Multiply.

(3.5×10−5)(3×10−10)

Express your answer in scientific notation.

A. 1.05×10−15

B.​ 1.05×10−14 ​

​C. 1.05×10−13 ​

D.​​ 1.05×1015 ​

The side length of the square rug is 10 feet and it is a rational number since it can be written as a ratio of two integers.

The area of a square is computed by squaring the length of one of its sides. The area of the rug is given as 100 square feet. Therefore, we can set up the following equation to find the side length:

S^2 = 100

Where 'S' represents the side length. To solve for 'S', we take the square root of both sides of the equation.

Therefore, S = √100

The square root of 100 is 10, so the side length of the rug is 10 feet.

Therefore, the rug has a side length of 10 ft. Since '10' can be expressed as a ratio of two integers, it is a rational number.

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Answer:

The unit cost for cherries is greater because the slope is greater than the slope for apples.

Explanation:

Slope is the rate of change of a line.  The slope of the graph for cherries is greater; we can see this because the line is steeper.

Since the slope is greater, the unit cost is greater.

The statement that represents the unit cost in the graph is that the unit cost for cherries should be more as the slope is more than the slope for apples.

The following information should be considered:

Therefore we can conclude that the first option is correct.

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Answer: About 111 of moons could be lined up in a row between Earth and the moon .

Step-by-step explanation:

Given : The diameter of the moon is about 3,476 kilometers.

The distance from Earth to the moon is about 384,400 kilometers.

Then , the number of moons could be lined up in a row between Earth and the moon will be :-

[tex]384,400\div3,476\\\\=110.586881473\approx111\text{ Rounded to the nearest whole number }[/tex]

Hence, about 111 of moons could be lined up in a row between Earth and the moon .

Answer:

There can be many example for this equation like:

1. There are three friends and all have the same amount of money. Together they give $25 in a restaurant and they are left with $125. How much money did each have?

We can solve this like:

Let each friend had 'x' money so three friends had 3x money.

They gave out $25, means 3x-25 and are left with $125.

So, complete equation becomes :

[tex]3x-25=125[/tex]

Solving for x we get;

[tex]3x=125+25[/tex]

[tex]3x=150[/tex]

x = 50

So, each friend had $50.

x/6 = 12/9

x = 12/9 * 6

x = 8

check:

8/6 = 1.3333

12/9 = 1.3333

Answer:

The number 1 is common factor between any set of numbers, but, sometimes is the only common factor.

Step-by-step explanation:

This happens when the numbers do not have common prime factors, like 5 and 7.

Since 1 is a prime number, you can consider it the common primer factor of every set of numbers.

Remember:

If 'a' is a number, a prime factor of it would be 1, since a*1=a

Answer:

[tex]5^4 = 625[/tex]

Step-by-step explanation:

There are 5 possible odd digits to choose from:  1,3,5,7,9.

When we chose our first digit, we have 5 choices (the possible odd digits). For every one of those 5 choices, we can chose our second digit in 5 different ways again, then we have 5*5 = 25 ways for choosing our first two digits. We can do the same again, as for every one of the 25 first two digits, we can chose our third digit in 5 different ways (again, the odd numbers). So we multiply it by 5 again. Repeating this one more time, because we have 5 different ways to chose our fourth digit. At the end we will have

[tex]5*5*5*5 = 5^4 = 625[/tex]

This is a commun counting technique.

Final answer:

The value of k for the equation kx^2 + x + 25k = 0 to have a repeated solution can be found by setting the discriminant to zero. Solving for k, we find that k = 0.1 and k = -0.1 are the values that yield a repeated solution for this quadratic equation.

Explanation:

To find the value of k such that the equation kx^2 + x + 25k = 0 has a repeated solution, we need to use the discriminant of a quadratic equation. The discriminant D is given by D = b^2 - 4ac. For a quadratic equation to have a repeated solution, its discriminant must be zero (D = 0). In this equation, a = k, b = 1, and c = 25k. Plugging these values into the discriminant formula gives us:

D = 1^2 - 4(k)(25k)

Setting D to zero and solving for k will give us the value(s) of k for which the equation has a repeated solution:

0 = 1 - 100k^2

k = ± 0.1

Therefore, there are two values of k that make the original equation have a repeated solution: k = 0.1 and k = -0.1.

The angles in transverse parallel lines are related through some theorems such as vertical angles, corresponding angles, etc. the measure of [tex]\angle 2[/tex] is [tex]50^o[/tex]

Given the attached diagram

First, we solve for x using the corresponding angle theorem

[tex]5x + 55 = 2x + 100[/tex] ---- corresponding angles are equal

Collect like terms

[tex]5x - 2x = 100 - 55[/tex]

[tex]3x = 45[/tex]

Divide both sides by 3

[tex]x = 15[/tex]

We then  solve for [tex]\angle 2[/tex] using the straight line theorem

[tex]\angle 2 + 5x + 55 = 180[/tex] ---- sum of angles on a straight line

Substitute 15 for x

[tex]\angle 2 + 5 \times 15 + 55 = 180[/tex]

[tex]\angle 2 + 75 + 55 = 180[/tex]

Collect like terms

[tex]\angle 2 =- 75 - 55 + 180[/tex]

[tex]\angle 2 =50[/tex]

Hence, the measure of [tex]\angle 2[/tex] is [tex]50^o[/tex]

Read more about parallel lines and corresponding angles at:

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Answer:

the temp is  65 and there was 224 chirps

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Took the test got it right