10. A cliff on the seashore is eroding at the rate of 17 centimeters per year. Write and solve an equation to find the number of
years in which the cliff will erode 85 centimeters.

Answer:

Part 1) [tex]P=[2\sqrt{29}+\sqrt{18}]\ units[/tex] or [tex]P=15.01\ units[/tex]

Part 2) [tex]P=2[\sqrt{20}+\sqrt{45}]\ units[/tex] or [tex]P=22.36\ units[/tex]

Part 3) [tex]P=4[\sqrt{13}]\ units[/tex] or [tex]P=14.42\ units[/tex]

Part 4) [tex]P=[19+\sqrt{17}]\ units[/tex] or [tex]P=23.12\ units[/tex]

Part 5) [tex]P=2[\sqrt{17}+\sqrt{68}]\ units[/tex] or [tex]P=24.74\ units[/tex]

Part 6) [tex]A=36\ units^{2}[/tex]

Part 7) [tex]A=20\ units^{2}[/tex]

Part 8) [tex]A=16\ units^{2}[/tex]

Part 9) [tex]A=10.5\ units^{2}[/tex]

Part 10) [tex]A=6.05\ units^{2}[/tex]

Step-by-step explanation:

we know that

The formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Part 1) we have the triangle ABC

[tex]A(0,3),B(5,1),C(2,-2)[/tex]

step 1

Find the distance AB

[tex]A(0,3),B(5,1)[/tex]

substitute in the formula

[tex]AB=\sqrt{(1-3)^{2}+(5-0)^{2}}[/tex]

[tex]AB=\sqrt{(-2)^{2}+(5)^{2}}[/tex]

[tex]AB=\sqrt{29}\ units[/tex]

step 2

Find the distance BC

[tex]B(5,1),C(2,-2)[/tex]

substitute in the formula

[tex]BC=\sqrt{(-2-1)^{2}+(2-5)^{2}}[/tex]

[tex]BC=\sqrt{(-3)^{2}+(-3)^{2}}[/tex]

[tex]BC=\sqrt{18}\ units[/tex]

step 3

Find the distance AC

[tex]A(0,3),C(2,-2)[/tex]

substitute in the formula

[tex]AC=\sqrt{(-2-3)^{2}+(2-0)^{2}}[/tex]

[tex]AC=\sqrt{(-5)^{2}+(2)^{2}}[/tex]

[tex]AC=\sqrt{29}\ units[/tex]

step 4

Find the perimeter

The perimeter is equal to

[tex]P=AB+BC+AC[/tex]

substitute

[tex]P=[\sqrt{29}+\sqrt{18}+\sqrt{29}]\ units[/tex]

[tex]P=[2\sqrt{29}+\sqrt{18}]\ units[/tex]

or

[tex]P=15.01\ units[/tex]

Part 2) we have the rectangle ABCD

[tex]A(-4,-4),B(-2,0),C(4,-3),D(2,-7)[/tex]

Remember that in a rectangle opposite sides are congruent

step 1

Find the distance AB

[tex]A(-4,-4),B(-2,0)[/tex]

substitute in the formula

[tex]AB=\sqrt{(0+4)^{2}+(-2+4)^{2}}[/tex]

[tex]AB=\sqrt{(4)^{2}+(2)^{2}}[/tex]

[tex]AB=\sqrt{20}\ units[/tex]

step 2

Find the distance BC

[tex]B(-2,0),C(4,-3)[/tex]

substitute in the formula

[tex]BC=\sqrt{(-3-0)^{2}+(4+2)^{2}}[/tex]

[tex]BC=\sqrt{(-3)^{2}+(6)^{2}}[/tex]

[tex]BC=\sqrt{45}\ units[/tex]

step 3

Find the perimeter

The perimeter is equal to

[tex]P=2[AB+BC][/tex]

substitute

[tex]P=2[\sqrt{20}+\sqrt{45}]\ units[/tex]

or

[tex]P=22.36\ units[/tex]

Part 3) we have the rhombus ABCD

[tex]A(-3,3),B(0,5),C(3,3),D(0,1)[/tex]

Remember that  in a rhombus all sides are congruent

step 1

Find the distance AB

[tex]A(-3,3),B(0,5)[/tex]

substitute in the formula

[tex]AB=\sqrt{(5-3)^{2}+(0+3)^{2}}[/tex]

[tex]AB=\sqrt{(2)^{2}+(3)^{2}}[/tex]

[tex]AB=\sqrt{13}\ units[/tex]

step 2

Find the perimeter

The perimeter is equal to

[tex]P=4[AB][/tex]

substitute

[tex]P=4[\sqrt{13}]\ units[/tex]

or

[tex]P=14.42\ units[/tex]

Part 4) we have the quadrilateral ABCD

[tex]A(-2,-3),B(1,1),C(7,1),D(6,-3)[/tex]

step 1

Find the distance AB

[tex]A(-2,-3),B(1,1)[/tex]

substitute in the formula

[tex]AB=\sqrt{(1+3)^{2}+(1+2)^{2}}[/tex]

[tex]AB=\sqrt{(4)^{2}+(3)^{2}}[/tex]

[tex]AB=5\ units[/tex]

step 2

Find the distance BC

[tex]B(1,1),C(7,1)[/tex]

substitute in the formula

[tex]BC=\sqrt{(1-1)^{2}+(7-1)^{2}}[/tex]

[tex]BC=\sqrt{(0)^{2}+(6)^{2}}[/tex]

[tex]BC=6\ units[/tex]

step 3

Find the distance CD

[tex]C(7,1),D(6,-3)[/tex]

substitute in the formula

[tex]CD=\sqrt{(-3-1)^{2}+(6-7)^{2}}[/tex]

[tex]CD=\sqrt{(-4)^{2}+(-1)^{2}}[/tex]

[tex]CD=\sqrt{17}\ units[/tex]

step 4

Find the distance AD

[tex]A(-2,-3),D(6,-3)[/tex]

substitute in the formula

[tex]AD=\sqrt{(-3+3)^{2}+(6+2)^{2}}[/tex]

[tex]AD=\sqrt{(0)^{2}+(8)^{2}}[/tex]

[tex]AD=8\ units[/tex]

step 5

Find the perimeter

The perimeter is equal to

[tex]P=AB+BC+CD+AD[/tex]

substitute

[tex]P=[5+6+\sqrt{17}+8]\ units[/tex]

[tex]P=[19+\sqrt{17}]\ units[/tex]

or

[tex]P=23.12\ units[/tex]

Part 5) we have the quadrilateral ABCD

[tex]A(-1,5),B(3,6),C(5,-2),D(1,-3)[/tex]

step 1

Find the distance AB

[tex]A(-1,5),B(3,6)[/tex]

substitute in the formula

[tex]AB=\sqrt{(6-5)^{2}+(3+1)^{2}}[/tex]

[tex]AB=\sqrt{(1)^{2}+(4)^{2}}[/tex]

[tex]AB=\sqrt{17}\ units[/tex]

step 2

Find the distance BC

[tex]B(3,6),C(5,-2)[/tex]

substitute in the formula

[tex]BC=\sqrt{(-2-6)^{2}+(5-3)^{2}}[/tex]

[tex]BC=\sqrt{(-8)^{2}+(2)^{2}}[/tex]

[tex]BC=\sqrt{68}\ units[/tex]

step 3

Find the distance CD

[tex]C(5,-2),D(1,-3)[/tex]

substitute in the formula

[tex]CD=\sqrt{(-3+2)^{2}+(1-5)^{2}}[/tex]

[tex]CD=\sqrt{(-1)^{2}+(-4)^{2}}[/tex]

[tex]CD=\sqrt{17}\ units[/tex]

step 4

Find the distance AD

[tex]A(-1,5),D(1,-3)[/tex]

substitute in the formula

[tex]AD=\sqrt{(-3-5)^{2}+(1+1)^{2}}[/tex]

[tex]AD=\sqrt{(-8)^{2}+(2)^{2}}[/tex]

[tex]AD=\sqrt{68}\ units[/tex]

step 5

Find the perimeter

The perimeter is equal to

[tex]P=\sqrt{17}+\sqrt{68}+\sqrt{17}+\sqrt{68}[/tex]

substitute

[tex]P=2[\sqrt{17}+\sqrt{68}]\ units[/tex]

or

[tex]P=24.74\ units[/tex]

Answer:

need points

Step-by-step explanation:

Here you don’t need to solve the equation,the value of the problem is zero

For both methods I will use the quadratic formula. Look at the image below

Hope this helped!    

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 need two points through which the line passes.

[tex](x_ {1}, y_ {1}) :( 1,4)\\(x_ {2}, y_ {2}) :( 3,2)[/tex]

Substituting:

[tex]m = \frac {2-4} {3-1} = \frac {-2} {2} = - 1[/tex]

Answer:

[tex]m = -1[/tex]

Answer:

323.75

Step-by-step explanation:

129.50=40% because it is the selling price not the marked price

if,129.50=40 what about 100

129.50×100/40

To calculate the discounted price of the MP3 player after a 60% markdown, multiply the original price of $129.50 by 60% to find the markdown amount of $77.70, then subtract it from the original price to get the final price of $51.80.

To find the price of an MP3 player with a markdown of 60%, you can perform the following calculations:

The original price of the MP3 player is $129.50 and the markdown is 60%. We calculate 60% of $129.50 which is 0.60 × 129.50 = $77.70. Next, we subtract this markdown from the original price: 129.50 - 77.70 = $51.80.

Therefore, the discounted price of the MP3 player is $51.80.

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ANSWER

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

EXPLANATION

We we're given that, the real part of the complex number is 2.

Let the imaginary part be y.

Then the complex number is

[tex]z = 2 + yi[/tex]

Also, we have that, the modulus is 4.

The modulus is given by the formula;

[tex] |z| = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

This implies that,

[tex] 4 = \sqrt{ {2}^{2} + {y}^{2} } [/tex]

We square both sides to obtain;

[tex] {4}^{2} = 4 + {y}^{2} [/tex]

[tex]16 - 4 = {y}^{2} [/tex]

[tex] {y}^{2} = 12[/tex]

[tex]y = \sqrt{12} = 2 \sqrt{3} [/tex]

Therefore the complex part is

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

Answer:

3.4

Step-by-step explanation:

i just did it

Answer:

not geometric

Step-by-step explanation:

If the sequence is geometric then the common ratio r between consecutive terms should be equal

[tex]\frac{42}{21}[/tex] = 2

[tex]\frac{126}{42}[/tex] = 3

[tex]\frac{504}{126}[/tex] = 4

There is no common ratio between consecutive terms

Hence the sequence is not geometric

Answer:

x° = 37°

Step-by-step explanation:

* Lets revise some facts of a circle

- The secant is a line intersect the circle in two points

- If two secants intersect each other in a point outside the circle,

 then the measure of the angle between them is half the difference

 of the measures of their intercepted arcs

* Now lets solve the problem

- There is a circle

- Two secants of this circle intersect each other in a point outside

  the circle

∴ The measure of the angle between them = 1/2 the difference of the

  measures of their intercepted arcs

∵ The measure of the angle between them is x°

∵ The measures of their intercepted arcs are 26° and 100°

- Use the rule above to find x

∴ x° = 1/2 [ measure of the large arc - measure of small arc]

∵ The measure of the large arc is 100°

∵ The measure of the small arc is 26°

∴ x° = 1/2 [100 - 26] = 1/2 [74] = 37°

∴ x° = 37°

No. It would be B because she multiplied by 0.02 which is 1 percent and the tip is 20 percent. 0.2 is 20 percent, so it is B

Answer:

Step-by-step explanation:

38.50 x 20%

38.50 x 0.20= 7.70

Answer: 7.70

Your answer is correct

I guess you wrote the correct answer

Answer:

A=36

Step-by-step explanation:

A=s^2

A=6^2

A=36

Answer:

36

Step-by-step explanation:

Formula ⇒ A = s²

We know that s = 6, so we substitute into A = s²

A = s²

A = 6²

A = 36

Answer:

Step-by-step explanation:

A function is a relation that associates each element x of a set X, to a single element y of another set Y.

In D) for x = 0 we have three values of y = f(x): -1, 4 and 6.

Therefore this table does not represent a function.

Answer:

for the first graph it is

a=1

b= 1/16

c=1/256

for the second graph it is

d=1

e=4/9

f=16/81

Check the picture below.

so the triangle has a height of 9 and a base of 9, since it's the radius anyway.

if we subtract the area of that triangle from the area of the circle's sector, what's leftover is just the shaded area.

20.25π - 40.5.

The ratio of the room's length to its area is 1:12, derived from length (22 feet) divided by area (264 square feet).

let's break it down step by step.

Step 1: Calculate the area of the room.

To find the area of a rectangle, you multiply its length by its width.

So, Area = Length × Width

Area = 22 feet × 12 feet

Area = 264 square feet

Step 2: Calculate the ratio of the length of the room to its area.

The ratio of length to area is:

[tex]\[ \text{Ratio} = \frac{\text{Length}}{\text{Area}} \][/tex]

Substituting the values:

[tex]\[ \text{Ratio} = \frac{22 \, \text{feet}}{264 \, \text{square feet}} \][/tex]

Step 3: Simplify the ratio.

[tex]\[ \text{Ratio} = \frac{22}{264} \][/tex]

Step 4: Simplify the fraction.

[tex]\[ \text{Ratio} = \frac{1}{12} \][/tex]

So, the ratio of the length of the room to its area is [tex]\( \frac{1}{12} \)[/tex].

Answer:

1st pic: 4

2nd pic: 70

3rd pic: 5

Step-by-step explanation:

Answer:

84 ft²

Step-by-step explanation:

Solve for Volume. Volume of a box is:

V = Length (base) x Width (base) x Height (of rectangular prism/square)

Change each measurement to have the same measurement (ft -> in, or vice versa).

Note that 1 ft = 12 in.

6 in = 1/2 ft, because 6/12 = 1/2

Length = 12 ft

Width = 14 ft

Height = 1/2 ft

Solve. Plug in the corresponding number to the corresponding words.

V = 12 x 14 x 1/2

Simplify. Solve.

V = 12 x (14 x 1/2)

V = 12 x (14/2)

V = 12 x 7

V = 84

84 ft² is your answer.

~

Answer:

1,008

Step-by-step explanation:

You multiply all three numbers to get your answer.

Answer:

Not a factor

Step-by-step explanation:

If (x - 3) is a factor then f(3) = 0

f(x) = x² - 4x + 30

f(3) = 2(3)² - 4(3) + 30 = 18 - 12 + 30 = 36 ≠ 0

Since f(3) ≠ 0 then (x - 3) is not a factor of f(x)

( x - 3 ) is not a factor of the polynomial 2x² - 4x + 30

What is Factor Theorem?

The Factor Theorem states that if f(x) is a polynomial of degree n greater than or equal to 1, and 'a' is any real number, then ( x - a ) is a factor of f ( x ) if f ( a ) = 0

Given data ,

f ( x ) = 2x² - 4x + 30

If ( x - 3 ) is a factor of f ( x ) , then by factor theorem f ( x ) = f ( 3 ) = 0

And , f ( 3 ) = 2 x 3 x 3 - 4 x 3 + 30

                            = 18 - 12 + 30

                            = 36

Therefore , f ( 3 ) ≠ 0 , so ( x - 3 ) is not a factor of 2x² - 4x + 30

Hence , ( x - 3 ) is not a factor of the polynomial 2x² - 4x + 30

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Answer:

The length is 5 cm and the width is 4 cm

Step-by-step explanation:

I assume that is a rectangle

Let

x----> the length of rectangle

y ---> the width of rectangle

we know that

The area of rectangle is

A=xy

A=20 cm²

so

20=xy -----> equation A

The perimeter of rectangle is

P=2(x+y)

P=18 cm

so

18=2(x+y)

9=x+y -----> y=9-x ----> equation B

Substitute equation B in equation A and solve for x

20=x(9-x)

20=9x-x²

x²-9x+20=0

Solve the quadratic equation by graphing

The solution is x=5 cm (I assume that the length is greater than the width)

see the attached figure

Find the value of y

y=9-5=4 cm

therefore

The length is 5 cm

The width is 4 cm

Answer:

volume  =  (1/3)(area of base)(height)

area of base  =  pi * radius2  =  pi * (10/2)2  =  pi * 52  =  25pi   cm2

volume  =  (1/3)( 25pi )( 9 )   cm3

volume  =  75pi   cm3

volume  ≈  236  cm3  

ANSWER

[tex]Volume = 235.6 {cm}^{3} [/tex]

EXPLANATION

The volume of a cone is calculated the using the formula:

[tex]Volume = \frac{1}{3} \pi {r}^{2} h[/tex]

From the given information the height of the cylinder is, h=9cm.

The diameter of the base is 10cm.

The radius is half of the diameter of the base, r=5cm.

We plug in the values into the formula to get:

[tex]Volume = \frac{1}{3} \times \pi \times {5}^{2} \times 9[/tex]

[tex]Volume = 75\pi {cm}^{3} [/tex]

[tex]Volume = 235.6 {cm}^{3} [/tex]

Final answer:

Jordan spent $14.85 in total, of which $2.85 was spent on snacks. After subtracting the cost of snacks, it's found that she spent $12.00 on bus fares.

Explanation:

The student asked how much Jordan spent on bus fares to and from the zoo if she spent a total of $14.85, including $2.85 on snacks. To find out the amount spent on bus fares, one needs to subtract the cost of the snacks from the total amount spent. Therefore, the calculation would be $14.85 (total spent) - $2.85 (snacks) = $12.00.

Hence, Jordan spent $12.00 on bus fares.

Answer:

y = 179x +1999

y = 249x

Step-by-step explanation:

Given:

down payment of cool cars= $1999

monthly lease rate of cool cars= $179

down payment of awesome autos= $0

monthly lease rate of awesome autos= $249

Number of months=x

total amount paid towards the lease after x months=y

Now creating a system of linear equations that describes the total amount, y, paid towards the lease after x months:

the slope intercept form of any linear function is given as y=mx +b

where m= slope  of function and b=y-intercept

In given case, slope m gives the monthly lease rate and y-intercept b gives the down payment.

So the equations for the two linear functions will be:

cool cars:

Putting the values of m=179 and b=1999, we get

y = 179x +1999

awesome autos:

Putting the values of m=249 and b=0, we get

y = 249x !

Answer:

3 21/100

just a fraction.

Answer:

5√2

Step-by-step explanation:

The question is on geometry

The formula for distance between two points is;

[tex]d= \sqrt{(X2-X1)^2 + (Y2-Y1)^2}[/tex]

where d is distance.

Given points;

(0,5)    and   (-5,0) ;

X1=0 ,X2= -5 , Y1= 5, Y2= 0

X2-X1 = -5 - 0= -5

Y2-Y1= 0-5= -5

[tex]d= \sqrt{(-5)^2 + (-5)^2}[/tex]

[tex]d=\sqrt{25+25}[/tex]

[tex]d=\sqrt{50}[/tex]

[tex]d=\sqrt{2*25} =\sqrt{2} *\sqrt{25} =\sqrt{2} *5\\\\\\\\d=5\sqrt{2}[/tex]

Answer:

[tex]d=5\sqrt{2}[/tex]

Step-by-step explanation:

Given : (0, 5) and (-5, 0)

To Find : Distance between the given points

Solution:

We will use distance formula :

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex](x_1,y_1)=(0,5)[/tex]

[tex](x_2,y_2)=(-5,0)[/tex]

Substitute the values in the formula .

[tex]d=\sqrt{(-5-0)^2+(0-5)^2}[/tex]

[tex]d=\sqrt{(-5)^2+(-5)^2}[/tex]

[tex]d=\sqrt{25+25}[/tex]

[tex]d=\sqrt{50}[/tex]

[tex]d=5\sqrt{2}[/tex]

Hence the distance between the given points is 5√2 units

Answer:

The inequality is y > 1/2 x - 2

Step-by-step explanation:

* To solve this problem we must to know how to make an equation

  of the line from two point

- If the line passes through points (x1 , y1) and (x2 , y2)

- The form of the equation is y = mx + c, where m is the slope of the

 line and c is the y-intercept

- The rule of the slope is m = (y2 - y1)/(x2 - x1)

- The y-intercept means the line intersect the y-axis at point (0 ,c)

* Now lets solve the problem

- To write the inequality we must to make the equation of the line

  from any two points on it

∵ The line passes through points (4 , 0) and (0 , -2)

- Let (4 , 0) is (x1 , y1) and (0 , -2) is (x2 , y2)

∵ m = (y2 - y1)/(x2 - x1)

∴ m = (-2 - 0)/(0 - 4)

∴ m = (-2)/-4 = 1/2

- Lets write the form of the equation

∵ y = mx + c ⇒ substitute the value of m

∴ y = 1/2 x + c

- The line intersects the y-axis at point (0 , -2)

∴ c = -2

∴ y = 1/2 x + -2

∴ y = 1/2 x - 2

- lets look to the line if it is dashed line then there is no equal with the

 inequality (> , <) sign, if it is solid line then there is equal with the

 inequality sign (≥ , ≤)

∵ The line is dashed line

∴ The sign of inequality is > or <

- Lets look to the shaded part, if it is over the line then the inequality

 will be y > 1/2 x - 2, if it is under the line then the inequality will

 be y < 1/2 x - 2

∵ The shaded part is over the line

∴ y > 1/2 x - 2

* The inequality is y > 1/2 x - 2

Answer:

The total weight of the packages of fruit that weigh less than half a pound is, 7/8.

Step-by-step explanation:

This reason being is because 2 of the 1/8ths are under 1/2 of a pound, and the 1/4th and the 3/8 is all under 1/2 of a pound. You add the 2 1/8ths together and get 2/8 + the 3/8 = 5/8. Then you add the 5/8 together with the only 1/4th and you get 7/8, as your answer.

Hope this helps!! :)

You start with the equation V = IR, plug the value 0.5 for I and you have

V = 0.5*R

So, the first three options are equivalent and correct.

V=IR

And current, Ampere is given as 0.5 so substituting it back in the main equation gives V = 0.5R

Answer:

C 18%

Step-by-step explanation:

To find  the percent increase ,take the new amount and subtract the old amount

12.39 - 10.50 = 1.89

Divide this by the original amount

1.89/10.50 = .18

Multiply this by 100 to get the percent

.18*100% = 18%

Answer:

60

Step-by-step explanation:

Answer:

About 57.48

Step-by-step explanation:

The lenght of each side is 24cm, 24cm, and 8cm.

In order to solve this problem, we know that the perimeter of a triangle equation is P = a + b + c, where a, b, and c are the sides of the triangle.

The perimeter is 56cm, we can write the equation as follow:

a + b + c = 56cm (1)

If each of the two longer sides of the triangles is three times as long as the shortest side, we can assume:

c = shortest side = x

a = b = longer sides = 3x

Substituting the values in the equation (1):

3x + 3x + x = 56cm

7x = 56cm

x = 56cm/7 = 8cm

c = shortest side = 8cm

a = b = longer sides = 3(8cm) = 24cm

Answer:

2 gallons per mile

To express 12X+36Y in different terms, we can use other variables or coefficients while maintaining the same relationship between X and Y. Two equivalent expressions are 4A+12B and 6C+18D.

To express the expression 12X+36Y in terms of equivalent mathematical expressions using different variables or coefficients, we can use any other variables or coefficients as long as they maintain the same relationship between X and Y. Here are two distinct expressions:

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The probable question may be:

Express the expression 12X+36Y in terms of equivalent mathematical expressions using different variables or coefficients. Provide at least two distinct expressions that are equivalent to 12X+36Y.