is this a one-to-one function? yes or no

The displacement of the man from Noth east of A from C is 12.2 km.

The displacement of the man is the distance between his initial position at A and final position at C.

The angle formed at position B is calculated as follows;

θ = 30⁰  + 90⁰

θ = 120⁰

The displacement of the man is calculated by applying cosine rule as follows;

d² = 8² + 6² - 2(8 x 6) cos (120)

d² = 148

d = √148

d = 12.2 km

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System of equations helps to solve real-life problems. The system of equations will not have no solution.

Inconsistent System

A system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.

The two of the system of equations given to us are,

\(y+x=19-x^2\)

\(x+y = 80\)

Now,

1. The first step is to isolate one variable in the system of equations,

\(y=19-x^2-x\)

\(y=80-x\)

2. The second step is to substitution to create a one-variable equation.

\(80-x=19-x^2-x\\x^2-x+x=19-80\\x^2 = -61\)

Now, since the value of x  is the negative square root. therefore, the system of equations will not have a real number of solutions.

If we plot the two equations on the graph, then the line of the system of equations will not intersect any point, therefore, the system of equations will have no solution.

Hence, the system of equations will not have no solution.

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Answer:

0 solutions

Step-by-step explanation:

Edge 2022

The Unit rate in 1999 was $0.33 per stamp, and the unit rate in 2018 was $0.50 per stamp.

In 1999, the U.S. Postal Service sold 15 stamps for $4.95. To find the unit rate, we need to divide the total cost by the number of stamps sold:

Unit rate in 1999 = Total cost / Number of stamps sold = $4.95 / 15 = $0.33 per stamp.

In 2018, the U.S. Postal Service sold 12 stamps for $6.00. To find the unit rate, we need to divide the total cost by the number of stamps sold:

Unit rate in 2018 = Total cost / Number of stamps sold = $6.00 / 12 = $0.50 per stamp.

Therefore, the unit rate in 1999 was $0.33 per stamp, and the unit rate in 2018 was $0.50 per stamp.

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Answer:

Step-by-step explanation:

The correct option related to enrollment of sam in university is C (We cannot be certain whether Sam is or is not a college freshman.)

What is enrollment?

The act of putting yourself or some other person onto the official list of members of a course, faculty or university, or group.

Main body:

as all college freshmen at highlands university take english composition , which means he is enrolled in university.

Sam is enrolled in english composition at highlands university which means he has English as a subject.

But it doses not tell us about his current year , which year he is studying.

therefore ,We cannot be certain whether Sam is or is not a college freshman.

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Answer:

  It will take 5.29 years to double our money if we invest $500 at 14 percent interest.                                    

Step-by-step explanation:

Let we invest $500 with the interest rate of  14% ,

Now we will find the time it is going to take to double the money

here, we use the formula of compound interest \(A= P( 1+\frac{r}{n}) ^{nt}\)

Here, A = the amount yielded,

P = principal,

r = interest rate ,

n = number of times per year,

and t =  time invested.

Now, put A= 1000 , P= 500 , R= 0.14   T= x and N= 1

      \(1000=500(1+ 0.14)^x\)      

      \(1000=500(1.14)^x\)

       \(2=1.14^x\)

     \(\log_{1.14} (2)=x\)

      \(x=5.29\)

so ,  It will take 5.29 years to double our money if we invest $500 at 14 percent interest.    

Hence , the answer is 5.29 years .                  

Answer:

292 and 2092

Step-by-step explanation:

Surface area:

Wall 1: 40 x 3 = 120m^2

Wall2: 40 x 3 = 120m^2

Wall 3: 15 x 3 = 45m^2

Wall 4: 15 x 3 = 45m^2

Ceiling: 15 x 40 = 600m^2

Total : 240 + 600 + 90 = 730

So, cost of painting = 730/25 x 10 = 29.2 x 10 = 292

Total: 292 + 1800 = 2092

The total cost of paint would be 2092 dollars.

The area of the cuboid is the sum of product of the length, breadth of the given prism.

Surface area:

Wall 1: 40 x 3 = 120m^2

Wall2: 40 x 3 = 120m^2

Wall 3: 15 x 3 = 45m^2

Wall 4: 15 x 3 = 45m^2

Ceiling: 15 x 40 = 600m^2

The Total area: 240 + 600 + 90 = 730

So, The cost of painting = 730/25 x 10

= 29.2 x 10

= 292

Total: 292 + 1800 = 2092

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Answer:

\((x+3)^2+(y-3)^2=13\).

Step-by-step explanation:

The center of the circle is \((-3,3)\) and the circle passes through \((0,1)\).

So, the square of the radius is \((-3-0)^2+(3-1)^2=13\).

Substituting into the center-radius form for the equation of a circle, the equation is \((x+3)^2+(y-3)^2=13\).

The equation of circle is \((x + 3 )^2 + (y - 3)^2 = 13\) whose center is at (-3, 3).

The standard form of the equation of a circle is:

\((x - h)^2 + (y - k)^2 = r^2\)

In this equation, (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.

From the figure, the center of circle is at (-3, 3) and the passing point is (0, 1).

So, the radius of circle is

= √( 3-1)² + (-3-0)²

= √2² + 3²

= √13

Now, the equation of circle is

\((x - (-3))^2 + (y - 3)^2 = \sqrt{13} \; ^2\)

\((x + 3 )^2 + (y - 3)^2 = 13\)

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To show that S = X (1) is sufficient for θ, we need to show that the conditional distribution of the sample \(X1, X2, ...., Xn\)given S and θ is independent of θ.  \(g(x, θ) = 0\)almost surely for all θ. Thus, S = X (1) is a complete statistic for estimating θ.

Now, the joint density of X1, X2, ...., Xn is given by \begin\({align*}L(\theta)=f_{X_{1}}(x_{1};\theta)f_{X_{2}}(x_{2};\theta).....f_{X_{n}}(x_{n};\theta)\\=e^{\sum_{i=1}^{n}\theta-x_{i}}I_{[\theta,\infty)}(x_{i})\end{align*}\)To find the conditional distribution of the sample X1, X2, ...., Xn given S = X (1) and θ, we \(\&=\int_{0}^{\infty}g(x,\theta)\frac{d}{dx}(1-e^{-\theta x})dx\\&=-\int_{0}^{\infty}g(x,\theta)\frac{d}{d\theta}e^{-\theta x}dx\\&=\int_{0}^{\infty}g(x,\theta)x e^{-\theta x}dx\end{align*}\)Now, since the above expression is zero for all θ, we must

Differentiating the second integral with respect to θ and using integration by parts, we have\begin\({align*}0=\frac{d}{d\theta}\int_{0}^{\infty}g(x,\theta)x e^{-\theta x}dx&=-\int_{0}^{\infty}g(x,\theta)x^{2} e^{-\theta x}dx\\&\geq 0\end{align*}\)

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Answer:

it's (-2) your drawing is correct and that's why i think it's -2 because it's on the negative side

Answer:

y=(1/2)x-4

Step-by-step explanation:

I calculated it

(btw, thx for the friend request)

Hope it helps

Answer:

1. 7*3 - 7*x = -63

2. 3-x = -63/7

Step-by-step explanation:

1. 7(3-x) = -63

7*3 - 7*x = -63

2. 3-x = -63/7

You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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The Answer is

7 - 2x

Step-by-step explanation:

23 -14x + 12x - 16

(23 - 16) + (-14x + 12x)

= 7 - 2x

hope this help a'lot

The expression equivalent to 23−14x+12x−16 is 7 - 2x

Here we simply take our expression to simplify it.

We start with:

23−14x+12x−16

First, we combine all the terms having x and combine other constant values.

(23 - 16) + (-14x + 12x)

Now we solve the two parts of the above expression we will get,

7 + (- 2x)

Simplifying we get,

7 - 2x

Therefore  the equivalent expression is 7 - 2x

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For the exponential equation, having variable x as superscript equation has solution as,

\(x=-5,2\)

According to the equality for exponential equation property, when the bases of both side of a equation is same, then the exponents of both the terms must be equal.

The equation given in the problem is,

\(12^{x^2+5x-4}=12^{2x+6}\)

In the given equation, the base of both side is equal. For the equal base, the exponents of them can be equate as,

\({x^2+5x-4}={2x+6}\)

Arrange all the terms one side of the equation as,

\({x^2+5x-4}-{2x-6}=0\)

Solve it further as,

\({x^2+3x-10}=0\)

To solve the above quadratic equation, use the split the middle term method as,

\({x^2-2x+5x-10}=0\\x(x-2)+5(x-2)=0\\(x-2)(x+5)=0\)

Equating both the factor to the zero, we get the value of the x as -5 and 2.

For the exponential equation, having variable x as superscript equation has solution as,

\(x=-5,2\)

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Answer:

88.50

Step-by-step explanation:

0.12x400=48 dollars +the 40.50 dollars answer 88.50

Answer:

Since all three of the interior angles are the same degree, the three sides must be the same length. So, 3x - 5, 4x - 30, and 2x + 20 must be equal.

To solve for x, you can just set one of the sides equal to another one of the sides. I will do 3x - 5 and 4x - 30.

3x - 5=4x - 30

Add 5 to both sides.

3x = 4x - 25

Subtract 4x from both sides.

-x = -25

Divide both sides by -1.

x=25

:)

Answer:

[see below]

Step-by-step explanation:

The triangle shown is equilateral, as all three angles are marked congruent.

This means that the sides are equal to each other.

\(4x - 30 = 2x + 20\\\rule{150}{0.5}\\4x - 2x - 30 = 2x - 2x + 20\\\\2x - 30 = 20\\\\2x -30 + 30 = 20 + 30\\\\2x = 50\\\\\frac{2x=50}{2}\\\\\boxed{x = 25}\)

Hope this helps you.

Answer:

7

Step-by-step explanation:

Wherever we see an x, we just input 4 to find f(4)

f(4) = 2(4) - 1 = 8 - 1 = 7

Hope this helps!!!!!!!

Answer:

Equivalent expressions are expressions that have the same value. Writing equivalent expressions can make them easier to work with and solve.

Sometimes when you are writing equivalent expressions, you will need to use the distributive property. Multiply a number outside of parentheses by each number inside the parentheses.

Look at the steps for 3(2+4t).

3(2+4t)  Multiply 3 by each addend.

3(2)+3(4t) To multiply 3 and 4t, multiply 3 and 4. The variable stays the same. So, 3(4t)=12t.

6+12t

So, 3(2+4t) and 6+12t are equivalent expressions.

Step-by-step explanation:

Answer:

y=7

Step-by-step explanation:

\( \sqrt[3]{x + 1} = 2\)

Let us cube both sides.

\( = > (\sqrt[3]{x + 1} ) ^{3} = {2}^{3} \)

Now, it will be only x + 1.

\( = > x + 1 = 8\)

Transpose 1 to the Right Hand Side.

\( = > x = 8 - 1\)

Now, subtract.

\( = > x = 7\)

Answer:

x = 7

Hope you could understand.

If you have any query, feel free to ask.

Answer:

To complete the square for the quadratic expression x^2 + 16x + 22, we need to add and subtract (16/2)^2 = 64 inside the parentheses. This gives us (x^2 + 16x + 64) - 64 + 22, which can be simplified to (x + 8)^2 - 42. So, the expression x^2 + 16x + 22 can be rewritten as a perfect square by completing the square as (x + 8)^2 - 42.

Step-by-step explanation:

There are 55 ways to form a train consisting of tank cars, boxcars, and flatcars by using concept of combinations.

If there are t tank cars, b boxcars, and f flatcars in the train yard, then the number of ways to form a train by selecting some of these cars is the same as the number of ways to distribute n = t + b + f identical objects into three distinct boxes, such that each box may receive any number of objects (including zero). The solution is given by the combination formula:

C(n + k - 1, k - 1)

where k is the number of boxes (in this case, k = 3). Therefore, the number of ways to form a train from t tank cars, b boxcars, and f flatcars is:

C(t + b + f + 3 - 1, 3 - 1) = C(t + b + f + 2, 2) = (t + b + f + 2)! / ((t + b + f)! * 2!)

There are 4 tank cars, 3 boxcars, and 2 flatcars in the train yard, then the number of ways to form a train is:

C(4 + 3 + 2 + 2, 2) = C(11, 2) = 55

Therefore, there are 55 ways to form a train consisting of tank cars, boxcars, and flatcars

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The given equation is solved to x as x=(58-b)/a.

The given equation is ax+b=58.

We need to solve the given equation for x.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, the equation ax+b=58 can be solved as follows:

Given equation:

ax+b=58

Now,

ax= 58-b

x=(58-b)/a

That is, x=(58-b)/a (when you bring a variable from LHS to RHS or vice versa the mathematical operations become inverse that is multiplication changes to division)

Therefore, the given equation is solved to x as x=(58-b)/a.

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The graph of f(x) = |x + 3| can be obtained by translating the graph of y = |x| three units to the left. The graph of y = |x| is a V-shaped graph that passes through the origin and opens upwards.

The absolute value function ensures that the output is always positive or zero. When we consider f(x) = |x + 3|, we are modifying the original function by adding 3 to the input variable x. This translates the entire graph of y = |x| horizontally three units to the left. As a result, the vertex of the graph is shifted from (0, 0) to (-3, 0), and the V-shape remains the same. The translation does not affect the orientation or shape of the graph; it simply shifts it horizontally.

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Answer is D (8,6)

I don’t know how but I know it is because I got it right and I’m smart

Using the .01 level of significance means that, in the long run, a Type I error occurs 1 time in 100. This means that if we perform a statistical test 100 times, and we set the level of significance at .01, then we can expect to observe one false positive result due to chance alone. So, the correct option is 1).

A Type I error occurs when we reject a true null hypothesis, or when we conclude that there is a significant difference or relationship between two variables when in fact there is not.

By setting the level of significance at .01, we are minimizing the risk of making a Type I error while increasing the risk of making a Type II error, which occurs when we fail to reject a false null hypothesis. So, the correct answer is 1).

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Researching the average earnings by major and by career can help you determine the return on investment of an institute of higher education.

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The Earth is estimated to be around 4.54 billion years old, while the oldest known rocks found on Earth date back to about 4 billion years ago.

Determining the age of the Earth is a complex process that involves a variety of scientific disciplines. Geologists and other scientists have used a variety of methods to estimate the age of the planet, including radiometric dating, which involves measuring the decay of radioactive isotopes in rocks and other materials.

The age of the oldest known rocks found on Earth has also been determined using radiometric dating techniques. These rocks, which are primarily found in Western Greenland, have been dated to around 3.8 to 4.0 billion years old. The rocks are believed to have formed during the Hadean Eon, a period of Earth's history when the planet was still in its early stages of formation and was subject to intense meteorite bombardment.

It's important to note that the age of the Earth and the age of the oldest known rocks found on its surface are not precise measurements.

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Answer:

5x

Step-by-step explanation:

NOte: it is an expression and not an equation as originally asked.

"Product" means the answer to a multiplication of two numbers.

You are asked to write the answer to 5 and a number being multiplied together.

Let the unknown number be

x

The product is therefore

5x

x

=

5x