A 17-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 10 feet from the base of the building. How high up the wall does the ladder reach?

The completely factored form of 4x^2 + 28x + 49 is given by: Option C: (2x+7)(2x+7)

If the given quadratic expression is of the form ax^2 + bx + c, then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:

[tex]b = \alpha + \beta \\ ac =\alpha \times \beta[/tex]

Then writing b in terms of alpha and beta would help us getting common factors out.

Sometimes, it is not possible to find factors easily, so using the quadratic equation formula can help out without any  trial and error.

For this case, the given quadratic expression is:

[tex]4x^2 + 28x + 49[/tex]

So we've to find two numbers such that:

Their sum = b =  28

Their product = [tex]ac = 4\times 49 = 196[/tex]

We can see that 196 is square of 14, and that 14 added twice forms 28, thus:

14 + 14 = 28

14×14 = 196

Writing b = 28 as sum of 14 twice, we get:

[tex]4x^2 + 28x + 49 = 4x^2 + 14x + 14x +49 \\4x^2 + 28x + 49 = 2x(2x+7) + 7(2x + 7)\\4x^2 + 28x + 49 = (2x+7)(2x+7)[/tex]

Thus, the completely factored form of 4x^2 + 28x + 49 is given by: Option C: (2x+7)(2x+7)

Learn more about factorization of quadratic expression here:

https://brainly.com/question/26675692

Answer:

73 m

Step-by-step explanation:

The formula for the area of a rectangle is a = w(l). Using this, we can plug in the given values and solve for l, the length.

4526 = 62(l)

[tex]\frac{4526}{62} =\frac{62l}{62}[/tex]

l = 73

hope this helps!

Answer: 73 meters

Step-by-step explanation:

The simple formula to calculate the area of a regular rectangle is (Length x Width)

Given the area is 4526, and the width 62, we can use "y" to represent the unknown length.

So, '

62(y)=4526

Divide both sides by 62

1/2[62(y)]=4526/62

Y= 73 meters.

To check, 73x62= 4526, which follows the formula

Answer:

To find the last term, divide the coefficient of the middle term by 2 then raise to the power of 2,that will be :

[tex]( \frac{ - 12}{2} )^{2} = { - 6}^{2} = 36 [/tex]

Answer:

add 36

Step-by-step explanation:

Answer:

i guess its A.

Step-by-step explanation:

I dont really know

The correct option is D. The cost of natural gas is $0.83 per unit.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation

Consider the provided equation.

116y=96.28

We need to solve the above equation for y.

Divide both sides by 116.

[tex]\dfrac{116y}{116}=\dfrac{96.28}{116}[/tex]

[tex]y=0.83[/tex]

Now consider the provided options.

Hence, the correct option is D. The cost of natural gas is $0.83 per unit.

To know more about Linear equations follow

https://brainly.com/question/14323743

Answer:

430 in^2

Step-by-step explanation:

Area of parallelogram =    base * height = 20 * 21.5 = 430 in^2

Answer:

Step-by-step explanation:

a c d are the answer

Answer:

12 divided by 1/9 is 1/108. In multiplication, its 1/108 * 12

Step-by-step explanation:

Answer:

7x+21

Step-by-step explanation:

Answer:

7x + 21

Step-by-step explanation:

Given

Solving

Step-by-step explanation:

make the figure into 1 rectangle with dimensions 25 and w,and rite triangle with hypotenuse = 18 and h = 8

applying Pythagoras theorem

18^2 = 8^2 + b^2

b^2 = 260

b = 2√65ft

area of rectangle = 2√65 * 25= 50√65

area of triangle = 1/2 * 2√65*8 = 8√65

total area = 58√65 ft^2

Area of bottom rectangle:-

Area of rectangle above it:-

Area of rectangle above it

Area of triangle:-

Total:-

Answer: v = 40mm * 25mm * 2mm = 2000 mm^3 so, the weight is 2000 mm^3 * .0005oz/1mm^3 = 1oz

Step-by-step explanation:

Answer: $6.75

Step-by-step explanation:

Popcorn95 × 0.75 = 71.25

Candy35 × 1.20 =42

Totally 113.25

Deduct from 120

Drinks6.75

answer

7

Step-by-step explanation:

cause I said so

Answer:

m=3/4

Step-by-step explanation:

Explanation:

The slope of a line parallel to a line L has the same slope as line L.

6x−8y=−2

6x+2=8y

y=6/8x+2/8

Simplfied= y=3/4x+1/4

Therefore the answer is 3/4.

Answer:

Square root of 20 :)

Step-by-step explanation:

Pythagorean theorem: a^2 + b^2 = c^2

Now lets solve!!

2^2 + 4^2 = c^2

4 + 16 = c^2

20 = c^2

Now lets find the square root if any :)

[tex]\sqrt{20}[/tex] = no square root

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

im answering so you can give other guy brainliest :)

Answer:

114

Step-by-step explanation:

25% = 25/100 = 0.25

152 × 0.25 = 38

152 - 38 = 114

Answer:

$114

Step-by-step explanation:

152x0.75 = 114

Answer:

A.

Step-by-step explanation:

4/5 = 0.8

3/4 = 0.75

0.75 < 0.8

The Area is a two-dimensional scalar quantity. The area of the composite figure is 264 cm².

The area of a two-dimensional region, form, or planar lamina in the plane is the quantity that represents its extent. On the two-dimensional surface of a three-dimensional object, the surface area is its counterpart.

The composite figure can be broken down into four parts a square(A), a triangle(B) and two rectangles(C and D).

Now, if the area of the composite figure is taken out it will be,

[tex]\text{Area of composite}=\text{Area of Square A} + \text{Area of triangle B} + \text{Area of Rectangle C} + \text{Area of Rectangle D}\\[/tex]

[tex]\text{Area of Composte}=(10^2)+(\dfrac12 \times 6 \times 4)+(8 \times 4)+(20 \times 6)\\\\\text{Area of Composte}= 100+ 12 + 32 + 120 =264\rm\ cm^2[/tex]

Thus, the area of the composite figure is 264 cm².

Learn more about the Area:

https://brainly.in/question/14759304

Answer:

A. ZA+ZB =180

B. ZA is 135 and ZB is 45

Step-by-step explanation:

Step-by-step explanation:since ZA and ZB are supplementary

ZA+Zb =180°

But ZA=3ZB

∴ 3ZB+ZB=180° ⇒4ZB=180°

∴ZB =45

Answer:

490.1 (If the radius is 6ft and height is 7ft)

571.8 (If the radius is 7ft and height is 6ft)

Step-by-step explanation:

A=2πrh+2πr2

Plug in the value for the radius and height. Then solve.

Answer:

[tex]\longmapsto \sf \: \: - 14x \cdot\sqrt{14x}[/tex]

Step-by-step explanation:

[tex] \sf \: if \: x > 0 [/tex]

[tex] \sf 6x \sqrt{14x} - 5 \sqrt{56 {x}^{3} } [/tex]

[tex] \sf Let's \: solve \: for \sqrt{56 {x}^{3} } \: first, \\\longmapsto \sf \sqrt{56 {x}^{3} } = \sqrt{14 \times 4 {x}^{2} \times x } \\ \sf \longmapsto \sqrt{56 {x}^{3} } = 4x \sqrt{14x} [/tex]

Substituting above value in given equation,

[tex]\longmapsto \sf 6x \sqrt{14x} - 5 \sqrt{56 {x}^{3} } \\ \longmapsto\sf 6x \sqrt{14x} - 5 \times 4x \sqrt{14x} \\ \longmapsto \sf \: 6x \sqrt{14x} - 20x \sqrt{14x} \\\longmapsto \sf \: \sqrt{14x}(6x - 20x) \\ \longmapsto \sf \: \: - 14x \cdot\sqrt{14x}[/tex]

Thanks for joining brainly community!

Answer:

Question 1 is statistical.

Question 2 is not statistical

Statistical means there will most likely be different answers, especially when it is being asked to several people. If it is a certain number for the answer it is considered not statistical.

Answer:

Step-by-step explanation:

open the page below

Answer:

please read through the ten symbols of logic mathematics

its lang allam ko. human is rescures till hitman

Answer:

2

Step-by-step explanation:

If 8cm divided by 4cm = 2cm

Answer:

A total of 142 units of water bottles must be sold to recover the costs of renting costumes.

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer:

40 cm

Step-by-step explanation:

10cm*4cm=40cm

Check the picture below.

Answer:

[tex]x^{9}[/tex] = ± 5

Step-by-step explanation:

([tex]x^{9}[/tex] )² = 25 ( take square root of both sides )

[tex]\sqrt{(x^{9})^2 }[/tex] = ± [tex]\sqrt{25}[/tex]

[tex]x^{9}[/tex] = ± 5

Answer:

x = - 3

Step-by-step explanation:

5x - 5 = 7x + 1 ( subtract 7x from both sides )

- 2x - 5 = 1 ( add 5 to both sides )

- 2x = 6 ( divide both sides by - 2 )

x = - 3

Answer: x = -3

Step-by-step explanation: Here is my explanation...

Step 1: Take away 5x from both sides 5x - 5x - 5 = 7x - 5x + 1.

Step 2: You should then get -5 = 2x + 1, then take away 1 from both sides -5 - 1 = 2x + 1 - 1

Step 3: -6 = 2x, divide 2x on both sides -6/2 = 2x/2

x = -3

Work Check:

5 (-3) - 5 = 7 (-3) + 1

-15 - 5 = -21 + 1

-20 = -20

If the -20 = -20 then this proves that x = -3. I hope this helped!