What is the Solution of the following system?

{-3x -2y = -12
{9x + 6y= -9

Imagine those two bracket things are one big one connecting both equations, and the answers are A (2,1) B No Solutions C (-2, -1) D Infinitely Many Solutions
@Emma11234

The number to fill the given blank is 384.

We need to figure out the pattern from the number sequence.

A number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers.

From the given figure we can see that the pattern following the sequence is as follows:

From the bottom blocks to the block just above that it is multiplied by two numbers in the bottom blocks to get the number in the corresponding top block.

That, 6×2=12, 2×2=4, 2×1=2, 12×4=48, 4×2=8 and 48×8=384.

Therefore, the number to fill the given blank is 384.

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The value of [tex]w[/tex] is [tex]24[/tex].

Given:

The equation is:

[tex]1000^8=10^w[/tex]

To find:

The value of [tex]w[/tex].

Explanation:

We have,

[tex]1000^8=10^w[/tex]

[tex](10^3)^8=10^w[/tex]

[tex]10^{24}=10^w[/tex]         [tex][\because (a^m)^n=a^{mn}][/tex]

On comparing the exponents of the same bases, we get

[tex]24=w[/tex]

Therefore, the value of [tex]w[/tex] is [tex]24[/tex].

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The amount of sales tax in dollars is $3.25.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

So the percentage actually means a part per 100.

Percentage is usually denoted by the symbol '%'.

Given that,

An item has a listed price of $65 and the sales tax rate is 5%.

Listed price of an item = $65

Rate of sales tax = 5%

To calculate the amount of sales tax, we have to calculate the amount of 5% of the listed price which is $65.

Amount of sales tax = 5% of $65

                                 = 5% × 65

                                 = (5/100) × 65

                                 = 0.05 × 65

                                 = 3.25

Hence the amount of sales tax for the item is $3.25.

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Answer:

115.50

Step-by-step explanation:

I took the test

Answer:

581.25

Step-by-step explanation:

Use the formula for when the last term is unknown. It is [tex]s_{n} = \frac{a_{1} - a_{1} (r)^{n} }{1-r}[/tex].

For this equation [tex]s_{n}[/tex] (sum of the numbers)= [tex]s_{5}[/tex], [tex]a_{1}[/tex] (amount of first term) = 300, r (ratio)= .5, and n (number of terms) = 5. Knowing this, we plug them into the equation. It would look like: [tex]s_{10} = \frac{300 - (300)(0.5)^{5} }{1-0.5}[/tex].

First, we solve the exponents. 0.5 to the fifth power = .03125. Now multiply it by the nearest number in parentheses, which is 300. You should get 9.375.

Now, subtract that from 300. 300 - 9.375 = 290.625. Your numerator is 290.625.

Simplify your denominator. 1 - 0.5 = 0.5.

Divide.

[tex]\frac{290.625}{0.5} = 581.25[/tex]

581.25

I tried to make sure there were no typos! Please let me know if I missed something :)

There are four questions related to this: how many number of ways are there to award the prizes if:

a)      There are no restrictions?  If k unalike awards are there for n people and no person can get more than one prize then there are: This leads to 100 × 99 × 98 × 97 = 94109400100 × 99 × 98 × 97 = 94109400 ways in your case where n=100 k=4.

b)The person holding ticket 47 wins the grand prize? After handing out the grand prize there are k=3 different rewards left for n = 99 persons. Apply the same formula. Answer: 941094941094

c)  The person holding ticket 47 wins one of the prizes? 4 times case because there are 4 likelihoods when it comes to the rewards that can be won by person 47. Answer: 37643763764376 

d) The person holding ticket 47 does not win a prize? k=4 and n =99. Person 4747 is left out. Answer: 9034502490345024 

e) The person holding ticket 19 and 47 both wins prize? First gave out a prize to 47. There are 4 possibilities. Then give out a prize to 19. There are 3 likelihoods. Then the other prizes are gave out: k=2 and n=98. Lastly you come to 4 × 3 × 98 × 97 =1140724 × 3 × 98 × 97 = 114072 possibilities.

The number of tickets sold of each type is required.

Number of general tickets sold is 3000 and kids tickets is 500.

The cost of general tickets is $2.5

Cost of kids tickets is $0.5

Number of general tickets sold = x

Number of kids tickets sold = y

Total value of tickets sold = $7750

Now,

[tex]x=6y[/tex]

[tex]2.5x+0.5y=7750\\\Rightarrow 2.5(6y)+0.5y=7750\\\Rightarrow 15.5y=7750\\\Rightarrow y=\dfrac{7750}{15.5}\\\Rightarrow y=500[/tex]

[tex]x=6\times 500=3000[/tex]

Number of general tickets sold is 3000 and kids tickets is 500.

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Answer:

1. Assign an identifying variable to the quantity to be found.

2. Write a sentence stating conditions placed on the quantity.

3. Solve the sentence for the variable.

Cereal is a heterogeneous mixture. Because it is not uniformly mixed together since it has a variety of components. Option A is correct.

When the composition of a mixture is not constant throughout the mixture, the mixture is said to be heterogeneous. A variety of ingredients make up vegetable soup. Each mouthful of soup will have variable proportions of the soup's various veggies and other ingredients.

Given that the ingredients are visible and diverse, it is unmistakably cereal. The remaining choices, whether they be mixes or natural components, are homogenous since the contents blend well.

Because it contains a variety of unbalanced ingredients like flakes, berries, and clusters, cereal is a wonderful illustration of a heterogeneous mixture. A homogeneous mixture is one in which the constituent parts are thoroughly combined, as seawater.

Thus, Cereal is a heterogeneous mixture. Because it is not uniformly mixed together since it has a variety of components. Option A is correct.

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Final answer:

Scott paid approximately $0.67 per pound of flour, calculated by dividing the total cost of $4 by the total weight of 6 pounds.

Explanation:

The student asked: Scott bought 6 pounds of flour for $4. How many dollars did he pay per pound of flour?

To figure out the cost per pound of flour, you need to divide the total cost by the number of pounds.

Step-by-Step Calculation:

Write down the total cost of the flour, which is $4.

Write down the total weight of the flour, which is 6 pounds.

Divide the total cost by the total weight to find the cost per pound: $4 ÷ 6 pounds

The result is approximately $0.67 per pound.

Scott paid approximately $0.67 for each pound of flour.

Answer:

The mass of a pencil is 3.295 greater than the mass of the crayon.

Step-by-step explanation:

Consider the provided information.

The mass of a pencil is 5.44 g. The mass of a crayon is 2.145 g.

We need to find how much greater is the mass of the pencil than the mass of the crayon?

To find this simply subtract the mass of a crayon from mass of a pencil.

5.44-2.145

This can be written as:

5.440

-2.145

3.295

Hence, the mass of a pencil is 3.295 greater than the mass of the crayon.

The mass of the pencil is 3.295 grams greater than the mass of the crayon.

To find out how much greater the mass of the pencil is compared to the crayon, we need to subtract the mass of the crayon from the mass of the pencil.

Mass of the pencil = 5.44 g

Mass of the crayon = 2.145 g

Mass difference = Mass of the pencil - Mass of the crayon

= 5.44 g - 2.145 g

= 3.295 g

Therefore, the mass of the pencil is 3.295 grams greater than the mass of the crayon.

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the answer is 3 1/8!

sorry if this is really late,,, hope this helps <3

We are given that the suitcase is 24 inches long and 18 inches high. Assuming a regular rectangular shape, the diagonal can be calculates using Pythagorean theorem, that is:

diagonal^2 = 24^2 + 18^2

diagonal^2 = 900

diagonal = 30 inches

Answer:

Step-by-step explanation:

Answer:

B the skills for arguments

Step-by-step explanation:

gurl just read the lesson lol

and it's not the opinions you have other person is incorrect

Answer:

D, E, and F

Step-by-step explanation:

D.  SAS can be used, side-angle-side.  The angle is the right angle in both and right angles always are congruent since they can only measure 90 degrees.  The heights of both triangles are marked with the same number of slashes, so they are congruent; likewise, the bases are marked with the same number of slashes, so they are congruent.  Since the angle is between the sides, or included, this is SAS.

E.  HL can also be used since the hypotenuses of both triangles are marked with the same number of slashes, they are congruent.  We already decided the legs of both were congruent to each other.

F.  LL (which is also exactly the same as SAS) can also be used since we already decided that the legs in both triangles are congruent.

More information about the diagram and angles and sides is needed to determine the congruence theorems or postulates that can be applied.

In order to determine which congruence theorems or postulates can be used to prove that triangles ABC and LMN are congruent, we need more information about the diagram and the given angles and sides. Without that information, it is not possible to determine which congruence theorems or postulates can be applied.

The lengths are 12 m, 16 m, and 20 m.

In a right triangle, the hypotenuse is the longest aspect, an "contrary" aspect is the one throughout from a given attitude, and an "adjacent" aspect is subsequent to a given perspective.

The hypotenuse is opposite to the right perspective and may be solved by means of using the Pythagorean theorem. In a right triangle with cathetus a and b and with hypotenuse c, Pythagoras' theorem states that: a² + b² = c². To clear up for c, take the rectangular root of both aspects to get c = √(b²+a²).

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Answer:

43.2 in

Step-by-step explanation:

I took it

If rectangular shaped desk has a length of 25 inches and a width of 18 inches. A desk with a similar shape has a length of 60 inches. then its width will be 43.2 inches.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

A rectangular shaped desk has a length of 25 inches and a width of 18 inches

A desk with a similar shape has a length of 60 inches. x is the width of this desk

We need to find the value of x.

Let us formulate a equation.

25/18=60/x

Apply cross multiplication

25x=18(60)

25x=1080

Divide both sides by 25.

x=43.2

Hence if  a desk with a similar shape has a length of 60 inches it will have 43.2 inches of width.

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Answer:

We know that Kevin moved at a constant speed, so his movement can be model by:

[tex]d=st[/tex]

Where [tex]d[/tex] is distance, [tex]s[/tex] is speed and [tex]t[/tex] is time.

So, we can find the speed first, to then find the expression of the distance at any time:

[tex]s=\frac{d}{t}=\frac{\frac{3}{4}mi}{12min}\\s=\frac{3}{48}mi/min\\s=\frac{1mi}{16min}[/tex]

The ratio of his movement is 1 miles each 16 minutes.

Then, the distance at any minute would be:

[tex]d=\frac{1}{16}t[/tex]

This expression model the entire movement of Kevin, because it gives the distance he traveled at any minute.

For example, the first minute, Kevin covered a distance of:

[tex]d=\frac{1}{16}(1)=0.063 miles[/tex]

So, we could say that he travels 0.063 miles per minute.

Answer:

523.33 cubic inches

Step-by-step explanation:

To find the measure of angle MNQ, we can set up an equation using the fact that ray NP is an angle bisector. Solving the equation gives us the value of x, and substituting that value back into the equation gives us the measure of angle MNQ.

To find the measure of angle MNQ, we can use the fact that ray NP is an angle bisector of angle MNQ. This means that angle PNQ is half of angle MNQ.

We are given that angle PNQ = 2x + 1, so we can set up the equation 2x + 1 = (1/2)(x^2 - 10) to find the value of x.

Solving this equation, we get x = 5. Therefore, the measure of angle MNQ is 5^2 - 10 = 15 degrees.

To multiply square roots, you multiply the numbers under the root (the radicands) and then take the square root of that result. So, square root of 6 multiplied by square root of 2 equals the square root of 12.

The student's question requires multiplication of square roots. When multiplying square roots, we multiply the numbers under the roots (i.e., the radicands) and then compute the square root of that result.

So, to solve √6 * √2, we multiply the radicands (6 * 2) to get 12. Hence, √6 * √2 = √12. In some cases, we can simplify this further by factoring the radicands into the product of two numbers, where one of those numbers is a perfect square. However, 12 is already a simplified form, so the final answer will be √12.

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Answer:

3404

Step-by-step explanation: