How far up will a 15 meters ladder reach, if the foot of the later must be 9 meters from the base of the wall

Answer:

√143

4π

√79+√63

Step-by-step explanation:

√143 gives 11.958

4π = 4 times 22/7 = 12.57

√79+√63 gives 16.825

In ascending order, i.e from the least to the greatest, we have

11.958

12.57

16.825

Which is same as

√143

4π

√79+√63

Answer:

The answer should be [tex]14x^{2} - 56 x + 51 = 0[/tex]

Step-by-step explanation:

Step 1: First, you add 51 to both sides

−56x + [tex]14x^{2}[/tex]+ 51= 0

Step 2: then you fix the order.

[tex]14x^{2} - 56 x + 51 = 0[/tex]

Answer:  37.5 is 5% of 57.6923077

Step-by-step explanation:

The number where 75% of it equals 37.5 is 50.

To find the number, we can set up an equation based on the given information: 75% of a certain number is equal to 37.5. Mathematically, this can be represented as:

0.75x = 37.5

To isolate x, we can divide both sides of the equation by 0.75:

x = 37.5 / 0.75

Evaluating the division:

x = 50

Therefore, the number we are looking for is 50.

The equation 0.75x = 37.5 states that 75% (or 0.75 as a decimal) of a certain number x is equal to 37.5. By dividing both sides of the equation by 0.75, we "undo" the multiplication and solve for x. Dividing 37.5 by 0.75 gives us the value of 50.

To check our solution, we can substitute x = 50 back into the original equation:

0.75 x 50 = 37.5

37.5 = 37.5

The equation holds true, confirming that 50 is indeed the number where 75% of it equals 37.5.

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Answer:

The dryer costs $350

Step-by-step explanation:

Step 1:  Make a system of equations

w + d = 652

w = d - 48

Step 2:  Plug in the know w into the first equation

d - 48 + d = 652

2d - 48 + 48 = 652 + 48

2d / 2 = 700 / 2

d = 350

Answer:  The dryer costs $350

The ratio of boys to girls will be 15 : 13.

There are 28 students in all.

The fraction of the students are girls will be 13/28.

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

Given that;

A class contains 13 girls and 15 boys.

Now,

Since, A class contains 13 girls and 15 boys.

Hence, Number of total students = 13 + 15

                                                   = 28

So, The ratio of boys to girls = Number of boys : Number of girls

                                             = 15 : 13

Hence, Number of total students = 13 + 15

                                                   = 28

And, The fraction of the students are girls is;

= Number of girls / Number of students

= 13 / 28

Thus, The ratio of boys to girls = 15 : 13.

Total number of students = 28

And, The fraction of the students are girls = 13/28.

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Answer: x= -2; y = 3

Step-by-step explanation:

y=-2x – 1

y = 8x + 19   -  

replacing "y"

-2x – 1 = 8x + 19

-2x - 8x = 19 + 1

-10x = 20

x = 20/-10

x= -2

y=-2x – 1

y= -2.(-2) - 1

y= 4 - 1

y = 3

Answer:

17=p+8

Step-by-step explanation:

Start by setting the equation equal to 17 on either the right or left side. Now, on the opposite side of the equation read out what the question is saying.

"8 more than a number (p)" the variable would be p, and 8 more than p is 17. Now that you have that in mind, write 17 is equal to p plus 8.

17=p+8

If the question asks you to solve this equation for p, subtract 8 from both sides to get 9 for p.

I hope this is easy to understand.

10 to the second power = 100

Since powers of TEN is 10 multiplied by itself, multiply 10 by 10 TWO times, because its 10 to the SECOND power

10x10=100

By the way do not multiply 10 by 2 at ALL IT IS WRONG!!!

For example, 10 to the 3rd power is 10x10x10 not 10x3

Answer: +100

Explanation: 10 raised to the 2nd power means the same thing as 10 squared and any number squared is that number times itself.

So 10² is just 10 · 10 or +100.

Time taken by the car to cover 260 km is 2.6 hrs

Step-by-step explanation:

Speed = Distance/Time = 150/1.5 = 100 km/hr

Time = Distance/Speed = 260/100 = 2.6 hrs

Answer:

15,825

Step-by-step explanation:

Because it is a square divide 63,300 by 4.

The front wheel turns around approximately 300 times.

To determine how many times Gia's bicycle wheel turns around during her 1,884 feet ride, we need to calculate the circumference of the wheel and then divide the total distance traveled by the circumference.

The diameter of the wheel is 24 inches. To find the circumference (C), we use the formula C = pi x d, where d is the diameter, and (pi) is approximately 3.14159.

C = 3.14159 x 24 inches = 75.39816 inches.

Next, we need to convert the distance Gia rode her bike from feet to inches because the circumference is in inches. There are 12 inches in a foot, so

1,884 feet x 12 inches/foot = 22,608 inches.

Now we divide the total distance traveled in inches by the circumference of the wheel to find out how many full revolutions there are:

22,608 inches / 75.39816 inches/revolution ≈ 300 revolutions.

To the nearest whole number, Gia's front bicycle wheel turns all the way around 300 times.

Answer: answer is D, descriptive, because the scientists are writing down observations but not making comparisons

Step-by-step explanation:

According to the question, the scientists were making individual notes on their observation about shape, colour, size and other characteristics of the living cells. We do not have enough information to show that they were making comparisons.

I hope this helps.

Answer:

anwser D

Step-by-step explanation:

discreptive because scientist are writing dow explanations

Answer:

  w > 20

Step-by-step explanation:

Perhaps you want the solution to the inequality 2w+5>45.

Subtract 5:

  2w > 40

Divide by 2:

  w > 20 . . . . this is the solution

_____

Comment on solving inequalities

An inequality is solved in virtually the same way that an equation is solved: undo what is done to the variable. The only difference is that when you perform an operation that reverses the ordering, you need to reverse the ordering symbol.

Multiplying or dividing by a negative number will reverse the ordering. Consider, for example, ...

  2 > 1

Multiplying both sides by -1, we get ...

  -2 < -1 . . . . . the > sign needs to be reversed to a < sign to keep the inequality true

[tex]3.15*10^{12}[/tex]  would be 3.15 trillion in scientific notation. When putting a number into scientific notation, move the decimal point until you have a number between 1 and 10.

To convert 3.15 trillion to scientific notation, express it as 3.15 × 10¹². This involves moving the decimal point 12 places to the left. Scientific notation helps manage very large or very small numbers efficiently.

To convert the number 3.15 trillion to scientific notation, follow these steps:

Scientific notation is particularly useful in fields where dealing with extremely large or small numbers, such as astronomy and other sciences, is common.

Answer:

Step-by-step explanation:

they were exchanged for iron, guns, gunpowder, mirrors, knives, cloth, and bead

Answer: 49m

Step-by-step explanation:

4m, 1m and 2m add up to 7m on the right side. so, L x W= 7x7 which is 49

Answer: $240

Step-by-step explanation:

Simple interest= Principal x Rate x Time

Where P= 1600, R= 5% = 0.05, T=3

= 1600 x 0.05 x 3

$240

Answer:

2/3

Step-by-step explanation:

2 / (1/a + 1/b)

2 / (1/1 + 1/(½))

2 / (1 + 2)

2/3

The harmonic mean is [tex]2\div 3[/tex]

Since the string lengths of 1 and 1/2

So,

[tex]= 2 \div (1/a + 1/b)\\\\= 2 \div (1/1 + 1/(1\div 2))\\\\= 2 \div (1 + 2) \\\\= 2\div 3[/tex]

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Answer:

5 hundreds

Step-by-step explanation:

5 is the hundreds place.  So, there are 5 hundreds

Answer:

5 hundreds

Step-by-step explanation:

500 divided by 100 = 5

so, there are 5 hundreds in the number 5

Option B: 13.9 is the value of y

Explanation:

Given triangle is a right angled triangle.

The legs of the triangle are 8 and y.

The hypotenuse of the triangle is x.

And the angle opposite to y is 60°

We need to determine the value of y.

Let us find the value of y using the tangent formula.

The formula for tan is given by

[tex]tan \ \theta=\frac{opp}{adj}[/tex]

Since, we know that [tex]\theta = 60^{\circ[/tex] , [tex]opp=y[/tex] and [tex]adj=8[/tex]

Substituting these values in the formula, we get,

[tex]tan \ 60^{\circ}=\frac{y}{8}[/tex]

Multiplying both sides by 8, we have,

[tex]8\times tan \ 60^{\circ}=y[/tex]

Substituting the value of [tex]\tan 60^{\circ}[/tex] , we get,

[tex]8\times 1.732=y[/tex]

Simplifying, we have,

[tex]13.856=y[/tex]

Rounding off, we get,

[tex]13.9=y[/tex]

Thus, the value of y is 13.9

Hence, Option B is the correct answer.

Answer:

<QRT = 130°

X = 135

<QRS = 180°

Step-by-step explanation:

1. A straight line is 180°.

180° - 50° = 130°

<QRT = 130°

2. x - 5 = 130°

130° + 5° = 135°

3. As stated before, a straight line is 180°.

Answer:2.2

Step-by-step explanation:

Boo

Answer:

1 5/6 is on the twelfth line/tick mark. 2 1/3 is on the 15 line/tick mark.

Step-by-step explanation:

Go to the 1 and count up five lines. (5/6) For the 2nd one convert the 1/3 into 6ths. You now have 2 2/6. go to the 2 and count up 2 lines.

Answer:

x=2, y= -1

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

the answers are A) 18p^3r and D) 54p^3

Good luck! :)

Answer:

A) 18p³r

D) 54p³

Step-by-step explanation:

The term 6p³ multiplies into (or goes into) both 18p³r and 54p³.

Answer:

The width is 12 inches, the length is 24 inches, and the height is 16 inches

Step-by-step explanation:

Please see the attached photo, it provides full information we need to solve this problem

We know that:

So the vomume fomula is = LWH = (36 -w)*w*(w+4)

<=> [tex]32w^{2}[/tex] + 114w - [tex]-w^{3}[/tex] - 4608

<=> w = 32 and w =  12 and w= -12

Disregard w= -12, because the width cannot be negative, and we also know that length is more than 10 inches so w =  12 is fit with the requirement.

=> Length = 36 -12 = 24

Width = 12 and Hight = 12 + 4 = 16

The length, width, and height of the terrarium that has a shape of a rectangular prism is:

Volume of rectangular prism = length × width × height.

Given the dimensions of the terrarium in the shape of a rectangular prism as:

Volume = 4,608 cubic in.

Length = (36 - w) in

Width = w in.

Height = (w + 4) in.

Plug in the values:

4,608 = (36 - w)(w)(w + 4)

4,608 = (36 - w)(w² + 4w)

4,608 = 36(w² + 4w) -w(w² + 4w)

4,608 = 36w² + 144w - w³ - 4w²

36w² + 144w - w³ - 4w² - 4,608 = 0

-w³ + 32w² + 144w - 4,608 = 0

Factorize

w = −12 or w = 12 or w = 32

Since we know the length is more than 10 inches and cannot be negative, therefore, w = 12.

Plug in the value of w

Length = (36 - 12) = 24 in

Width = 12 in.

Height = (12 + 4) = 16 in.

Therefore, the length, width, and height of the terrarium that has a shape of a rectangular prism is:

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Here we know that at 3:17 pm you started to bake the cake. The total revolution the minute hand on the clock makes is:

[tex]\frac{5}{8}+\frac{13}{24}=\frac{7}{6} \ revolutions[/tex]

We know that:

[tex]1 \ revolution ----------- 60min \\ \\ 7/6 \ revolutions -----------x[/tex]

Solving for x:

[tex]x=\frac{7}{6}\times 60=70 minutes[/tex]

So it takes 70 minutes after you put the cake in the oven. But:

[tex]70minutes=1h \ 10min[/tex]

Adding this to the initial time:

[tex]3:17pm+1h \ 10min=4:27pm[/tex]

Finally, the cake is done at 4:27 pm, option C.

Answer: Johnny will have 12 soap bottles left