Last PreCalc Question, Need help with writing piecewise functions with graphs. Giving brainliest!

The center and the radius of the circle (x – 2)²+ (y + 1)² = 5 are

(2, -1) and √5, respectively.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.

And the general formula of the circle,

(x – h)²+ (y - k)² = r²,

where (h, k) is the center and r is the radius of the circle.

Given:

The equation of the circle,

(x – 2)²+ (y + 1)² = 5.

And the general formula of the circle,

(x – h)²+ (y - k)² = r²,

where (h, k) is the center and r is the radius of the circle.

Comparing the equations, we get,

h = 2 and k = -1 and r = √5

That means,

the center = (2, -1) and the radius = √5

Therefore, the center = (2, -1) and the radius = √5.

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The correct answer is Michelle makes a quarter turn to her right and Rebecca makes a three eight turn to her left.

Speed is the rate of change of position. It is the physical quantity that measures how quickly an object moves from one place to another. It is measured in units such as meters per second, kilometers per hour, or miles per hour. Speed is related to velocity, which is the measurement of how quickly an object moves in a specific direction. Speed is an important concept in physics and is necessary for understanding how the universe works.

Michelle makes a quarter turn to her right and Rebecca makes a three eight turn to her left. By making these turns, they will both end up facing north. A quarter turn to the right is the same as a three eight turn to the left. This is because a full turn is 360 degrees, so a quarter turn is 90 degrees and a three eight turn is also 90 degrees.

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Qualitative with 2 possible outcomes of variable is required to construct a confidence interval for a population proportion.

The goal of qualitative research is to collect and analyze non-numerical (descriptive) data in order to comprehend people's attitudes, beliefs, and motivations in relation to their social reality. In-depth interviews, focus groups, or observations are frequently used in this kind of study to gather the information that is rich in context and detail.

To investigate complicated phenomena or to learn more about people's viewpoints and experiences on a certain subject, qualitative research is frequently used. It is especially helpful for academics who wish to comprehend the meaning that individuals attribute to their experiences or who want to identify the fundamental causes of people's conduct. Ethnography, grounded theory, discourse analysis, and interpretative phenomenological analysis are examples of qualitative approaches.

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Therefore , the solution to the given problem of quadratic equation comes out to be real.

The quadratic equation x ax2+bx+c=0 is a non - linear regression model in a single variable. a 0. According to the First Theorem of Algebra, this polynomial has at least single solution because it is of second order. There could be simple or complex solutions. A four-variable equation is referred to as a quadratic equation. This implies that it must have at least one squared word. A typical formula for resolving quadratic formula is "ax2 + bx + c = 0," where the numerical factors or constant a, b, and c stand in for the undefined variable "X."

Here,

The graph is shown.

For this graph, we must discover the inequality.

The parent role is:

f(x) = x²

When we move the parent function back three units, we get,

f(x) = x² - 3

It is evident from this that option B is incorrect.

Check the additional disparities we obtain now.

Using the 1 and 3 choices we receive, choose any location from the shaded area.

x=-2 and y=0 are entered one by one into the inequality to yield,

FIRST CHOICE

y >= x²-3

0 >= (-2)²-3

0 >= 4-3

0>= 1

That is untrue.

3rd option

y<= x² - 3

0<= (-2)² -3

0<=1

This is real.

Choice 3 is the right one, thus.

Therefore , the solution to the given problem of quadratic equation comes out to be real.

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The statements are:

(a) If a linear system has n variables and m equations, then the augmented matrix has n rows equations = False

(b) A consistent linear system must have infinitely many solutions. = False

(c) If a row operation is done to a consistent linear system, the resulting system must be consistent = True

(d) If a series of row operations on a linear system results in an inconsistent system, the original system is inconsistent = True

(A) An equation with n variables. Order of the matrix is m*m=. enhanced matrix Instead of (m+1) rows, this matrix has m rows. Thus, the claim is false.

(b) Either a singular or infinite linear system that is consistent. This technology is reliable and offers a distinctive solution. Therefore, statement (c) is false. If a consistent linear system is subjected to a row operation, the new system must also be consistent. We are aware that the matrix's rank remains unchanged after conducting a row action. So, it is accurate.

(d) The initial system is inconsistent if a succession of row operations on a linear system yields an inconsistent system. We are aware that the resulting system is identical to the original system of linear equations after conducting a sequence of row operations. So, it is true.

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A: To find the intersection of the sets A and B, we need to find the elements that are common to both sets.

A = {x ∈ ℕ : 2 ≤ x < 19}

B = {x ∈ ℕ : x is even}

The intersection of the sets A and B is {x ∈ ℕ : 2 ≤ x < 19, x is even}

∩ = {4,6,8,10,12,14,16,18}

B: To find the difference of the sets A and B, we need to find the elements that are in set A but not in set B.

A = {x ∈ ℕ : 2 ≤ x < 19}

B = {x ∈ ℕ : x is even}

The difference of the sets A and B is {x ∈ ℕ : 2 ≤ x < 19, x is not even}

∖ = {3,5,7,9,11,13,15,17}

So the solution for A is ∩={4,6,8,10,12,14,16,18} and for B is ∖={3,5,7,9,11,13,15,17}

Answer: 53.6 degrees Farenheit

Step-by-step explanation:

The question says that the temperature in Washington was 12 degrees Celsius.

To convert that into Fahrenheit, plug in the value 12 in the equation given.

F = 1.8*12+32

= 53.6

Answer:

The question is incomplete, but if I had to guess, it's an exercise in using the intermediate value theorem. The IVT says that for a continuous function , there is some value of  within any interval , i.e. , in the domain of such that  when , or  when .We're told that  and . The IVT then guarantees the existence of some value of  between -2 and 8 such that .It looks like  is one of several possible answer choices. We can't say anything about the value of  because we only know how  behaves between -2 and 8; the number 13 falls outside of this range. So this choice is not correct.

Step-by-step explanation:

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[tex](\dfrac{2}{9} )^2[/tex]

Can be written as:

[tex]\dfrac{2}{9} \times\dfrac{2}{9}[/tex]

To multiply two fractions, you need to multiply the numerator by the numerator and multiply the denominator over the denominator.

Multiply:

[tex]\dfrac{2}{9} \times\dfrac{2}{9}[/tex]

[tex]\dfrac{2\times2}{9\times9}[/tex]

[tex]=\fbox{$\dfrac{4}{81} $}[/tex]

Therefore , the solution to the given problem of combination comes out to be thus, we might deduce that Brooklyn has 720 options from which to choose.

Combinations are mathematical procedures that count the number of possible configurations from a set of things, where the ordering of the selection of the elements is not important. You can select any set of items in any arrangement. Combinations and permutations are frequently wrong.

Here,

For the predicament,

six pants pairs

8 t-shirts

5 pairs equal 1 pair.

hoodies= 3

The formula to determine how many ways there are in a combination is = C. (n,r)

The number of possible outfit combinations is equal to C(n,r)* C(n,r)* C(n,r)* C (n,r)

=> C(6,1)*C(8,1)* C(5,1)* C(3,1) (3,1)

=> 6*8*5*3

=> 720

Therefore , the solution to the given problem of combination comes out to be thus, we might deduce that Brooklyn has 720 options from which to choose.

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Answer:

720

Step-by-step explanation below:

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A. The interest amount will be $12.8.

B. He must pay Annual amount of $412.8 at the end of 6 months.

Interest is the idea that one party should be compensated for taking a risk and giving up the chance to use funds, while another party should be punished for using someone else's money.

The person who temporarily part with their money is entitled to compensation, and the person who temporarily uses those funds is frequently required to make this payment.

The simple interest is calculated as :

S.I = P×T×R

where,

S.I is the simple interest

P = Principal

T = Time period in years

R = Annual interest rate

The above problem,

Amount borrowed which would be the principal (P) = $400

Time period = 6 months = 1/2 year

Annual interest rate = 6.8% = 6.8/100 = 0.068

Substitute the details in formula

Simple Interest = 400×1/2×0.068

                         = 200 ×0.068

                         = 12.8

Amount to be paid = 400 + 12.8

                                = 412.8

Thus, the interest will be $12.8 and he must pay $412.8 at the end of 6 months.

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The total volume of cough syrup that the pharmacist will have left would be = 2,400ml. That is option B.

A pharmacist is an individual that is trained and licensed to dispense prescribed medication to individuals in the correct proportion.

The volume of the cough syrup the pharmacist has = 4.3L

But 1 L = 1000 ml

4.3 L = 4.3 × 1000 = 4300ml

The quantity of syrup transferred to a bottle = 1,900 ml

Therefore the amount remaining = 4300 - 1900 = 2,400ml.

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Answer:

the equation for the ellipse that describes the arch is:

(x^2/20^2) + (y^2/6^2) = 1

Step-by-step explanation:

An ellipse can be represented by the equation (x^2/a^2) + (y^2/b^2) = 1, where a and b are the lengths of the semi-major and semi-minor axes of the ellipse, respectively. In this case, the x-axis coincides with the water level and the y-axis passes through the center of the arch, so the center of the ellipse is at the point (0, 6).

For the arch in question, the semi-major axis is 20 meters (since the arch spans a river 20 meters wide) and the semi-minor axis is 6 meters (since the center of the arch is 6 meters above the center of the river).

So the equation for the ellipse that describes the arch is:

(x^2/20^2) + (y^2/6^2) = 1

Answer: D. base currency

Step-by-step explanation: In the foreign exchange market, currencies are traded in pairs.  A currency pair consists of two currencies, with one currency being quoted against the other.

In a currency pair, the base currency is the first currency listed.  It is the currency against which the exchange rate is quoted.  In the case of USD/CAN, USD is the base currency.  The base currency serves as a reference point for calculating exchange rates. It helps determine the value of the quote currency which  is the second currency listed in a currency pair.  It represents the value of the quote currency needed to purchase one unit of the base currency.  

Furthermore, changes in the exchange rate reflect the strength or weakness of the base currency relative to the quote currency.

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Answer:

17/40

Step-by-step explanation:

4/5-3/8

32/40-15/40

17/40

Answer:

[tex]w(z(7))=189[/tex]

Step-by-step explanation:

[tex]z(7)=7+5=12 \\ \\ w(z(7))=w(12)=12^2+4(12)-3=189[/tex]

The maximum and minimum x-coordinates at the point of inflection are, respectively,[tex]$\left(\frac{\pi}{4}+2 \pi n, \sqrt{2}\right)$[/tex] and [tex]$\left(\frac{5 \pi}{4}+2 \pi n,-\sqrt{2}\right)$[/tex], and the function f is defined as f(x)=cos x+sin x for 0≤x≤ 2.

[tex]$\frac{d}{d x}(\cos (x)+\sin (x))$[/tex]

Continuity of [tex]$\cos (x)+\sin (x): \quad 2 \pi$[/tex]

Domain of [tex]$\cos (x)+\sin (x):\left[\begin{array}{cc}\text { Solution: } & -\infty < x < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$[/tex]

Range of [tex]$\cos (x)+\sin (x):\left[\begin{array}{cc}\text { Solution: } & -\sqrt{2} \leq f(x) \leq \sqrt{2} \\ \text { Interval Notation: } & {[-\sqrt{2}, \sqrt{2}]}\end{array}\right]$[/tex]

Axis points of interception [tex]$\cos (x)+\sin (x)$[/tex] [tex]: X Intercepts: $\left(\frac{3 \pi}{4}+2 \pi n, 0\right),\left(\frac{7 \pi}{4}+2 \pi n, 0\right)$,[/tex]

The Y intercept: (0,1)

the asymmetrical [tex]$\cos (x)+\sin (x)$[/tex] : None

Excessive Points of [tex]$\cos (x)+\sin (x): \quad$[/tex] Maximum [tex]$\left(\frac{\pi}{4}+2 \pi n, \sqrt{2}\right)$[/tex] ,  Minimum [tex]$\left(\frac{5 \pi}{4}+2 \pi n,-\sqrt{2}\right)$[/tex]

We put the second derivative of the function equal to zero to get the x-coordinate of the point of inflection. Re-inserting the x-coordinate into the initial function yields the point's y-coordinate.

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Answer:3:5

Step-by-step explanation:

12/4 is 3 and 20/4 is 5

so 3:5

Answer:9 and 5

Step-by-step explanation:k12

Market price of goods is 3942.86 Rs.

The price at which a goods, assets, instruments or raw materials are bought and sold at a wholesale market.

let, market price of Nepali goods = X

after allowing discount and vat the price of goods = 4140 Rs

discount = 10 %

the amount of discount = X 10/ 100

Vat added = 15%

the amount of vat added = X 15/ 100

Now, discount is subtracted from market price and vat is added to it.

The equation will be

X - X10/100 + X15/100 = 4140 Rs

X = 3942.86 Rs

market price of goods = 3942.86 Rs

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The statement that is true about the probabilities is;

B: The student will be equally likely to join the Zoology Club or Robotics Club because P(Robotics) = P(Zoology).

We are given the various students club and their probabilities of being randomly selected;

Garden club = 0.1

Robotics club = 0.2

Technology club = 0.5

Zoology Club = 0.2

Now, it is clear that Technology cub has the highest probability of being selected at 0.5 while Garden club has the least probability of being selected.

However we see that Robotics club and zoology club have the same probability and as such looking at the options, only option B is true.

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The monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.

What is simple interest?

Simple interest is based on the principal amount of a loan or the first deposit in a savings account. Simple interest doesn't compound, which means a creditor will only pay interest on the principal amount and a borrower would never have to pay more interest on the previously accumulated interest.

The simple interest earned can be calculated by using this formula

A = P(1 + rt)

Where,

A is the future value.

P is the principal value.

r is the interest rate.

t is the time.

Now Substituting the values into the formula, we have,

A = 16,000[1 + (0.08 × 3)]

A = 16,000[1 + 0.24]

A = 16,000× 1.24

Future value, A = $19,840.

Following that, we will compute the monthly payment over a 36-month period as follows:

Monthly payment = Future value/Time

Monthly payment = 19,840/36

Monthly payment = $551.11

Similarly, we will compute the credit card's compound interest:

A = 16000[1 + (0.15/12)]⁽¹² ˣ ⁷⁾

A = 16000[1 + 0.025]⁸⁴

A = 16000× 1.025⁸⁴

A = 9000 × 3.49258954

Future value, A = $45425.80

Following that, we will compute the monthly payment over an 84-month period as follows;

Monthly payment = Future value/Time

Monthly payment = 45425.80/84

Monthly payment = $540.78.

Hence, the monthly credit card payment would be $540.78, which is lower than the monthly payment on the bank loan.

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On solving the provided question, we can say that  equation that has a solution of 4 is -8+16=0

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

If we solve   -8+16=0, we get

-4-4n+16=0

(-4)-4(-4)=0

(-4)(-4)=0

which give -4=0

=4

Hence, the equation  -8+16=0 has solution =4.

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Answer:

x=3-3/5y

Step-by-step explanation:

5x+3y=15

5x=15-3y

x=(15-3y)/5

x=3-3/5y

Answer:

x= 3 y=5

Step-by-step explanation:

solving for x

5x + 3y = 15 Zero out the substitute

5x +( 3y * 0) = 15

5x + 0 = 15 Adding by zero can be ommited

5x = 15 Divide both side by 5

x = 3

if solving for y

5x + 3y = 15

(5x*0) + 3y = 15 zero out the substitute

0 + 3y = 15

3y = 15 devide by the number in front of x

y= 5

There is no evidence to reject the claim that there a difference in the proportion of people who think Red label is produced in Russia.

It should be noted that we want to test the claim at 5% level of significance. The z critical value at 5% level of significance for two tailed test is 1.96.

The test statistic is 0.5. Since the z critical value is greater than the test statistic we do not reject the null hypothesis at 5% level of significance.

Therefore, we do not have enough evidence to reject the claim that there a difference in the proportion of people who think Red label is produced in Russia and the proportion of people who think Hennessy is produced in Russia.

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The number of songs written by the guitarist and by the drummer is given as follows:

The number of songs written by each is obtained using a system of equations, for which the variables are given as follows:

The guitarist wrote 8 fewer than twice the number of songs that the drummer wrote, hence:

x = 2y - 8.

They wrote a total of 46 songs, hence:

x + y = 46.

Replacing the first equation into the second, the number of songs written by the drummer is of:

2y - 8 + y = 46

3y = 54

y = 18.

Hence the number of songs written by the guitarist is given as follows:

x = 46 - 18

x = 28.

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Answer:

$4.76

Step-by-step explanation:

7% x 4.90 = 0.34

4.90 + 0.34 = 5.24

10 - 5.24 = 4.76

The reasons are  When two lines intersect, the angles formed opposite to each other are termed as vertical angles

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Answer:

Volume = 2094.40 ft³ (2 d.p.)

Surface area = 1016.64 ft² (2 d.p.)

Step-by-step explanation:

If the diameter of a cone is 20 ft, then its radius is 10 ft since d = 2r.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

Given:

Substitute the given values of r and h into the formula for the volume of a cone and solve for V:

[tex]\implies V=\dfrac{1}{3} \pi \cdot 10^2 \cdot 20[/tex]

[tex]\implies V=\dfrac{1}{3} \pi \cdot 100 \cdot 20[/tex]

[tex]\implies V=\dfrac{1}{3} \pi \cdot 2000[/tex]

[tex]\implies V=\dfrac{2000}{3} \pi[/tex]

[tex]\implies V=2094.40\;\rm ft^3\;\;(2\;d.p.)[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Surface Area of a cone}\\\\$SA=\pi r \left(r+\sqrt{h^2+r^2}\right)$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

Given:

Substitute the given values of r and h into the formula for the surface area of a cone and solve for SA:

[tex]\implies SA=10\pi \left(10+\sqrt{20^2+10^2}\right)[/tex]

[tex]\implies SA=10\pi \left(10+\sqrt{400+100}\right)[/tex]

[tex]\implies SA=10\pi \left(10+\sqrt{500}\right)[/tex]

[tex]\implies SA=10\pi \left(10+\sqrt{100\cdot 5}\right)[/tex]

[tex]\implies SA=10\pi \left(10+10\sqrt{5}\right)[/tex]

[tex]\implies SA=100\pi +100\sqrt{5}\: \pi[/tex]

[tex]\implies SA=1016.64\; \rm ft^2\;\;(2\;d.p.)[/tex]