are no price increases, and therefore the initial price of each sponge is unchanged.

Now,

If there are no price increases, then the value of x in the function P(x) is 0, since x represents the number of price increases.

Substituting x = 0 into the function, we get.

P(0) = -0.1(0)^2 + 15(0) + 120 = 120

Therefore,

The company's profit if there are no price increases is $120.

We can also see this from the graph of the function, which starts at (0, 120) and represents the profit when there are no price increases.

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