Find the value of x

The statement that best describes the solutions to the given system of equations - There are two possible solutions, but only one of the solutions is viable.

"It is a point or set of points (x, y) that satisfies all the constraints of the given problem."

"It is a solution that makes sense in context as well as mathematically. "

"It is a set of equations for which we find a common solution."

For given question,

Three classmates want to know when a tennis ball and a balloon will reach the same vertical height above the ground.

Given that, x represents the time, in seconds, since the timer starts.

The graph shows the vertical height of the tennis ball and balloon, in feet.

The solution to the system of equations are the points at which the graphs to the system of equations intersect each other.

From the given graph we can observe that,

the graphs intersect at points having the x values near x = 1.2 and x = -3.2 This means, there are two possible solutions.

But we know that the negative value of x (time) is not viable.

Therefore, the statement that best describes the solutions to the given system of equations - There are two possible solutions, but only one of the solutions is viable.

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Answer:

what are yo tring to sya

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

22.5/9=2.5

Answer: The average rate of change in the number of public library visits from 1998 to 2002 = 0.05 billion per year.

Step-by-step explanation:

Given: Number of visits in 1998 = 1.3 billion

Number of visits in 2002 = 1.5 billion

The average rate of change in the number of public library visits from 1998 to 2002 = [tex]\dfrac{\text{Number of visits in 2002 - Number of visits in 1998}}{2002-1998}[/tex]

[tex]=\dfrac{1.5-1.3}{4}\\\\=\dfrac{0.2}{4}\\\\= 0.05 \text{ billion per year.}[/tex]

Hence, the average rate of change in the number of public library visits from 1998 to 2002 = 0.05 billion per year.

Answer:

the data shows a linear relationship because the rate of change in decreasing

Step-by-step explanation:

hope it helps

Answer:

Hope this helps xD

Step-by-step explanation:

Given:

Consider the expression is

[tex]\dfrac{n^4}{n^{\frac{1}{2}}}[/tex]

To find:

The simplified form of the given expression.

Solution:

We have,

[tex]\dfrac{n^4}{n^{\frac{1}{2}}}[/tex]

Using the properties of exponents, we get

[tex]=n^{4-\frac{1}{2}}[/tex]               [tex]\left[\because \dfrac{a^m}{a^n}=a^{m-n}\right][/tex]

[tex]=n^{\frac{8-1}{2}}[/tex]

[tex]=n^{\frac{7}{2}}[/tex]

Therefore, the simplified form of the given expression is [tex]n^{\frac{7}{2}}[/tex].

Answer:

Ricky had 1205 hits. Pedro had 1481 hits.

Step-by-step explanation:

Set variables.

Set up an equation.

Pedro and Ricky got 2686 base hits total.

Pedro had 276 more hits than Ricky.

Plug p into your first equation.

Combine like terms.

Divide both sides by 2 to isolate r.

You now know that Ricky had 1205 hits. Pedro had 276 more hits than Ricky. Therefore,

Pedro had 1481 hits.

Check your work.

total hits = Pedro's + Ricky's

2686 = 1481 + 1205

2686 = 2686

Pedro's hits = Ricky's hits + 276

1481 = 1205 + 276

1481 = 1481

Your answers are correct.

Answer:

B. 1,500’

Step-by-step explanation:

Given;

dimension of the rectangular house, = 35’ x 40’

The actual total linear footage of lumber needed = 35’ x 40’ = 1,400'

The rough estimate should be greater than the actual estimate in 100s;

rough estimate = 1,400' + 100' = 1,500'

Therefore, the rough estimate of the total linear footage of lumber needed is 1,500'.

Answer:

here I drew it digitally Hope it helps

Step-by-step explanation:

The graph of the function is a V-shaped curve.

Given that we need to determine the graph of the function f(x) = 7|x - 4| - 1.

To graph the function f(x) = 7|x - 4| - 1, you can follow these steps:

Start by identifying the key points of the function. In this case, the function involves an absolute value, which means it may change direction at the point inside the absolute value.

Set the expression inside the absolute value equal to zero and solve for x to find this critical point:

|x - 4| = 0

x - 4 = 0

x = 4

So, the critical point is x = 4.

Next, consider the behavior of the function on each side of the critical point.

Choose some values of x less than and greater than 4 and substitute them into the function to determine the corresponding y-values.

Let's choose x = 2:

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

f(2) = 7|-2| - 1

f(2) = 7(2) - 1

f(2) = 14 - 1

f(2) = 13

Let's choose x = 6:

f(6) = 7|6 - 4| - 1

f(6) = 7|2| - 1

f(6) = 7(2) - 1

f(6) = 14 - 1

f(6) = 13

Therefore, we have the points (2, 13) and (6, 13) on the graph.

Plot the critical point and the points you found on the coordinate plane. Mark them on the x-axis and y-axis.

To graph the absolute value part of the function, draw a V-shaped curve with the vertex at the critical point (4, 0).

The arms of the V-shaped curve will pass through the plotted points (2, 13) and (6, 13).

Extend the arms of the V-shaped curve indefinitely in both directions.

Finally, add the constant term (-1) by shifting the entire graph down by 1 unit. This means that every y-value on the graph should be reduced by 1 unit.

Your completed graph of the function f(x) = 7|x - 4| - 1 should resemble a V-shaped curve with its vertex at (4, -1), passing through the points (2, 12) and (6, 12), and extending infinitely in both directions.

The graph of the function is attached.

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Answer: y=0.5x-6. She forgot the y-intercept

Step-by-step explanation: use the slope formula to get the slope of 0.5 and just add in the y-intercept of -6 since:

y=mx+b

m=slope

b=y-intercept

Answer:

y = 0.5x - 6

Step-by-step explanation:

[tex]since \: there \: are \: two \: points \: \\ m = \frac{y2 - y1}{x2 - x1} [/tex]

[tex]m = \frac{ - 5 - ( - 7.5)}{2 - ( - 3)} = \frac{2.5}{5} = \frac{1}{2} \: or \: 0.5[/tex]

Standard form of slope-intercept:

y = mx + b

wherein m is the slope and b is the y-intercept.

Let's substitute all values into the equation

[tex]y = 0.5x - 6[/tex]

-20 + -3

-10 + -13

-15 + -8

-5 + -18

I hope this helps!

Answer:

The cost of 432 meters square = $21924

Step-by-step explanation:

The length of the plot = l = 27m

The width of the plot = w = 16m

We know that the area of a rectangular object can be determined by multiplying the length and width.

Thus, the area of the rectangular vegetable plot will be:

[tex]A = wl[/tex]

substituting w = 16 and l = 27

A = 16 × 27

A = 432 m²

Therefore, the vegetable plot will be:

A = 432 meter square

Given

The cost of ploughing field of 1 meter square =  $50.75

so

The cost of ploughing field 432 meters square = 50.75 × 432

                                                                               = $21924

Therefore, the cost of 432 meters square = $21924

Answer:

4

Step-by-step explanation:

2+2 = 4

hope this helps...

Answer:

4

Step-by-step explanation:

Answer:

(5,-3)

Step-by-step explanation:

On the x-axis, go 5 points to the right and on the y-axis go 3 points down the the negative 3 and the point N crosses at (5,-3)

Answer:

vxdfvdvdxv

Step-by-step explanation:

svvddddddddddddddddddd

Answer:

7/9

Step-by-step explanation:

Step-by-step explanation:

3 divide 180 230 7 c=mc square that eaquls 2

Answer:

A unit rate is a rate with 1 in the denominator

Answer:

The function that has an inverse that is also a function is [tex]x = 3\cdot y + \frac{9}{4 }[/tex].

Step-by-step explanation:

The only function whose inverse is also a function is the linear function, also named first-order polynomial. The inverse of a linear function is also a linear function. That is:

[tex]y = \frac{1}{3}\cdot x -\frac{3}{4}[/tex]

[tex]\frac{1}{3}\cdot x = y + \frac{3}{4}[/tex]

[tex]x = 3\cdot y + \frac{9}{4 }[/tex]

The function that has an inverse that is also a function is [tex]x = 3\cdot y + \frac{9}{4 }[/tex].

Answer:

Larissa takes 59.141 seconds to complete both laps.

Step-by-step explanation:

The complete time is the sum of time taken on each lap. We translate the two statements into mathematical expressions to determine the required output:

(i) She completes her first lap in 31.135 seconds:

[tex]x_{1} = 31.135\,s[/tex]

(ii) She completes her second lap 3.129 seconds faster than the first lap:

[tex]x_{2} = x_{1}-3.129\,s[/tex]

[tex]x_{2} = 31.135\,s - 3.129\,s[/tex]

[tex]x_{2} = 28.006\,s[/tex]

Then, the time taken by Larissa to complete both laps is:

[tex]\Delta x = x_{1} + x_{2}[/tex]

[tex]\Delta x = 31.135\,s+28.006\,s[/tex]

[tex]\Delta x = 59.141\,s[/tex]

Larissa takes 59.141 seconds to complete both laps.

Answer:

14.62=d divided by 4

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Step-by-step explanation:

The given inequality is :

x – 2y > 16

We need to draw the graph of this inequality.

If x = 0,

-2y>16

y>-8

If y = 0,

x>16

So, we can draw the graph as follows :

Answer:

i am not pretty sure what is X but the answer is 1/2 i think!

Step-by-step explanation:

Answer:

O negative

Step-by-step explanation:

Answer:

Negative

Step-by-step explanation:

The slope is going diagonally to the bottom right which makes it negative.

A slope would be undefined if it went straight up.

A slope would be zero if it went horizontally.

A slope would be positive if it were going up (opposite of negative!)

Hope this helps!

Answer:

Step-by-step explanation:

Rate of change is:

Substitute values with ordered pairs:

Correct option is D. 15

Answer:

A line is shown passing through the ordered pairs (1, 15) and (2, 30) and (3, 45) and (4, 60).

The rate of change of height :---

[tex]slope( = m) = \frac{(60 - 15)}{(4 - 1)} = \frac{45}{3} = 15\\[/tex]

Answer:

[tex]7 \frac{26}{15}[/tex]

Step-by-step explanation:

[tex]8 \frac{11}{15} = 7 \frac{?}{15}[/tex]

Remember the multiply and add rule or improper fractions. To convert from a mixed number to an improper fraction, one must multiply the number part of the mixed number by the bottom (denominator) on the fraction. Then one must add that to the numerator (top) of the fraction. Since 7 is 1 less than 8, then one would have to multiply 15 by 1, and add it to 11, to get the value on top of [tex]7 \frac{?}{15}[/tex] The value would be;

[tex]7 \frac{26}{15}[/tex]

Answer:

7 26/18

Step-by-step explanation:

Answer: 1.5x

Step-by-step explanation:

If the figure dilates by 1.5 times it will increasingly do the same with the perimeter. It keeps the same ratio of 1.5x.

Ex: If a side of the figure was originally 10 and the dilation factor is 1.5 the side now with be 15. This goes for all sides.

Hope this helps!