Armando leans an 18 -foot ladder against the side of his house to clean out the gutters. The base of the ladder is 5 feet from the wall. How high up the side of the house does the ladder reach? Express your answer in feet, rounded to the nearest tenth.

Applying the distance formula, the value of a is 2 or -2.

The distance formula is:

d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

Given the following:

d = XY = 10 units

X(a - 5, -2a) = (x1, y1)

Y(a + 1, 2a) = (x2, y2)

Plug in the values into the distance formula

10 = √[((a + 1) - (a - 5))² + (2a - (-2a))²]

10 = √[(a + 1 - a + 5)² + (2a + 2a)²]

10 = √(6² + (4a)²)

10 = √(36 + 16a²)

10² = 36 + 16a²

100 = 36 + 16a²

0 = -100 + 36 + 16a²

0 = 16a² - 64

16a² - 64 = 0

Factorize

16(a² - 4) = 0

16(a - 2)(a + 2) = 0

a = 2 or a = -2

Therefore, applying the distance formula, the value of a is 2 or -2.

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Answer:

x=2.5

Step-by-step explanation:

R = 4x − 9y

We know that R=1 and y=1 so we can substitute that in

1=4x-9

Then solve as a normal algebraic equation

add 9 to both sides

10=4x

divide both sides by 4

2.5=x

Answer:

7-5=2

2+4=6

2×6=12

you always work the Parenthesis 1st

Answer:

2 times as much

Step-by-step explanation:

1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes

3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins

200 is twice as much as 100

The number of apples in the 12th bag is 9.

There are 12 bags of apples on the market stalls.

The mean number of apples in each bag is 8.

Therefore, the number of apples in the 12th bag can be calculated as follows:

mean = ∑fx / ∑f

Hence,

let the number of apples in the 12th bag = a

mean = 6 × 1 + 7 × 4 + 8 × 2 + 9 × 3 + 10 × 1 + x × 1/ 1 + 4 + 2 + 3 + 1 + 1

mean = 6 + 28 + 16 + 27 + 10 + x / 12

mean = 87 + x / 12

8 = 87 + x / 12

cross multiply

96 = 87 + x

x = 96 - 87

x = 9

Hence, the number of apples in the 12th bag is 9.

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The absolute inequality will be x ≥ | 8.9 ± 0.15 |mm and the compound inequality will be x > 8.75, x< 9.05.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

Given that the length is 8.9 mm with a tolerance of 0.15mm.

The absolute inequality will be written as below:-

x ≥ | 8.9 ± 0.15 |mm

The compound inequality will be written as:-

x  > 8.75,

x < 9.05.

Therefore, the absolute inequality will be x ≥ | 8.9 ± 0.15 |mm and the compound inequality will be x > 8.75, x< 9.05.

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Answer:

If it is [tex]6(5)^2[/tex] then the answer is 150

Step-by-step explanation:

So, follow PEMDAS
Parenthesis

Exponent

Multiplication

Division

Addition

Subtraction

First square 5 because there is an exponent [tex]6(5)^2 = 6(25)[/tex]

Next multiply 6 times 25 and you get 150!

Answer:

d) 155

Step-by-step explanation:

The value of x is,

→ x = 5

Now the expression is,

→ 6x² + x

Let's solve the expression,

→ 6x² + x

→ 6(5)² + 5

→ 6(25) + 5

→ 150 + 5

→ 155

Hence, the answer is 155.

According to the question, the Fibonacci series is a series of sequence of numbers. It follows one standard property which states that every third term in the series is the addition of first term and second term.

Now, the first ten terms of the Fibonacci sequence is as follows:

Fibonacci Series = [tex]{1,1,2,3,5,8,13,21,34,55}[/tex]

The sum of the first ten number of the Fibonacci series is as follows:

Sum = [tex]1+1+2+3+5+8+13+21+34+55 = 143[/tex]

As per question, divide the calculated sum by eleven. Therefore, it can be written as:

Required Division = [tex]\frac{143}{11} = 13[/tex]

Hence, the solution for the given series is [tex]13[/tex].

What is a Fibonacci series?

Fibonacci series is an infinite series of sequences of numbers. The important property of this series is, every third term is the addition of the first and second term. In this, the first term either starts with zero or one.

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Answer:

10 to the 5th power times 9 to the 2nd power over 6 to the 4th power

Answer:

1) 256, -128, 64, -32

2) 27, 9, 3, 1, 1/3

3) 5x², 5x⁴, 5x⁶, 5x⁸, 5x¹⁰,

Step-by-step explanation:

1. In this geometric series each term is obtained by multiplying the previous term by (-1/2) or dividing by (-2).

256 ÷ (-2) = - 128

-128 ÷ (-2) = 64

64 ÷ (-2) = (-32)

The geometric series is:

     256, -128, 64, -32...

We can find the common ratio by dividing the second term by first term.

2) 27, 9, ___, _________, 1/3

       [tex]\sf \boxed{\bf common \ ratio= \dfrac{second \ term}{first \ term}}[/tex]

                                 [tex]\sf = \dfrac{9}{27}\\\\ = \dfrac{1}{3}[/tex]

  [tex]\sf 9*\dfrac{1}{3}=3\\\\3*\dfrac{1}{3}=1[/tex]

The geometric series is:

  27, 9, 3, 1, 1/3....

3) 5x², _____, 5x⁶, 5x⁸, _____, ....

Here, we can take 3rd term and 4th term to find the common ratio.

  [tex]\sf common \ ratio = \dfrac{5x^8}{5x^6}\\\\[/tex]

                       [tex]\s = x^{8-6}\\\\=x^2[/tex]

5x² * x² = 5x⁴

8x⁸ * x² = 8x¹⁰

The geometric serious is:

5x², 5x⁴, 5x⁶, 5x⁸, 5x¹⁰, ...

[tex]\sf 1.) \ 256, -128, 64, -32,..\\ \\ 2.) \ 27, 9, 3, 1, 1/3,... \\ \\3.) \ 5x^2, 5x^4, 5x^6, 5x^8,5x^{10} , ...[/tex]

[tex]\sf Geometric \ formula: ar^{n-1}[/tex]

Find the common ratio:

Equation: [tex]256(-\frac{1}{2} )^{n-1}[/tex]

2nd term: [tex]256(-\frac{1}{2} )^{2-1}=-128[/tex]

3rd term: [tex]256(-\frac{1}{2} )^{3-1}=64[/tex]

Find common ratio:

Equation: [tex]27(\frac{1}{3} )^{n-1}[/tex]

3rd term: [tex]27(\frac{1}{3} )^{3-1}=3[/tex]

4th term: [tex]27(\frac{1}{3} )^{4-1}=1[/tex]

Find the common ratio:

Equation: [tex]5x^2 (x^2)^{n-1}[/tex]

2nd term: [tex]5x^2 (x^2)^{2-1} = 5x^2 (x^2) = 5x^{4}[/tex]

5ht term: [tex]5x^2 (x^2)^{5-1} = 5x^2 (x^8) = 5x^{10}[/tex]

-9, -10/32, 13/16, 79/8]

Step-by-step explanation:

use ur brain

Answer:

Step-by-step explanation:

brackets first

5 - (3-2) + 2

5 - (1) + 2

5 - 1 + 2

4 + 2

6

Answer:

5-(3-2)+2

5-1+2

4+2

6

Step-by-step explanation:

Follow PEMDAS

P ()

E: Exponent

M: Multiplication

D: Division

A: Addition

S: Subtraction

And you answer each equation going from Left to Right

According to the given function, we can throw it to the height of 6.6 m.  So, yes we can throw it high enough to reach the ledge.

The given equation is quadratic. A quadratic equation is defined as an equation of a single variable with the highest power of 2. In general, the quadratic equation can be expressed as h(x)= [tex]ax^2- bx + c[/tex], where a, b and c are arbitrary constants. The solution for a quadratic equation is given by:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

The maximum of a quadratic equation is given by:

= [tex]c-\frac{b^2}{4a}[/tex]

The length to be covered by throwing=6 meters

It is given that the height of the grappling hook you throw is a function h(t) = -4.9t² + 10t + 1.5

Here a =4.9, b = 10 and c = 1.5

The maximum of a quadratic equation is given by:

[tex]c-\frac{b^2}{4a}[/tex]

[tex]1.5-\frac{10^2}{4*(-4.9)}[/tex]

6.6

A throw can be made to reach the wall since the height of wall is less than the maximum value that is 6.6 m.

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The answer is :

a) 27 m= 2700 cm.

b) 38 dam = 380 m.

c) 34 m = 0.34 hm.

Lets know about the given prefix first,

    m = Meter means one hundred centimeter so,

1 m = 100 cm

   cm =  Centimeter means one-hundredth of a meter so,

1 cm = 0.01 m

  mm = Millimeter means one-thousandth of a meter so,

1 mm = 0.001m

  hm = Hectometer means one hundred meters so,

1 hm = 100 m

  dam = Decameter means ten meters so,

1 dam = 10 m

So,  

a) 27 m = 2700 cm

b) 38 dam = 380 m

c) 34 m = 0.34 hm.

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Answer:

x=8

Step-by-step explanation:

starts with 0.5x+2=6, so move the constant to the right, 0.5x=6-2, then calculate the right side, 0.5x=4, then divide both sides, and x=8

Answer:

x = 8

Step-by-step explanation:

Get variable on left and constants on right

0.5x = 6 - 2

0.5x = 4

Divide both sides by 0.5

x = 8

Two vertex angles of an isosceles triangle are equal but not necessarily all three so the given statement is not always true.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

In a triangle, the sum of all three angles is 180°

Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.

An isosceles triangle is a triangle whose two sides will be the same, but the third side may or may not be equal.

So, the angle associated with the same side will same but the remaining angle will or will not be the same.

Hence "Two vertex angles of an isosceles triangle are equal but not necessarily all three so the given statement is not always true".

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Answer:

Step-by-step explanation:

Solution for Point C is located on AB such that the ratio of AC : CB is 3:2. ... A: Here point B lies on the line AC with coordinates A(-3,4) and C(2,-6), ...

Answer: try 1 or 0

Step-by-step explanation:

Answer: 8

Step-by-step explanation:

(-8)= 8

Answer:

About 1 and 1/4 chapters per day.

Step-by-step explanation:

There are 11 chapters, and eight days to read them. So we divide 11 by 8. 11/8 = 1.375, which is approximately 1 and 1/4.

if d increases c will decrease AND  if c increases d will decrease.

If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio. A proportion is an equation that equalizes two ratios. For illustration, the ratio may be expressed as follows: 1: 3 (If there are 1 boy and 3 girls, then there are 3 girls for every 1 boy.)

since c and d are inversely proportional

a) if d increases c will decrease

because it is the property of the ratio and proportion

and same will be applied in b

b) if c increases d will decrease

that is obvious....

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The number of windows which can be framed with three 10-foot long pieces of lumber given the dimensions of the windows is; two and a half.

It follows from the task content that the number of windows that can be made given the dimensions of the windows be determined.

On this note, it follows that since the windows are 3 feet high and 3 feet width, the perimeter of each window(square shaped) covered by lumber is;

P = 4s

P = 4 × 3

P = 12 feet.

Hence, each window requires 12 feet of lumber.

However, since the builder has only three 10-foot long pieces of lumber which is equivalent to; 3 × 10 = 30 feet worth.

The number of windows that can be made is;

= 30/12

= 2.5.

Ultimately, only 2 and a half windows can be framed from the three 10-foot long pieces of lumber.

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Answer:y/5=5/6

Step-by-step explanation:based on given conditons

what scale factor did you find and is there a photo of the rectangle?

The equation of line is y = -4

Given the points:

(x₁, y₁) = (-1, -4)

(x₂, y₂) = ( 3, -4)

The slope-intercept form:

y = mx + b

Where, m is the slope and b is the y-intercept, that is (0, b)

The formula for slope:

m = (y₂ – y₁) / (x₂ – x₁)

We have given

x₁ = -1

x₂ = 3

y₁ = -4

y₂ = -4

So,

m = (-4 – (-4)) / (3 – (-1)) = (-4 + 4) / (3 + 1) = 0/4 = 0

Therefore we have the equation of the line as:

y = mx + b

-4 = 0(x) + b

-4 = 0 + b

b = -4

Therefore, the equation of line y = -4

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