A man walks 10 miles in x hours. How far does he walk in one hour?
Which expression represents this?
10+x miles
10x miles
10/x miles

Answer:

[tex]\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}=\tan\left(x\right)[/tex]

Step-by-step explanation:

[tex]\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}[/tex]

Apply formula:

[tex]\cos\left(A\right)-\cos\left(B\right)=-2\cdot\sin\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right)[/tex] and

[tex]\sin\left(A\right)+\sin\left(B\right)=2\cdot\sin\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right)[/tex]

We get:

[tex]=\frac{-2\cdot\sin\left(\frac{2x+4x}{2}\right)\cdot\sin\left(\frac{2x-4x}{2}\right)}{2\cdot\sin\left(\frac{2x+4x}{2}\right)\cdot\cos\left(\frac{2x-4x}{2}\right)}[/tex]

[tex]=\frac{-\sin\left(\frac{2x-4x}{2}\right)}{\cos\left(\frac{2x-4x}{2}\right)}[/tex]

[tex]=\frac{-\sin\left(\frac{-2x}{2}\right)}{\cos\left(\frac{-2x}{2}\right)}[/tex]

[tex]=\frac{-\sin\left(-x\right)}{\cos\left(-x\right)}[/tex]

[tex]=\frac{-\cdot-\sin\left(x\right)}{\cos\left(x\right)}[/tex]

[tex]=\frac{\sin\left(x\right)}{\cos\left(x\right)}[/tex]

[tex]=\tan\left(x\right)[/tex]

Hence final answer is

[tex]\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}=\tan\left(x\right)[/tex]

How many classes could Anna take so that the total cost for the month would be the same?

5 classes

What is the total monthly cost when it is the same for both gyms?

$37.50

Step-by-step explanation:

The number of classes Anna could take so the total cost for the month would be the same is 5.

The total monthly cost when it is the same for both gyms would be $37.50.

When the total cost is the same, both equations for the gym would be equal to each other.

7.5x = 5.5x + 10

In order to determine the value of x, take the following steps:

Combine similar terms

7.5x - 5.5x = 10

Add similar terms together

2x = 10

Divide both sides by 2

x = 5

Total cost = 7.5 x 5 = $37.50

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Answer:

Option C is correct

Step-by-step explanation:

The relationship between Roberts age and Julia’s age is given by:

r = j+3            ....[1]

where,

r is the Robert's age and j represents the Julia's age in years

We have to find the table of values represents the relationship between Roberts age and Julia’s age

if r = 9 years

then;

[tex]9 = j+3[/tex]

Subtract 3 from both sides we have;

6 = j

or

j = 3 years

Similarly:

if r = 15 years

then;

[tex]15= j+3[/tex]

Subtract 3 from both sides we have;

12 = j

or

j = 12 years

If r = 21 years

then;

[tex]21= j+3[/tex]

Subtract 3 from both sides we have;

18 = j

or

j = 18 years

Therefore, the table of values represents the relationship between Roberts age and Julia’s age is, Table C

option c is the right answer

Let's open up parenthesis:

20x+15-2x

Then simplify.

18x+15

...Which is A.

Hope I helped!

~Mshcmindy

Answer:

The correct answer is option A. 18x + 15

Step-by-step explanation:

It is given an expression in variable x,

5(4x + 3) - 2x

To simplify the given expression

5(4x + 3) - 2x = (5 * 4x) + (5 * 3) - 2x   (open the bracket)

  = 20x + 15 - 2x

  = 20x - 2x + 15

  = 18x + 15

Therefore the correct answer is 18x + 15

The correct option is option A.  18x + 15

The sum of the integers -9, 4, 10, -4, 8, -4 is calculated by adding the numbers together, which totals 5.

To find the sum of the integers -9, 4, 10, -4, 8, -4, we add them together:

-9 + 4 + 10 + (-4) + 8 + (-4) = 5.

We can group the positive and negative numbers to make this simpler:

(4 + 10 + 8) = 22

(-9 - 4 - 4) = -17

Adding the results of the positive and negative groups gives us:

22 + (-17) = 5.

Therefore, the sum of the given integers is 5.

Convert the exponential equation to a logarithmic equation using the logarithm base

(

4

)

(

4

)

of the right side

(

16

)

(

16

)

equals the exponent

(

2

)

(

2

)

.

log

4

(

16

)

=

2

Answer:

8/45

Step-by-step explanation:

Write 4 5/8 as an improper fraction:  45/8.

Then invert this result, obtaining:

 .  This is the "reciprocal" of 4 5/8.

Answer:

37/8

Step-by-step explanation:

attachement ---

If a local city collects 8% sales tax if the total purchase was $216 then $17.28 is collected for sales tax.

A relative value indicating hundredth parts of any quantity is known as Percentage.

Given that a  local city collects 8% sales tax

The total purchase was $216.

We need to find the amount collected for sales tax.

To find this we have to find 8% of 216.

Convert 8% to the decimal value.

8/100=0.08

Now multiply 0.08 with 216

0.08×216

$17.28

Hence, if a local city collects 8% sales tax if the total purchase was $216 then $17.28 is collected for sales tax.

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The amount collected for sales tax is $16.

Step 1: Understand the Problem

The total purchase amount ($216) includes the sales tax. We need to find how much of this amount is the sales tax itself.

Step 2: Convert the Percentage to a Decimal

Convert the sales tax rate from a percentage to a decimal.

[tex]\[ \text{Sales Tax Rate} = \frac{8}{100} = 0.08 \][/tex]

Step 3: Set Up the Equation

Let ( P ) be the pre-tax purchase amount and ( T ) be the total amount including tax. The relationship can be written as:

[tex]\[ T = P + \text{Sales Tax} \][/tex]

Since the sales tax is 8% of the pre-tax amount,

[tex]\[ \text{Sales Tax} = 0.08 \times P \][/tex]

Thus, the total amount is:

[tex]\[ T = P + 0.08P = 1.08P \][/tex]

Step 4: Solve for the Pre-Tax Amount

We know the total amount ( T ) is $216.

[tex]\[ 216 = 1.08P \][/tex]

To find ( P ):

[tex]\[ P = \frac{216}{1.08} \][/tex]

[tex]\[ P \approx 200 \][/tex]

Step 5: Calculate the Sales Tax

Now, find the sales tax:

[tex]\[ \text{Sales Tax} = 0.08 \times P \][/tex]

[tex]\[ \text{Sales Tax} = 0.08 \times 200 \][/tex]

[tex]\[ \text{Sales Tax} = 16 \][/tex]

Therefore the amount collected for sales tax is $16.

The answer for your question is d

Answer:

D)15+15+10+10+6+6

Step-by-step explanation:

the formula to find the SA of a rectangular prism is:

2(lw)+2(lh)+2(hw)

where

l=length

w=width

and

h=height

let's substitute the values,3,2,and 5 into the equation

2(5*3)+2(5*2)+2(3*2)=62

62 is the SA

from the options:

10+6=16

10+10+6+6=32

15+15+10+10+6=56

and

15+15+10+10+6+6=62

so option D is correct

Answer: the meaning of data is pretty simple

Step-by-step explanation: data is something you record or write down after you do a experiment. after you jot it down you can show your work to other scientests to show what you know. I hope this helps!

The mean of a data set is equal to the sum of the set of numbers divided by how many numbers are in the set.

Let's look at an example.

6, 8, 9, 14, 23

To find the mean of the data set shown above,

start by adding the numbers.

Adding the numbers, we get 60.

60 will be divided by the number of numbers in the set, which is 5.

So, 60 divided by 5 is 12.

So the mean of this data set is 12.

Answer:

C

Step-by-step explanation:

The degree of a polynomial is determined by the value of the largest exponent of a term in the expression.

The largest exponent is 4 from the term [tex]x^{4}[/tex]

Hence the degree of the polynomial is 4 → C

Answer:

C (4)

Step-by-step explanation:

[tex]5 \times 3 \times 2 + \frac{3}{0} - \frac{45}{3} + 1 = \\ \\ = \frac{3}{0} \\ \\ or \\ \\ 1. \: 30 + \frac{3}{0} - \frac{45}{3} + 1 \\ 2. \: 30 + \infty - \frac{45}{3} + 1 \\ 3. \: 30 + \infty - 15 + 1 \\ 4. \: \infty [/tex]

Yeah it's Impossible

Answer:

Yeah it's Impossible

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

How many selfies did Tania take? (my first answer would be too many, but that's probably not the answer you're looking for :-) )

We know that each cousin appear 2 or 3 times overall.

If she would have taken each cousin exactly 2 times, that would be 16 cousins/photos

If she would have taken each cousin exactly 3 times, that would be 24 cousins/photos

We know there's exactly 5 cousins per photo...

so we have to find a multiple of 5 cousins/photos that is between 16 and 24.

The only possibility is 20 cousins/photos.  20 / 5 = 4 photos.

Final answer:

Tania took 4 selfies with her cousins. Each cousin appeared in exactly 2 selfies, with some appearing a third time to account for 16 total cousin appearances divided by 5 cousins per selfie.

Explanation:

The problem presented is a combinatorial puzzle involving selfies and cousins. Since each cousin is in either 2 or 3 pictures, we can try to minimize the number of pictures by assuming each cousin is in exactly 2 pictures first. If there are 8 cousins and 5 cousins per picture, then by multiplying 8 by 2 (every cousin appears exactly 2 times), we get 16 cousin appearances in total.

Since each selfie has 5 cousins, we divide the total cousin appearances by the number of cousins per picture: 16 / 5, which results in 3.2. However, since it's not possible to have a fraction of a picture, we need at least 4 selfies to cover all appearances. Yet, this leaves us 4 extra appearances (because 4 pictures would mean 20 cousin appearances in total).

These 4 extra appearances account for the fact that some cousins appear 3 times instead of just 2. Therefore, Tania must have taken 4 selfies with her cousins to cover the 16 cousin appearances with some cousins appearing an additional third time.

Each pencil box usually contains same amount of pencils. In given context  the number of pencils in five boxes is 10 pencils.

Suppose that its given that 'a' boxes contains 'b' items, then, assuming that each box contains 'x' items, then

[tex]x + x + ... + x \text{ (a times)} = b\\\\x \times a = b\\\\x = \dfrac{b}{a}[/tex]

Thus, there are 'b/a' items contained in each box.

Since there are six pencils in three boxes, let there are 'x' pencils in one box, then we have:

[tex]x + x + x = 6\\3 \times x = 6\\\\\text{Dividing both sides by 3}\\\\x = \dfrac{6}{3} = 2[/tex]

Thus, there are 2 pencils in each pencil box.

Thus, for 5 boxes, we get [tex]2 \times 5 = 10[/tex] pencils.

Thus,

In given context  the number of pencils in five boxes is 10 pencils.

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Final answer:

By using proportional reasoning, if three boxes contain 36 pencils, then five boxes would contain 60 pencils.

Explanation:

If thirty-six pencils are packed in three boxes, then there are twelve pencils per box because 36 divided by 3 equals 12.

To find out how many pencils are packed in five boxes, we multiply twelve pencils (the number of pencils per box) by five boxes.

Therefore, 12 pencils/box × 5 boxes = 60 pencils in five boxes.

This is a simple proportional reasoning problem, often encountered in mathematical exercises in school.

Answer: 12.20 feet.

Step-by-step explanation:

Observe in the figure attached that a right triangle is formed.

Then, you  need to remember the identity:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

In this case you can identify that:

[tex]adjacent=10\\hypotenuse=x[/tex]

[tex]\alpha=35\°[/tex]

Then, to find the length of the wooden board (x), you need to substitute values and solve for x.

Therefore, you get:

[tex]cos(35\°)=\frac{10}{x}\\\\(x)(cos(35\°))=10\\\\x=\frac{10}{cos(35\°)}\\\\x=12.20[/tex]

The length of the wooden board is: 12.20 feet.

Answer:

640

Step-by-step explanation:

Expanding the binomial :

r⁵ - 40r⁴ + 640r³ - 5120r² + 20480r - 32768

The coefficient of r³ is 640

Answer:

Step-by-step explanation:

Apply binomial theorem to expand (a+b)^n where a = r, b = -8 n n = 5

the r^3 term is (5!/(2!*(5-2)!)*r^3*(-8)^(5-3)

=(5*4*3*2*1/1*2*1*2*3)*r^3*(-8)^2

=640*r^3

So the coefficient is 640.

Answer:

d

Step-by-step explanation:

she has 16 quarters

1$=4 quarters

so 4$= 16 quarters

plus one more from the thirty cense

she could have 17 which is strange it’s not an option so go with B ig

Answer:

60x + 18

Step-by-step explanation:

6 (9x + 3) + 6x

distribute

54x + 18 + 6x

combine like-terms

60x + 18

Answer:

Simplify

Step-by-step explanation:

6(9x+3)+6x

Distribute:

=(6)(9x)+(6)(3)+6x

=54x+18+6x

Combine Like Terms:

=54x+18+6x

=(54x+6x)+(18)

=60x+18

Answer:

[tex]f * g = 21x ^ 2 + 32x +12[/tex]

Domain: all real numbers [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

We have the functions [tex]f (x) = 3x + 2[/tex] and [tex]g (x) = 7x + 6[/tex]

We want to find f*g. Then we must multiply the function f by the function g.

Note that the function [tex]f (x) = 3x +2[/tex] is a linear function, therefore its domain is all real numbers. In the same way the function [tex]g (x) = 7x + 6[/tex] is also a linear function and its domain is all real numbers.

The multiplication of f * g will be

[tex]f * g = (3x + 2) (7x + 6)\\\\f * g = 21x ^ 2 + 18x + 14x +12\\\\f * g = 21x ^ 2 + 32x +12[/tex]

The function g(x) is a quadratic function and its domain is the intercept of the domain of f(x) with the domain of g(x), that is, all real numbers.

Answer:

Function for given situation is : [tex]V(t)=3000(0.70)^t[/tex]

Value of computer after 4 years = $720.3.

Step-by-step explanation:

Given that the value of a $3000 computer decreases about 30% each year. Now we need to write a function for the computers value V(t). then we need to find about how much will the computer be worth in 4 years.

It clearly says that value decreases so that means function represents decay.

For decay we use formula:

[tex]A=P(1-r)^t[/tex]

where P=initial value = $3000,

r= rate of decrease =30% = 0.30

t= number of years

A=V(t) = future value

so the required function is [tex]V(t)=3000(1-0.30)^t[/tex]

or [tex]V(t)=3000(0.70)^t[/tex]

Now plug t=4 years to get the value of computer after 4 years.

[tex]V(4)=3000(0.70)^4[/tex]

[tex]V(4)=720.3[/tex]

Hence final answer is $720.3.

Answer:

A = $3000(0.70)^t

Step-by-step explanation:

100% - 30% = 70%.  Thus, the common ratio in this exponential function is 0.70.

Use a formula with the form of the compound amount formula:

A = P(1 + r)^t, where r is the common ratio as a decimal fraction and t is the number of years.

Here, A = $3000(1 - 0.30)^t, or    A = $3000(0.70)^t

Answer:

a = -3

b = -2

c = 6

Step-by-step explanation:

The quadratic formula states that for an equation of the form:

[tex]ax^{2} + bx + c = 0[/tex]

The solution to that equation is:

[tex]\frac{-b±\sqrt{b^{2}-4ac}}{2a}[/tex]

In this case we have:

0=-3x^2-2x+6

Where:

a = -3

b = -2

c = 6

I would make a table and plug values(or just plug in x values) in to figure out the equation's graph:  (plug in values that will make it easy for you since you have a √)

f(x) = 3(√x)

x = 0

f(0) = 3(0) = 0       ------> (0 , 0)

x = 1

f(1) = 3(√1) = 3(1) = 3  ------> (1 , 3)

x = 4

f(4) = 3(√4) = 3(2) = 6   ------>    (4 , 6)

Now that you have found some points, find a graph/line that goes through these points

These are the factors of 36:

1, 2, 3, 4, 6, 9, 12, 18, 36

1, 2, 3, 4, 6, 9, 12, 18, 36

1 x 36 = 36

1, 2, 3, 4, 6, 9, 12, 18, 36

2 x 18 = 36

1, 2, 3, 4, 6, 9, 12, 18, 36

3 x 12 = 36

1, 2, 3, 4, 6, 9, 12, 18, 36

4 x 9 = 36

1, 2, 3, 4, 6, 9, 12, 18, 36

6 x 6 = 36

Hope this helped!

Answer:

1, 2, 3, 4, 6, 9, 12, 18, 36

Step-by-step explanation:

I took test on edge 2021

Halving the height halves the volume, but halving the radius quarters it; their effects on volume differ.

It seems there might be a typo or a mistake in your reasoning. Let's reassess the situation:

Original cone:

- Radius, [tex]\( r = 2 \)[/tex]

- Height, [tex]\( h = 6 \)[/tex]

- Volume, [tex]\( V_1 = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (2)^2 (6) = 8\pi \)[/tex] cubic units

Now, you're considering two scenarios:

1. If the height is changed to [tex]\( h = 3 \)[/tex]:

  - New volume, [tex]\( V_2 = \frac{1}{3} \pi (2)^2 (3) = 4\pi \)[/tex] cubic units

2. If the radius is changed to \( r = 1 \):

  - New volume, [tex]\( V_3 = \frac{1}{3} \pi (1)^2 (6) = 2\pi \)[/tex] cubic units

Now, let's analyze the effects:

- Changing the height from 6 to 3 reduces the volume by half (from [tex]\( 8\pi \)[/tex] to [tex]\( 4\pi \)[/tex]).

- Changing the radius from 2 to 1 reduces the volume by a factor of [tex]\( \frac{1}{4} \)[/tex] (from [tex]\( 8\pi \)[/tex] to [tex]\( 2\pi \))[/tex].

So, changing the height to half of its original value reduces the volume by half, while changing the radius to half of its original value does not reduce the volume by half but rather by a quarter. Therefore, the effects are not the same.

Answer:

Step-by-step explanation:

The distributive property: a(b + c) = ab + ac

[tex]3(2x-5)=5(x-4)+x\\\\(3)(2x)+(3)(-5)=(5)(x)+(5)(-4)+x\\\\6x-15=5x-20+x\qquad\text{combine like terms}\\\\6x-15=6x-20\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\-15=-20\qquad\bold{FALSE}[/tex]

Answer:

[tex](5y^2+2z)(5y^2-2z)[/tex]

Step-by-step explanation:

Use the difference of squares formula.

[tex]a^2-b^2=(a+b)(a-b)[/tex]

[tex]a=5y^2 \\ b=2z[/tex]

[tex](5y^2+2z)(5y^2-2z)[/tex]

Answer:6/36

Step-by-step explanation:

The probability of rolling a number less than 5 and even on a die is 1/2.

To find the probability of rolling a number less than 5 and even, we need to determine the number of outcomes that satisfy both conditions and divide it by the total number of possible outcomes.

There are three outcomes that satisfy both conditions: {2, 4, 6}. The total number of possible outcomes is six since a die has six sides.

Therefore, the probability of rolling a number less than 5 and even is 3/6, which simplifies to 1/2.

The first graph the X is 45° because it right angle is 90 degrees Larry give us 55 degrees so 55 subtract the equals 45

The second graph has a degree of 113 because 180 subtracted by 67 is 113 because they straight angle has 180.

The first one is 45

The second one is 113

Answer:

17. x= 35

19. a= 113

Step-by-step explanation:

17.   55+x=90

90-55= 35

19. 180= 67+a

180-67=113

Check the picture below.

recall that range is the interval over the y-axis for the graph of the function.

The range of the function shown is [4, ∝]

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Step-by-step explanation:

[tex]100xh=1,150\qquad\text{divide both sides by}\ 100x\neq0\\\\\dfrac{100xh}{100x}=\dfrac{1,150}{100x}\\\\\boxed{h=\dfrac{115}{x}}[/tex]

To solve the equation \( 1,150 = 100 \times x \times h \) for \( h \), you want to isolate \( h \) on one side of the equation. Follow these steps:
**Step 1: Understand the equation**
The equation is saying that 100 times the product of \( x \) and \( h \) is equal to 1,150.
**Step 2: Isolate \( h \)**
To solve for \( h \), you need to get \( h \) by itself on one side of the equation. Right now \( h \) is being multiplied by \( 100 \times x \). To undo this, you'll divide both sides of the equation by \( 100 \times x \).
**Step 3: Perform the division**
Divide both sides of the equation by \( 100 \times x \):
\[
\frac{1,150}{100 \times x} = \frac{100 \times x \times h}{100 \times x}
\]
**Step 4: Simplify both sides**
On the right-hand side, \( 100 \times x \) in the numerator and \( 100 \times x \) in the denominator cancel each other out:
\[
\frac{1,150}{100 \times x} = h
\]
**Step 5: Result**
You are left with \( h \) by itself on one side of the equation and \( \frac{1,150}{100 \times x} \) on the other:
\[
h = \frac{1,150}{100 \times x}
\]
Now \( h \) has been solved in terms of \( x \), and you can find the value of \( h \) if you know the value of \( x \) by simply substituting that value into this equation and performing the calculation.