Use the number line to find the ratio AC/CF simplify the ratio

A. 8/20
B 2/5
C 8/12
D 2/3

This one helps too.

Ur welcome.

Answer:

21

Step-by-step explanation:

The two consecutive numbers are 7 and 8.

Consecutive numbers are numbers that follow each other. For example, 1,2,3,4 are consecutive numbers.

Let:

x = first number

(x + 1) = second number

From the question, this expression can be derived:

[(x) + (x + 1)] ²

This can be simplified to (2x +1)²

The second expression is : x² + (x +1)²

(2x +1)² -  [x² + (x +1)²] = 112

expanding the bracket gives:

(4x²  + 4x + 1) - [x² + (x² + 2x +1) = 112

4x²  + 4x + 1 - 2x² - 2x - 1 = 112

Add like terms

2x² + 2x = 112

Divide both sides by 2

x² + x = 56

x² + x - 56 = 0

Factorise the equation

The factors of -56x² that add up to x are : 8x and -7x

(x² - 7x) (8x - 56)  = 0

x(x - 7) 8(x -7) = 0

x = 7

or

x = -8

Since x cannot be a negative number, x is 7 and (x + 1) = 8

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Answer:

[tex]\text{Hence, the approx. area of circle }2827 cm^2[/tex]

Step-by-step explanation:

Given the diameter of circle 60 cm

we have to find the area of circle

Diameter=60 cm

Radius=30 cm

[tex]\text{Area of circle=}\pi r^2[/tex]

[tex]=\frac{22}{7}\times (30)^2=2828.57143\sim 2827(approx)[/tex]

[tex]\text{Hence, the approx. area of circle }2827 cm^2[/tex]

Option A is correct

Answer:

1. 49

2. 169

3. 81

4. 100

5. 441

6. 36

Step-by-step explanation:

1. [tex](343)^{\frac{2}{3}}=\sqrt[3]{(343)^{2} }[/tex]

= [tex]\sqrt[3]{(343)(343)}=\sqrt[3]{(7^{3})(7)^{3}}[/tex]

= 7×7 = 49

2. [tex](2197^{\frac{1}{3}})^{2}=(\sqrt[3]{2197})^{2}[/tex]

= [tex](\sqrt[3]{13^{3}})^{2}=13^{2}[/tex]

= 169

3. [tex]729^{\frac{2}{3} }=(\sqrt[3]{729})^{2}[/tex]

= [tex](\sqrt[3]{9^{3}})^{2} = 9^{2}[/tex]

= 81

4. [tex](1000^{2})^{\frac{1}{3}}=(\sqrt[3]{1000})^{2}[/tex]

= 10²

= 100

5. [tex](\sqrt[3]{9261})^{2}=(\sqrt[3]{(21)^{3} })^{2}[/tex]

= 21²

= 441

6. [tex](\sqrt[3]{216})^{2}=(\sqrt[3]{6^{3} })^{2}[/tex]

= 6²

= 36                                        

Hi there!

My name is Chris and I'll be helping you today!

So your question states that a boat departed the port at 36.8 km/h.

After 1.75 hours, a second boat emerges from the port.

After 1.8 hours, the second boat is 86.9 km away from the first boat.

Also, remember that speed equals distance over time.

Therefore, your answer will be: The speed boat's speed in km/h was 24.3 km/h. Forgive me if I am incorrect.

Enjoy your day!

Answer:

It is one.

Step-by-step explanation:

If you didn't get 1 re read the problem

The width of the garden is 12 feet and the length of the garden is 20 feet.

Let's denote the width of the garden as 'w'. The length will then be 'w + 8'. Measurements are in feet. The garden is surrounded by a 4-foot sidewalk. Therefore, the total length of the garden including the sidewalk is 'w + 8 + 4 + 4 = w + 16', and the total width is 'w + 4 + 4 = w + 8'.

The area of the sidewalk surrounding the garden is the area of the large rectangle minus the area of the garden. So, we set up the following equation:
(w + 16)(w + 8) - (w)(w + 8) = 320.

After simplifying, we can get a quadratic equation: w² + 8w - 320 = 0 and then solve this equation, which gives us w = 12 or w = -28. We ignore the negative solution as the width cannot be negative. So, the dimensions of the garden are:
Width: 12 feet
Length: 20 feet.

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Answer:

10 years old

Step-by-step explanation:

I will use the letter r to denote Ryanne's age:

r = 14

And  according to the problem, her brother's age is THREE MORE THAN HALF HER AGE

so, we start by finding  how much is half of Ryanne's age:

r/2 = 14/2 = 7

and next, we find that three more than half her age is:

7 + 3 = 10

Her brother is 10 years old

The approximate solution of the equation log₂(3·x - 1) = log₄(x + 8), obtained algebraically is about x = 1.353. The solution cain be verified using the attached graph created with MS Excel

The steps used to find the solution of the logarithm equation can be presented as follows;

The logarithm equation is;  [tex]\log_2(3\cdot x - 1) = \log_4(x + 8)[/tex]

Converting the logarithm to the same base, we get;

[tex]\log_4(x + 8) = \frac{\log_2(x + 8)}{\log_2 4}[/tex]

[tex]\log_4(x + 8) = \frac{\log_2(x + 8)}{2}[/tex]

[tex]\log_2(3\cdot x - 1) = \frac{\log_2(x + 8)}{2}[/tex]

2 × log₂(3·x - 1) = log₂(x + 8)

log₂(3·x - 1)² = log₂(x + 8)

(3·x - 1)² = (x + 8)

(3·x - 1)² - (x + 8) = 0
9·x² - 7·x - 7 = 0

Solving using technology, we get; x ≈ 1.353 and x ≈ -0.575

Plugging in the value of x = 1.353, we get;

log₂(3 × 1.353 - 1) ≈ 1.613

log₄(1.353 + 8) ≈ 1.613

The value of the logarithm are much different when x ≈ -0.575, the expression log₂(3·x - 1) have no solution. The solution is therefore; x ≈ 1.353

Please find the attached the graph of the equation log₂(3·x - 1) = log₄(x + 8), showing the solution as x ≈ 1.353

Final answer:

To solve the equation log2(3x-1) = log4(x+8), we can rewrite the equation and simplify it to calculate the approximate solution as x = 4.5.

Explanation:

To solve the equation log2(3x-1) = log4(x+8), we can start by using the property of logarithms that states log(a) = log(b) if and only if a = b. Based on this property, we can rewrite the equation as 3x - 1 = x + 8. Simplifying this equation, we get 2x = 9. Finally, by dividing both sides by 2, we find that x = 4.5. Therefore, the approximate solution to the equation is x = 4.5.

Final answer:

The interest rate is 100%, or 1 as a decimal, for continuously compounded interest.

Explanation:

To find the interest rate, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

Using the given information, we can plug in the values and solve for r:

The interest rate is 100%, or 1 as a decimal, for continuously compounded interest.

The interest rate, for continuous compounding, is approximately 5.775%.

To find the interest rate for continuous compounding, we can use the formula for compound interest:

[tex]\[ A = P \times e^{rt} \][/tex]

Where:

- [tex]\( A \)[/tex] is the final amount of money,

- [tex]\( P \)[/tex] is the principal amount (initial investment),

- [tex]\( r \)[/tex] is the interest rate (annual rate in decimal),

- [tex]\( t \)[/tex] is the time the money is invested for (in years),

- [tex]\( e \)[/tex] is the base of the natural logarithm, approximately equal to 2.71828.

Given:

- [tex]\( P = $750 \)[/tex],

- [tex]\( A = $1500 \)[/tex],

- [tex]\( t = 12 \)[/tex] years.

We need to solve for [tex]\( r \)[/tex], the interest rate.

**Substitute the Given Values into the Formulaa :

[tex]\[ 1500 = 750 \times e^{12r} \][/tex]

**Divide Both Sides by 750**:

[tex]\[ \frac{1500}{750} = e^{12r} \][/tex]

[tex]\[ 2 = e^{12r} \][/tex]

**Take the Natural Logarithm of Both Sides**:

[tex]\[ \ln(2) = \ln(e^{12r}) \][/tex]

[tex]\[ \ln(2) = 12r \ln(e) \][/tex]

[tex]\[ \ln(2) = 12r \][/tex]

**Solve for [tex]\( r \)[/tex]**:

[tex]\[ r = \frac{\ln(2)}{12} \][/tex]

[tex]\[ r = \frac{0.693}{12} \][/tex]

[tex]\[ r = 0.05775 \][/tex]

**Convert the Interest Rate to a Percentage**:

[tex]\[ r_{\text{percentage}} = 0.05775 \times 100\% \][/tex]

[tex]\[ r_{\text{percentage}} = 5.775\% \][/tex]

So, the interest rate is approximately 5.775%.

Tldr: The answer is 9

When 4 banana caramel cream pies are sliced into 1/8 servings, the number of pieces of pie obtained is 32.

To determine the number of pieces of pie obtained when 4 banana caramel cream pies are sliced into 1/8 servings, we need to find the total number of pie servings. Each pie is sliced into 1/8 servings, so if we have 4 pies, we can calculate the total number of servings by multiplying 4 by 1/8.

Therefore, we will have 1/2 pie when 4 banana caramel cream pies are sliced into 1/8 servings. Since 1/2 pie is equivalent to 4/8 pie, the answer is D) 32 pieces.

Answer:

Step-by-step explanation:

Given is a sample with 4 items as

12,9,14,21

Mean = average of 4 = 14

s is the square root of sample variance

Sample variance is the sum of squares divided by n-1

But Yuri divided by 4 = n instead of 3 = n-1

That is the only mistake he did and all other steps are right.

Answer:

Option A is correct

equation [tex]2(x+14)=42[/tex] could be used.

Step-by-step explanation:

Given: The length of a rectangle [tex](l)[/tex] is 14 inches and perimeter of rectangle is 42 inches.

Perimeter(P)of a rectangle in inches is given by:

[tex]P= (2l+w)[/tex] ; where [tex]l[/tex]  is the length of the rectangle and w is the width of the rectangle.

Substitute the value of  P=42 inches , w =x inches and [tex]l = 14[/tex] inches in the above formula we get;

[tex]42 = 2 \cdot (14+x)[/tex]

Divide by 2 on both sides  we get;

[tex]21 = 14+x[/tex]

On simplify, we get;

x = 21-14 = 7 inches

therefore, the width of the rectangle is, x = 7 inches

Check :

Substitute the value of x =7 in option A.

[tex]2(x+14) =42[/tex]

[tex]2(7+14)=42[/tex]

[tex]2\cdot 21 =42[/tex]

42 = 42      

Hence, the only equation that could be used to find the width, x is,  [tex]2(x + 14) = 42[/tex]