A rectangle is 1/3 yards long and 2/3 yards wide. What is the area of the rectangle? Enter your answer in the box as a fraction in simplest form.
To find the area of a rectangle, multiply the length by the width. For a rectangle that is 1/3 yards long and 2/3 yards wide, the area is 2/9 square yards, which is the answer in simplest form.
The question asks us to calculate the area of a rectangle that is 1/3 yards long and 2/3 yards wide. The formula to compute the area of a rectangle is length imes width.
First, multiply the length and the width:
Length: 1/3 yards
Width: 2/3 yards
Area = (1/3) times (2/3) yards sq
Area = 2/9 square yards
This is the simplest form of the fraction, so this is the final answer: The area of the rectangle is 2/9 square yards.
How many real number solutions exist for 2x2 + 8x + 8 = 0?
Final answer:
There are no real number solutions for the given equation.
Explanation:
The given equation is 2x² + 8x + 8 = 0. To find the number of real number solutions for this equation, we can use the discriminant of the quadratic equation. The discriminant is given by the formula D = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation.
In this case, a = 2, b = 8, and c = 8. Substituting these values into the formula, we get D = 8² - 4(2)(8) = 16 - 64 = -48.
Since the discriminant is negative (-48), there are no real number solutions for the equation. Therefore, the answer is 0.
The graph illustrates a reflection of abc . What line is abc reflected across to create a'b'c'?
How much water can be held by a cylindrical tank with a radius of 12 feet and a height of 30 feet?
Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 4x2 + 24x + 30?
The graph of f(x) = x2 is widened.
The graph of f(x) = x2 is shifted left 3 units.
The graph of f(x) = x2 is shifted up 30 units.
The graph of f(x) = x2 is reflected over the x-axis.
The graph of f(x) = x2 is shifted left 3 units.
A 3500.00 $ principal earns 3% annual interest, Compounded semiannually after 20 years, what is the balance in the account
The base of a parallelogram is 24 inches longer than three times the height. The area of the parallelogram is 384 square inches. What is the height?
The height is x = ________ inches.
To find the height of the parallelogram, set up the equation (3x + 24) x = 384 using the formula for the area of a parallelogram. Solve the resulting quadratic equation to find that x, representing the height, is 8 inche
The student is trying to find the height of a parallelogram when the base is 24 inches longer than three times the height and the area is 384 square inches. Let the height of the parallelogram be represented by x inches. According to the problem, the base (b) is 3x + 24 inches. Using the formula Base x Height = Area of parallelogram, we can set up the equation:
(3x + 24) x= 384
Now solve for x using the distributive property:
3x^2 + 24x = 384
Next, set the equation to zero:
3x^2 + 24x - 384 = 0
Divide the entire equation by 3 to simplify:
x^2 + 8x - 128 = 0
Factor the quadratic equation:
(x + 16)(x - 8) = 0
Set each factor equal to zero:
x + 16 = 0 or x - 8 = 0
Since the height cannot be negative, x = 8 is the solution. Therefore, the height of the parallelogram is 8 inches.
Adventure Play sells an mp3 player for $18.00 and charges $3.25 per song. King Music sells a player for $23.00 and charges $2.00 per song. For how many songs will the cost be the same?
Answer:
4 songs
Step-by-step explanation:
What power do you raise a number to to get the square root of it?
Find the equation for the line that passes through the point (1, 3), and that is perpendicular to the line with the equation −3x − 4y = 13.
What is the value of n?
Enter your answer in the box.
n =____m
Two circle are inscribed inside squares. Write a function f in terms of the radius r that represents the area of the shaded region. Leave your answer in terms of π.
f(r)=___
The function [tex]f[/tex] in terms of the radius [tex]r[/tex] that represents the area of the shaded region is [tex]f(r) = 2\pi\cdot r^{2}[/tex].
The area of the shaded region is the sum of the areas of the two circles of same radius, each of them represented by the following formula:
[tex]A_{r} = \pi\cdot r^{2}[/tex] (1)
Where:
[tex]A_{r}[/tex] - Area of the circle.[tex]r[/tex] - Radius of the circle.Then, the formula for the shaded area is:
[tex]f(r) = 2\cdot A_{r}[/tex]
[tex]f(r) = 2\pi\cdot r^{2}[/tex] (2)
The function [tex]f[/tex] in terms of the radius [tex]r[/tex] that represents the area of the shaded region is [tex]f(r) = 2\pi\cdot r^{2}[/tex]. [tex]\blacksquare[/tex]
RemarkThe figure is missing and the statement present mistakes. Correct statement is shown below:
Two circle are inscribed inside squares. Write a function [tex]f[/tex] in terms of the radius [tex]r[/tex] that represents the area of the shaded region. Leave your answer in terms of π.
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BC is tangent to circle A at B and to circle D at C. AB= 10 BC= 21 DC= 8 find AD to the nearest tenth
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The vertical height of a right circular conical tent is 4m and the volume of space inside it is 968/7 cubic metre. Find the canvas required to make the tent.
The solution set for 7q2 − 28 = 0 is { }. (Separate the solutions with a comma) NextReset
Answer:
{ 2,-2}
Step-by-step explanation:
In order to solve this set we just have to first clear the "q":
[tex]7q^{2} -28=0\\7q^{2} -28+28=+28\\7q^{2} =28\\\frac{7q^{2}}{7} =\frac{28}{7} \\q^{2}=4\\\sqrt{q^{2}} =\sqrt{4} \\q= 2, -2[/tex]
So as we know the solution for a square root is always a negative and positive number, so the solutions ser for 7q2-28=0 is 2 and -2
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3. At a zoo, the lion pen has a ring-shaped sidewalk around it. The outer edge of the sidewalk is a circle with a radius of 11 m. The inner edge of the sidewalk is a circle with a radius of 9 m.
(a) Write and simplify an expression for the exact area of the sidewalk.
(b) Find the approximate area of the sidewalk. Use 3.14 to approximate π.
A machine can produce 27 inches of ribbon in 3 minutes.how much ribbon can the machine produce in 1 hour produce in 1 hour?
Which ordered pair will be the solution for the function y = 12 - x?
(7, 4)
(6, 6)
(4, 9)
(2, 14)
The solution to the function y = 12 - x is the ordered pair (6, 6) because when we substitute x = 6 into the function, the result, y, is also 6, which matches the given y-value in the pair.
Explanation:To find the ordered pair that is a solution for the function y = 12 - x, we need to substitute the x-values of each given ordered pair into the equation and see which one gives a resulting y-value that matches the one in the pair.
(7, 4): y = 12 - 7 = 5 – This does not match the y-value of 4.(6, 6): y = 12 - 6 = 6 – This is correct, as it matches the y-value of 6.(4, 9): y = 12 - 4 = 8 – This does not match the y-value of 9.(2, 14): y = 12 - 2 = 10 – This does not match the y-value of 14.Therefore, the solution to the function is the ordered pair (6, 6).
Ava rounded 19,350 to the nearest thousand and got 20,000. Which of the following statements is true? Ava rounded correctly. Ava rounded incorrectly; the answer should be 19,400. Ava rounded incorrectly; the answer should be 19,000. Ava rounded incorrectly; the answer should be 19,300.
The sum of the first 30 terms of the sequence an=6n+5 is
Answer:
[tex]S_{30}=2940[/tex].
Step-by-step explanation:
Given : [tex]a_{n} =6n+5[/tex].
To find : The sum of the first 30 terms .
Solution: We have given [tex]a_{n} =6n+5[/tex].
For n = 1
[tex]a_{1} =6(1)+5[/tex].
[tex]a_{1} =6+5[/tex].
[tex]a_{1} =11[/tex].
For n =2
[tex]a_{2} =6(2)+5[/tex].
[tex]a_{2} =17[/tex].
Common difference = 17 - 11 = 6.
Sum of nth term : [tex]S_{n} =\frac{n}{2}[2a+(n-1)d][/tex].
d = common difference = 6.
For n = 30 .
[tex]S_{30} =\frac{30}{2}[2(11+(30-1)6][/tex].
[tex]S_{30} =15[22+29 *6][/tex].
[tex]S_{30} =15[22+29 *6][/tex].
[tex]S_{30} =15[22+174][/tex].
[tex]S_{30} =15[196][/tex].
[tex]S_{30}=2940[/tex].
Therefore, [tex]S_{30}=2940[/tex].
Jerry goes to the bank and borrows $9,000 for farm equipment. The simple yearly interest is 9.5% and he pays off the loan over a period of 2 years with 24 equal monthly payments. What’s Jerry’s monthly payment
Jerry's monthly payment can be calculated using the formula for the monthly payment on a loan. Plugging in the given values will give the exact monthly payment amount.
Explanation:To calculate Jerry's monthly payment, we can use the formula for the monthly payment on a loan:
Monthly Payment = P × r × (1 + r)^(n) / ((1 + r)^(n) - 1)
Where:
P is the principal amount borrowed, which is $9,000r is the monthly interest rate, which is calculated by dividing the annual interest rate by 12 and converting it to a decimal. In this case, it would be 9.5% / 12 = 0.0079 (rounded to four decimal places)n is the total number of payments, which is 2 years × 12 months = 24 monthsPlugging in the values:
Monthly Payment = $9,000 × 0.0079 × (1 + 0.0079)^(24) / ((1 + 0.0079)^(24) - 1)
Simplifying this equation will give us the monthly payment amount.
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♦Dawson, a 42-year-old male, bought a $180,000, 20-year life insurance policy. What is Dawson's annual premium? Use the table.
♦Rachel, a 45-year-old female, bought a $120,000, a 20-year life insurance policy through her employer. Rachel is paid biweekly. How much is deducted from each of her paychecks for life insurance? Use the Table.
♦Dawson, a 42-year-old male, bought a $180,000, 20-year life insurance policy. What is Dawson's annual premium? Use the table.
Dawson is 42, with a 20 year premium coverage, which will amount to $13.68 per $1000. Multiply $13.68 with 180 (because there are 180 $10,000)
13.68 x 180 = $2462.40
annual premium = $2462.40
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To solve the next one, Rachel bought a 20 year life insurance, which amounts to $17.56 per $1000
$63.14 is your answer
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hope this helps
The coordinates of triangle DEF are Upper D left parenthesis 3 comma 3 right parenthesis, Upper E left parenthesis 8 comma 3 right parenthesis, and Upper F left parenthesis 5 comma 7 right parenthesis. If you translate triangle DEF 2 units right and 3 units down, what are the coordinates of Upper E'?
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The least common denominator of two fractions is 30. If you add the two denominators, their sum is 17. What are the denominators?
What is general form of equation of a circle with center at (a,b) and radius of length m?
The general form of the equation of a circle with centre at [tex]\((a, b)\)[/tex] and radius [tex]\(m\)[/tex] is: [tex]\[ x^2 + y^2 - 2ax - 2by + (a^2 + b^2 - m^2) = 0 \][/tex].
The general form of the equation of a circle is [tex]\( (x - h)^2 + (y - k)^2 = r^2 \)[/tex], where [tex]\((h, k)\)[/tex] represents the centre of the circle and [tex]\(r\)[/tex] represents the radius.
If we expand and rearrange this equation, we get [tex]\( x^2 + y^2 - 2hx - 2ky + (h^2 + k^2 - r^2) = 0 \)[/tex].
Comparing this with the given options, we see that [tex]\( h = a \), \( k = b \), and \( r = m \)[/tex].
Substituting these values into the general form, we get [tex]\( x^2 + y^2 - 2ax - 2by + (a^2 + b^2 - m^2) = 0 \)[/tex], which matches the correct option.
Complete Correct Question:
What is the general form of the equation of a circle with center at (a, b) and radius of length m?
a. x2 + y2 - 2ax - 2by + (a2 + b2 - m2) = 0.
b. x2 + y2 + 2ax + 2by + (a2 + b2 - m2) = 0.
c. x2 + y2 - 2ax - 2by + (a2 + b2 + m2) = 0.
d. x2 + y2 + 2ax + 2by + a2 + b2 = -m2.
The perimeter of a rectangular outdoor patio is 60 ft. the length is 4 ft greater than the width. what are the dimensions of the patio? l w
The length of rectangular outdoor patio is 17 feet and the width is 13 feet.
Given that, the perimeter of a rectangular outdoor patio is 60 ft.
What is the perimeter of a rectangle?The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).
Let the width of the rectangular outdoor patio be x.
Then, the length is 4 ft greater than the width = x+4
Now, perimeter = 2(x+x+4)
⇒ 2(2x+4) = 60
⇒ 4x+8=60
⇒ 4x=52
⇒ x=13
Length = x+4 = 17
Therefore, the length of rectangular outdoor patio is 17 feet and the width is 13 feet.
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A small tree was planted at a height of 10 feet. The tree has been planted for 14 months, and is now 49.2 feet tall. Which equation could be used to find x, the average number of feet the tree grew each month?
There are 20,000 owls in the wild. Every year the population decreases by 8%. How many owls will there be after 8 years?
After 8 years, there will be approximately 10,260 owls remaining in the wild. This calculation is based on an initial population of 20,000 owls decreasing by 8% annually, yielding a final population using the formula for exponential decay.
To find out how many owls will remain after 8 years, we can use the formula for exponential decay:
[tex]\[ \text{Final population} = \text{Initial population} \times (1 - \text{Rate of decrease})^{\text{Number of years}} \][/tex]
Given:
Initial population (P) = 20,000 owls
Rate of decrease (r) = 8% = 0.08
Number of years (t) = 8
Plugging in the values:
[tex]\[ \text{Final population} = 20,000 \times (1 - 0.08)^8 \][/tex]
[tex]\[ \text{Final population} = 20,000 \times (0.92)^8 \][/tex]
[tex]\[ \text{Final population} \approx 20,000 \times 0.513 \][/tex]
[tex]\[ \text{Final population} \approx 10,260 \][/tex]
So, after 8 years, there will be approximately 10,260 owls remaining in the wild.