((Image Included))
If x = 27 inches, what is the perimeter of the figure above?
A. (108 + 54 + 54) inches
B. (54 + 108) inches
C. (364.5 + 729) inches
D. (27 + 54 + 81) inches
Answers
Answer:
=204.13 inches.
Step-by-step explanation:
Using the side x, we can use sine to find the hypotenuse of the triangle with the angle marked 30°.
Sin 30 =x/hypotenuse.
sin 30 = 27/hyp
hyp= 27/sin 30
=54 inches
We can also find the adjacent as follows.
Cos 30 = adjacent/ 54
Adjacent= 54 cos 30
=46.77 inches
Using the angles marked 45 we can find the hypotenuse of the isosceles triangle.
sin 45= x/hypotenuse
sin 45 =27/hypotenuse
hypotenuse = 27/sin 45
=38.18 inches
The hypotenuse of both the triangles making the isosceles triangle are 38.18 inches long.
Perimeter = 54+ 46.77+27+ 38.18+38.18
=204.13 inches.
The total perimeter of the given figure is 204.13 inches
Let's break down the solution step by step:
1. Triangle with 30° Angle:
- We have a right triangle with one angle measuring 30°.
- The side opposite the 30° angle (labelled as "x") is 27 inches.
- We want to find the hypotenuse (the longest side).
- Using the sine function:
[tex]\[ \sin(30°) = \frac{x}{\text{hypotenuse}} \] - Solving for the hypotenuse: \[ \text{hypotenuse} = \frac{27}{\sin(30°)} = 54 \text{ inches} \][/tex]
2. Adjacent Side of the 30° Triangle:
- We can also find the adjacent side (labelled as "adjacent") using the cosine function:
[tex]\[ \cos(30°) = \frac{\text{adjacent}}{54} \] - Solving for the adjacent: \[ \text{adjacent} = 54 \cos(30°) = 46.77 \text{ inches} \][/tex]
3. Isosceles Triangle with 45° Angles:
- We have an isosceles triangle with two angles measuring 45° each.
- The side opposite each 45° angle is also 27 inches (since it's an isosceles triangle).
- We want to find the hypotenuse of this triangle.
- Again using the sine function:
[tex]\[ \sin(45°) = \frac{x}{\text{hypotenuse}} \] - Solving for the hypotenuse: \[ \text{hypotenuse} = \frac{27}{\sin(45°)} = 38.18 \text{ inches} \][/tex]
4. Total Perimeter:
- The perimeter of the entire figure is the sum of all sides:
[tex]\[ \text{Perimeter} = 54 + 46.77 + 27 + 38.18 + 38.18 = 204.13 \text{ inches} \][/tex]
Therefore, the total perimeter of the given figure is 204.13 inches.
Related Questions
Joan had a garden 10.1 m long and 4.2 m wide. She decides to fence it in to keep out the deer. The dimensions of the fence are 11.2 m long and 5.0 m wide. What is the area between the fence and the garden?
Answers
Answer:
14.08 m
Step-by-step explanation:
Start by finding the area of the fence and the area of the garden. Garden- 10.1*4.2=42.42 Fence-11.3*5=56.5
Now subtract the two values. 56.5-42.42=14.08
Can someone please help me Factor 4x^2 - 81
Answers
Answer:
(2x-9)(2x+9)
Step-by-step explanation:
This is a difference of squares because it can be written as (2x)^2-9^2
The formula for factoring a difference of squares is a^2-b^2=(a-b)(a+b)
So replace a with 2x and b with 9 giving us
4x^2-81=(2x-9)(2x+9)
4x^2-81
2^2 x^2-9^2
(2x)^2-9^2
(2x-9)(2x+9)
evaluate the expression 3x +(z+2y)-12 if x=3,y=8 and z=5
Answers
Answer:
18
Step-by-step explanation:
First you need to plug in the numbers for each variable.
3(3)+(5+2(8))-12
Now you solve
3(3)+(21)-12
9+21-12
18
which expression is equivalent to 4 square root 6 divided by 3 root 2
Answers
The equivalent expression to 4 √6 divided by 3 √2 is 4/3 × √3. This is achieved by expressing the square roots as fractional exponents and simplifying.
Explanation:The student is asking which expression is equivalent to the following mathematical expression: √(4 √6) / (3 √2).
To simplify this expression, we'll use the properties of exponents and radicals.
The square root of a number x can be written as x raised to the power of 0.5, so:
√6 = 60.5
√2 = 20.5
The given expression thus becomes:
(4 × 60.5) / (3 × 20.5) = 4/3 × 60.5/20.5
Since the exponents are the same, we can simplify the radicals by dividing the numbers inside the radicals:
4/3 × (6/2)0.5 = 4/3 × (3)0.5
And as (3)0.5 is the square root of 3:
4/3 × √3
Therefore, the equivalent expression is 4/3 × √3.
if my friend and i went to get ice cream, I have $30 and each ice cream is $5. What equation would help me solve this?
Answers
Answer:
[tex]5x\leq30[/tex]
Step-by-step explanation:
Let
x -----> the number of ice cream
we know that
[tex]5x\leq30[/tex]
Solve for x
Divide by 5 both sides
[tex]x\leq30/5[/tex]
[tex]x\leq 6\ ice\ cream[/tex]
therefore
The maximum number of ice cream is 6
What is the Least Common Multiple of 8 and 24
Answers
Answer: 24
Step-by-step explanation:
Break down the numbers until they have no way to be broken down anymore
8 = 4*2 = 2*2*2
24 = 6*4 = 3*2*2*2
The one that has more products is 24, so, it is 24.
Factor the expression.
125x^3+512
Answers
Answer:
its (5x+8)(25x^2-40x+64
Step-by-step explanation:cuz
Three runners competed in a race. Data were collected at each mile mark for each runner. If the runner ran at a constant pace, the data would be linear. A regression line fitted to their data. Uses the residual plots to decide which data set is best fit by the regression line, and then identify the runner that kept the most consistent pace.
Answers
Linear data is data lying across a straight line. The runner which kept the most consistent pace was runner B.
How does linear regression works?Firstly, there is a data set. Then, we try to fit a line which will tell about the linear trend. This line is made using the least squares method.
For the given case, the second runner(runner B)'s data is almost forming a linear trend, whereas, for the first runner, its more spread, and the third graph, its a quadratic trend.
For non-linear trends like in third graph(runner C), we use polynomial regression to fit polynomial curves of higher degrees.
Thus, as the runner B's data set is lying more near to a line than other runners, thus,
The runner which kept the most consistent pace was runner B.
Learn more about linear regression here:
https://brainly.com/question/18854090
Subtract 8 1/6 - 4 5/6 . Simplify the answer and write as a mixed number.
Answers
Answer:
3 1/3
Step-by-step explanation:
8 1/6 - 4 5/6 Borrow 1 or 6/6 from the 8 so you have something to subtract.
7 7/6 - 4 5/6 Subtract the whole numbers.
7 - 4 = 3 Subtract the fractions.
7/6 - 5/6 Do the subtraction
2/6 Reduce
2/6 = 1/3 Put the two parts together.
3 1/3
the result of subtracting the two mixed numbers is [tex]3\frac{1}{3}[/tex]
To subtract the mixed numbers [tex]8\frac{1}{6}[/tex] and [tex]4\frac{5}{6}[/tex] we need to first understand how to subtract it. To subtract mixed numbers we need to first convert them to improper fraction. For the new fraction, the denominator remains same but new numerator is calculated by finding the product of whole number and denominator and then adding it to the numerator. This can be done as follows:
[tex]8\frac{1}{6} = \frac{ 8 \times 6 +1}{6} = \frac{49}{6}[/tex]
[tex]4\frac{5}{6} = \frac{ 4 \times 6 +5}{6} = \frac{29}{6}[/tex]
Now we subtract them as follows:
[tex]\frac{49}{6} - \frac{29}{6} = \frac{20}{6} = \frac{10}{3}[/tex]
To convert this back into mixed fraction we divide 10 by 3 and the quotient becomes the whole number while the remainder becomes numerator and 3 remains as denominator
[tex]\frac{10}{3} = 3\frac{1}{3}[/tex]
Therefore, the result of subtracting the two mixed numbers is [tex]3\frac{1}{3}[/tex]
Which of the following Best describes the function -x^4+1
a)The degree of the function is even so the ends of the graph continue in opposite directions. Because the leading coefficient is positive the left side of the graph continues down the coordinate plane and the right side continues upward.
b) The degree of the function is even so the ends of the graph continue in the same direction. because the leading coefficient is negative the left side of the graph continues down the coordinate plane and the right side also continues downward
c) The degree of the function is even so the ends of the graph continue in opposite directions. because the leading coefficient is negative the left side of the graph continues up the coordinate plane and the right side continues downward
d) The degree of the function is even so the ends of the graph continue in the same direction. because the leading coefficient is positive the left side of the graph continues of the coordinate plane and the right side also continues upward.
Answers
ANSWER
b) The degree of the function is even so the ends of the graph continue in the same direction. because the leading coefficient is negative the left side of the graph continues down the coordinate plane and the right side also continues downward
EXPLANATION
The given polynomial function is
[tex]f(x) = - {x}^{4} + 1[/tex]
The degree of this function is even which is 4.
The function extends in the same direction at both ends.
In other words both ends continue in the same direction.
Since the coefficient of the leading term is negative, the graph extends to negative infinity at both ends.
The correct answer is B
the segments shown below could form a triangle
Answers
Answer:
False
Step-by-step explanation:
a^2+b^2=c^2 so the biggest number would be c and that would be 11 9^2=81 4^2=16 adding these together gets 97. 97=/=11^2 which is 121
Answer:
A. True.
Step-by-step explanation:
We have been given lengths of three segments. We are asked to determine whether the given segments could form a triangle or not.
Triangle inequality theorem states that sum of two sides of triangle must be greater than third side of the triangle.
Using triangle inequality theorem, we will get:
[tex]9+4>11[/tex]
[tex]13>11[/tex] True
[tex]9+11>4[/tex]
[tex]20>4[/tex] True
[tex]4+11>9[/tex]
[tex]15>9[/tex] True
Since our given segments satisfies triangle inequality theorem, therefore, the given segments could form a triangle.
Taylor makes $45 an hour for tutoring. If she tutored for a total of 16 hours last month, how much money did she make?
Answers
Answer:
$720
Step-by-step explanation:
1 hour of tutoring = $45
16 hours of tutoring = $45 x 16 hours = $720
Answer:
$720
Step-by-step explanation: just multiply 45 and 16 together, boom theres your answer
Leticia charges $8 per hour to babysit. She babysat Friday night for 4 hours,
and then she babysat again on Saturday. She earned a total of $72. How
many hours did Leticia babysit on Saturday?
Choose two answers: one for the equation that models this situation and one
for the correct answer.
A. Equation: 8(4 + x) = 72
B. Equation: 4(8 + x) = 72
C. Answer: 5 hours
D. Answer: 11 hours
Answers
For this case we have that the variable "x" represents the number of hours that Leticia uses to take care of children on Saturday.
IF on Friday I use 4 hours ($ 8 each) and on Saturday "x" hours ($ 8 each) obtaining a profit of $ 72, we have the following equation:
[tex]8 (4 + x) = 72[/tex]
We apply distributive property:
[tex]32 + 8x = 72\\8x = 72-32\\8x = 40\\x = \frac {40} {8}\\x = 5[/tex]
So, on Saturday she spent 5 hours.
Answer:
[tex]8 (4 + x) = 72\\x = 5[/tex]
Answer:
Option A.
Option C.
Step-by-step explanation:
Let be "x" the amount of hours Leticia babysat on Saturday.
We know that she charges $8 per hour to babysit, she babysat Friday night for 4 hours and the total amount of money she earned on those two days was $72. Knowing this, we can set up the followin equation models this situation:
[tex]8(4+x)=72[/tex]
Finally, we must solve for "x":
[tex]8(4+x)=72\\\\32+8x=72\\\\8x=72-32\\\\8x=40\\\\x=\frac{40}{8}\\\\x=5[/tex]
3(x - 4) + 5 - x= 2x - 7
how many solutions are there to this equation?
Answers
2x-7 = 2x -7
Infinitely many solutions
Hope this helps!
Answer:
The equation has infinity solutions
Step-by-step explanation:
3( x - 4 ) + 5 - x = 2 x - 7
⇒ Expand brackets
3 x - 12 + 5 - x = 2 x - 7
⇒ Simplify
2 x - 7 = 2 x - 7
PLEASE HELP, I WILL MARK BRAINLIEST
Ted creates a box plot using 14, 13, 21, 10, 28, 30, and 35 as the data. Which of the following box plots shows the data accurately? A box plot is drawn with end points at 10 and 35.The box extends from 13 to 30 and a vertical line is drawn inside the box at 21. A box plot is drawn with end points at 10 and 35.The box extends from 15 to 32 and a vertical line is drawn inside the box at 23. A box plot is drawn with end points at 10 and 35.The box extends from 11 to 28 and a vertical line is drawn inside the box at 19. A box plot is drawn with end points at 10 and 35.The box extends from 17 to 34 and a vertical line is drawn inside the box at 25.
PLEASE HELP
Answers
a box plot is drawn with end points at 10 and 35. The box extends from 13 to 30 and a vertical line is drawn inside the box at 21.
A=4(14-1)
———- +7
3(6)-5
Answers
Answer:
Im boutta fail my final
Step-by-step explanation:
1 like= 1 prayer
PLEASE HELP! BRAINIEST WILL BE MARK IF RIGHT!
Answers
Answer:
X int : 5
Y int : 15
Step-by-step explanation:
y=15
-
3x=15
3/3 15/3
x=5
Answer:
y-intercept=15 and x-intercept = 5
Step-by-step explanation:
We have the following equation:
3x + y = 15.
To find the x-intercept and y-intercept we have to do the following:
1. To find the y-intercept we need to make x=0, and solve for 'y' as follows:
3x + y = 15 ⇒ 3(0) + y = 15 ⇒ y=15
2. To find the x-intercept we need to make y=0, and solve for 'x' as follows:
3x + y = 15 ⇒ 3x + (0) = 15 ⇒ 3x = 15 ⇒ x=5
Therefore, the y-intercept=15 and x-intercept = 5
1. In a 30-60-90 triangle, the length of the hypotenuse is 6. What is the length of the shortest
side?
a. 2
b. 3
c. 3.12
d. 31/3
e, 6-3
Answers
Answer:
b. 3
Step-by-step explanation:
In a 30°-60°-90° triangle, the short side is ½ the hypotenuse [the long side is double the short side].
30°-60°-90° Triangles
x√3 → long side
x → short side
2x → hypotenuse
45°-45°-90° Triangles
x → two legs
x√2 → hypotenuse
I am joyous to assist you anytime.
Which absolute value inequality represents the given graph?
A. 18x + 91 < 57
B. 18x + 91 > 57
C. 18x +91 557
D. 18x +9 57
Answers
Answer:
Distribute the -9 into the values in the parentheses.
STEP BY STEP
-9(-2x-3)
-9*-2x=18x
-9*-3=27
Therefore, the equation then becomes: 18x+27.
The answer is the first choice, or A.
The first ferris wheel was 250 feet in diameter. It was invented by John Ferris in 1893. Assuming it made one revolution every 30 seconds, what was the linear speed of a passenger ( assuming the passenger is on the edge of the ferris wheel) in feet per minute.
Answers
Step-by-step explanation:
The wheel has a diameter of 250 feet, so its circumference is:
C = 2πr = πD
C = 250π feet
It makes one revolution in 30 seconds, or half a minute, so the linear speed of the passenger is:
v = d / t
v = 250π / 0.5
v = 500π ft/min
v ≈ 1571 ft/min
This is about the same as 17.9 mph.
Final answer:
The linear speed of a passenger on the original Ferris wheel with a diameter of 250 feet, making one revolution every 30 seconds, was approximately 1570.8 feet per minute.
Explanation:
The question asks to calculate the linear speed of a passenger on the edge of the first Ferris wheel, which was 250 feet in diameter, and made one revolution every 30 seconds. To find the linear speed, we first need to determine the circumference of the Ferris wheel, which can be done by using the formula for the circumference of a circle, C = πd, where d is the diameter.
For the first Ferris wheel:
Diameter (d) = 250 feet
Circumference (C) = π * 250 feet = 785.398163 feet (approximately)
Time for one revolution = 30 seconds
Since the question requires the speed in feet per minute, we need to convert the time for one revolution to minutes:
30 seconds = 0.5 minutes
The linear speed (v) can be found using the formula v = C / time. Substituting our values in:
v = 785.398163 feet / 0.5 minutes = 1570.79633 feet per minute
Therefore, the linear speed of a passenger at the edge of the Ferris wheel was approximately 1570.8 feet per minute.
The sum of three consecutive integers is 45. What are the integers
Answers
Divide 45 by 3 ( the quantity of consecutive numbers) This will give you the middle number, then use the number higher and lower.
45/3 = 15
14 + 15 + 16 = 45
The 3 numbers are 14, 15 and 16
If set D is not the empty set but is a subset of set E, then which of the following is true? D ∩ E = D D ∩ E = E D ∩ E = ∅
Answers
Answer:
D intersect E=D (the first one you have)
Step-by-step explanation:
D is a subset of E
That means all the elements in D are also in E
So the intersection of D and E is D.
The first thing you wrote is correct, that is, D intersect E=D is right
Answer:
[tex]D\cap E[/tex]=D
Step-by-step explanation:
We are given that D is not empty set but D is a subset of set E.
We have to find the true statement.
[tex]D\neq \phi[/tex]
D is a subset of set E
Therefore,[tex]D\subset E\neq \phi[/tex]
Intersection: It is the set of common elements of two sets.
Therefore,[tex]D\cap E[/tex]=D
Because E contains all elements of D .
Hence, Option A is true.
What value for n makes this equation true?
9xn=(9x40)+(9x6)
A.6
B.15
C.36
D.46
Answers
F(n+1)=f(n)-8. If f(2)=100, what is f(6)
Answers
Answer:
f(6) = 68
Step-by-step explanation:
f(6)
f(n+1)=f(n)-8
n = 5, so
f(6)=f(5)-8
and with n = 4
f(5)=f(4)-8 , so
f(4) = f(3) - 8
f(3) = f(2) - 8 = 100 - 8 = 92
f(3) = 92
Then, we can go and find the result
f(4) =[92] - 8 = 84
f(5)=[84] - 8 = 76
f(6) = [76] -8 = 68
[tex]f(n+1)=f(n)-8\\f(2)=100\\\\f(3)=100-8=92\\f(4)=92-8=84\\f(5)=84-8=76\\f(6)=76-8=68[/tex]
Solve for x: 2/x-2+7/x2-4=5/x
Answers
Answer:
x = 11/6
Step-by-step explanation:
You need to reduce this fraction to the lowest terms.
This can be done by dividing out those factors that appear both in the numerator and in the denominator.
Please mark brainliest and have a great day!
Answer: [tex]\bold{x=-\dfrac{4}{3}\qquad x=5}[/tex]
Step-by-step explanation:
[tex]\dfrac{2}{x-2}+\dfrac{7}{x^2-4}=\dfrac{5}{x}\\\\\\\text{Multiply each term by the LCD x(x-2)(x+2) to clear the denominator:}\\\dfrac{2}{x-2}[x(x-2)(x+2)]+\dfrac{7}{x^2-4}[x(x-2)(x+2)]=\dfrac{5}{x}[x(x-2)(x+2)]\\\\\\\text{Simplify - cross out like terms:}\\2[x(x+2)]+7[x]=5[(x-2)(x-2)]\\\\\\\text{Distribute:}\\2x^2+4x+7x=5x^2-20\\\\\\\text{Set equation equal to zero and Add like terms:}\\0=5x^2-2x^2-7x-4x-20\\0=3x^2-11x-20\\\\\text{Factor, set each factor equal to zero, and solve for x:}[/tex]
[tex]0=(3x+4)(x-5)\\0=3x+4\qquad 0=x-5\\\large\boxed{x=-\dfrac{4}{3}\qquad x=5}[/tex]
The length of a rectangle is three times its width. If the perimeter is at most 112 centimeters, what is its greatest possible value for width?
Answers
Answer:
Step-by-step explanation:
Perimeter= 2L+2W. If L=3W(three times the width) then 2(3W)+2W=112. Or 6W+2W=112 which is equal to 8W=112. To solve for the width, divide both sides by 8 and find 112/8=14, therefore W=14.
Answer:
14 cm
Step-by-step explanation:
Given the length is 3 times the width
If each width is denoted by W, then each length is L = 3W
Perimeter (add up all lengths and widths),
= L + L + W + W
= 3W + 3W + W + W
= 8W
Given that the max perimeter is 112cm
hence 8W = 112,
W = 14 cm at most
Merrida uses a pattern in the multiplication table below to find ratios that are equivalent to 7:9. If Merrida multiplies the first term, 7, by a factor of 6, what should she do to find the other term for the equivalent ratio? Multiply 9 by 1. Multiply 9 by 6. Multiply 9 by 7. Multiply 9 by 9.
Answers
Answer:
Multiply 9 by 6
Step-by-step explanation:
7:9 is the ratio
We multiply the first term by 6.
What we do to one side, we do to the other
7*6=42
9*6 = 54
That way we keep the ratio in the same proportion
42:54
Answer: Multiply 9 by 6.
Step-by-step explanation:
find the missing side
Answers
Answer:
[tex]x=15.56[/tex]
Step-by-step explanation:
We can use the law of sines here. However, we will first need to solve for the missing angle.
The interior angles of a triangle add up to 180.
Therefore,
[tex]35+90+x=180[/tex]
where [tex]x[/tex] is the missing angle.
[tex]35+90+x=180[/tex]
[tex]x+125=180[/tex]
[tex]x=55[/tex]
So the missing angle is 55 degrees.
Now we can use the law of sines to set up a proportion.
[tex]\frac{19}{sin(90)}=\frac{x}{sin(55)}[/tex]
Now simplify the equation.
[tex]x=15.56[/tex]
Rounded to the nearest hundredth.
Answer:
x ≈ 19.6
Step-by-step explanation:
Since the triangle is right use the cosine ratio to solve for x
cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{19}[/tex]
Multiply both sides by 19
19 × cos35° = x, hence
x ≈ 19.6 ( to 1 dec. place )
How to slove the equation 6.8x+9.3=-9.4+3.4(2-5x)
Answers
What type of triangle can a right triangle be?
scalene
acute
obtuse
isosceles
Answers
Answer:
acute
Step-by-step explanation:
Please mark brainliest and have a great day!
Answer:
acute and obtuse
Step-by-step explanation:
In an obtuse triangle, one angle is greater than a right angle—it is more than 90 degrees. An obtuse triangle may be isosceles or scalene. In an acute triangle, all angles are less than right angles—each one is less than 90 degrees. Please mark me as branliest. Thank you :3