quadrilateral PQRS is a square whos side length is 10. Let X and Y be points outside the square so that XQ = YS = 6 and XP = YR = 8. Find XY^2.
Answers
Answer:
392
Step-by-step explanation:
You want the value of the square of the length XY, given X and Y are outside and symmetrically opposite the center of a 10-unit square and each is 6 units and 8 units from the two nearest vertices.
LocationThe attached drawing shows the positions of points X and Y. Each is 4.8 units horizontally and 3.6 units vertically from the nearest vertex of the square. That means their locations relative to each other are ...
horizontally: 2×4.8 +10 = 19.6 units
vertically: 6.4 -3.6 = 2.8 units
DistanceThe square of the distance between X and Y will be given by the Pythagorean theorem:
XY² = 19.6² +2.8² = 384.16 +7.84
XY² = 392
__
Additional comment
The locations of X and Y relative to the side of the square can be found using the "geometric mean" relations for a right triangle. Triangle QXP has side lengths 6, 8, 10, which are a multiple of the well-known {3, 4, 5} right triangle. So ∆QXP is a right triangle with a right angle at X.
The length QX is the geometric mean √(QA·QP), so we have ...
6 = √(10·QA)
36 = 10·QA
QA = 3.6 ⇒ PA = 6.4
and
XA = √(QA·PA) = √(3.6·6.4)
XA = 4.8
The value of [tex]\( XY^2 \)[/tex] is 100.
Let's begin by visualizing the problem. We have a square PQRS with side length 10. Points X and Y are outside the square such that XQ = YS = 6 and XP = YR = 8. We need to find the square of the distance between X and Y, denoted as [tex]\( XY^2 \)[/tex].
To solve this, we can use the Pythagorean theorem. Let's consider triangle XPQ. Since PQRS is a square, angle PQX is a right angle. Therefore, triangle XPQ is a right-angled triangle with PQ as the hypotenuse and XQ and XP as the other two sides.
Using the Pythagorean theorem for triangle XPQ, we have:
[tex]\[ 8^2 = 6^2 + XQ^2 \][/tex]
[tex]\[ 64 = 36 + XQ^2 \][/tex]
[tex]\[ XQ^2 = 64 - 36 \][/tex]
[tex]\[ XQ^2 = 28 \][/tex]
Now, we have found the square of the distance XQ, which is [tex]\( 28 \)[/tex].
Similarly, for triangle YRQ, which is also a right-angled triangle with YR as one leg and YS as the other leg, and RQ as the hypotenuse, we can write:
[tex]\[ 8^2 = 6^2 + RQ^2 \][/tex]
[tex]\[ 64 = 36 + RQ^2 \][/tex]
[tex]\[ RQ^2 = 64 - 36 \][/tex]
[tex]\[ RQ^2 = 28 \][/tex]
We have found that [tex]\( RQ^2 = 28 \)[/tex], which is the same as [tex]\( XQ^2 \)[/tex].
Now, to find [tex]\( XY^2 \)[/tex], we need to consider the distance between points X and Y. Since X and Y are outside the square and their distances to the square are equal (XQ = YS and XP = YR), the line segment XY is parallel to side PQ of the square and is also equal to the side length of the square, which is 10.
Therefore, [tex]\( XY^2 \)[/tex] is simply the square of the side length of the square PQRS:
[tex]\[ XY^2 = PQ^2 \][/tex]
[tex]\[ XY^2 = 10^2 \][/tex]
[tex]\[ XY^2 = 100 \][/tex]
Related Questions
find an obtuse angle whose sine is
a) 0.25
b) 0.75
c) 0.875
d) 0.3465
Answers
Answer:
a) 165.52 degrees.
b) 131.41 degrees.
c) 118.96 degrees.
d) 159.73 degrees.
Step-by-step explanation:
The sine of an obtuse angle is positive as it is in the second quadrant.
a) Using a calculate the angle whose sine ( arcsin) is 0.25 = 14.478 degrees
so the obtuse angle = 180 - 14.478 = 165.52 degrees to nearest hundredth
b) c) and d) are calculated in the same way.
1. X-2y7-8
xty2 1
X-2y>-8
X+y>1
Answers
Answer:
x+y>1
Step-by-step explanation:
Solve the system is of linear equations by substitution.What is the solution to x=2y+7 and 3x+2y=3?
Answers
Answer:
(5/2, -9/4)
Step-by-step explanation:
What is the volume of this cylinder?
Use π ≈3.14 and round your answer to the nearest hundredth.
Answers
Answer:
301.59 or estimated value is 301.60
first you have to find the circumference and then multiply the height by the circumference.
hope it helps
Find the value of x and y. Round to the nearest hundredth (2 decimal places)
Answers
To find the values of x and y requires solving equations, refining the solution through iterative methods like the extended Newton-Raphson technique, and validating results with approximation checks.
Explanation:In answering this mathematical question, we are attempting to find specific values for the variables x and y. To solve for these variables, we employ various mathematical methods such as the Newton-Raphson technique for refinement.
Keeping the referenced data in consideration, the equations provided reveal that we manipulate these equations to gradually reach a more accurate result. For instance, taking the quadratic equation y²-0.30068y +0.022500 = 0 and using the quadratic formula y = 0.30068 ± √(0.30068)² – (4)(1)(0.022500) allows us to find the value for y, and an iterative process enhances the precision of x and y.
Remember to always retain a few extra significant figures to minimize rounding errors in the computational process. Additionally, entering our data into a calculator or a computer program will help in writing the linear equation, which needs to be rounded to an appropriate number of decimal places for accuracy. Examples mentioned illustrate evaluating the coordinates of a point, substituting values into equations, and analyzing the relation between variables through a graphical approach.
To validate our results, we compare the approximation to the actual value to ensure that our error margin is acceptable, especially when dealing with extrapolations from implicit differentiation in calculus contexts.
Write the polynomial in factored form.
p(x) = (x + 5)(x - 1 )(x +
Answers
Answer: 4)
Step-by-step explanation:
Answer:
1st one is 3, 2nd is 4
Step-by-step explanation:
Which expressions are equivalent to 5 (one-third x + 7) minus 3 (one-half x minus 4)? Select three options.
5 and one-third x minus 3 and one-half x + 35 minus 12
One-sixth x + 47
1 and two-thirds x + 35 minus 1 and one-half x + 12
5 (one-third x) + (5) (7) minus (3) (one-half x) + (3) (4)
1 and one-third x + 35 minus 1 and one-half x minus 12
Answers
Answer:
One-sixth x + 47
1 and two-thirds x + 35 minus 1 and one-half x + 12
1 and one-third x + 35 minus 1 and one-half x minus 12
Step-by-step explanation:
The original expression in this problem is
[tex]5(\frac{1}{3}x+7)-3(\frac{1}{2}x-4)[/tex]
We start by applying the distributive property and multiplying each factor outside the brackets by each factor inside:
[tex]5\cdot \frac{1}{3}x+5\cdot 7 -3\cdot \frac{1}{2}x+3\cdot 4[/tex]
So we get:
[tex]\frac{5}{3}x+35-\frac{3}{2}x+12[/tex]
Now we can rewrite this using mixed fractions:
[tex]1\frac{2}{3}x+35-1\frac{1}{2}x+12[/tex] (1)
Which can be also written as
[tex]1\frac{2}{3}x+35-(1\frac{1}{2}x-12)[/tex] (2)
And finally, by solving it, we find
[tex]\frac{1}{6}x+47[/tex] (3)
So the three correct options are
One-sixth x + 47
1 and two-thirds x + 35 minus 1 and one-half x + 12
1 and one-third x + 35 minus 1 and one-half x minus 12
What is the place value of the underlined number 4,382
Answers
Answer:4 is thousands place
3 is hundredths place
8 is tens place
2 is ones place
Step-by-step explanation:
The place value of the underlined number 4,382 is,
4 is thousands place
3 is hundredths place
8 is tens place
2 is ones place.
What is place value?Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value.
The number 42,316 is different from 61,432 because the digits are in different positions.
here, we have,
the underlined number 4,382
so, we get the place value,
4 is thousands place
3 is hundredths place
8 is tens place
2 is ones place.
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PLEASE ANSWER
What is the slope of the graph?
Answers
Answer:
[tex]\frac{5}{3}[/tex]
Step-by-step explanation:
Slope = [tex]\frac{4-(-1)}{3-0} =\frac{5}{3}[/tex]
Assuming she worked at a constant rate, how many rows had been completed before Elena started working?
12
14
15
19
Answers
The answer is 12 :)
The number of rows she had been completed before Elena started working is 12 rows.
How do we make graph of a function?
Suppose the considered function whose graph is to be made is
f=f(x) f(x)
The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values
f=f(x) f(x)
are plotted on the vertical axis.
They are together plotted on the point
f(x)) (x,y) = (x, f(x))
This is why we usually write the functions as:
f(x) y = f(x)
We are given that;
The points= (14,19), (20,22), (30,27)
Now,
To find the number of rows completed before Elena started working, we need to find the equation of the line that passes through the given points on the graph.
Using the slope formula, we can find that the slope of the line is (27-22)/(30-20) = 0.5.
Using the point-slope form of a line, we can write the equation as y - 22 = 0.5(x - 20).
Simplifying the equation, we get y = 0.5x + 12.
To find the y-intercept, which is the number of rows completed before Elena started working, we plug in x = 0 and get y = 12.
Therefore, by the given graph the answer will be 12 rows.
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The complete question is;
Elena agrees to finish a knitting project for a friend. The graph shows the number of rows Elena completes compared to the amount of time spent knitting. The points on graph are (14,19), (20,22), (30,27).
Assuming she worked at a constant rate, how many rows had been completed before Elena started working?
You are selling lemonade for $1.50,a bag of kettle corn for $3, and a hot dog for $2.50 at a fair.write and simplify an expression for the amount of money you receive when p people but one of each item.
Answers
Answer:
$7
Step-by-step explanation:$1.50 + $2.50 will equal to $4. $4 added with$3 would be $7. There's your answer
In 20 days Ken drove 334.9 miles. How many miles did Ken drive each day?
Answers
334.9/20=16.745 miles/day
april bought some sports drinks and slices of pizza for her friends. She bought 3 more sports drinks than slices of pizza. If her total order was 21.25, how many sports drinks did she purchase? one slice of pizza cost 2.25 and one sport drink cost 1.25
Answers
Answer: She purchased 8 sports drinks,
Step-by-step explanation:
Let be "d" the number of sports drinks that April purchased and "p" the number of slices of pizza that April purchased.
Set up a System of equations:
[tex]\left \{ {{d=p+3} \atop {2.25p+1.25d=21.25}} \right.[/tex]
In order to solve the System of equations you can use the Substitution Method:
1. Solve for "p" from the first equation:
[tex]d=p+3\\\\p=d-3[/tex]
2. Substitute it into the second equation:
[tex]2.25(d-3)+1.25d=21.25[/tex]
3. Finally, you must solve for "d" in order to find its value. You get that this is:
[tex]2.25(d-3)+1.25d=21.25\\\\2.25d-6.75+1.25d=21.25\\\\3.5d=21.25+6.75\\\\d=\frac{28}{3.5} \\\\d=8[/tex]
Answer:
Step-by-step explanation:
8 sport drinks
Explain how you find a solution to a system of linear inequalities.
Answers
The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Graph one line at a time in the same coordinate plane and shade the half-plane that satisfies the inequality.
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Hair Color Boys Girls
Black 4 5
Blonde 4 6
Brown 10 8
Red 2 1
The table shows the number of boys and girls that have black, blonde, brown, or red hair color.
What is the probability that a student has brown hair? (round to nearest hundredth)
A) 0.42
B) 0.45
C) 0.58
Eliminate
D) 0.82
Answers
Answer:
B) 0.45
Step-by-step explanation:
The total number of students is:
4 + 5 + 4 + 6 + 10 + 8 + 2 + 1 = 40
The number of students with brown hair is 10 + 8 = 18.
So the probability is:
P = 18/40 = 0.45
Answer: B.) 0.45
~~~~~~~~~~~~~~
Please help me with this question im stuck on it for an hour im so confused i dont know how to do a but i can do b :)
Answers
96 m
2 m/sec²
Step-by-step explanation:
Step 1:
In a velocity and time graph , the area which is under the plotted line represents the distance traveled
In the given graph , the plotted line from t=0 to t=4 ( for the first 4 secs) is a triangle with base = 4 and height = 8
Area of this triangle is (1/2) * b * h = (1/2)* 4*8 = 16 m
Step 2 :
The plotted line from t = 4 to t = 14 is a rectangle with length equal to 10 and breadth equal to 8
Hence its area = length * breadth = 10 * 8 = 80 m
Step 3 :
Total distance traveled is 80 + 16 = 96 m
Step 4 :
In the velocity time graph , slope denotes the acceleration at any given time. Since we want the acceleration for the first 4 secs, we need to find slope of line in from t = 0 to t= 4
when t = 0, v =0 and t= 4, v = 8
Slope = 8-0/4-0 =2 m/sec²
Substitution:
y=3x+2
-4x+2y=8
Answers
GET 20 PTS AND BE NAMED BRAINLIEST AND A THANK YOU PLEASE HELP!!!!!!!!!!!!!!!
Given the percent bar graphs, which best represents the responses of the Economy Majors?
Very Good = 4, Good = 20, Neutral = 11
Very Good = 6, Good = 19, Neutral = 10
Very Good = 18, Good = 55, Neutral = 27
Very Good = 5, Good = 18, Neutral = 12
Answers
Answer:
The answer is C) Very good = 18 Good = 55 Neutral = 27
Step-by-step explanation:
The answer is C) Very good = 18 Good = 55 Neutral = 27
the other person was right
and i feel really bad that somebody else got their answer deleted
help hurry plzzzzzzzzzz
Answers
Answer:
The percentage of Guanine will be 17%
Step-by-step explanation:
As we know from Chargaff's rule, DNA from any organism will contain 1:1 purine and pyrimidine ratio.
so, The adenine (Purine) ratio is 33% because the Thymine is 33%(Pyrimidine)
Then Guanine (Purine) will be 17% because the Cytosine (Pyrimidine) is 17%
I
Jerry is building an indoor beach volleyball court.
He has ordered 14,000 cubic feet of sand.
The dimensions of the court will be 30 feet by 60 feet.
Jerry needs to have a 10-foot boundary around the
court for safety. Be a math detective and determine
how deep the sand will be if Jerry uses all the sand.
Answers
Answer:
The deep of the sand will be 3.5 feet
Step-by-step explanation:
step 1
Find out the area of the court plus a 10-foot boundary around the court for safety
[tex]A=(30+10+10)(60+10+10)\\A=(50)(80)\\A=4,000\ ft^2[/tex]
step 2
Find the deep of the sand
we know that
The volume of the sand is equal to
[tex]V=Ah[/tex]
where
A is the area of the base
h is the height or deep of the sand
substitute the given values
[tex]14,000=(4,000)h[/tex]
Solve for h
[tex]h=14,000/4,000=3.5\ ft[/tex]
Jerry's indoor beach volleyball court, including a 10-foot boundary, would have an area of 4,000 square feet, and with 14,000 cubic feet of sand, it would result in the sand being 3.5 feet deep.
Explanation:Since Jerry wants to build an indoor beach volleyball court with a 10-foot boundary around it and has ordered 14,000 cubic feet of sand, we need to calculate the volume of the sand to determine how deep it will be when spread evenly over the entire area, including the boundary. The dimensions of the volleyball court are 30 feet by 60 feet, and adding a 10-foot boundary around it increases each dimension by 20 feet (10 feet on each side), resulting in a total area dimension of 50 feet by 80 feet.
To calculate the depth of the sand, we first calculate the area of the court including the boundary: Area = length × width = 50 feet × 80 feet = 4,000 square feet. Next, we divide the total amount of sand by the area to find the depth: Depth = volume / area = 14,000 cubic feet / 4,000 square feet = 3.5 feet deep. Therefore, if Jerry uses all the sand, it will be 3.5 feet deep.
Melanie read 45 pages of a hundred page book her younger sister read half of a 10 page book who read a greater fraction of her book Melanie or her sister
Answers
Determind the total area of the rectangle. Give your answer in factorised form.
Answers
Answer:
2(x + 3)(4x + 1)
Step-by-step explanation:
The area (A) of the rectangle is calculated as
A = length × width
length = 2(x + 3)
width = 2x + x + 1 + x = 4x + 1
Thus
A = 2(x + 3)(4x + 1)
write the linear equation that goes through the points (2, 20) and (-3, 8). *
Answers
Answer:
2.4x+15.2
Step-by-step explanation:
Answer:
y=-12x
Step-by-step explanation:
equation to solve with: m=y2-y1/x2-x1
m=8-20/-3-2
Then solve for m which is the slope
m=-12/-1
m=-12
equation: y=-12x
martin throws a ball straight up in the air. the equation h(t) = -16t^2 + 40t + 5 gives the height of the ball, in feet, t seconds after martin releases it.
how many seconds before the ball martin threw hits the ground?
show your work.
(pls answer asap!!)
Answers
Answer:
2.62 seconds
Step-by-step explanation:
Let
t ----> the time in seconds
h(t) ----> he height of the ball, in feet
we have
[tex]h(t)=-16t^2+40t+5[/tex]
we know that
When the ball hits the ground, the height is equal to zero
so
[tex]-16t^2+40t+5=0[/tex]
The formula to solve a quadratic equation of the form
[tex]at^{2} +bt+c=0[/tex]
is equal to
[tex]t=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]-16t^2+40t+5=0[/tex]
so
[tex]a=-16\\b=40\\c=5[/tex]
substitute in the formula
[tex]t=\frac{-40\pm\sqrt{40^{2}-4(-16)(5)}} {2(-16)}[/tex]
[tex]t=\frac{-40\pm\sqrt{1,920}} {-32}[/tex]
[tex]t=\frac{-40+\sqrt{1,920}} {-32}=-0.12\ sec[/tex]
[tex]t=\frac{-40-\sqrt{1,920}} {-32}=2.62\ sec[/tex]
therefore
The solution is t=2.62 seconds
The organic garden at a restaurant is rectangular in shape and has a perimeter of 84 feet. If the length l
l
of the garden is 24 feet longer than the width w
w
of the garden, what is the area of the garden, in square feet?
Answers
Hope this helps
Answer:
Area of the garden is [tex]306feet^2[/tex]
Step-by-step explanation:
Given:
Perimeter of the garden=84 feet
Let the width of the garden be 'W'
Length of the garden is 24 feet longer than the width of it
so, length of the garden= W+24 feet
To find the width 'W'
Perimeter of a rectangle= 2(Length+Width)
[tex]84 =2(W+24+W)\\ 84 =4W+48\\ 84-48=4W\\ 4W=36\\ W=9[/tex] feet
Width=9 feet
Length=W+24= 9+24= 34 feet
Area of the garden= Length*width
[tex]=34*9\\ =306 feet^2[/tex]
Area of the garden is 306 square feet
5,-15,45,-135,? what is the next number
Answers
This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by
3
gives the next term. In other words,
a
n
=
a
1
⋅
r
n
−
1
.
Geometric Sequence:
r
=
3
This is the form of a geometric sequence.
a
n
=
a
1
r
n
−
1
Substitute in the values of
a
1
=
5
and
r
=
3
.
a
n
=
(
5
)
⋅
(
3
)
n
−
1
Remove parentheses.
a
n
=
5
⋅
3
n
−
1
10. A cube has surface area 6534 square feet.
What is its volume?
Answers
Answer:
Step-by-step explanation:
[tex]6a^{2}=6534\\\\a^{2}=\frac{6534}{6}\\=1089\\\\a=\sqrt{1089}\\\\ a=33ft\\\\volume=a^{3}\\\\=33*33*33\\\\=35937[/tex]
To find the volume of a cube with a given surface area, we can use the formula for surface area and rearrange it to find the side length. Once we have the side length, we can calculate the volume of the cube.
Explanation:To find the volume of a cube, we need to determine the length of one side. Since a cube has 6 equal sides, we can calculate the length of each side using the formula for surface area: surface area = 6 * side length * side length. Let's rearrange the formula to find the side length: side length = sqrt(surface area / 6). Once we have the side length, we can calculate the volume using the formula: volume = side length * side length * side length. Plugging in the given surface area of 6534 square feet, we find that the volume of the cube is approximately 2314 cubic feet.
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Help ASAP!!! Which expression gives the length of the transverse axis of the hyperbola
shown below?
Answers
The expression which gives the length of the transverse axis of the hyperbola is; Choice D; a-b.
Which expression gives the length of the transverse axis of the hyperbola?The transverse axis is by definition, a line segment that passes through the center of the hyperbola and has vertices as its endpoints. The foci therefore lies on the line that contains the transverse axis. Hence, it follows that the correct answer choice is; a-b.
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Pleeease help, I've been stuck on this for weeks!!
Answers:
complementary Angles
Supplementary Angles
definition of complementary angles
definition of supplementary angles
distributive property
substitutive property
Answers
Answer:
It is given that [tex]\angle ABC[/tex] and [tex]\angle CBD[/tex] are complimentary angles.
[tex]m\angle ABC + m\angle CBD = 90 \textdegree[/tex] using the definition of complementary angles.
given that [tex]m\angle ABC = 35 \textdegree .[/tex] Using the substitutive property
[tex]35 \textdegree + m \angle CBD = 90\textdegree[/tex]
Therefore, using subtraction property of equality [tex]m \angle CBD = 55 \textdegree[/tex]
Step-by-step explanation:
It is given that [tex]\angle ABC[/tex] and [tex]\angle CBD[/tex] are complimentary angles.
[tex]m\angle ABC + m\angle CBD = 90 \textdegree[/tex] using the definition of complementary angles.
given that [tex]m\angle ABC = 35 \textdegree .[/tex] Using the substitutive property
[tex]35 \textdegree + m \angle CBD = 90\textdegree[/tex]. Therefore, using subtraction property of equality [tex]m \angle CBD = 55 \textdegree[/tex]
Solve for n: -6(n-8)=4(12-5n)+14n
Answers
Answer: use calculated
Step-by-step explanation:
Calculator
Answer:
Everything
Step-by-step explanation:
-6(n-8)=4(12-5n)+14n Given
-6n+48=48-20n+14n Distribute
-6n+48=48-6n Simplify
-6n=-6n Subtraction Property of Equality(Subtract 48 from both sides)
n=n Division Property of Equality(Divide both sides by -6)