Martina begins a dive at sea level. She dives down 20 feet, and then rises 7 feet.

She dives again, going down 9 more feet. How far below sea level is Martina?

Answer:

the number of $10 bills = 17

the number of $20 bills = 37

Step-by-step explanation:

Let x be the number of $10 bills  and y be the number of $20 bills

Total bills = 54

So [tex]x+y= 54[/tex]

Total value of money is $910

[tex]10x+20y= 910[/tex]

now we solve for x  and y

Solve the first equation for y

[tex]x+y= 54[/tex]

[tex]y=54-x[/tex]

Now replace y in second equation

[tex]10x+20y= 910[/tex]

[tex]10x+20(54-x)= 910[/tex]

[tex]10x+ 1080-20x= 910[/tex]

[tex]1080-10x= 910[/tex]

Subtract 1080 from both sides

[tex]-10x= -170[/tex]

Divide both sides by -10

x= 17

[tex]y=54-x[/tex]

Replace x with 17

[tex]y=54-17=37[/tex]

the number of $10 bills = 17

the number of $20 bills = 37

Answer:

B. 3

Step-by-step explanation:

First of all we will define rotational symmetry.

Rotational symmetry is when a shape looks the same after some rotation or less than one rotation.

The order of rotational symmetry is how many times it matches the original shape during the rotation.

So, for the given shape the rotated shape will match the original shape three times so the order for symmetry for the given shape is 3.

Hence,

the correct answer is B. 3 ..

Answer:

.333333... can be expressed as 1/3.

Step-by-step explanation:

A rational number is defined as:

any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

aka, any number that you can express as a fraction.

Any person who has spent enough time in math should be familiar with the fact that the thirds (aka 1/3, 2/3) are repeating decimals, but are rational numbers as they can be written as whole number fractions.

If you didn't know this, don't worry. You'll get it soon enough.

Hope this helped!

Answer:

- [tex]\frac{27}{7}[/tex]

Step-by-step explanation:

Given

f(x) = [tex]\frac{3}{x+2}[/tex] - [tex]\sqrt{x-3}[/tex]

Evaluate f(19) by substituting x = 19 into f(x)

f(19) = [tex]\frac{3}{19+2}[/tex] - [tex]\sqrt{19-3}[/tex]

       = [tex]\frac{3}{21}[/tex] - [tex]\sqrt{16}[/tex]

       = [tex]\frac{1}{7}[/tex] - 4

       = [tex]\frac{1}{7}[/tex] - [tex]\frac{28}{7}[/tex] = - [tex]\frac{27}{7}[/tex]

Answer:

It would be 7/2s, however if you want to solve it completely, you do 7 ÷ 2. It would give you 3.5 so, s = 3.5.

Answer:

83 square inches

Step-by-step explanation:

Let's find the answer, you can see the attached file for clarity.

Because we have a rectangle measuring 8 inches by 5 inches, we can use the area of the rectangle as follows:

A1=base*height=(8 inches)*(5 inches)=40 square inches

Now, because we have a triangle over the square side of 8 inches long, we can divide the triangle into 2 rectangle triangles, each of them with a base of 4 inches and a height of 7 inches, obtaining:

A2=2*(base*height/2)=2*(4 inches)*(7 inches)/2=28 square inches

Doing the same for the other triangle we get 2 triangles with a base of 2.5 inches and a height of 6 inches, obtaining:

A3=2*(base*height/2)=2*(2.5 inches)*(6 inches)/2=15 square inches

The addition of all areas is:

A=A1+A2+A3=40 square inches + 28 square inches + 15 square inches

A=83 square inches.

In conclusion we have an area of 83 square inches.

Answer:

83

Step-by-step explanation:

Answer:

Hanan collect [tex]\frac{3}{8}[/tex] of a bag of clothes

Step-by-step explanation:

Let

x ------> amount of clothing bag that Jenny collected

y ------> amount of clothing bag that Hanan collected

we know that

[tex]y=\frac{1}{2}x[/tex] -----> equation A

[tex]x=\frac{3}{4}[/tex] -----> equation B

Substitute equation B in equation A

[tex]y=\frac{1}{2}(\frac{3}{4})[/tex]

[tex]y=\frac{3}{8}[/tex]

therefore

Hanan collect [tex]\frac{3}{8}[/tex] of a bag of clothes

Your question asks how much money was collected at the toll for a period of 8 hours.

To find the answer, we would need to gather some important information from the question.

Important information:

With the information above, we can solve the problem.

First, let's find how much money the toll makes in one hour. To find this, we need to multiply 1.50 by 160 cars, since the toll costs $1.50 and 160 cars go through it per hour.

[tex]1.50*160=240[/tex]

The toll makes $240 per hour.

Now, since we need to find how much the toll makes in 8 hours, we need to multiply 240 by 8.

[tex]240 * 8=1,920[/tex]

When you're done solving, you should get 1,920.

This means that the toll makes $1,920 in 8 hours.

Answer:

7m

Step-by-step explanation:

The volume of a pyramid is given by the following formula: 1/3bh. Where 'b' represents the area of the base and 'h' the height of the pyramid.

The area of the base is: b = (3m)(4m) = 12m^2

Now, we know that the volume is 28m^3, then:

28m^3 = (1/3)(12m^2)(h)

Solving for 'h':

h = 7m

Answer:

5m^6 + 2m^4 + 5m^3

hope this works!!!!

To divide (10m⁸ + 4m⁶ + 10m⁵) by 2m², simplify each term by subtracting 2 from the exponents. The result is 5m⁶ + 2m⁴ + 5m³. The correct answer is D).

To divide (10m⁸ + 4m⁶ + 10m⁵) by 2m², follow these steps

Write the given expression: (10m⁸ + 4m⁶ + 10m⁵) / 2m².

Divide each term in the numerator by 2m² separately:

(10m⁸ / 2m²) + (4m⁶ / 2m²) + (10m⁵ / 2m²).

Simplify each term:

5m⁶ + 2m⁴ + 5m³.

The final result is 5m⁶ + 2m⁴ + 5m³.

The correct option is D).

In this division, we use the rule of exponents: when dividing terms with the same base, subtract the exponents.

The division by 2m² reduces the power of 'm' in each term by 2. So, 10m⁸ becomes 10m⁶, 4m⁶ becomes 2m⁴, and 10m⁵ becomes 5m³. The constants 10 and 4 remain unchanged. The simplified expression is the final result.

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[tex]5x + 3x -4 = 10\\8x=14\\x=\dfrac{14}{8}=\dfrac{7}{4}[/tex]

one

Answer:0ne

Step-by-step explanation:

Answer:

The vertex is (-2,-17).

Step-by-step explanation:

We have given y=2x²+8x-9

To find the x-coordinates we use:

xv= -b/2a

where a=2 and b=8

Now put the values in the formula:

xv= -(8)/2(2)

xv=-8/4

xv= -2

Now to find the y coordinates, we will simply substitute the value in the given equation:

y=2x²+8x-9

y=2(-2)²+8(-2)-9

y=2(4)-16-9

y=8-16-9

y=-8-9

y= -17

Therefore the vertex is(-2, -17)....

Answer:

[tex]\tt{(8^{-3})}^{-4}; \ \ \ {(8^{1})}^{12}; \ \ \ {(8^{6})}^{2}[/tex]

Step-by-step explanation:

[tex]\boxed{\tt {(a^m)}^n=a^{m\cdot n}}\\\\\\ \tt{(8^{-3})}^{-4}=8^{-3\cdot(-4)}=8^{12}\\\\{(8^{1})}^{12}=8^{1\cdot12}=8^{12}\\\\{(8^{6})}^{2}=8^{6\cdot2}=8^{12}\\\\[/tex]

Answer:A,D,F

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

The quadratic equation looks like:

ax + by + c = 0

"c" is the variable that stands for the "constant", or the number that does not have an extra variable attached, and so is "unchanging". In this case, your answer is 7, which is the constant of the equation. Once defined, the number cannot be changed.

~

Area of a full circle is PI x r^2

Area = 3.14 x 8^2 = 200.96

Area of a sector is area *  central angle / full circle

Area = 200.96 x 5PI/3 / 2PI = 160PI/3

Answer is C.

Answer:[tex]\frac{160\pi }{3} units^2[/tex]

Step-by-step explanation:

Given

Angle subtended by sector is[tex]\frac{5\pi }{3}[/tex]

radius =8 units

[tex]Area of sector=\frac{\theta }{2\pi }\pi r^2 [/tex]

[tex]A=\frac{20\times 8\pi }{3}[/tex]

[tex]A=\frac{160\pi }{3}[/tex]

(4 - 7n) – (20+5)

Simplify:

(4 -7n) - 25

Remove parenthesis:

4 - 7n -25

Combine like terms:

4-25 = -21

Now you have:  -21-7n

The term with the variable is usually rearranged to be in front, so it becomes:  -7n-21

Answer:

20 in

Step-by-step explanation:

The radius is half the diameter.

You are given the diamter is 40 in.

So the radius is half of 40 in.

Half of 40 in means what is 40 in divided by 2.

Half of 40 in or 40 in ÷ 2 is 20 in.

The radius is 20 in.

Answer: 20 inches

Step-by-step explanation: A radius is half of the circle, and a diameter is a whole circle. 2 radius are equal to one diameter. So divide the diameter by 2 to get the radius.

40/2 = 20

The radius of the circle is 20 inches.

Answer:

√(3)/2

Step-by-step explanation:

To find the quotient, rationalize the denominator by multiplying both the numerator and denominator by √(6)

3√(8)*√(6)    =     3√(48)

4√(6)*√(6)              24

Next, simplify the top radical

12√(3) =  √(3)/2, This is the answer, it cannot be simplified any further.

 24  

For this case we must find the quotient of the following expression:

[tex]\frac {3 \sqrt {8}} {4 \sqrt {6}} =[/tex]

We combine [tex]\sqrt {6}[/tex] and [tex]\sqrt {8}[/tex] into a single radical:

[tex]\frac {3 \sqrt {\frac {8} {6}}} {4} =\\\frac {3 \sqrt {\frac {4} {3}}} {4} =\\\frac {3 \frac {\sqrt {4}} {\sqrt {3}}} {4} =\\\frac {3 \frac {2} {\sqrt {3}} * \frac {\sqrt {3}} {\sqrt {3}}} {4} =[/tex]

[tex]\frac {3 * \frac {2 \sqrt {3}} {3}} {4} =\\\frac {\frac {6 \sqrt {3}} {3}} {4} =\\\frac {6 \sqrt {3}} {12} =\\\frac {\sqrt {3}} {2}[/tex]

Answer:

[tex]\frac {\sqrt {3}} {2}[/tex]

Answer:

D it is a horizontal line . .  .horizontal lines do not have a slope

Step-by-step explanation:

Answer:

B. the slope is zero

Step-by-step explanation:

The line shown is a horizontal line.  Horizontal lines have zero slope.

Vertical (up and down) lines do not have a slope ( or what we usually call undefined slope)

Answer:

where is rectangle???

Answer:

10

Step-by-step explanation:

The length of AB is 10 and the length of BC is 13. CD is parallel to AB so its 10.

Answer:

60 different votes.

Step-by-step explanation:

This is a permutations question. There are a total of 5 bands to be voted for, and Rafeal has to vote only for 3 of the bands. It is also mentioned that the voting has to be done for the favorite, the second favorite, and the third favorite bands from the list. This means that the order of selection is important. This means that permutations will be used. Thus, 3 bands out of 5 have to be selected in an order. This implies:

5P3 = 5*4*3 = 60 possibilities.

There are 60 different votes!!!

Answer: 60 different votes are possible

Step-by-step explanation:

We have a list of 5 bands and we must choose 3 of them. In this case, the order of the election is important. Therefore this is a problem that is solved using permutations.

The formula for permutations is:

[tex]nPr=\frac{n!}{(n-r)!}[/tex]

Where n is the number of bands you can choose and you choose 3 of them.

Then we calculate:

[tex]5P3 =\frac{5!}{(5-3)!}\\\\5P3=\frac{5!}{2!}\\\\5P3 = 60[/tex]

Finally, the number of possible votes is 60

Answer:

Susanne is 16 years old.

Step-by-step explanation:

You're gonna need three equations.

Key: B = Bob, D = Dakota, s = Susanne

B = 4s

D = s - 3

B + D + s = 93

Now plug in B and D into the third equation:

4s + (s - 3) + s = 93

Now solve it:

4s + s - 3 + s = 93

6s - 3 = 93

+3 +3

6s = 96

6s/6 = 96/6

s = 16

Bob's age is 4 times greater than Susanne's age, and Dakota is 3 years younger than Susanne.

The sum of their ages is 93. Susanne's age is 16.5.

Let's assign variables to represent the ages of the individuals involved:

We are given that Bob's age is 4 times greater than Susanne's age, so we can write the equation B = 4S.

We are also told that Dakota is three years younger than Susanne, so we can write the equation D = S - 3.

The sum of their ages is given as 93, so we can write the equation B + S + D = 93.

Substituting the first equation into the second equation, we get D = 4S - 3.

Substituting the values from the second and third equations into the fourth equation, we have (4S - 3) + S + (S - 3) = 93.

Simplifying this equation, we get 6S - 6 = 93. Adding 6 to both sides, we have 6S = 99. Dividing both sides by 6, we find that S = 16.5.

Therefore, Susanne's age is 16.5.

Answer:

Part 1) [tex]f(x)=\frac{2x-1}{x+2}[/tex] -------> [tex]f^{-1}(x)=\frac{-2x-1}{x-2}[/tex]

Part 2) [tex]f(x)=\frac{x-1}{2x+1}[/tex] -------> [tex]f^{-1}(x)=\frac{-x-1}{2x-1}[/tex]

Part 3) [tex]f(x)=\frac{2x+1}{2x-1}[/tex] -----> [tex]f^{-1}(x)=\frac{x+1}{2(x-1)}[/tex]

Part 4) [tex]f(x)=\frac{x+2}{-2x+1}[/tex] ----> [tex]f^{-1}(x)=\frac{x-2}{2x+1}[/tex]

Part 5) [tex]f(x)=\frac{x+2}{x-1}[/tex] -------> [tex]f^{-1}(x)=\frac{x+2}{x-1}[/tex]

Step-by-step explanation:

Part 1) we have

[tex]f(x)=\frac{2x-1}{x+2}[/tex]

Find the inverse  

Let

y=f(x)

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

Exchange the variables x for y and t for x

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

Isolate the variable y

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

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=\frac{-2x-1}{x-2}[/tex]

Part 2) we have

[tex]f(x)=\frac{x-1}{2x+1}[/tex]

Find the inverse  

Let

y=f(x)

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

Exchange the variables x for y and t for x

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

Isolate the variable y

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

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=\frac{-x-1}{2x-1}[/tex]

Part 3) we have

[tex]f(x)=\frac{2x+1}{2x-1}[/tex]

Find the inverse  

Let

y=f(x)

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

Exchange the variables x for y and t for x

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

Isolate the variable y

[tex]x=\frac{2y+1}{2y-1}\\ \\2xy-x=2y+1\\ \\2xy-2y=x+1\\ \\y[2x-2]=x+1\\ \\y=\frac{x+1}{2(x-1)}[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=\frac{x+1}{2(x-1)}[/tex]

Part 4) we have

[tex]f(x)=\frac{x+2}{-2x+1}[/tex]

Find the inverse  

Let

y=f(x)

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

Exchange the variables x for y and t for x

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

Isolate the variable y

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

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=\frac{x-2}{2x+1}[/tex]

Part 5) we have

[tex]f(x)=\frac{x+2}{x-1}[/tex]

Find the inverse  

Let

y=f(x)

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

Exchange the variables x for y and t for x

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

Isolate the variable y

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

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=\frac{x+2}{x-1}[/tex]

Answer:

Step-by-step explanation:

Answer:

59.25 cm

Step-by-step explanation:

The perimeter means the sum of all the sides of a figure.

The perimeter of a triangle would be sum of all 3 sides (triangle has 3 sides).

The measure oof 3 sides are given, so we just need to add them to get the perimeter.

Perimeter = 16.3 + 18.75 + 24.2 = 59.25 cm

To find the perimeter of the triangle, add the side lengths of 16.3 cm, 18.75 cm, and 24.2 cm to get a total of 59.25 cm. The formula used is simple addition of all side lengths.

To find the perimeter of a triangle, you need to add up the lengths of all its sides. The side lengths given are 16.3 cm, 18.75 cm, and 24.2 cm.

Therefore, the perimeter of the triangle is 59.25 cm.

Answer:

Step-by-step explanation:

Let the base of the board is x feet away from the wall .

And the hypotenuse, which is represented by the length of the board be 15 foot .

So here we have adjacent represented by the base and the hypotenuse .

And cosine function relates adjacent and hypotenuse , which is cos 60=15/x

And the value of cos 60 is half .

Performing cross multiplication

1/2=15/x

Dividing both sides by 2

x=7.5ft

Answer:

7.5 feet.

Step-by-step explanation:

The boardgame resting against the wall is creating a triangle rectangle and as it is forming a 60º angle with the ground that would be solve with the cosine of 60, which is the value of the division of the hypotenuse by the adjacent side, which would be the distance from the base of the board game to the wall:

Cos60= .5

cos60=adjacent side/hypotenuse

.5= adjacent side/15

adjacent side= 15x.5

Adjacent side=7.5 feet

On this line, for all y-values, the x-value will always be -3.

Since it is a vertical line it has no run, only a rise. This makes the slope undefined.

This said, the equation for this line is x = -3

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

16 packs

Step-by-step explanation:

u just have to divide 224 by 14 to get 16

the school wants to get 224 clocks, they clocks come in packs of 14, so each pack has 14 clocks, how many packs are needed?

well, how many times does 14 go into 224? 224 ÷ 14, and you know what that is.

For this case we have that by definition, the slope of a line is given by:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]

We have the following points:

[tex](x_ {1}, y_ {1}) :( 3,2)\\(x_ {2}, y_ {2}): (- 2,3)[/tex]

Substituting we have:

[tex]m = \frac {3-2} {- 2-3} = \frac {1} {- 5} = - \frac {1} {5}[/tex]

Finally, the slope is:

[tex]m = - \frac {1} {5}[/tex]

Answer:

[tex]m = - \frac {1} {5}[/tex]

Answer:

the angle Ф is 63.9 degrees.

Step-by-step explanation:

A right triangle describes this situation.  The height of the triangle is 45 ft and the base is 22 ft.  The ratio height / base is the tangent of the angle of elevation and is tan Ф.  We want to find the angle Ф:

                opp

tan Ф = ---------- = 45 / 22 = 2.045.  

               adj

Using the inverse tangent function on a calculator, we find that the angle Ф is 63.9 degrees.

Answer:

Oops I went too far.

The other point is (9,4).

The average rate of change is 1/5.

Step-by-step explanation:

So I think your function is [tex]f(x)=\sqrt{x}+1[/tex]. Please correct me if I'm wrong.

You want to find the slope of the line going through your curve at the points (4,f(4)) and (9,f(9)).

All f(4) means is the y-coordinate that corresponds to x=4 and f(9) means the y-coordinate that corresponds to x=9.

So if [tex]f(x)=\sqrt{x}+1[/tex], then

[tex]f(4)=\sqrt{4}+1=2+1=3[/tex] and

[tex]f(9)=\sqrt{9}+1=3+1=4[/tex].

So your question now is find the slope of the line going through (4,3) and (9,4).

You can use the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] but I really like to just line up the points vertically and subtract then put 2nd difference over 1st difference. Like this:

( 9  ,   4)

-( 4  ,   3)

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

 5         1

So the slope is 1/5.

The average rate of change of the function f on the interval [4,9] is 1/5.

A function describes the relationship between related variables.

Given that:

[tex]f(x) = \sqrt x + 1,\ 4 \le x \le 9[/tex]

The average rate of change (m) is calculated as:

[tex]m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}[/tex]

[tex]m = \frac{f(9) - f(4)}{9 - 4}\\[/tex]

So, we have:

[tex]m = \frac{f(9) - f(4)}{5}[/tex]

Calculate f(4)

[tex]f(x) = \sqrt x + 1[/tex]

[tex]f(4) = \sqrt 4 + 1[/tex]

[tex]f(4) = 2 + 1[/tex]

[tex]f(4) = 3[/tex]

Calculate f(9)

[tex]f(x) = \sqrt x + 1[/tex]

[tex]f(9) = \sqrt 9 + 1[/tex]

[tex]f(9) = 3 + 1[/tex]

[tex]f(9) = 4[/tex]

So, we have:

[tex]m = \frac{f(9) - f(4)}{5}[/tex]

[tex]m = \frac{4 - 3}{5}[/tex]

[tex]m = \frac{1}{5}[/tex]

Recall that:

[tex]f(4) = 3[/tex] --- this represents the coordinate of the start interval

[tex]f(9) = 4[/tex] --- this represents the coordinate of the end interval

Hence, the coordinates of the end interval is (9,4)

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