You are making the kite shown at the right from
five pairs of congruent panels. In parts (a)-(d)
below, use the given information to find the side
lengths of the kite's panels.
Answers
Answer:
a. Side lengths of ΔBEX are;
BE = 15 ft.
EX = 12 ft.
BX = 9 ft.
b. Side lengths of XEFY are;
XY = 6 ft.
EX = 12 ft.
FY = 7.5 ft.
EF = 7.5 ft.
c. Side lengths of YFGZ are;
GZ = 6 ft.
FY = 7.5 ft.
YZ = 2 ft.
FG = 2.5 ft.
d. Side length of triangle ZGC
GZ = 6 ft.
GC = 10 ft.
ZC = 8 ft.
Step-by-step explanation:
The given parameters are;
XY : YZ : ZC is 3 : 1 : 4
The length of BC = 25 in.
The length of EB = 15 in.
Therefore, EC = √(BC² - EB²) = √(25² - 15²) = √400 = 20 in.
Given that EX║ YF║GZ, we have;
EF : FG : GC is 3 : 1 : 4 (Parallel lines cut segments in equal proportions)
Therefore;
EF = 20 × 3/(3 + 1 + 4) = 7.5 ft.
FG = 20×1/8 = 2.5 ft.
GC = 20×4/8 = 10 ft.
EC/EX = BC/EB
20/EX = 25/15
EX = 15×20/25 = 12 ft.
XC = √(EC² - EX²) = √(20² - 12²) = 16
XY : YZ : ZC is 3 : 1 : 4
Therefore;
XY = 16 × 3/8 = 6 ft.
YZ = 16 × 1/8 = 2 ft.
ZC = 16 × 4/8 = 8 ft.
GZ = √(GC² - ZC²) = √(10² - 8²) = 6
Area of triangle ΔZGC = 1/2×6×8 = 24 ft²
XB = BC - XC = 25 - 16 = 9 ft.
Area of ΔBEX = 1/2×9×12 = 54 ft²
a. Side lengths of ΔBEX are;
BE = 15 ft.
EX = 12 ft.
BX = 9 ft.
FY = √(FC² - YC²) = √((10 + 2.5)² - (8 + 2)²) = 7.5 ft.
Area of YFGZ = (GZ + FY)/2 × YZ = (6 + 7.5)/2 × 2 = 13.5 ft²
Area of YFGZ = 13.5 ft²
Area of XEFY = XY × (EX + FY)/2 = 6 × (12 + 7.5)/2 = 58.5 ft.²
b. Side lengths of XEFY are;
XY = 6 ft.
EX = 12 ft.
FY = 7.5 ft.
EF = 7.5 ft.
c. Side lengths of YFGZ are;
GZ = 6 ft.
FY = 7.5 ft.
YZ = 2 ft.
FG = 2.5 ft.
d. Side length of triangle ZGC
GZ = 6 ft.
GC = 10 ft.
ZC = 8 ft.
Related Questions
The US Department of Health and Human Services wants to know whether the healthcare system is achieving its goals in Virginia. Much information about
healthcare comes from patient records, but that source doesn't allow us to compare people who use health services with those who don't. Therefore, the US
Department of Health and Human Services conducted the Virginia Health Survey, which was used to interview a random sample of 65,439 people who live in
the state of Virginia.
Part A: What is the population for this sample survey? What is the sample? (4 points)
Part B: The survey found that 71% of males and 88% of females in the sample had visited a general practitioner at least once during the past year. Do you
think these estimates are close to the truth about the entire population? Explain. (6 points)
Answers
Answer:
Part A: All the residents of the state of Virginia make up the population, while the sample is the number of those interviewed–65,439 people.
Part B: No
Step-by-step explanation:
Part A: In statistical analysis, the population refers to the study area of the research; and in this case– the state of Virginia. While the sample represents a considerable representation of the population in the survey.
Part B: No because we are told The US Department of Health and Human Services used a random sample, not a non-random sampling technique; which implies that the feedback was random and may not likely be close to the truth about the entire population.
Find the greatest possible value for a+b+c+d if b is a positive integer and a,b,c,d satisfy the system of equations
a+b=c
b+c=d
c+d=a
Answers
Answer:
[tex]a+b+c+d = -5\cdot b[/tex]
Step-by-step explanation:
The given system of equations is now reduced:
1) [tex]a+b = c[/tex], [tex]b+c = d[/tex], [tex]c+d=a[/tex], [tex]b > 0[/tex] Given
2) [tex]a = c+d[/tex] By 1)
3) [tex](c+d)+b=c[/tex] 2) in 1)
4) [tex]d = b + c[/tex] By 1)
5) [tex][c+(b+c)]+b = c[/tex] 4) in 3)
6) [tex]2\cdot b + 2\cdot c = c[/tex] Algebra
7) [tex]c = -2\cdot b[/tex] Algebra
8) [tex]d = -b[/tex] 7) in 4)/Algebra
9) [tex]a = -3\cdot b[/tex] 7) and 8) in 2)/Algebra
10) [tex]a+b+c+d = -5\cdot b[/tex] 9), 1), 7) and 8)/Algebra/Result
If a triangle has two of its shorter sides measuring 7 and 12, what is a possible length of the longest side of the triangle to make it acute?
Answers
Answer:
13
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
|5x + 1 over 2y2| What is the value of the expression above when x = 3 and y = 2? You must show all work and calculations to receive full credit.
Answers
Answer:
2
Step-by-step explanation:
The value of the expression |5x + 1 / 2y²| when x = 3 and y = 2 will be 2.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The expression is given below.
⇒ |5x + 1 / 2y²|
The value of the expression at x = 3 and y = 2, then we have
⇒ |5(3) + 1 / 2(2)²|
⇒ |15 + 1 / 2(4)|
⇒ |16 / 8|
⇒ 2
The value of the expression |5x + 1 / 2y²| when x = 3 and y = 2 will be 2.
More about the function link is given below.
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Find the value of m∠ACD. A. 30º B. 15º C. 60º D. 90º
Answers
Answer:
A. 30 degrees
Step-by-step explanation:
Set the two angles equal to each other:
3x-15 = 45-x
Solve for x:
4x -15 = 45
4x = 60
x = 15
Finally, plug in the x to one of the equations (preferably 45 - x since it's easier to solve) and solve for x.
45 - 15 = 30
Answer:
A 30 degrees
Step-by-step explanation:
PLEASE HELP!!! WILL GIVE BRAINLIEST AND 20 POINTS!!!
Triangles △DEF and △ABC are congruent. Which of the following sequences of transformations maps △DEF onto △ABC? ___________________________________________________________Sequence A --> A translation along the directed line segment DB, then a 90° rotation about point B.
Sequence B --> A 90° rotation about point F, then a translation along the directed line segment FC. ___________________________________________________________ a) Only sequence A
b) Only sequence B
c) Both
d) Neither
**note: picture attached below.**
Answers
The answer is D because then triangles DEF and ABC would map onto one another
What is a Triangle?
Triangle is a plane figure with three straight sides and three angles.
How to determine?The answer is D because then triangles DEF and ABC would map onto one another.
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If dn = ‾‾√24, what value of n makes this equation true?
Answers
Answer:
1/24
Step-by-step explanation:
Answer:
1/24 makes this equation true
can someone explain how to do this please
Answers
Answer:
2/5 [tex]cm^2[/tex]
Step-by-step explanation:
To find the area of a rectangle do A = bh
When you substitute 4/6 for base and 3/5 for height it will be A = 4/6 x 3/5
This means the area is 2/5
Answer:
2/5 cm^2
Step-by-step explanation:
The area of a rectangle is found by
A = l*w
A = 4/6 * 3/5
Rewriting
=4/5 * 3/6
= 4/5 *1/2
= 2/5 cm^2
Hi. Please i need help with this question.
Find the operation used in determining each of the values in the diagram.
Workings Please.
Answers
Answer:
3*3+1=10
4*4+5=21
Step-by-step explanation:
You square the number in the first box
3*3=9
4*4=16
And add the number in the second box with the result.
3*3=9+1=10
4*4=16+5=21
Hope this helps ;) ❤❤❤
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
We must square the number on the left box, then add with the number in the right box to get the result in the boxes below.
3² + 1 = 9 + 1 = 10
4² + 5 = 16 + 5 = 21
What will I get for this 16 + x = 12
Answers
Second step: simplify to x= -4
Third step: fill it back into the equation to check, 16 + -4 = 12, and 12=12 this is a true statement
Answer:
x = -4
Step-by-step explanation:
16 + x = 12
16 - 16 + x = 12 - 16
x = -4
Sheila was given $20.00 for her birthday and spent $14.79 on a CD. How much was her change?
Answers
Answer:
$5.21
Step-by-step explanation:
20.00 - 14.79 = 5.21
Answer:
5 dollars and 21 cents or $5.21
Step-by-step explanation:
20.00 - 14.79 = 5.21
08.01) Which of the following statements shows a characteristic of a statistical question? (4 points) Select one: a. The question is focused. b. The distribution can be broken into categories. c. The question asks for a quantitative response. d. The question allows for surveys to be conducted
Answers
Answer:
the distribution can be broken into categories
Statement c shows a characteristic of a statistical question.
What is statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
So, based on the definition of statistics we can say.
1)Statistical data can be analysed.
2)Statistical data can be used to interpret many things.
3)Statistical data can forecast the results.
Out of the given statements, only statement c falls under the category of statistical statement.
Hence, statement c shows a characteristic of a statistical question.
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help me plz can somewon help me i am bad at math mostly
Answers
Answer:
Definitely the bottom left
Step-by-step explanation:
you move up 7 units and left 6 units. you end at (-1,5). where did you start?
Answers
Answer:I beleive it is (5,-2)
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAINLY!!!!!!!
Which are the roots of the quadratic function f(q) = q^2 - 125? Select two options.
A) q= 5/5
B) q= -5/5
C) q= 3/5
D) q= -3/5
E) q= 25/5
Answers
Answer:
q = -5[tex]\sqrt{5}[/tex]
q = 5[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Since there is no constant value. This must be a special case.
So,
(q+5[tex]\sqrt{5}[/tex])(q-5[tex]\sqrt{5}[/tex])
q = -5[tex]\sqrt{5}[/tex]
q = 5[tex]\sqrt{5}[/tex]
URGENT!!! REALLY NEED HELP!!!
FIRST *CORRECT* ANSWER WILL BE BRAINLIST!!!!!
The bar graph shows the percent of students that chose each drink in the school
cafeteria. Which statement about the graph is true?
Answers
Answer:
1st option
Step-by-step explanation:
Because .3*300=90
.3=30%
Answer:
If 300 lunches were served, then 90 chose milk (7).
Step-by-step explanation:
To determine that this is the correct answer, you can just divide 90/300, which is equal to 0.3 or 30%. When you look at the graph, you can see that "milk" is equal to 30%, so this statement is true.
Determine whether the lines given by the vector equations r1=2i + 2j + 3k + s(i + 3j + k) and r2=2i + 3j + 4k + t(i + 4j + 2k) intersect. If they intersect, give the coordinates of their point of intersection.
Answers
Answer:
i -j +2k . . . at s=t=-1
Step-by-step explanation:
For the lines to intersect, there must be values of s and t that make the coordinates of r1 equal to those of r2.
Equating i coefficients, we have ...
2 +s = 2 +t
Equating j coefficients, we have ...
2 +3s = 3 +4t
Equating k coefficients, we have ...
3 +s = 4 +2t
The first equation tells us s = t. Using t = s in each of the other two equations, they become ...
2 +3s = 3 +4s ⇒ s = -1
3 +s = 4 +2s ⇒ s = -1
Then the point of intersection is where s = t = -1. That point is ...
(2 +s)i +(2 +3s)j +(3 +s)k = (2 -1)i +(2 -3)j +(3 -1)k
= i -j +2k . . . . the point of intersection
the formula for a trapezoid is A= 1/2h(b1+b2) which equations are equivalent to the formula
Answers
Answer:
A=[tex]\frac{a+b}{2} (h)[/tex]
Step-by-step explanation:
Option first, option second, and option fourth are correct this expression is equivalent to the formula for a trapezoid.
What is a trapezoid?It is defined as the quadrilateral having four sides in which two sides are parallel to each other, it is a 2-dimensional geometry.
The options are:
h=2A/(b1+b2)b1=2A/h - b2b2= 2A/b1 - hb2= 2A/h - b1b1= 2A//b2 - hWe have a formula for finding the area of the trapezoid:
[tex]\rm A= \dfrac{1}{2}h(b_1+b_2)[/tex]
Make a subject h and solve for h:
[tex]\rm \dfrac{2A}{(b_1+b_2)}= h[/tex]
or
[tex]\rm h = \dfrac{2A}{(b_1+b_2)}[/tex]
[tex]\rm b_2 = \dfrac{2A}{h}- b_1[/tex]
[tex]\rm b_1 = \dfrac{2A}{h}- b_2[/tex]
Thus, option first, option second, and option fourth are correct this expression is equivalent to the formula for a trapezoid.
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A regular octagon is inscribed in a circle with a radius of 10 cm. What is the length of one side of the octagon?
Answers
Answer:
The length of one side of the octagon is 7.65 cm
Step-by-step explanation:
The parameters given are;
A regular octagon inscribed in a circle of radius, r, of 10 cm.
The length of each side is found from the isosceles triangle formed by the radius and one side of the octagon
The sum of interior angles in a polygon, ∑θ[tex]_i[/tex] = 180 × (n - 2)
Where;
n = The number of sides of the polygon
θ[tex]_i[/tex] = The interior angle of the polygon
For the octagon, we have;
n = 8, therefore;
∑θ[tex]_i[/tex] = 180 × (8 - 2) = 1080
Given that there are eight equal angles in a regular octagon, we have;
∑θ[tex]_i[/tex] = 8 × θ[tex]_i[/tex] = 1080
θ[tex]_i[/tex] = 1080/8 = 135°
The sum of angles at the center of the circle = 360
Therefore, the angle at the center (tip angle) of the isosceles triangle formed by the radius and one side of the octagon = 360/8 = 45°
The base angles of the isosceles triangle is therefore, (180 - 45)/2 = 67.5° = θ[tex]_i[/tex]/2
The length of the base of the isosceles triangle formed by the radius and one side of the octagon = The length of one side of the octagon
From trigonometric ratios, the length of the base of the isosceles triangle is therefore;
2 × r × cos(θ[tex]_i[/tex]/2) = 2×10 × cos(67.5°) = 7.65 cm
The length of the base of the isosceles triangle = 7.65 cm = The length of one side of the octagon.
If you're good at angles of elevation pls help meeee
Adam notices that the angle of elevation to the top of a building is 22 degrees. He walks 120m towards the building and the angle of elevation is now 28 degrees. How tall is the building?
Answers
Answer:
202m
Step-by-step explanation:
Please see attached picture for full solution.
Let x meters be the height of the building.
Find the perimeter and area of the shaded region.
Answers
Answer:
Perimeter of the shaded region= 22/7cm
Area = 36.48 cm²
Step-by-step explanation:
First of all for the perimeter.
The radius of the arc is 8cm
At an angle of 90°
Perimeter of of the shape is perimeter of the the 2 arc
The both arc are equal so let's determine the perimeter of one first.
Perimeter of the arc= 2πr*(90/360)
Perimeter of the arc= 2*22/7*1/4
Perimeter of the arc= 11/7 cm
Perimeter of the shades region= 2*11/7
Perimeter of the shaded region= 22/7cm
Area of the sector = πr²*(90/360)
Area of the sector= 50.24cm²
Area of non sector= 64-50.24
= 13.76
But non sector is two
Area of non sector= 2*13.76
= 27.52
Area of the shaded region = area of the square -(area of non sector)
= 64-27.52
= 36.48 cm²
Someone pls help me . Thank you sm
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
X = 24
m = 13/7 or about 1.86
▹ Step-by-Step Explanation
X/3 + 7 = 15
X + 3 * 7/3 = 15
X + 21/3 = 15
X = 24
3.5m - 1.5 = 5
35/10m - 15/10 = 5
5 * 7/2 * 5m - 3 * 5/2 * 5 = 5
m = 13/7 or about 1.86
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
explanation:
Plz help I’ll mark brainliest
Answers
Answer:
Step-by-step explanation:
Using Pythagoras Theorem, hypotenuse = 5
[tex]h = \sqrt{a^{2}+ b^{2}[/tex]
[tex]h = \sqrt{9+16 }\ = \sqrt{25}\ = 5[/tex]
sin x = height / hypotenuse = 3 / 5
cos y = base / hypotenuse = 3 / 5
sin x = cos y = 3 / 5
Jill has two dimes she is going to use to perform a probability experiment. What is the theoretical probability that at least one of the two coins will turn up
heads?
75%
50%
Answers
Answer:
50%
Step-by-step explanation:
its a 50/50 chance on it landing either heads or tails
A dime has two sides with a 50% chance of landing on either one.
Ms. Canton has a book case. On three of the shelves there are the same amount of books. On another shelf there are four of her favorite books. Write an expression to represent all of the books in Ms. Canton's book case. Explain your answer
Answers
Answer:
y=3x+4
Step-by-step explanation:
x= the equal amount of books on 3 bookshelves
+4=the other 4 books on the fourth bookshelf
y=the total amount of books
Determine what type of model best fits the given situation: Farmer Joe has 1,000 bushels of corn to sell. Presently the market price for corn is $5.00 a bushel. He expects the market price to increase by $0.15 per week. For each week he waits to sell, he loses ten bushels due to spoilage. A. none of these B. exponential C. quadratic D. linear
Answers
Answer:
The correct option is;
C. Quadratic
Step-by-step explanation:
The given information are;
The quantity of corn Farmer Joe has to sell = 1,000 bushels
The present market price for corn = $5.00 a bushel
The amount by which he expects the market price to rise per week =$0.15
The number of bushels lost to spoilage per week = 10
Therefore, we have;
The value of the corn = Amount of corn left × Price of corn
The price of the corn per bushel with time = 5 + 0.15×t
The amount of corn left = 1000 - 10×t
Where;
t = Time in minutes
Therefore, the total value of corn = (1000 - 10×t)×(5 + 0.15×t) = -1.5·t²+100·t+5000 which is a quadratic model.
Therefore, the correct option is a quadratic model.
The distance from the Sun to Earth is about 1.5 × 10^11 meters. Suppose light travels at a speed of 3 × 10^8 meters per second. About how long does it take light from the Sun to reach Earth?
PLZ ANSWER ACCURATELY AND QUICKLY WILL MARK BRALINLIEST
Answers
Answer:
Si se tiene en cuenta que la velocidad de la luz en el vacío es de 299.792 km/s. La distancia existente entre el 'astro rey' y la Tierra es de unos 149,6 millones de kilómetros, una pequeña operación matemática indica que la luz del Sol tarda aproximadamente 8 minutos y 19 segundos en llegar a nuestro planeta.
Step-by-step explanation:
It takes light from the Sun about 500 seconds, or 8 minutes and 20 seconds, to reach Earth.
What is speed?Speed is the ratio of the given distance and time.
It shows how fast an object is moving at a given time.
The formula is Distance / Time.
We can find the distance or time when the required values are given using this formula.
We have,
To find the time it takes for light to travel from the Sun to Earth,
We can use the formula:
Time = distance/speed
where distance is the distance from the Sun to Earth and speed is the speed of light.
Plugging in the given values.
Time = (1.5 × 10^11 meters) / (3 × 10^8 meters per second)
Simplifying.
time = 500 seconds
Therefore,
It takes light from the Sun about 500 seconds, or 8 minutes and 20 seconds, to reach Earth.
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Use the table shown in the image! 1. Which equation expresses “y” in terms of “x”? A. y=17x B. y=25x C. x=51y D. x=85y 2. What is the charge for renting a machine for 3.5 hours? A. $51.50 B. $59.50 C. $65.50 D. $86.50
Please include all work!
Answers
Answer: 1. A. y=17x
2. $59.50
Step-by-step explanation:
1. In the table , it can be seen that as x increases y increases with the proportionality constant k = [tex]\dfrac{y}{x}=\dfrac{51}{3}=\dfrac{85}{5}=\dfrac{119}{7}=17[/tex],.
Equation of direct variation between x and y : [tex]y=kx[/tex]
Put k= 17 , we get
[tex]y=17x[/tex] , which is the required equation.
So correct option is "A".
2. To find : The charge for renting a machine for 3.5 hours.
Put x= 3.5 in above equation , we get
[tex]y=17(3.5)=59.5[/tex]
Hence, the charge for renting a machine for 3.5 hours is $59.50.
So correct option is "B".
Find the radius, diameter, circumference and the approximate area for the circle in the image attached. To find the approximate area, please use 3.14 for π. SHOW WORK!
Answers
Answer:
The radius is already given, which is 6 in.
Diameter is equal to 2 times the radius (2x6), which is 12 in.
Finally, circumference is equal to 3.14 times the diameter, which is 37.68 in.
Let me know if this helps!
6.28 * 6 : 37.68
note:
radius is the length of half the circle. and diameter is always double the radius.
the graph of y=f(x) is shown below. find all the values of x where f(x)=1
Answers
When you substitute the value of x = 3, you get f(x) = 1.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
f(x) = ax² + b x + c. The graph of the parabola is downward (or opens down), when the price of a is much less than 0, a < 0. The graph of the parabola is upward (or opens up) when the value of a is more than 0, a > 0.
parabola, open curve, a conic segment produced via the intersection of a proper circular cone and a plane parallel to an element of the cone.
Here the given graph of y = f(x) is shown.
When you substitute the value of x = 3, you get f(x) = 1.
Hence, you can get f(x) = 1 by substituting the value of x = 3
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