Peter needs approximately 34 inches of ribbon to create an 'X' across his 12-inch square flag, calculated using the Pythagorean theorem to find the length of the diagonals needed for the 'X'.
Explanation:Peter is making an "X marks the spot" flag, which requires calculating the amount of ribbon needed to create the 'X'. The flag is a square with sides of 12 inches each. For an 'X', two ribbons will be needed, each stretching diagonally across the square. The diagonal length of a square can be determined using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the square has sides of 12 inches, making the formula for the diagonal:
d = √(12^2 + 12^2) = √(144 + 144) = √288 ≈ 16.97 inches.
Since Peter needs two diagonals to form the 'X', the total ribbon length will be 2 × 16.97 inches, which equals 33.94 inches. Therefore, Peter will need approximately 34 inches of ribbon to create the 'X' on his flag.
3/4 of what number is 8?
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We have to find the value of 'x' in [tex] \sin (x+22)^{\circ}=\cos (2x-7)^{\circ} [/tex]
By using the complementary angle formula which states:
[tex] \cos (90-\Theta )=\sin \Theta [/tex]
Now,
[tex] \cos (90^{\circ}-(x+22)^{\circ})=\cos (2x-7)^{\circ} [/tex]
Therefore, we get
[tex] 90-(x+22)= (2x-7) [/tex]
[tex] 90-x-22= (2x-7) [/tex]
[tex] 68=3x -7 [/tex]
[tex] 75=3x [/tex]
[tex] x=25^{\circ} [/tex]
Answer:
Lets go by a step-by-step process.
Step-by-step explanation:
\cos (90-\Theta )=\sin \Theta
Now,
\cos (90^{\circ}-(x+22)^{\circ})=\cos (2x-7)^{\circ}
Now we have...
90-(x+22)= (2x-7)
90-x-22= (2x-7)
68=3x -7
75=3x
x=25^{\circ}
What is the area of a sector with a central angle of π3 radians and a radius of 12.4 m? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box.
Answer: [tex]80.47\ m^2 [/tex]
Step-by-step explanation:
The area of a sector is given by :-
[tex]\text{Area of sector}=\frac{\theta}{2}\times( r^2), \text{where }\theta\text{ is measure of central angle in radians.}[/tex]
Given :Central angle = [tex]\theta=\frac{\pi}{3}[/tex]
radius = 12.4 m
Then,
[tex]\text{Area of sector}=\frac{\frac{\pi}{3}}{2}\times( (12.4)^2)\\\\\Rightarrow\ \text{Area of sector}=\frac{\pi}{6}\times153.76\\\\\Rightarrow\ \text{Area of sector}=\frac{3.14}{6}\times153.76\\\\\Rightarrow\ \text{Area of sector}=80.4677333333\approx80.47\ m^2 [/tex]
Twenty-seven minus of a number (x) is not more than 36. What is the number? x > 42 x ≥ -6 x < 3 x ≤ -6
Can someone help me please I would appreciate it.
I well mark brainliest if u explain
Please.
help me please asap!!!!!!!
express the perimeter of the rectangle as a polynomial. help please.
A pair of shoes that normally costs $75 is on sale for $55. What is the percent decrease in the price, to the nearest whole percent?
Which polynomial is a quintic trinomial?
x³ + 2x² -8x + 16
x² + 4
3x⁵ + 7x² -9x⁴
-x⁴ -5x² +1
Answer:
3x⁵ + 7x² -9x⁴
Step-by-step explanation:
In the order given, the polynomials have degrees 3, 2, 5, 4. The one of degree 5 is "quintic." That one also happens to be a trinomial. It is ...
3x⁵ + 7x² -9x⁴
Kim solved the equation below by graphing a system of equations. log2(3x-1)= log4(x+8) What is the approximate solution to the equation?
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.
the width of an architects desk is represented by four times x squared and the length is represented by the expression 2x cubed. what represents the area of the tabletop
How many pieces of pie will you have if 4 banana caramel cream pies are sliced into 1 8 servings? A) 12 B) 18 C) 24 D) 32
When 4 banana caramel cream pies are sliced into 1/8 servings, the number of pieces of pie obtained is 32.
Explanation: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.
4 x 1/8 = 4/8 = 1/2Therefore, 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.
The length of a rectangular garden is 8 feet longer than the width. The garden is surrounded by a 4-foot sidewalk. The sidewalk has an area of 320 square feet. Find the dimensions of the garden.
The width of the garden is 12 feet and the length of the garden is 20 feet.
Explanation: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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The profits of mr cash’s company is represented by the equation p(t)=-3t^2+18t-4, where p(t) is the amount of profit in hundreds of thousands of dollars and t is the number of years of operation. he realizes his company is on the down turn and wishes to sell before he ends up in debt. in what year of operation does mr cash’s business show the maximum profit?
The perimeter of a rectangle is 42 inches. If the length of the rectangle is 14 inches, which equation could be used to find the width, x? A. 2(x + 14) = 42 B. x + 2(14) = 42 C. 14(x + 2) = 42 D. x + 14 = 42
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]
A FIELD HOCKEY TEAM IS A RECTANGLE 60YARDS BY 100YARDS .WHAT IS THE LENGTH OF THE DIAGONAL FROM ONE CORNER TO THE FIELD TO THE OPPOSITE CORNER ROUND YOUR ANSWER TO THE NEAREST HUNDRETH
Find the value of the missing side of a triangle practice
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out of a port departed a steam boat with a speed of 36.8km/h. In 1.75 hours out of the same port and going the Sam direction departed a speed boat. In 1.8 hours after the the department of the speed boat, the distance between the speed boat and the steam boat was 86.9km. What was the speed boats speed in km/h?
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!
Nadia needs half of a dollar for bus fare. Which amount is equivalent to her bus fare?
Ryanne is 14. her brother's age is three more than half her age. how old is her brother?
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
table Mary used Delicious (d) and Golden Delicious (g) apples to make homemade applesauce. Delicious apples are $0.75 each and Golden Delicious apples are $1.25 each. Mary spent $21.00 on 22 apples. How many Golden Delicious apples did Mary buy?
Tldr: The answer is 9
99 POINT QUESTION!!!!!
The prime factorization of a number is 2^3*3^2*5. Which is a true statement about the factors of the number?
which or the following will happen if you miss a monthly credit card payment?
A)You will be charged a late fee.
B)You loose reward points
C)Your APR will increase the next month
D)Both A & B
what is the slope of the line through (2,-2) and (9,3)
what is a possible value for the missing term of the geometric sequence ?
50, blank, 450, ..
a. 1,350
b. 150
c. 3
d. 53
An investment of $750 will be worth $1500 after 12 years of continuous compounding at a fixed interest rate. What percent is the interest rate?
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:
A is the final amount ($1500)P is the principal amount ($750)r is the interest rate (unknown)n is the number of times interest is compounded per year (continuously compounded)t is the time in years (12)Using the given information, we can plug in the values and solve for r:
$1500 = $750(1 + r/1)^(1*12)$2 = 1 + rr = $2 - 1 = $1The 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.
Step 1 :**Substitute the Given Values into the Formulaa :
[tex]\[ 1500 = 750 \times e^{12r} \][/tex]
Step 2 :**Divide Both Sides by 750**:
[tex]\[ \frac{1500}{750} = e^{12r} \][/tex]
[tex]\[ 2 = e^{12r} \][/tex]
Step 3 :**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]
Step 4 :**Solve for [tex]\( r \)[/tex]**:
[tex]\[ r = \frac{\ln(2)}{12} \][/tex]
[tex]\[ r = \frac{0.693}{12} \][/tex]
[tex]\[ r = 0.05775 \][/tex]
Step 5 :**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%.
Match each whole number with a rational exponential expression. HELPP ME PLEEASE FASTTT
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
Could someone explain this to me?
What is the approximate area of the circle shown below 60cm
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
The prime factorization of a number is 2^3*3^2*5. Which is a true statement about the factors of the number?
1. Fifteen is a factor of the number because both 3 and 5 are prime factors.
2. Fifteen is not a factor of the number because 15 is odd and the number is even.
3. Sixteen is a factor for the number because 2^3=8 and 16 is divisible by 8.
4. Sixteen is not a factor of the number because the exponent of 2 is not even.
Fifteen is a factor of the number because both 3 and 5 are prime factors and this can be determined by using the arithmetic operations.
Given :
Number -- [tex]2^3\times 3^2\times 5[/tex]
The following steps can be used in order to determine the correct statement:
Step 1 - Write the given number.
[tex]2^3\times 3^2\times 5[/tex]
Step 2 - Simplify the above expression.
[tex]= 8\times 9 \times 5[/tex]
Step 3 - Multiply 8 by 9 in the above expression.
[tex]= 72\times 5[/tex]
Step 4 - Multiply 72 by 5 in the above expression.
= 360
Step 5 - 15 is a factor of 360.
Therefore, the correct option is 1).
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