Answer:
Step-by-step explanation:
"Rectangular" includes "square," and in fact treating the rectangle as a square is the fastest way to "solve" this problem. The perimeter of the rectangular area is 160 ft; dividing that by 4 yields 40 ft. "40 ft square" describes the rectangle maximum area: (40 ft)^2 = 1600 ft^2.
Alternatively, let W and L represent the width and length of the rectangle. Then:
P = perimeter = 2W + 2L = 160 ft, or W + L = 80 ft, or W = 80 ft - L.
A = area = L*W = L(80 ft - L) = 1600 ft^2. Rewriting this as a proper quadratic:
80L - L^2 - 1600 = 0, or L^2 - 80L + 1600. Note that this last result factors into (L - 40)^2 = 0, so L = 40 ft. Then W = 80 ft - 40 ft = 40 ft.
This confirms that the max area is 1600 ft^2 = (40 ft)^2.
Final answer:
To find Tina's dog's fenced area dimensions, use an algebraic model with area and perimeter equations to solve for the dimensions optimizing the given constraints.
Explanation:
To determine the dimensions of the rectangular area for Tina's dog:
Algebraic Model: Let the length of the rectangle be 'l' and the width be 'w'. The algebraic equation to represent the area and perimeter constraints is lw = 1600 and 2l + 2w = 160, respectively.Calculations: Using the constraint equations, you can solve for the dimensions. For example, you can write 'l = 80/w' from the perimeter equation, substitute it into the area equation, and solve to find the dimensions.Reasoning: By setting up and solving the system of equations, you can find the dimensions that maximize the area within the given perimeter, ensuring Tina's dog has the desired 1600 square feet while staying within the budget of 160 feet of fence.Which of the following is the correct point-slope equation for the line that passes through the point (5,-6) and is parallel to the line given by y= -10x+ 3?
A. y+6= -10 (x-5)
B. y-6=-10(x-5)
C. y-60=-10 (x-5)
D. y-60=-4x-5
bearing in mind that parallel lines have the same exact slope, hmmm what is the slope of y = -10x + 3 anyway?
[tex]\bf y=\stackrel{\downarrow }{-10}x+3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies (\stackrel{x}{5},\stackrel{y}{-6})~\hfill \begin{array}{llll} y-(-6)=-10(x-5) \\\\\\ y+6=-10(x-5) \end{array}[/tex]
A 20 foot ladder is resting against the side of the house the base of the latter is 4 feet away from the house approximately how high above the ground is the latter touch the house
The ladder resting against the house forms a triangle similar to the one in the image below
To answer this question you must use Pythagorean theorem
[tex]a^{2} +b^{2}=c^{2}[/tex]
a and b are the legs (the sides that form a perpendicular/right angle)
c is the hypotenuse (the side opposite the right angle)
In this case...
a = x
b = 4
c = 20
^^^Plug these numbers into the theorem
[tex]x^{2} +4^{2} =20^{2}[/tex]
solve for x
[tex]x^{2}[/tex] + 16 = 400
[tex]x^{2}[/tex] = 384
x = 8√6
or
x ≈ 19.5959....
Hope this helped!
~Just a girl in love with Shawn Mendes
What is the value of x?
A. 52
B.60
C.86
D.26
Answer:
26
Step-by-step explanation:
x is a degree so it can't be no more then 60 so the angle should be 26
The value of x is 60 degrees, as determined through a series of geometric deductions based on the properties of triangles and semicircles. Here option B is correct.
The sum of the angles in a triangle is 180 degrees.
The sum of the angles in a semicircle is 180 degrees.
The angle opposite to the diameter of the circle is 90 degrees.
Therefore, the angle x in the first triangle is 180 - 90 - 52 = 38 degrees.
The angle x in the second triangle is 180 - 38 - x = 142 - x degrees.
The angle x in the second triangle is also equal to the angle x in the semicircle, which is 180 - 52 - x = 128 - x degrees.
Equating the two expressions for the angle x in the second triangle, we get 142 - x = 128 - x.
Solving for x, we get x = 60 degrees. Here option B is correct.
To learn more about value
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19. The probability that Roberto wins is the
probability that Roberto loses. What is the
probability that Roberto loses?
-
who ales
Answer:
Roberto wins:1/4
roberto loses:3/4
Step-by-step explanation:
Answer:
Roberto wins:1/4
roberto loses:3/4
Step-by-step explanation:
35 points?with explanation
Answer:
m∠7 = 142°
Step-by-step explanation:
Note that a straight line's degree measurement = 180°
Note that the angle directly next to (to the left of) m∠7 has a measurement of 38°. Subtract 38 from 180:
180 - 38 = 142
m∠7 = 142°
~
Answer:
m∠7 = 142°
straight line's degree measurement = 180°
Then get the adjacent angle of 38. Subtract 38 from 180:
180 - 38 = 142
m∠7 = 142°
Hope this helped
Find the 6th term of the geometric sequence whose common ratio is 1/2 and whose first term is 6.
Answer:
3/16
Step-by-step explanation:
The nth term of a geometric series is:
an = a₁ (r)^(n - 1)
Given a₁ = 6, r = 1/2, and n = 6:
a₆ = 6 (1/2)^(6 - 1)
a₆ = 3/16
The circumference of Z is 104 cm. What is the length of xy (the minor arc)?
A. 13 cm
B. 416 cm
C. 52 cm
D. 208 cm
E. 6.5 cm
F. 26 cm
A full circle is 360 degrees.
XY is 45 degrees.
Multiply the circumference by the fraction of the angle:
104 x (45/360) = 13
The answer is A. 13 cm.
Answer:
Arc length = 13 cm.
Step-by-step explanation:
Given : A circle with circumferences = 104 cm , central angle = 45°.
To find : what is the length of arc AB.
Solution : We have given circle with circumference = 104 cm , central angle = 45°.
Arc length = [tex]\frac{theta }{360} * circumference[/tex].
Plug the values circumference = 104 cm , central angle = 45°.
Arc length = [tex]\frac{45 }{360} * 104[/tex].
Arc length = 0.125 * 104
Arc length = 13 cm .
Therefore, Arc length = 13 cm.
What is the equation of the quadratic graph with a focus of (3, 6) and a directrix of y=4
Final answer:
The equation of the quadratic graph with a focus of (3, 6) and a directrix of y=4 is (x-3)² = 4(y-5).
Explanation:
To find the equation of a quadratic graph with a focus of (3, 6) and a directrix of y=4, you'll need to use the definition of a parabola. A parabola is the set of all points that are equidistant from a single point, called the focus, and a line, known as the directrix. In this case, since the directrix is horizontal (parallel to the x-axis) and the focus has a y-coordinate greater than the directrix, the parabola opens upwards.
The vertex of the parabola is equidistant from the focus and directrix, so its y-coordinate is halfway between the focus's y-coordinate and the directrix's y-value, which is 5. Because the x-coordinate of the focus is 3, the vertex is at (3, 5). The equation of a parabola in vertex form is (x-h)² = 4p(y-k), where (h,k) is the vertex and 4p is the distance between the vertex and the focus or the vertex and the directrix.
In this problem, the distance p is 1 (since the y-coordinates of the vertex and focus differ by 1). Thus, the equation of the parabola is (x-3)² = 4(y-5). This is the standard quadratic form for a parabola opening upwards with vertex at (3, 5) and focus at (3, 6).
Translate “the sum of 6 and the product of 8 and x” into a mathematical expression
Answer:
8x+ 6 is the translated mathematical expression.
Step-by-step explanation:
We are given the following English expression which are to translate into a mathematical expression:
'The sum of 6 and the product of 8 and x” into a mathematical expression'
Translating it in small chunks:
1. the sum of 6 ---> +6
2. product of 8 and x ---> 8x
Therefore, combining these we get the mathematical expression 8x + 6
For this case we must rewrite the given expression mathematically.
The sum of 6 and something else is written as:
[tex]6+[/tex]
The product of 8 and x is written as:
[tex]8x[/tex]
Finally, the expression is given by:
[tex]6 + 8x[/tex]
Answer:
The expression is given by:
[tex]6 + 8x[/tex]
at a local soccer game, 6/7 of the people were fans. one-half of those fans were wearing hats. what fraction of the people was wearing hats?
- If 2x2 + 8y = 121.5 and x2 - 8y = 121.5, then x =
9
6.36
16
7
Step-by-step explanation:
2x² + 8y = 121.5
x² - 8y = 121.5
Add the equations together to eliminate the y terms.
3x² = 243
x² = 81
x = 9
A parabola passes through the points (-3,0), (-2,3), and (-1,4). What function does it represent? Use the graphing tool to determine the function.
A.
f(x) = -x2 + x + 3
B.
f(x) = -2x2 − x + 3
C.
f(x) = -x2 − 2x + 3
D.
f(x) = 2x2 − x − 3
Answer: C
Step-by-step explanation:
(-1,4) is the vertex. reflect (-2,3) and (-3,0) onto the other side of the y-axis. you may use desmos to plug in the functions and the answer will be C, since it goes through the points given and reflected.
Final answer:
The function represented by the given set of points is f(x) = -x^2 - 2x + 3.
Explanation:
To determine the function represented by the given set of points, we can use the general form of a quadratic equation, y = ax^2 + bx + c. Substituting the points (-3,0), (-2,3), and (-1,4) into the equation, we can set up a system of equations and solve for the values of a, b, and c. The resulting function is f(x) = -x^2 - 2x + 3, which corresponds to option C.
Which arrow do I follow left or right?
6 < k
k is greater then 6. That means that you will go to the right of 6. This will show that k can be any number larger then 6
Hope this helped!
~Just a girl in love with Shawn Mendes
Which of the following is the measure of an acute angle?
There is no image, but I can help you by telling you what an acute angle is:
An acute angle is any angle that has a measure LESS then 90 degrees
Hope this helped!
~Just a girl in love with Shawn Mendes
A measure of an acute angle is equal to 86°.
What is an acute angle?An acute angle can be defined as an angle that is formed by a right-angle triangle. Also, the measure of the angle of an acute angle is generally less than ninety (90) degrees.
In geometry, any angle that is lesser than ninety (90) degrees is generally referred to an acute angle such as:
86°45°60°70°Read more on acute angle here: https://brainly.com/question/10651142
Which set of angle measures could be the measures of the interior angles of a triangle?
• 90°, 42°, and 58°
60°, 60°, and 60°
LO 100°, 48°, and 42°
31°, 75°, and 70°
Answer:
B
Step-by-step explanation:
The sum of the 3 interior angles of a triangle = 180°
Check the sums of the given sets of angles
90° + 42° +58° = 190° ≠ 180° ← not valid
60° + 60° + 60° = 180° ← Valid
100° + 48° + 42° = 190° ← not valid
31° + 75° + 70° = 176° ← not valid
Answer:
The answer is
60°, 60°, and 60°
Rewrite square root of -49-4
Answer:
[tex]\sqrt{53i}[/tex]
Step-by-step explanation:
We need to find [tex]\sqrt{-49-4}[/tex]
We know that √-1 = i
Adding -49 and -4 and solving
[tex]\sqrt{-49-4}\\\sqrt{-53}\\\sqrt{53i}[/tex]
Since 53 is not a perfect square so our answer is:
[tex]\sqrt{53i}[/tex]
A painter needs 5 gallons of paint to finish a house. He has 3 quarts and 1 pint. How much more paint does he
need?
Make a Selection:
A. 3 gallons
B. 4 gallons, 1 pint
C. 3 gallons, 1 pint
D. 4 gallons, 1 quart
NEXT >>
Answer:
4 1/4 gallons
Step-by-step explanation:
5 gallons are needed.
Convert one gallon into quarts and one quart into pints.
3 quarts and 2 pints, minus 3 quarts and 1 pint.
The result is 4 gallons and 1 pint.
He needs 4 galloons and 1 pint .
What is Unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Given:
A painter needs 5 gallons of paint to finish a house.
He has 3 quarts and 1 pint.
Now, Convert one gallon into quarts and one quart into pints.
3 quarts and 2 pints
= 0.75 + 0.125
= 0.875 gallons
So, amount of paint needs = 5- 0.875
= 4.125
Hence, 4 gallons and 1 pint paint does he need.
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Find the product. -3x^ 3(-2x^ 2 + 4x + 7)
6x6 - 12x4 + 21x3
6x5 - 12x4 - 21x3
6x5 + 12x4 + 21x3
For this case we must find the product of the following expression:[tex]-3x ^ 3 (-2x ^ 2 + 4x + 7)[/tex]
We apply distributive property to the terms within parentheses:
[tex](-3x ^ 3 * -2x ^ 2) + (- 3x ^ 3 * 4x) + (- 3x ^ 3 * 7) =[/tex]
We take into account that:
[tex]- * - = +\\- * + = -[/tex]
To multiply powers of the same base, put the same base and add the exponents.
[tex]6x ^ {3 + 2} -12x ^ {3 + 1} -21x ^ 3 =\\6x ^ 5-12x ^ 4-21x ^ 3[/tex]
Answer:
Option B
Which represents the inverse of the function f(x) = 4x?
h(x) = x + 4
h(x) = x – 4
h(x) = x
h(x) = x
To find the inverse of the given function, we need to switch the roles of x and y and solve for y.
Explanation:To find the inverse of a function, we need to switch the roles of x and y, and then solve for y. So, let's start:
Given f(x) = 4x
Switching the roles, we have x = 4y
Now, solve for y:
x = 4y
Divide both sides by 4:
y = x/4
The inverse function is h(x) = x/4. Therefore, the correct option is h(x) = x/4.
Which graph represents y=
[tex]3 \sqrt{ \times + 6 - 3} [/tex]
y = ∛ (x + 6 - 3) = ∛ (x +3) -----------> graph this
(see attached)
Check: from formula above, when x = -3, y = 0
Check that this point exists on the graph... it does (check OK!)
edit reason: typo
Which of the following statements is true for the figures shown?
Answer:
I think is A
Hope it helpsv
Step-by-step explanation:
Answer:
B.
Step-by-step explanation:
Its has been dilated using O as the center.
Solve for x with steps.
Answer:
no real solution is the answer
If you have to list your extraneous solutions somewhere, that would be x=0.
Step-by-step explanation:
Cool thing here is the radical, the thing with the square root, is already isolate.
So we need to square both sides as a first step. (Whenever you raise both sides to even power, you must definitely check your solutions as some might not actually be solutions to the original equation)
So upon squaring both sides I get:
x^4+16=(x^2-4)^2
Now I will write (x^2-4)^2 as (x^2-4)(x^2-4) and foil it! This gives me:
x^4+16=x^4-8x^2+16
Subtract x^4 and 16 on both sides:
0=-8x^2
Divide both sides by -8
0=x^2
Therefore x=0.
0 isn't actually a solution though because when you plug it in you get 4=-4 which is not true.
17. The Colosseum in Rome was the largest amphitheater built in the Roman Empire. The interior of the Colosseum is a perfect circle. The roof of this enormous amphitheater was about 600 feet in diameter. If the center of the Colosseum is assumed to be at origin, then write an equation for the circle that represents the roof of the Colosseum.
Answer:
[tex](x)^{2}+(y)^{2}=90,000[/tex]
Step-by-step explanation:
we know that
The equation of the circle (the roof of the Colosseum) in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
(h,k) is the center and r is the radius
we have
(h,k)=(0,0) ----> is the origin
[tex]r=600/2=300\ ft[/tex] ----> the radius is half the diameter
substitute
[tex](x-0)^{2}+(y-0)^{2}=300^{2}[/tex]
[tex](x)^{2}+(y)^{2}=90,000[/tex]
Lisle building supplies sold 291 rolls of damaged insulation at a $3 loss per roll. What was the total loss?
Answer:
$873
Step-by-step explanation:
Each roll results in a loss of $3.
There are 291 rolls in all.
Multiply 291 with 3: 291 x 3 = 873
The total loss is $873 for the 291 rolls.
~
Answer:
$873
Step-by-step explanation:
3$ per roll.
291 rolls in total.
291 x 3 = 873
How many significant figures are in the number 123.9?
Solve the multi-step equation by combining like terms and using inverse operations and the properties of equality.
Equation: –4x – 5 + 2x = –11
Answer:
Step-by-step explanation:
X=3
1. simplify both sides of the equation by combining like terms
2. add 5 to both sides
3.divide both sides by -2
For this case we have the following equation:
[tex]-4x-5 + 2x = -11[/tex]
To solve, we add similar terms to the left side of the equation:
[tex]-2x-5 = -11[/tex]
We add 5 to both sides of the equation:
[tex]-2x = -11 + 5\\-2x = -6[/tex]
We divide between -2 on both sides of the equation:
[tex]x = \frac {-6} {- 2}\\x = 3[/tex]
Thus, the solution of the equation is 3.
Answer:
[tex]x=3[/tex]
Which of the following nonlinear inequalities is graphed below
Answer:
(x²/4) + (y²/16) ≤ 1
Step-by-step explanation:
The general form of the ellipse in the graph is
x²/4 + y²/16 = 1
we want to find the inequality which represents the shaded area this will determine whether which of the following 2 choices are correct
Choice 1: x²/4 + y²/16 ≥ 1
Choice 2: x²/4 + y²/16 ≤ 1
we note that point (0,0) lies inside the shaded area. Which means if we substitute (0,0), it should create an equality that is valid.
try choice 1: 0²/4 + 0²/16 = 0 ≥ 1 (not valid because obviously zero is smaller than 1)
try choice 1: 0²/4 + 0²/16 = 0 ≤ 1 (this is valid, hence choice 2 is the answer)
Evaluate the step function for the given input values. g(x) = g(2) = g(–2) = g(5) =
Answer:
Step-by-step explanation:
Answer: 3,-4,5
Step-by-step explanation:
9 Peter walked 8,900 feet from home to school.
1 mile = 5,280 feet
How far, to the nearest tenth of a mile, did he walk?
[tex]\bf \begin{array}{ccll} miles&feet\\ \cline{1-2} 1&5280\\ x&8900 \end{array}\implies \cfrac{1}{x}=\cfrac{5280}{8900}\implies 8900=5280x \\\\\\ \cfrac{8900}{5280}=x\implies 1.6856\approx x\implies \stackrel{\textit{rounded up}}{1.7=x}[/tex]
Answer:
I would try 1.7
I need help!
can someone help me?
thank you
Answer:
12
Step-by-step explanation:
For the sake of showing work I will replace the empty space with an x like so...
[tex]\frac{1}{6} =\frac{2}{x}[/tex]
To find out what x is you must cross multiply (aka butterfly)
1*x = 2*6
1x = 12
x = 12
***If you don't understand the "cross multiply" technique let me know in the comments and I'll be happy to explain.
To make these fractions equivalent the empty spot must be 12
[tex]\frac{1}{6} = \frac{2}{12}[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes