Select the statement that best justifies the conclusion based on the given information. Conclusion: l1 and l 2 intersect only at point P. A line contains at least two points. Through any two different points, exactly one line exists. If two lines intersect, then their intersection is exactly one point. If two lines intersect, then exactly one plane contains both lines.

The round off to nearest half is 1/2.

Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.

Given:

The fraction = 5/9.

Now, rounded to the nearest half is 1/2

we know 9 halved value is 4.5 which is much closer to 5.

So, we can write it as 5/10 = 1/2.

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Answer:

There are 8 band members in each row

Step-by-step explanation:

Given : A band performed at halftime during the football game.

There were 64 band members marching in 8 equal rows.

To Find : How many band members were in each row?

Solution :

Let there are x members in each row .

Since there are 8 rows

So, no. of members in 8 rows = 8x

We are also given that there are 64 band members .

⇒[tex]8x=64[/tex]

⇒[tex]x= \frac{64}{8}[/tex]

⇒[tex]x= 8[/tex]

Thus there are 8 band members in each row

Answer:

A) 2 13/15 x + 3

B) 2 7/12 x - 7 4/5 over 2 3/5

C) 5 16/21 x - 18 6/7

D) 16 4/7 x - 2 2/5

Step-by-step explanation:

Answer:

1/4 and 1/4

Step-by-step explanation:

I got it correct and you also stated it.

[tex]\text{Consider the sum of the finite arithmatic series}\\ \\ 7.6+6.3+5+3.7+2.4+1.1+(-0.2)+(-1.5)\\ \\ \text{We know that the sum of the finite arithmatic series }\\ \\ a_1,a_2, a_3, ..., a_n \text{ is given by the formula}\\ \\ S_n=\frac{n}{2}\left ( a_1+a_n \right )\\ \\ \text{here in the given series, we can see that }a_1=7.6, \ a_n=-1.5 \text{ and}\\ \text{the number of terms is, }n=8. \text{ so using above formula, we get}[/tex]

[tex]S_8=\frac{8}{2}\left ( 7.6+(-1.5) \right )\\ \\ =4\left ( 7.6-1.5 \right )\\ \\ =4\left ( 6.1 \right )\\ \\ =24.4[/tex]

Hence the sum of the finite Arithmetic series is: 24.4

The distance between two points in a coordinate plane can be found using the Pythagorean theorem. For the points (-9,-8) and (-6,-4), the distance is 5 units.

The Pythagorean theorem can be used to find the distance between two points in a coordinate plane. To find the distance between the points (-9,-8) and (-6,-4), we can consider the horizontal and vertical differences as the legs of a right triangle. The horizontal difference is 3 and the vertical difference is 4.

Using the Pythagorean theorem, we have:
a^2 + b^2 = c^2
3^2 + 4^2 = c^2
9 + 16 = c^2
25 = c^2
c = sqrt(25) = 5

Therefore, the distance between the two points is 5 units.

Yes, the equation provided can be used to calculate the original price of the phone case. After solving the equation, we found out that the original price of the phone case was approximately $80.

Yes, the equation you provided, 3/4(0.7c) = 42, can certainly be used to find the original price of the phone case (c). The equation is obtained by recognizing that you're receiving two discounts: a 30% or 0.3 discount off the original price (leaving 70% or 0.7 of the original price) and then a 25% or 0.25 discount (meaning you're paying 75% or 0.75 of the price after the first discount).

To find the original price, you want to solve this equation for 'c'. That would involve dividing both sides by 3/4(0.7) equaling to 0.525. So, it will look like: 42 ÷ 0.525 = c. Doing the calculation, c equals approximately $80.

Therefore, the original price of the phone case was $80.

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Final answer:

The expression equivalent to 32 might refer to a mathematical manipulation or a unit conversion. In equations, 32 is what remains when you subtract 32 from one side of an equation like x + 32 = 64. Meanwhile, in conversions, multiplying the number of quarts by 32 gives you the equivalent volume in fluid ounces.

Explanation:

The expression is equivalent to 32 and could be interpreted in different contexts. Using mathematical manipulation, when you subtract 32 from both sides of an equation, the equality holds. For example, if you have an equation like x + 32 = 64, subtracting 32 from both sides gives us x = 64 - 32, which simplifies to x = 32. This demonstrates an application of the principle that you can add or subtract the same number from both sides of an equation without changing its solution.

In relation to conversion between different units of measurement, specifically volume, when you convert quarts to fluid ounces, the conversion factor is 32 because there are 32 fluid ounces in one quart. Consequently, to find how many fluid ounces are in a given number of quarts, you multiply the number of quarts by 32. For example, 4 quarts equal 4 × 32, which is 128 fluid ounces.

Furthermore, when dealing with electrical resistance, 'equivalent resistance' is another situation where the number 32 might be relevant. Depending on the context and the specific details of an electrical circuit, one of the listed equivalent resistances may be the correct answer to a problem involving calculating the total resistance.

let x = amount invested at 3%

so, (2600 - x) is invested at 7%

.07 *(2600 - x) + .03 *(x) = 138

182 - .07x + .03x = 138

-.07x + .03x = 138 - 182

-.04x = -44

-.04x / -.04 = -44 / -.04

x = 1,100

so amount invested at 7% is (2600 - 1100) or 1500

consequently amount invested at 3% is 1100

$1,100 invested at 3%

$1,500 invested at 7%

The money invested in both of the funds are $800 and $1800 respectively.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

Suppose the money invested in one of the funds be x.

Then, in the other fund the investment is (2600 - x).

Now, the equation for the total profit from both investments can be obtained as,

7% × x + 3% × (2600 - x) = 150

⇒ 7/100 × x + 3/100 × (2600 - x) = 150

⇒ 4x/100 = 150 - 78

⇒ x = 1800

Thus, the investment in the other fund is 2600 - 800 = $800.

Hence, the investment for both the funds are $800 and $1800 respectively.

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Answer:

The percentage is 0.008%

Step-by-step explanation:

The number of songs purchased each day from an online music store is 0.8% greater than the number purchased the previous day.

The original number of songs purchased from the online music store on the first day was 300,000. The number of songs purchased on any given day x is represented by the expression 300,000 ([tex]1.008^n[/tex]), where n is the number of days after the first day. To find the percent increase each day, you examine the multiplicative factor 1.008. This reflects a 0.8% (or 0.008 in decimal form) increase in the number of songs purchased from one day to the next. Therefore, each day the number of songs purchased is 0.8% greater than the previous day.

Hey there!

4 + (5 - 3) 5 + 7

= 4 + (2)(5 + 7)

= 4 + 2(5) + 7

= 4 + 10 + 7

= 14 + 7

= 21

Therefore, your answer is: 21

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

The answer to your question is 162.75

Final answer:

Solomon has 2/3 of the book left to read. To finish it over 5 nights, he needs to read 2/15 of the book each night.

Explanation:

Solomon has read 1/3 of his book already. To finish the remaining 2/3 of the book in 5 nights, we need to calculate the fraction of the book he should read each night. Since he has to evenly distribute the remaining portion over 5 nights, we will divide 2/3 by 5.

Here's the calculation step-by-step:

First, represent the remaining part of the book as a fraction, which is 2/3.

To divide this fraction by 5, we multiply the denominator by 5. This gives us (2/3) × (1/5).

Multiplying these fractions, we get (2 × 1) / (3 × 5), which simplifies to 2/15.

Thus, Solomon reads 2/15 of the book each night for the next 5 nights.

area of triangle is = 1/2 * base * altitude

1- each side is made 8 times

so the net change in area is 64 times

The area of A'B'C' is 64 times the area of ABC

2- each side is made 4 times

so the net change in area is 16 times

The area of D'E'F' is 16 times the area of DEF

3- each side is made 3 times

so the net change in area is 9 times

The area of A'B'C' is 9 times the area of ABC

The volume of the cylinder with given diameter and height is 136.02 cm³.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, the diameter of a cylinder =7.6 cm and the height of a cylinder = 3 cm.

Radius =7.6/2 =3.8 cm

We know that, the volume of a cylinder is πr²h

Now, volume = 3.14×3.8²×3

= 136.02 cm³

Therefore, the volume of the given cylinder is 136.02 cm³.

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Answer:

the polynomial is: 3x^2-21x+30

Step-by-step explanation:

go it right on edge

A polynomial function with rational real coefficients, a leading coefficient of 3, and roots of square root of 5 and 2 can be represented as f(x) = 3(x - 2)(x - √5).

A polynomial function with rational real coefficients, a leading coefficient of 3, and roots of square root of 5 and 2 can be represented as:

f(x) = 3(x - 2)(x - √5)

To find the polynomial function, we use the fact that the roots of a polynomial are the values of x for which the polynomial is equal to zero. Since the leading coefficient is 3, we multiply the expression (x - 2)(x - √5) by 3 to obtain the polynomial function.

In this case, the polynomial function of lowest degree is a quadratic function.