MATHEMATICS HIGH SCHOOL

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Answer 1
Answer:

Answer:

y does not vary directly with x

Step-by-step explanation:

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A can of 3 tennis balls sells for $2. If Sal spent more than $24 on tennis balls, which inequality can be used to find n, the number of tennis balls Sal could have bought? Two-thirds n greater-than 24 Three-halves n greater-than 24 2 n greater-than 24 3 n greater-than 24.

Seven times a number increased by three is 38

Answers

n-the\ number\n\n7* n+3=38\n7n+3=38\ \ \ \ |subtract\ 3\ from\ both\ sides\n7n=35\ \ \ \ |divide\ both\ sides\ by\ 7\n\n\boxed{n=5}
So,

If we translate this into mathematical form, we get
7n + 3 = 38

Subtract 3 from both sides
7n = 35

Divide both sides by 7
n = 5

The quotient of the difference of a number and 24 divided 8 is the same as the number divided by 6

Answers

The number that satisfies the given condition is -72.

Let's break down the given statement step by step:

The difference of a number and 24:

Let's assume the number is represented by 'x'.

The difference of 'x' and 24 can be written as (x - 24).

Divided by 8: We divide the difference of 'x' and 24 by 8, which gives us ((x - 24) / 8).

The quotient of the difference of a number and 24 divided by 8: So, the quotient is ((x - 24) / 8).

The number divided by 6: We divide the number 'x' by 6, which gives us (x / 6).

The given statement says that the quotient obtained in step 3 is equal to the number divided by 6.

Mathematically, we can represent this as:

((x - 24) / 8) = (x / 6)

To solve this equation for 'x', we can cross-multiply:

6(x - 24) = 8x

Now, we can simplify and solve for 'x':

6x - 144 = 8x

Subtracting 6x from both sides:

-144 = 2x

Dividing by 2:

x = -72

Therefore, the number that satisfies the given condition is -72.

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x-the\ number\n\n(x-24)/(8)=(x)/(6)\ \ \ \ |multiply\ both\ sides\ by\ 24\n\n3(x-24)=4x\n\n3x-72=4x\ \ \ \ |subtract\ 3x\ from\ both\ sides\n\n\boxed{x=-72}

A bakery makes 260 donuts in 4 hours. At this rate, how many donuts can they make in 6 hours?

Answers

Answer:

390

Step-by-step explanation:

A bakery makes 260 donuts in 4 hours At this rate the bakery can make 390 donuts in 6 hours .

To find out how many donuts the bakery can make in 6 hours at the given rate, you can use a proportion based on the information provided:

Let's denote the number of donuts made as "x" in 6 hours.

The rate of making donuts is 260 donuts in 4 hours.

So, the rate can be expressed as: 260 donuts / 4 hours = 65 donuts/hour.

Now, you can set up a proportion:

260 donuts / 4 hours = x donuts / 6 hours

Cross-multiply and solve for x:

260 * 6 = 4 * x

1560 = 4x

Divide both sides by 4:

x = 1560 / 4

x = 390

So, at this rate, the bakery can make 390 donuts in 6 hours .

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Coleton just bought a new mp3 player. It has a capacity of 1,000 minutes. He has already downloaded 304 minutes of music. Each song he can download is 4 minutes in length. Coleton wants to know how many more songs he can download until the mp3 player is full. Is 76 songs a reasonable answer?

Answers

Using mathematical operations, we know that 76 is not a reasonable answer and 174 songs in actuality can be downloaded.

What are mathematical operations?

  • Calculating a value using operands and a math operator is referred to as performing a mathematical "operation."
  • The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.
  • In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.

So, the number of songs Coleton can download more are:

  • Total capacity: 1000 minutes
  • Songs downloaded: 304 minutes
  • Each song length: 4 minutes

More songs that can be downloaded:

  • 1000 - 304 = 696
  • 696/4 = 174

So, 174 more songs can be downloaded.

Therefore, using mathematical operations, we know that 76 is not a reasonable answer and 174 songs in actuality can be downloaded.

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Answer:

No 76 is not a reasonable answer. 174 is a reasonable answer.

Step-by-step explanation:

76×4=304

304+304=608

375×4=1500

174×4=696

696×4=2784

Factor the trinomial: x2 + 12x + 32A. (x - 2)(x + 16)


B. (x + 16)(x + 16)


C. (x + 4)(x + 8)


D. prime

Answers

x^2 + 12x + 32 = x^2 + 4x + 8x + 32 = x(x + 4) + 8(x + 4) = (x + 4)(x + 8)

Find dy/dx if y= (1+x)e^x^2

Answers

y=(1+x)e^(x^2)\ny'=(1+x)'\cdot e^(x^2)+(1+x)\cdot(e^(x^2))'\ny'=1\cdot e^(x^2)+(1+x)\cdot e^(x^2)\cdot (x^2)'\ny'=e^(x^2)+(1+x)e^(x^2)\cdot2x\ny'=e^(x^2)(1+(1+x)\cdot2x)\ny'=e^(x^2)(1+2x+2x^2)\ny'=e^(x^2)(2x^2+2x+1)\n
You first need to know that:

If\quad y=u\cdot v\n \n \frac { dy }{ dx } =u\frac { dv }{ dx } +v\frac { du }{ dx } \n \n

Knowing that u is a function of x and that v is a function of x.

So:

y=\left( 1+x \right) { e }^{ { x }^( 2 ) }=u\cdot v\n \n u=1+x,\n \n \therefore \quad \frac { du }{ dx } =1

\n \n v={ e }^{ { x }^( 2 ) }={ e }^( p )\n \n \therefore \quad \frac { dv }{ dp } ={ e }^( p )={ e }^{ { x }^( 2 ) }\n \n p={ x }^( 2 )\n \n \n \therefore \quad \frac { dp }{ dx } =2x

\n \n \therefore \quad \frac { dv }{ dp } \cdot \frac { dp }{ dx } =2x{ e }^{ { x }^( 2 ) }=\frac { dv }{ dx }

And this means that:

\frac { dy }{ dx } =\left( 1+x \right) \cdot 2x{ e }^{ { x }^( 2 ) }+{ e }^{ { x }^( 2 ) }\cdot 1\n \n =2x{ e }^{ { x }^( 2 ) }\left( 1+x \right) +{ e }^{ { x }^( 2 ) }

\n \n ={ e }^{ { x }^( 2 ) }\left( 2x\left( 1+x \right) +1 \right) \n \n ={ e }^{ { x }^( 2 ) }\left( 2x+2{ x }^( 2 )+1 \right) \n \n ={ e }^{ { x }^( 2 ) }\left( 2{ x }^( 2 )+2x+1 \right)
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