How far from the base of the house do you need to place a 15 foot ladder so that it exactly reaches the top of a 12 foot wall?

Answer:

Step-by-step explanation:

If the triangle is equilateral :

2x +y/2 =  5x/3+y + ½  = 2/3x +2y +5/2

so the perimeter is : P = 3(2x +y/2) or 3(5x/3+y + ½) or 3(2/3x +2y +5/2)

the simplest is :  P = 3(2x +y/2)

                            P = 6x + (3y)/2

Answer:

Yes

Step-by-step explanation:

The standard form for a quadratic equation in the US has the terms in decreasing order by power on the left of the equal sign, and the right side zero. Preferably, the leading coefficient is positive. This might also be called "general form." Elsewhere, the "standard form" may be different.

Answer:

A = 55 cm²

Step-by-step explanation:

Here, L = W + 6 cm, and P = 2W + 2L = 2W + 2(W + 6 cm) = 32 cm

Then 2W + 2(W + 6 cm) = 32 cm becomes:

         2W + 2W + 12 cm = 32 cm, or

               4W                   = 20 cm.

Therefore, W = 20 cm / 4  =  5 cm

The area of this rectangle is A = L · W = (5 cm + 6 cm) · (5 cm), or

                                                             A = (11 cm)(5 cm), or A = 55 cm²

Final answer:

The area of the rectangle is calculated by solving for the width using the given perimeter, then finding the length, and finally multiplying the two. The width is 5 cm, the length is 11 cm, and the area is 55 cm².

Explanation:

Let's denote the width of the rectangle as w centimeters. According to the problem, the length of the rectangle is 6 cm longer than its width, so we can express the length as w + 6 cm.

The perimeter of a rectangle is calculated by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Given the perimeter is 32 cm, we can write the equation 2(w + 6) + 2w = 32.

Solving this equation:

2w + 12 + 2w = 32

4w = 32 - 12

4w = 20

w = 5 cm

Now that we have the width, we can find the length:

l = w + 6

l = 5 + 6

l = 11 cm

The area of the rectangle is found by multiplying the length by the width, A =[tex]l \(\times\) w[/tex], which gives us:

A = [tex]11 \(\times\) 5[/tex]

A = 55 cm²

Answer:

Radius of the cone is 6 unit.

Step-by-step explanation:

Given:

Lateral Surface Area of Cone, LSA = 100π unit²

Total Surface Area of cone, TSA = 136π unit²

Let, r be the radius of cone.

According to the question,

Total Surface area = lateral surface area + Area of circle

136π = 100π + πr²

πr² = 36π

r² = 36

r = 6

Therefore, Radius of the cone is 6 unit.

The radius of the cone is 6 units.

To solve for the radius of the cone, we need to use two formulas: the lateral area (LA) and the total surface area (TSA) of a cone. The given values are:

We use the following formulas:

From the given values:

From the first equation, we can express l in terms of r:

l = 100 / r

Substitute l in the second equation:

136 = r² + r(100 / r)
=> 136 = r² + 100

Rearrange the equation to solve for r:

r² = 136 - 100
=> r² = 36
=> r = √36
=> r = 6.

The verbal statement 'three times a number increased by 8 is at most 40 more than the number' is expressed as the inequality 3x + 8 ≤ x + 40 in mathematical terms. This inequality simplifies to x ≤ 16, indicating that the original number must be 16 or less.

The question involves translating a verbal statement into a mathematical inequality. The phrase 'three times a number increased by 8 is at most 40 more than the number' can be represented algebraically. Begin by letting the variable 'x' represent the unknown number. The phrase 'three times a number' translates to '3x', 'increased by 8' means we add 8, and 'is at most' indicates that the expression is less than or equal to something. '40 more than the number' is translated to 'x + 40'. Combining these elements, we have the inequality 3x + 8 ≤ x + 40.

To solve this inequality, we would subtract 'x' from both sides to get 2x + 8 ≤ 40, and then subtract 8 from both sides to find 2x ≤ 32. Next, we would divide both sides by 2 to get x ≤ 16. This tells us that the original number must be 16 or any number less than 16 to satisfy the condition described in the question.

Understanding how to translate verbal statements into mathematical expressions and inequalities is a fundamental math skill. Knowing terms such as 'at most' is crucial for setting up the correct inequality. This situation is an application of basic algebra to interpret and solve problems.

Answer:

33 laps

Step-by-step explanation:

we know that

There are 6.6 laps in a mile

so

using proportion

Find how many laps will you have to make to run 5 miles

so

Let

x ----> the number of laps

[tex]\frac{6.6}{1}\frac{laps}{mile}=\frac{x}{5}\frac{laps}{mile} \\ \\x=6.6*5\\ \\ x=33\ laps[/tex]

Answer:

option C

Step-by-step explanation:

Answer:

c: no solution

Step-by-step explanation:

Final answer:

The function f(x) = 3x^2 + 2x + 4 has no real zeros because the discriminant (b^2 - 4ac) is negative, indicating that the roots of the quadratic equation are complex.

Explanation:

The question asks us to identify the real zeros of the function f(x) = 3x2 + 2x + 4. To find the real zeros, we look for values of x that make f(x) equal to zero. We can approach this by attempting to solve the quadratic equation 3x2 + 2x + 4 = 0 using the quadratic formula, which is x = [-b ± √(b2 - 4ac)]/(2a), where a = 3, b = 2, and c = 4.

Inserting these values into the formula, we get:

x = [-2 ± √((2)2 - 4*3*4)]/(2*3)

x = [-2 ± √(4 - 48)]/(6)

x = [-2 ± √(-44)]/(6)

Since the part under the square root (√(-44)) is negative, this indicates that the solutions for x are complex, not real. Therefore, the equation 3x2 + 2x + 4 has no real solutions.

Answer:

The total revenue generated by the firm is:

[tex]P(x) = 75x^3-5x^{\frac{5}{2}}[/tex]

Step-by-step explanation:

The average cost per TV is:

[tex]r(x) =\frac{P(x)}{x}[/tex]

Where x is the number of televisions sold and P is the firm's income for all the televisions sold

In this problem we know the equation r(x).

Then P(x) will be:

[tex]P(x) = x*r(x)[/tex]

Therefore if [tex]r(x)=75x^2-5x^{3/2}[/tex] then

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

[tex]P(x) = 75x^{2+1}-5x^{\frac{3}{2}+1}\\\\P(x) = 75x^3-5x^{\frac{5}{2}}[/tex]

Answer:

Px =75x^3-5x^5/2

Step-by-step explanation:

To find the volume of a rectangular prism, multiply the 3 side lengths by each other.

Volume  = 7.9 x 6.3 x 12.4 = 617.148 cubic cm.

Rounded to the nearest tenth = 617.2 cubic cm.

Answer: [tex]617.1\text{ cm}^3[/tex]

Step-by-step explanation:

In the given picture, we have a rectangular prism.

Height : 7.9 cm

Length = 12.4 cm

Width = 6.3 cm

The volume of a rectangular prism is given by :-

[tex]V=l\times w\times h[/tex], where l is length, w is width and h is height of the prism.

Now, the volume of a rectangular prism will be :-

[tex]V=12.4\times 6.3\times 7.9\\\\\Rightarrow\ V=617.148\approx617.1\text{ cm}^3[/tex]

Hence, the  volume of a rectangular prism = [tex]617.1\text{ cm}^3[/tex]

The number that when added to 43, would give the result of 112 can be found to be 69.

To find the number that, when added to 43, equals 112, you can use algebraic reasoning.

Let's represent the unknown number with the variable "x". The equation can be set up as:

43 + x = 112

To solve for "x," we need to isolate it on one side of the equation.

First, subtract 43 from both sides of the equation:

43 + x - 43 = 112 - 43

The 43 on the left side cancels out:

x = 112 - 43

Simplifying the right side of the equation:

x = 69

Find out more on addition at https://brainly.com/question/31055008

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To solve the equation 43 + x = 112, subtract 43 from both sides to isolate 'x'. The value of 'x' is 69.

To find the number that, when added to 43, equals 112, we can use algebra. Let's use the variable 'x' to represent the unknown number. So, the equation is 43 + x = 112.

To isolate 'x', we need to move 43 to the other side of the equation.

By subtracting 43 from both sides, we get x = 112 - 43. Evaluating the subtraction, we find that x = 69.

Answer:

[tex]\large\boxed{6\times\dfrac{2}{3}=4}[/tex]

Step-by-step explanation:

[tex]6\times\dfrac{2}{3}=\dfrac{6^{:3}}{1}\times\dfrac{2}{3_{:3}}=\dfrac{2}{1}\times\dfrac{2}{1}=2\times2=4[/tex]

should be 20%

Hope this helps

Answer:it's 12.20

Step-by-step explanation:

Answer:

Volume: 8x1x12=96 inches^3

Surface area: 8x1x2=16

1x12x2=24

8x12x2=192

the total surface is: 16+24+192=232 inches^2

12 in tall * 8 in wide = 96 in area. You need a third value to find a volume.

The answer are:

1.D

2.C

3.A

Explanation is in above pictures.

is this the full question?

Answer:

x=20

Step-by-step explanation:

20-10=10

Answer:

x = 20

Step-by-step explanation:

x - 10 = 10

   +10

cancel out the 10 and do the same thing to both sides

x = 20

very simple

Answer:

939,520

Step-by-step explanation:

You round up because you have a 5 in the tens place and as the saying goes: "Five or more up the score, four or less let it rest"

The number  939,515 rounded to the nearest tens is 939520.

We round off numbers to make them easier to remember and it also keeps their value approximately to the place it has been rounded off.

To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.

Given, A number 939515 and we have to round it to the nearest ten.

To round this number to the nearest ten we'll look at the digit at the unit's place.

The digit at the unit place is 5 so we'll add 1 to the tens digit and make the unit digit zero.

Therefore the number 939515 rounded to the nearest tens place is

939520.

learn more about rounding of numbers here :

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Answer:

Step-by-step explanation:

fv xcfvsvsvfber

Answer:

D

Step-by-step explanation:

The area (A) of a triangle is calculated using the formula

A= [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 8 and h = 2, so

A= 0.5 × 8 × 2 = 8 units² → D

Answer:

55

Step-by-step explanation:

17 and 8

Step-by-step explanation:

8 is the shortest board so multiply 8 by 2 add the 1 foot more gives you 17

Well I guess I can do it tomorrow but I’m not sure if it’s a good

Answer:

(-2,-8)

Step-by-step explanation:

y=4x

3x+5y=-46

3x+5(4x)=-46

3x+20x=-46

23x=-46

x=-2

y=4(-2)

y=-8

Answer:

x=1 and y = 9

Step-by-step explanation:

Solving using elimination method:

In elimination method we solve equations such that one variable cancels out and we find the value of other variable.

x + 7y = 64

x + 3y = 28

Subtracting both equations:

x + 7y = 64

x + 3y = 28

-   -       -

___________

0 +4y = 36

y= 36/4

y=9

Putting value of y in one of the equation,

x+7y = 64

x + 7(9) = 64

x + 63 = 64

x = 64-63

x = 1

So, x=1 and y=9

Solving using substitution method:

In substitution method, we substitute value of one variable into other value

x + 7y = 64   (1)

x + 3y = 28   (2)

From 1

x = 64 -7y

Putting value of x in eq(2)

(64 -7y) + 3y = 28

64 -7y +3y =28

64 - 4y = 28

-4y = 28 -64

-4y = -36

y = -36/-4

y = 9

Putting value of y in eq (1)

x + 7y = 64

x + 7(9) = 64

x + 63 = 64

x = 64 - 63

x = 1

So, x=1 and y = 9.

Answer:

- 2

Step-by-step explanation:

Given

9x + 3xy - 2

Substitute x = 3 and y = - 3 into the expression

= 9(3) + 3(3)(- 3) - 2

= 27 - 27 - 2 = - 2

Answer:

C

Step-by-step explanation:

Just did it on edg

Answer

5000

Step-by-step explanation:

You convert the numbers into  standard #'s which gets you 7000 and 2000. Subtract 7000 - 2000 and you get 5000.

7x10^3 is 3-1/2 times the size of 2x10^3.

Answer: v = 1

1v + 6v = 7             Combine like terms

7v = 7                    Divide both sides by 7

v = 1                       Answer!

Answer:

v=1

Step-by-step explanation:

You can add the similar variables (1v and 6v) to get 7v. now your equation should be 7v=7. divide each side by 7 so that the variable stands alone. 7/7 = 1, so v=1.

3.5-2.6=0.9

0.9÷3=0.3

2.6+0.3=2.9

answer is 2.9

Answer:

Maximum number of relative extremes contained in the graph of this function = 3.

Step-by-step explanation:

We have been given function [tex]f\left(x\right)=3x^4-x^2+4x-2[/tex].

Now we need to find about what is the maximum number of relative extremes contained in the graph of the given function [tex]f\left(x\right)=3x^4-x^2+4x-2[/tex].

Degree of the given function = 4.

Because degree is the highest power of variable.

Then relative number of extrema = degree - 1 = 4 - 1 = 3

Hence final answer is 3.

[tex]\bf \textit{volume of a right-circular cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=12\\ h=15 \end{cases}\implies V=\cfrac{\pi (12)^2(15)}{3}\implies V=720\pi[/tex]