Samuel places a ladder against his house. The base of the ladder is 6 feet from
the house and the ladder is 10 feet long. How high above the ground does the ladder
touch the wall of the house?

Solution :

Given that :

The radius of circle A = 6 cm

The radius of circle C = 4 cm

In circle A

[tex]\angle EAF = \theta = 140^\circ[/tex]

The length of arc EF = [tex]$2 \pi r \times \frac{\theta}{360^\circ}$[/tex]

                                   [tex]$=2 \times 3.14 \times 6 \times \frac{140^\circ}{360^\circ}$[/tex]

                                    = 14.653 cm

In circle C

[tex]\angle GCH = \theta = 140^\circ[/tex]

The length of arc GH = [tex]$2 \pi r \times \frac{\theta}{360^\circ}$[/tex]

                                   [tex]$=2 \times 3.14 \times 4 \times \frac{140^\circ}{360^\circ}$[/tex]

                                    = 9.769 cm    

Therefore,

The length of EF is 14.653 cm

The length of GH is 9.769 cm

The length of EF is  1.5 times the length of GH

i.e.                   14.653  = 1.5 x 9.769

                       14.653 = 14.653

Hence proved.

Answer:

Step-by-step explanation:

sorry dont know ut

Answer:

here is the answer bae. Feel free to ask for more

[tex]f(x) = \log_b(x)[/tex] is a decreasing function when [tex]0 < b < 1[/tex]

This is because we can use the change of base formula to say

[tex]\log_b(x) = \frac{\log(x)}{\log(b)}[/tex]

If b is between 0 and 1, not including either endpoint, notice how the log(b) term is negative.

For example, if b = 0.5, then log(b) = log(0.5) = -0.301 approximately. I'm using log base 10 to get log(0.5) = -0.301

So for b = 0.5, we have,

[tex]\log_{0.5}(x) = \frac{\log(x)}{\log(0.5)} \approx \frac{\log(x)}{-0.301} \approx -3.322\log(x)[/tex]

The log(x) part on its own is always increasing. The negative coefficient out front flips it to always decreasing.

By applying the behavior rules we notice that the expression [tex]F(x) = \log_{b} x[/tex]decreasing function if the base of the logarithm is 0 < b < 1. (Correct choice: D) #SPJ5

Logarithms are trascendent functions whose form is defined by the following expression:

[tex]\log _{b} x[/tex] such that [tex]x = b^{a}[/tex], where b > 0.

Where b is the base of the power.

Whose rules are described below:

By applying the behavior rules we notice that the expression [tex]F(x) = \log_{b} x[/tex] is a decreasing function if the base of the logarithm is 0 < b < 1. (Correct choice: D)

The statement is poorly formatted and reports several mistakes. Correct form is shown below:

For what values of b will [tex]F(x) = \log_{b} x[/tex] be a decreasing function?

A. b > 0

B. 0

C. b < 0

D. 0 < b < 1

To learn more on logarithms, we kindly invite to check this: https://brainly.com/question/20785664 #SPJ5

Answer:

360°

Step-by-step explanation:

360°

Answer:

360 degrees

Step-by-step explanation:

For a polygon of n sides, the sum of the measures of the interior angles is

(n - 2)180.

A quadrilateral has 4 sides, so n = 4.

(4 - 2)(180) = 2(180) = 360

Answer: 360 degrees.

Answer:

[tex]18cm[/tex]

Step-by-step explanation:

A of triangle =

[tex] \frac{1}{2} bh[/tex]

[tex] \frac{1}{2} \times 9 \times 8[/tex]

[tex] = 36cm2[/tex]

A of square=

[tex]s2[/tex]

[tex]36 = s2[/tex]

[tex] \sqrt{36cm2} = \sqrt{s2} [/tex]

[tex]18cm = s[/tex]

Answer:

x=13/3

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

2+(-2) is basically 2-2 which is 0

Answer:

74 cm

Step-by-step explanation:

Perimeter Pentagon = 48 + (38 - 12)

48 + 26 = 74

74 cm

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Step-by-step explanation:

1.V=LWH L is the length, W is the width and H is the height.

12×6×3=216

2.V=Ah A is the area of the base, h is the height

18×16=288

3.V=LWH L is the length, W is the width and H is the height

10×14×5=700

Answer:

x= 20

y = 10

Step-by-step explanation:

Angles 3x° and 60° are Corrosponding angles so they are equal:

[tex]3x = 60 \\ \frac{3x}{3} = \frac{60}{3} \\ x = 20[/tex]

Angles (5y-5)° and 135° are Cointerior so add to give 180°:

[tex]5y - 5 + 135 = 180 \\ 5y + 130 = 180 \\ 5y = 180 - 130 \\ \frac{5y}{5} = \frac{50}{5} \\ y = 10[/tex]

Substitute y and x into the respective formula's to get your angles.

Answer:

ONE...

total of three angles that add up to 180

if you had a second, that would be 180 none left for the third angle

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Divide total pieces of candy by total people:

35 / 5 = 7

Each person receives 7 pieces of candy

Answer:

7

Step-by-step explanation:

35 divided by 5 equals 7

Answer:

c

Step-by-step explanation:

Answer:

f'(2) = 1/4

Step-by-step explanation:

We know that:

g(x) = x^3 + x

and f(x) is the inverse function of g(x), such that:

f(2) = 1

this is because:

g(1) = 1^3 + 1 = 2

We want to find:

f'(2)

The general formula for this case is:

if f(x) is the inverse of g(x)

and f(x) = y

then:

f'(y) = 1/g'(x)

Then in this case,

f'(2) = 1/g'(1)

so we just need to differentiate g(x)

g'(x) = 3*x + 1

and:

g'(1) = 3*1 + 1 = 4

Then:

f'(2) = 1/g'(1) = 1/4

f'(2) = 1/4

Answer:

I think it would be 1 out of 6 or B.

Step-by-step explanation:

I think so because there are 6 sides to a cube and if Mrs.Clever only rolls it once then it would be 1 out of 6.

Answer:

43º

Step-by-step explanation:

complementary angles total 90

(2x - 13) + (4x - 5) = 90

Combine like terms

6x - 18 = 90

6x = 72

x = 12

ZB = 4x - 5

ZB = 4(12) - 5

ZB = 43º

Answer:

1 ruler costs $0.60

Step-by-step explanation:

$20-$4.70=$15.30

Calculator =$7.50

3 Packs of Pens = $1.80 each

4 rulers= x each

$7.50 + 3($1.80) + 4x = $15.30

7.50 + 5.40 + 4x = 15.30

12.90 + 4x = 15.30

4x = 2.40

x = 0.60

Answer:

10

Step-by-step explanation:

a^2+b^2=c^2

9^2+3^2=c^2

81+9=c^2

100=c^2

c=10

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {√7}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex] =\frac{7}{ \sqrt{7} }\\ [/tex]

[tex] = \frac{7}{ \sqrt{7} } \times \frac{ \sqrt{7} }{ \sqrt{7} }\\ [/tex]

[tex] = \frac{7 \sqrt{7} }{ \sqrt{7} \times \sqrt{7} }\\ [/tex]

[tex] = \frac{7 \sqrt{7} }{7}\\ [/tex]

[tex](∵ \sqrt{a} \times \sqrt{a} = a)\\[/tex]

[tex] = √7[/tex]

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}[/tex]

Step-by-step explanation:

Given,

7/√7

The denominator is √7.

We know that

Rationalising factor of √a is √a.

Therefore, the rationalising factor of √7 is √7.

On rationalising the denominator them

=> (7/√7) × (√7/√7)

=> 7(√7)/(√7 × 7)

=> 7√7/7.

Hence, the denominator is rationalised.

Answer:

The answer is 3y - 10x - 27

Answer:

8

Step-by-step explanation:

count up from where s is (-7) to where v is (1) there are 8 numbers in between them. making that he length

Answer:

S= -7 to V= 1 so your answer is 8

Answer:

x=8

x=5/3

Step-by-step explanation:

evey bracket equal =0 to get solution

x-8=0

x=8

3x-5=0

3x=5

x=5/3

Answer:

x=5/3 or x=8

Step-by-step explanation:

0=3x^2-29x+40

-3x^2+29x-40=0

(3x-5)(x-8)=0

-3x+5=0 or x-8=0

x=5/3 or x=8

Answer:

A,C

Step-by-step explanation:

i took the test

Answer:

D

Step-by-step explanation:

She spent $12 and *$ on two separate things, meaning she spent $20 on both.

So, 12 + 8 = 20.

If she started with 25, we subtract 20 from 25 to get how much she has left.

So, 25 - 20 = y.

Therefore, the answer is D.

Answer:

D

Step-by-step explanation:

I agree with the previous answer, it's D.

Sandra spent $12  on apples and $8 on fruit, so you would add.

That's $20, so to find out how much money she has left you do 25 - 20.