Use a sign chart to solve the inequality. Express the solution in inequality notation and in interval notation. X2 - 5x - 36 < 0 The solution expressed in inequality notation is.

we get two possible solutions: L = 6 and W = 4. Therefore, the length of the land could be 6 meters.

If the rectangular plot has length L and width W, then we know that 2L + 2W = 20 since 20 meters of wire mesh were used. We also know that L × W = 24 since the area of the plot is 24 square meters. Solving these two equations simultaneously, We have the equations:

2L + 2W = 20

L × W = 24

From the first equation, we can solve for L in terms of W:

2L = 20 - 2W

L = 10 - W

Substituting this into the second equation, we get:

(10 - W) × W = 24

Expanding the brackets, we get: 10W - W² = 24

Rearranging and setting equal to zero, we get: W² - 10W + 24 = 0

We can solve this quadratic equation by factoring: (W - 6) × (W - 4) = 0

So the possible solutions for W are: W = 6 or W = 4

If W = 6, then L = 10 - W = 4, so the rectangular plot has dimensions 4 meters by 6 meters. If W = 4, then L = 10 - W = 6, so the rectangular plot has dimensions 6 meters by 4 meters. Therefore, the length of the land is 6 meters. because the length is assumed as the longer side of a shape or an object.

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Complete Question

To enclose a rectangular plot of 24 m², 20 m of wire mesh were used, what is the length of the land?

Answer:616 dollars, didn't include his hours worked overtime.

Step-by-step explanation:

Alright, so he makes $14 per hour and it doubles on overtime.

28 for overtime

and 44(hours worked) times 14(amount earned each hour) equals 616 dollars

An explicit description of Nul A is given by the set of vectors {[0, 0, 1, 0], [0, 0, 0, 1]}.

What is the explicit description of a null space matrix?

To find an explicit description of the null space of matrix A, we can find a spanning set of vectors that span the null space.

The null space of matrix A, denoted Nul A, is the set of all vectors x that satisfy the equation Ax = 0. In other words, the null space consists of all vectors that are mapped to the zero vector by the matrix A.

To find a spanning set for Nul A, we can use the following steps:

Row reduces the matrix A to a reduced row-echelon form using elementary row operations.

Identify the free variables in the row-reduced matrix.

For each free variable, create a vector with a 1 in the position corresponding to the free variable and 0's in all other positions.

The set of vectors created in step 3 form a spanning set for Nul A.

For example, consider the matrix A = [1, 2, 3, 0; 0, 0, 1, 0]. To find a spanning set for Nul A, we can row reduce the matrix to reduced row-echelon form:

[1, 2, 3, 0] -> [1, 2, 3, 0]

[0, 0, 1, 0] -> [0, 0, 1, 0]

The matrix is already in reduced row-echelon form, so there are no more elementary row operations to perform. The free variables in this matrix are the third and fourth columns, which correspond to the variables x3 and x4, respectively. Therefore, we can create the following vectors:

x3 = [0, 0, 1, 0]

x4 = [0, 0, 0, 1]

These vectors form a spanning set for Nul A, as they are linearly independent and span the null space.

Hence, an explicit description of Nul A is given by the set of vectors {[0, 0, 1, 0], [0, 0, 0, 1]}.

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Answer:

10

Step-by-step explanation:

it is 10 cause 634+10=644

Answer:

10

Step-by-step explanation:

What is the missing addend?

We can fill in the blank with x

634+x=644

Now we need to get x to the other side

The rule to do this is what we do on one side we have to do the same thing to the other side

so if we subtract 634 on one side we also have to do that on the other side as well:

634-634+x=644-634

634-634 is 0

So it is

x=644-634

644-634 is 10

x=10

So the missing addend is 10

Hope this helps!

The correct option for the expression (5 + 9) + 10 showing the associative property is  5+ (9 + 10) = 5 + 19 = 24

The associative property of addition states that the sum of three or more numbers remains the same regardless of how the numbers are grouped.

Given that, an expression, (5 + 9) + 10

According to associative property of addition, (a+b)+c = a+(b+c)

Therefore,

(5 + 9) + 10 = 5+(9+10)

= 5+19

= 24

Hence, the correct option for the expression (5 + 9) + 10 showing the associative property is  5+ (9 + 10) = 5 + 19 = 24

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The coordinates of the y-intercept are (0, 3.5) and the coordinates of the x-intercepts are (-17.5, 0). Using these coordinates, the graph of the equation is shown below.

From the question, we are to graph the given linear equation.

To graph the equation,

We will determine the coordinates of the x-intercepts and y-intercepts.

When x = 0

y = 1/5x + 3.5

y = 1/5(0) + 3.5

y = 3.5

(0, 3.5)

When y = 0

y = 1/5x + 3.5

0 = 1/5x + 3.5

Multiply through by 5

0 = x + 17.5

x = -17.5

(-17.5, 0)

Using the coordinates of the x-axis and y-axis, the graph of the equation is shown below.

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The 19  tykes  given away by the Shelter, that have room for only 4  tykes  per family.        

The number of different canine families that could be created from the 19  tykes  given away by the  sanctum, we need to calculate the number of combinations. room for only 4  tykes , we need to choose 4  tykes  from the aggregate of 19  tykes . The order of the  tykes  in the family doesn't count, as long as we choose different  tykes  for each family.  The number of combinations can be calculated using the formula for combinations  C( n, r) =  n!/( r!( n- r)!)  Where C( n, r) represents the number of combinations of choosing r  particulars from a set of n  particulars.  In this case, we've n =  19( total number of  tykes ) and r =  4( number of  tykes  per family).  Plugging these values into the formula, we get  C( 19, 4) =  19!/( 4!( 19- 4)!)  Calculating the factorial values  19! =  19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 =  ! =  4 × 3 × 2 × 1 =  24  15! =  15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 =   Substituting these values into the formula  C( 19, 4) = /( 24 ×)  ≈ 91,390  The 19  tykes  given away by the  sanctum, considering that you have room for only 4  tykes  per family.

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Combining like terms yields 7x⁵ - x³ - x² + 4x.

1000 ml of sodium silicate is used to make 10 liters soap

An equation is a expression that shows the relationship between numbers and variables.

The standard form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Let y represent the amount of sodium silicate in x ml of liquid soap.

From the graph, using the points (1000, 100) and (3000, 300):

y - 100 = [(300 - 100)/(3000 - 1000)](x - 1000)

y - 100 = 0.1(x - 1000)

y = 0.1x

For 10 L (10000 ml)of soap:

y = 0.1(1000) = 1000 ml

1000 ml of sodium silicate is used to make the soap

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Answer:

f(5) = 32

g(5) = 40

Step-by-step explanation:

For f(x) we can realize that each term for the value of x is twice the value before it. This means the missing value is 32 or f(5) = 32.

For g(x) we can realize that each term is 10 more than the previous. This means g(5) = 40.

Answer:

The letter "x" is often used in algebra to mean an unknown value. It is often called a "variable".

Example:

In x + 5 = 12, x is a variable, but we can work out its value if we try!

Answer:To evaluate the function for f(2), we simply substitute x = 2 into the function

:f(2) = 8(2) + 7

Simplifying the expression:

f(2) = 16 + 7f(2) = 23

Therefore, f(2) = 23.

Step-by-step explanation:

Answer:

Point a is correct.

Step-by-step explanation:

hope I helped.

Answer:

the answer for question 2 is (D)

The number of square inches of cardboard that are needed to make one

the container is 18.

We have,

The volume of the triangular prism.

= Area of the triangle x height

Now,

Height = 6 in

And,

To find the area of a triangle, we can use Heron's formula.

A = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.

Let's calculate the area using Heron's formula:

s = (3.2 + 3.2 + 2) / 2 = 4.2

A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))

A = √(4.2 x 1 x 1 x 2.2)

A = √(9.24)

A ≈ 3.04 square inches

Now,

The volume of the triangular prism.

= Area of the triangle x height

= 3.04 x 6

= 18.24 in²

Now,

Area of one cardboard.

= 1² in²

= 1 in²

Now,

The number of square inches of cardboard that are needed to make one

container.

= The volume of the triangular prism / Area of one cardboard

= 18.24 in² / 1 in²

= 18.24

= 18

Therefore,

The number of square inches of cardboard that are needed to make one

the container is 18.

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Answer:

The approximate volume of the cone is 14 cube inches.

Step-by-step explanation:

Circumference of the base of the cylinder = 3π inches

Height of the cylindrical piece of wood = 6 inches

volume of a cone = \(\frac{1}{3}\)\(\pi\)\(r^{2}\)h

But,

circumference = 2πr

3π = 2πr

r = \(\frac{3}{2}\)

  = 1.5 inches

Radius of the base of the cylinder is 1.5 inches.

So that;

volume of cone =  \(\frac{1}{3}\) x \(\frac{22}{7}\) x \((\frac{3}{2}) ^{2}\) x 6

                          =  \(\frac{1}{3}\) x \(\frac{22}{7}\) x \(\frac{9}{4}\) x 6

                          = 14.143

volume of cone = 14.143 cube inches

The approximate volume of the cone is 14 cube inches.

Answer:

undefined

Step-by-step explanation:

The slope is found by the formula

m = (y2-y1)/(x2-x1)

   = (-3-1)/(-6- -6)

   = (-3-1)/(-6+6)

  = -4/0

Since we are dividing by zero, the slope is undefined

The net worth of the entrepreneur can be found to be $ 1, 785, 000

The net worth of a person can be found by the formula :

= Assets - liabilities

The assets of this entrepreneur include the savings, the house, the piece of land and the car. But, he has liabilities of $ 35, 000.

The net worth of the entrepreneur is therefore :

= 350, 000 + 850, 000 + 500, 000 + 120, 000 - 35, 000

= 1, 820, 000 - 35, 000

= $ 1, 785, 000

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The full question is:

Un empresario ha podido ahorrar $350.000, tiene una casa de $850.000, un terreno de $500.000, un carro de $120.000 pero tiene deudas de $35.000 en sus tarjetas, sus gastos mensuales son de $5.000 para sus empleados.

Cuál es su patrimonio neto?

The percentage is 6.25%

Calculate the percentage increase

The ability to calculate percentage increases is a crucial one for geographers to possess. The outcomes may improve when geographers gather data over time. A geographer can determine the degree of change in their data by computing a percentage increase. For instance, learning how much a river channel widens as you move downstream may be helpful.

calculate the difference between the two figures being compared.

Divide the increase by the starting amount, then multiply the result by 100. % Increase equals an increase of 100 initial numbers.

Based on the given conditions, formulate: (17-16)/16

Calculate the sum or difference: 1/16

Rewrite a fraction as a decimal:0.0625

Multiply a number by both the numerator and the denominator: 0.0625×100÷100

Calculate the product or quotient: 6.25÷100

Rewrite a fraction with a denominator equal to 100 to a percentage:6.25%

Solution:6.25%

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The end-points of the line segment will be negative 1.25 and 0.25.

A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.

The length of the line segment is 1.50 units and the midpoint of the line segment is negative 0.50. Then the end-points of the line segment are given as,

⇒ - 0.50 ± (1.50) / 2

Simplify the expression, then we have

⇒ - 0.50 ± (1.50) / 2

⇒ - 0.50 - (1.50) / 2, - 0.50 + (1.50) / 2

⇒ - 0.50 - 0.75, - 0.50 + 0.75

⇒ - 1.25, 0.25

The end-points of the line fragment will be negative 1.25 and 0.25.

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Answer:

$760

Step-by-step explanation:

Set up an equation:

Variable x = regular price

34/100 = 258.40/x

Cross multiply

34 × x = 100 × 258.40

34x = 25,840

Divide both sides by 34

x = 760

Check your work:

760 × 34%

Convert the percentage into a decimal:

760 × 0.34

$258.40

Correct!

Answer:

This expression has no roots.

Step-by-step explanation:

Using the discriminant: b² - 4ac, we get:

2² - 4 × 3 × 1

= 4 - 12

= -8

So this equation has no real solutions.  Let's prove that by trying to solve for x:

3x² + 2x + 1 = 0

9x² + 6x + 3 = 0

9x² + 6x + 1 = -2

(3x + 1)² = -2

3x + 1 = i√2

3x = -1 ± i√2

x = (-1 ± i√2) / 3

The only solutions available then are indeed complex.

This expression has no roots. the discriminant of the equation is -8.

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Using the discriminant: b² - 4ac, we get:

2² - 4 × 3 × 1

= 4 - 12

= -8

So this equation has no real solutions.  Let's prove that by trying to solve for x:

3x² + 2x + 1 = 0

9x² + 6x + 3 = 0

9x² + 6x + 1 = -2

(3x + 1)² = -2

3x + 1 = i√2

3x = -1 ± i√2

x = (-1 ± i√2) / 3

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Answer

25/1 and 43/125

Step-by-step explanation:

Answer:

C) 24 in

Step-by-step explanation:

We can use Pythagorean theorem:

a²+b²=c²

18²+b²=30²

324 + b² = 900

b² = 576

b = 24

Missing side length is C) 24 in

Emilio can find that the critical value t* for a 90% confidence level and 11 degrees of freedom is approximately 1.796.

To construct a t interval for the mean lifespan with 90% confidence, Emilio needs to use a t-distribution with n-1 degrees of freedom. The confidence interval for the population is given by:

confidence interval = x ± t × (s·x/√n)

Where x is the sample mean, s·x is the sample standard deviation, n is the sample size, and t is the critical value of the t-distribution.

Since the sample size is n=12, the degrees of freedom for the t-distribution will be (n-1) = 11. To find the critical value t* for a 90% confidence level and 11 degrees of freedom, Emilio can use a t-distribution table or a statistical software.

Using a t-distribution table or calculator, Emilio can find that the critical value t* for a 90% confidence level and 11 degrees of freedom is approximately 1.796.

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we have:

first, we can multiply and divide by sqrt{72} (to get the sqrt of the denominator)

now we can simplify sqrt{72} writing 72 as 2*36

So the answer is:

Answer:

(B) 18 cm x 8 cm

Step-by-step explanation:

let the length be x,

then the width is \(\frac{1}{3}\)x + 2

2( \(\frac{1}{3}\)x + 2 + x ) = 52

\(\frac{1}{3}\)x + 2 + x  = 26

\(\frac{4}{3} x\) = 24

x = (24*3)/4

x = 18

then the length is 18 cm

and width is (1/3)*18 + 2 = 8

Therefore the dimensions are length:width = 18 cm : 8 cm

Answer:

(B) 18cm x 8cm

Step-by-step explanation:

Perimeter of a rectangle  =  52 cm

2(length + width)  =  52 ==>  l + w  =  26

Let x be the length

width  =  (x/3) + 2

x + (x/3) + 2  =  26

[(3x + x)/3]  + 2 =  26

4x / 3  =  24

4x  =  24 (3)

x  =  6(3) ==>  18 cm

Width  =  (18/3) + 2

=  6 + 2  =  8 cm

So, the required dimension is 18 cm x 8 cm.