A mother is three times as old as her son, and in 11 years she will be just twice his age. Find their present ages

Answer:

Length of the ladder used by worker = 17 feet

Step-by-step explanation:

Given:

Height of the window from the ground = 13 ft

Distance of fence from the building = 3 ft

Distance of ladder from the building = (3+8) = 11 ft

We have to find the length of the ladder.

Let the length of the ladder be 'x'

From the diagram we can also say that 'x' is the hypotenuse of the right angled triangle.

Using Pythagoras formula:

⇒ [tex]hypotenuse\ 'x' =\sqrt{(perpendicular)^2+(base)^2}[/tex]

Here base length = 11 ft

Perpendicular = 13 ft

Plugging the values:

⇒ [tex]x=\sqrt{(13)^2+(11)^2}[/tex]

⇒  [tex]x=\sqrt{(169+121)}[/tex]

⇒ [tex]x= \sqrt{290}[/tex]

⇒ [tex]x=17.02[/tex] feet

The length of the ladder = 17 feet to its nearest tenth.

The worker will need a ladder that is approximately 8.5 feet long. This calculation is based on the Pythagorean theorem, considering the ladder's placement 8 feet from the fence and the need to reach a window 13 feet above the ground.

To find the length of the ladder the worker needs, we can use the Pythagorean theorem, as the ladder, the distance from the building, and the distance from the fence form a right triangle.

Let:

L be the length of the ladder.

D be the distance from the building to where the ladder rests (8 ft).

F be the distance from the fence to where the ladder rests (3 ft).

According to the Pythagorean theorem, we have:

[tex]L^2 = D^2 + F^2[/tex]

Substitute the known values:

[tex]L^2 = 8^2 + 3^2[/tex]

[tex]L^2 = 64 + 9[/tex]

[tex]L^2 = 73[/tex]

Now, take the square root of both sides:

L ≈ √73 ≈ 8.54 ft (rounded to the nearest tenth)

So, the worker will need a ladder that is approximately 8.5 feet long to safely reach the window 13 feet above the ground when placed 8 feet from the fence for stability.

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Answer:

The territorial dispute over Taiwan originated in 1949 when the Chinese people fled to Taiwan due to the complete control of Communists in Mainland China.

Explanation:

The event happened after the "Chinese Civil War," a war between the Kuomintang and the Communist Party of China (CPR). This resulted to many Chinese people fleeing from Southern China to Taiwan in order to prevent the advances of the Communist Party. This was also a sign of retreat from the war.

Moving to Taiwan from China took 4 months and this was meant to be a temporary solution rather than being permanent. However, the plan could not be realized thus, resulting to many Chinese people living in Taiwan until today.

So, this led to the controversial issue that Taiwan is, somehow, part of China. In connection with this, territorial disputes arose whether Taiwan should be unified with Mainland China.

Answer:

  $1299.50

Step-by-step explanation:

It appears that the graph shows the percentage of market value of a 6-year-old car is about 10%. So the value of such a car with an original value of $12,995 would be ...

  $12,995 × 0.10 = $1299.50

The current market value is $1299.50.

The current market value of the car is $1299.50

The original cost is given as:

Original = $12,995.

From the graph, the worth of the car after 6 years is

Rate = 10%

So, the current market value of the car is:

Value = $12,995 * 10%

Evaluate the product

Value = $1299.50

Hence, the current market value of the car is $1299.50

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Answer:

37

Step-by-step explanation:

Students who applied or a scholarship=95

Of that:

Men= 41

Minorities= 36

Minorities who are women= 19

Minorities who are men = 36-19=17

Women+ Minorities who are women=Students who applied or a scholarship-(Men+Minorities who are men)

x + 19=95-(41+17)

x+19=95-58

x+19=37

x= 37-19

x=18

Women who are NOT minority=18

Total women=Minorities who are women+Women who are NOT minority

Total women=18+19

Total women=37

By understanding the problem as a basic arithmetic problem, we determine there are 54 women who applied for the scholarship by subtracting the number of men (41) from the total number of students (95).

To resolve the question, 'how many women applied for the scholarship', it's essential to understand the problem as a basic addition and subtraction problem. The numbers provided in the question give us initial points. It's stated that there are 41 men who applied, and if there are 95 students in total, we can calculate the total women by subtracting the number of men from the total. So, 95 total students - 41 men = 54 women. This calculation gives us the number of women that applied for the scholarship.

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Answer:

Distance in meters D = 167.75 meters

Step-by-step explanation:

Distance covered in 5 seconds is given by:

Distance, D = Speed (S) X Time (T)

Where,

Distance = ?

Speed = 75mph

Time = 5s

Since we are calculating distance in meters, we have to convert 75miles per hour to meters per second

75mph = 75miles/1hr X 1km/0.621miles X 1000m/1km X 1hr/60mins X 1min/60s

            = (75X1000) / (0.621X60X60) meter per second

            = 75000/2235.6 meter per second

            = 33.55 meter per second

∴ Distance D = 33.55 meter per second X 5 seconds

                      = 167.75 meters

Answer:

79716.98

Step-by-step explanation:

Woahhhhhh numbers

Step-by-step explanation:

I don’t know.

Answer:

  The equation has a greater constant of variation

Step-by-step explanation:

The graph is of a line through point (0, 0) can be represented by the equation ...

   y = kx

Using the given values for x and y, we see that ...

  3 = k·1

  k = 3 . . . . . the constant of variation for the graph

__

The given fraction can be rewritten as ...

  y = (10/3)x = (3 1/3)x

In this form, the constant of variation is 3 1/3, greater than that of the graph.

Answer:

The equation has a greater constant of variation

Step-by-step explanation:The equation has a greater constant of variation

Answer:

-2

Step-by-step explanation:

Answer:

1.067

Step-by-step explanation:

Answer:

40% decrease

Step-by-step explanation:

6.5*40%=2.6

6.5-2.6=3.9

Answer:

40%

Step-by-step explanation:

Original Mass of the pumpkin = 6.5kg

After carving, the mass of the pumpkin became = 3.9 kg

Decrease in mass = 6.5 — 3.9 = 2.6kg

Therefore, the percentage decrease in mass of the pumpkin = (2.6/6.5)x100 = 40%

answer: $215.10

the TV's original price is $239, but with 10% off, it is now 90% of the original price. therefore we have to find 90% of 239:

0.90*239=215.10

Answer:

215.10 here ya go

Final answer:

By calculating and comparing the price per pound of meat for each shopper, it is clear that they paid different prices per pound ($3.29 and $4.19), indicating they did not buy the same kind of meat.

Explanation:

To determine if both shoppers bought the same kind of meat, we need to calculate the price per pound that each shopper paid and compare the results. The first shopper bought 3 pounds for $9.87. To find the price per pound, we divide $9.87 by 3 pounds, which gives us $3.29 per pound.

The second shopper bought 4 pounds for $16.76. Similarly, we divide $16.76 by 4 pounds to get $4.19 per pound. Since the price per pound for each shopper is different, we can deduce that they did not buy the same kind of meat.

Answer:

First add 0.2 to both sides

x = 0.53

Step-by-step explanation:

4x - 0.2 = 1.9

4x - 0.2 + 0.2 = 1.9 + 0.2

4x = 2.1

Divide both sides by 4

4x/4 = 2.1/4

x =0.53

Lets first make it easier.

If you add the 20 minutes to 12:50 it will turn to 1:10.

After this you add the 5 hours.

This will turn 1:10 into 6:10.

Hope this helps :)

Answer:

Step-by-step explanation:

i'm pretty sure that you will have to add it.

so, when we add two fractions such as 3/4 + 3/4, we make sure that the denominators (the bottom numbers) are the same and then we simply add the numerators (the  top numbers).

in this problem, the denominators are the same so we will simply add 3+3 which equals to 6/4. the denominator will remain the same.

               answer:

                      3/4 + 3/4    =   6/4

i hope this is helpful.

The required weight of the candy box is 3 pounds.

Given that,
A balance scale was in perfect balance when Jane placed a box of candy on one pane of the balance and 3/4 of the same-sized candy box together with 3/4 pound weight on the other pane.
To determine how much the full box of candy weighs.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Let the weight of the candy box be x,
3/4 of the same-sized candy box
weight = 3/4 pound
x = 3/4x + 3/4
x / 4 = 3/4
x = 3

Thus, the required weight of the candy box is 3 pounds.

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Solution:

Given that,

Kate wants to build a fence around her garden to prevent her rabbits from eating her vegetables

Given is a square garden

Area = 144 square meter

[tex]Area = (side)^2\\\\144 = (side)^2\\\\Take\ square\ root\ on\ both\ sides\\\\side = 12[/tex]

Thus length of side of square is 12 meter

Perimeter = 4(side)

Perimeter = 4(12)

Perimeter = 48 meter

[tex]Cost = perimeter \times 7.50\\\\Cost = 48 \times 7.50\\\\Cost = 360[/tex]

Thus it costs $ 360 to enclose a square garden with an area of 144 square meter

Answer:

p>3

Step-by-step explanation:

<=> 3p - 9 - 5p > -3p - 6

<=> -2p + 3p > -6 + 9

<=> p > 3

To solve the inequality 3(p-3) - 5p > -3p - 6:

Simplify and combine like terms to get p > 3 as the solution.

An inequality is a mathematical statement that uses the inequality symbol to indicate the relationship between two expressions. Both sides of an inequality sign have different expressions.

The given expression is:

3(p-3) – 5p>-3p- 6

Distribute the 3 to the terms inside the parentheses:

3p - 9 - 5p > -3p - 6

Combine like terms on both sides of the inequality:

-2p - 9 > -3p - 6

Move all the terms containing p to one side by adding 3p to both sides: -2p + 3p - 9 > -6

Simplify:

p - 9 > -6

Move the constant term to the other side by adding 9 to both sides:

p - 9 + 9 > -6 + 9

Simplify: p > 3

Hence,

The solution of the given inequality is p > 3.

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Answer:

Step-by-step explanation:

A square is equal on each side. There are a total of 4 sides so we would take 320 and divide it by four to find the size of one side.

320/4

80

A = lw

A = 80 x 80

A = 6400 m^2

Answer:

See explanation

Step-by-step explanation:

Assuming we want to find the slope and equation of the line going through:

(0,1) and (1,2).

Then the slope is given by:

[tex]m = \frac{2 - 1}{1 - 0} [/tex]

This implies that:

[tex]m = 1[/tex]

The equation is given by:

[tex]y = mx + b[/tex]

Where b=1 is the y-intercept since the line passes through (0,1).

Hence the equation is:

[tex]y = x + 1[/tex]

Answer:

1

Step-by-step explanation:

Answer:

14

Explanation:

2  l     7

4  l    14

6  l   21

8  l   28

10 l  35

12 l  42

14 l  49

If you noticed the italized, bold, and underlined number fourteen, you would notice that 2 and 7 both have number fourteen as a multiple and it is also the least common multiple.

Answer:

Step-by-step explanation:

hello :

a)

let  f(x) = y     so : x = g(y)

in expression = f(x) =3x+12

means : y = 3x +12  calculate : x

3x = y -12

x = (1/3)y - 4

the inverse is : g(x) = (1/3)x - 4

b)f(g(-2) = f(-14/3)

because: g(-2) = (1/3)(-2)-4 = -2/3-4 = -14/3

so : f(g(-2) = f(-14/3)=3(-14/3)+12 = - 2

1. The inverse of the function is g(x) = (1/3)x - 4.

3. The value of f(g(–2)) is -2.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x)= 3x+ 12

1. let  f(x) = y then x = g(y)

y = 3x+ 12

y- 12 = 3x

x= y/3 + 4

So, the inverse of the function is g(x) = (1/3)x - 4.

2. For showing the function are inverse we have to that  

(fog)(x) = f(g(x)) =x and (gof)(x) =g(f(x)) = x

Take (fog)(x) = f(g(x))

= f( (1/3)x - 4.)

= 3 ((1/3)x - 4) 12

= x - 12 + 12

= x

Now, (gof)(x)

=g(f(x))

= g(3x+ 12)

= (1/3) ( 3x+ 12) -4

= x + 4 - 4

= x

3. f(g(-2))

So,  g(-2)

= (1/3)(-2)-4

= -2/3-4

= -14/3

Then, f(g(-2)) = f(-14/3)

=3(-14/3)+12

= - 2

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Answer:

The system has infinite solutions

Is a consistent dependent system

Step-by-step explanation:

we have

First equation

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

Isolate the variable y

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

Multiply by 3 both sides

[tex]y=\frac{3}{2}x-15[/tex] ----> equation A

Second equation

[tex]x=\frac{2}{3}y+10[/tex] -

Isolate the variable y

[tex]\frac{2}{3}y=x-10[/tex]

Multiply by 3/2 both sides

[tex]y=\frac{3}{2}x-15[/tex] ---> equation B

Compare equation A and equation B

The equations are identical

therefore

The system has infinite solutions

Is a consistent dependent system

x=14  and y=109

Step-by-step explanation:

Given

y= 5x +39

y= 3.5x +60

5x+39 = 3.5 x+60

5x-3.5x = 60-39

1.5x =21

x= 21/1.5 = 14

Use the value of x = 14 in equation  y=5x+39

y=5*14 +39

y=109

Hence, x=14  and y=109

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Final answer:

To solve the given system of linear equations, we use the elimination method to find the intersection point (14, 109), which is where the two lines represented by the equations meet.

Explanation:

To solve the system of equations:

y = 5x + 39

y = 3.5x + 60

We can use the method of substitution or elimination. In this case, elimination is the straight-forward choice. Since both equations are already solved for y, set them equal to each other and solve for x:

5x + 39 = 3.5x + 60

Now, subtract 3.5x from both sides:

1.5x + 39 = 60

Subtract 39 from both sides:

1.5x = 21

Divide both sides by 1.5:

x = 14

Now, plug the value of x into one of the original equations to solve for y:

y = 5(14) + 39

y = 70 + 39

y = 109

The solution to the system is (14, 109). This represents the point where the two lines intersect on a graph.

Answer:

Shown in the picture

Step-by-step explanation:

A:

Set the value of x to "5" and "30" to find the corresponding values of y (i.e. the altitudes of the plane at 5 or 30 minutes after beginning descent).

B:

Use the the same method to determine the set of coordinates (/ordered pairs) at each of the values for x given in part B of the question.

C:

The initial value is simply the starting value of y, or in other words, the altitude at which the plane begins to descend in this context;

So it will be 0 mins after the beginning of descent of the plane, i.e. when x = 0, therefore the answer is (0, 28000) as an ordered pair or simply 28000 ft.

D:

Rate of change is a fancy or more technical way of referring to the gradient of a function;

In this case of the context of a plane descending, it refers to the change in altitude over time;

This can be calculated using any two ordered pairs (or coordinates as I call them) using the formula of the difference in the y values divided by the difference in the x values.

Missing value is Decreased by 20%

Step-by-step explanation:

We need to find the missing term.

As we can see from the figure we go from Decreased 10% and then decreased 10% to reach the final goal.

If we directly go from starting point to end point the total will be decreased by 20% as (10%+10%= 20%)

So, Missing value is Decreased by 20%

Answer:

810 cubes

Step-by-step explanation:

step 1

Find the volume of the rectangular prism

The volume of the rectangular prism is

[tex]V=LWH[/tex]

we have

[tex]L=2\frac{1}{2}\ in=2+\frac{1}{2}=\frac{5}{2}\ in[/tex]

[tex]W=2\ in\\H=6\ in[/tex]

substitute

[tex]V=(\frac{5}{2})(2)(6)[/tex]

[tex]V=30\ in^3[/tex]

step 2

Find the volume of the cube

The volume of the cube is

[tex]V=b^3[/tex]

where

b is the length side of the cube

we have

[tex]b=\frac{1}{3}\ in[/tex]

substitute

[tex]V=(\frac{1}{3})^3[/tex]

[tex]V=\frac{1}{27}\ in^3[/tex]

step 3

Find out how many unit cubes with edge lengths of 1/3 inch can fit inside the prism

Divide the volume of the prism by the volume of the cube

[tex]30:\frac{1}{27}=30(27)=810\ cubes[/tex]

Answer:

Step-by-step explanation:

(17 1/2) / (5/6) =

(35/2) / (5/6) =

35/2 * 6/5 =

105/5 =

21 <===

Answer:

y=6x+5

Step-by-step explanation:

y-2=6x+3

y=6x+3+2

y=6x+5