The angle the longer chain makes with the ceiling is 38.5°
The two chains and ceiling form a triangle and with two sides and an angle, we use the sine rule to find the other angle
What is the sine rule?The sine rule states in any triangle with sides a, b, c and angles A, B and C, repsectively, we have that
a/sinA = b/sinB = c/sinC
Since one chain is 46cm long and forms an angle of 60° with the ceiling. the other chain 64cm long. So, we find the other angle.
So, a/sinA = b/sinB where
a = 46 cm, b = 64 cmA = other angleB = 60°The value of the other angleMaking A subject of the formula, we have
A = sin⁻¹(asinB/b)
So, substituting the values of the variables into the equation, we have
A = sin⁻¹(asinB/b)
A = sin⁻¹(46 cm × sin60/64 cm)
A = sin⁻¹(46 cm × 0.8660/64 cm)
A = sin⁻¹(39.84 cm/64 cm)
A = sin⁻¹(0.6225)
A = 38.49°
A ≅ 38.5°
So, the angle the longer chain makes with the ceiling is 38.5°
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G
ewrite the equation in Ax+By=C form.
se integers for A, B, and C.
y+4= -4(x-2)
Step-by-step explanation:
y + 4 = -4(x - 2) = -4x + 8
y - 4 = -4x
-4x - y = -4
4x + y = 4
Find g(x), where g(x) is the translation 8 units left of f(x)=x
Using translation concepts, it is found that function g(x) is given by:
g(x) = x + 8.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, function g(x) is a translation 8 units left of f(x) = x, hence x -> x + 8 and:
g(x) = f(x +8) = x + 8.
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HELP
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real world and mathematical problems in two and three dimensions
You did not provide any question. I will give general advice.
Pythagorean Theorem: a² + b² = c²
If you know two sides, you know ll three sides.
A house sits in the shade.
The house is 18 feet tall. The shadow is 24 feet long. What is the hypotenuse of this triangle?
We know a and b here! a=18, b=24.
18 * 18 = 324.
24 * 24 = 576.
324+576 = 900
The square root of 900 is what will be your answer:
18*18 + 24*24 = 30*30.
I hope this helps!
Write 320 g as a fraction of 2 kg. Give your answer in its simplest form.
Answer:
4/25
Step-by-step explanation:
Let's make the units the same :
2 kg = 2000 g
Now lets simplify this fraction :
Divide top and bottom by 2 until you can't :
320/2000 = 160/1000
160/1000 = 80/500
80/500 = 40/250
40/250 = 20/125
Now we divide top and bottom by 5 as 2 is not a factor of 125 :
20/125 = 4/25
This is our final answer
Hope this helped and brainliest please
Frank bought 6 pens and 3 highlighters in the school store and paid $21 for the whole purchase. His friend, Andy, paid $19 for 2 pens and 4 highlighters. If all pens cost the same and all highlighters cost the same, what is the price of one pen?
Answer:one pen = $1.50
Step-by-step explanation:
See picture for the math if that helps
Using p for pens, h for highlighter,
A for first equation
B for second equation
I used equation A to reduce to a usable substitute by dividing all by 3
And then isolating “h”.
Now substitute the value of “h” into equation B and solve for “p”
P=$1.50
To check your work, substitute p ($1.50) into equation B and solve for “h”
h=$4.00
Now substitute the p and h values into either equation A or B and solve, they equal the numbers given
Help plsss i dont get it
Part A
The pattern of squares is 1, 4, 9, ... which is the set of perfect squares
1 = 1^24 = 2^29 = 3^2and so on
The 7th figure will have 49 squares because 7^2 = 49
Answer: 49==============================================================
Part B
Each pattern has one circle per corner (4 circles so far). In addition, there's one circle per unit side to form the perimeter.
Pattern 1 has 4+4(1) = 8 circlesPattern 2 has 4+4(2) = 12 circlesPattern 3 has 4+4(3) = 16 circlesThe nth term will have 4+4n circles. The first '4' is the number of circles at the corners. The 4n is the circles along the perimeter. If you wanted, 4+4n factors to 4(1+n).
Plug in n = 20 to find the 20th figure has 4+4n = 4+4(20) = 84 circles
Answer: 84==============================================================
Part C
Pattern 1 has 1 square + 8 circles = 9 items totalPattern 2 has 4 squares + 12 circles = 16 items totalPattern 3 has 9 squares + 16 circles = 25 items totalThis seems to suggest if the pattern number is odd, then we need an odd number of tiles (square + circular).
Let n be the pattern number. Pattern n needs n^2 square tiles and 4+4n = 4n+4 circular tiles. Overall, n^2+4n+4 tiles are needed.
It turns out that if n is odd, then n^2+4n+4 is always odd. The proof is shown below.
Side note: n^2+4n+4 factors to (n+2)^2
Answer: B) will always be oddUse the listing method to represent the following set. {x | x I, x ≤ 3}
....,0,1,2,3
4,5,6,7...
3,4,5,6....
Here the set given is
{x|x,x≤3}So the set should be
(-oo,3]The set elements are
{..,1,2,3}
Answer:
{ ..., 0, 1, 2, 3}
Step-by-step explanation:
Set notation is used in math to list numbers, objects or outcomes.
It uses curly brackets called "braces". Objects placed within the braces are the elements of the set.
Given set notation: { x | x ∈ I, x ≤ 3 }
The ∈ symbol means "is an element of".
Therefore, x ∈ I means that x is an element of the set of integers. (Integers are whole numbers that can be positive, negative, or zero).
The ≤ symbol means "less than or equal to".
Therefore, x ≤ 3 means that x is less than or equal to 3.
Therefore, the given set notation means:
x is an element of the set of integers less than or equal to 3
The listing method of set notation simply lists the numbers in the set.
The three dots "..." means it is infinite (goes on forever).
Therefore:
{ x | x ∈ I, x ≤ 3 } = { ..., 0, 1, 2, 3}
this question confuses me any help
Answer:
42.25π m²
Step-by-step explanation:
Let's solve!
⇒ Take the radius of the lawn to be 'r'
===========================================================
Then, area of the path equals :
⇒ Area of (lawn + path) - Area of lawn
⇒ π (r + 2)² - πr² = 30π
⇒ πr² - πr² + 4πr + 4π = 30π
⇒ 4πr = 26π
⇒ r = 6.5 m
===========================================================
Area of the lawn :
⇒ Area = πr²
⇒ Area = π × (6.5)²
⇒ Area = 42.25π m²
Mr. Franco's class wants to raise at least $750 for a fundraiser. Let r be the amount of money, in dollars, the class raised.help ASAP..
Answer:
>
Step-by-step explanation:
Cause 750 was the least they could raise
Answer:
>=
Step-by-step explanation:
>= because the teacher wants AT LEAST 750. at least meaning you can raise 750 or MORE
Calcula el valor de la expresion
m + (m – 3), si m = –5
Answer: -13
Step-by-step explanation:
m = -5
-5 + (-5-3)
-5 -8
-13
Answer:
-13
Step-by-step explanation:
dado m= -5
m+(m-3) = -5+(-5-3) = -5 + (-8) = -5-8 = -13
The quadratic function
d=-9x² + 40 models a
skateboarder's distance, in
feet, from the bottom of a hill
x seconds after the skateboarder
starts moving down the hill.
After how many seconds is the
skateboarder 4 ft from the
bottom of the hill?
A) 3s B) 4s C) 2s D) 3.5s
Please help!! Also if you could explain that would be great! Tysm!
Answer:
C
Step-by-step explanation:
equate d to 4 and solve for t , that is
- 9x² + 40 = 4 ( subtract 40 from both sides )
- 9x² = - 36 ( divide both sides by - 9 )
x² = 4 ( take square root of both sides )
x = [tex]\sqrt{4}[/tex] = 2
It takes 2 seconds for the skateboarder to be 4m from bottom of hill
What is the standard form of y=2x-2
Answer:
A standard form of a linear equation would look like this Ax+ By = C A x + B y = C
Step-by-step explanation:
Write the equation of the trigonometric graph
The equation for the trigonometric graph given above is:
y = 4sin(2x + (π/2))
y = 4 cos 2x
It is to be noted that the domain value of θ is displayed on the horizontal x-axis and the range value is depicted on the vertical y-axis in the graphs of trigonometric functions.
What is the step-by-step solution to the question?Note that
y = A Sin (Bx - C) + D
The vertical shift → D
Horizontal [Phase] shift → C/B
Wavelength [Period] → (2/B) π
Amplitude → | A |
Vertical Shift → 0
Horizontal | Phase | Shift → C/B → [- (π/4)] → (-π/2/2)
Wavelength | Period | → (2/B)π → π → (2/2)π
Amplitude → 4
Hence, working the above further we get:
y = 4sin(2x + (π/2))
y = 4 cos 2x
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Answer(s):
[tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}) \\ y = -4cos\:(2x \pm \pi) \\ y = 4cos\:2x[/tex]
Step-by-step explanation:
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]
OR
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 4sin\:2x,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{4}} = \frac{-\frac{\pi}{2}}{2}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-1\frac{1}{4}\pi, 0],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{4}, 0],[/tex]they are obviously [tex]\displaystyle \pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
A scientist cools some water at a constant rate. The graph and table show
how the temperature of the water changes with time.
Which function models this situation?
Water Temperature
8
7
8
Time (minutes)
Temperature (°C)
2899 228 229
55
50
45
40+
35+
30
25
20
15
10
5
Time (minutes)
Temperature (°C)
A. a(n) = 46-n-(4-1)
B. a(n) = 46 - 40+1
C. a(n) = 46-(n-1)-4
D. a(n) = 46-47-1
9 10
5
30
6
26
The correct function that matches the data in the graph is a(n) = 46-(n-1)-4 (option C)
How to choose the correct option?The only way is to verify the function matches the data by replacing n.
For example, we know at 5 seconds the temperature is 30. Let's use 5 (n) to verify the function.
a(n) = 46-(5-1) x 4a(n) = 46- 4x 4a(n) = 46- 16a (n) = 30This option matches the value of the temperature.
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What are the values of x and y?
A- x=56, y=68
B- x=68, y=56
C- x=57, y=66
D- x=66, y=57
The value of "x" and "y".
Solution:Let's solve "x" first.
Given is a supplementary angle so it should add up to 180°
[tex]x=180-123[/tex]
[tex]\large\boxed{x=57°}[/tex]
Now, we can solve "y"
Given is an isosceles triangle so the opposite sides will be equal.
[tex]57+57[/tex]
[tex]114°[/tex]
Angle sum of triangle is 180° so, it should add up to 180°
[tex]y=180-114[/tex]
[tex]\large\boxed{y=66°}[/tex]
Therefore, the correct answer is option C
The function f(x) = 5x - 4 is changed to f(x) = 5x + 3. What is the result?
Answer: move up or add 7 in positive direction
Explain how to solve
Answer:
198 cm^3
Step-by-step explanation:
volume = 22/7 * 3^2 * 7
volume = 22/7 * 7 * 3^2
volume = 22 * 3^2
volume = 22 * 9
volume = 198
Find the equation of a line that passes through the points (-4, -2) and (6, 3).
Answer:
[tex]y=\frac{1}{2} x[/tex]
Step-by-step explanation:
The equation of a line through two points can usually (except when the line is a vertical line) be written in slope intercept form, [tex]y=mx+b[/tex] , where "m" is the slope of the line, and "b" is the y-intercept of the line.
General outlineFind the slopeFind the y-interceptTo find "m", use the formula for slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{(3)-(-2)}{(6)-(-4)}[/tex]
[tex]m=\dfrac{3+2}{6+4}[/tex]
[tex]m=\dfrac{5}{10}[/tex]
[tex]m=\dfrac{1}{2}[/tex]
So, the slope is 1/2 and we know that the equation for the line that passes through these two points should look like: [tex]y=\frac{1}{2} x+b[/tex]
Step 2. Find the y-interceptTo find "b", substitute one of the known points, and solve for "b":
[tex]y=\frac{1}{2} x+b[/tex]
[tex](3)=\frac{1}{2} (6)+b[/tex]
[tex]3=3+b[/tex]
Subtracting 3 from both sides to isolate the "b"...
[tex](3)-3=(3+b)-3[/tex]
[tex]0=b[/tex]
So, the y-intercept is 0. Substituting into our line equation, [tex]y=\frac{1}{2} x+(0)[/tex] which simplifies to [tex]y=\frac{1}{2} x[/tex]
3x+5y = 15 find the slope of a line perpendicular to each given line
Answer:
Slope = 5/3
Step-by-step explanation:
See attached image
Please help me with this
Answer:
1 and 4
Step-by-step explanation:
(x²+1)(x²-4) = x^4 -3x²-4
The green blank is 1 and the blue/purple is 4.
Hope this helped and brainliest please
Graph the inverse of the line provided on the graph.
Drawing Tools
Click on a tool to begin drawing.
I need help with this question . I have 1 answer and this question has 4 answers I already found 1.
Answer:
A , C , E , F
Step-by-step explanation:
If you have to write the solution, just tell me.
What is the exact volume of the sphere?
56.3¯π ft³
274.625π ft³
366.16¯π ft³
1464.6¯π ft³
Answer:
1150.35 ft^3
Step-by-step explanation:
4/3πr^3 is the equation to find the volume of a sphere.
we know the radius is 6.5 feet so all we have to do is input it and calculate.
please give brainliest!
hope this helps
40% of the students in a class are girls and the number of boys is 24 find the total number of students and the number of girls
Answer:
Girls = 16
Total students = 40
Step-by-step explanation:
40% of the students are girls, this means 60% of the students are boys.
To find the number of girls, setup a proportion using the percentages and actual number of students in the class. I am going to make the numerator the numbers that go with the girls and the denominator will be the numbers that go with the boys.
Also let's convert the percentages to decimals by moving the decimal two places left.
40% = 0.4 and 60% = 0.6
[tex]\frac{.4}{.6} =\frac{g}{24} \\.6g=9.6\\\frac{.6g}{.6} =\frac{9.6}{.6} \\g=16[/tex]
Now let's find the total number of students by adding the number of girls to the number of boys.
16 + 24 = 40
1 Pound brown sugar is equivalent to _____ cups
Answer:
3 1/2 or said as 3.5 cups is equal to 1 pound
Step-by-step explanation:
1 Pound brown sugar is equivalent to ___3 1/2 or 3.5 __ cups
Hope This Helped
A soup can lid has a diameter of 8 cm and it is 15 cm tall. what is the area of the lid?
Answer:
50.27
Step-by-step explanation:
area for a circle is (pie)r^2
r^2=16
16xpie=50.27
Can you guys help me with this math questions
Answer:
2) $40 per shirt
3) 80/9 m = 8.9 m (nearest tenth)
Step-by-step explanation:
The first question has been answered here: https://brainly.com/question/27846862
------------------------------------------------------------------------------------------------------
Question 2
Given information:
Previous sales = 300 shirts at $20 eachFor every $1 increase in price, the number of sales diminishes by 5Let [tex]x[/tex] = number of $1 increases
Let [tex]y[/tex] = total revenue (in dollars)
From the given information:
Price change of shirt: [tex](20 + x)[/tex]Number of sales change: [tex](300 - 5x)[/tex]Therefore, we can create a quadratic equation with the given information:
[tex]\implies y = (20+x)(300-5x)[/tex]
As we need to find the maximum amount of revenue, we need to find the vertex of [tex]y[/tex]. As the equation is already factored, the quickest way to do this is to the find the mid-point of the zeros (since a quadratic curve is symmetrical).
[tex]\begin{aligned}y & =0\\\implies (20+x)(300-5x) & =0\\\implies (20+x) & =0 \implies x=-20\\\implies (300-5x) & = 0 \implies x=60\end{aligned}[/tex]
[tex]\textsf{Midpoint}=\dfrac{-20+60}{2}=20[/tex]
Therefore, Sammy should have 20 $1 increases to maximize the revenue, so the new price will be:
[tex]\implies \$20 + 20 \times \$1 = \$40\: \sf per\:shirt[/tex]
------------------------------------------------------------------------------------------------------
Question 3
Given information:
Bridge is modeled as a parabolaWidth of bridge = 30 mMax height of bridge = 10 m high (in the middle)As the bridge is modeled as a parabola, and we have been given the width and height, we can create a quadratic equation using the vertex form.
Vertex form: [tex]y=a(x-h)^2+k[/tex]
where:
x is the horizontal distance of the bridgey is the height of the bridge(h, k) is the vertexa is some constantMiddle of the bridge = 30 m ÷ 2 = 15 m
Max height of the bridge = 10 m
Therefore, the vertex of the parabola is (15, 10)
[tex]\implies y=a(x-15)^2+10[/tex]
We know that when [tex]x = 0, y = 0[/tex]. Therefore, substitute these values into the equation and solve for a:
[tex]\implies 0=a(0-15)^2+10[/tex]
[tex]\implies 0=225a+10[/tex]
[tex]\implies 225a=-10[/tex]
[tex]\implies a=-\dfrac{10}{225}[/tex]
[tex]\implies a=-\dfrac{2}{45}[/tex]
Therefore, the equation of the parabola is:
[tex]\implies y=-\dfrac{2}{45}(x-15)^2+10 \quad \quad \textsf{for }0\leq x\leq 30[/tex]
The horizontal distance at 5 m right of the middle is:
[tex]\implies \dfrac{30}{2}+5=20\:\sf m[/tex]
Therefore, to find the height at this point, input [tex]x=20[/tex] into the equation and solve for y:
[tex]\implies -\dfrac{2}{45}(20-15)^2+10=\dfrac{80}{9}\:\sf m[/tex]
Therefore, the height of the bridge at 5 m to the right of the middle is:
[tex]\dfrac{80}{9}\:=8.9\: \sf m\:(nearest\:tenth)[/tex]
2. Given 4x² + bx + 25, select a possible b value that will make this factorable. [A] b=-50 [B] b = -29 [C] b = 10 [D] b= 100
Answer:
b = 40 and -40
General form of Perfect square trinomial is
a
2
+
2
a
b
+
b
2
Therefore from
16
x
2
−
b
x
+
25
a
2
=
√
16
x
2
,
b
2
=
25
, then
a
=
±
4
x
,
b
=
±
5
take consideration a=4x and b=-5 (different sign), then
−
b
x
=
2
(
4
x
)
(
−
5
)
−
b
x
=
−
40
x
b
=
40
The perfect square is
(
4
x
−
5
)
2
=
16
x
2
−
40
x
+
25
.
if we consider a=4x and b=5 (same sign), then
−
b
x
=
2
(
4
x
)
(
5
)
−
b
x
=
40
x
b
=
−
40
The perfect square is
(
4
x
+
5
)
2
=
16
x
2
+
40
x
+
25
.
The first solution
(
4
x
−
5
)
2
is the best solution after comparing the expression given.
An 8in x 11in photo is enlatged by 200% what are the Dimensions of the enlargement?
Answer:
16in x 22in
Step-by-step explanation:
8in = 100%
x = 200%
(200*8) / 100 = 16
11in = 100%
X = 200%
(200*11) / 200 = 22
The trick is to cross multiply (without multiplying the X) and then divide by the number that was not multiplied :)
Answer:
16 in by 22 in
Step-by-step explanation:
Each dimension is multiplied by the scale factor when a photo is enlarged or reduced.
__
The enlarged photo will have dimensions ...
(200% × 8 in) by (200% × 11 in) = 16 in by 22 in
_____
Additional comment
The factor 200% is equal to 200/100 = 2. (% and /100 are interchangeable)
Which of the following is not a triangle congruence theorem?
AAA
AAS
ASA
Answer:
A. (AAA)
Step-by-step explanation:
.....(AAA) "does not work because it can produce similar but not congruent triangles"
.....(AAS) "If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent."
.....(ASA)"triangles are congruent if any two angles and their included side are equal in the triangles."
Hope This Helped