Find the perimeter using the area

The polynomial equation is 4x³ - 16x² - 5x - 75 = 0.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The passenger section of a train has a width of (2x - 7), a length of (2x + 3), and a height of (x - 2).

Now,

Volume = 117 m³

Length x width x height = 117

(2x + 3) x (2x - 7)  x (x - 2) = 117

(2x + 3) x (2x² - 4x - 7x + 14 = 117

(2x + 3) x (2x² - 11x + 14) = 117

4x³ - 22x² + 28x + 6x² - 33x + 42 = 117

4x³ - 16x² - 5x - 75 = 0

Thus,

The equation is

4x³ - 16x² - 5x - 75 = 0

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Answer:

$100

Step-by-step explanation:

Answer:

10.7 hrs

Step-by-step explanation:

For each of the three legs    time = distance / rate

so

2.4 / 2.2   +    112 / 20.8   +   26.2 /6.2   = 10.7 hrs

According to the problem the expression is 2x + 9.

Expression in mathematics is an arrangement of symbols that represents a value, quantity, or an idea. Expressions are used to represent a wide range of concepts, from equations, inequalities, and functions, to more abstract topics such as probability and set theory. An expression is composed of a combination of symbols and numbers that are used to create a mathematical statement. Expressions can include constants, variables, operators, and functions. Constants are values that remain unchanged throughout a calculation, such as numbers like 2, 4, or 6. Variables are used to represent unknown quantities and are usually represented as letters like x, y, and z.

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Answer: 55%

Step-by-step explanation:

Step 1

To find the students who participate in at least one activity after school, take the number of students who participate (825) and divide by the total number of students (1500).

825/1500 = 0.55

Step 2

Take the answer from step 1 and multiple it by 100 to find the percentage.

0.55 x 100% = 55%

Answer:

below

Step-by-step explanation:

'x' cannot be zero because you would then have an illegal fraction with a zero denominator

the only interval listed that does not include zero  is  ( 1, +inf)

Answer:

D.

Step-by-step explanation:

f(x) = |x|

|x| = x for x > or = 0

|x| = -x for x < 0

At x = 0

Left limit = Right limit = Function value = 0

|x| = is continuous at x = 0.

Left derivative (at x = 0) = -1

Right derivative (at x = 0) = 1

Answer: 69 bozo LLLLLLLLLLLLLLLLLLLLLLLLLLL

Step-by-step explanation:

69

Answer:

Step-by-step explanation:

Let the height of the house be "h".

Using the triangle formed by the object, the man, and the base of the house, and using the tangent function, we have:

tan(45°) = h / 18√2

h = (18√2) * tan(45°)

Since tan(45°) = 1,

h = 18√2 * 1 = 18√2 m

So the height of the house is 18√2 meters.

18√2 can be simplified to:

18 * √2 = 18 * 1.414 = 25.656 (approximately)

The triangle was created, using a diagonal as a hypotenuse, where the length of the horizontal and vertical lines is similar.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
Step to create the triangle,
1. Draw a horizontal line parallel to the x-axis from the endpoints of the diagonal.
2. Draw a vertical line parallel to the y-axis from the endpoints of the diagonal.

3. The intersection point of these horizontal and vertical lines is the vertex of the triangle formed and the diagonal line is the common hypotenuse between the triangle.

4. When measuring the horizontal and vertical lines we will see they are equal for both the triangle formed.

Thus, the triangle was created, using a diagonal as a hypotenuse, where the length of the horizontal and vertical lines is similar.

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Answer:

3 - 4x + 2x + 11 + 5x - 9 - x = 3 + (2x - 4x) + (5x - x) + 11 - 9 = 3 + -2x + 4x + 11 - 9 = 3 - 2x + 2 = -2x + 5

Area of a Triangle = A = ½ (b × h) square units

where b and h are the base and height of the triangle, respectively. Now, let's see how to calculate the area of a triangle using the given formula.

Define right triangle?

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The correct ratio of right angled triangle is [tex]\frac{c}{b} = \frac{b}{s}[/tex]

There are a few unique varieties of right triangles, including the 45°-45° and the 30°-60° varieties.

Theorem: In a triangle, the angle across from the first side is a right angle if the square of one side equals the sum of the squares of the other two sides. To demonstrate: B=90° Proof: ABC has the formula [tex]AC^2 = AB^2 + BC^2[/tex]

The right triangle. A triangle with one right angle, or 90°, is referred to as a right triangle. The longest side, which is the side opposite the right angle, is referred to as the hypotenuse. The remaining two sides are referred to as the right triangle's legs because they intersect to form the right angle.

The hypotenuse, along with the two legs, make up a right triangle. The hypotenuse, the longest side of the right triangle and the side opposite the right angle, is where the two legs of a right triangle come together at a 90° angle. [tex]AC^2 = AB^2 + BC^2[/tex]

Given,

b/s = ratio of hypotenuse to height

c / b = ratio of hypotenuse to height

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The upper bound of a 99% confidence interval is found as 57.07.

A random sample of size 18.

Normal population gives 36.5.

Explain the term upper confidence bound (UCB)?

Whenever a machine is often used frequently than other machines, the border shrinks.

For the stated question-

sample size n = 18

normal population mean x = 36.5

variance  s² = 1148; s = 33.88

z(α/2) for 99% confidence interval = 2.576

Thus, upper confidence bound (UCB) is estimated as;

UCB = [tex]x + z(\frac{\alpha}{2} )*\frac{s}{\sqrt{n} }[/tex]

UCB = 36.5 + 2.576×33.88/√18

UCB = 36.5 + 20.57

UCB = 57.07

Therefore, the upper bound of a 99% confidence interval is found as 57.07.

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Answer:

y=3x-3

y=9/3x-3=3x-3

Equation of the quadratic kind: ax2+bx+c=0

Our ability to solve any quadratic equation is aided by the quadratic formula. First, we change the equation's form to read as ax2+bx+c=0, where a, b, and c are the coefficients. As a result, we enter these coefficients into the formula: (-b(b2-4ac))/(2a). See illustrations of how the formula can be used to solve various equations.

Ax2 + bx + c = 0 is the form of a quadratic equation, which is an expression in second-degree algebra. Square-sounding "quad" is the root of the term "quadratic," which signifies "quadratic." An "equation of degree 2" is another way to describe a quadratic equation. A quadratic equation is utilised in a wide variety of situations.

For 2nd order polynomial equations of the type an x 2 + b x + c = 0, the quadratic formula is an equation that is employed.

Quadratic Formula

 ax^2+bx+c=0

When a 0 x = the unknown,

a, b, and c are known numbers.

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Equation of the quadratic form: ax²+bx+c=0.

Our ability to solve any quadratic equation is aided by the quadratic formula. First, we change the equation's form to read as ax²+bx+c=0, where a, b, and c are the coefficients. As a result, we enter these coefficients into the formula: (-b(b²-4ac))/(2a).

Ax² + bx + c = 0 is the form of a quadratic equation, which is an expression in second-degree algebra. Square-sounding "quad" is the root of the term "quadratic," which signifies "quadratic." An "equation of degree 2" is another way to describe a quadratic equation. A quadratic equation is utilised in a wide variety of situations

For 2nd order polynomial equations of the type an x² + b x + c = 0, the quadratic formula is an equation that is employed.

Quadratic Formula

ax²+bx+c=0

When a 0 x = the unknown,

a, b, and c are known numbers.

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Answer:

Step-by-step explanation:

15-12=03

3X 11 =33

33-5=28

28-9=19

19-3=16

16 divided by 4= 4

so the awser is 4

Answer:

none of the above

Step-by-step explanation:

112 square inches make up the ABCD figure.

The area of trapezoid is given by :Area [tex]$=\frac{1}{2} \times(a+b) h$[/tex], where h is the trapezoid's height and a and b are the parallel opposite sides.

The area of trapezoid A B C D with height 7 inches and opposite parallel sides 14 inches and 18 inches is calculated from the provided image by:-

[tex]& \text { Area }=\frac{1}{2} \times(14+18) 7 \\[/tex]

[tex]& \Rightarrow \text { Area }=\frac{1}{2}(32)(7) \\[/tex]

[tex]& \Rightarrow \text { Area }=16 \times 7 \\[/tex]

[tex]& \Rightarrow \text { Area }=112 \text { inches }^2[/tex]

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Answer: The answer is 12

Step-by-step explanation:

Answer:

x÷11+6=54

Step-by-step explanation:

all information is given

Answer:

(A) 6

Step-by-step explanation:

since the question is about the integral and not the area of the curve, we indeed need to count the last part under the x-axis as negative.

it is an isoceles (both legs are equally long) right-angled 2×2 triangle. it's area is

2×2/2 = 2 units²

the first part is just a large rectangle 5×2, where we have to deduct two 2×1 right-angled triangles (one top left, one right).

so, we have

5×2 = 10 units²

-

2×1/2 × 2 = -2 units²

= 8 units²

and as we need to subtract the right triangle below the x-axis, the total integral is

8 - 2 = 6 units²

FYI

if the quarto was about the area under the curve, we would have to consider all parts as positron values, and we would have to calculate absolute value of the integral 0 to 5 plus the absolute value of the integral 5 to 7.

W1 is not a subspace of R3 under the operations of addition and scalar multiplication due to its failure to contain the zero vector. W3 is a subspace that satisfies the three properties of a subspace: it contains the zero vector (0, 0, 0), it is closed under addition, and if two elements of W3 are added together, the result is also an element of W3.

Subspaces are groupings of subspaces inside a larger space or vector space. They are a subset of a wider space described by a set of linear equations. Subspaces are useful in linear algebra for studying linear transformations and other linear operations.

(a) W1 is not a subspace of R3 when addition and scalar multiplication are performed because it fails the closure property of a subspace. Consider the numbers (2, -14, 7) and (3, -21, 10) in W1. When these two vectors are combined, the result is (5, -35, 17), which is not a W1 element.

(b) Since it lacks the zero vector, W2 is not a subspace of R3 for addition and scalar multiplication operations. To constitute a subspace, a set must contain the zero vector, which in this case is (0, 0, 0).

(c) W3 is a subspace of R3 with addition and scalar multiplication operations. To demonstrate this, we must demonstrate that it meets the three qualities of a subspace. It includes the zero vector (0, 0, 0). It is closed under addition, which means that if two W3 items are combined together, the result is likewise a W3 element. This is demonstrated by ensuring that the equation 201 - 4a2 + 5a3 = 0 still applies for any two vectors in W3 joined together. Lastly, it is closed under scalar multiplication, which means that each element of W3 multiplied by a scalar produces an element of W3. This too can be seen by checking that the equation 201 – 4a2 + 5a3 = 0 still holds for any element of W3 multiplied by a scalar.

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Answer:

To calculate the average speed for the second lap, we need to know the overall average speed for the two laps. If the average speed for the first lap is s, then the overall average speed for the two laps is (s + x)/2, where x is the average speed for the second lap.

We are told that the overall average speed for the two laps is three times the average speed for the first lap, so we can set up the following equation:

(s + x)/2 = 3s

To solve for x, we can multiply both sides of the equation by 2:

s + x = 6s

Subtracting s from both sides:

x = 5s

So, to make the overall average speed for the two laps three times the average speed for the first lap, the average speed for the second lap should be 5 times the average speed for the first lap.

a. The model predicts that the economic growth based on a barrel of oil priced at $55 is approximately -5.132 + 0.0912 * 55 = 3.8012.

b. The residual is 0.3 - 3.8012 = -3.5012, which indicates that the model is overestimating the economic growth based on a barrel of oil priced at $55. The negative value of the residual suggests that the model needs to be refined in order to provide more accurate predictions.

The least squares regression line model is used to find the best-fit line that minimizes the sum of the squared differences between the observed and predicted values.

The residual is the difference between the actual and predicted values for a given data point. In this case, the residual of -3.5012 suggests that the model is overestimating the economic growth based on a barrel of oil priced at $55.

To improve the accuracy of the model, we could consider additional factors that may impact the relationship between oil price and economic growth, or use different regression techniques to better fit the data.

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We kindly invite to check the image attached below to see the triangle constructed on Cartesian plane.

The measure of angle A is approximately equal to 46.102° and the measure of side AC is equal to 2√13 centimeters.

Triangles are figures generated by three distinct points set on Cartesian plane, with three line segments (AB, BC, AC) and three internal angles. In this problem we show all steps to construct a triangle with the help of a graphing tool. First, set point B at origin.

B(x, y) = (0, 0)

Second, add point C along x-axis:

C(x, y) = (6, 0)

Third, determine point A and add it on Cartesian plane:

A(x, y) = (8 · cos 60°, 8 · sin 60°)

A(x, y) = (4, 6.928)

Fourth, draw all line segments in triangle ABC. The result is shown in the image attached below.

Finally, we determine the measure of angle A and side AC by trigonometry:

Angle A:

First, determine the length of line segment AC by law of cosine:

AC = √(AB² + BC² - 2 · AB ·BC · cos B)

AC = √(8² + 6² - 2 · 8 · 6 · cos 60°)

AC = 2√13

Second, calculate the angle A by law of cosine:

cos A = (BC² - AB² - AC²) / (- 2 · AB · AC)

cos A = [6² - 8² - (2√13)²] / [- 2 · 8 · 2√13]

A ≈ 46.102°

Side AC:

AC = 2√13

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The solution be [tex]$x=\frac{\pi}{4}+\pi n, x=\frac{3 \pi}{4}+\pi n, x=\frac{\pi}{2}+\pi n$$[/tex].

A trigonometric identity is an equation involving the trigonometric functions that holds true regardless of the value of the variables.

Trigonometric Identities are equality conditions that apply to all values of the equation's variables and which require trigonometry functions. There are numerous unique trigonometric identities that involve both the side length and angle of a triangle.

In contrast to trigonometric equations, which ask us to identify the precise values of the variables that make two expressions equal, trigonometric identities describe the equality between related trigonometric expressions.

Let the equation be [tex]$$\cos ^2(2 x)+\cos (2 x)=0$$[/tex]

Solve by substitution

[tex]$$\begin{aligned}& \cos (2 x)=0, \cos (2 x)=-1 \\& \cos (2 x)=0 \quad: \quad x=\frac{\pi}{4}+\pi n, x=\frac{3 \pi}{4}+\pi n \\& \cos (2 x)=-1 \quad: \quad x=\frac{\pi}{2}+\pi n\end{aligned}$$[/tex]

Combine all the solutions

[tex]$x=\frac{\pi}{4}+\pi n, x=\frac{3 \pi}{4}+\pi n, x=\frac{\pi}{2}+\pi n$$[/tex]

Therefore, the solution be [tex]$x=\frac{\pi}{4}+\pi n, x=\frac{3 \pi}{4}+\pi n, x=\frac{\pi}{2}+\pi n$$[/tex].

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The required sample space randomly picked balls S = {A, B, C, D, E, F} and the outcomes for the event of choosing c to f is S' = {C, D, E, F}.

Sets are an orderly collection of items in mathematics that can be expressed in set-builder or roster form.

here,
For six ball sample space is given as,
S = {A, B, C, D, E, F}
n(s) = 6

Now,
Sample space choosing a ball at a time =
n(s) = 6

Outcomes for the event of choosing c to f.
From C to F there are 4 balls,
Sample space = {C, D, E, F}
n(S') = 4

Thus, the required sample space randomly picked balls S = {A, B, C, D, E, F} and the outcomes for the event of choosing c to f is S' = {C, D, E, F}.

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Answer:

C.

Step-by-step explanation:

correct answer is C:

[tex]y=5-\sqrt{x} ;[/tex]

where -sqrt(x) means one half of quadratic parabola, +5 means moving up the curve.