In order to determine the coordinates of the circumcenter of triangle DEF with the given vertices, let its circumcenter be P(x, y). Hence, PD = PE = PF.
By squaring all sides of triangle DEF, we have:
PD² = PE² = PF²
From PD² = PE², we have:
(x - 6)² + (y - 0)² = (x - 0)² + (y - 6)²
x² - 12x + 36 + y² = x² + y² - 12y + 36
-12x + 12y = 0 ..........equation 1.
From PE² = PF², we have:
(x - 0)² + (y - 6)² = (x - (-6))² + (y - 0)²
x² + y² - 12y + 36 = (x + 6)² + y²
x² + y² - 12y + 36 = x² + 12x + 36 + y²
-12x - 12y = 0 ..........equation 2.
Solving eqn. 1 and eqn. 2 simultaneously, we have:
x = 0 and y = 0.
Therefore, the coordinates of the circumcenter of triangle DEF with the given vertices are (0, 0).
At D (0,0) E (6,0), F (0,4).From PD² = PE², we have:
(x - 0)² + (y - 0)² = (x - 6)² + (y - 0)²
x² + y² = x² - 12y + 36 + y²
12y = 36
y = 3.
From PE² = PF², we have:
(x - 6)² + (y - 0)² = (x - 0)² + (y - 4)²
x² - 12x + 36 + y² = x² + y² - 8y + 16
-12x - 8y = -20
-12x - 8(3) = -20
-12x - 24 = -20
12x = -4
x = -1/3.
Therefore, the coordinates of the circumcenter of triangle DEF with the given vertices are (-1/3, 3).
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If sin(θ)=−24/25, and θ is in Quadrant III, then what is tan(θ/2)?
Recall the Pythagorean identity,
[tex]\sin^2(\theta) + \cos^2(\theta) = 1[/tex]
Since [tex]\theta[/tex] belongs to Q3, we know both [tex]\sin(\theta)[/tex] and [tex]\cos(\theta)[/tex] are negative. Then
[tex]\cos(\theta) = -\sqrt{1 - \sin^2(\theta)} = -\dfrac7{25}[/tex]
Recall the half-angle identities for sine and cosine,
[tex]\sin^2\left(\dfrac\theta2\right) = \dfrac{1 - \cos(\theta)}2[/tex]
[tex]\cos^2\left(\dfrac\theta2\right) = \dfrac{1 + \cos(\theta)}2[/tex]
Then by definition of tangent,
[tex]\tan^2\left(\dfrac\theta2\right) = \dfrac{\sin^2\left(\frac\theta2\right)}{\cos^2\left(\frac\theta2\right)} = \dfrac{1 - \cos(\theta)}{1 + \cos(\theta)}[/tex]
[tex]\theta[/tex] belonging to Q3 means [tex]180^\circ < \theta < 270^\circ[/tex], or [tex]90^\circ < \theta < 135^\circ[/tex], so that the half-angle belongs to Q2. Then [tex]\sin\left(\frac\theta2\right)[/tex] is positive and [tex]\cos\left(\frac\theta2\right)[/tex] is negative, so [tex]\tan\left(\frac\theta2\right)[/tex] is negative.
It follows that
[tex]\tan\left(\dfrac\theta2\right) = -\sqrt{\dfrac{1 - \cos(\theta)}{1 + \cos(\theta)}} = \boxed{-\dfrac43}[/tex]
marcus plans to paint a bright green rectangle on the bottom of his pool. He has enough to cover an area of 273 square feet. He wants the width of the rectangle to be 13 feet. Determine what the length of the rectangle should be
The length of the rectangle that makes the area to be 273 square feet is 21 feet.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the length of the rectangle, hence:
Length * width = area
13 * x = 273
x = 21 feet
The length of the rectangle that makes the area to be 273 square feet is 21 feet.
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cuantos parque solares hay en china
The translation of the question is:
What are solar parks?The solar park is a concentrated zone of development of solar power generation projects and provides developers an area that is well characterized, with proper infrastructure and access to amenities and where the risk of the projects can be minimized.
How many solar parks are there in China?
Huanghe Hydropower Hainan Solar Park – 2.2GWTengger Desert Solar Park – 1.55GW Datong Solar Power Top Runner Base – 1.1GWYanchi Ningxia Solar Park – 1GWLongyangxia Dam Solar Park – 850MWLearn more about solar energy here:
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Suzanne is looking at taking out a personal loan. Opportunity Loans is offering her $1600 at 3.45% for 1 year, with interest compounding monthly. General Loans is offering her $1600 at 4.2% for 1 year, with interest compounding quarterly. Assuming she makes no payments until the 1 year is up, how much interest will have accrued on each loan? On which loan will she earn the least amount of interest?
Step-by-step explanation:
So the general formula for compound interest is [tex]A = P(1+\frac{r}{n})^{nt}[/tex] where r is the interest rate, t is the time in years, and n is the amount of compounds per year. So plugging in the values for both equations you'll get
Opportunity Loans:
[tex]A = 1600(1+\frac{0.0345}{12})^{(12)(1)}[/tex]
[tex]A = 1600(1.002875)^{12}[/tex]
[tex]A \approx 1600(1.035)[/tex]
[tex]A = \$1,656.08[/tex]
Now to find the interest accrued on this loan you simply subtract 1600 from the A or final amount
[tex]Interest=1656.08-1600\\Interest=56.08[/tex]
General Loans:
[tex]A = 1600(1+\frac{0.042}{4})^{(4)(1)}[/tex]
[tex]A = 1600(1.0105)^4[/tex]
[tex]A \approx 1600(1.042)[/tex]
[tex]A = 1,668.27[/tex]
To find the interest we do the same thing we did in the previous problem
[tex]interest = 1668.27-1600\\interest=68.27[/tex]
Opportunity loans has the least amount of interest after a year
In the diagram of AABC shown below, DE || BC.
B
A
3) 3
4) 15
E
If AB= 10, AD = 8, and AE = 12, what is the
length of EC?
1) 6
2) 2
C
dd or create
k as done
nments
As
to Susan Guha
Answer:
3
Step-by-step explanation:
AD/AB = AE/AC
8/10 = 12/AC
AC = 12(10/8) = 15
EC = 15 - 12 = 3
What is the slope of a line perpendicular to
the line whose equation is 9x + 3y = 36.
Fully simplify your answer.
[tex]m = \frac{ - u}{v} = \frac{ - 9}{3} = - 3 [/tex]
[tex]km = - 1 \\ k = - \frac{1}{m} = \frac{ - 1}{-3}=1/3 [/tex]
The slope of the perpendicular line will be 1/3.
What is the equation of a perpendicular line?Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation of the line is given below.
9x + 3y = 36
3y = 36 - 9x
y = 12 - 3x
The slope of the given equation is - 3.
Let m be the slope of the perpendicular line. Then the slope of the perpendicular line will be 1/3.
m (-3) = -1
Simplify the equation, then we have
m (-3) = -1
3m = 1
m = 1/3
The slope of the perpendicular line will be 1/3.
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9
10
11
12
13
14
15
16
17
18
19
data
[Graphs generated by this script: setBorder(15); initPicture(9,19,-3,4);axes(1,100,1,null,null,1,'off');text([14,-3],"data");line([9,2],[9,4]); rect([11,2],[18,4]); line([15,2],[15,4]);line([19,2],[19,4]); line([9,3],[11,3]); line([18,3],[19,3]);]
Based on the boxplot above, identify the 5 number summary
,
,
,
,
The 5 number summary are
Minimum = 10, Lower quartile = 11, Median = 12, Upper quartile = 17 and Maximum = 19
How to identify the 5 number summary?The complete question is in the attached image
The 5 number summary of box plot are:
MinimumLower quartileMedianUpper quartileMaximumEach of these summaries are represented by the vertical lines of the box plot
From the attached box plot, we have:
Minimum = 10, Lower quartile = 11, Median = 12, Upper quartile = 17 and Maximum = 19
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Answer set notation Please answer fast
Answer:
The set notation for the diagram is P-Q
What is the common denominator of y+y=3/3 in the complex fraction y + y-3/3/5/9+2/3y? Options: 3y(y-3), y(y-3), 3y, 3
We currently have two fractions: y / 1 and (y - 3) / 3.
In both cases, we are only concerned with the denominator. Yes, the numerator will change when we change the denominator, but that will not affect the answer to this question.
As such, we need to find the least common multiple of 1 and 3. That is 3. Therefore, the common denominator is 3.
Hope this helps!
Bernice received the following scores on five science tests: 96, 77, 86, 97, and 89.
Which of the following statements is true?
O The mean of the set is less than the median.
O The mode of the set of scores is 96.
O The median of the set of scores is 86.
o The mean and the median of the set of scores are the same.
Answer:
the mean and the median of the set of scores are the same.
Step-by-step explanation:
median = 89
mean = 96+77+86+97+89 = 445 / 5
= 89
mode = none
The mean and the median of the set of scores are the same.
What is mean and median?Introduction to Mean, Median, and Mode: In statistics, we frequently choose a representative value to roughly characterise the entire collection of data. The name "measure of central tendency" denotes that this representative value is one around which the data is centred. The mean, median, and mode are these central tendencies. The most typical way to measure central tendency is with the mean. In actuality, it represents the mean of the specified set of data. Both continuous and discrete data can be used with it. In most cases, the median shows the midpoint of the given set of data when it is arranged in a specific order.
Mean: - Average value
Median: - Middle term (after arranging in either accending or descending order)
Mean = 445/5 = 89
Median = Middle term = 3rd term = 89
Mean and median are equal.
Hence, option D is correct
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Write each phrase as a mathematical expression.
The sum of the profit, P, times 8 and 6
What is the equation of a quadratic equation with a vertex of (3,5) and a y intercept of (0,12)? Show your work. 
Answer:
Step-by-step explanation:
hello :
f(x) = a(x+h)²+k
(h;k) the vertex so : h=3 and k= 5
now calculate a given f(0) = 12
means : a(0+3)²+5 = 12
9a=7 so : a=7/9
the equation is : y= (7/9)(x+3)²+5
please help! thankssss
find the difference (2x^2+6x-11)-(5x^2-
A.
7 x 2 + 7 x - 18
B.
- 3 x 2 + 5 x - 4
C.
7 x 2 + 5 x - 4
D.
- 3 x 2 + 7 x - 18
he difference between the expressions (2x² + 6x – 11) and (5x² – x + 5) will be –3x² + 7x – 18. Then the correct option is D.
What is subtraction?It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.
The expressions are given below.
(2x² + 6x – 11) and (5x² – x + 5)
Then the difference between the expressions (2x² + 6x – 11) and (5x² – x + 5) will be
⇒ (2x² + 6x – 11) - (5x² – x + 5)
⇒2x² + 6x – 11 – 5x² + x – 5
⇒ –3x² + 7x – 18
Then the correct option is D.
The complete expression is given below.
(2x² + 6x – 11) and (5x² – x + 5)
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there is a canned food sale at the supermarket. a case of 24 cans of peas is prices at $19.68. at the same rate what is the price of 10 cans?
Answer:
8.2
Step-by-step explanation:
We can find the unit rate of this problem by dividing 18.68 by 24 to get .82. .82*10 is equal to 8.2.
What is the value of a in this equation?
Substituting into vertex form, we can write the equation of the parabola as
[tex]y=a(x-0)^{2}+9\\\\y=ax^{2}+9[/tex]
To find the value of a, we can substitute in the coordinates of another point the graph passes through, such as (3,0).
[tex]0=a(3)^{2}+9\\\\0=9a+9\\\\-9=9a\\\\a=\boxed{-1}[/tex]
find x and y
please help i don’t understand this !
Answer:
x = 47°
y = 27°
Explanation:
The angles lie on parallel lines which sum ups to 180 degrees.
Solve for x2x + 1 + 85 = 180
2x = 180 - 86
2x = 94
x = 47
Solve for y2y + 126 = 180
2y = 180 - 126
2y = 54
y = 27
A student found the solution below for the given inequality. Which of the following explains whether the student is correct? The student is completely correct because the student correctly wrote and solved the compound inequality. The student is partially correct because only one part of the compound inequality is written correctly. The student is partially correct because the student should have written the statements using “or” instead of “and.” The student is completely incorrect because there is “ no solution “ to this inequality.
The statement which best explains whether the student is correct is: D. the student is completely incorrect because there is "no solution" to this inequality.
What is an inequality?An inequality refers to a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).Since |x-9| is greater than or equal (≥) to zero (0), we can logically infer that this student is completely incorrect because there is "no solution" to this inequality.
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Complete Question:
A student found the solution below for the given inequality.
|x-9|<-4
x-9>4 and x-9<-4
x>13 and x<5
Which of the following explains whether the student is correct?
A. The student is completely correct because the student correctly wrote and solved the compound inequality.
B. The student is partially correct because only one part of the compound inequality is written correctly.
C. The student is partially correct because the student should have written the statements using “or” instead of “and.”
D. The student is completely incorrect because there is “ no solution “ to this inequality.
PLS HELP 1HOUR LEFT Select the expression that is modeled on the number line. A number line from zero to one partitioned into sixths. There are four hops beginning at one sixth and ending at five sixths one sixth plus five sixths
one sixth plus four sixths
five sixths minus one sixth
five sixths minus four sixths
Answer:
one sixth plus 4 sixths
Step-by-step explanation:
from one sixth you have to add 4/6 to get to 5 sixths(5/6)
6) You have a rectangular backyard that is 90 feet wide. It has an area of 10,800 square feet. You are
putting a fence along one length of the yard.
a. Use the formula for the area of a rectangle A = 1 w, where I is the length, and w is the width. Find
the length of your backyard.
b. The fence costs $12.50 per linear foot. What is the total cost of the fence for one length of the yard?
Answer:
Length = 120 ft
Total cost = 1500$
Step-by-step explanation:
First, to find the length of the backyard we reverse the formula (A = l * w) and divide 10,800 by 90.
10,800 ft^2 / 90 ft = 120 ft.
we can check this by plugging the length of 120 ft into the formula:
120 ft * 90 ft = 10,800 ft^2.
Next, to find the cost of the single length of fence we multiply our length (120 ft) by the cost ($12.50):
120 * 12.50 = $1500
pls I need answers of these questions help
Step-by-step explanation:
1A
the travel paths of the plane build a right-angled triangle.
one travels north, which creates the vertical leg.
the other travels west, which creates the horizontal leg.
their distance is the Hypotenuse (the baseline opposite of the 90° angle), which we can get via Pythagoras
c² = a² + b²
c being the Hypotenuse, a and b being the legs.
how long are the legs ?
the plane going north travels at 240 km/h for 90 minutes.
the plane going west travels at 180 lm/h for 90 minutes.
90 minutes = 1.5 hours (1 hour 30 minutes).
so,
plane 1 went 240×1.5 = 360 km.
plane 2 went 180×1.5 = 270 km.
distance² = 360² + 270² = 129600 + 72900 = 202500
distance = sqrt(202500) = 450 km
2A
again Pythagoras :
130² = 80² + (2nd leg)²
16900 = 6400 + (2nd leg)²
10500 = (2nd leg)²
2nd leg = 102.4695077... m
so, the full perimeter is
130 + 80 + 102.4695077... = 312.4695077... m
312.4695077... = 100%
1% = 100%/100 = 3.124695077... m
how many % are 220 m ? well as many as how often 1% fits into 220 m :
220 / 3.124695077... = 70.40686998... %
3A
again Pythagoras :
the legs of that inner right-angled triangle are (as you correctly wrote) 40 m and 45 m.
the fence is the Hypotenuse, and we get
fence² = 40² + 45² = 1600 + 2025 = 3625
fence = 60.20797289... m ≈ 60 m
please burn that into your brain forever for any right-angled triangle situations :
a² + b² = c²
Pythagoras
Find B in degrees.
B
A
a
C
A b C
A = 40°
a = 8
b=7
B = [?] degrees
Round to the nearest tenth.
Answer:
34.2°
Step-by-step explanation:
sinB/b = sinA/a
sinB/7 = sin(40°)/8
sinB = 7sin(40°)/8
B=arcsin(7sin(40°))/8
So, to the nearest tenth, B is 34.2°.
What do you think would happen to the average if you kept rolling the number cube over and over?
The average would keep increasing.
The average would keep decreasing.
The average would approach a set value.
The average would not follow any pattern.
Answer: ( C ) the average would approach a set value.
A disk is in the form of square and measures 5.25 inches on each side. Find
the diagonal length of the disk?
Answer:
The diagonal length of the desk is 7.42462120246 inches.
Step-by-step explanation:
Since it is a square then all sides are equal which means we can easily formulate the pythagorean theorem on the diagonal length of the desk.
a^2 + b^2 = c^2
A and B are the same (width and length) since it is a square.
5.25^2 + 5.25^2 = c^2
27.5625 + 27.5625 = c^2
55.125 = c^2
Put c^2 under a square root (apply to both sides)
square root of 55.125 = 7.42462120246 = c
If y = x then dy, the differential of y, as a changes from 64 to 64.1 is given
by
Answer:
[tex]dy \ = \ 0.1[/tex]
Step-by-step explanation:
Considering the Leibniz notation to represent the derivative of [tex]y[/tex] with respect to [tex]x[/tex], suppose [tex]y \ = \ f\left(x\right)[/tex] is a differentiable function, let [tex]dx[/tex] be the independent variable such that it can be designated with any nonzero real number, and define the dependent variable [tex]dy[/tex] as
[tex]dy \ = \ f'\left(x\right) \ dx[/tex],
where [tex]dy[/tex] is the function of both [tex]x[/tex] and [tex]dx[/tex]. Hence, the terms [tex]dy[/tex] and [tex]dx[/tex] are known as differentials
Dividing both sides of the equation by [tex]dy[/tex], yield the familiar expression
[tex]\displaystyle\frac{dy}{dx} \ = \ f'\left(x\right)[/tex].
Given that [tex]f\left(x\right) \ = \ x[/tex] and [tex]dx \ = \ 64.1 \ - \ 64 \ = \ 0.1[/tex], hence
[tex]f'\left(x\right) \ = \ 1[/tex].
Subsequently,
[tex]dy \ = \ f'\left(64\right) \ \times \ 0.1 \\ \\ dy \ = \ 1 \ \times \ 0.1 \\ \\ dy \ = \ 0.1[/tex].
Factorize completely
(m+n) (2x-y)-x(m+n)
Answer:
(m+n) [x-y]
Step-by-step explanation:
(m+n) (2x-y)-x(m+n)
We can factor out (m+n)
(m+n) [(2x-y)-x]
Combine like terms
(m+n) [2x-x-y]
(m+n) [x-y]
what are the zeros of the function f(x)=x^4-4x^2-5
Answer:
[tex]x =\sqrt{5} ,-\sqrt{5} ,-i,i[/tex]
Step-by-step solution:
[tex]0=x^4-4x^2-5[/tex] [tex]u = x^2[/tex]
[tex]0 = u^2-4u-5[/tex]
[tex]0 = (u -5)(u+1)[/tex]
[tex]u = 5[/tex] [tex]u=-1[/tex]
[tex]x^2 =5[/tex] [tex]x^2 = -1[/tex]
[tex]x= +-\sqrt{5}[/tex] [tex]x = +-i[/tex]
wice a number added to a smaller number is 5. The difference of 5 times the smaller number and the larger number is 3. Let x represent the smaller number and y represent the larger number. Which equations represent the situation?
2 y + x = 5. 5 x minus y = 3.
2 x + y = 5. 5 y minus x = 3.
2 y + x = 5. y minus 5 x = 3.
2 x + y = 5. x minus 5 y = 3.
Answer:
2 y + x = 5 , 5 x − y = 3
Step-by-step explanation:
suppose x represents the smaller number and y represent the larger number.
Then
• The statement: “Twice a number added to a smaller number is 5”
means 2 y + x = 5
On the other hand,
•• The statement: “The difference of 5 times the smaller number and the larger number is 3”
means 5 x − y = 3
The midpoint of STis W(-3, 1). Point S is located at (-7,-9).
What are the coordinates of point T?
O (-5,5)
O (4,4)
O (1,11)
O (10,-10)
Answer:
T [1;11].
Step-by-step explanation:
x-coordinate of the point T is:
x(T)=2*x(W)-x(S); ⇒ x(T)=2*(-3)+7=1;
y-coordinate of the point T is:
y(T)=2*y(W)-y(S); ⇒ y(T)=2*1+9=11.
Finally, T(1;11).
Juan owns 7 pairs of pants, 3 shirts, 5 ties, and 6 jackets. How many different outfits can he wear to school if he must wear one of each item?
To solve this problem, just use multiplication.
[tex]7\text{ pairs of pants}*3\text{ shirts}*5\text{ ties}*6\text{ jackets}=\large\boxed{630\text{ outfits}}[/tex]
You can somewhat think of this situation as a sort of tree. You start with 7 large branches representing the pants, then for every one of those you have 3 medium-sized branches to represent the pairs of pants. Each one of those has 5 sticks for the ties, which in turn each have 6 leaves to represent the jackets and therefore a complete outfit. The solution is found by getting the total number of leaves on the tree.
QUESTION IS DOWN BELOW 15 POINTS EACH
The surface area of the given triangular prism is 960 yd²
Calculating surface areaFrom the question, we are to calculate the surface area of the given figure
The given figure is a triangular prism
Surface area of the triangular prism =
[tex](26 \times 12 )+ 2(\frac{1}{2} \times 10\times 24) + (24 \times 12) + (12 \times 10)[/tex]
= 312 + 240 + 288 + 120
= 960 yd²
Hence, the surface area of the given triangular prism is 960 yd²
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