Chris should construct the enclosure with a width of 5 feet and a length of 10 feet, using her 15 feet of fencing material, which will result in a maximum enclosed area of 50 square feet.
Chris wants to construct an enclosed rectangular area for a mulch pile and use her backyard's corner fence effectively, thereby constructing only two sides of the mulch pile enclosure. She has 15 feet of fencing material to use and wants the length of the rectangular enclosure to be twice the width. To find the dimensions that will produce the maximum area, we can set up an equation.
Let x represent the width (in feet) and 2x represent the length (in feet), since the length is twice the width.
Since Chris is using the corner of the yard, she only needs to construct two sides of the fence.
Therefore, the amount of fencing material she will use (perimeter of two sides) is given by the equation x + 2x = 15, which simplifies to 3x = 15.
Solving for x, we find that x = 5 feet. Thus, the width of the enclosure is 5 feet, and the length is twice that, or 10 feet.
The maximum area that Chris can enclose is therefore 5 ft imes 10 ft = 50 square feet.
If a < 0 and b > 0, then the point (a, b) is in Quadrant A) I. B) II. C) III. D) IV.
Answer:
The actual answer is D
The point (a, b) lies in the second quadrant. Then the correct option is B.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
If a < 0 and b > 0.
Then the point (a, b) is in Quadrant will be given as,
If a > 0 and b > 0, then the points is in first quadrant.If a < 0 and b > 0, then the points is in second quadrant.If a < 0 and b < 0, then the points is in third quadrant.If a > 0 and b < 0, then the points is in fourth quadrant.Thus, the point (a, b) lies in the second quadrant.
Then the correct option is B.
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In a parking lot of 240 red and blue cars, the ratio of red cars to blue cars is 3 : 5.
How many red cars are in the parking lot?
3+5 = 8
240/8 = 30
30*3 = 90 red cars
PLEASE HELP ME ASAP 40 POINTS AND BRAINLIEST SHOW WORK
Find the variables and the lengths of the sides of this kite
Which quotient is equivalent to the mixed number
2
2---------- =
3
answer in fractions
Final answer:
To convert 2 2/3 to an improper fraction, multiply the whole number by the denominator and add the numerator, resulting in 8/3. The question lacks details to provide another specific quotient to compare this with. In dividing fractions, multiplication by the reciprocal is used to find equivalent quotients.
Explanation:
To find which quotient is equivalent to the mixed number 2 2/3, we must first convert the mixed number to an improper fraction. A mixed number is composed of a whole number and a fraction, which can be converted into an improper fraction by multiplying the denominator by the whole number and then adding the numerator to this product.
For the mixed number 2 2/3, we multiply the whole number 2 by the denominator 3, giving us 6, and then add the numerator 2, resulting in 8. Therefore, 2 2/3 as an improper fraction is 8/3.
However, without context, it's unclear what other quotient we are being asked to compare with the mixed number 2 2/3. Quotients can refer to the result of any division. Nonetheless, in contexts of dividing fractions, we use the multiplication of the inverse to find equivalent quotients. For example, if dividing by 3/1 (which is the same as dividing by 3), we would multiply by its reciprocal, 1/3.
In cases of conversion factors, we could use a factor that equals 1 to convert units without changing the value. For instance, 1 m / 100 cm is a conversion factor that equals 1, allowing us to convert meters to centimeters without changing the quantity.
Remember, multiplication and division in fractions can be seen as interconnected operations, where dividing by a number is the same as multiplying by its reciprocal.
solve for t. use the quadratic formula.
d=−16t^2+12t
Answer:
[tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{3+\sqrt{9+4d}}{8}[/tex]
Step-by-step explanation:
Given: d = -16t² + 12t
To find: t using quadratic formula
If we have quadratic equation in form ax² + bx + c = 0
then, by quadratic formula we have
[tex]x\,=\,\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Rewrite the given equation,
-16t² + 12t - d = 0
from this equation we have,
a = -16 , b = 12 , c = d
now using quadratic formula we get,
[tex]t\,=\,\frac{-12\pm\sqrt{12^2-4\times(-16)\times d}}{2\times(-16)}[/tex]
[tex]t\,=\,\frac{-12\pm\sqrt{144+64d}}{-32}[/tex]
[tex]t\,=\,\frac{-12\pm\sqrt{16(9+4d)}}{-32}[/tex]
[tex]t\,=\,\frac{-12\pm4\sqrt{9+4d}}{-32}[/tex]
[tex]t\,=\,\frac{4(-3\pm\sqrt{9+4d})}{-32}[/tex]
[tex]t\,=\,\frac{-3\pm\sqrt{9+4d}}{-8}[/tex]
[tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:,\:\:\frac{-3-\sqrt{9+4d}}{-8}[/tex]
[tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{-(3+\sqrt{9+4d})}{-8}[/tex]
[tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{3+\sqrt{9+4d}}{8}[/tex]
Therefore, [tex]t\,=\,\frac{-3+\sqrt{9+4d}}{-8}\:\:and\:\:\frac{3+\sqrt{9+4d}}{8}[/tex]
Answer:
[tex]\frac{3-\sqrt{9-d}} {8}\text{ or }t=\frac{3+\sqrt{9-d}} {8}[/tex]
Step-by-step explanation:
Here, the given expression,
[tex]d= -16t^2+12t[/tex]
[tex]\implies -16x^2+12t-d=0[/tex] ------(1)
Since, if a quadratic equation is,
[tex]ax^2+bx+c=0[/tex] ------(2)
By using quadratic formula,
We can write,
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
By comparing equation (1) and (2),
We get, a = -16, b = 12, c = -d,
[tex]t=\frac{-12\pm \sqrt{12^2-4\times -16\times -d}}{2\times -16}[/tex]
[tex]t = \frac{-12\pm \sqrt{16\times 9-16\times d}}{-32}[/tex]
[tex]t = \frac{-12\pm \sqrt{16}\times \sqrt{9-d}} {-32}[/tex]
[tex]t = \frac{-12\pm 4\sqrt{9-d}} {-32}[/tex]
[tex]t = \frac{4(-3\pm \sqrt{9-d})} {4(-8)}[/tex]
[tex]t = \frac{-3\pm \sqrt{9-d}} {-8}[/tex]
[tex]t = \frac{-3+\sqrt{9-d}} {-8}\text{ or }t=\frac{-3-\sqrt{9-d}} {-8}[/tex]
[tex]\implies t = \frac{3-\sqrt{9-d}} {8}\text{ or }t=\frac{3+\sqrt{9-d}} {8}[/tex]
Which is the required solution.
WILL GIVE A BRAINLESTTTT
What is the solution of 3x+8/x-4 >= 0
Answer:
The inequality is given to be :
[tex]\frac{3x+8}{x-4}\geq 0[/tex]
The inequality will be greater than or equal to 0 if and only if both the numerator and denominator of the left hand side will have same sign either both positive or both negative.
CASE 1 : Both positive
3x + 8 ≥ 0
⇒ 3x ≥ -8
[tex]x\geq \frac{-8}{3}[/tex]
Also, x - 4 ≥ 0
⇒ x ≥ 4
Now, Taking common points of both the values of x
⇒ x ∈ [4, ∞)
CASE 2 : Both are negative
3x + 8 ≤ 0
⇒ 3x ≤ -8
[tex]x\leq \frac{-8}{3}[/tex]
Also, x - 4 ≤ 0
⇒ x ≤ 4
So, Taking common points of both the values of x we have,
[tex]x=(-\infty,-\frac{8}{3}][/tex]
So, The solution of the equation will be the union of both the two solutions
So, Solution is given by :
[tex]x=(-\infty,-\frac{8}{3}]\:U\:[4,\infty)[/tex]
What is the area of the composite figure whose vertices have the following coordinates? (−1, 5) , (3, 5) , (7, 3) , (3, 0) , (−1, 1)
Answer:
28
Step-by-step explanation:
Square: 4 * 4 = 16
Small Triangle: 1 * 4 = 4 / 2 = 2
Large Triangle: 5 * 4 = 20 / 2 = 10
16 + 2 + 10 = 28
Find the area of the given triangle. Round the answer to the nearest tenth.
A.
7.9 square units
B.
149.4 square units
C.
2,055.6 square units
D.
2,071.8 square units
Answer:
B) Area of triangle = 149.4 square units.
Step-by-step explanation:
Given : A triangle with sides 16 , 19, 27 .
To find : Area of a triangle.
Solution : We have given that triangle with sides 16 , 19, 27 .
Using heron's formula :
Area of triangle: [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex].
Where, s = [tex]\frac{a+b+c}{2}[/tex] and a,b,c are sides of triangle.
Then s = [tex]\frac{16+19+27}{2}[/tex].
s = 31 units.
Area of triangle = [tex]\sqrt{31(31-16)(31-19)(31-27)}[/tex].
Area of triangle = [tex]\sqrt{31(15)(12)(4)}[/tex].
Area of triangle = [tex]\sqrt{22320)}[/tex].
Area of triangle = 149.39 square units.
Area of triangle = 149.4 square units. ( nearest tenth)
Therefore, B) Area of triangle = 149.4 square units.
Write the quadratic equation whose roots are −4 and 3 , and whose leading coefficient is 1 .
Final answer:
To write a quadratic equation with roots −4 and 3 and a leading coefficient of 1, we start with the factored form (x - root1)(x - root2) = 0, substitute the given roots, and simplify to x² + x - 12 = 0.
Explanation:
The question asks us to write the quadratic equation whose roots are −4 and 3, and whose leading coefficient is 1. To find a quadratic equation given its roots, we can use the factored form of a quadratic equation, which is (x - root1)(x - root2) = 0, where root1 and root2 are the roots of the equation.
Given that the roots are −4 and 3, we substitute these values into the equation to get (x - (−4))(x - 3) = 0. Simplifying this, we first eliminate the double negative to get (x + 4)(x - 3) = 0. Multiplying these two binomials gives us the expanded form, which is x² + x - 12 = 0. This is the quadratic equation with roots −4 and 3, and a leading coefficient of 1.
Bill and Greg are walking in opposite directions with speeds of 45 and 75 feet per minute. When they started, the distance between them was 20 feet. What will be the distance between them in 2.5 min?
Answer:
320 ft
Step-by-step explanation:
I'm not sure how the other person was awarded brainliest answer because that answer is pretty far off. But the work was good just they messed up. Also kinda sad he is a brainly teacher and still has incorrect answers.
Check my answers? GIving medal:
7. What is the slope of the line that passes throught the pair of points (1, 7) and (10, 1)?
a. 3/2
b. -2/3
c. -3/2
d. 2/3 <--
8. What is the slope of the line that passes through the points (-5.5, 6.1) and (-2.5, 3.1)?
a. -1
b. 1
c. -3 <--
d. d
9. what is the slope of the line that passes through the pair of points (-7/3, -3) and (-5, 5/2)?
a. 6/22 <--
b. -6/22
c. 22/6
d. -22/6,
Number seven Is B. -2/3
MEDAL!
This Chinese painting is composed small cliffs in the background and a small building with trees in the foreground. This composition reflects what Taoist and Buddhists principle or philosophy?
a) simplicity
b) perseverance
c) harmony
or...
d) balance
btw- I know this is in the wrong section but no one was answering it in the art history section
A square is cut out of a circle whose diameter is approximately 14 feet. What is the approximate area of the remaining portion of the circle in square feet?
A square is cut from a circle with a 14-foot diameter. Remaining circle area ≈ 53.86 sq ft here nearest round off option is c. 50 square feet.
To find the area of the remaining portion of the circle after a square with a side of 10 feet is cut out,
Find the area of the square:
Area of square
= side × side
= 10 feet × 10 feet
= 100 square feet
Find the radius of the circle:
The diameter is approximately 14 feet, so the radius is half of that:
Radius = 14 feet / 2 = 7 feet
Find the area of the entire circle:
Area of circle = π × radius²
Area of circle
= π × (7 feet)²
≈ 153.86 square feet (using π ≈ 3.14)
Subtract the area of the square from the area of the circle to find the remaining portion:
Remaining area = Area of circle - Area of square
Remaining area
≈ 153.86 square feet - 100 square feet
≈ 53.86 square feet
Therefore, the approximate area of the remaining portion of the circle is approximately 53.86 square feet nearest option is c. 50 square feet.
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The above question is incomplete , the complete question is:
A square is cut out of a circle whose diameter is approximately 14 feet. What is the approximate area of the remaining portion of the circle in square feet?
Attached figure
need help so much ...
Dominik paid three-quarters of a dollar for a newspaper. Which amount is equivalent to the cost of the newspaper?
A $250,000 home loan is used to purchase a house. The loan is for 30 years and has a 5.4% APR. Use the amortization formula to determine the amount of the monthly payments.
If the expected adult of a 2 week old puppy is 20 pounds how many grams per day should they gain?
PLEASE HELP ASAP
EXTRA POINTS
Sheila places a 54 square inch photo behind a 12-inch-by-12-inch piece of matting.
The photograph is positioned so that the matting is twice as wide at the top and bottom as the sides.
Write an equation for the area of the photo in terms of x.
Which foundation drawing matches this orthographic drawing? ( just tell me what picture)
The function graphed approximates the height of an acorn, in meters, x seconds after it falls from a tree.
After about how many seconds is the acorn 5 m above the ground?
The equation of the parabola is y = – 5x² + 20. The time when an acorn is 5 m above the ground in 1.7 seconds. Then the correct option is C.
What is the parabola?It is the locus of a point that moves so that it is always the same distance from a non-movable point and a given line. The non-movable point is called focus and the non-movable line is called the directrix.
The function graphed approximates the height of an acorn, in meters, x seconds after it falls from a tree.
We know that the equation of the parabola will be given as
y = a(x - h)² + k
where (h, k) is the vertex of the parabola and a is the constant.
We have
(h, k) = (0, 20)
Then
y = ax² + 20
The parabola is passing through (2, 0), then we have
0 = 4a + 20
a = -5
Then we have
y = – 5x² + 20
The time in seconds when the acorn is 5 m above the ground.
–5x² + 20 = 5
–5x² = –15
x = 1.7
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Write the first five terms of a sequence. Don’t make your sequence too simple. Write both an explicit formula and a recursive formula for a general term in the sequence. Explain in detail how you found both formulas.
Answer: The answer is 5, 10, 20, 40 and 80.
Step-by-step explanation: We are to write the first five terms of a sequence, along with the explicit and recursive formula for the general term of the sequence.
Let the first five terms of a sequence be 5, 10, 20, 40 and 80. These terms are taken from a geometric sequence with first term [tex]a_1 5[/tex] and common ratio [tex]r=2.[/tex]
Therefore, we have
[tex]a_2=a_1\times r,\\\\a_3=a_2\times r,\ldots[/tex]
Therefore, the recursive formula is
[tex]a_{n+1}=2a_n,~~a_1=5.[/tex]
And explicit formula is
[tex]a_n=a_1r^{n-1}.[/tex]
Answer:
Let the first five terms of a sequence be, 4,8,12,20,24
Ok, let me explain the meaning of term explicit and Recursive formula.
Explicit formula ,is the general formula to find any term of the sequence.
And, Recursive formula, is the method by which, we can find the nth term of the sequence if (n-1)th term of the sequence is known.
So,the explicit formula for the sequence is,
y = 4 n, where , n is any natural number.
And the recursive formula is .
y = 4 (n-1), with the help of (n-1)th term we can find nth term.
First term =4=4 × 1
Second term =8 =4 × 2
Third term =12=4×3
Fourth term =16 =4 × 4
.....................
...........................
.................................
(n-1) th term =4 × (n-1)
nth term =4 × n
Applying the simple procedure by looking at the first , second and the way the next term goes , the general and recursive formula is obtained.
As, you said you don't want simpler sequence
Consider the first five terms of the sequence, 0, 3,8,15, 24.
Explicit formula =n² + 2 n
Recursive formula=(n-1)²+2(n-1)
If,you will look at the sequence, it is neither Arithmetic nor geometric .
First term =0=0²+0×0
Second term =3=1+2=1²+2 × 1
Third term =8=4+4=2²+2×2
Fourth term =15=9+6=3²+2×3
Fifth term =24=16 +8=4²+2×4
So, Explicit formula= n²+ 2 n, where n is a whole number.
Use the Remainder Theorem to find the remainder: (–6x3 + 3x2 – 4) ÷ (2x – 3).
23
-17.5
-4.4444444...
-0.8888888...
The remainder obtained when we carry out the operation (-6x³ + 3x² - 4) ÷ (2x - 3) is -17.5 (2nd option)
How do i determine the remainder?The following data were obtained from the question:
Expression = (-6x³ + 3x² - 4) ÷ (2x - 3)Remainder =?Using the remainder theorem, we can obtain the remainder as illustrated below:
Let
f(x) = -6x³ + 3x² - 4
2x - 3 = 0
From 2x - 3 = 0, make x the subject as shown below:
2x - 3 = 0
x = 3/2
Substitute the value of x into f(x). We have:
f(x) = -6x³ + 3x² - 4
f(3/2) = -6(3/2)³ + 3(3/2)² - 4
= -6(27/8) + 3(9/4) - 4
= -20.25 + 6.75 - 4
= -17.5
Thus, we can conclude that the remainder obtained when (-6x³ + 3x² - 4) is divided by (2x - 3) is -17.5 (2nd option)
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Ella sold 37 necklaces for $20 each at the craft fair. She is going to donate half of the money she earned to charity. Use the Commutative Property to mentally find how much money she will donate. Explain the steps you used.
Ella sold 37 necklaces for $20 each at the craft fair. She is going to donate half of the money she earned to charity. Use the Commutative Property to mentally find how much money she will donate. Explain the steps you used.
Solution:
Earning from 1 necklace=$20
Earning from 37 necklaces=$20*37
Half of the earnings= [tex] \frac{20*37}{2} =\frac{20}{2}*37=10*37 [/tex]
Half of the earnings=$10*37
Now, Applying Commutative Propert, a*b=b*a
So, Money she need to donate= Half of the earnings= 10*37 =37*10
So, Money she donates=$370
money she will donate=$370
A car travels 3 times around a traffic circle whose radius is 80 feet. What is the distance the car will travel? Use 3.14 for π . Enter your answer in the box. ft
Answer : Distance will be 1507.2 feet .
Explanation :
Since we have given that
Radius of circle = 80 feet
So,
Circumference of circle is given by
[tex]2\pi r=2\times 3.14\times 80=502.4 \text{ feet}[/tex]
Since , a car travels 3 times around a traffic circle.
So,
[tex]\text{ Distance covered by the car will travel}= 3\times 502.4= 1507.2 \text{ feet }[/tex]
So, Distance will be 1507.2 feet .
A new car is purchased for 20700 dollars. The value of the car depreciates at 13.75% per year. What will the value of the car be, to the nearest cent, after 12 years?
Answer:
USD 3,508.16
Step-by-step explanation:
Hello
Let´s see what happens the first year when the car depreciates 13.75% of 20700 USD
[tex]depreciation=20700*\frac{13.75}{100} =2846.25 USD\\[/tex]
at the end of the first year the car will have a price of 20700-2486.25=17853.75 USD, and this will be the price at the beginning of the second year.
completing the data for the 12 years with the help of excel you get
depreciation New Value
end of year 1 USD 20,700.00 USD 2,846.25 USD 17,853.75
end of year 2 USD 17,853.75 USD 2,454.89 USD 15,398.86
end of year 3 USD 15,398.86 USD 2,117.34 USD 13,281.52
end of year 4 USD 13,281.52 USD 1,826.21 USD 11,455.31
end of year 5 USD 11,455.31 USD 1,575.10 USD 9,880.20
end of year 6 USD 9,880.20 USD 1,358.53 USD 8,521.68
end of year 7 USD 8,521.68 USD 1,171.73 USD 7,349.94
end of year 8 USD 7,349.94 USD 1,010.62 USD 6,339.33
end of year 9 USD 6,339.33 USD 871.66 USD 5,467.67
end of year 10 USD 5,467.67 USD 751.80 USD 4,715.87
end of year 11 USD 4,715.87 USD 648.43 USD 4,067.43
end of year 12 USD 4,067.43 USD 559.27 USD 3,508.16
after 12 years the car will ha a value of USD 3508.16
you can verify this by applying the formula
[tex]v_{2} =v_{1} (1-\frac{depreciatoin}{100} )^{n} \\\\v_{2} =20700 (1-\frac{13.75}{100} )^{12} \\v_{2} = 20700*0.1694\\v_{2} = 3508.16 USD[/tex].
Have a great day.
The value of a new car, originally priced at $20,700 and depreciating at 13.75% per year will be approximately $1446.63 after 12 years. This is calculated using a compound interest formula with a negative rate.
Explanation:In order to solve this, we are going to use the formula for compound interest. Although we're actually dealing with depreciation, the calculation is the same as for interest, we just use a negative rate. The formula is P(t) = P0 * (1 + r) ^t, where P(t) is the value of the car after time t, P0 is the initial price of the car, r is the rate of depreciation, and t is time.
Here P0 = $20,700, r = -13.75% = -0.1375 (remember to convert rate from percentage to a proportion), and t = 12 years.
Substituting these values into the formula, we get: P(t) = 20700 * (1 - 0.1375)^12. Using a calculator, the value of the car after 12 years, to the nearest cent, is approximately $1446.63.
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if you received an annual salary of 33500 paid monthly what would your gross pay be each pay period
Look at the data in the table below
X Y
4. 9
12. 28
7. 14
9. 20
5. 9
12. 30
10. 22
Which graph shows the best fit for this data
Abit is planning a birthday party for his grandfather. He bought a cake for $18. He also wants to buy some balloons, which are $4 each. Abit has $35 to spend all together. How much money will Abit have left after he buys the cake and as many balloons as possible?
***mathtest timed***
Given the data set for the length of time a person has been jogging and the person's speed, hypothesize a relationship between the variables.
A) I would expect the data to be positively correlated.
B)I would expect the data to be negatively correlated.
C) I would expect no correlation.
D) There is not enough information to determine correlation.
Your assigned 32 math exercises for homework you complete 87.5of these before dinner how many do you hav to do after dinner.