A ladder is leaning against the side of a 10cm house. If the base of the ladder is a 3cm away from the house, how tall is the Ladder

Answer:

(x-4)(x+4)

Step-by-step explanation:

x^2 - 64 = x^2 - 4^2 = (x-4)(x+4)

Answer:   [tex]\frac{10}{\sqrt{3}}[/tex]

This is equivalent to [tex]\frac{10\sqrt{3}}{3}[/tex]

======================================================

Explanation:

To get the first value mentioned above, we simply divide the long leg (10) over the square root of 3.

This is due to the fact that if x is the short leg, then x*sqrt(3) is the long leg. We go in reverse of this process to go from long leg to short leg.

The expression [tex]\frac{10}{\sqrt{3}}[/tex] is the same as [tex]\frac{10\sqrt{3}}{3}[/tex] after we multiply top and bottom by sqrt(3) to rationalize the denominator.

Side notes:

Y =k√x

12 = 3k

k = 4

now X = 1\2

y = 4√1/2

y = 2√2

Answer:

y = 2[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Given y is directly proportional to [tex]\sqrt{x}[/tex] then the equation relating them is

y = k[tex]\sqrt{x}[/tex] ← k is the constant of variation

To find k use the condition when x = 9, y = 12

12 = k[tex]\sqrt{9}[/tex] = 3k ( divide both sides by 3 )

4 = k

y = 4[tex]\sqrt{x}[/tex] ← equation of variation

When x = [tex]\frac{1}{2}[/tex] , then

y = 4[tex]\sqrt{\frac{1}{2} }[/tex] = 4 × [tex]\frac{1}{\sqrt{2} }[/tex] ← rationalise the denominator by multiplying by [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex]

y = [tex]\frac{4}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex] = [tex]\frac{4\sqrt{2} }{2}[/tex] = 2[tex]\sqrt{2}[/tex]

Step-by-step explanation:

A:x=5-7

x=-2

B:x=-16+2

x=-14

l have answered only A and B

Answer:

4000 fish left in lake after 5 years

Step-by-step explanation:

12 x 5 = 60 (60%)

10000 - 60% = 4000

Answer:

False

Step-by-step explanation:

Precision  describes repeatability.  

Accuracy  describes the closeness of a measurement to the actual value.

 So your measurements may be precise but not accurate; for example if you used a faulty measurement system. And of course, you could get accurate results SOME of the time (which describes the exprerience of most researchers).

Errors in precision are usually detected.........eventually, invariably after you have shot your mouth off to your professor.

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Jon:

Initial investment (PV)= $14,500

Interest rate (i)= 0.05/4= 0.0125

Number of periods (n)= 4 quarters

Sara:

Initial investment (PV)= $16,250

Interest rate (i)= 0.04/365= 0.00011

Number of periods (n)= 365 days

To calculate the Future Value, we need to use the following formula:

FV= PV*(1+ i)^n

Jon:

FV= 14,500*(1.0125^4)

FV= $15,238.71

Sara:

FV= 16,250*(1.00011^365)

FV= $16,915.67

Sara will have $1,676.96 more than Jon.

Rhombus LMNO is shown with its diagonals.

Rhombus L M N O is shown. Diagonals are drawn from point M to point O and from point L to point N and intersect at point P. All sides are congruent.

Angle MLO measures 112°. What is the measure of angle MLP?

45°

56°

68°

90°

Step-by-step explanation:

B

Answer:

Number of cups water require for 30 muffins = 2.82 cups (Approx.)

Option "D"

Step-by-step explanation:

Given:

24 bran muffins required = 2.25 cups of flour

Find:

Number of cups water require for 30 muffins

Computation:

Assume;

Number of cups water require for 30 muffins = x

So,

24 / 2.25 = 30 / x

x = [30 × 2.25] / 24

x = 67.65 / 24

x = 2.8187

Number of cups water require for 30 muffins = 2.82 cups (Approx.)

Answer:

Step-by-step explanation:

A+B+C+D=360 degree (being one complete turn)

360 degrees

Step-by-step explanation:

because it a venticular angle you one side(180) and the other side (180) given you 360 degrees

Answer: about 3 buses

Step-by-step explanation: 162+24=186 and 65*3=195 so 3 buses is enough

Hope this helps:)

Answer:

D). 100

Step-by-step explanation:

The range is the highest number-lowest number in data. 150 is the highest, 50 is the lowest. Therefore, 150-50=100

Answer:

see below

Step-by-step explanation:   5 25  14 02

herb garden is 1/8 The area of her vegetable garden

herb garden is 6 square feet

vegetable garden = ???

herb garden / vegetable garden  =   1/8      solve for vegetable garden

herb garden × 8  =  vegetable garden

       6 ft² ×  8  =  __________ ft²      

Step-by-step explanation:

add 3

x = - 7___________..........

Answer:

i think the * is 100000, each number times 10

Answer:

D. 144

Step-by-step explanation:

Find volume of shipping container:

2 2/3 = 8/3

2 x 1 = 2

8/3 x 2/1 = 16/3

Find volume of cube:

1/3 x 1/3 = 1/9 x 1/3 = 1/27

Find how many boxes fit in container:

16/3 ÷ 1/27

16/3 x 27/1

Simplify:

16/1 x 9/1 = 144/1

Answer: 144

Answer:

4/5

Step-by-step explanation:

here ya are. I hope this helps, it's just 1 pair out of the 5 that don't fit. Meaning the 4 out of 5 fit. therefore 4/5

Answer:

(1,4)

Step-by-step explanation:

(1,-4) is over 1 and down negative 4 so reflected over the x-axis(the horizontal one) it would be four up so the answer is (1,4)

Answer: (1,4)

Step-by-step explanation:

The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same. For example, when point P with coordinates (1,-4) is reflecting across the X axis and mapped onto point P', the coordinates of P' are (1,4)

Answer:

Area = 77ft²

Perimeter = 44 9/20 feets

Step-by-step explanation:

Area of a triangle = 1/2 * base * height

Base = 19 1/4 feets = 77/4 feets

Height = 8 feets

Area = 1/2 * 77/4 * 8

Area = (77 * 8) / 8

Area = 77 feet²

Perimeter of a triangle :

Sum of the sides

Perimeter = a + b + c

Perimeter = 19 1/4 + 10 + 15 1/5

Perimeter = 44 + (1/4 + 1/5)

Perimeter = 44 9/20

Uh oh, looks like you need the graph to answer this question! If you post the graph then I can answer in numbers but for now, I'll try to explain:

1) I assume the graph looks like a dome shape, so based on that, where the line comes back down and hits the bottom line on which x value is larger will be whose stone hit the water second and what time will be what x value represents the time it hit the water.

2) look at the highest value on the purple graph and that is the maximum height (the y value of that point) and the x value of that highest point will be the time it took for the stone to reach its maximum height.

3) based on this question, the graph should start not on the 0 but at a point on the y axis, so whoever's starting y value is higher will be this answer and what that is will be the number answer to the what was it part.

Hope this helps and if you post the graph then I can do more! :)

Answer:

1586.91 m³

Step-by-step explanation:

From the diagram attached,

Applying,

A = πrl.................. Equation 1

Where A = surface area of the cone, l = slight heigth of the cone, π = pie.

make l the subject of the equation,

l = A/πr.............. Equation 2

From the question,

Given: A = 628.32 m², π = 3.14, r = 8 m

Substitite these values into equation 2

l = 628.32/(3.14×8)

l = 25 m

But,

l² = h²+r².................... Equation 3

Where h = height of the cone.

h = √(l²-r²)

h = √(25²-8²)

h = √(625-64)

h = √(561)

h = 23.69 m

Also Applying,

V = 1/3πr²h

Where V = volume of the cone.

Therefore,

V = (3.14×8²×23.69)/3

V = 1586.91 m³

Answer:

Step-by-step explanation:

stay safe, stay healthy and blessed.

thank u

Answer:

a b c d e

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Inscribed Angle =  1/2 Intercepted Arc

<A = 1/2 (80)

<A = 40

Answer:

[tex]P(x \le 21) = 0.69146[/tex]

Step-by-step explanation:

The missing parameters are:

[tex]n = 64[/tex] --- population

[tex]\mu = 20[/tex] --- population mean

[tex]\sigma = 16[/tex] -- population standard deviation

Required

[tex]P(x \le 21)[/tex]

First, calculate the sample standard deviation

[tex]\sigma_x = \frac{\sigma}{\sqrt n}[/tex]

[tex]\sigma_x = \frac{16}{\sqrt {64}}[/tex]

[tex]\sigma_x = \frac{16}{8}[/tex]

[tex]\sigma_x = 2[/tex]

Next, calculate the sample mean [tex]\bar_x[/tex]

[tex]\bar x = \mu[/tex]

So:

[tex]\bar x = 20[/tex]

So, we have:

[tex]\sigma_x = 2[/tex]

[tex]\bar x = 20[/tex]

[tex]x = 21[/tex]

Calculate the z score

[tex]x = \frac{x - \mu}{\sigma}[/tex]

[tex]x = \frac{21 - 20}{2}[/tex]

[tex]x = \frac{1}{2}[/tex]

[tex]x = 0.50[/tex]

So, we have:

[tex]P(x \le 21) = P(z \le 0.50)[/tex]

From the z table

[tex]P(z \le 0.50) = 0.69146[/tex]

So:

[tex]P(x \le 21) = 0.69146[/tex]

Answer:

e) The company's daily cost to manufacture 80 items of the product is $500.

Step-by-step explanation:

We have that:

c is the cost in hundreds of dollars to manufacture n items. The input is the number of items, and the output is the cost, in hundreds of dollars.

Inverse function:

In the inverse function, the input and the output are exchanged from the original function, that is, in this situation, the input in the cost, in hundreds of dollars, and the output is the number of manufactured items.

c^-1(5)=80

Input of the inverse function is 5, which is the cost, in hundreds of dollars, that is, $500, to manufacture 800 itens. This means that the correct answer is given by option e.

Answer:

Below.

Step-by-step explanation:

y + 2 > -3(x + 1)

y + 2 > -3x - 3

y > -3x - 5

The graph will be the graph of the line y = -3x - 5 (dotted line),  with the area above the line shaded.

Answer:

[tex] - 3x + 4y = 24 \\ 3x - 4y = - 24 - - - (a) \\ 6x + 2y = - 18 - - - (b) \\ 2 \times (a) - (b) : \\ = > 0x - 10y = - 30 \\ 10y = 30 \\ y = 3 \\ \\ 3x = - 12 \\ x = - 4 \\ { \boxed{x = - 4}} \: \: \\ { \boxed{y \: = \: 3}}[/tex]

Answer:

Step-by-step explanation:

Answer:

[tex]\frac{2\sqrt{3} + 6}{12}[/tex]

Step-by-step explanation:

Simplify the denominator of [tex]\frac{1 + \sqrt{3} }{\sqrt{12} }[/tex] completely.

[tex]=> \frac{1 + \sqrt{3} }{ \sqrt{(4 \times 3)} } = \frac{1 + \sqrt{3} }{\sqrt{4} \times \sqrt{3} } = \frac{1 + \sqrt{3} }{2\sqrt{3} }[/tex]

Now, to rationalise it you need to make the denominator rational.

[tex]=> \frac{1 + \sqrt{3} }{2\sqrt{3} } \times \frac{2\sqrt{3} }{2\sqrt{3} }[/tex]

[tex]=> \frac{(1 + \sqrt{3})\times 2\sqrt{3} }{2\sqrt{3} \times 2\sqrt{3} }[/tex]

[tex]=> \frac{2\sqrt{3} + 6 }{12}[/tex]

Answer:

-1247400

Step-by-step explanation:

See the Image below:) I believe this is what you are looking for.