Which statement correctly describes the solution to this system of equations?

{−3x+2y=−22−5y=−4x+27

Answer:

4000/3 * π

Step-by-step explanation:

The formula for the volume of a sphere is;

V = (4/3) * π * r^3

Where;

r = the radius of the sphere

Substituting the given value, we get;

r = 10

V = (4/3) * π * (10)^3

= (4/3) * π * 1000

= 4000/3 * π

Therefore the volume of the sphere is (4000/3)π cubic units.

Answer: Not true

Step-by-step explanation:

This isn't true.

There is no way to manipulate the number 20 to get the number 5908 by subtraction or any other arithmetic operation.

Therefore, "20-4=5908" is false.

The average rate of change of the function is 3.

The average rate of change of a function is given by the formula:

average of change = (f(b) - f(a)) / (b - a)

Where [a, b] is the interval of the function

f(x) = x³ + 2x;  [-1, 1]

average rate of  change = ([ 1³ + 2(1)] - [ (-1)³ + 2(-1)]) / (1 - (-1))

average rate of change = (3 - (-3))/(1 + 1)

average rate of change = 6/2

average rate of change = 3

Learn more about average of change on:

https://brainly.com/question/25184007

#SPJ1

[tex]Step-by-step-explanation-& Answer[/tex]

Well if our friend Rick continues the pattern that is shown in the question then the answer is at the bottom

Lets do some addition:

(6+3) * 5 ( 5 x 2 = 10 )

First find the parenthesis, 6 + 3 = 9

Next multiply, 9 x 5 = 45

Thus the answer to your problem is:

[tex]\left[\begin{array}{ccc}A&N&S\\=&=&=\\4&5&!\end{array}\right][/tex]

Answer:

d

Step-by-step explanation:

trust me bro im a math teacher

Answer:

linear function

Step-by-step explanation:

straight line then add up

[tex] \:\:\:\:\:\:\:\:\:\:\:\star\:\sf \underline{Circumference\: of\: circle = 2πr}\\[/tex]

As per question, the radius of a circle is 13 in and we are asked to find out it's circumference in terms of π. Here-

Now that we are given the value of radius of the circle, so we can substitute it into the formula and solve for circumference-

[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{Circumference_{( circle)} = 2\pi r}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf Circumference_{( circle)} = 2 \times \pi \times 13\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf \underline{Circumference_{( circle)} = 26 \pi \:inch}\\[/tex]

Answer:

Step-by-step explanation:

99+988

Answer:

Step-by-step explanation:

In (b) you may be more used to the formula for arc length: [tex]P=\frac{\theta }{180} \times \pi r[/tex].

The result is the same.

Answer:

  [tex]\frac{20}{19}[/tex] or ≈ 1.053

Step-by-step explanation:

We Know

220 responded 'yes', and 209 responded 'no'

Find the probability that if a person is chosen at random, they had run a red light in the last year.

The probability is: [tex]\frac{220}{209}[/tex] = [tex]\frac{20}{19}[/tex] ≈ 1.053

So, the answer is [tex]\frac{20}{19}[/tex] or ≈ 1.053

Answer: 175

Step-by-step explanation:

Answer:     change in y divided by change in x

Step-by-step explanation:    The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run"

The flux density is 3000 uT.

Flux density (B) is a measure οf the strength οf a magnetic field in a given regiοn.

It is defined as the amοunt οf magnetic flux () that passes thrοugh a unit area (A) perpendicular tο the magnetic field's directiοn.

The flux density (B) can be calculated using the fοrmula:

B = Φ / A

where 'Φ' is -> flux and A is the -> crοss-sectiοnal area.

Plugging in the values given, we get:

B = 1500 uWb / 0.5 m²

B = 3000 uT (micrοtesla)

Therefοre, the flux density is 3000 uT.

To learn more about Flux density, visit:

https://brainly.com/question/25949656

#SPJ1

The relationship between the lines are they have same slope and they are parallel.

What is slope?

If [tex](x_1,y_1) \: and \: (x_2,y_2) [/tex] are two points on line then slope of the line will be [tex]m= \frac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

To determine the relationship between the two lines, we need to find out if they are parallel, perpendicular, or neither.

First, we can find the slope of the line passing through (7,1) and (10,5) using the slope formula:

[tex]m_1 = \frac{(y_2 - y_1)}{(x_2 - x_1)} \\ m_1 = \frac{ (5 - 1)}{(10 - 7)} \\ m_1 = \frac{4}{3} [/tex]

Similarly, we can find the slope of the line passing through (-8,5) and (-5,9):

[tex]m_2 = \frac{ (y_2 - y_1) }{ (x_2 - x_1)} \\ m_2 = \frac{(9 - 5) }{(-5 - (-8))} \\ m_2 = \frac{4}{3} [/tex]

Since both lines have the same slope of 4/3, they are parallel to each other.

Learn more about slope here,

https://brainly.com/question/3605446

#SPJ1

Answer: We can simplify the expression by using the identity for the tangent of half an angle:

tan(x/2) = sin(x) / (1 + cos(x))

where x is the angle in radians. We can use this identity by setting x = 56° since 2*28°= 56°.

So, we have:

sin(28°) / (1 + cos(28°)) = tan(56°/2)

We know that 56°/2 = 28°, so we have:

tan(28°)

Therefore, the expression simplifies to a single trigonometric function:

tan(28°)

Step-by-step explanation:

Suzie must pay $27,864 on delivery for the new truck. To determine how much Suzie must pay on delivery, we need to add the extra charges to the base price of the truck and subtract the down payment she already made.

Let's first list the extra charges:

Freight and PDI: $1,650

Air Tax: $100

Tire Tax: $20

GST (Goods and Services Tax): 5%

To calculate the extra charges, we can use the following formula:

Extra charges = Freight and PDI + Air Tax + Tire Tax + (GST x Base Price)

Substituting the given values, we get:

Extra charges = 1650 + 100 + 20 + (0.05 x 27280)

Extra charges = 1650 + 100 + 20 + 1364

Extra charges = 3134

Therefore, the total cost of the truck, including extra charges, is:

Total cost = Base price + Extra charges - Down payment

Total cost = 27280 + 3134 - 2450

Total cost = 27864

Thus, Suzie must pay $27,864 on delivery for the new truck.

It's important to note that the amount Suzie will actually pay will depend on the financing and payment options available to her. She may be able to spread out the payments over a longer period of time or negotiate a different down payment amount. It's always a good idea to research and compare different financing options before making a major purchase like a new vehicle.

To know more about down payment  click here:

brainly.com/question/1114543

#SPJ1

The final answer for linearizing the function f(x) = cos^5(x) around a = 0 is:

f(x) ≈ 1.

Linearizing a function is the process of approximating the behavior of a function by a linear function (i.e., a function of the form y = mx + b) in a certain region around a specific point.

Linearization is useful because linear functions are easy to work with mathematically, and they can provide a good approximation of the original function near the point of interest. By linearizing a function, we can simplify calculations and make predictions about the behavior of the function in the vicinity of the point of interest.

In the given question,

To linearize the function f(x) = cos^5(x) around a point a, we can use the first two terms of the Taylor series expansion:

f(x) ≈ f(a) + f'(a)(x - a)

where f'(a) is the first derivative of f evaluated at x = a.

In this case, we want to linearize around a = 0, so we have:

f(x) ≈ f(0) + f'(0)(x - 0)

To find f(0) and f'(0), we need to evaluate the function and its derivative at x = 0:

f(x) = cos^5(x)

f(0) = cos^5(0) = 1

f'(x) = 5cos^4(x)(-sin(x))

f'(0) = 5cos^4(0)(-sin(0)) = 0

Therefore, the linearization of f(x) = cos^5(x) around a = 0 is:

f(x) ≈ 1 + 0(x - 0) = 1

So the linearization is simply the constant function f(x) = 1. This means that for small values of x, the function cos^5(x) can be approximated by the constant function 1. The accuracy of this approximation depends on how small x is and how far away x is from 0.

To know more about Linearization, visit:

https://brainly.com/question/15830007

#SPJ1

If inversion be defined on K as a physical act of turning a member of K upside down. Then it will be the upside-down triangle.

consider the set K = (triangle, upside-down triangle, square, rectangle). Inversion is defined on K as the act of turning a member of K upside down.

To determine which shape is the triangle, follow these steps:
1. Identify the properties of each shape in set K:
  - Triangle: 3 sides and 3 angles
  - Upside-down triangle: same properties as a triangle, but inverted
  - Square: 4 sides, all equal in length, and 4 right angles
  - Rectangle: 4 sides, opposite sides equal in length, and 4 right angles
2. Analyze the effect of inversion on each shape:
  - Triangle: Inverting a triangle results in an upside-down triangle.
  - Upside-down triangle: Inverting an upside-down triangle results in a regular triangle.
  - Square: Inverting a square does not change its appearance.
  - Rectangle: Inverting a rectangle does not change its appearance.
3. Identify the shape that becomes a triangle after inversion:
  - The upside-down triangle becomes a regular triangle after inversion.
So, the shape in set K that corresponds to the triangle after applying inversion is the upside-down triangle.

For similar question on upside-down triangle.

https://brainly.com/question/369629

#SPJ11

Answer:

4550

Step-by-step explanation:

Answer:

4,550

Step-by-step explanation:

4,550 x 2% = 91

Answer: To obtain triangle A'B'C' from triangle ABC by reflection over the line y = 2, we reflect each point of the triangle over the line. This gives us:

A' = (A_x, 4 - A_y)

B' = (B_x, 4 - B_y)

C' = (C_x, 4 - C_y)

To obtain triangle A"B"C" from triangle A'B'C' by translation by the directed line segment from (0,0) to (3,2), we add the vector (3,2) to each point of the triangle. This gives us:

A" = (A'_x + 3, A'_y + 2) = (A_x + 3, 6 - A_y)

B" = (B'_x + 3, B'_y + 2) = (B_x + 3, 6 - B_y)

C" = (C'_x + 3, C'_y + 2) = (C_x + 3, 6 - C_y)

Therefore, the vertices of triangle A"B"C" are (A_x + 3, 6 - A_y), (B_x + 3, 6 - B_y), and (C_x + 3, 6 - C_y).

Step-by-step explanation:

Answer:

[tex]2 {x}^{2} + 10x - 48[/tex]

[tex]2( {x}^{2} + 5x - 24)[/tex]

[tex]2(x + 8)(x - 3)[/tex]

So C is correct.

Answer:

C, D

Step-by-step explanation:

Any rigid transformation (rotation, translation, reflection) will result in a congruent polygon. To make a similar (smaller) polygon, a dilation by a factor less than 1 must be used.

C. a dilation about the origin by a scale factor of 2/3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left

D. a dilation about the origin by a scale factor of 5/7 followed by a reflection over the y–axis and a dilation about the origin by a scale factor of 3/4

The coordinate of the complex numbers are plotted on a graph below

i) Z₁ + Z₂ = (2+j4) + (3-j) = (2+3) + (j4-j) = 5 + j3

ii) Z₁ - Z₂ = (2+j4) - (3-j) = (2-3) + (j4+j) = -1 + j5

iii) Z₂ - Z₁ = (3-j) - (2+j4) = (3-2) + (-j-4j) = 1 - j5

iv) To represent these complex numbers on an Argand diagram, we plot the real part on the x-axis and the imaginary part on the y-axis.

Z₁ = 2 + j4 can be represented as a point in the complex plane with coordinates (2,4).

Z₂ = 3 - j can be represented as a point in the complex plane with coordinates (3,-1).

Using these coordinates, we can plot the results from parts (i) to (iii) as follows:

(i) Z₁ + Z₂ = 5 + j3 can be represented as a point in the complex plane with coordinates (5,3).

(ii) Z₁ - Z₂ = -1 + j5 can be represented as a point in the complex plane with coordinates (-1,5).

(iii) Z₂ - Z₁ = 1 - j5 can be represented as a point in the complex plane with coordinates (1,-5).

Learn more on argand diagram here;

https://brainly.com/question/31156683

#SPJ1

Answer: 3.625 or 3 5/8

Step-by-step explanation:

So I personally would turn everything into decimals and subtract.

21.250 -17.625

And using our handy calculator, you get

3.625

Ruth will have the principal is approximately $5,534.04 in 1 year at earns 12% interest compounded annually.

What is principal?

To find how much Ruth will have in 1 year, we can use the formula for compound interest:

A = [tex]P(1 + r/n)^{n*t}[/tex]

where A is the amount after t years, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years.

Plugging in the given values, we get:

A =  [tex]$4,942(1 + 0.12/1)^{1*1}[/tex]

A = $4,942(1.12)

A = $5,534.04

Therefore, Ruth will have approximately $5,534.04 in 1 year.

What is an interest?

Interest is the amount of money charged by a lender to a borrower for the use of money over a period of time. It is typically calculated as a percentage of the amount borrowed or invested, and is often expressed as an annual percentage rate (APR). Interest can be simple or compound, depending on whether it is calculated only on the principal amount or on both the principal and accumulated interest. Interest is an important concept in finance and economics, and is used in a wide range of financial transactions, including loans, investments, and savings accounts.

To know more about principal, visit:

https://brainly.com/question/1902400

#SPJ9

the total cost of leather purchased to make the football is $30.79.

The volume of a football can be calculated using the formula for the volume of a sphere:

V = (4/3)πr³

Where r is the radius

Given that the diameter of the football is 14 cm and  the radius is half of the diameter, so radius is 7 cm.

So, the volume of the football is:

V = (4/3)π(7 cm)³

= 1437.33 cm³

Now, we know that 3% of the leather is wasted,

so the amount of leather to make the football is:

(100% - 3%) = 97% of the total leather purchased.

Therefore, the amount of leather used to make the football is:

0.97 × 1437.33 cm³ = 1394.19 cm³

To find the total cost of the leather purchased, we need to know the cost of leather per square centimeter. Let's assume that the cost of leather including labor is $0.05 per square centimeter.

The surface area of a sphere can be calculated using the formula:

A = 4πr²

So, the surface area of the football is:

A = 4π(7 cm)²

= 615.75 cm²

the total cost of the leather:

Cost of leather = Cost per square centimeter × Surface area of the football

= $0.05/cm² × 615.75 cm²

= $30.79

know more about sphere visit

https://brainly.com/question/11374994

#SPJ1

The purchasing decisions in both scenarios were affected by the prices of the products/services being considered.

What is meant by budget?

In general, a budget is a financial plan or estimate that outlines the expected income and expenses over a specific period.

The purchasing decisions in both scenarios were affected by the prices of the products/services being considered.

In scenario 1, Carlos chose a more expensive cereal because he recognized it from a TV commercial, which may have influenced his perception of its quality or desirability.

In scenario 2, Evelyn decided not to purchase a plane ticket because the prices were too high for her budget, despite there being multiple airlines offering flights to London.

Therefore,The purchasing decisions in both scenarios were affected by the prices of the products/services being considered.

To learn more about budget visit:

https://brainly.com/question/5168855

#SPJ1

Answer:

true

Step-by-step explanation: