What is the circumference of the circle shown below, given that the length of
AB (the minor arc) is 4?​

Answer:

[tex]c=7[/tex]

Step-by-step explanation:

They are just asking you to compare

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

[tex]3x^2+5x+7=0[/tex].

What constant values are in the place of [tex]a,b, \text{ and } c[/tex].

[tex]a=3[/tex]

[tex]b=5[/tex]

[tex]c=7[/tex]

Answer:

Step-by-step explanation:

Actually, you have not "given" the domain.

The domain of F(x)=x^2+2 is "the set of all real numbers," because F(x)=x^2+2 is a polynomial.

F(x^2) = (x^2) + 2 = x^4 + 2.  Again, this is a polynomial and the domain is "the set of all real numbers."

Double check to ensure that you have copied down this problem correctly.

Step-by-step explanation:

:

  2-csc²A

▬▬▬▬▬▬▬

csc²A + 2cotgA

  2 - 1/sin²A

= ▬▬▬▬▬▬▬▬▬▬

 1/sin²A + 2cosA/sinA

  2sin²A - 1

= ▬▬▬▬▬▬▬

  1 - 2cosAsinA

    sin²A + sin²A - 1

= ▬▬▬▬▬▬▬▬▬▬▬▬

 sin²A - 2cosAsinA + cos²A

  sin²A - cos²A

= ▬▬▬▬▬▬▬

  (sinA - cosA)²

 (sinA - cosA)(cosA + sinA)

= ▬▬▬▬▬▬▬▬▬▬▬▬

   (sinA - cosA)²

 sinA + cosA

= ▬▬▬▬▬▬ <-- Let check "+" and "-"

 sinA - cosA

By taking a common Equation denominator and simplifying, we will see that LHS = RHS. To prove that the given equation is true, we can simplify both sides step by step and show that they are equal.

To show that the left-hand side (LHS) is equal to the right-hand side (RHS) of the given equation, let's simplify both sides step by step.

LHS = 2 - cosec²A / cosec²A + 2cotA

= 2 - (1/sin²A) / (1/sin²A) + 2cosA/sinA

= 2 - 1/sin²A / 1/sin²A + 2cosA/sinA

RHS = sinA - cosA / sinA + cosA

By taking a common denominator and simplifying, we will see that LHS = RHS.

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The probable questionShow that the LHS = RHS.

2-cosec^2A/cosec^2A+2cotA=sinA-cosA/sinA+cosA may be:

Answer:

(1, 1 )

Step-by-step explanation:

Given the 2 equations

2x + 3y = 5 → (1)

3x + 2y = 5 → (2)

We can eliminate the term in x by multiplying (1) by 3 and (2) by - 2

6x + 9y = 15 → (3)

- 6x - 4y = - 10 → (4)

Add (3) and (4) term by term

(6x - 6x) + (9y - 4y) = (15 - 10), that is

5y = 5 ( divide both sides by 5 )

y = 1

Substitute y = 1 in either (1) or (2) and solve for x

Substituting in (1), then

2x + (3 × 1) = 5

2x + 3 = 5 ( subtract 3 from both sides )

2x = 2 ( divide both sides by 2 )

x = 1

Solution is (1, 1 )

Answer: 14 gallons of gas.

Step-by-step explanation: For the fractions, find a common denominator, which would be 10. To get 1/5 to have a denominator of 10, multiply each number by 2. You would get 2/10. 7 gallons fills his tank from 2/10 to 7/10. Subtract the two fractions.

7/10 - 2/10 = 5/10.

7 gallons filled his tank half way. We are trying to find the amount to fill his tank all the way. So multiply 7 by 2.

7 x 2 = 14

14 gallons of gas will fill his tank all the way.

I hope this helps!

Ivan's gas tank can hold 17.5 gallons when full after being 1/5 full and then adding 7 gallons.

The total capacity of Ivan's gas tank:

[tex]y=x^2-6x+6\\y=x^2-6x+9-3\\y=(x-3)^2-3[/tex]

The vertex form of the quadratic equation is y = (x-3)^2 + 3.

The vertex form of a quadratic function is given by y = a(x-h)^2 + k, where (h,k) represents the coordinates of the vertex. To convert the quadratic equation y = x^2-6x+6 into vertex form, we need to complete the square.

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Answer:

Option C: (x − 3)(x + 3)(2x + 1)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (3, 1), hence

y = a(x - 3)² + 1

To find a substitute (- 2, - 4) into the equation

- 4 = a(- 2 - 3)² + 1

- 4 = 25a + 1 ( subtract 1 from both sides )

25a = - 5 ( divide both sides by 25 )

a = - [tex]\frac{5}{25}[/tex] = - [tex]\frac{1}{5}[/tex]

y = - [tex]\frac{1}{5}[/tex] (x - 3)² + 1 ← in vertex form

Answer:

[tex]y+6=m(x+2)[/tex]

where I would have to look at the table to know [tex]m[/tex].

Step-by-step explanation:

Point-slope form of a line is

[tex]y-y_1=m(x-x_1)[/tex]

where [tex]m \text{ is the slope and } (x_1,y_1) \text{ is a point on that line}[/tex]

You are given [tex](x_1,y_1)=(-2,-6) \text{, but no value for }m[/tex].

So we know we are looking for an equation that looks like this:

[tex]y-(-6)=m(x-(-2))[/tex]

If you simplify this looks like:

[tex]y+6=m(x+2)[/tex]

Answer:

d

Step-by-step explanation:

Step-by-step explanation:

Draw a picture (like the image below).

Notice that triangles ABC and ACD both contain right angles, and both contain angle A (20°).  Since angles of a triangle add up to 180°, that means their third angle must also be the same (70°).

Also notice that triangles ABC and CBD both contain right angles, and both contain angle B (70°).  So their third angle must also be the same (20°).

Therefore:

m∠CDB = 90°

m∠CBD = 70°

m∠BCD = 20°

m∠CDA = 90°

m∠CAD = 20°

m∠ACD = 70°

The methods that we can use to calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,15) are: Option B: Count by hand, Option D: Dividie 15 by 2

Midpoint of a line segment that lies in the mid of that line segment, as the name 'midpoint' suggests.

If the endpoints of the considered line segments are (a,b), and (c,d), then the coordinates of the midpoint would be:

[tex](x,y) = \left(\dfrac{c-a}{2}, \dfrac{d-b}{2}\right)[/tex]

We're specified here that:

Since the line is vertical, we can easily find its midpoint by going up by half of the length of the line segment.

The y-coordinate starts from 0 and goes to 15 and x-coordinate is still all along the line as the line is vertical, so the length's half is (15-0)/2 =15/2 = 7.5 units. This gives the y-coordinate of the midpoint as visible in the formula specified above.

If we go this units up, we will reach the midpoint. Since x-coordinates of the points in the line segment are fixed to 0, so the midpoint's coordinates are (0, 7.5)

We can also count by hand as there is motion only in y-coordinates, so move half of the total motion upwards from (0,0) or half of the total length downwards from (0,15).

So we see, that the second method and the fourth method listed in the option can be used.

Thus, the methods that we can use to calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,15) are: Option B: Count by hand, Option D: Dividie 15 by 2

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Final answer:

To find the y-coordinate of a vertical line segment midpoint between (0,0) and (0,15), you can count by hand to get an approximate location, add the y-coordinates of the endpoints and then divide by 2, or simply divide 15 by 2 to get the correct value of 7.5.

Explanation:

To calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0,0) and (0,15), you can use the following methods:

Option d is the most direct mathematical approach to finding the midpoint's y-coordinate. Option b is a valid but less precise method that relies on visual estimation. Option c is essentially part of the formula used in option d.

Let c be children and a adults.

3.5c + 7a = 1771 (the total revenue is equal to the amounts made off of people)

c + a = 331 (total number of people)

The second formula becomes a = 331 - c. This can be substituted into the first formula.

3.5c + 7(331 - c) = 1771 = 7*331 - 3.5c = 1771. 7*331 = 2317, so 3.5c = 2317 - 1771 = 546.

546/3.5 = 156 = c (number of children).

c + a = 156 + a = 331 => a = 331 - 156 = 175 (number of adults).

There are 156 children and 175 adults

Answer:

156 children

175 adults

Step-by-step explanation:

Let's call x the number of children admitted and call z the number of adults admitted.

Then we know that:

[tex]x + z = 331[/tex]

We also know that:

[tex]3.50x + 7z = 1,771.00[/tex]

We want to find the value of x and z. Then we solve the system of equations:

-Multiplay the first equation by -7 and add it to the second equation:

[tex]-7x - 7z = -2,317[/tex]

[tex]3.50x + 7z = 1,771[/tex]

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

[tex]-3.5x = -546[/tex]

[tex]x =\frac{-546}{-3.5}\\\\x=156[/tex]

Now we substitute the value of x in the first equation and solve for the variable z

[tex]156 + z = 331[/tex]

[tex]z = 331-156[/tex]

[tex]z = 175[/tex]

The equation that reveals the minimum value for the equation is 2(x + 3)² = 32

Which reveals the minimum value for the equation

From the question, we have the following parameters that can be used in our computation:

2x² + 12x − 14 = 0

Rewrite as

2x² + 12x = 14

So, we have

2(x² + 6x) = 14

Take the coefficient of x

k = 6

Divide by 2

k/2 = 3

Square both sides

(k/2)² = 9

So, we have

2(x² + 6x + 9) = 14 + 2 * 9

2(x² + 6x + 9) = 32

Express as squares

2(x + 3)² = 32

Hence, the equation that reveals the minimum value for the equation is 2(x + 3)² = 32

Question

Which of the following reveals the minimum value for the equation 2x^2 + 12x - 14 = 0?

2(x + 6)^2 = 26

2(x + 6)^2 = 20

2(x + 3)^2 = 32

Soccer ball reaches its highest position when its equation turns from positive slope to zero and then negative. Mathematically it is where the derivative of the its function equals to zero. so:

d(-3x^2 + 6x + 3) / dx = -6x + 6

-6x + 6 = 0 -> x = 1 ->

[tex]y = 6[/tex]

it seems Paige's ball reaches higher than Viaola's with only 6 meters height.

Step-by-step explanation:

exponential decay functions are written in the form :

[tex]y=ab^{x}[/tex]

where b is less than 1

if we look at the 3rd choice and consider the term on the right.

[tex](8/7)^{-x}[/tex]

= [tex](7/8)^{x}[/tex]

If we compare this to the general form above,

b = 7/8 (which is less than 1)

hence the 3rd choice is correct.

The function which is an exponential decay function is:

                       [tex]f(x)=\dfrac{3}{2}(\dfrac{8}{7})^{-x}[/tex]

We know that an exponential  function is in the form of:

          [tex]f(x)=ab^x[/tex]

where a>0 and  if 0<b<1 then the function is a exponential decay function.

and if b>1 then the function is a exponential growth function.

a)

[tex]f(x)=\dfrac{3}{4}(\dfrac{7}{4})^x[/tex]

Here

[tex]b=\dfrac{7}{4}>1[/tex]

Hence, the function is a exponential growth function.

b)

[tex]f(x)=\dfrac{2}{3}(\dfrac{4}{5})^{-x}[/tex]

We know that:

[tex]a^{-x}=(\dfrac{1}{a})^x[/tex]

Hence, we have the function f(x) as:

[tex]f(x)=\dfrac{2}{3}(\dfrac{5}{4})^x[/tex]

Here

[tex]b=\dfrac{5}{4}>1[/tex]

Hence, the function is a exponential growth function.

c)

[tex]f(x)=\dfrac{3}{2}(\dfrac{8}{7})^{-x}[/tex]

We know that:

[tex]a^{-x}=(\dfrac{1}{a})^x[/tex]

Hence, we have the function f(x) as:

[tex]f(x)=\dfrac{3}{2}(\dfrac{7}{8})^x[/tex]

Here

[tex]b=\dfrac{7}{8}<1[/tex]

Hence, the function is a exponential decay function.

d)

[tex]f(x)=\dfrac{1}{3}(\dfrac{9}{2})^x[/tex]

Here

[tex]b=\dfrac{9}{2}>1[/tex]

Hence, the function is a exponential growth function.

Answer:

(3,2)

Step-by-step explanation:

We are given the system:

3x-y=7

2x-2y=2.

We are asked to solve this by substitution.  We need to pick an equation and pick a variable from that equation to solve for that variable.

I really like either for this.  Some people might go with the first one though. Let's do that.  I will solve the first one for y.

3x-y=7

Subtract 3x on both sides:

   -y=-3x+7

Divide both sides by -1:

     y=3x-7

Now we are ready for substitution.  We are going to plug this equation into the second equation giving us:

2x-2y=2 with y=3x-7 gives us:

2x-2(3x-7)=2

Distribute:

2x-6x+14=2

Combine like terms:

-4x+14=2

Subtract 14 on both sides:

-4x      =2-14

Simplify:

-4x       =-12

Divide both sides by -4:

  x       =-12/-4

Simplify:

 x         =3

So using y=3x-7 and x=3, I will find y now.

y=3x-7 if x=3

y=3(3)-7   (I inserted 3 for x since we had x=3)

y=9-7       (Simplified)

y=2           (Simplified)

The answer is (x,y)=(3,2).

Answer:

The concentric circles are

[tex]3x^{2}+3y^{2}+12x-6y-21=0[/tex]  and [tex]4x^{2}+4y^{2}+16x-8y-308=0[/tex]

[tex]5x^{2}+5y^{2}-30x+20y-10=0[/tex]  and [tex]3x^{2}+3y^{2}-18x+12y-81=0[/tex]

[tex]4x^{2}+4y^{2}-16x+24y-28=0[/tex]  and [tex]2x^{2}+2y^{2}-8x+12y-40=0[/tex]

[tex]x^{2}+y^{2}-2x+8y-13=0[/tex]  and  [tex]5x^{2}+5y^{2}-10x+40y-75=0[/tex]

Step-by-step explanation:

we know that

The equation of the circle in standard form is equal to

[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]

where

(h,k) is the center and r is the radius

Remember that

Concentric circles, are circles that have the same center

so

Convert each equation in standard form and then compare the centers

The complete answer in the attached document

Part 1) we have

[tex]3x^{2}+3y^{2}+12x-6y-21=0[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex](3x^{2}+12x)+(3y^{2}-6y)=21[/tex]

Factor the leading coefficient of each expression

[tex]3(x^{2}+4x)+3(y^{2}-2y)=21[/tex]

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

[tex]3(x^{2}+4x+4)+3(y^{2}-2y+1)=21+12+3[/tex]

[tex]3(x^{2}+4x+4)+3(y^{2}-2y+1)=36[/tex]

Rewrite as perfect squares

[tex]3(x+2)^{2}+3(y-1)^{2}=36[/tex]

[tex](x+2)^{2}+(y-1)^{2}=12[/tex]

therefore

The center is the point (-2,1)                                  

Part 2) we have

[tex]5x^{2}+5y^{2}-30x+20y-10=0[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex](5x^{2}-30x)+(5y^{2}+20y)=10[/tex]

Factor the leading coefficient of each expression

[tex]5(x^{2}-6x)+5(y^{2}+4y)=10[/tex]

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

[tex]5(x^{2}-6x+9)+5(y^{2}+4y+4)=10+45+20[/tex]

[tex]5(x^{2}-6x+9)+5(y^{2}+4y+4)=75[/tex]

Rewrite as perfect squares

[tex]5(x-3)^{2}+5(y+2)^{2}=75[/tex]

[tex](x-3)^{2}+(y+2)^{2}=15[/tex]

therefore

The center is the point (3,-2)      

Part 3) we have

[tex]x^{2}+y^{2}-12x-8y-100=0[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex](x^{2}-12x)+(y^{2}-8y)=100[/tex]

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

[tex](x^{2}-12x+36)+(y^{2}-8y+16)=100+36+16[/tex]

[tex](x^{2}-12x+36)+(y^{2}-8y+16)=152[/tex]

Rewrite as perfect squares

[tex](x-6)^{2}+(y-4)^{2}=152[/tex]

therefore

The center is the point (6,4)      

Part 4) we have

[tex]4x^{2}+4y^{2}-16x+24y-28=0[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex](4x^{2}-16x)+(4y^{2}+24y)=28[/tex]

Factor the leading coefficient of each expression

[tex]4(x^{2}-4x)+4(y^{2}+6y)=28[/tex]

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

[tex]4(x^{2}-4x+4)+4(y^{2}+6y+9)=28+16+36[/tex]

[tex]4(x^{2}-4x+4)+4(y^{2}+6y+9)=80[/tex]

Rewrite as perfect squares

[tex]4(x-2)^{2}+4(y+3)^{2}=80[/tex]

[tex](x-2)^{2}+(y+3)^{2}=20[/tex]

therefore

The center is the point (2,-3)  

Part 5) we have

[tex]x^{2}+y^{2}-2x+8y-13=0[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex](x^{2}-2x)+(y^{2}+8y)=13[/tex]

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

[tex](x^{2}-2x+1)+(y^{2}+8y+16)=13+1+16[/tex]

[tex](x^{2}-2x+1)+(y^{2}+8y+16)=30[/tex]

Rewrite as perfect squares

[tex](x-1)^{2}+(y+4)^{2}=30[/tex]

therefore

The center is the point (1,-4)  

Part 6) we have

[tex]5x^{2}+5y^{2}-10x+40y-75=0[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex](5x^{2}-10x)+(5y^{2}+40y)=75[/tex]

Factor the leading coefficient of each expression

[tex]5(x^{2}-2x)+5(y^{2}+8y)=75[/tex]

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

[tex]5(x^{2}-2x+1)+5(y^{2}+8y+16)=75+5+80[/tex]

[tex]5(x^{2}-2x+1)+5(y^{2}+8y+16)=160[/tex]

Rewrite as perfect squares

[tex]5(x-1)^{2}+5(y+4)^{2}=160[/tex]

[tex](x-1)^{2}+(y+4)^{2}=32[/tex]

therefore

The center is the point (1,-4)  

Part 7) we have

[tex]4x^{2}+4y^{2}+16x-8y-308=0[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex](4x^{2}+16x)+(4y^{2}-8y)=308[/tex]

Factor the leading coefficient of each expression

[tex]4(x^{2}+4x)+4(y^{2}-2y)=308[/tex]

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

[tex]4(x^{2}+4x+4)+4(y^{2}-2y+1)=308+16+4[/tex]

[tex]4(x^{2}+4x+4)+4(y^{2}-2y+1)=328[/tex]

Rewrite as perfect squares

[tex]4(x+2)^{2}+4(y-1)^{2}=328[/tex]

[tex](x+2)^{2}+(y-1)^{2}=82[/tex]

therefore

The center is the point (-2,1)  

Part 8) Part 9) and Part 10)  in the attached document

Answer:

(3v-7)(2v^2+5)

Step-by-step explanation:

To factor 6v^3-14v^2+15v-35 by grouping we are going to try pair to up the pair two terms and also the last two terms. Like this:

(6v^3-14v^2)+(15v-35)

Now from each we factor what we can:

2v^2(3v-7)+5(3v-7)

Now there are two terms: 2v^2(3v-7) and 5(3v-7).

These terms contain a common factor and it is (3v-7).

We are going to factor (3v-7) out like so:

2v^2(3v-7)+5(3v-7)

(3v-7)(2v^2+5)

[tex]\bf (\sqrt{5x+6})^2\implies \sqrt{(5x+6)^2}\implies 5x+6[/tex]

Answer:

s(x) = f(x) + g(x) = (5x + 2) + (7x + 4) = 12x + 6

p(x) = 6*g(x) = 6(7x + 4) = 42x + 24

Step-by-step explanation:

Answer:

x=0

Step-by-step explanation:

(x-5)=4x-5

Subtract x from each side

x-5-x=4x-x-5

-5 = 3x-5

Add 5 to each side

-5+5 = 3x-5+5

0 = 3x

Divide by 3

0/3 = 3x/3

0 =x

x=0

Answer:

yes

Step-by-step explanation:

let me explain more in depth. 1: yes, it's the point where the function crosses the x axis. 2: the absence of acceleration. 3: I think it can be negative

Answer:

98.1% chance of being accepted

Step-by-step explanation:

Given:

sample size,n=56

acceptance condition= at most 2 batteries do not meet specifications

shipment size=7000

battery percentage in shipment that do not meet specification= 1%

Applying binomial distribution

In this formula, a is the acceptable number of defectives;

 n is the sample size; 

p is the fraction of defectives in the population.  

Now putting the value

a= 2

n=56

p=0.01

[tex]\frac{56!}{0!\left(56-0\right)!}\left(0.01\right)^0\:\left(1-0.01\right)^{\left(56-0\right)} + \frac{56!}{1!\left(56-1\right)!}\left(0.01\right)^1\:\left(1-0.01\right)^{\left(56-1\right)} +[/tex][tex]\:\frac{56!}{2!\left(56-2\right)!}\left(0.01\right)^2\:\left(1-0.01\right)^{\left(56-2\right)}[/tex]

=0.56960+0.32219+0.08949

After summation, we get 0.981 i.e. a 98.1% chance of being accepted.  As this is such a high chance, we can expect many of the shipments like this to be accepted!

Answer:

C, E, F

Step-by-step explanation:

The range of the function [tex]g(x)=x^2[/tex] is [tex]y\in [0,\infty)[/tex], the range of the function [tex]h(x)=-x^2[/tex] is [tex](-\infty,0][/tex]

This means that for any value of x, the value of [tex]g(x)[/tex] is always greater or equal to the value of [tex]h(x)[/tex] (the values are equal at x=0).

So, options A and B are false, because at x=0 the values are equal and h(x) cannot be greater than g(x)

Options C, E and F are true, because for all non-zero x, g(x)>h(x).

Option D is false (the reason is the same as for option B)

The answer to the given expression when [3(1/6) - 1(5/8)] divided by [8{3/4} - 1.35) will be equal to 0.00896.

Convert mixed numbers to fractions:

[tex]3(\frac{1}{6}) = \frac{(3 \times 6 + 1) }{6} = \frac{19 }{ 6}\\\\8(\frac{3}{4}) = \frac{(8 \times 4 + 3) }{ 4} = \frac{35 }{ 4}[/tex]

Substitute the fractions into the expression:

[tex]\frac{[ (\frac{19}{6}) - 1(\frac{5}{8}) ] }{ [ (\frac{35}{4}) - 1.35 ]}[/tex]

Simplify the expression:

Numerator:

Common denominator for (19/6) and (5/8) is 24

19/6 - 1(5/8) = (19/6) - (15/8) = (19*4 - 6*15)/24 = 1/24

Denominator:

Convert 1.35 to fraction: 1.35 = 135/100 = 27/20

Common denominator for (35/4) and (27/20) is 20

(35/4) - 1.35 = (35/4) - (27/20) = (35 * 5 - 27 * 1) / 20 = 123/20

Divide the numerator and denominator by their greatest common divisor (GCD):

GCD(1, 24) = 1

GCD(123, 20) = 1

Simplify the expression:

[tex]\frac{(\frac{1 }{ 24}) }{ (\frac{123 }{ 20})}\\\\ = \frac{1 }{ \frac{24 \times 123 }{ 20}}\\\\ = \frac{1 }{ 111.6}[/tex]

1 / 111.6 ≈ 0.00896

Answer:

Step-by-step explanation:

Two consecutive odd intergers: x, x + 2.

The sum: 36

The equation:

x + (x + 2) = 36

x + x + 2 = 36

2x + 2 = 36             subtract 2 from both sides

2x = 34      divide both sides by 2

x = 17

x + 2 = 17 + 2 = 19

Answer:

2.4 years

Step-by-step explanation:

you have to first convert the trees' heights into inches. three feet is equivalent to 36 inches and four feet is equivalent to 48 inches. Since three A grows at 15 inches a year it'll become a the expression 15x+36 and the expression for tree B will be 10x+48. You set them up to each other and simplify it.

15x+36=10x+48

 -10x        -10x

5x+36=48

   -36        -36

5x=12

/5    /5

x=2.4

So it'll be 2.4 years

so the price difference is 19500 - 16770 = 2730.

if we take 19500 to be the 100%, what is 2730 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 19500&100\\ 2730&x \end{array}\implies \cfrac{19500}{2730}=\cfrac{100}{x}\implies \cfrac{50}{7}=\cfrac{100}{x}\implies 50x=700 \\\\\\ x=\cfrac{700}{50}\implies x=14[/tex]

Answer:

The answer is 14%

Step-by-step explanation:

1) Divide 19500 by 16770

16770/19500= 0.86

2) Multiply by 100 (this is the percentage between the original and find prices of the car)

0.86(100)= 86%

3) Subtract 86% from 100% to find the change in percentage

100-86= 14%

Therefore, the percentage decrease of the price of the car is 14%.

Hope this helps!