A room is 12 m long and the width is 1.5 m more than the height. If the area of the four walls is 105 m², find the height of the room giving your answer correct to 2 decimal places.​

Answer: 0.71428 or 5:7 or 5/7

Step-by-step explanation: just divide on a calculator

The values of {m} that is greater than 4.6 represent the solution of the given inequality.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

The given inequality is -

5m - 7 > 16

Adding 7 on both sides, we get -

5m - 7 + 7 > 16 + 7

5m > 23

m > 23/5

m > 4.6

Therefore, the values of {m} that is greater than 4.6 represent the solution of the given inequality.

To solve more questions on inequality, visit the link-

brainly.com/question/11897796

#SPJ1

Using the standard format of a perfect-square quadratic sum, it is found that the value that completes the expression is 169.

It is represented by:

(a + b)² = a² + 2ab + b².

In this problem, we have that the expression is:

a² + 2ab + b² = h² + 26 + b².

Hence a = 1, 2ab = 26 -> b = 13, thus the value that completes the expression is:

b² = 13² = 169.

More can be learned about perfect-squares at https://brainly.com/question/13136492

The graph that represents the function y= tanx is Option A.

The graph of y =tan (x) is a periodic function that has vertical asymptotes at x = (n + 1/2)π, where n is an integer.

It oscillates between positive and   negative infinity, creating a wave-  like pattern.

It has a repeating pattern of sharp peaks and valleys, exhibiting both positive and negative slopes.

Thus, option A is the correct answer.

Learn more about graph:
https://brainly.com/question/25184007
#SPJ1

Answer:

Each square on the travel chessboard is 0.75 inches by 0.75 inches

Step-by-step explanation:

A scale factor of 1/3 when dilating means that we divide 2.25 by 3. That equals 0.75 :)

Answer:

X= -12 +6√10

X= 6.973

Step-by-step explanation:

Volume of the box= (36-2x)(24-2x)x

Volume of the box

=( 864 -96x -4x²)x

But 864 -96x -4x²

=216 - 24x-x²

Solving for x quadratically

X= (24+12√10)/-2

X= -12 -6√10

X= -30.97

Or

X= (24-12√10)/-2

X= -12 +6√10

X= 6.973

X will definitely be a positive number

So X= -12 +6√10

X= 6.973

Increasing or decreasing the side length of the square that gives the

maximum volume, gives a volume that is less than the maximum.

Reasons:

The given dimensions of the box = 24 in. by 36 in.

Let x represent the dimensions of the square removed from the corners, we have;

Width of box = 24 - 2·x

Length of box = 36 - 2·x

Height of the box = x

Volume of a box = Width × Length × Height

Therefore;

Volume of the box, V = (24 - 2·x)·(36 - 2·x)·x = 4·x³ - 120·x² + 864·x

At the maximum or minimum point of the volume, we have;

Which gives;

12·x² - 240·x + 864 = 0

x² - 20·x + 72 = 0

Which gives;

\(\displaystyle x = \dfrac{20\pm \sqrt{(-20)^{2}-4\times 1\times 72}}{2\times 1} = \mathbf{10 \pm 2\cdot \sqrt{7}}\)

At x = 10 + 2·√7, we have;

\(\displaystyle 10 + 2 \cdot \sqrt{7} > \frac{24}{2}\)

2 × (10 + 2·√7) in. > 24 in. which is the width of the cardboard

Therefore, (10 + 2·√7) is too long to be cut from the cardboard

At x = 10 - 2·√7, we have;

V = 4·(10 - 2·√7)³ - 120·(10 - 2·√7)² + 864·(10 - 2·√7) ≈ 1,828.3

Therefore;

The maximum volume corresponds with a cut out square of side length x = 10 - 2·√7 inches  ≈ 4.71 inches

Learn more here:

https://brainly.com/question/11879766

https://brainly.com/question/14573161

If the discriminant (the expression inside the square root) is negative, then the solutions will be complex conjugates. If the discriminant is zero, then the two solutions will be equal, and if the discriminant is positive, then there will be two distinct real solutions.

The quadratic equation \(Ax^2 + Bx + C = 0\) can be solved using the quadratic formula:

\(x = (-B ± \sqrt{ (B^2 - 4AC)) / 2A\)

where A, B, and C are the coefficients of the quadratic equation.

In your case, the quadratic equation is Ax^2 + bx + c = 0, so we can substitute A = a, B = b, and C = c into the quadratic formula:

\(x = (-b ± \sqrt{(b^2 - 4ac)) / 2a\)

This formula will give us two possible solutions for x: one with a plus sign before the square root, and one with a minus sign. These solutions correspond to the points where the parabola defined by the quadratic equation intersects the x-axis.

It's worth noting that the solution(s) may be real or complex numbers depending on the values of a, b, and c. If the discriminant (the expression inside the square root) is negative, then the solutions will be complex conjugates. If the discriminant is zero, then the two solutions will be equal, and if the discriminant is positive, then there will be two distinct real solutions.
To know more about discriminant go through:-
https://brainly.com/question/2507588
#SPJ9

y = 1/3x - 21 is the equation of the line in slope-intercept form.

What is a slope?

Slope is a measure of the steepness or incline of a line. It describes how much the dependent variable (usually y) changes for a given change in the independent variable (usually x).

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

We are given that the slope is 1/3 and that the line passes through the point (3, -20). We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

where (x1, y1) is the point through which the line passes, and m is the slope. Plugging in the values we have:

y - (-20) = 1/3(x - 3)

Simplifying this equation:

y + 20 = 1/3x - 1

Subtracting 20 from both sides:

y = 1/3x - 21

This is the equation of the line in slope-intercept form.

To learn more about slope from the given link:

https://brainly.com/question/3605446

#SPJ1

Answer:

Step-by-step explanation:

Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:

First, we need to calculate the area of the rectangular base, which is simply length x width:

Area of rectangular base = 13 x 13 = 169 square units

Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.

To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:

a² + b² = c²

where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.

13² + 13² = c²

338 = c²

c ≈ 18.38

Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:

Area of isosceles triangle = (1/2) x base x height

Area of isosceles triangle = (1/2) x 13 x 18.38

Area of isosceles triangle ≈ 119.14 square units

To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:

Area of right triangle = (1/2) x base x height

Area of right triangle = (1/2) x 13 x 18.38

Area of right triangle ≈ 119.14 square units

Since there are two of each type of triangular face, the total surface area of the pyramid is:

Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle

Surface area = 169 + 2 x 119.14 + 2 x 119.14

Surface area = 546.28 square units

Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.

The correct solution of the given the system of inequalities is graph D.

A system of inequalities is a set of two or more inequalities in one or more variables. Systems of inequalities are used when a problem requires a range of solutions, and there is more than one constraint on those solutions.

Given that, a system of inequalities, y > 2x²+x-3 and y ≤ -x²+5x, we need to identify the graph for thus system,

y > 2x²+x-3

The graph for this equation will be an upward parabola, with solid curve.

y ≤ -x²+5x

The graph for this equation will be a downward parabola, with dotted curve.

The graphs will intersect at (-0.535, -2.962) and (1.869, (5.851)

The parabola y ≤ -x²+5x will be right downwards to y > 2x²+x-3  

Hence, the correct solution of the given the system of inequalities is graph D.

Learn more about system of inequalities, click;

https://brainly.com/question/19526736

#SPJ1

The rational function graphed in this problem is defined as follows:

y = -2(x - 1)/(x² - x - 2).

The vertical asymptotes of the rational function for this problem are given as follows:

x = -1 and x = 2.

Hence the denominator of the function is given as follows:

(x + 1)(x - 2) = x² - x - 2.

The intercept of the function is given as follows:

x = 1.

Hence the numerator of the function is given as follows:

a(x - 1)

In which a is the leading coefficient.

Hence:

y = a(x - 1)/(x² - x - 2).

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

-1 = a/2

a = -2.

Thus the function is given as follows:

y = -2(x - 1)/(x² - x - 2).

More can be learned about rational functions at brainly.com/question/1851758

#SPJ1

Answer:

The answer is point A' (3, -2).

The length of the other two sides are 4m and 5m

Using the Pythagorean theorem, we have that the square of the hypotenuse sides is equal to the sum of the squares of the other two sides of the triangle

This is represented as;

x² = y² + z²

From the information given, we have that;

z = 3m

x = x + 1

y = x

Substitute the values, we get

(x + 1)² = x² + 3²

Find the squares

(x + 1) ² = 9 + x²

expand the bracket

(x + 1) ( x + 1) - x² = 9

x² + x + x + 1 - x² = 9

collect like terms

2x = 8

x = 4

Then,

x + 1 = 5

x = 4

Hence, the values are 4m and 5m

Learn about triangles on:

https://brainly.com/question/14285697

#SPJ1

Answer:

the solution to the system of equations is (x, y) = (3, -2).

Step-by-step explanation:

y = -2x + 4 (Equation 1)

y = x - 5 (Equation 2)

To solve for x, we can equate the right sides of the equations:

-2x + 4 = x - 5

Now, we can solve for x:

-2x - x = -5 - 4

-3x = -9

x = (-9) / (-3)

x = 3

Substituting the value of x back into Equation 2, we can solve for y:

y = 3 - 5

y = -2

Answer:

77%

Step-by-step explanation:

Given:

A parallelogram must be a rectangle.

If the diagonals are congruent then the parallelogram must be a rectangle.

Option B is the final answer.

Answer:

Infinite

Step-by-step explanation:

I hope this helps, if it doesn't then just message me and ill be more than happy to help :)

The surface areas are 110 in², 87.6 mm² and 49 m².

Given that are solid figure, we need to find the surface area of them,

1) Triangular prism = perimeter × length + 2 × base area

= (5 + 5 + 6) × 5 + 2(3×5) = 110 in²

2) Triangular pyramid = base area + perimeter × slant height / 2

= 1/2 × 5.2 × 6 + 3 × 6 × 8/2

= 87.6 mm²

3) Cube = 4side²

= 4 × (3 1/2)²

= 4 × 3.5²

= 49 m²

Hence the surface areas are 110 in², 87.6 mm² and 49 m².

Learn more about surface areas click;

https://brainly.com/question/29298005

#SPJ1

Answer:

405 of the students

Step-by-step explanation:

Answer:

P(A) = 0.2, P(B) = 0.5, P(A\B) = 0.3:

P(A\B) = P(A and B) P(B)

0.3 = P(A and B) 0.5

0.15 P(A and B)

P(A and B) = 0.15

B. P(A or B) = P(A) + P(B) - P(A and B)

0.2 + 0.5 - 0.15

0.70 - 0.15 = 0.55

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

  Option B is correct

b

   \(P(\= A ) = 0.997\)

Step-by-step explanation:

From the question \(\= A\) denote the compliment of A and what this mean is that  \(\= A\) consist of all the outcomes in which event A does not occur

  Given that  P(A)  = 0.003

Then the value of

                   \(P(\= A ) = 1- 0.003\)

                    \(P(\= A ) = 0.997\)

Answer:

6 * 2 = 12 cans

Answer:

$0.08

Step-by-step explanation:

20 x .08 = 1.60

Answer:

8 cents

Step-by-step explanation:

because if you multiply 8 by 20 you get 1.60

Answer:

3

Step-by-step explanation:

1) Substitute x with 2

b^8

b^2

2) subtract the index

b^8-2

=b^6

3)b^6 ≠ b^8

therefore, 3 is a lie

Answer:

12 hours

Step-by-step explanation:

15/2=7.5

90/7.5 = 12

The cubic model that fits the given data is: y ≈ 0.00006204x³ + 0.00231059x² - 0.10811757x + 18.2

Let's set up a system of equations using the given data points:

For x = 0 (year 1950):

18.2 = a(0)³ + b(0)² + c(0) + d ==> d = 18.2

For x = 10 (year 2000):

65.5 = a(10)³ + b(10)² + c(10) + 18.2

For x = 20 (year 2010):

75.3 = a(20)³ + b(20)² + c(20) + 18.2

For x = 25 (year 2015):

78.1 = a(25)³ + b(25)² + c(25) + 18.2

For x = 30 (year 2020):

78.5 = a(30)³ + b(30)² + c(30) + 18.2

For x = 40 (year 2030):

80.5 = a(40)³ + b(40)² + c(40) + 18.2

For x = 50 (year 2040):

86.6 = a(50)³ + b(50)² + c(50) + 18.2

For x = 60 (year 2050):

91.5 = a(60)³ + b(60)² + c(60) + 18.2

Simplifying these equations, we have: d = 18.2

1000a + 100b + 10c + 18.2 = 65.5

8000a + 400b + 20c + 18.2 = 75.3

15625a + 625b + 25c + 18.2 = 78.1

27000a + 900b + 30c + 18.2 = 78.5

64000a + 1600b + 40c + 18.2 = 80.5

125000a + 2500b + 50c + 18.2 = 86.6

216000a + 3600b + 60c + 18.2 = 91.5

We can solve this system of equations to find the coefficients a, b, and c.

Using a cubic regression calculator or a matrix solver, the solution is:

a ≈ 0.00006204

b ≈ 0.00231059

c ≈ -0.10811757

Therefore, the cubic model that fits the given data is: y ≈ 0.00006204x³ + 0.00231059x² - 0.10811757x + 18.2

Learn more about equations on

https://brainly.com/question/13763238

#SPJ1

The half-distance left is 40/7 or 5.714 miles

Given that:

The total race is 16 miles long.

Kim walked for 2/6 of the race, which is (2/6) * 16 = 16/3 miles.

After walking 16/3 miles, there are 16 - 16/3 = 32/3 miles left in the race.

Kim then sprints for 3/7 of the remaining distance, which is (3/7) * 32/3 = 32/7 miles.

Half of the race is left after she finished sprinting and walking, which is

16 - 32/7 = 80/7 miles

Divide this by 2:

80/7 ÷2

= 40/7 miles are left.

Read more about distance here:

https://brainly.com/question/2854969

#SPJ1

Answer: Shade 6 pieces

Step-by-step explanation:

Because 2/5 of 15 is 6