What is the slope of the line? 6x + 2y= -14

The radius of the sphere is 2.048 units .

The volume of a sphere is :

substituting into the formula:

36 = 4/3πr³

36 × 3 = 4 πr³

108 = 4πr³

πr³ = 27

r³ = 27/π

r³ = 8.59436

r = 2.048

Hence, the radius of the sphere is 2.048 units .

Answer:

  D. the extraneous solution is x = 4

Step-by-step explanation:

You want to know the statement that describes if there is an extraneous solution to the equation √x-3 = x-5.

A straightforward (blind) solution to the problem proceeds by squaring both sides and solving the quadratic:

  x -3 = x² -10x +25
  x² -11x +28 = 0
  (x -7)(x -4) = 0   ⇒   x = 4 or x = 7

When you try these solutions in the original equation, you get ...

  √(4 -3) = 4 -5   ⇒   1 = -1 . . . . . x = 4 is an extraneous solution, choice D

  √(7 -3) = 7 -5   ⇒   2 = 2 . . . . . x = 7 is the solution

The square root function is only defined for non-negative values, so the left side of the equation is only defined for x ≥ 3.

The left side of the equation produces non-negative values. The right side of the equation will have non-negative values only for x ≥ 5.

Considering the domain of the equation is x ≥ 5, we know that x = 4 cannot be a solution. It can be ignored. This value only arises because squaring the radical allows values of x that require the root to be negative.

__

Additional comment

The attached graph shows the only solution is x=7, the value that makes the difference between the sides of the equation be zero. We find it useful to write radical equations in the form f(x) = 0, making the x-intercepts of the graph of f(x) be the solution(s). The graphing calculator does not graph the function where it is undefined, so the domain restrictions are automatically accommodated.

The number of sides that the polygon with each exterior angle measuring 30° has is 12.

A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.

The sum of all the exterior angles of a regular polygon is always equal to 360°. Therefore, the measure of an exterior angle for a regular polygon is given as,

[tex]\theta = \dfrac{360^o}{n}[/tex]

where n is the number of sides.

Given that the measure of the exterior angle is 30°. Therefore, the number of sides will be,

[tex]\theta = \dfrac{360^o}{n}\\\\ 30^o = \dfrac{360^o}{n}\\[/tex]

n = 12

Learn more about Polygon:

https://brainly.com/question/10441863

#SPJ5

Answer:

13.6 is the correct answer

Step-by-step explanation:

got it right on the test

Final answer:

To find the perimeter of the given quadrilateral, calculate the distance between each pair of consecutive points using the distance formula and sum these distances. The perimeter is the sum of √17 + √20 + 3 + 2 which is 13.59 units.

Explanation:

The question you've asked involves finding the perimeter of a four-sided figure, known as a quadrilateral, with vertices R, S, T, and U located at (-1, 3), (-2, 7), (2, 5), and (-1, 5) respectively. To find the perimeter of this shape, we need to calculate the distance between each pair of consecutive vertices and sum these distances up.

Firstly, use the distance formula – d = √((x2 - x1)² + (y2 - y1)²) – to calculate the length of each side:

RS = √((-2 - (-1))² + (7 - 3)²) = √(1 + 16) = √17=4.12

ST = √((2 - (-2))² + (5 - 7)²) = √(16 + 4) = √20 = 4.47

TU = √((-1 - 2)² + (5 - 5)²) = √(9 + 0) = 3

UR = √((-1 - (-1))² + (3 - 5)²) = √(0 + 4) = 2

Finally, sum these distances to find the perimeter: √17 + √20 + 3 + 2 which comes out to be 13.59 units. The exact perimeter involves square roots since we're dealing with irrational distances.

Answer:

The line going to the right with a filled in circle plotted on 2.

Step-by-step explanation:

I did the review test and got it right

Using unitary method, the actual distance between the two towns is 105 km.

The formula of the unitary method is to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.

1 cm = 30 km

3.5 cm = 30 * 3.5 = 105 km

Learn more about unitary method here

https://brainly.com/question/22056199

#SPJ2

Answer:

"70, because 528 divides by 264 is 2, which means each picture is 2 megabytes, so therefore 35x2 = 70"

Step-by-step explanation:

this is good

70 megabytes can do 35 of these picture take up.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

It is given that kiara downloaded 264 pictures from her cellphone to her computer. These pictures took up 528 megabytes of space on her computer.

Each picture took up the same amount of space.

We have to find that how many megabytes do 35 of these picture take up.

therefore, we have to first divide the 528 by 264 then multiply it with 35.

So, we get

= 528/264 x 35

= 35 x 2 = 70

Hence, 70 megabytes can do 35 of these picture take up.

Learn more about the unitary method;

https://brainly.com/question/23423168

#SPJ6

The material i.e. needed should be 18.

Given that,

Based on the above information, the calculation is as follows:

[tex]a^2+b^2=c^2 \\\\ 24^2+b^2=30^2\\\\ 576+b^2=900 \\\\ b^2=324 [/tex]

18=b

Learn more: https://brainly.com/question/10309631?referrer=searchResults

Since lines L and M are parallel, corresponding angles such as angle 5 and angle 3 will be equal. Thus, if angle 5 is 132°, angle 3 will also be 132°.

This question concerns parallel lines and the angles formed by a transversal cutting across them. The lines L and M in the given diagram are parallel. Parallel lines have a special property where corresponding angles are equal. If angle 5 measures 132°, then the corresponding angle, angle 3, also measures 132°, because of this property of parallel lines.

Learn more about Parallel Lines here:

https://brainly.com/question/32035102

#SPJ2

The height of the trapezoidal section is approximately 3.6 centimeters.

To find the height of the trapezoidal section, we can use the formula for the area of a trapezoid: A = 1/2 * (top base + bottom base) * height. In this case, the top base is 1 centimeter and the bottom base is 3.5 centimeters. We are given that the area is 8.1 square centimeters. Plugging these values into the formula:

Therefore, the height of the trapezoidal section is approximately 3.6 centimeters.

The height of the trapezoidal section of stained glass is calculated using the area formula for trapezoids. With the given measurements, the height is found to be 3.6 centimeters.

To find the height of a trapezoid section in a stained glass window with a top base of 1 centimeter, a bottom base of 3.5 centimeters, and an area of 8.1 square centimeters, we use the formula for the area of a trapezoid, which is Area = 1/2 × (base1 + base2) × height. In this case, base1 is the top base, base2 is the bottom base, and Area is already given as 8.1 cm2.

Plugging the values into the formula gives us:

8.1 = 1/2 × (1 + 3.5) × height

8.1 = 1/2 × 4.5 × height

8.1 = 2.25 × height

To find the height, we divide both sides by 2.25:

height = 8.1 / 2.25

height = 3.6 centimeters

Thus, the height of the trapezoid section is 3.6 centimeters.

Answer:

between 4 and 10

Step-by-step explanation:

i did the quiz.

The area covered by the planter is 220¹/₂ in² = 220,5 in²

To solve the above questions, we need to recall some of the formulas as follows:

Area of Square = (Length of Side)²

Perimeter of Square = 4 × (Length of Side)

Area of Rectangle = Length × Width

Perimeter of Rectangle = 2 × ( Length + Width )

Area of Rhombus = ½ × ( Diagonal₁ + Diagonal₂ )

Perimeter of Rhombus = 4 × ( Length of Side )

Area of Kite = ½ × ( Diagonal₁ + Diagonal₂ )

Perimeter of Kite = 2 × ( Length of Side₁ + Length of Side₂ )

Let us now tackle the problem !

Given:

Length of Rectangle = L = 3¹/₂ inches

Width of Rectangle = W = 1³/₄ inches

Unknown:

Area of Plainter = A = ?

Solution:

This problem is about Area of Rectangle.

[tex]\texttt{Area of Rectangle} = \texttt{Length} \times \texttt{Width}[/tex]

[tex]\texttt{Area of Rectangle} = \texttt{Length} \times \texttt{Width}[/tex]

[tex]\texttt{Area of Rectangle} = 3\frac{1}{2} \times 1\frac{3}{4}[/tex]

[tex]\texttt{Area of Rectangle} = \boxed {6\frac{1}{8} ~ \texttt{in}^2}[/tex]

There is a 6 × 6 array of these planters with no space.

[tex]\texttt{Total Area Covered} = 6 \times 6 \times \texttt{Area of Rectangle}[/tex]

[tex]\texttt{Total Area Covered} = 6 \times 6 \times 6\frac{1}{8}[/tex]

[tex]\texttt{Total Area Covered} = \boxed {220\frac{1}{2} ~ \texttt{in}^2}[/tex]

Grade: College

Subject: Mathematics

Chapter: Two Dimensional Figures

Keywords: Perimeter, Area , Square , Rectangle , Side , Length , Width

complete question:

Write an expression in simplest form that represent the total amount.

Sal scored g goals this season. Ben has scored four times as many goals as Sal. Chun has scored three fewer goals than Ben.

a. 9g - 3

b. 3g - 9

c. g - 4g

d. 3g + 9

Answer:

a. 9g - 3

Step-by-step explanation:

Sal scored g number of goals this season . Ben has scored 4 times as many goals as Sal . Chun has scored 3 fewer goals than Ben. There goals can be expressed as follows

Sal's goal = g

Ben's goal = 4(g) = 4 × g = 4g

Chun's goal = 4g - 3

sum of their goals = g + 4g + (4g - 3)

sum of their goals = g + 4g + 4g - 3

sum of their goals = 9g - 3

Answer:

Part A: The center of The inscribed circle is the point S

Part B: The center of The circumscribed circle is the point P

Step-by-step explanation:

Part A: Find the center of The inscribed circle of ΔABC

The inscribed circle will touch each of the three sides of the triangle in exactly one point,

The center of the inscribed circle is the point of intersection between the angle bisectors of the triangle.

So, According to the previous definition:

A₁A₂ and B₁B₂ are the angle bisectors of ∠A and ∠B

So, the inter section between them is the center of The inscribed circle

So, the center of The inscribed circle is the point S

=====================================================

Part B: Find the center of The circumscribed circle of ΔABC

The circumscribed circle is the circle that passes through all three vertices of the triangle.

The center of the circumscribed circle is the point of intersection between the perpendicular bisectors of the sides.

So, According to the previous definition:

P₁P₂ and Q₁Q₂ are the perpendicular bisectors of AB and BC

So, the inter section between them is the center of The circumscribed circle

So, the center of The circumscribed circle is the point P

Answer:

The measure of arc is 216°

Step-by-step explanation:

Length of arc, L = 12π inches

Radius of the circle, R = 10 inches

Formula: [tex]\theta=\dfrac{L}{R}[/tex]

Where, [tex]\theta[/tex] in radian.

By substituting L and R into formula.

[tex]\theta=\dfrac{12\pi}{10}[/tex]

[tex]\theta=\dfrac{6\pi}{5}[/tex]

Now we change radian to degree

[tex]\text{Degree }=\dfrac{\text{Radian}}{\pi}\times 180^\circ[/tex]

[tex]\text{Degree }=\dfrac{6\pi}{5\pi}\times 180^\circ[/tex]

Central angle = 216°

Hence, The measure of arc is 216°