Alexis and Mariana are hiking. Alexis climbs to the
top of a ridge 417 feet above sea level. Mariana goes to
the bottom of a valley, 30 feet below sea level. What is
the vertical distance between Alexis and Mariana?

Answers:

Domain is [tex](-\infty, \infty)[/tex]

Range is [tex](-\infty, 4][/tex]

============================================

Explanation:

We can replace x with any real number we want. We don't have any restrictions to worry about since there are no division by zero issues for instance. Also, there isn't any issues of things like taking the square root of a negative number.

Therefore, the domain is the set of all real numbers which translates to the interval notation of [tex](-\infty, \infty)[/tex]

This interval notation can be thought of as [tex]-\infty < x < \infty[/tex]

----------------------------

The range on the other hand isn't the set of all real numbers. It might help to graph this parabola (see below). You should see that the highest point occurs at the vertex (5, 4). This then tells us that the largest y can get is y = 4.

In other words, y = 4 or y can be smaller than this.

In symbols, we would say the range is [tex]y \le 4[/tex] and that translates to the interval notation of [tex](-\infty, 4][/tex]

The curved parenthesis always goes with either infinity. The square bracket says "include the endpoint 4 as part of the interval".

Answer:

She bought 20 eggs that were 12 cents, and she bought 30 eggs that were 14 cents.

Step-by-step explanation:

Create a system of equations where x is the number of 12 cent eggs and y is the number of 14 cent eggs.

x + y = 50

0.12x + 0.14y = 6.6

Solve by elimination by multiplying the top equation by -0.12:

-0.12x - 0.12y = -6

0.12x + 0.14y = 6.6

Add these together and solve for y:

0.02y = 0.6

y = 30

So, she bought 30 eggs that were 14 cents. Plug in 30 as y into one of the equations, and solve for x:

x + y = 50

x + 30 = 50

x = 20

So, she bought 20 eggs that were 12 cents.

She bought 20 eggs that were 12 cents, and she bought 30 eggs that were 14 cents.

Answer:

The author sold a total of 30240 books following this trend.

Step-by-step explanation:

Let's find 5% of 14400 first;

14400 * 5%

14400 * 5/100

144 * 5

720 (So now we know that they are decreasing by 720 each month; therefore thats the constant)

=> aₙ = a₁ + r(n - 1)

=> a₂₃ = 14400 + 720(23 - 1)

=> a₂₃ = 14400 + 720(22)

=> a₂₃ = 14400 + 15840

=> a₂₃ = 30240

Hope this helps!

The author sold a total of 30240 books following this trend.

Let's find 5% of 14400 first;

[tex]14400 * 5\%\\14400 * 5/100\\144 * 5=720[/tex]

A, is a type of numerical sequence studied by Mathematics, where each term or element counting from the second is equal to the sum of the previous term with a constant.

So using the arithmetic progression we have:

[tex]a_n = a_1 + r(n - 1)\\a_{23} = 14400 + 720(23 - 1)\\ a_{23} = 14400 + 720(22)\\ a_{23} = 14400 + 15840\\a_{23} = 30240[/tex]

See more about arithmetic progression at brainly.com/question/20385181

Answer:

2/11

Step-by-step explanation:

12-4-5=3

So now we know that we have:

4 pairs of polo socks

5 pairs of plain white socks

3 pairs of grey socks

To pull a grey sock one time is 3/12 since there are 12 total socks and 3 pairs of grey socks but since we remove a sock, in the second time, the probability would be 2/11.

Hope this helps! Brainliest?

Answer:

I think it's 9/22

Step-by-step explanation:

Probability of A given B = (probability of A and B)/probability of B

[tex]\frac{(14/22)(9/22)}{14/22} \\=\frac{9}{22}[/tex]

P(B) = P(1 checked bag) = 14/22

P(A) = P(silver status) = 9/22

P(A ∩ B) = (14/22)(9/22)

Step-by-step explanation:

[tex]y = {x}^{2} - 4x \\ y = x(x - 4) - - - (a) \\ 2x - y = 2 \\ y = 2x - 2 \\ y = 2(x - 2) - - - (b) \\ (a) = (b) : \\ x(x - 4) = 2(x - 2) \\ {x}^{2} - 4x = 2x - 2 \\ {x}^{2} - 6x + 2 = 0 \\ x = 5.6 \: \: and \: \: 0.4 \\ y = 2(5.6 - 2) \: \: and \: \: 2(0.4 - 2) \\ y = 7.2 \: \: and \: \: - 3.2[/tex]

Answer:

A. Conditional Statement

Step-by-step explanation:

In a conditional statement, A would be the premise, and B would be the conclusion.

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Have a great summer :)

Answer:

$0

Step-by-step explanation:

Answer:

$84

Step-by-step explanation:

Do 3/5*140 which will give you 84 dollars

Answer:

Step-by-step explanation:

Recall that the argument of the square root function y = √x must always be 0 or greater.

If you meant y=√x+8 -7, the domain is therefore [0, infinity).

But if you meant y=√(x+8) -7, the domain is [-8, infinity).

Those parentheses are important!

Answer:

h = 5/2

Step-by-step explanation:

[tex]\frac{3}{4} *\frac{1}{2} *h=\frac{15}{16} \\\\\frac{3}{8} *h=\frac{15}{16}[/tex]

divide both sides by 3/8

[tex]h=\frac{5}{2}[/tex]

Answer:

8

Step-by-step explanation:

7 x 8 = 56 56 - 4 = 52.

3 x 8 = 24 24 + 28 = 52

Answer:

Step-by-step explanation:

In the rectangular complex number -9√3 + 9i, which has a standard form a + bi, the a = -9√3 and the b = 9. We need this in polar form (r, θ) where

[tex]r=\sqrt{a^2+b^2}[/tex] and filling in:

[tex]r=\sqrt{(-9\sqrt{3})^2+(9)^2 }[/tex] (notice we do not put the i in there with the 9).

[tex]r=\sqrt{243+81}[/tex] so

r = 18. Now let's move on to the angle, which is a little more difficult. The angle is found in the inverse tangent ratio:

[tex]tan^{-1}(\frac{b}{a})[/tex] so filling that in, we have:

[tex]tan^{-1}(\frac{9}{-9\sqrt{3} })=\frac{1}{-\sqrt{3} }[/tex] Since tangent is the side opposite over the side adjacent, y is positive and x is negative in the second quadrant. This is a 30 degree angle in QII, which has a reference angle of 150 degrees. This angle in radians is [tex]\frac{5\pi}6}[/tex], so the polar form of that number is (18, [tex]\frac{5\pi}{6}[/tex])

Answer:

its d

Step-by-step explanation:

i guessed lol

Answer: Hi the Range is 4

Step-by-step explanation: The range of a data set in statistics is the difference between the largest and the smallest values. While range does have different meanings within different areas of statistics and mathematics, this is its most basic definition, and is what is used by the provided calculator. Using the same example:

18, 16, 19, 15, 17

19,18,17,16,15

19-15= 4

Answer:

y = -2x+7

Step-by-step explanation:

Parallel lines have the same slope

y = 1-2x has a slope of -2

So the new line has a slope of -2

We have a slope of -2 and a point of (3,1)

y = mx+c

1 = -2(3)+c

1 = -6+c

Add 6 to each side

1+6 =c

7 =c

y = -2x+7

Answer:

x = 6

Step-by-step explanation:

The sum of the angles of a quadrilateral is 360

69+111+12x-3 +111 = 360

Combine like terms

12x+288=360

Subtract 288 from each side

12x+288-288 = 360-288

12x = 72

Divide by 12

12x/12 = 72/12

x = 6

Answer:

x = 6

Step-by-step explanation:

All angles together equal 360

Us this to set up your formula

360 = 111 + 111 + 69 + 12x-3

360 = 288 + 12 x

360 - 288 = 12x

72 = 12x

72/12 = x

6 = x

You could also use the fact that angle t and r are equal to set your formula up as

69 = 12x-3

69+3=12x

72=12x

72/12=x

6=x

Answer:

c

Step-by-step explanation:

If he could clean the house alone in one hour, then it wouldve taken him and his sister less than that. if he could clean it in 3 hours, it wouldve tkane him and his sister 1.5 hours.

Answer:

Step-by-step explanation:

c. 6 hours

Answer:  The total number of colored papers is 18.

Step-by-step explanation:

Given: The ratio of coloured papers to wight papers is 3:8.

Let total number of colored papers = 3x

and total number of wight papers = 8x

Since, there are 48 wight papers , then

[tex]8x=48[/tex]

[tex]\Rightarrow\ x=6[/tex]

Now , number of colored papers = 3(6)=18

Hence, the total number of colored papers is 18.

Answer:

x = 45

Step-by-step explanation:

x = 20 + 25

as x is vertically opposite to GED

and vertically opposite angles are equal

Answer:

I would answer but I have no numbers to give the answer

Answer:

a y intercept (0,8)

Flat rate 8

b  slope is 4

c  3.5 hours

Step-by-step explanation:

The y intercept is where it crosses the y axis, which is (0,8)

The flat rate is the y intercept which is 8

The rate per hour is the slope

m = ( y2-y1)/(x2 -x1)

Using 2 point ( 1,12) and ( 2,16)

    = (16 -12)/(2-1)

     = 4/1

    = 4

The equation is

y = mx+b

y = 4x+8

Let y = 22

22 = 4x+8

Subtract 8 from each side

22-8 = 4x+8-8

14 = 4x

Divide by 4

14/4 = 4x/4

3.5 = x

3.5 hours

(0,8) is the y intercept because it crosses the y axis.

We can see that the flat rate is 8, which is the y intercept.

[tex] \quad\quad\quad\boxed{ \tt{m = \frac{rise}{run} = \frac{ y \tiny{2} \: \small{ - } \: y \tiny{1}}{x \tiny{2} \: \small{ - } \: x \tiny{1}} }}[/tex]

[tex]\quad\quad\quad\boxed{ \tt{m = \frac{16 - 12}{2 - 1} }}[/tex]

[tex]\quad\quad\quad\boxed{ \tt{m = \frac{4}{1} }}[/tex]

[tex] \quad\quad\quad\boxed{ \color{green}\tt{m = 4}}[/tex]

[tex] \quad \quad \quad \boxed{ \tt{y = mx + b}}[/tex]

[tex] \quad \quad \quad \boxed{ \tt{y = mx + b}}[/tex]

[tex] \quad \quad \quad \boxed{ \tt{22 =4x + 8}}[/tex]

[tex] \quad \quad \quad \boxed{ \tt{22 - 8 = 4x + 8 - 8}}[/tex]

[tex] \quad \quad \quad \boxed{ \tt{14 = 4x \: \:\cancel{ \color{red}+ 8 - 8}}}[/tex]

[tex]\quad \quad \quad \boxed{ \tt{ \frac{14 = \cancel4x}{ \cancel{4} }}}[/tex]

[tex]\quad \quad \quad \boxed{ \color{green} \tt{3.5 = x}}[/tex]

_________

#LetsStudy

#HikariSquad

Answer:

Aidan saved 115.67 over five weeks.

Step-by-step explanation:

After x weeks:

The amount of money saved by Aidan is given by:

[tex]y(x) = 17.63x + 27.52[/tex]

How much aidan saved over five weeks?

This is y when x = 5. So

[tex]y(x) = 17.63x + 27.52[/tex]

[tex]y(5) = 17.63*5 + 27.52 = 115.67[/tex]

Aidan saved 115.67 over five weeks.

Answer:

Jomar needs to study for 3 hours on Thursday to be prepared for his test.

Step-by-step explanation:

If we want to make the average a certain amount of time over a certain number of days, we can first figure out the number of days and total amount needed. Here, we can see that the average is 1 hour and 30 minutes, and there are 6 days (Saturday-Thursday). Therefore, as

average = total / length, we can multiply both sides by length to get

average * length = total

Plugging 1.5 hours in for average and 6 days for length, we get

1.5 * 6 = 9 hours as the total amount needed to get an average of 1.5 hours a day

Our total so far is 2 hours for Saturday, 2 hours for Sunday, and 2 hours for Monday. This adds up to 6 hours, and we need 9. The difference between 9 and 6 is 3, meaning that Jomar needs to study for 3 hours on Thursday to be prepared for his test.

Answer:

3 : 7

Step-by-step explanation:

24/56 = 3 / 7

Answer:

3:7 helpful answer to your question have a nice evening

Answer:

$74.36 sorry all i got

Step-by-step explanation:

First, we need to determine the sales price of the skateboard. The formula for find the discounted prices is:

Where:

is the sales price of the item: what we are solving for in this part of the problem.

is the regular price of the item: $79.16 for this problem.

is the discount rate: 12% for this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore 12% can be written as  

12

100

Substituting and calculating  

gives

79.16

79.16

12

100

79.16

949.92

100

79.16

9.4992

69.6608

69.66

rounded to the nearest cent.

Now we can find the total price of the item with tax included. The formula for this is

#t = p + (p * r)

Where, this time:

is the total price: what we are solving for in this problem.

is the price of the item: it is the sales price of the item for this problem which is $69.66

is the tax rate: 6.75% or, using the same rule as in the formula above:  

6.75

100

Substituting and calculating  

gives:

69.66

69.66

6.75

100

69.66

470.205

100

69.66

4.70205

74.36205

74.36

rounded to the nearest cent.

Noah would pay a total cost (with the discount and after tax) of $74.36

Answer:

4 minutes

Step-by-step explanation:

Let the time taken for them to have the same number of strawberries be x minutes.

Initially

Ruby: 10 strawberries

Sapphire: 30 strawberries

After x minutes

Ruby: (10 +3x) strawberries

Sapphire: (30 -2x) strawberries

Since we let x minutes be the amount of time that has passed when they have the same amount of strawberries,

10 +3x= 30 -2x

Bring all x terms to one side, constant to the other:

3x +2x= 30 -10

Simplify:

5x= 20

Divide both sides by 5:

x= 20 ÷5

x= 4

∴ It will take 4 minutes.

Answer:

26.2

Step-by-step explanation:

From the given diagram;

Opposite side IJ = 22

Hypotenuse HI = x

Angle of elevation = 57degrees

Using the SOH CAH TOA;

sin theta = opposite/hypotenuse

sin theta = IJ/HI

sin57 = 22/x

x = 22/sin57

x = 22/0.8387

x = 26.2

Hence the legnth of HI is 26.2

Answer: The correct answer is D, also for part B, do you need help with that one too?

Step-by-step explanation:

Answer:

a. Total of 45 students.

b. 18 Boys.

Answer:

There are 45 students and 18 boys in the class