Name the property of equality that justifies: If x = 3 and y = x + 5, then y = 8

Final answer:

The division and multiplication of signed numbers follow the same sign rules: two positive numbers yield a positive result, two negatives give a positive, and a pair of numbers with different signs results in a negative outcome.

Explanation:

The rules for the division of signed numbers are similar to the rules for multiplication of signed numbers. Both operations follow the same pattern concerning the signs of the numbers involved:

When two positive numbers are involved, the result is positive (e.g., [tex]\frac{2}{1} = 2[/tex] or 2 x 1 = 2).

When two negative numbers are involved, the result is also positive (e.g., [tex]\frac{-2}{-1} = 2[/tex] or (-4) x (-3) = 12).

When one positive and one negative number are involved, irrespective of the operation, the result is negative (e.g., [tex]\frac{-3}{1} = -3[/tex] or (-3) x 2 = -6).

Therefore, both division and multiplication of signed numbers primarily depend on the signs of the numbers to determine the sign of the answer.

Final answer:

The surface area of a cone with height h and base radius a, excluding the base, is found using the lateral surface area formula A = π · a · l, where l is the slant height given by √(a² + h²).

Explanation:

To find the general formula for the surface area of a cone with height h and base radius a using a surface integral, excluding the base, we consider the lateral surface area of the cone. This is given by the integral along the slant height of the cone. To derive the formula, the slant height, l, can be found using the Pythagorean theorem, since the triangle formed by the slant height, radius of the base, and the height of the cone is a right triangle. The relationship is given by l = √(a² + h²).

The lateral surface area A can then be expressed as A = π · a · l. Substituting for the slant height, we get A = π · a · √(a² + h²), which is the desired formula.

This formula assumes that the cone is a right circular cone and the lateral surface is a smooth curve.

Answer:

1)  12in

Step-by-step explanation:

The circumference is 75, so to find the diameter you have to divide 75 by 3.14. You get 24 approximately. Then divide the diameter by 2, so 24/2=12.

By calculating the number of heartbeats in a day (based on the heart rate of 60 bpm) and dividing the total number of heartbeats by that value, we can estimate that Jenna is 7 days old.

The subject of this question is Mathematics, and it's suitable for high school grade level. To find out the number of days Jenna has lived using her heartbeats, you first need to calculate how many beats her heart makes in one day. Knowing that her heart rate is 60 beats per minute, we can calculate the number of beats in one hour by multiplying by 60 (number of minutes in one hour). So in one hour, we get 60 * 60 = 3600 beats. In 24 hours (one day), the heart will beat 3600 * 24 = 86,400 times. So, if Jenna's heart has beat 604,800 times in her life, we divide that number by the number of beats in one day to find out the number of days: 604,800 / 86,400 = 7 days. Therefore, Jenna is 7 days old.

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Final answer:

The first number is 2 and the second number is 5.

Explanation:

Let's represent the first number as x and the second number as y.

According to the problem, we have the following equations:

3x - y = 1 (Equation 1)

x + 2y = 12 (Equation 2)

To solve this system of equations, we can use the method of substitution. We can rearrange Equation 2 to solve for x:

x = 12 - 2y

Now, we substitute this value of x into Equation 1:

3(12 - 2y) - y = 1

Expand and solve for y:

36 - 6y - y = 1

Combine like terms:

-7y = -35

Divide both sides by -7:

y = 5

Now, substitute this value of y back into Equation 2 to find x:

x + 2(5) = 12

x + 10 = 12

Subtract 10 from both sides:

x = 2

Therefore, the first number is 2 and the second number is 5.

divide total gallons by rate:

4290 / 78 = 55 hours

Answer:

[tex]\large \textsf{Read below}[/tex]

Step-by-step explanation:

[tex]\large \text{$ \sf log_2\:(log_5\:x) = 3$}[/tex]

[tex]\large \text{$ \sf log_2\:(log_5\:x) = log_2\:8$}[/tex]

[tex]\large \text{$ \sf log_5\:x = 8$}[/tex]

[tex]\large \text{$ \sf log_5\:x = log_5\:390,625$}[/tex]

[tex]\large \boxed{\boxed{\text{$ \sf x= 390,625$}}}[/tex]

The x-intercept would be, (3,0). And the y-intercept would be, (0,-3/2).

Answer: False. Both angles are not equal therefore the lines l and m are not parallel.

Answer:

Part 1:

In order to find how many radians the minute hand moves from 1:20 to 1:55, we need to remember that there are 60 minutes in an hour (clock) and there are 360 degrees in the clock since the clock is a circle. After dividing 360 by 60, we find that each minute is equal to 6 degrees. After that, we can subtract the times, which tells us that there are 35 minutes between 1:20 and 1:55. Using this we can just multiply this out, to get 35 times 6, which is equal to 210 degrees. We can get our final answer by converting this into degrees. Since one 1 degree is about 0.0174, we can set up a proportion. After solving, we will get that the minutes hand moves 3.555 radians in total.

The quotient in standard form for (8 - 7i) / (1 - 2i) is (22 + 9i) / 5. In this form, the numerator has real and imaginary components, while the denominator is a real number.

The division is simplified, providing a representation of the complex number in a standard format.

To write the quotient result of division in standard form,

Get rid of the imaginary unit 'i' from the denominator.

To do that, multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of 1 - 2i is 1 + 2i.

So, let's perform the multiplication:

(8 - 7i) / (1 - 2i) × (1 + 2i) / (1 + 2i)

Now, use FOIL (First, Outer, Inner, Last) method to expand the numerator:

Numerator = (8 - 7i)(1 + 2i)

= 8 + 16i - 7i - 14i² (remember that i² is -1)

= 8 + 9i - 14(-1)

= 8 + 9i + 14

= 22 + 9i

Now, let's expand the denominator:

Denominator = (1 - 2i)(1 + 2i)

= 1 + 2i - 2i - 4i²

= 1 - 4i²

= 1 - 4(-1)

= 1 + 4

= 5

Therefore, the quotient in standard form is (8 - 7i) / (1 - 2i) = (22 + 9i) / 5.

learn more about quotient here

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Final answer:

To represent the growth of Bangkok flu cases over time mathematically, the derivative dn/dt equals 10, indicating a constant increase of 10 cases per month.

Explanation:

To rewrite the statement in mathematical notation where n is the number of cases of Bangkok flu and t is time, we will express the changing number of cases as a function of time. Given that there are currently 450 cases and the number of cases is growing by 10 every month, we would write the instantaneous rate of change of the number of cases with respect to time as dn/dt = 10.

This is because the phrase 'growing by 10 new cases every month' implies a constant rate of growth over time, which is directly translated into a derivative in mathematical terms. In more complex scenarios, rates of growth could follow a pattern that might be represented by a function of t. However, in this case, the growth is linear and constant, which simplifies to the derivative being equal to the rate of growth: 10 cases per month.

Final answer:

To find John's original savings, we set up an equation based on the information given and solved for the total savings, which was found to be approximately $154.29.

Explanation:

John spent $24 on a watch and then 1/5 of the remainder of his savings on a shirt. After these purchases, he had 2/3 of his savings left. To determine John's original savings, let's represent his total savings as S. After purchasing the watch, John had S - $24 remaining. He then spent 1/5 of this remainder on a shirt. After buying the shirt, 2/3 of his savings was left, which can be represented by the equation:

2/3 * S = (S - $24) - 1/5 * (S - $24)

Now, we can solve for S, by first distributing the 1/5 on the right-hand side of the equation:

2/3 * S = (S - $24) - 1/5 * S + 24/5

Then, we combine like terms:

(2/3 - 1/5) * S = $24 - 24/5

To combine the fractions, find a common denominator, which in this case is 15:

(10/15 - 3/15) * S = 96/5 - 24/5

(7/15) * S = 72/5

Finally, we multiply both sides of the equation by the reciprocal of 7/15 to solve for S:

S = (72/5) * (15/7)

S = (72*15)/(5*7)

S = $154.29

Therefore, John's original savings was approximately $154.29.

Answer:

1. The meaning of (2, 40) is that - when 2 gallons of fuel is used, then the distance covered will be 40 miles.

2. Equation will be :

[tex]y=20x[/tex]

where y is the total distance in miles and x is the number of gallons used.

3. When we have to tell as per graph, that the car travels 27 miles in 1 gallon, the points will be : (1,27) , (2,54) , (3,81) and so on.

Answer:

[tex]\frac{17}{16} [/tex]pounds of chicken are needed to make[tex]8\frac{1}{2}[/tex] servings.

Step-by-step explanation:

Chicken required for 1 serving = [tex]\frac{1}{8}[/tex] pounds

Number of serving required for salad = [tex]8\frac{1}{2}=\frac{17}{2}[/tex]

Chicken required for [tex]8\frac{1}{2}[/tex] servings be x.

[tex]x=\frac{1}{8}\times \frac{17}{2} pounds[/tex]

[tex]=\frac{17}{16} pounds[/tex]

[tex]\frac{17}{16} [/tex]pounds of chicken are needed to make[tex]8\frac{1}{2}[/tex] servings.