The shorter leg of a right triangle has a measure of x + 5. The longer leg is one less than three times the length of the shorter leg. The hypotenuse is thirteen more than two times the shorter leg. The area of the triangle, A, is 2.5 times the magnitude of the perimeter.
Create a system of equations to model the situation above. Determine if there are any solutions, and, if possible, whether or not they are viable.

How many total possible solutions of the form (x, A) are there for this situation?

How many total viable solutions of the form (x, A) are there for this situation?

Answer:

  a)  y = 3.80x +5.00

  b)  see attached

Step-by-step explanation:

A graph shows the given table values lie on a straight line.

__

Finding the slope of the line is made easier by an appropriate choice of a pair of table values:

  m = (y2 -y1)/(x2 -x1)

  m = (24 -20.20)/(5 -4) = 3.80/1 = 3.80 . . . . using (4, 20.20) and (5, 24)

The y-intercept can likewise be found with an appropriate choice of table values. Solving the slope-intercept equation for b, we get ...

  y = mx +b

  b = y -mx

  b = 8.80 -3.80 × 1 = 5.00 . . . . using the first table value

An equation that represents the cost of parking could be ...

  y = 3.80x +5.00

__

A graph of the table values and the equation is shown in the attachment.

Answer:

[tex]\huge\boxed{\bf\:1}[/tex]

Step-by-step explanation:

[tex]\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \times \frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }[/tex]

Take [tex]\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 }[/tex] & factorise it at first.

[tex]\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \\= \frac{\left(x-3\right)\left(x-1\right)}{\left(x-4\right)\left(x-3\right)}\\= \frac{x-1}{x-4}[/tex]

Now factorise the next set : [tex]\frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }[/tex].

[tex]\frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\\= \frac{\left(x-4\right)\left(x+6\right)}{\left(x-1\right)\left(x+6\right)}\\= \frac{x-4}{x-1}[/tex]

Now, multiply the two simplified results.

[tex]\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \times \frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\\= \frac{x-1}{x-4}\times \frac{x-4}{x-1} \\= \frac{\left(x-1\right)\left(x-4\right)}{\left(x-4\right)\left(x-1\right)} \\= \boxed{\bf\: 1}[/tex]

[tex]\rule{150pt}{2pt}[/tex]

Answer:

[tex]y \geqslant - x - 4[/tex]

Step-by-step explanation:

y≥-x-4 is the required equation

Answer:

i think they are unlike terms

Step-by-step explanation:

Answer:

7.07106781

simplified

7.07

Step-by-step explanation:

started= 2:30 PM

ended= 4:00 PM

the duration of the concert.

( just find the difference of finishing time and starting time)

= 1 hour 30 mins

so, the duration of the concert is 1 hour 30 mins.

0400-0230

= 1 hour 30 minutes

hope this helps :)

Answer:

0 < x < 28

Step-by-step explanation:

The triangle inequality theorem states that the sum of any two sides of the triangle should be greater than the third side.

Therefore,

All the possible values of x are 26 < x < 28.

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

So a triangle has three sides.

We have the triangle inequality theorem which states that,

The length of any side of the triangle is always less than the sum of the other two sides.

And the range of the possible measure of the third side is the sum and the difference of the other two sides.

So x < 27 + 1 = 28

and,

x > 27 - 1 = 26

So 26 < x < 28

Hence the measures of third side is 26 < x < 28.

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Answer:

It's (5,4)

Step-by-step explanation:

hope this helps :)

Answer: $950

1250-299=951

round off to nearest hundred, $950

The estimated sale price of the couch after rounding each number to the nearest hundred is $901.

To estimate the sale price of the couch, we first need to round each number to the nearest hundred.

Original price: $1250

Rounded to the nearest hundred: $1200

Discount amount: $299

Now, let's calculate the estimated sale price by subtracting the discount from the rounded original price:

Estimated Sale Price = Rounded Original Price - Discount Amount

Estimated Sale Price = $1200 - $299

Estimated Sale Price = $901

The estimated sale price of the couch after rounding each number to the nearest hundred is $901.

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The cross sections have side length equal to the vertical distance between y = √x and y = 1, or |√x - 1|. The two curves meet at the point (1, 1), and y = √x meets x = 4 at (4, 2), so we'll be integrating with respect to x on the interval [1, 4]. Over this interval, √x ≥ 1, so |√x - 1| = √x - 1.

A cross section of thickness ∆x has volume

(√x - 1)² ∆x = (x - 2√x + 1) ∆x

Then the volume of the solid is

[tex]\displaystyle \int_1^4 (x - 2\sqrt x + 1) \, dx = \boxed{\frac76}[/tex]

Answer:

See below ↓↓

Step-by-step explanation:

Equation of line k

a. parallel line

b. perpendicular line

The temperature difference between the pan and room temperature would be 77.9⁰C in the next 15 minutes,

Let y represent the temperature difference after x minutes.

The difference between the pan and room temperature is currently 197°C and is decreasing by 6% every minute, hence:

y = 197(100% - 6%)ˣ

y = 197(0.94)ˣ

The temperature in the next 15 minute is:

y = 197(0.94)¹⁵ = 77.9⁰C

The temperature difference between the pan and room temperature would be 77.9⁰C in the next 15 minutes.

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The approximate value of P(-0.78 ≤ Z ≤ 1.16) is obtained being 0.6593

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

If we have  [tex]X \sim N(\mu, \sigma)[/tex]

(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex])

then it can be converted to standard normal distribution as

[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

[tex]P(Z \leq z) = P(Z < z) )[/tex]

Also, know that if we look for Z = z in z-tables, the p-value we get is

[tex]P(Z \leq z) = \rm p \: value[/tex]

For this case, we have to find:

[tex]P(-0.78\leq Z \leq 1.16)[/tex]

It can be rewritten as:

[tex]P(-0.78\leq Z \leq 1.16) = P(Z \leq 1.16) - P(Z < -0.78) \\P(-0.78\leq Z \leq 1.16) = P(Z \leq 1.16) - P(Z \leq -0.78)[/tex]

The p-values for Z = 1.16 and Z = -0.78 from the z-table is found as 0.8770 and 0.2177 respectively, and therefore, we get:

[tex]P(-0.78\leq Z \leq 1.16) = P(Z \leq 1.16) - P(Z \leq -0.78)\\P(-0.78\leq Z \leq 1.16) = 0.8770 - 0.2177 = 0.6593[/tex]

Thus, the approximate value of P(-0.78 ≤ Z ≤ 1.16) is obtained being 0.6593

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Answer:

B.) The answer is 66% if you convert it from decimals

Answer:

I think for A It is 3.

Step-by-step explanation:

Answer:

3/5

Step-by-step explanation:

6x  - 10y = -100

Write this equation in slope-intercept form: y = mx +b

-10y = -6x - 100

Divide the entire equation by (-10)

[tex]\dfrac{-10}{-10}y=\dfrac{-6}{-10}x-\dfrac{100}{-10}\\\\y =\dfrac{3}{5}x+10[/tex]

Slope = 3/5

Parallel lines have same slope.

Slope of the parallle line = 3/5

Answer:

h = 13.4cm

Step-by-step explanation:

BAC + ACB = 90°

BAC + 48° = 90°

BAC = 42°

cos(BAC) = AB/BC

cos(42°) = h/18

h = 13.377 ≈ 13.4cm

Answer:

Step-by-step explanation:

The given relation between length and width can be used to write an expression for area. The equation setting that equal to the given area can be solved to find the shed dimensions.

__

Let x represent the width of the shed. Then the length is (2x+3), and the area is ...

  A = LW

  20 = (2x+3)(x) . . . . . area of the shed

__

Completing the square gives ...

  2x² +3x +1.125 = 21.125 . . . . . . add 2(9/16) to both sides

  2(x +0.75)² = 21.125 . . . . . . . write as a square

  x +0.75 = √10.5625 . . . . . divide by 2, take the square root

  x = -0.75 +3.25 = 2.50 . . . . . subtract 0.75, keep the positive solution

The width of the shed is 2.5 feet; the length is 2(2.5)+3 = 8 feet.

Step-by-step explanation:

[tex]area \: of \: rectangle = length \times \: width[/tex]

Given

[tex]l = 2w - 3[/tex]

using this

[tex]area = l \times w = (2w - 3)(w) = 27[/tex]

[tex]2 {w}^{2} - 3w = 27[/tex]

[tex]2 {w}^{2} - 3w - 27 = 0[/tex]

[tex]2 {w}^{2} - 9w + 6w - 27 = 0[/tex]

[tex]2w(w - 4.5) + 6(w - 4.5) = 0[/tex]

[tex](2w + 6)(w - 4.5) = 0[/tex]

[tex]w = - 3 \: \: or \: \: w= 4.5[/tex]

Since size cannot be negative therefore

[tex]w = 4.5cm[/tex]

[tex]l = 2w - 3 = 9 - 3 = 6[/tex]

Hence length of the rectangle=6m

width of the rectangle=4.5m

Answer:

Let length and breadth of rectangle be x metres and y metres respectively.

xy = 27 ---- eqn 1

x = 2y-3 ---- eqn 2

Sub eqn 2 into eqn 1:

(2y-3) × y = 27

2y² - 3y = 27

2y² - 3y - 27 = 0

(y+3)(2y-9) = 0

y+3=0 or 2y-9=0

y=-3 (rejected) 2y=9

y=4.5

Sub y=4.4 into eqn 2:

x = 2(4.5) - 3

= 6

Hence,

length of rectangle = x metres

= 6m

breadth of rectangle = y metres

= 4.5m

Answer:

56 miles

Step-by-step explanation:

According to the question, lets say the miles at x they charge the same rental

       34 + 0.50x = 20 + 0.75x (Solve equation)

       0.75x - 0.50x = 34 - 20

       0.25x = 14

       x = [tex]\frac{14}{0.25}[/tex]

       x = 56

So at 56 miles, they charge the same rental.

Answer:

Step-by-step explanation:

20x+21=0

20x=-21

x=-1.05

Answer:

A 4h

Step-by-step explanation:

[tex]7 + 2 - 5 = 9 - 5 = 4[/tex]

Answer:

The cross section of a cube is square...

and we know that ,Area of square = side²

so, Area of cross section= l²

Hope it helps you

The area of the rectangle whose perimeter is 24 units and one side is of 'a' units, in terms of 'a' is given as: S = a(12-a) unit²

Suppose that the two adjacent sides of a rectangle be of 'a' units and 'b' unit lengths.

Then, we get the area of that rectangle as:

[tex]S = a \times b \: \rm unit^2[/tex]

For this case, we're specfied that:

Let the other side (adjacent) be of 'b' units length

Then, as perimeter of a rectangle = 2(sum of lengths of one pair of adjacent sides of the rectangle)

Therefore, we get:

[tex]24 = 2(a+b)\\\text{Dividing both the sides by 2}\\12 = a + b\\b = 12 - a[/tex]

We expressed 'b' in terms of 'a' so that we can represent the area of the considered rectangle in terms of 'a' alone.

The area of the rectangle is:

[tex]S =a \times b = a \times (12 - a) \: \rm unit^2[/tex]

Thus, the area of the rectangle whose perimeter is 24 units and one side is of 'a' units, in terms of 'a' is given as: S = a(12-a) unit²

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The expression that represents the value of the stock after two years have passed is 1.5498x

Percentage is the fraction of an amount expressed as a number out of hundred. The sign used to represent percentages is %.

The value of the stock after year 1 = worth of the stock when it was bought x (1 + percentage increase in year one)

1.23x

The value of the stock after year 2 = worth of the stock in year 1 x (1 + percentage increase in year two)

1.26 x 1.23x = 1.5498x

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Answer:

1099in²

Step-by-step explanation:

SA = [tex] \sf A=2\pi rh+2 \pi r² [/tex]

⇒ SA=2πrh+2πr²

⇒ SA = 2((3.14)(5)(30)+(2)(3.14)(5²)

⇒ SA = 2((3.14)(5)(30)+(2)(3.14)(25)

⇒ SA = 1099

Surface Area = 1,099 in²