12.) Find the value of x and y. Show ALL work.

Answer:

Step-by-step explanation: max is already 3 times older than max. 6*3=18 and 6+12=18

Final answer:

Max cannot be 3 times as old as Leo based on the given information.

Explanation:

To find out how many years it will be until Max is 3 times as old as Leo, we can set up an equation.

Let's assume that it takes x years for Max to be 3 times as old as Leo.

So, Max's age in x years will be 12 + x, and Leo's age in x years will be 6 + x. According to the problem, Max will be 3 times as old as Leo, so we can write the equation as: 12 + x = 3(6 + x).

To solve for x, we can start by simplifying the equation: 12 + x = 18 + 3x. Now, let's isolate the variable x by moving all the x terms to one side and the constant terms to the other side. Subtracting x from both sides gives us: 12 = 18 + 2x. Subtracting 18 from both sides gives us: -6 = 2x. Finally, dividing both sides by 2 gives us: -3 = x.

This means that it will take -3 years for Max to be 3 times as old as Leo. However, since time cannot be negative, we can conclude that it is not possible for Max to be 3 times as old as Leo based on the given information.

Answer:

Length 19.11 and width 5.89.

Step-by-step explanation:

Let the length be x and width be y metres.

Then,  using the  Pythagoras theorem:-

x^2 + y^2 =  20^2 = 400....................(1)

The perimeter = 50 so:-

2x + 2y = 50

Dividing through by 2:-

x + y = 25 .............................(2)

So  y = 25 - x

Substitute for y in  equation (1):-

x^2 + (25 - x)^2 = 400

x^2 + 625 - 50x + x^2 = 400

2x^2 - 50x + 225 = 0

x = 19.11 , 5.89,     x = 19.11 as its the length

and y = 25 - 19.11 = 5.89  ( from equation (2).

"Parameter" = Perimeter.

Look at the picture.

We have the perimeter = 50 m.

The perimeter is 2l + 2w (l - length, w - width). Therefore

2l + 2w = 50      divide both sides by 2

l + w = 25     subtract w from both sides

l = 25 - w.

Use the Pythagorean theorem:

[tex]l^2+w^2=20^2\to(25-w)^2+w^2=20^2[/tex]

Use (a - b)² = a² - 2ab + b²

[tex]25^2-2(25)(w)+w^2+w^2=400\\\\625-50w+2w^2=400\qquad\text{subtract 400 from both sides}\\\\225-50w+2w^2=0\\\\2w^2-50w+225=0[/tex]

Use quadratic formula:

[tex]ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a};\ x_2=\dfrac{-b+\sqrt\Delta}{2a}[/tex]

We have:

[tex]a=2,\ b=-50,\ c=225[/tex]

Substitute:

[tex]\Delta=(-50)^2-4(2)(225)=2500-1000=1500\\\\\sqrt\Delta=\sqrt{1500}=\sqrt{100\cdot15}=\sqrt{100}\cdot\sqrt{15}=10\sqrt{15}\\\\w_1=\dfrac{-(-50)-10\sqrt{15}}{2(2)}=\dfrac{50-10\sqrt{15}}{4}=\dfrac{25-5\sqrt{15}}{2}\\\\w_2=\dfrac{-(-50)+10\sqrt{15}}{2(2)}=\dfrac{50+10\sqrt{15}}{4}=\dfrac{25+5\sqrt{15}}{2}[/tex]

[tex]l_1=25-w_1\\\\l_1=25-\dfrac{25-5\sqrt{15}}{2}=\dfrac{50}{2}-\dfrac{25-5\sqrt{15}}{2}=\dfrac{50-25+5\sqrt{15}}{2}=\dfrac{25+5\sqrt{15}}{2}\\\\l_2=25-w_2\\\\l_2=25-\dfrac{25+5\sqrt{15}}{2}=\dfrac{50}{2}-\dfrac{25+5\sqrt{15}}{2}=\dfrac{50-25-5\sqrt{15}}{2}=\dfrac{25-5\sqrt{15}}{2}[/tex]

[tex]Answer:\ \boxed{\dfrac{25+5\sqrt{15}}{2}\ m\times\dfrac{25-5\sqrt{15}}{2}\ m}[/tex]

[tex]a_n=72\left(\dfrac{1}{3}\right)^{n-1}\\\\\text{Put}\ n=1,\ n=2,\ n=3,\ n=4,\ n=5\ \text{to the equation}:\\\\n=1\to a_1=72\left(\dfrac{1}{3}\right)^{1-1}=72\left(\dfrac{1}{3}\right)^0=72(1)=72\\\\n=2\to a_2=72\left(\dfrac{1}{3}\right)^{2-1}=72\left(\dfrac{1}{3}\right)^1=72\left(\dfrac{1}{3}\right)=\dfrac{72}{3}=24\\\\n=3\to a_3=72\left(\dfrac{1}{3}\right)^{3-1}=72\left(\dfrac{1}{3}\right)^2=72\left(\dfrac{1}{9}\right)=\dfrac{72}{9}=8\\\\n=4\to a_4=72\left(\dfrac{1}{3}\right)^{4-1}=72\left(\dfrac{1}{3}\right)^3=72\left(\dfrac{1}{27}\right)=\dfrac{72}{27}=\dfrac{8}{3}\\\\n=5\to a_5=72\left(\dfrac{1}{3}\right)^{5-1}=72\left(\dfrac{1}{3}\right)^4=72\left(\dfrac{1}{81}\right)=\dfrac{72}{81}=\dfrac{8}{9}\\\\Answer:\ \boxed{72,\ 24,\ 8,\ \dfrac{8}{3},\ \dfrac{8}{9}}[/tex]

Answer:

The first five terms are as follows:

72, 24, 8, 2.66, 0.88

Step-by-step explanation:

1) Explicit formula:

[tex]72 * 1/3^{n-1}[/tex]

2) Simply replace "n" with 2,3,4 and 5 in order to find the numbers associated with these terms.

a(1) = 72

a(2) = 24

a(3) = 8

a(4) = 2.66

a(5) = 0.88

Note:

In the explicit formula the first term is already provided, so you do not have to find the first term if it has already been given.

Answer: No solutions

The two lines are parallel. They never intersect. You need a point of intersection to have a solution. Note how the lines have the same slope (2) but different y intercepts (3 and -4). This fact backs up the idea the lines are parallel.

The system has no solution, so we consider this system to be inconsistent. If we were to convert each equation into standard form, then we would have 2x-y = -3 and 2x-y = 4. If we made z = 2x-y, then z = -3 and z = 4 at the same time; but z is only one number at a time. This is one way to see the inconsistency.

Answer:

Step-by-step explanation:

Alright, lets get started.

The original photo size is 4 inches wide and 6 inches tall.

So, the ratio of width and height will be = [tex]\frac{4}{6}=\frac{2}{3}[/tex]

The new enlarged photo will be of the same ratio means 2:3

The width of enlarged photo is given as 12 inches.

Suppose new height of enlarged photo is H, so

[tex]\frac{12}{H}=\frac{2}{3}[/tex]

Cross multiplying

[tex]2H=36[/tex]

Dividing 2 in both sides

[tex]H=18[/tex] inches

So the height of new enlagred photo will be 18 inches.  :   Answer

Hope it will help :)

Answer:

The first one is correct the rest are not

Step-by-step explanation:

I don't know if you need an explanation or not.

Answer:

it 1,2,and 4 just took it

Step-by-step explanation:

Answer:

think 5 meters

Step-by-step explanation:

Answer:

The diameter at the center of the tower is 4 meters. The center of the tower is 8 meters above the ground.

Step-by-step explanation:

4x^2-y^2+16y-80=0

Completing squares in variable "y": Common factor -1:

4x^2-(y^2-16y)-80=0

4x^2-[(y-16/2)^2-(16/2)^2]-80=0

4x^2-[(y-8)^2-(8)^2]-80=0

4x^2-[(y-8)^2-64]-80=0

Eliminating the brackets:

4x^2-(y-8)^2+64-80=0

Adding like terms (constants):

4x^2-(y-8)^2-16=0

Adding 16 both sides of the equation:

4x^2-(y-8)^2-16+16=0+16

4x^2-(y-8)^2=16

Dividing all the terms by 16:

4x^2/16-(y-8)^2/16=16/16

Simplifying:

x^2/4-(y-8)^2/16=1

The hyperbola has the form:

(x-h)^2/a^2-(y-k)^2/b^2=1

Then:

h=0

k=8

a^2=4→sqrt(a^2)=sqrt(4)→a=2

The diameter (d) at the center of the tower is:

d=2a→d=2(2)→d=4 meters

The center of the tower is 8 (k) meters above the ground.

Look at the picture.

[tex\alpha+\beta=180^o[/tex] - supplementary angles

Therefore we hve the equation:

[tex](14x-6)+(15+5x)=180\\\\(14x+5x)+(-6+15)=180\\\\19x+9=180\qquad\text{subtract 9 from both sides}\\\\19x=171\qquad\text{divide both sides by 19}\\\\\boxed{x=9}[/tex]

Answer:

68 m^2

Step-by-step explanation:

Area of The entire enclosure ( rectangle)

Area of the triangle

Area of the Trapezoid

Formula

Solution

Area of the Lawn

Answer:

Step-by-step explanation:

At a sales rate of 56 boxes of gummy bears per week, the movie theater will sell

= 56 × 6

= 336 boxes

This is on the assumption that the rate is sustained.

At that rate (of 56 boxes per week), the company (movie theater) would have sold 336 boxes.

Answer:

(3,1)

Step-by-step explanation

All you have to do is change the y-coordinate to its opposite. Ex- (-2,3) coordinates of reflection. (-2,-3)

Tienes que usar la fórmula cuadrática:

(-b +/- √(b^2-4ac))/2a

Primero identificas los valores de a,b y c en kx^2-3x+2=0

K=a, b=-3, c=2

Luego sustituis en la fórmula y te queda:

(3+/-√(9-8k))/2k

Para que las raíces Sena reales se tienen que cumplir que 9-8k>=0

Answer:

Step-by-step explanation:

Therefore discriminant = b^2-4ac =0

b=-k, a=3,c=2

b^2-4ac= (-k)^2-4*3*2=0

k^2-24=0

k^2=24

k= +/- 2sqrt(6)

Answer: options b and c

Step-by-step explanation:

∠ACD is supplementary to ∠ACE  given

∠ACD is supplementary to ∠BCD   given

⇒ ∠ACE is supplementary to ∠BCD   transitive property

∠ACD ≅ ∠BCE   given

⇒ ∠BCE is supplementary to ∠ACE  substitution

and ∠BCE is supplementary to ∠BCD   substitution

********************************************************************************

multiple choice options:

a) ∠ACE is supplementary to ∠BCD    False

b) ∠BCE is supplementary to ∠ACE    TRUE

c) ∠BCD is supplementary to ∠BCE    TRUE

d) ∠ACE ≅ ∠BCE                                   False

e) ∠BCD ≅ ∠ACE                                   False

Answer:2/9

Step-by-step explanation:

If you count the lines form zero like 0/9 1/9 2/9 3/9 4/9 5/9 6/9 7/9 8/9 then 1 is the whole so that would be 9/9

Answer:

2/9 is the answer

Answer:

A. Definition of Segment Bisector

Step-by-step explanation:

One have to understand that according to data given in the question, we only know that AD and BC are bisected at the intersection point E. Now two triangles are formed which are ΔABE and ΔCDE.

Now by definition of segment bisector, we know that

AE = DE

BE = CE

Now, what is to understand that this information is based on the clue which is given in the question that AD and BC bisects each other. All the remaining options like SAS postulate, SSS postulate and definition of congruent triangle are not useful here if we don't know that these two lines bisect each other. Because, the fact that  

AE = DE

BE = CE

is only derived by the information that AD and BC bisect each other. Now we can derive SSS and SAS postulate both because we know by the theorems of trigonometry that if two sides of two different triangles are equal in length,  then their third sides must be equal, or when two lines bisect or intersect each other, vertical angles are always equal. So the answer is A.

Answer:

A = B

Step-by-step explanation:

This is because they are alternate exterior angles and they equal the same thing.

Answer:

Equation in point-slope form=  [tex]{y+3}=\frac{-1}{2}(x+3)[/tex]

Step-by-step explanation:

The given end points are B(−1,1) and C(−5,−7)

Mid point M of BC= [tex]\frac{-5-1}{2}[/tex] , [tex]\frac{-7+1}{2}[/tex]

Mid point M of BC = -3 , -3

Slope of BC =  [tex]\frac{-7-1}{-5+1}[/tex] = 2

Slope of bisector= m= [tex]\frac{-1}{2}[/tex]

Equation of perpendicular bisector : [tex]\frac{y+3}{x+3}=\frac{-1}{2}[/tex]

                                                           ⇒   [tex]{y+3}=\frac{-1}{2}(x+3)[/tex]

                                                          ⇒   2(y+3)= -(x+3)

                                                          ⇒  [tex]2y+x=-9[/tex]

by the transitive property of equality

Answer:

the transitive property of equality

Step-by-step explanation:

The perimeter of any polygon is equal to the sum of the length of all sides of this polygon.

Therefore:

Answer:

So, we know that sides are 29, 15 and 4xy long. The perimeter would be

[tex]P=29+15+4xy[/tex]

Now, we sum like terms

[tex]P=44+4xy[/tex]

[tex]P=44+4xy[/tex]

The sum converges to 1000.

The [tex]n[/tex]-th partial sum of the series is

[tex]S_n=\displaystyle\sum_{i=1}^n100\left(\dfrac9{10}\right)^{i-1}=100\left(1+\dfrac9{10}+\left(\dfrac9{10}\right)^2+\cdots+\left(\dfrac9{10}\right)^{n-1}\right)[/tex]

Then

[tex]\dfrac9{10}S_n=100\left(\dfrac9{10}+\left(\dfrac9{10}\right)^2+\left(\dfrac9{10}\right)^3+\cdots+\left(\dfrac9{10}\right)^n\right)[/tex]

so that

[tex]S_n-\dfrac9{10}S_n=\dfrac1{10}S_n=100\left(1-\left(\dfrac9{10}\right)^n\right)[/tex]

[tex]\implies S_n=1000\left(1-\left(\dfrac9{10}\right)^n\right)[/tex]

As [tex]n\to\infty[/tex], [tex]\left(\dfrac9{10}\right)^n\to0[/tex], so we're left with

[tex]\displaystyle\sum_{i=1}^\infty100\left(\dfrac9{10}\right)^{i-1}=\lim_{n\to\infty}S_n=1000[/tex]

The given infinite series is a converging geometric series with an initial term of 100 and a common ratio of 9/10. Using the formula for the sum of an infinite geometric series, we find that the sum is 1000.

To evaluate an infinite sum, or a series, we need to recognize the series structure. The given series ∑^{∞}_{i=1} 100(9/10)^{i-1} is a geometric series where the initial term (a) is 100 and the common ratio (r) is 9/10.

A geometric series converges only when the absolute value of r is less than 1, which is true in this scenario. When it converges, the sum (S) of the infinite geometric series can be calculated using the formula S = a / (1 – r).

By plugging into this formula, we get: S = 100 / (1 - 9/10) = 100 / (1/10) = 1000.

Therefore, the sum of the infinite series ∑^{∞}_{i=1} 100(9/10)^{i-1} is 1000.

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Answer:

60

Step-by-step explanation:

Mr Jone's home distance is 60 miles away from his appointment place .

Distance = Speed x Time

Distance planned & distance covered is same.

Time covered is 20 minutes more than time planned ; Actual Speed is 15mph lower than planned speed (60 mph) , ie = 45 mph.

Let the planned time be = t , Actual time = t + 20 mints = t + 20 / 60 = t + 1/3 =  4 t / 3

As distance is same : 60 t = 45 ( 4t / 3)

60t = 60t

t = 1 hour

Distance = Speed x Time :

60 x 1 = 45 ( 4/3) = 60 miles

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Answer:

x = ln (7/5) - 2

Step-by-step explanation:

4+5e^(x+2)=11

Subtract 4 from each side

4-4+5e^(x+2)=11-4

5e^(x+2)=7

Divide by 5 on each side

5/5e^(x+2)=7/5

e^(x+2)=7/5

Take the natural log on each side

ln (e^(x+2))= ln (7/5)

x+2    = ln (7/5)

Subtract 2 from each side

x = ln (7/5) - 2

Answer:

option 1

Step-by-step explanation:

Answer:

1000*(1,025)=1025 $ the 1st year

After 4 years, the account will be 4* 1025=4100

Answer:

Amount after 4 years = 1000+100=$1100

Step-by-step explanation:

To solve this, we will simply use the simple interest formula;

S.I = PRT/100

where p=principal

R=rate   and   T= time

S.I = simple interest

From the question

Principal=$1000

Rate = 2.5    and time=4

We can now proceed to inert the values into the equation

S.I = 1000×2.5×4   /100

Two zeros at the numerator will cancel-out the two zeros at the denominator, Hence;

S.I = 10×2.5×4

S.I =$100

Amount after 4 years = 1000+100=$1100

Answer:

values of j are: 2 , -1

Step-by-step explanation:

In the given case, The solutions are j = -4 and j = 1, and the solution set is  {-4, 1}.

The given equation is:

j+4/j+2=2−1/j

We can solve for j by cross-multiplying:

(j+4)(j) = (j+2)(2-1/j)

Expanding the left side and right side, we get:

[tex]j^2 + 4j = 2j + 4 - 2/j[/tex]

Moving all the terms to the left side of the equation, we get:

[tex]j^2 + 2j - 4 = 0[/tex]

We can factor the left side of the equation as:

(j+4)(j-1) = 0

Therefore, the solutions are j = -4 and j = 1.

Note that the given equation is defined when j ≠ 0 and j ≠ -2. Therefore, the solutions are j = -4 and j = 1, and the solution set is  {-4, 1}.

Here is a step-by-step solution:

n first move the constant term to the right side of the equation.

j² + 2j = 4

We can then factor the left side of the equation.

(j+4)(j-1) = 0

The solutions are j = -4 and j = 1.

We check that these solutions are valid by substituting them back into the original equation.

j+4/j+2=2−1/j

When j = -4, the left side of the equation is 0/-2 = 0, and the right side of the equation is 2 - 1/-4 = 2 + 0.5 = 2.5.

The equation is satisfied.

When j = 1, the left side of the equation is 5/3, and the right side of the equation is 2 - 1/1 = 2 - 1 = 1. The equation is satisfied.

Therefore, the solutions are j = -4 and j = 1, and the solution set is  {-4, 1}.

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Answer: the number of students participating this year is 57.

Step-by-step explanation:

5% of 60 is 3.

60-3=57

I believe this is correct :)

Answer: Number of students participated this year = 57

Step-by-step explanation: Number of student participated  last year = 60

                                          Decreased by 5%

                                          Decreased in number = 5% of 60 = 0.05x 60 =3

    Number of Students this year = Number of student last year - decreased

                                                        =               60    -   3

                                                        =  57

Answer:

197

Step-by-step explanation:

Initial population of rabbit is 139

after 2 years , rabbit population is 556

For exponential growth use y=ab^x

where a is the initial population

x is the time period

b is the growth rate, y is the final population

a= 139 is already given

when x=2, the value of y = 557

plug in all the values  in the formula and find out 'b'  

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

[tex]557=139(b)^2[/tex]

Divide both sides by 139

[tex]\frac{557}{139} =b^2[/tex]

take square root on both sides

b=2.00180 and b=-2.00180

growth factor cannot be negative

So b= 2.0018

The equation y=ab^x  becomes

[tex]y=139(2.0018)^x[/tex]

To find population after 6 months

1 year = 12 months

so 6 months = 0.5 years

we plug in 0.5 for x

[tex]y=139(2.0018)^{0.5}[/tex]

y= 196.66

so population after 6 months = 197

Answer:

D. [tex]x=3[/tex]

Step-by-step explanation:

We have been graph of two functions on coordinate plane. We are asked to find the input value that produces the same output value for the two functions.

To find the input value that produces the same output value for the two functions, we need to find x-value for which both functions has same y-value.

Upon looking at our given graph, we can see that at [tex]x=3[/tex], the value of both functions is [tex]-1[/tex].

Therefore, our required input value is [tex]x=3[/tex] and option D is the correct choice.

Answer:

Density of material would be 4.09 [tex]g/cm^3[/tex]

units is [tex]g/cm^3[/tex]

Step-by-step explanation:

Given: The mass of a material is 45 grams and the volume of the material is 11 cubic centimeter

Density is defined as mass per unit volume.

It is given by:

[tex]p= \frac{m}{V}[/tex] where p is the density , m is the mass and V is the volume of the material respectively.

Here, Density is expressed in grams per centimeter cubed (g/cubic cm)

Here, m = 45 g , V = 11 cubic cm

We get;

[tex]p= \frac{45}{11}[/tex] = 4.09 [tex]g/cm^3[/tex]

therefore, density of a material would be, [tex]4.09 g/cm^3[/tex]

and its units is [tex]g/cm^3[/tex]

Answer:

y=10 is the value of y

Step-by-step explanation:

The given equation is

3y - 7 =23                               ..............................(i)

We have to find out the value of y from the equation (i)

Now the equation is

3y - 7 = 23

adding 7 on both sides of the equation

3y - 7 + 7 = 23 + 7

3y = 30

as we need the value of y so

Dividing both sides of the equation by 3

[tex]\frac{3y}{3}=\frac{30}{3}[/tex]

which will lead us to

y = 10

so this is the value of y

Answer:

y=10

Step-by-step explanation:

3y-7 =23

3y = 23+7  -move 7 over

3y=30 -add remaing

3y/3 =30/3 -divide 3

y=10 -answer

check work 3x10-7=23