Answers
the correct graph is bottom left
the one that the 2 lines cross each other
Related Questions
Suppose you have 48 feet of fencing to enclose a rectangular dog pen. The function : A = 24x-x^2 , where x = width , gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area ?
PLEASE HELP ASAP!! *if you can give explanation/work it would be great* if not that is okay ..
Answers
and this one is not exception, so where's the vertex? what's A or the y-coordinate when the vertex is reached?, well, let's check.
[tex]\bf A=24x-x^2\implies A=-1x^2+24x+0\\\\ \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{lccclll} A = &{{ -1}}x^2&{{ +24}}x&{{ +0}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left(-\cfrac{24}{2(-1)}~~,~~0-\cfrac{24^2}{4(-1)} \right)\implies \left(12~~,~~ 0+\cfrac{576}{4} \right) \\\\\\ \left(\stackrel{width}{12}~~,~~\stackrel{Area}{144} \right)[/tex]
so, that's the vertex, and when the width is that much, the Area reaches a maximum of that much.
The width that gives the maximum area of the rectangular pen is 12 feet, and the maximum area is 144 square feet.
Explanation:To maximize the area of a rectangle with a fixed perimeter, you want to make the rectangle as close to a square as possible. This maximizes the area because it distributes the available fencing evenly among the sides, optimizing the area enclosed. The given function, A = 24x - x^2, represents the area of a rectangle with width 'x' and length 'L' where L = (48-2x) / 2.
Maximization or minimization of a function occurs at its turning point. For a quadratic function like ours, the maximum or minimum happens at the vertex. The x-coordinate of the vertex is given by -b/2a. So, in our function A = -x^2 + 24x (which is the same as 24x - x^2), a = -1, b = 24.
Substitution gives: x = -(24) / 2*(-1) = 12 feet. Therefore, the width that gives you the maximum area is 12 feet.
Substitute x = 12 into the function to find the maximum area: A = 24*12 - 12^2 = 288 - 144 = 144 square feet.
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Tanisha bought 4 bundled packs of comic books. The price of each pack was the same. After she bought the packs, her account balance showed a change of −$86.64. What would have been the change to Tanisha's account balance had she bought only 1 bundled pack of comic books?
A) 21.60
B) -21.60
C) 21.66
D) 21.66
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Lines that never intersect are perpendicular True or False
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The answer is false. Two lines that intersect and form right angles are called perpendicular lines.
Hope this helps!
PLEASE HELP 30 POINTS!!!!!!
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3x + 6 = 4x - 2
6 (+2) = 4x (-3x)
8 = x
plug in x to both of the expressions
3(8) + 6 = 24 + 6 = 30
4(8) - 2 = 32 - 2 = 30
True
x = 8
hope this helps
B is wrong, because you do not set them equal to 180 ( you set them equal to each other). Next, it is wrong, because they messed up the end too.
hope this helps
_______________________________
By examining the image attached, we notice that:
_______________________________________________
The 2 (two) particular angles with the following measurements:
_________________________________________________
1) 4x - 2 ; and:
2) 3x + 6 ;
_________________________________________________
are equal; since they are "alternate interior angles" ; since the 2 (two) horizontal lines in the figure are parallel; and since alternate interior angles are equal in measurement.
___________________________________________
The question asks to solve for "x" ;
As such:
4x - 2 = 3x + 6 ;
Solve for "x" ;
Subtract "3" from each side of the equation ; & add "2" to each side of the equation ;
4x - 2 = 3x + 6 ;
-3x +2 = -3x + 2 ;
_________________________
1x = 8 ;
_________________________
→ x = 8 .
____________________________________
Now, we can check our answer:
____________________________________
" 4x - 2 = 3x + 6 " ;
→ Plug in "8" for "x" ; to see if both sides of the equation are equal ;
4(8) - 2 =? 3(8) + 6 ??
→ 32 - 2 =? 24 + 6 ??
→ 30 = ? 30 ? Yes!
____________________________________________________
Use a quadratic equation to find two real numbers that satisfies the situation. The sum of the two numbers is 2, and their product is –48.
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To find two real numbers whose sum is 2 and product is -48, we form a quadratic equation x^2 - 2x - 48 = 0. Using the quadratic formula, we get two pairs of numbers (8, -6) and (-6, 8) that satisfy the given conditions.
Explanation:To find two real numbers that satisfy the given conditions, namely their sum being 2 and their product being –48, we can set up a system of equations or use a . Let's denote the two numbers as x and y. We know:
x + y = 2xy = -48We can express y in terms of x from the first equation: y = 2 - x. Substituting this into the second equation gives us:
x(2 - x) = -48
This simplifies to a quadratic equation:
x^2 - 2x - 48 = 0
Using the, x = (-b ± √(b^2 - 4ac)) / (2a), with a = 1, b = -2, and c = -48, we find the two possible values for x, which in turn gives us the corresponding values for y:
x = (2 ± √(4 + 192)) / 2
x = (2 ± √196) / 2
x = (2 ± 14) / 2
Therefore, the two solutions are x = 8 or x = -6. Since we were looking for two numbers, using x + y = 2, the corresponding y values are y = -6 and y = 8, respectively. Hence, the two pairs of numbers that satisfy the conditions are (8, -6) and (-6, 8).
Which equation can be used to solve for b?
A) tan(30°) = 5/b
B) tan(30°) = b/5
C) tan(30°) = 10/b
D) tan(30°) = b/10
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tan(x) = opposite / adjacent
the hypotenuse is the longest side of 10, so C and D are not correct.
Side b is adjacent to the 30° angle
Side 5 is opposite of the 30° angle
tan(30) = 5/b
In this exercise we want to calculate the value of angle B, so we have to:
Letter A
So knowing the tangent formula as:
[tex]tan(x) = opposite / adjacent[/tex]
Knowing some information given in the exercise such as:
the hypotenuse is the longest side of 10Side b is adjacent to the 30° angleSide 5 is opposite of the 30° angleSo we have:
[tex]tan(30)=5/b[/tex]
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A bag contains 80 marbles: 40 are red, 20 are blue, and 20 are black. what is the probability of selecting a red or blue marble at random
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20% out of 80 for blue
The diagram shows triangle MNP. Which term describes point Q?
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Answer:
(B) Incenter
Step-by-step explanation:
From the given figure, it can be seen that PMN is a triangle where MQ is the angle bisector of ∠NMP, PQ is the angle bisector of∠NPM and NQ is the angle bisector of ∠MNP.
Also, It is equally distant from the three line segments forming the sides of the triangle. Thus, By the definition of incenter, Q can be named as the incedntre of the given triangle PMN.
Since, the centroid, circumcenter and orthocenter does not satisfy the conditions given in the figure, thus Q can not be considered as centroid, circumcenter and orthocenter.
Hence, option B is correct.
Answer:
the answer is incenter
Step-by-step explanation:
took the apex quiz got it correct !
Carly is making 3 and 1/2 batches of biscuits. If one batch calls for 2and 1/3 cups of flour, how much flour will she need?
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Find the tangent of the angle in standard position in which the terminal side passes through the point (3,4)
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angle = 36.87 degrees
Plz see picture and question attached
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because it is square, meaning the width and height are the same, so therefore the width is also 4. to get the area of a square of rectangle, you times the width by the height. 4 × 4 = 16. so the answer is 16m² because the unit is metre so we write m²
if 161 is 35% of students at school who play sports how many students are at school?
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[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ x&100\\ 161&35 \end{array}\implies \cfrac{x}{161}=\cfrac{100}{35}\implies x=\cfrac{161\cdot 100}{35}[/tex]
Can someone explain to me how to solve these ?
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Which linear system of equations does the matrix represent?
-3 5 | 15
2 3 | -10
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-3x + 5y = 15
2x + 3y = -10
The matrix represents the system of linear equations: -3x + 5y = 15 and 2x + 3y = -10.
Explanation:The matrix represents the system of linear equations. Each row corresponds to an equation and each column to a coefficient of the unknowns. So, the given matrix:
-3 5 | 15
2 3 | -10
Represents the system of linear equations:
-3x + 5y = 15
2x + 3y = -10
Where x and y are the unknown variables that we are trying to solve for.
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Find the length of the hypotenuse of a right triangle with legs of lengths 12 ft and 16 ft answer
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Answer:
Step-by-step explanation:
but what ab this one: Find the length of the hypotenuse of a right triangle with legs of 5 ft and 12 ft.
A right triangle in which one angle is the right angle and the two sides are perpendicular to each other. Hence, the length of the hypotenuse is [tex]20ft[/tex].
What s the right triangle?
A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangle triangle, is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular.
Here, the lengths of the triangle are [tex]12ft[/tex] and [tex]16ft[/tex] .
As we know,
[tex]H^{2}=P^{2}+B^{2}[/tex] ..........[tex](1)[/tex]
Now, substituting the values in the equation [tex](1)[/tex], we get
[tex]H^{2}=(12)^{2}+(16)^{2}\\H^{2}=144+256\\H^{2}=400\\H=\sqrt(400)\\H=20ft[/tex]
Hence, the length of the hypotenuse is [tex]20ft[/tex].
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Mrs. hensen cataloged a group of incoming library books in 8 hours. mr. taylor can catalog the same number of books in 4 hours. mrs. phillips can catalog them in 6 hours. how long would it take if they all worked together?
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Mrs. Hensen's working rate is
x = n/8 books/h
Mr. Taylor's working rate is
y = n/4 books/h
Mrs. Phillip's working rate is
z = n/6 books/h
When they work together, they can catalog n books in
(n books)/(x+y+z books/h)
= n/(n/8 +n/4 + n/6)
= 1/(1/8 + 1/4 + 1/6)
= 1/(13/24)
= 24/13 hours
The time required is 24/13 h = 1.8462 h = 1 hour, 51 min
Answer: 1.8462 hours (or 1 hour, 51 minutes)
Newton uses a credit card with a 18.6% APR, compounded monthly, to pay for a cruise totaling $1,920.96. He can pay $720 per month on the card. What will the total cost of this purchase be?
Answers
Find the approximate value of the circumference of a circle with the given radius. Use = 3.14. Round your results to one more decimal than in the given radius. 4 inches C = 12.5 inches 12.6 inches 25.1 inches 25.2 inches
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Answer:
[tex]25.1\ inches[/tex]
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=4\ in[/tex]
substitute
[tex]C=2(3.14)(4)=25.1\ in[/tex] -----> one more decimal than the given radius (nearest tenth)
An angle measures 150° less than the measure of a supplementary angle. what is the measure of each angle?
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The measure of the angle is 30 degrees
What is a supplementary angle?A supplementary angle can be defined as an angle that sum up t0 180 degrees.
The two angles must add up to 180 degrees, that is, angles on a straight line.
The properties of supplementary angles are;
The two angles are supplementary angles when they add up to 180°The two angles together make a straight line, but the angles need not in a place“S” of supplementary angles represents a “Straight” line. This means they form 180°From the information given, we have that;
The angle measures 150 degrees less of supplementary angles
Then,
180 - 150
30 degrees
Hence, the value is 30 degrees
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The two supplementary angles in question measure 15° and 165° respectively, with one angle being 150° less than the other.
We are given that one angle measures 150° less than its supplementary angle. By definition, supplementary angles add up to 180°. Let's call the angle in question 'A', and its supplementary angle 'B'.
We thus have the following relationship:
A = B - 150°
and
A + B = 180°
Substituting the first equation into the second, we get:
(B - 150°) + B = 180°
This simplifies to:
2B - 150° = 180°
2B = 330°
B = 165°
Now that we know the measurement of B, we can find A:
A = 165° - 150°
A = 15°
So, the two angles are 15° and 165° respectively.
Holes drilled several kilometers into Earth’s crust provide direct evidence about Earth’s interior in the form of a. seismic waves. b. rock samples. c. liquid iron. d. volcanic eruption. Please select the best answer from the choices provided A B C D
Answers
Answer:
b. Rock Samples
Explanation:
Rock samples are obtained by drilling with special drills into the substance.
So, holes drilled several kilometers into Earth's crust provide direct evidence about Earth's interior in the form of a rock samples.
What is the measurement of angle R?
Answers
make sure your calculator is in Degree mode.
What is the common difference of the arithmetic sequence 1/5, 6/5 , 11/5 ,16/5 , ...?
Answers
hope this helps
Abigail drives at an average speed of 60 miles per hour for 3 hours. The graph shows her distance versus time. Which statements are true? Check all that apply. As Abigail’s time increases, her distance increases. As Abigail’s time increases, her distance decreases. At 2 hours, Abigail has traveled 120 miles. At 1.5 hours, Abigail has traveled 100 miles. At 3 hours, Abigail has traveled 180 mile
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At 2 hours, Abigail has traveled 120 miles.
At 3 hours, Abigail had traveled 180 miles.
The statements are to be checked whether they are true or not.
The true statements are:
As Abigail’s time increases, her distance increases.
At 2 hours, Abigail has traveled 120 miles.
At 3 hours, Abigail has traveled 180 mile
Abigail is driving at a speed of 60 miles per hour for 3 hours.
The function representing the situation will be
[tex]y=60x[/tex]
where,
[tex]y[/tex] is the distance in miles
[tex]x[/tex] is the time in hours
If time increases this means [tex]x[/tex] increases so, distance [tex]y[/tex] will also increase.
At 2 hours [tex]x=2[/tex]
[tex]y=60\times 2=120[/tex]
The distance traveled is 120 miles.
At 1.5 hours [tex]x=1.5[/tex]
[tex]y=60\times 1.5=90[/tex]
The distance traveled is 90 miles.
At 3 hours [tex]x=3[/tex]
[tex]y=60\times 3=180[/tex]
The distance traveled is 180 miles.
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Isaac and his sister plan to surprise their parents by buying them each a pair of shoes. They agree that Isaac will pay 68% of the price since he receives a greater allowance. Use an estimation strategy to determine how much Isaac will pay if the total bill is $97.65. Show the step-by-step process you used to solve the problem.
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Issac will pay $66.40.
This finds 1% of 97.65
0.9765 x 68 = 66.402
This finds 68% of 97.65
Isaac will pay $66.40
What two numbers can you multiply to get 84?
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Check it to make sure.
2 × 42 = 84
42 and 2 can be multiplied to get 84.
how many times must 24 be added until the sum is 1500
Answers
60 times must 24 be added until the sum is 1500
If I set a goal of signing up 30% of customers to receive emails. that means that if I speak to 130 customers today I need to collect email addresses from ?
Answers
^^^^^^^^^
Answer:39
Step-by-step explanation:
130+30%=39
Naomi has 50 red and white beads.the number of red beads is 1 more than 6 times the number of white beads. how many red beads does naomi have
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Crystal estimated that repairs to her car would cost about $100. The cost of repairs was actually $175. Fill in the box with Crystal's percent error
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percent error=100 times error/predicted
error=175-100=75
predicted=100
percent error=100 times 75/100=75
the answer si 75% error
So the question says...
Suppose you have ∠SMB and m ∠SMB =125.35 °.
Part A: Determine the angle measure that is complement to ∠SMB, if possible. If ∠SMB does not have a complementary angle, then explain why it does not.
Part B: Determine the angle measure of the supplement of ∠SMB.
Part C: Determine the angle measure of the angle complement to ∠SMB’s supplement.
I’m stuck on this question so if anyone can help me with it that would be greatly appreciated. Thanks!
Answers
Part B. Two angles are supplementary if their sum is equal to 180°. So,
Supplementary angle = 180 - 125.35 = 54.65°
Part C. Complementary angle = 90 - 54.65 = 35.35°
Part A: ∠SMB does not have a complementary angle
Part B: The angle measure of the supplement of ∠SMB is 54.65°
Part C: The angle measure of the angle complement to ∠SMB's supplement is 35.35°
The given angle is ∠SMB and m ∠SMB =125.35 °
For Part AComplementary angles are angles that sum up to 90°.
To determine the angle measure that is complement to ∠SMB, we will find the angles that adds up to ∠SMB to give 90°. Since ∠SMB is already greater than 90°, therefore, ∠SMB does not have a complementary angle.
For Part B.Supplementary angles are angles that sum up to 180°.
To determine the angle measure of the supplement of ∠SMB, we will find the angle that adds up to ∠SMB to give 180°. Let the measure of the angle be x, that is
x + 125.35° = 180°
∴ x = 180° - 125.35°
x = 54.65°
∴ The angle measure of the supplement of ∠SMB is 54.65°
For Part C
To determine the angle measure of the angle complement to ∠SMB's supplement, we will determine the measure of the angle that adds up to ∠SMB's supplement to give 90°. Let the angle be y
Then,
y + 54.65° = 90°
(NOTE: ∠SMB's supplement is 54.65°)
∴ y = 90° - 54.65°
y = 35.35°
∴ The angle measure of the angle complement to ∠SMB's supplement is 35.35°
Hence,
Part A: ∠SMB does not have a complementary angle
Part B: The angle measure of the supplement of ∠SMB is 54.65°
Part C: The angle measure of the angle complement to ∠SMB's supplement is 35.35°
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