The volume of rectangular prism is 300 cubic inches.If the length of the prism is 5 inches and the width is 8 inches.What is the height of the rectangular prism ?

Final answer:

1 kilogram is 10^9 times greater than 1 microgram because 1 kg equals 1000 grams, and there are 10⁶ micrograms in a gram, equating to 10⁹ µg/kg.So,option A.10⁹ is correct.

Explanation:

To determine how many times greater 1 kilogram is than 1 microgram, we need to understand the metric prefixes and their corresponding values. Knowing that 'micro' denotes 10⁻⁶, we can establish that 1 microgram (µg) equals 10⁻⁶grams (g). Since 1 kilogram (kg) equals 1000 grams, we then convert kilograms to micrograms by multiplying by 10⁶:

1 kg = 1000 g x 10⁶ µg/g = 10⁹ µg.

Thus, 1 kilogram is 10⁹ times greater than 1 microgram, which corresponds to option A.

Answer:

4

Step-by-step explanation:

$21-$13=$8

$8÷$2=4 bottles

Answer:

y = 10

Step-by-step explanation:

Given

10 - y = y - 10 ( subtract y from both sides )

10 - 2y = - 10 ( subtract 10 from both sides )

- 2y = - 20 ( divide both sides by - 2 )

y = 10

Answer:

Part 1)  441km in 45s   --> Has the same speed as Saige's spaceship

Part 2) 215km in 25s --> Does not have the same speed as  Saige's spaceship

Part 3) 649km in 110s --> Does not have the same speed as  Saige's spaceship

Step-by-step explanation:

The complete question is

Saige's spaceship traveled 588 kilometers in 60 seconds.

Determine whether or not each spaceship trip below has the same speed as Saige's spaceship.

441km in 45s

215km in 25s

649km in 110s

we know that

The speed is equal to divide the total distance traveled by the total time

In this problem we have that

The speed of Saiges spaceship is equal to

[tex]\frac{588}{60}=9.8\ \frac{km}{sec}[/tex]

case 1) we have

441km in 45s

Find out the speed of the  spaceship trip

[tex]\frac{441}{45}=9.8\ \frac{km}{sec}[/tex]

Compare the speed of the spaceship trip with the speed of Saiges spaceship

[tex]9.8\ \frac{km}{sec}=9.8\ \frac{km}{sec}[/tex]

therefore

Has the same speed as Saige's spaceship

case 2) we have

215km in 25

s

Find out the speed of the  spaceship trip

[tex]\frac{215}{25}=8.6\ \frac{km}{sec}[/tex]

Compare the speed of the spaceship trip with the speed of Saiges spaceship

[tex]8.6\ \frac{km}{sec}\neq 9.8\ \frac{km}{sec}[/tex]

therefore

Does not have the same speed as  Saige's spaceship

case 3) we have

649km in 110s

Find out the speed of the  spaceship trip

[tex]\frac{649}{110}=5.9\ \frac{km}{sec}[/tex]

Compare the speed of the spaceship trip with the speed of Saiges spaceship

[tex]5.9\ \frac{km}{sec}\neq 9.8\ \frac{km}{sec}[/tex]

therefore

Does not have the same speed as  Saige's spaceship

The square root of 10 lies between two whole numbers, 3 and 4. This concept can be understood using number sense and geometry.

The square root of 10 falls between two whole numbers. To determine these two numbers, we need to consider the closest perfect square numbers to 10. These are 9 (the square root of 9 is 3) and 16 (the square root of 16 is 4). Hence, the square root of 10 must be somewhere between 3 and 4. Using a calculator, we find the approximate square root of 10 to be around 3.16. So, the square root of 10 lies between 3 and 4.

This kind of problem is related to number sense and geometry, especially when it comes to understanding square roots.

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Answer:

the answer is A.

Step-by-step explanation:

The values of the system of equations y=[tex]x^{2}[/tex]-3x+6, y=2x+6 is (0,6),(5,16).

Equation is relationship between two or more variables that are expressed in equal to form.Equations of two variables look like ax+by=c.It may be linear equation, quadratic equation,cubic equation.

We have been given two equations as y=[tex]x^{2}[/tex]-3x+6 and y=2x+6 and we are required to solve the equations for the value of x.

Putting the value of y from second equation in first equation.

2x+6=[tex]x^{2}[/tex]-3x+6

Cancellng 6 from both sides.

[tex]x^{2}[/tex]-5x=0

x(x-5)=0

x=0,x-5=0

x=0,x=5

Putting the values of x in second equation to get the value of y.

y=2x+6

y=2(5)+6

=10+6

y=16

y=2x+6

y=2*0+6

=6

Points will be (0,6),(5,16).

Hence the values of the system of equations y=[tex]x^{2}[/tex]-3x+6, y=2x+6 is (0,6),(5,16).

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Answer:

(x+7, y-3)

Step-by-step explanation:

7 units to the right and 3 units down

Answer:

10.9

Step-by-step explanation:

So you add or subtract the number, leaving the bottom number the same and then simplify if you need to.

Answer:

(10, 5 )

Step-by-step explanation:

To determine which points lie on the graph or not.

Substitute the x- coordinate of the point into the equation and if the value agrees with the y- coordinate of the point then the point is on the graph.

(2, 7 )

y = 2 + 5 = 7 ← True thus point is on the graph

(6, 11 )

y = 6 + 5 = 11 ← True thus point is on the graph

(220, 225 )

y = 220 + 5 = 225 ← True thus point is on the graph

(10, 5 )

y = 10 + 5 = 15 ≠ 5 ← Point is not on the graph

Answer:

Step-by-step explanation:

Answer:

19.2

Step-by-step explanation:

Answer:

205  miles per hour.

Step-by-step explanation:

1 mile = 5280 feet so:

300 ft / second = 300/ 5280 miles/second.

There are 3600 seconds in an hour so

this converts to  300 * 3600 / 5280 miles per hour

= 204.55 miles per hour.

Hey!

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Solution:

Let's use dimensional analysis!

[tex]= \frac{1mi}{5280ft} * \frac{3600}{1hr} * \frac{300ft}{1sec}[/tex]

[tex]= \frac{1,080,000}{5,280}[/tex]

[tex]= 204.454545...[/tex]

[tex]= 205[/tex]

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Answer:

205

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Hope This Helped! Good Luck!

Answer 15 20 10 2.5 7.5

Answer:

the answer is 8.5

Step-by-step explanation:

yeet

Answer:

I think the closest would be 8 :3

Answer:

the answer is -8 13/30

Step-by-step explanation:

Answer:

666 divided by 6 is 111. So, they would need 111 vans.

Answer:x             f(x) = 2.5x − 10.5              g(x) = 64(0.5x)

2            f(2) = 2.5(2) - 10.5             g(2) = 64(0.5*2)

             f(2) = 5 - 10.5                    g(2) = 64(1)

             f(2) = -5.5                          g(2) = 64

3            f(3) = 2.5(3) - 10.5             g(3) = 64(0.5*3)

             f(3) = 7.5 - 10.5                 g(3) = 64(1.5)

             f(3) = -3                             g(3) = 96

4            f(4) = 2.5(4) - 10.5             g(4) = 64(0.5*4)

             f(4) = 10 - 10.5                  g(4) = 64(2)

             f(4) = -0.5                          g(4) = 128

5            f(5) = 2.5(5) - 10.5             g(5) = 64(0.5*5)

             f(5) = 12.5 - 10.5               g(5) = 64(2.5)

             f(5) = 2                              g(5) = 160

6            f(6) = 2.5(6) - 10.5             g(6) = 64(0.5*6) 

             f(6) = 15 - 10.5                  g(6) = 64(3)

             f(6) = 4.5                           g(6) = 192

Answer:

0 because it doesn't cross the x-axis

Step-by-step explanation:

Interpreting the graph, it is found that the function has no real solutions.

The number of different real solutions that a function has is given by the number of times it crosses the x-axis(also known as the horizontal axis) on the graph.

In this problem, the function never crosses the x-axis, thus, it has zero real solutions.

A similar problem, in which the real solutions are taken from a graph, is given at https://brainly.com/question/16349072

Answer:

The length of the short leg is 5 inches and the leg of the long leg is 12 inches

Step-by-step explanation:

Let

a -----> the long leg of a right triangle

b ----> the short leg of a right triangle

c ----> the hypotenuse of a right triangle

we know that

Applying the Pythagoras Theorem

[tex]c^{2} =a^{2}+b^{2}[/tex] -----> equation A

we have that

[tex]a=b+7[/tex] -----> equation B

[tex]c=13\ in[/tex] ----> equation C

Substitute equation B and equation C in equation A and solve for b

[tex]13^{2} =(b+7)^{2}+b^{2}[/tex]

[tex]169=b^2+14b+49+b^2[/tex]

[tex]2b^2+14b+49-169=0[/tex]

[tex]2b^2+14b-120=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]b=5\ in[/tex]

see the attached figure

Find the value of a

[tex]a=b+7[/tex] ----> [tex]a=5+7=12\ in[/tex]

therefore

The length of the short leg is 5 inches and the leg of the long leg is 12 inches

The lengths of the leg : 12 and 5

Quadratic function is a function that has the term x²

The quadratic function forms a parabolic curve

The general formula is

[tex]\large {\boxed {\bold {f (x) = ax ^ 2 + bx + c}}}[/tex]

where a, b, and c are real numbers and a ≠ 0.

There are 3 ways to solve quadratic equations

a. factoring b. perfect squared c. quadratic formula

We use the factoring method

Quadratic equation x² + bx + c = 0 is equivalent to quadratic equation

[tex]{\displaystyle {x ^ 2 + (p + q) \times \: pq}}[/tex]

where p + q = b and px q = c

for a = 1, the result of factoring is (x + p) (x + q)

If at an angle there is an angle of 90 degrees, this triangle is said to be a right angle

There is a hypotenuse in this triangle which is the sum of the two sides

where c = hypotenuse

This formula is known as the Pythagorean theorem which states that:

the hypotenuse or the longest side in a right triangle equal to the sum of the squares of the other sides.

then c = 13

then a = b + 7

Then the phytagorean equation becomes:

(b + 7)² + b² = 13²

49+14b+b²+b²=169

49+14b+2b²=169

2b²+14b-120=0

b²+7b-60=0

factoring

(b-5)(b+12)=0

b=5 or b=-12

we use positive number ⇒5

So :

the long leg = b+7=5+7=12

the short leg = b = 5

the triangle angle

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Prove the converse of the Pythagorean Theorem

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Use Pythagoras' theorem

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Keywords :  Pythagorean Theorem , hypotenuse, the long leg

Answer:

Forty and three hundred two thousandths.

Step-by-step explanation:

40 = forty

300 = three hundred

.02 = two thousandths

Hope this helps.

Answer:

Step-by-step explanation:

Forty and three hundred two thousandths.

Answer:

Share sold by Stock A = 4000, Stock B = 1000 and Stock C = 5000

Step-by-step explanation:

Total sold sold = 10000

i.e. [tex]A + B + C = 10000[/tex] ....(1)

Shares sold by stock A = 4 × Shares sold by stock B

i.e. [tex]A = 4B[/tex] ....(2)

Shares sold by stock C = Shares sold by stock A + Shares sold by stock B

i.e. [tex]C = A + B[/tex] ....(3)

substituting value of [tex]A[/tex] from (2) in (3) we get

[tex]C = 4B + B = 5B[/tex] ....(4)

substituting value of [tex]A[/tex] and [tex]C[/tex] from (2) and (4) in (1) we get

[tex]4B + B + 5B = 10000\\10B = 10000\\B = 1000[/tex]

[tex]A = 4B = 4*1000 = 4000[/tex]

[tex]C = 5B = 5*1000 = 5000[/tex]

Answer:

If your asking us to just combine like terms it would be -3b^2-2b^2+1.4b+4c+c

but if your asking us to answer the question it would be -5b^2+1.4b+5c

Hope I helped :)

Answer:

4.5 foot shadow

Step-by-step explanation:

By looking at this you can make a ratio that very every 5 feet there is a 1.5 foot shadow.

So 1.5 x 3 = 4.5 foot shadow

(Very sorry If it is incorrect Good luck!)

Hey!

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[tex]\large\boxed{The~plant~grew~2\frac{1}{2}~feet!}[/tex]

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Steps To Solve:

~Find common denominators

6/7 = 54/63

2/9 = 14/63

~Turn into improper fractions

1 54/63 = 117/63

4 14/63 = 266/63

~Subtract.

266/63 - 117/63 = 149/63

~Turn into mixed number

149/63 = 2 23/63

~Round

2 23/63 ≈ 2 1/2

Answer:

2 1/2

Step-by-step explanation:

because 4 2/9 － 1 6/7 equal to 2 half which equal to 2 1/2

Answer: The Statement is true

Step-by-step explanation: the lines in the graph are constantly parallel to each other, showing that when one increases, so does the other

Answer:

The given statement is true.

Step-by-step explanation:

We are given the following graph in the picture:

On the x-axis years are shown from 1959 to 2005.

The y axis shows the poverty rate and the number of people in poverty.

The blue strips in the graph are the recession time.

Now, for each blue strip, we could see the line for poverty rate and the number of people in poverty increases. There is an upward trend in the line in the blue strip.

In other words we could say that the slope increases for all the blue strips which actually represents that the number of people in poverty increases in recession.

Thus, the given statement is true.

Answer:

x = ± [tex]\sqrt{\frac{ab+2}{3} }[/tex]

Step-by-step explanation:

Given

3x²  - 2 = ab ( isolate the x² term by adding 2 to both sides )

3x² = ab + 2 ( divide both sides by 3 )

x² = [tex]\sqrt{\frac{ab+2}{3} }[/tex] ( take the square root of both sides )

x = ± [tex]\sqrt{\frac{ab+2}{3} }[/tex]

Answer:

x =  √ [(ab + 2)/ 3]

Step-by-step explanation:

3x^2 - 2 = ab

3x^2 = ab + 2

x^2 = (ab + 2)/ 3

x =  √ [(ab + 2)/ 3]

[tex]\bf \lim\limits_{x\to \infty}~-4x^9-3x^3+2x-11 \\\\\\ \lim\limits_{x\to \infty}~-4x^9~~+~~\lim\limits_{x\to \infty}~-3x^3~~+~~\lim\limits_{x\to \infty}~2x~~+~~\lim\limits_{x\to \infty}~-11[/tex]

for any positive value of "x" as it races off towards ∞, our first limit  of -4x⁹ will give us a rather large negative value, our second limit of -3x³ will also give us a large negative value and both will combine to produce an even larger negative value.

our third limit of 2x will give us a positive value, however a much smaller than its previous siblings, and our last limit is just a fixed of -11, not moving at all.

since the negative values are moving faster than the positive ones, and thus overwhelming the positive ones, the limit will increasingly be racing towards -∞.

The limit of the function, [tex]\lim_{n \to \infty} f(x)= -4x^2 - 3x^3+2x - 11[/tex] is - ∞.

Here, given function is,

f(x)=−4x^9−3x^3+2x−11

We have to find the value of [tex]\lim_{n \to \infty} f(x)= -4x^2 - 3x^3+2x - 11[/tex].

What is limit of function?

Limit of function means the value towards which a function moves when the value of independent variable moves to infinity.

Now,

[tex]\lim_{n \to \infty} f(x)= -4x^2 - 3x^3+2x - 11[/tex]

[tex]\lim_{n \to \infty} f(x)= \lim_{n \to \infty} (-4x^2) - \lim_{n \to \infty} (3x^3) + \lim_{n \to \infty} 2x - \lim_{n \to \infty} 11[/tex]

[tex]\lim_{n \to \infty} f(x)= -[/tex]∞

Here, limit of [tex]-4x^{2}[/tex] is -∞,  limit of [tex]-3x^{3}[/tex] is -∞ and limit of 2x is ∞.

For any positive value of x as it races off towards ∞ but here we find the limits as, -∞.

Since the negative values are moving faster than positive.

Hence, the limit will be towards  -∞.

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Answer:

It makes 5/3 it is less than two!

Step-by-step explanation:

Topic: Fractions and Mixed Numbers

You have to remember the concept of fractions, let's represent by cake diagrams, it says that Gary says that 3, let's say it's 3 cakes, as the fractions are represented in terms of thirds, let's draw the cakes each one divided in 3.

and the statement says that taking away 1 and 1/3 it will make more than 2.

As you can see in the picture below, we take away 1 cake and we will take away another third of a second cake represented by the brown region of the cakes. it means that the yellow region is what's left after taking the 1 and 1/3. as you can see it doesn't make two, makes less than two exactly 5/3.

PS: Try and do it mathematically now!

Answer:

The 1000 ml bags, over $3000

Step-by-step explanation:

First, determine how many bags you need from each vendor. Then find the cost per bag with each vendor. Remember, the bags are reported to be only half full when discarded, therefore you need the equivalent of 5,000 1,000 ml bags and 5,000 500ml bags.

Answer:100ml bag is 3000

Step-by-step explanation: