Answers
Answer:
Approximately [tex]22.2\; \rm m[/tex].
Step-by-step explanation:
By sine rule, the length of each side of a triangle is proportional to the sine value of the angle opposite to that side. For example, in this triangle [tex]\triangle ABC[/tex], angle [tex]\angle A[/tex] is opposite to side [tex]BC[/tex], while [tex]\angle C[/tex] is opposite to side [tex]AB[/tex]. By sine rule, [tex]\displaystyle \frac{BC}{\sin{\angle A}} = \frac{AB}{\sin \angle C}[/tex].
It is already given that [tex]BC = 22.4\; \rm m[/tex] and [tex]\angle A = 58^\circ[/tex]. The catch is that the value of [tex]\angle C[/tex] needs to be calculated from [tex]\angle A[/tex] and [tex]\angle B[/tex].
The sum of the three internal angles of a triangle is [tex]180^\circ[/tex]. In [tex]\triangle ABC[/tex], that means [tex]\angle A + \angle B + \angle C = 180^\circ[/tex]. Hence,
[tex]\begin{aligned}\angle C &= 180^\circ - \angle A - \angle B \\ &= 180^\circ - 58^\circ - 65^\circ \\ &= 57^\circ\end{aligned}[/tex].
Apply the sine rule:
[tex]\begin{aligned} & \frac{BC}{\sin{\angle A}} = \frac{AB}{\sin \angle C} \\ \implies & AB = \frac{BC}{\sin{\angle A}} \cdot \sin \angle C \end{aligned}[/tex].
[tex]\begin{aligned}AB &= \frac{BC}{\sin{\angle A}} \cdot \sin \angle C \\ &= \frac{22.4\; \rm m}{\sin 58^\circ} \times \sin 57^\circ \\ &\approx 22.2\; \rm m\end{aligned}[/tex].
Related Questions
A city has a population of 300000 people. Suppose that each year the population grows by 8.5%. What will the population be after 15 years? Use the calculator provided round your answer to the nearest whole number.
Answers
Answer:
682,500 people
Step-by-step explanation:
so just find how many people per year it grows by then add that number 15 times to 300,000
so 8.5% of 300,000 is 25,500 people
now multiply that by 15 to get 382,500
add that to 300,000
Final answer:
Using the exponential growth formula, the population of a city with an initial population of 300,000 and an annual growth rate of 8.5% will be approximately 962,100 after 15 years.
Explanation:
To calculate the future population of a city with an initial population of 300,000 people and an annual growth rate of 8.5% over 15 years, we use the formula for exponential growth:
P = P_0 (1 + r)[tex]^{t}[/tex]
where:
P is the future population,
P_0 is the initial population (300,000),
r is the annual growth rate (expressed as a decimal, so 8.5% becomes 0.085), and
t is the number of years (15).
Substituting the values we get:
P = 300,000 (1 + 0.085)¹⁵
Calculating this, we find:
P = 300,000 (1.085)¹⁵
P = 300,000 (3.207)
P ≈ 962,100
Therefore, after 15 years, the population is expected to be approximately 962,100, rounding to the nearest whole number.
A city pool sells full-day and half-day passes during the summer. The goal is to make $1000 each day from pool pass sales. The graph shows the number of full-day and half-day passes they need to sell to make $1000.
What is the maximum number of half-day passes the pool can sell and make exactly $1000?
Answers
The maximum number of half-day passes that the pool can sell and make exactly $1000 is 200 half-day passes.
In Mathematics and Geometry, the x-intercept of any function is the point at which the graph of a function crosses or touches the x-axis and the y-value or value of "y" is equal to zero (0).
By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following x-intercept:
x-intercept = (200, 0)
In this context, we can logically conclude that the maximum number of half-day passes that the pool can sell and make exactly $1000 is 200 half-day passes.
Complete Question:
A city pool sells full-day and half-day passes during the summer. The goal is to make $1000 each day from pool pass sales. The graph shows the number of full-day and half-day passes they need to sell to make $1000.
What is the maximum number of half-day passes the pool can sell and make exactly $1000?
Factor both plz :)
p^2–16c^2–p–4c
x^2–7x+7y–y^2
Answers
The factored forms are [tex]\((p + 4c)(p - 4c - 1)\)[/tex] for the first expression and [tex]\(-(x - 7)(y - 7)\)[/tex] for the second expression.
Let's factor the given expressions:
1. [tex]\(p^2 - 16c^2 - p - 4c\)[/tex]:
To factor this quadratic expression, we can use the difference of squares formula, [tex]\(a^2 - b^2 = (a + b)(a - b)\)[/tex]. In this case, [tex]\(p^2 - 16c^2\)[/tex] is a difference of squares, so we can factor it as [tex]\((p + 4c)(p - 4c)\)[/tex]. The remaining terms are [tex]\( - p - 4c\)[/tex], and thus, the factored form is [tex]\((p + 4c)(p - 4c) - (p + 4c)\)[/tex]. Factoring out the common factor of -1 from the last two terms gives us the final factored expression: [tex]\((p + 4c)(p - 4c - 1)\)[/tex].
2. [tex]\(x^2 - 7x + 7y - y^2\)[/tex]:
This expression is a quadratic trinomial, and to factor it, we need to find two binomials whose product equals the given expression. The expression can be rewritten as [tex]\(x^2 - 7x - y^2 + 7y\)[/tex]. Now, we can group the terms as [tex]\((x^2 - 7x) - (y^2 - 7y)\)[/tex]. Factoring out \(x\) from the first group and y from the second group, we get [tex]\(x(x - 7) - y(y - 7)\)[/tex]. Now, we notice that both terms have a common factor of -1, so we can factor that out to obtain the final result: [tex]\(-(x - 7)(y - 7)\)[/tex].
can you expand 8(3x-y) please
Answers
Answer:
24x − 8y
Step-by-step explanation:
8(3x-y)
apply distributive property;
1. 8 (3x) + 8 (−y)
multiply 3 by 8 ;
2. 24x + 8 (-y)
multiply -1 by 8;
3. 24x - 8y
Regroup terms ;
4. 24x − 8y
Graph f(x)=(x−2)(x−6) .
Use the parabola tool then choose the vertex followed by one point on the parabola.
Answers
Here is the graph for the equation
Given function to be graphed is,
f(x) = (x - 2)(x - 6)
We will convert the equation of the function into the vertex form,
(x - 2)(x - 6) = x(x - 6) - 2(x - 6)
= x² - 6x - 2x + 12
= x² - 8x + 12
= x² - 2(4x) + 16 - 4
f(x) = (x - 4)²- 4
By comparing this equation with the vertex form of the equation of a parabola,
g(x) = a(x - h)² + k
Here, (h, k) is the vertex of the parabola.
Therefore, vertex of the function 'f' will be (4, 4).
Now we will find the x-intercepts and y-intercept of the function.
For x-intercept, put f(x) = 0
0 = (x - 4)²- 4
(x - 4) = ±2
x = 4 ± 2
x = 2, 6
Therefore, x-intercepts of the function are (2, 0) and (6, 0).
For y-intercept, put x = 0
f(0) = (0 - 2)(0 - 6)
f(0) = 12
Therefore, y-intercept of the function is (0, 12).
By plotting these ordered pairs and joining them by a curve we can get the graph of the parabola.
Learn more how to graph a curve,
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the mustard factory has 20,000 ounces of mustard to put into small packets.uf each packets holds 1/4 ounce,how many packets can be filled
Answers
All you have to do is multiple both the numbers
6. © Assessment Emma has two $10 bills,
three $5 bills, and two $1 bills. How much
more money does she need to buy a
game that costs $45? Explain.
What bills can you use to show how much
more money Emma needs?
Answers
Answer:
Emma needs one more $5 bill and 3 more $1 bills to buy the game that costs $45.
Step-by-step explanation:
10+10=20
5+5+5=15
1+1=2
20+15+2= 37
45-37=8
5+3 =8
Emma will need $8 more to buy the game
$10+$10= $20
$5+$5+$5= $15
$1+$1=$2
$20+$15+$2= $37
$45-$37= $8
The bills you can use to show how much more money Emma needs is a $5 bill and 3 $1 bills. Or you can use 8 $1 bills.
Hope this helps :)
pls help me find out the answer for number 12 please and thank you
Answers
Answer:
D:step 4
Step-by-step explanation:
Use the distributive property to remove the parentheses.
Simplify your answer as much as possible.
3/4(3--16)
Answers
I believe it is 14.25
Step-by-step:
3/4(3 - -16)
First do what’s in the parentheses
(3 - -16) -> (3 + 16)
because two negatives make a positive (aka when you subtract -16 from 3 it becomes positive 16)
Then (3 + 16) = (19)
3/4(19) you multiply and get 14.25
Joe and Beth both wash cars for extra cash. Joe charges a base fee of $15 and $8 per car after that. Beth charges a base fee of $45 and $6 per car after that. At least how many cars will joe need to wash to have more money that Beth? A. 13 cars B. 14 cars C. 15 cars. D. 16 cars
Answers
Answer:
C- 15 cars.
Step-by-step explanation:
To do this, you will need to set up an equation as follows:
8x+15=6x+45
Then you will subtract 6x from each side. Then you will have this:
2x+15=45
Then you will subtract 15 from each side, and then you will have:
2x=30
Then you will divide each side by 2 and you will get 15. Hope this helped!
The cuboid ABCDEFGH has sides AB = 3 cm, BC = 4 cm and CG = 5 cm.
What is the length AG? Give your answer in cm correct to 3 significant figures.
Answers
Answer:
7.071 cm
Step-by-step explanation:
Final answer:
To find the length AG in the cuboid ABCDEFGH, use the three-dimensional Pythagorean theorem twice. First finding the diagonal AC (which is equal to 5 cm), and then using it to find AG. The length AG, to three significant figures, is approximately 7.07 cm.
Explanation:
The length AG of a cuboid ABCDEFGH can be found by using the Pythagorean theorem in three dimensions. This theorem is an extension of the traditional Pythagorean theorem used in two dimensions. For the given cuboid, we start by using the Pythagorean theorem on triangle ABC to find the diagonal AC. The formula for the Pythagorean theorem is:
c2 = a2 + b2
Where c is the diagonal and a and b are the sides of the right triangle:
AC2 = AB2 + BC2
Plugging in the given values, we have:
AC2 = 32 + 42 = 9 + 16 = 25
So, AC = 5 cm.
Now, to find AG, we use the diagonal AC and side CG in another application of the Pythagorean theorem for the right triangle ACG:
AG2 = AC2 + CG2
AG2 = 52 + 52 = 25 + 25 = 50
AG = √50 ≈ 7.071 approximately.
Therefore, the length AG, expressed to three significant figures, is approximately 7.07 cm.
What's the supplimentary angle ?
Answers
Answer:
Step-by-step explanation:
A supplementary angle is equal to 180 degrees. So subtract 96.7 degrees from 180. 180-96.7= 83.3 degrees
Your answer is 83.3 degrees.
Answer: 83.7 is supplimentary
Step-by-step explanation: 180 - 96.7 = 83.7
1. A firefighter is called to rescue a cat caught in a tree. If the firefighter is standing 30
m from the base of the tree and if the angle to the cat is 20'. How high in the tree is
the cat?
Answers
Answer:
10.92m
Step-by-step explanation:
See attached picture for more illustration
Using SOH CAH TOA,
Tan 20° = opposite / adjacent
Tan 20° = x / 30
x = 30 * tan20
x = 10.919m = 10.92m
The height of the tree is 10.92m
Final answer:
The height of the cat in the tree is 10.44m
Explanation:
The question involves finding the height of a cat caught in a tree using trigonometry, specifically the tangent function. If the firefighter is standing 30m from the base of the tree and the angle to the cat is 20 minutes (which should be converted to degrees for typical trigonometric calculations), we can calculate the height of the cat in the tree. First, we need to convert the angle from minutes to degrees. Since 1 degree = 60 minutes, 20 minutes is equal to 20/60 degrees or approximately 0.33 degrees.
To find the height of the cat, we can use the tangent function (tan) in trigonometry, which is the ratio of the opposite side (the height of the cat in the tree, which we're trying to find) to the adjacent side (the distance from the firefighter to the base of the tree). Thus, the formula becomes height = tan(angle) × distance.
Using the formula:
distance = 30m
angle = 0.33 degrees
height = tan(0.33 degrees) × 30
Tan(20') x Distance
Calculating: Height = Tan(20') x 30m = 10.44m
I will mark brainliest if correct please answer fast I will give 10 points to the first person who answers
Answers
.answer:
120
step-by-step explanation:
10+10+10+10=40
8+8+8+8. =32
12+12+12+12=48
add everything up (the numbers that we got) and you would get 120cm
Answer:
960
Step-by-step explanation:
You multiply the base x height x width. So you do 10 x 8 x 12 = 960 cm.
Ms G has 16 hw papers and 14 quiz and MS M has 64 hw papers and 60 quiz to return. What tge ratio to represent the number of he papers to quiz that have to be returned.
Answers
The two teachers have 16 and 64 homework papers to return, totalling in 80.
They also have 14 and 60 quizzes to return, totalling in 74.
The ratio of homework papers to quizzes that need to be returned is 80:74
In total, there are 80 homework papers and 74 quizzes to be returned. The ratio for the total would be 80 : 74 (or 80/74), and 40 : 37 (or 40/37) simplified.
For Ms. G alone, the ratio would be 16 : 14 (or 16/14), and 8 : 7 (or 8/7) simplified.
For Ms. M alone, the ratio would be 64 : 60 (or 64/60), and 16 : 15 (or 16/15) simplified.
Hope this helps!! :)
Solve for θ if cosθ = 0.81. Round answer to the nearest degree.
Answers
Answer:
the answer is 36 degrees
the lengths of the sides of a triangle are shown. 8.73, 12.4, and 10.075. what is the perimeter of the triangle
Answers
Answer:
31.205
Step-by-step explanation:
The perimeter is the sum of the side lengths:
8.73 +12.4 +10.075 = 31.205
_____
If you're after an answer that has the appropriate precision (assuming these are measured values), that would be one that is rounded to 1 decimal place: 31.2.
Find the 88th term of the arithmetic sequence 4,-1,-6
Answers
Answer:
an = a1 + d(n - 1)
a88 = 4 + (-5)(88 - 1)
a88 = 4 + (-5)(87)
a88 = 4 - 435
a88 = -431
So, the 88th term of the arithmetic sequence is -431.
The 88th term of the given arithmetic sequence is equal to -431.
Given the following data:
First (1st) term = 4Second term = -1To calculate the 88th term of the given arithmetic sequence:
Mathematically, the nth term of an arithmetic sequence is given by the formula:
[tex]a_n = a_1 + d(n - 1)[/tex] ...equation 1.
Where:
d is the common difference.[tex]a_1[/tex] is the first term of an arithmetic sequence.First of all, we would determine the common difference as follows:
[tex]d = a_2 - a_1\\\\d=-1-4[/tex]
d = -5
Substituting the values into eqn. 1, we have:
[tex]a_{88} = 4 + [-5](88 - 1)\\\\a_{88} = 4 -5(87)\\\\a_{88} = 4 -435\\\\a_{88} = -431[/tex]
Read more on arithmetic sequence: https://brainly.com/question/12630565
is the difference in length between a monarch butterfly and a bumblebee greater or less than the difference in length between a walking stick and grasshopper explain your reasoning.PLS HELP HURRY I KNOW ITS LATE HURRY!
Answers
The difference in length between a monarch butterfly and a bumblebee greater than the difference in length between a walking stick and grasshopper.
Solution:
Length of Monarch butterfly = [tex]3\frac{1}{2}[/tex] in
Length of Bumble bee = [tex]\frac{5}{8}[/tex] in
Difference between their lengths
[tex]=3\frac{1}{2}-\frac{5}{8}[/tex]
To convert mixed fraction into improper fraction.
[tex]=\frac{7}{2}-\frac{5}{8}[/tex]
To make the denominator same, multiply and divide the first term by 4.
[tex]=\frac{28}{8}-\frac{5}{8}[/tex]
[tex]=\frac{23}{8}[/tex]
Difference between length of Monarchy and Bumble bee is [tex]\frac{23}{8}[/tex] in.
Length of Walking stick = 4 in
Length of Grasshopper = [tex]1\frac{3}{4}[/tex] in
Difference between their lengths
[tex]=4-1\frac{3}{4}[/tex]
To convert mixed fraction into improper fraction.
[tex]=\frac{4}{1}-\frac{7}{4}[/tex]
To make the denominator same, multiply and divide the first term by 4.
[tex]=\frac{16}{4}-\frac{7}{4}[/tex]
[tex]=\frac{9}{4}[/tex]
Difference between length of Walking stick and Grasshopper is [tex]\frac{9}{4}[/tex] in.
Compare: [tex]\frac{23}{8}[/tex] and [tex]\frac{9}{4}[/tex]
To compare the fractions, make the denominator same.
So multiply and divide [tex]\frac{9}{4}[/tex] by 2, we get
[tex]\frac{23}{8}[/tex] and [tex]\frac{18}{8}[/tex]
[tex]$\frac{23}{8}>\frac{18}{8}[/tex]
Hence the difference in length between a monarch butterfly and a bumblebee greater than the difference in length between a walking stick and grasshopper.
What is 32+8(y-6) simplified
Answers
Answer:
8y - 16
Step-by-step explanation:
Step 1: Distribute
32 + 8(y - 6)
32 + 8y - 48
8y - 16
Answer: 8y - 16
If needed solve for y:
8y - 16 + 16 = 0 + 16
8y / 8 = 16 / 8
y = 2
Answer:
8y - 16
Step-by-step explanation:
The leaning tower of Pisa in Italy appears to be cylindrical in shape. It’s height is about 56 meters. If the volume of the tower is about 9,891 cubic meters, what is the diameter of the base?
Please explain how you found your answer
Answers
The diameter of the base of the tower is approximately 15m.
The height of the leaning tower = 56 m
The leaning tower is cylindrical in shape.
Suppose the diameter of the base of the tower is d
What is the volume of a cylinder?The volume of a cylinder with a diameter d and height h is [tex]\frac{\pi }{4} d^{2} h[/tex].
Given that the volume of the tower is about 9,891 cubic meters.
This means [tex]\frac{\pi }{4} d^{2} h=9891[/tex]
[tex]\frac{\pi }{4} d^{2} *56=9891[/tex]
[tex]d=15m[/tex]
Hence, the diameter of the base of the tower is approximately 15m.
To get more about cylinders visit:
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Answer pleas I’ll give 20 points
Answers
Given that Z = X m W = 4x + 20 and m Y = x + 26 find the value of x for which WXYZ must be a parallelogram
Answers
To find the value of x for which WXYZ must be a parallelogram, set up an equation by equating the lengths of opposite sides. Solve the equation to find the value of x.
Explanation:To find the value of x for which WXYZ must be a parallelogram, we first need to understand the properties of parallelograms. One important property is that opposite sides are equal in length. Given that WZ = XY, we can set up an equation: 4x + 20 = x + 26. By solving this equation, we can find the value of x.
4x + 20 = x + 26
Subtracting x from both sides, we get:
3x + 20 = 26
Subtracting 20 from both sides, we get:
3x = 6
Dividing both sides by 3, we get:
x = 2
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In a 45-45-90 triangle, the ratio of the length of the hypotenuse to the length of a side is
Answers
See the figure below for a better understanding of the problem. Since we have a 45-45-90 triangle, this is an isosceles triangle, so both the adjacent and opposite sides measure the same value, say, x. Then the hypotenuse would be:
[tex]H=\sqrt{x^2+x^2} \\ \\ H=2\sqrt{2}[/tex]
Then. the ratio of the length of the hypotenuse to the length of a side is:
[tex]\boxed{r=\frac{2\sqrt{x}}{x}}[/tex]
In a 45-45-90 triangle, the ratio of the length of the hypotenuse to the length of a side is √2:1. This means that if one of the legs (the sides opposite the 45-degree angles) has a length of "x" units, then the hypotenuse (the side opposite the 90-degree angle) will have a length of "x√2" units.
Each side of a square is increasing at a rate of 8 cm/s. At what rate is the area of the square increasing when the area of the square is 25 cm2?
Answers
Answer:
80cm^2/s
Step-by-step explanation:
This is a related rates problem where we are considering the rate at which the area of a square changes with respect to time.
So lets consider the area of a square:
A = s^2 (where s represents the length of one side of the square)
Related rates problem deal with functions of time so if we take the area and side length as a function of time and then differentiate implicitly we get:
[tex]\frac{dA}{dt} = 2s(\frac{ds}{dt})[/tex]
The problem states that the side of a square is increasing at a rate off 8cm/s so we can conclude that ds/dt = 8cm/s leaving us with:
[tex]\frac{dA}{dt} = 16s[/tex]
Now, to solve for s we have to consider the other value given. If the area of the square is initially 25cm^2 we can plug this into our formula for area to solve for the side length.
25 = s^2
s = +/- 5 (since side lengths are only positive we only consider +5)
s = 5
Now we can plug this back in for s:
[tex]\frac{dA}{dt} = 80[/tex]
Therefore, the rate at which the area of the square is increasing is 80cm^2 per second.
-2x+ 12 <-4
Solve the inequality
Answers
Answer:
x > 8
Step-by-step explanation:
-2x + 12 < -4 (Given)
-2x < -16 (Subtracted 12 on both sides.)
x > 8 (Divided by -2 on both sides.)
*Note that if you multiply or divide by a negative number, the sign will flip.*
PLLLSSS HURRRYYY
The Problem:
Mrs. Ashe is planning to take her study group on a field trip to an amusement park. The regular cost is $55 per person. There is a party special that costs $46 per person with an additional $45 fee for a private room where students can eat lunch. Mrs. Ashe is trying to decide if she should use the regular price or the party special.
Part 1:
A) Write an equation in slope-intercept form (y=mx+b) to show the total cost of the regular price with x people, where x = number of students in the study group and y = the total cost. (50 points)
B) Write an equation in slope-intercept form (y=mx+b) to show the total cost of the party special with x people, where x = number of students in the study group and y = the total cost. (50 points)
Answers
Answer:
y = 55xy = 46x +45Step-by-step explanation:
A. The regular cost is 55 per person. Using the given variable definitions, that cost can be expressed as ...
y = 55x
__
B. The party special cost is 46 per person, with an added fee of 45. That cost can be expressed as ...
y = 46x +45
_____
As you know, the cost of a purchase is the product of the cost of an item and the number of items. Here, the cost of entry is the cost of the item of interest, and the number of persons needing entry is the number of items. The party special has the addition item of a private room, so its cost is added to the total for the party special.
Today is your friend's birthday. She is y years
old. Her brother is 5 years younger.
Answers
I need the answer to y=2x+7 in a graph and passes through (3,3)
I need the given, parallel, slope intercept form
Answers
The slope-intercept form is y = 2x-3.
Step-by-step explanation:
Given,
The equation of the line is y=2x+7.The general equation of the line is in the form y= mx+c.where 'm' represents the slope of the line.Comparing the given equation with general equation, it can be determined that :
m = 2 and c = 7 (y-intercept).
The given line passes through the point (3,3) which is equal to (x1,y1)
Therefore, x1=3 and y1=3.
Substitute m=2 and the values of (x1,y1) in the slope-intercept form,
The slope-intercept form is (y-y1) = m (x-x1)
(y-3) = 2(x-3)
y = 2x-6+3
y = 2x-3
EXPLAIN what equivalent fractions are and give an example. PLEASE answer me.
Answers
Answer: Equivalent fractions are fractions with different numbers representing the same part of a whole. They have different numerators and denominators, but their fractional values are the same.
Step-by-step explanation : For example, think about the fraction 1/2. It means half of something. You can also say that 6/12 is half, and that 50/100 is half. They represent the same part of the whole. These equivalent fractions contain different numbers but they mean the same thing: 1/2 = 6/12 = 50/100
Multiply both the numerator and denominator of a fraction by the same whole number. As long as you multiply both top and bottom of the fraction by the same number, you won't change the value of the fraction, and you'll create an equivalent fraction.
Find fractions equivalent to 3/4 by multiplying the numerator and denominator by the same whole number ! Again, hoped this helped. If you do used, don't word for copy. Make it into your own words.
Equivalent fractions are fractions with different numbers representing the same part of a whole. They have different numerators and denominators, but their fractional values are the same.
For example, think about the fraction 1/2. It means half of something. You can also say that 6/12 is half, and that 50/100 is half. They represent the same part of the whole. These equivalent fractions contain different numbers but they mean the same thing: 1/2 = 6/12 = 50/100