A large beetle can be 2x2x2x2x2x2x2 millimeters long. One of the smallest beetles can be 2(-2 (power)) millimeter long. How many times as great is the length of the large beetle than the length of the small beetle?

Answer:

a = 2 and b = - 1

Step-by-step explanation:

distribute the left side of the equation and compare the like terms with terms on the right side

7ay² + 7by - 21

compare the coefficients of like terms with 14y² - 7y - 21

7a = 14 ⇒ a = 2

7b = - 7 ⇒ b = - 1

The value of a and b  from the given equation is 2 and -1 respectively;

Given the equation [tex]7(ay^2+by-3)=14y^2-7y-21[/tex]

In order to get the value of a and b that will make the equality equation true, we will have to factorize first;

[tex]7(ay^2+by-3)=14y^2-7y-21\\7ay^2+7by-21=14y^2-7y-21\\[/tex]

Next is to compare both sides to get the unknown value

[tex]7ay^2=14y^2\\7a=14\\a=\frac{14}{7}\\a =2[/tex]

Get the value of "b"

[tex]7by=-7y\\7b=-7b\\b=\frac{-7}{7}\\b=-1[/tex]

Hence the value of a and b  from the given equation is 2 and -1 respectively;

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For this case we have to, by definition:

The sum of fractions with the same denominator consists of adding the numerators and placing the same denominator.

For example:

[tex]\frac {a} {b} + \frac {c} {b} = \frac {a + c} {b}[/tex]

So:

When fractions have the same denominator, their sum also has the same denominator.

Answer:

When fractions have the same denominator, their sum also has the same denominator.

Answer: The Y in the problem = 2/7, Good Luck!

Step-by-step explanation:

Simplify both sides of the equation!

Answer:

the answer would be one

Step-by-step explanation:

you simply have to put the question in parts that makes it easy use PEMDAS

it is really helpful on math that looks like this

Answer:

They bought 3 hot dogs and 5 drinks

Step-by-step explanation:

Well, its mostly guess and check.

x=hot dogs                   y= drinks                    x+y=8

2x + 1y =11

2(1) + 1(7) = 9 (wrong answer)

2(2) + 1(6)= 10 (wrong answer)

2(3) + 1(5) = 11 (right answer)

The reason I pick these numbers is because the x and the y need to add up to 8 and as you can see on each try they added up to 8 but it also had the equation itself had to add up to $11. So, you substitute the numbers that add up to 8 to x and y to make sure the equation equals 11.

Final answer:

Keisha and her friends purchased 3 hotdogs and 5 drinks at the concession stand. This was determined by setting up a system of equations based on the given costs for items and the total amount spent and solving for the variables representing hotdogs and drinks.

Explanation:

To solve Keisha's concession stand problem, we need to use a system of equations. Let's define two variables: x for hotdogs and y for drinks. According to the problem, the friends bought a total of 8 items for $11. The price is $2 per hotdog and $1 per drink. We can set up the following equations:

1) x + y = 8 (for the total number of items)
2) 2x + y = 11 (for the total cost)

Solving the system, we can subtract the first equation from the second to find the number of hotdogs:

2x + y - (x + y) = 11 - 8

x = 3

Now, we substitute x back into the first equation to find y:

3 + y = 8

y = 5

Therefore, Keisha and her friends bought 3 hotdogs and 5 drinks.

Answer:

(a) 112, 28, 7, (7/4), (7/16)

Step-by-step explanation:

The sequence is given by the explicit formula

[tex]a_{n} = 112 (\frac{1}{4} )^{n-1}[/tex]

The terms of the sequence are :

[tex]a_{1} = 112 (\frac{1}{4} )^{1-1} = 112  (\frac{1}{4} )^{0} =112 [/tex]

[tex]a_{2} = 112 (\frac{1}{4} )^{2-1} = 112(\frac{1}{4} ) =28 [/tex]

[tex]a_{3} = 112 (\frac{1}{4} )^{3-1} = 112(\frac{1}{4} )^{2} = 7 [/tex]

[tex]a_{4} = 112 (\frac{1}{4} )^{4-1}=112(\frac{1}{4} )^{3} = \frac{7}{4}[/tex]

[tex]a_{5} = 112 (\frac{1}{4} )^{5-1}=112 (\frac{1}{4} )^{4} = \frac{7}{16}[/tex]

Answer:

3(2y+1)

Step-by-step explanation:

First we need to find the factors of each term

6y = 2*3*y

3 = 3*1

The greatest common factor is 3.  Take that out and what remains goes inside the parentheses

3(2y+1)

Toby has to pay 22.1$ in total for the wallet.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given that, Toby found a $52 wallet on the clearance rack for 60% off.

So.

The price of wallet after discount = 52 * (1 - 60%)

The price of the wallet after the discount = 52*0.4

The price of the wallet after the discount =  20.8

Since there is a sales tax of 6.25%

Thus the purchasing Price of the wallet = 20.8(1 + 6.25%)

the purchasing Price of the wallet = 22.1

therefore,  If the sales tax is 6.25%, he will pay $22.1 in total.

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Answer:

I'm sorry i couldn't understand your question. If you wanna take it litterally, around the world there is gas station that could be 5 minutes, 15 or 30 minute from a hospital. could you clarify me on your question

1. a+9

2. 12-x

3. x-7

4. 2a

5. 2a

6. a:8

7. a/3

8. 2(8+a)

[tex]b)\\\tan x=\dfrac{\sin x}{c\os x}\\\\\tan^2x=\dfrac{\sin^2x}{\cos^2x}=\dfrac{2\sin^2x}{2\cos^2x}=\dfrac{\sin^2x+\sin^2x}{\cos^2x+\cos^2x}\\\\=\dfrac{\sin^2x+\sin^2x+\cos^2x-\cos^2x}{\cos^2x+\cos^2x+\sin^2x-\sin^2x}=\dfrac{(\sin^2x+\cos^2x)-(\cos^2x-\sin^2x)}{(\cos^2x+\sin^2x)+(\cos^2x-\sin^2x)}\\\\=\dfrac{1-\cos2x}{1+\cos2x}\\\\\text{Used}:\\\\\sin^2x+\cos^2x=1\\\\\cos^2x-\sin^2x=\cos2x[/tex]

[tex]\tan^2\left(\dfrac{7\pi}{8}\right)=\dfrac{1-\cos\left(2\cdot\dfrac{7\pi}{8}\right)}{1+\cos\left(2\cdot\dfrac{7\pi}{8}\right)}=\dfrac{1-\cos\left(\dfrac{7\pi}{4}\right)}{1+\cos\left(\dfrac{7\pi}{4}\right)}=(*)\\\\\cos\left(\dfrac{7\pi}{4}\right)=\cos\left(2\pi-\dfrac{\pi}{4}\right)=\cos\left(-\dfrac{\pi}{4}\right)=\cos\left(\dfrac{\pi}{4}\right)=\dfrac{\sqrt2}{2}\\\\(*)=\dfrac{1-\frac{\sqrt2}{2}}{1+\frac{\sqrt2}{2}}=\left(\dfrac{2}{2}-\dfrac{\sqrt2}{2}\right):\left(\dfrac{2}{2}+\dfrac{\sqrt2}{2}\right)[/tex]

[tex]=\dfrac{2-\sqrt2}{2}\div\dfrac{2+\sqrt2}{2}=\dfrac{2-\sqrt2}{2}\cdot\dfrac{2}{2+\sqrt2}=\dfrac{2-\sqrt2}{2+\sqrt2}\\\\\text{Use}\ (a+b)(a-b)=a^2-b^2\\\\=\dfrac{2-\sqrt2}{2+\sqrt2}\cdot\dfrac{2-\sqrt2}{2-\sqrt2}=\dfrac{(2-\sqrt2)^2}{2^2-(\sqrt2)^2}\\\\\text{Use}\ (a-b)^2=a^2-2ab+b^2\\\\=\dfrac{2^2-2(2)(\sqrt2)+(\sqrt2)^2}{4-2}=\dfrac{4-4\sqrt2+2}{2}=2-2\sqrt2+1\\\\=(\sqrt2)^2-2(\sqrt2)(1)+1^2=1^2-2(1)(\sqrt2)+(\sqrt2)^2\\\\\text{Use}\ (a-b)^2=a^2-2ab+b^2\\\\=(1-\sqrt2)^2\\\\\text{Therefore}:[/tex]

[tex]\tan^2\left(\dfrac{7\pi}{8}\right)=(1-\sqrt2)^2\to\boxed{\tan\left(\dfrac{7\pi}{8}\right)=1-\sqrt2}[/tex]

[tex]c)\\\tan\left(\dfrac{\pi}{8}\right)=\tan\left(\pi-\dfrac{7\pi}{8}\right)=\tan\left(-\dfrac{7\pi}{8}\right)=-\tan\left(\dfrac{7\pi}{8}\right)\\\\=-(1-\sqrt2)=\sqrt2-1\\\\y=\sin(2x-1)+a\tan\dfrac{\pi}{8}\\\\\text{We know}\ -1\leq\sin(2x-1)\leq1.\\\\y\geq0\ \text{therefore}\ a\tan\dfrac{\pi}{8}\geq1\\\\\text{We have to move the graph at least one unit up}\\\\a(\sqrt2-1)\geq1\qquad\text{divide both sides by}\ (\sqrt2-1)>0\\\\a\geq\dfrac{1}{\sqrt2-1}\cdot\dfrac{\sqrt2+1}{\sqrt2+1}\\\\a\geq\dfrac{\sqrt2+1}{(\sqrt2)^2-1^2}[/tex]

[tex]a\geq\dfrac{\sqrt2+1}{2-1}\\\\a\geq\dfrac{\sqrt2+1}{1}\\\\a\geq\sqrt2+1\\\\Answer:\ \boxed{a=\sqrt2+1}[/tex]

Answer:

[tex]y=\frac{1}{2}x[/tex].

Step-by-step explanation:

We have been given that the graph of a proportional relationship contains the point 8 and 4.

Since we know that a proportional equation is in form: [tex]y=kx[/tex], where k is constant of proportionality.

Let us substitute x=8 and y=4 in proportional equation to find constant of proportionality for our equation.

[tex]4=k*8[/tex]

Upon dividing both sides of equation by 8 we will get,

[tex]\frac{4}{8}=\frac{k*8}{8}[/tex]

[tex]\frac{4}{8}=k[/tex]

[tex]\frac{1}{2}=k[/tex]

Let us substitute k=1/2 in proportional equation.

[tex]y=\frac{1}{2}x[/tex]

Therefore, our desired equation will be [tex]y=\frac{1}{2}x[/tex].

Answer:

∠S = 45°

Step-by-step explanation:

As given in the question, ∠R = 3x ; ∠S=2x ; ∠T=3x

So by using angle sum property of a triangle that sum of all the angles of a triangle is 180°.

We get, ∠R+∠S+∠T =   180

[tex]3x+2x+3x=180\\8x=180\\x=\frac{180}{8}[/tex]

So, ∠S=2x

∠S=[tex]2\cdot \frac{180}{8}[/tex]

∠S=45°

Answer:

m∠S= 45°

Step-by-step explanation:

Given an isosceles triangle ABC.

& m∠R = m∠T = 3 x,  m∠S = 2 x

The sum of all the angles of triangle is equal to 180°

⇒  m∠R + m∠S + m∠T = 180°

     3 x + 2 x + 3 x = 180°

     ⇒    8 x = 180°

     ⇒       x = [tex]\frac{180}{8}[/tex]

     ⇒       x = [tex]\frac{45}{2}[/tex]

Hence, m∠S = [tex]2\times\frac{45}{2}[/tex]

                     = 45°

Answer:

Step-by-step explanation:

Let the larger number = x

Let the smaller number = y

I can't really tell if I'm reading it correctly, but I think the answer is

x - y = 5

Answer:

Step-by-step explanation:

Suppose you have given two numbers say (x and y ).

Now we can have 3 conditions here:

   i . x and y are equal

   ii. x is greater than y

  iii . y is greater than x .

For x and y are equal  : - Difference between two numbers will be zero.

For x and y greater or lesser :- There will be some difference between two numbers x and y. And if this difference between x and y is 5, then it will look like:

x is greater than y

x - y = 5  

or

y is greater than x

y - x = 5

Answer: D

Step-by-step explanation:

5,000 + 500x = 5,500x

Answer:

D. There were 5,000 of that species in 1955.

Step-by-step explanation:

The initial population of the species is equal to the y-intercept of the first-order polynomial. Hence, the right answer is D.

Answer:

A)one is 3 inches and the other is 2 inches.2:5 and 3:5

B)It would be still b three and two because 3/5 of the chocolate bar is 60% and 2/5 is 40%.

Step-by-step explanation:

A) If the bar is 5 inches long and it is broken into two pieces with one that measures an inch longer then you would find that if broken in half it   would be 2.5, so if you take the other point 0.5 off of the other 2.5 and add it to the other half then it would have on piece that is an inch longer than the other piece.3+2=5

B)  5(0.6) =3

For Scenario A, the Milky Way bar is divided into two pieces where one piece is 1 inch longer than the other, resulting in lengths of 3 inches and 2 inches, with a ratio of 3:2. In Scenario B, one piece is 60% of the entire bar, equating to 3 inches and 2 inches for the two pieces, again with a ratio of 3:2.

A Milky Way bar is 5 inches long and is split into two pieces.

Scenario A: One Piece Is 1 Inch Longer Than the Other

Let's denote the length of the shorter piece as x. According to the problem, the longer piece would then be x + 1 inch. Since the two pieces together must add up to the total length of the bar, which is 5 inches, we can set up the following equation:

x + (x + 1) = 5 inches

2x + 1 = 5 inches

2x = 5 inches - 1 inch

2x = 4 inches

x = 2 inches

The shorter piece is 2 inches, meaning the longer piece is 2 inches + 1 inch = 3 inches.

The ratio of the longer piece to the shorter piece is therefore 3:2.

Scenario B: One Piece Is 60% of the Bar

In this case, one piece is 60% of 5 inches. We calculate this piece as follows:

60% of 5 inches = 0.60 * 5 inches

= 3 inches

Since one piece is 3 inches, the other piece must be 5 inches minus 3 inches, which is 2 inches. The ratio of the larger piece to the smaller piece is 3:2, the same as in Scenario A.

Answer:

20 gallons

Step-by-step explanation:

you would have to divide 4 and 8 which equals 2

then you multiply 2 by 10

which equals 20

Answer:

10 big water bottles hold 20  gallons of water

Step-by-step explanation:

Simplify the equation given. Divide 4 from both the numerator and denominator

(4 big water bottles/8 gallons of water) = (1 big water bottle/ 2 gallons of water)

Next, solve for 10 big water bottles. Multiply 10/10 to the fraction gotten previously

(1 big water bottle / 2 gallons of water) x (10/10) = (10 big water bottle / 20 gallons of water).

10 big water bottles / 20 gallons of water is your answer

~

The correct answer is D, which includes the empty set, each individual element as a subset, and the set itself containing both elements {-8, 4}.

The question asks for all subsets of the set {-8, 4}. A subset of a set includes any set formed from its elements, including the empty set and the set itself. Therefore, the subsets of the set {-8, 4} are:

So the correct answer is D: Ø, {-8}, {4}, {-8, 4}.

Answer:

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

Multiplica tres por 18

[tex]\sqrt{9*4}= \sqrt{36} =6[/tex]

A.) [tex]\sqrt{9}*\sqrt{4}=3*2=6[/tex]

B.) 18

C.) [tex]\sqrt{\frac{9}{4}}=\frac{3}{2}[/tex]

D.) 36

Your answer is A

The multiplication of 9 • 4 equals 36, which is the result of adding 9 to itself 4 times.

The question 'which of the following is equal to 9 • 4?' is asking us to perform a multiplication operation. In Mathematics, when we multiply two numbers, we are essentially adding one of the numbers to itself the number of times indicated by the other number. Therefore, 9 multiplied by 4, which is written as 9 • 4, is equal to adding 9 to itself 4 times: 9 + 9 + 9 + 9.

Let's do the math:

So, 9 • 4 equals 36. This is a basic multiplication concept that is foundational in math.

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

The common difference is 7

Since the common difference is 7

a_n = 12+(n-1)7

a_n = 12+7n -7

a_n = 5+7n

Answer:

The answer is A and b=18.

Step-by-step explanation:

27=b+9 and then subtract 9 from each side to get b=18

Answer:

Distributive property

Step-by-step explanation:

12(x+4)

We would use the Distributive property to get to

12x+48

Distributive Property

x(a+b) = ax + bx

[tex]10 < -2b\qquad\text{change the signs}\\\\-10>2b\qquad\text{divide both sides by 2}\\\\-5>b\to \boxed{b<-5}\\\\2b+3>11\qquad\text{subtract 3 from both sides}\\\\2b>8\qquad\text{divide both sides by 2}\\\\\boxed{b>4}[/tex]

Answer:

x =16

Step-by-step explanation:

A right angle has 90 degrees.

The two given angles add to 90 degrees

3x + 2 + 40 = 90                      Combine the left side

3x + 42 = 90                            Subtract 42 from both sides

3x + 42 - 42 = 90 - 42             combine

3x = 48                                     Divide by 3

3x/3 = 48/3                              Do the division

x = 16