You have inherited land that was purchased for $65,000 in 2015. The value of the land
increased by approximately 5% per year. What is the approximate value of the land in
the year 2030?

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

A = 228 tickets

Step-by-step explanation:

We need to set up a system of equation to find the number of adult tickets sold, where A represents the adult tickets and S represents the student tickets.

Because the number of adult and student tickets together equals 506, we have A + S = 506.

Because there are 56 more student tickets than adult tickets we have A + 56 = S

And the way the system is already set up allows us to use substitution.

Thus, we have:

\(A + S=506\\A+56 = S\\\\A+A+56 =506\\2A+56=506\\2A=456\\\\A=228\\228+56=S\\278=S\)

The number of student tickets was not necessary to find in this problem, but I found anyway just in case you wanted check the work or wanted to prove the validity of the values.

Answer:  The answer is c

9514 1404 393

Answer:

  (c)  5x and 3x, and 4 and 1

Step-by-step explanation:

Like terms have the same variable(s) to the same power(s).

The terms of this expression are ...

The like terms are {5x, -3x}, which have the x-variable to the first power, and {4, -1}, which have no variable.

Answer:

Step-by-step explanation:

15+5x=20x

   -5x  -5x  => Subtract 5x from each side

You get

15 = 15x

Divide both sides by 15

1=x

The probability of the given situation through which the given relation is satisfied is 0.78

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur.

The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if you flip a fair coin, there are two possible outcomes: heads or tails. The probability of getting heads is 1/2, or 0.5, since there is one favorable outcome (heads) out of two possible outcomes (heads or tails).

Probabilities can also be expressed as percentages or fractions. For example, a probability of 0.25 can be expressed as 25%, or as a fraction of 1/4.

Probability theory is a branch of mathematics that deals with the analysis of random events and the quantification of uncertainty. It has applications in a wide range of fields, including statistics, physics, finance, and engineering.

Flexible hour work = 78%

Don't Know = 9%

Rigid hour = 13%

The probability of that 4 people choose flexible hour for work is,

0.78

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Answer:

Y = -½x + 3/2

Y = -3x + 5

Y = 1/4x - 3¼

Step-by-step explanation:

Parallel implies they have the same gradient

Perpendicular implies the gradient is a negative reciprocal of the other.

The statement fourth "No, the flowers were not put into groups first and then randomly assigned the two additives would be correct.

Any well-defined method that yields an observable outcome that cannot be precisely predicted in advance is referred to as a random experiment. To avoid any ambiguity or surprise, a random experiment must be properly defined.

We have:

Total number of flowers selected  = 20

And puts in each vase with same amount of water.

10 flowers have been assigned to receive the new additive.

The remaining 10 flowers receive the original additive.

Based on the data, this is not a randomized block design for the experiment because the flowers were not put into groups first and then randomly assigned the two additives.

Thus, the statement fourth "No, the flowers were not put into groups first and then randomly assigned the two additives would be correct.

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The equation for the polynomial in this problem is given as follows:

\(y = \frac{1}{16}(x^4 - 17x^2 + 16)\)

We are given the roots for each function, hence the factor theorem is used to define the functions.

The function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

The roots for this problem are given as follows:

Hence the polynomial is:

y = a(x + 4)(x + 1)(x - 1)(x - 4)

y = a(x² - 16)(x² - 1)

\(y = a(x^4 - 17x^2 + 16)\)

When x = 0, y = 1, hence the leading coefficient a is given as follows:

a = 1/16.

Thus the equation is:

\(y = \frac{1}{16}(x^4 - 17x^2 + 16)\)

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Let \(b\) be the number of baseball and \(k\) be the number of basket ball.

We have the following system:

\(\begin{cases}b=4k\\b+k=25\end{cases}\)

Substitute the first equation into the second:

\(4k+k=25 \iff 5k=25 \iff k=5\)

which yields

\(b=4k=4\cdot 5 = 20\)

So, there are 20 baseballs and 5 basketballs, meaning that there are 15 more baseballs than basketballs.

Answer:

4/15

Step-by-step explanation:

2/5 drive

1/3 bus

and rest walk

fraction of those who walk is 1-(2/5+1/3)

2/5+1/3=(6+5)/15=11/15

15/15-11/15=4/15

Arcs get their angle measure from the central angle they're in, in this case the central angle of 86°, central to arcED, has a counterpart of a twin vertical angle across the center, since both vertical angles are identical twins that means the central angle for arcAB is 86° also, and that's the arcAB's measure too.

Answer:

1.26

Step-by-step explanation:

° 2.1

____ x 60

100

° 0.021 x 60

° 1.26

Answer:

1.26

Step-by-step explanation:

to find a specific percentage of a number, you multiply the number [60]

by the second number/percent--but you move the decimal of this number two places to the left

(for example, 20 becomes .20 , 3% becomes 0.03)

   20.00

0. 20

  03.00

0.03

So, if we move the decimal of 2.1 to the left two places,

  02.1

0.021

So, if we multiply

60 × 0.021 , = 1.26

So, 2.1 percent of 60 is 1.26

Answer:

\(\textsf{1)}\quad y = \dfrac{4}{3}x-\dfrac{13}{3}\)

\(\textsf{2)} \quad y = \dfrac{3}{2}x-6\)

Step-by-step explanation:

To find the equation of a line parallel to the line joining (1, 2) and (-2, -2) and passing through (4, 1), we first need to find the slope of the line joining (1, 2) and (-2, -2).

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-2}{-2-1}=\dfrac{-4}{-3}=\dfrac{4}{3}\)

Parallel lines have the same slope, so the slope of the parallel line is m = 4/3.

Substitute the found slope and point (4, 1) into the point-slope formula:

\(\begin{aligned} y - y_1 &= m(x - x_1)\\\\y - 1 &= \dfrac{4}{3}(x - 4)\\\\y - 1 &= \dfrac{4}{3}x-\dfrac{16}{3}\\\\y &= \dfrac{4}{3}x-\dfrac{13}{3}\end{aligned}\)

Therefore, the equation of the line parallel to the line joining (1, 2) and (-2, -2) and passing through (4, 1) is:

\(\boxed{y = \dfrac{4}{3}x-\dfrac{13}{3}}\)

\(\hrulefill\)

To find the equation of a line perpendicular to the line joining (2, -3) and (-1, -1) and passing through (2, -3), we first need to find the slope of the line joining (2, -3) and (-1, -1).

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-(-3)}{-1-2}=\dfrac{2}{-3}=-\dfrac{2}{3}\)

The slopes of perpendicular lines are negative reciprocals, so the slope of the parallel line is m = 3/2.

Substitute the found slope and point (2, -3) into the point-slope formula:

\(\begin{aligned} y - y_1 &= m(x - x_1)\\\\y - (-3) &= \dfrac{3}{2}(x - 2)\\\\y+3&= \dfrac{3}{2}x-3\\\\y &= \dfrac{3}{2}x-6\end{aligned}\)

Therefore, the equation of the line perpendicular to the line joining (2, -3) and (-1, -1) and passing through (2, -3):

\(\boxed{y = \dfrac{3}{2}x-6}\)

A function is a relationship between a few different inputs and an output, where each input can only lead to one possible outcome.

(i) The exponential function that models the decay of the substance is given by:

\(N(t) = Noe^(-0.088t)\)

(ii) If \(400g\) of the substance is present at to, then  \(No = 400g\) . Therefore, the amount of the substance remaining after 3 days is:

\(N(3) = 400e^(-0.0883) = 309.21g\)  (rounded to two decimal places)

(iii) The rate of change of the amount of the substance after 3 days is given by:

 \(dN/dt = -0.088N(3) = -0.088309.21 = -27.21 g/day\) (rounded to two decimal places)

(iv) To find the number of days it takes for half of the original \(400g\) of the substance to remain, we need to solve the equation:

\(N(t) = 0.5No\)

\(0.5No = Noe^(-0.088t)\)

\(0.5 = e^(-0.088t)\)

\(ln(0.5) = -0.088t\)

\(t = ln(0.5)/(-0.088) = 7.89 days\) (rounded to two decimal places)

Therefore, after  \(7.89\) days, half of the original  \(400g\) of the substance will remain.

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Step-by-step explanation:

Difference of Squares: a² - b² = (a + b)(a - b)

(x² - 16) / (x - 4)

= [(x + 4)(x - 4)] / (x - 4)

= x + 4, where x =/= 4.

Answer:

1.    (x+4)

2.     4

Step-by-step explanation:

got right on edge

Answer:

The  variable are

A and  B

Step-by-step explanation:

Generally we can define a variable as a name of a placeholder representing a value  now considering the option to be selected from we see that

    The students' verbal SAT scores is a variable  because it is a phrase or a place holder that represent a value (in the is case a  numerical value)  which the score its self

    The second option  The students' percentage of words that were correctly recognized on the original list is also a variable because it is a placeholder of a name (in this case a phrase ) that represented the actual value itself

  The  third option The 75 students is not a variable because it is not representing any value but itself is the value

  The  third option The 750 students is not a variable because it is not representing any value but itself is the value

Answer:

6x+1

Step-by-step explanation:

3x+3x=6x

-5+6=1

Answer:

6x+1

Step-by-step explanation:

First remove the parentheses

the combine like terms!

6x+1

Hoped it help!

Answer: 69 square meters

Step-by-step explanation:

Answer:

answer is 10

Step-by-step explanation:

(4x+12)+(4x+12)+(5x+26)=180[sum of isosceles triangles]

8x+34+5x+26=180

X=10

Answer:

576

Step-by-step explanation:

Answer:

0.99 ≈ 1

Step-by-step explanation:

Given expression,

\( \sf \rightarrow{3}^{ - 1} \times (4 \times 6) \times {2}^{ - 3} \)

Solving the given expression,

\( \sf \rightarrow{3}^{ - 1} \times (4 \times 6) \times {2}^{ - 3} \)

\(\sf \rightarrow0.33 \times (24) \times 0.125\)

\(\sf \rightarrow7.92 \times 0.125\)

\(\sf \rightarrow0.99 ≈ 1\)

Hence, answer is 0.99 ≈ 1.

Answer:

x=3, y=-6

Step-by-step explanation:

As you know there are many ways to solve this question! First is Subsitutuion, Second is Elimination, and Third is Graphing!

Let’s begin with our detailed answer:

As you know subsitution is solving for a variable and then it can be used as a variable substitution to figure out x and y.

So in our system of equations:

\(\left \ {3x+2y=-3}} \atop {9x+4y=3}} \right.\)

I will just take one equation and solve for x but it actually dosent matter which variable you subsitutue and solve for.

\(\left \ {3x+2y=-3}} \atop {9x+4y=3}} \right.\)

To eliminate this question we can divide the top part by -3:

\(\left \ {-9x-6y=9}} \atop {9x+4y=3}} \right.\)

Let‘s sum these system of equation and we get: \(y=-6\)

We can now insert y as -6 and solve for x:

\(3x-12=-3\)

\(x=3\)

So, \(x=3, y = -6\)

Answer:

(3, - 6 )

Step-by-step explanation:

3x + 2y = - 3 → (1)

9x + 4y = 3 → (2)

Multiplying (1) by - 3 and adding to (2) will eliminate the x- term

- 9x - 6y = 9 → (3)

Add (2) and (3) term by term to eliminate x

0 - 2y = 12

- 2y = 12 ( divide both sides by - 2 )

y = - 6

Substitute y = - 6 into either of the 2 equations and solve for x

Substituting into (1)

3x + 2(- 6) = - 3

3x - 12 = - 3 ( add 12 to both sides )

3x = 9 ( divide both sides by 3 )

x = 3

solution is (3, - 6 )

Answer:

Domain: [-2, infinity)

Range: [-4, infinity)

Step-by-step explanation:

There's only one graph I see.

Domain is how far the graph extends on the x axis.

Range is how far the graph extends on the y axis.

Answer: 6.25%

Step-by-step explanation:

Percent Decrease = ( ( Starting Value - Final Value ) / Starting Value ) * 100

So 672,000-630000 = 42,000

42,000 / 672,00 = 0.0625

Finally multiply by 100 soooooo 0.0625 * 100 = 6.25%

The relationship in this problem is not proportional, as there are different ratios between the number of people and the number of cars washed.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The ratios between the output and the inputs are given as follows:

Different ratios, hence the relationship is not proportional.

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we have the following:

A.

B.

Answer:

\(\frac{62!}{56!}\)

Step-by-step explanation:

We can either look at all 62 characters (2 * 26 in the alphabet and 10 digits), choose 6 of them, and add the fact that we care about their order - so multiply by 6! and we get \(\binom{62}{6}\cdot 6! = \frac{62!}{6!\cdot 56!} \cdot 6! = \frac{62!}{56!}\)

Or, we can look atr all the permutations of all the characters and take into account that we DON'T care about the order of the 56 after the first six. Getting \(\frac{62!}{56!}\) immediately.