an office has an area 120 square meters and a width of 12 meters write an equation to represent the area

Final answer:

The real numbers a and b that make the equation a+bi=13+9i true are a = 13 and b = 9. We match real and imaginary parts of the complex numbers to find a and b.

Explanation:

To find the real numbers a and b such that the equation a+bi=13+9i is true, we simply match the real parts and the imaginary parts of the complex numbers on both sides of the equation. The real part of a+bi is a, and the real part of 13+9i is 13. Therefore, a = 13. Similarly, the imaginary part of a+bi is bi and the imaginary part of 13+9i is 9i. Thus, b = 9. Hence, the values we are looking for are a = 13 and b = 9.

The common speed of the blocks just after the collision is 0.4 times the initial velocity of the first block (v₁).

To determine the common speed of the blocks just after the completely inelastic collision, we can use the principle of conservation of linear momentum.

According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

Let's denote the velocity of the first block (m = 0.050 kg) before the collision as v₁ and the velocity of the second block (m = 0.075 kg) before the collision as v₂. Since the second block is stationary, its initial velocity, v₂, is 0.

1. Before the collision, the total momentum is given by:

Initial momentum = m₁v₁ + m₂v₂

where m₁ and m₂ are the masses of the first and second blocks, respectively.

Plugging in the values, we have:

Initial momentum = (0.050 kg) v₁ + (0.075 kg) 0

Initial momentum = (0.050 kg)v₁

2. After the collision, the two blocks stick together and move as a single unit with a common velocity, denoted as vf.

The final momentum is given by:

Final momentum = (m₁ + m₂) vf

where (m₁ + m₂) is the total mass of the system.

Plugging in the values, we have:

Final momentum = (0.050 kg + 0.075 kg) × vf

Final momentum = 0.125 kg × vf

According to the principle of conservation of linear momentum, the total momentum before the collision is equal to the total momentum after the collision:

0.050 kg × v₁ = 0.125 kg × vf

To determine the common speed of the blocks just after the collision, we need to solve for vf:

vf = (0.050 kg × v₁) / (0.125 kg)

Calculating the numerical value, vf = 0.4 ×  v1

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Priscilla and Herb would take approximately 44.44 hours to address 10,000 envelopes together, as Priscilla can address 100 envelopes per hour and Herb can address 125 envelopes per hour.

The question asks about the combined work rate of Priscilla and Herb in addressing 10,000 envelopes. To solve this, we calculate each of their rates of work and then combine them to find the total rate. Priscilla completes 10,000 envelopes in 100 hours, so her rate is 100 envelopes per hour. Herb completes 10,000 envelopes in 80 hours, so his rate is 125 envelopes per hour. Working together, their combined rate is 100 + 125 = 225 envelopes per hour. To address 10,000 envelopes at this rate, we divide 10,000 by 225, which equals approximately 44.44 hours.

The inverse is f⁻¹(x) = -3(x + 1)/(x + 2).

To find the inverse of the given function f(x), follow these steps:

Thus, the inverse function is f⁻¹(x) = -3(x + 1)/(x + 2).

Jose bought a bag of [tex]6[/tex] oranges for [tex]\$2.82[/tex] and Jose also bought [tex]5[/tex]  pineapples each cost [tex]\$3.15[/tex].

Explanation:

Given: Jose bought a bag of [tex]6[/tex] oranges for [tex]\$2.82[/tex]. He also bought [tex]5[/tex] pineapples. He gave the cashier [tex]\$20[/tex] and received [tex]\$1.43[/tex] change.

Let cost of a pineapple be [tex]x[/tex].

According to the question:

Cost of pineapple is calculated as [tex]20-(2.82+5x)=1.43[/tex]

                                                            [tex]20-2.82-5x=1.43\\[/tex]

                                                                               [tex]5x=17.18-1.43\\[/tex]

                                                                                 [tex]x=\frac{15.75}{5} \\x=3.15[/tex]

Therefore, cost of each pineapple is [tex]\$3.15[/tex].

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The added zeros when changing a number from scientific notation to expanded notation are usually not considered significant. They primarily serve as placeholders and do not indicate precision of measurements.

In the field of Mathematics, specifically when working with numbers in scientific notation and expanded notation, the concept of significant zeros comes into play. When you convert a number from scientific notation to expanded notation, zeros that are included in this process are not considered to be significant. Rather, the concept of significant zeros mostly applies to measurements and the precision of those measurements. For example, in the measurement 300.0, the zero at the end is significant because it shows the measurement was precise to the tenth's place. However, in changing a number from scientific to expanded notation, any added zeros primarily serve as placeholders and are typically not considered significant.

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Given: Angle 1 and angle 2 are supplementary.

Angle 3 and angle 4 are supplementary.

Angle 1 is congruent to angle 3.

Prove: Angle 2 is congruent to angle 4.

Answer:

Approximately 83 bags each carrying 50 pounds of soil will carry 1 cubic yard of soil or 4,128 pounds of soil.

Step-by-step explanation:

We are given the following information in the question:

1 cubic yards is equal to 4128 pounds that is

[tex]1~yard^3 = 4,128~pounds[/tex]

Amount of soil 1 bag can hold = 50 pounds

Number of bags to hold 1 cubic yard of soil or 4,128 pounds of soil:

Formula:

[tex]\text{Number of bags} = \displaystyle\frac{\text{Total amount of soil}}{\text{Amount of soil 1 bag can hold}}[/tex]

[tex]= \displaystyle\frac{4128}{50} = 82.56[/tex]

Thus, approximately 83 bags each carrying 50 pounds of soil will carry 1 cubic yard of soil or 4,128 pounds of soil.

Answer:

The LA theorem is a special case of the AAS theorem and the ASA postulate.

Step-by-step explanation:

The LA theorem is a special case of the AAS theorem and the ASA postulate.

LA(Leg - Acute) theorem states that if the leg and one acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent.

AAS (Angle Angle Side) states that if two angles and the non included side of one triangle are congruent to two angles and the non included side of another triangle, then these two triangles are congruent.

ASA (Angle Side Angle) postulate states that if two angles and one included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

The scientific notation of the decimal number 0.0013 is [tex]0.0013 \times 10^{-3}[/tex].

Scientific notation is a way to express numbers in a concise form, particularly useful for very large or very small numbers.

It consists of two parts: a coefficient and an exponent of 10.

In the case of 0.0013, we can convert it to scientific notation as follows:

[tex]0.0013 \times 10^{-3}[/tex].

Hence, the scientific notation of 0.0013 is [tex]0.0013 \times 10^{-3}[/tex].

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Answer:

Yes

No

Step-by-step explanation:

It is appropriate to eliminate parentheses as a first step. This can be done using the distributive property, resulting in either of ...

or by dividing the equation by the factor outside parentheses, resulting in ...

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Any of the equations other than these represent violations of the equal sign. Something has been done to one side of the equation without the same thing being done to the other side.