1) The angle the shelf makes with the floor is approximately 77.905°. (Choice A)
2) The approximate angle of inclination of the sun is approximately 51.340°. (Choice A)
How to apply trigonometric relations to determine angles
1) In this case we know that shelf has a vertical height ([tex]h[/tex]) of 7 feet and a horizontal distance between the floor from the wall to the front of the shelf ([tex]l[/tex]) is 1.5 feet. The angle ([tex]\theta[/tex]), in degrees, is determined by tangent function:
[tex]\theta = \tan^{-1} \frac{7\,ft}{1.5\,ft}[/tex]
[tex]\theta \approx 77.905^{\circ}[/tex]
The angle the shelf makes with the floor is approximately 77.905°. (Choice A) [tex]\blacksquare[/tex]
2) The length of the shadow ([tex]l[/tex]) is 12 feet and the height of the building ([tex]h[/tex]) is 15 feet. The angle of inclination of the sun is determined by tangent function:
[tex]\theta = \tan^{-1} \frac{15\,ft}{12\,ft}[/tex]
[tex]\theta \approx 51.340^{\circ}[/tex]
The approximate angle of inclination of the sun is approximately 51.340°. (Choice A) [tex]\blacksquare[/tex]
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Analyze the key features of the graph of the quadratic function f(x) = -x2 + 2x + 10. A. Does the parabola open up or down?
B. Is the vertex a minimum or a maximum?
C. Identify the axis of symmetry, vertex and the y-intercept of the parabola.
SOS
Answer
A: Down
B: Max
C:
AOS: x = 1Vertex: (1, 11)Y-Int: (0, 10)Step-by-step explanation:
A: If the leading coefficient (a) is positive, the graph opens UP. If it is negative, the graph opens DOWN.
B: Anytime the graph goes UP, there's a minimum. Anytime the graph goes DOWN, there's a maximum
C:
AOS: [tex]x = \frac{-b}{2a}, a=-1, b=2, c=10[/tex]
Vertex: [tex](\frac{-b}{2a}, y)[/tex]
Y-INT: let x=0 and solve for y. The coordinate of the y-intercept is (0, y).
Hope this helps!!
a basketball player made 27 free throws in her last 45 tries. what is the experimental probability that she will make her next free throw?
I need to spend exactly £200, how?
PLEASE HELP ME QUICKLY!!!
BRAINLIEST AVAILABLE TO CORRECT ANSWER
You have a cd-rw drive that advertises speeds of 32x/12x/48x. what is the read speed of the drive?
help me please asap and plz be correct :)
The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except –3. What describes the domain of (gºf)(x)?
△ABC∼△LMN , AB is 8 inches, BC is 14 inches, and LM is 12 inches.
What is MN ?
What are the solutions to the equation?
n^2−8n+16=25
Enter your answers in the boxes.
n1=
n2=
Answer:
help
Step-by-step explanation:
Tiny's Tattoo Parlor sold 389 tattoos this month. 43 of those tattoos were arm tattoos. Based on this data, what is a reasonable estimate of the probability that the next customer does not get an arm tattoo?
Answer:
346/389
Step-by-step explanation:
correct on khan academy!
The reasonable estimate of the probability that the next customer does not get an arm tattoo is 346/389.
What is Probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
Here, Based on the given conditions, formulate
Probability = Favorable outcome / Total outcome
Calculate the sum or difference: (389-43)/389
get the result: 346/389
Thus.the reasonable estimate of the probability that the next customer does not get an arm tattoo is 346/389.
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1. Write using exponents. (–4)(–4)
Jenna throws a stone off a pier and into the ocean. The graph models how the height of the stone, above sea level, changes over time.
Select from the drop-down menu to interpret the decreasing interval of the graph.
The stone was falling toward the water from
https://static.k12.com/nextgen_media/assets/8090396-NG_AL1_O_07_012_Quiz_05.png
This should get you a hundred on the 4.11 quiz. :)
Using the graph below, what is the 10th term of the arithmetic sequence?
A.a10 = 26
B.a10 = 31
C.a10 = 30
D.a10 = 436
The 10th term of an arithmetic sequence can be found using the formula an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference. Without the graph or additional information, we cannot compute the 10th term for the given sequence.
Explanation:The question asks us to determine the 10th term of an arithmetic sequence using a provided graph. Unfortunately, the actual graph is not provided in the question. An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference. To find the 10th term of an arithmetic sequence, we would use the formula:
an = a1 + (n - 1)d
where an is the nth term of the sequence, a1 is the first term, n is the term number, and d is the common difference. However, without the graph or additional information such as the first term or the common difference, we cannot accurately determine the 10th term, and any answer from the provided options would be purely a guess.
To find the 10th term of an arithmetic sequence, we need to use the formula an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference. In this case, the common difference is -3. Substituting the values into the formula, the 10th term is -24.
Explanation:To find the 10th term of an arithmetic sequence, we need to identify the common difference and use the formula:
an = a1 + (n-1)d
where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.
In this case, the given sequence is 3; 14; 11; 5; 16; 17; 28; 41; 31; 18. By comparing the terms, we can see that the common difference is -3.
Substituting the values into the formula:
a10 = 3 + (10-1)(-3) = 3 - 27 = -24
The 10th term of the arithmetic sequence is -24.
Today a car is valued at $42000. The value is expected to decrease at a rate of 8% each year. Choose the equation that can be used to solve the problem.
A.) y=42000(1+.08)^6
B.) y=42000(1+6)^8
C.) y=42000(1−.08)^6
D.) y=42000(1−.8)^6
And then: What is the value of the car expected to be 6 years from now?
This is the only question I don't understand, someone help please!
Answer:
Option (c) is correct.
[tex]y=42000(1-0.08)^6[/tex] equation that can be used to solve the given problem and the value of the car expected to be 6 years from now is $25466.91
Step-by-step explanation:
Given : Today a car is valued at $42000. The value is expected to decrease at a rate of 8% each year.
We have to choose the equation that can be used to solve the given problem.
We know
Depreciation formula given as,
[tex]A=P(1-\frac{r}{100} )^n[/tex]
Where A is the amount value after depreciation.
P is present value
r is depreciate rate.
n is time period.
Given : P = 42000 and r= 8% also given time period is 6.
Substitute , we have,
[tex]y=42000(1-\frac{8}{100} )^6[/tex]
Simplify , we have,
[tex]y=42000(1-0.08)^6[/tex]
Simplify we get,
[tex]y=25466.91[/tex]
Thus, [tex]y=42000(1-0.08)^6[/tex] equation that can be used to solve the given problem and the value of the car expected to be 6 years from now is $25466.91
Sue's Sushi placed two orders with its fish supplier. One order was for 15 pounds of salmon and 8 pounds of tuna; the order totaled $259. The other order was for 12 pounds of salmon and 6 pounds of tuna; this order totaled $204. What is the cost for one pound of salmon and one pound of tuna?
What is the interior angle if the outside equals 110?
Reggie currently has a square rug in his living room. He is moving soon and has determined that for his new living room, he will need a rug that has a width that is two feet shorter than his current rug and a length that is five feet longer than his current rug. Let x represents the side measure of Reggie's current rug, in feet. Determine the equation that represents the area, y, in square feet, of the rug needed for his new living room.
y = x2 + 3x - 10
y = x2 - 7x + 10
y = x2 - 3x - 10
y = x2 + 7x + 10
Answer:
C. y = x² + 3x - 10
Step-by-step explanation:
Reggie's current rug has a square shape.
This means that:
length of rug = x ft
width of rug = x ft
For the new rug:
1- the length is 5 ft longer than the current rug. This means that:
new length = x + 5 ft
2- the width is 2 ft shorter than the current rug. This means that:
new width = x - 2 ft
The area of the new rug can be calculated as follows:
area of new rug = new length * new width
area of new rug = (x + 5)(x - 2)
area of new rug = x(x) - 2(x) + 5(x) - 5(2)
area of new rug = x² - 2x + 5x - 10
area of new rug = x² + 3x - 10 ft²
Just took the test <3.A rectangle is 1/2 feet long and 3/4 feet wide. What is the area of the rectangle?
The area of the rectangle having a length of 1.2 feet and a width of 3/4 feet is 3/8 sq feet.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know the area of a rectangle is (length×width).
Given, A rectangle is 1/2 feet long and 3/4 feet wide.
Therefore, The area of this rectangle is,
= (1/2×3/4) sq feet.
= 3/8 sq feet.
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helppppppppppppppppppppppp
A $4,000.00 principal earns 5% interest, compounded annually. After 4 years, what is the balance in the account?
$500,000.00
$4,862.03
$4,600.00
$20,250.00
24.
A $6,000.00 principal earns 8% interest, compounded semiannually. After 35 years, what is the balance in the account?
$22,800.00
$39,600.00
$88,712.07
$93,429.71
25.
A tractor costs $15,450.00 and depreciates in value by 14% per year. How much will the tractor be worth after 3 years? $22,889.85
$15,408.00
$8,451.28
$9,827.07
algebra 2 unit 2 question. connexus.
The subject of this question is Mathematics, specifically Algebra 2.
Explanation:The subject of this question is Mathematics, specifically Algebra 2.
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Choose the correct box of the best buy available.
a .a box of cookies for $1.89
b. two boxes of cookies for $3.69
Which pair of measurements is equivalent?
8,600 mg, 86 g
2,500 g, 250 kg
3.4 kg, 3,400 g
480 g, 4.8 mg
Answer:
3.4 kg, 3,400 g
Suppose that F(x) = x^3 and G(x) = (4x)^3 − 5. Which statement best compares the graphs of F(x) and G(x)?
A.The graph of G(x) is the graph of F(x) stretched vertically and shifted 5 units down.
B.The graph of G(x) is the graph of F(x) stretched horizontally and shifted 5 units down.
C.The graph of G(x) is the graph of F(x) compressed vertically and shifted 5 units down.
D.The graph of G(x) is the graph of F(x) compressed horizontally and shifted 5 units down.
The graph of G(x) is the graph of F(x) stretched horizontally by a factor of 4 and shifted 5 units down.
Explanation:Comparing the functions [tex]F(x) = x^3[/tex] and [tex]G(x) = (4x)^3 - 5[/tex]reveals the relationship between their graphs. G(x) is a horizontal stretch of F(x) by a factor of 4 due to the presence of "4x." Additionally, the constant term "-5" shifts the graph downward by 5 units. Consequently, G(x) can be accurately characterized as a horizontal stretching of F(x) and a vertical shift downward by 5 units, altering the shape and position of the original cubic function F(x).
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BRAINLIESTTT ASAP!!!!!!!!!
Math question help :)
Answer:
Step-by-step explanation:
I think its D.
△JKL∼△QRS , JK is 8 centimeters, QR is 12 centimeters, and RS is 9 centimeters.
What is KL ?
Enter your answer in the box.
Answer:
The measure of KL is 6 centimeters.
Step-by-step explanation:
It is given that △JKL∼△QRS.
The corresponding sides of two similar triangles are proportional.
[tex]\frac{JK}{QR}=\frac{KL}{RS}[/tex]
[tex]\frac{8}{12}=\frac{KL}{9}[/tex]
[tex]8\times 9=KL\times 12[/tex]
Divide both sides by 12.
[tex]KL=\frac{72}{12}[/tex]
[tex]KL=6[/tex]
Therefore we can say that if △JKL∼△QRS, then the measure of KL is 6 centimeters.
Answer:
6
Step-by-step explanation:
He did too much math lol, a simple way of this is by dividing both sides initially.
12/9 = 1.5
9/1.5 = 6
How could you find an equation of a quadratic function with the zeroes of -3 and 1?
One of the factors of 6x3 − 864x is
A. 4
B. X^2
C. X + 12
D. X - 8
Consider the expression [tex]6x^3-864x.[/tex] This expression consists of two terms: [tex]6x^3[/tex] and [tex]-864x.[/tex]
These two terms have common factors 6 and x, because:
[tex]6x^3=6x\cdot x^2;[/tex][tex]-864x=6x\cdot (-144).[/tex]Then
[tex]6x^3-864x=6x(x^2-144).[/tex]
You know that [tex]144=12^2.[/tex] Use the formula for the difference of squares:
[tex]x^2-144=x^2-12^2=(x-12)(x+12).[/tex]
Therefore,
[tex]6x^3-864=6x(x-12)(x+12).[/tex]
Answer: correct choice is C.
a cylinder has a circumgerence of 12pi cm and a height that is half the radius. what is the total surface