Given y varies directly as x, use the given x-value and y-value to find an equation that relates x and y. x = 24 and y = 360 A) y = 15x B) x = 15xy C) y = .15x D) y = 15 x

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:

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:

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:

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

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°

[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.

The graph of [tex]y=x^2+11x+24[/tex] is equivalent to the graph of this equation: A. y= (x + 8)(x + 3)

In Geometry, a factored form is a type of quadratic equation that is typically written as the product of two (2) linear factors and a constant;

f(x) = a(x - r)(x - r)

a is the leading coefficient.

r is the roots or x-intercets.

Based on the information provided, we can logically deduce the following quadratic function;

[tex]y=x^2+11x+24[/tex]

By factorizing the quadratic function above completely, we have the following;

[tex]y=x^2+11x+24\\\\y=x^2+8x+3x+24\\\\y=x(x+8)+3(x+8)\\\\y=(x+8)(x+3)[/tex]

Complete Question:

The graph of [tex]y=x^2+11x+24[/tex] is equivalent to the graph of which equation?

y= (x + 8)(x + 3)

y = (x + 4)(x + 6)

y= (x + 9)(x+2)

y = (x + 7)(x + 4)

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

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:

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

1. a+9

2. 12-x

3. x-7

4. 2a

5. 2a

6. a:8

7. a/3

8. 2(8+a)

To find the distance the hula hoop rolls in 4 full rotations, we calculate the circumference as 2πr and then multiply by 4. The total distance is then rounded to the nearest centimeter, resulting in 880 cm.

The question asks us to calculate the distance a hula hoop travels in 4 full rotations given its radius. The distance traveled in one rotation is equal to the circumference of the hoop.

To find the circumference, we use the formula C = 2πr, where r is the radius. Since the radius is given as 35 cm, the circumference is 2π×35 cm. To find the total distance for 4 rotations, we multiply the circumference by 4. This gives us 4×2π×35 cm. Using the approximate value of π (3.1416), we can calculate the distance, and then round it to the nearest centimeter.

Circumference C = 2π×35 cm = 219.91 cm

Total distance for 4 rotations = 4×C = 4×219.91 cm = 879.64 cm

Rounded to the nearest centimeter: 880 cm

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)

Answer:

A

Step-by-step explanation:

[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]

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:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

[tex]\frac{7}{9}[/tex] × [tex]\frac{3}{4}[/tex] × [tex]\frac{2}{7}[/tex]

the 7 on the numerator/ denominator cancel to 1

the 3 and 9 cancel ( 3 → 1 and 9 → 3 )

the 2 and 4 cancel ( 2 → 1 and 4 → 2 )

= [tex]\frac{1}{3}[/tex] × [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{1}[/tex]

multiply the remaining values on the numerators/ denominators

= [tex]\frac{1(1)(1)}{3(2)(1)}[/tex] = [tex]\frac{1}{6}[/tex]

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:

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

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:

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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Answer: x=-13

Step-by-step explanation:

X= 65/5

X=-13

Checked work .

-5x=65

-5x-13=65

65=65

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].

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:

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

~

[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]

34.5 kilometers is equal to 21.41 miles.

To convert kilometers to miles, you can use the conversion factor 1 mile = 1.609 kilometers. So, to convert 34.5 kilometers to miles, you would multiply 34.5 by the conversion factor:

34.5 kilometers × 1 mile/1.609 kilometers = 21.41 miles

Therefore, 34.5 kilometers is equal to 21.41 miles.

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