9514 1404 393
Explanation:
In a cyclic quadrilateral, opposite angles are supplementary. This means ...
A + C = 180° ⇒ A/2 +C/2 = 90° ⇒ C/2 = 90° -A/2
B + D = 180° ⇒ B/2 +D/2 = 90° ⇒ D/2 = 90° -B/2
It is a trig identity that ...
tan(α) = cot(90° -α)
so we have ...
tan(A/2) = cot(90° -A/2) = cot(C/2)
and
tan(B/2) = cot(90° -B/2) = cot(D/2)
Adding these two equations together gives the desired result:
tan(A/2) +tan(B/2) = cot(C/2) +cot(D/2)
Besties I'm..WELL I'M ME AND I NEED HELP
Answer:
h = 30°
Step-by-step explanation:
All angles in a triangle add up to 180°, so:
60° + 90° + h° = 180°
Solving for h, we should get 30 as our answer.
This is a 30-60-90 triangle. What is the measure of x? rationalize the denominator.
Answer:
[tex] x=\frac{[2] \sqrt {[21] }}{[3] }[/tex]
Step-by-step explanation:
Since, given is a 30°-60°-90° triangle.
[tex] \therefore \sqrt 7 = \frac{\sqrt3}{2} \times x[/tex]
[tex] \therefore 2\sqrt 7 = \sqrt3 \times x[/tex]
[tex] \therefore x=\frac{2\sqrt 7}{\sqrt 3}[/tex]
[tex] \therefore x=\frac{2\sqrt 7(\sqrt 3)}{\sqrt 3(\sqrt 3)}[/tex]
[tex] \huge \therefore x=\frac{[2] \sqrt {[21] }}{[3] }[/tex]
the sum of a number squared and 12 is identical to four added to the same number
Answer: x^2+12=x+4
Step-by-step explanation:
A circle is centered at the point (-3, 2) and passes through the point (1, 5) what is the radius of the circle
Answer:
5 units
Step-by-step explanation:
Center of the circle = (-3, 2)
Point on the circle = (1, 5)
Radius of the circle will be equal to the distance between the points (-3, 2) & (1, 5)
[tex] \therefore \: radius \: of \: the \: circle \\ = \sqrt{ {( - 3 - 1)}^{2} + {(2 - 5)}^{2} } \\ = \sqrt{ {( - 4)}^{2} + {( - 3)}^{2} } \\ = \sqrt{16 + 9} \\ = \sqrt{25} \\ \therefore \: radius \: of \: the \: circle = 5 \: units[/tex]
4x^2 + 4y^2 - 24x - 32y + 72 = 0 is a circle. What is the radius of the cirlce?
Answer:
√7
Step-by-step explanation:
(4x²-24x)+(4y²-32y)= -72
(4x²-24x+36)+(4y²-32y+64)= -72+36+64
4(x-3)²+4(y-4)²= 28
(x-3)²+(y-4)²=7
The radius of the circle 4x² + 4y²- 24x - 32y + 72 = 0 is √7.
CircleWe know that the general equation for a circle is ( x - h )² + ( y - k )² = r², where ( h, k ) is the center and r is the radius.
How to find the radius of the circle?The given equation is 4x² + 4y²- 24x - 32y + 72 = 0
Simplify the given equation in general equation for a circle.
(4x²-24x)+(4y²-32y)= -72
Add 100 on both side of equality
(4x²-24x)+(4y²-32y)+100= -72+100
(4x²-24x+36)+(4y²-32y+64)= 28
4(x-3)²+4(y-4)²= 28
(x-3)²+(y-4)²=7
(x-3)²+(y-4)²=(√7)²
Hence the radius of the circle is √7.
Learn more about radius here: https://brainly.com/question/24375372
#SPJ2
What is the scale factor of this dilation?
Answer:
1.333333333333
Step-by-step explanation:
Crystal left her running shoes at school yesterday. Today she walked 44 miles to school to get her shoes, she ran home along the same route, and the total time for both trips was 22 hours. Crystal walked and ran at constant speeds, and she ran 33 miles per hour faster than she walked.
What was Crystal’s walking speed in miles per hour?
Answer:
We can conclude that her walking speed is 2.1 miles per hour.
Step-by-step explanation:
We have the relation:
Speed = distance/time.
Here we know:
She walked for 44 miles.
And she ran along the same route, so she ran for 44 miles.
The total time of travel is 22 hours, so if she ran for a time T, and she walked for a time T', we must have:
T + T' = 22 hours.
If we define: S = speed runing
S' = speed walking
Then we know that:
"and she ran 33 miles per hour faster than she walked."
Then:
S = S' + 33mi/h
Then we have four equations:
S'*T' = 44 mi
S*T = 44 mi
S = S' + 33mi/h
T + T' = 22 h
We want to find the value of S', the speed walking.
To solve this we should start by isolating one of the variables in one of the equations.
We can see that S is already isoalted in the third equation, so we can replace that in the other equations where we have the variable S, so now we will get:
S'*T' = 44mi
(S' + 33mi/H)*T = 44mi
T + T' = 22h
Now let's isolate another variable in one of the equations, for example we can isolate T in the third equation to get:
T = 22h - T'
if we replace that in the other equations we get:
S'*T' = 44mi
(S' + 33mi/h)*( 22h - T') = 44 mi
Now we can isolate T' in the first equation to get:
T' = 44mi/S'
And replace that in the other equation so we get:
(S' + 33mi/h)*( 22h -44mi/S' ) = 44 mi
Now we can solve this for S'
22h*S' + (33mi/h)*22h + S'*(-44mi/S') + 33mi/h*(-44mi/S') = 44mi
22h*S' + 726mi - 44mi - (1,452 mi^2/h)/S' = 44mi
If we multiply both sides by S' we get:
22h*S'^2 + (726mi - 44mi)*S' - (1,425 mi^2/h) = 44mi*S'
We can simplify this to get:
22h*S'^2 + (726mi - 44mi - 44mi)*S' - (1,425 mi^2/h) = 0
22h*S'^2 + (628mi)*S' - ( 1,425 mi^2/h) = 0
This is just a quadratic equation, the solutions for S' are given by the Bhaskara's equation:
[tex]S' = \frac{-628mi \pm \sqrt{(628mi)^2 - 4*(22h)*(1,425 mi^2/h)} }{2*22h} \\S' = \frac{-628mi \pm 721 mi }{44h}[/tex]
Then the two solutions are:
S' = (-628mi - 721mi)/44h = -30.66 mi/h
But this is a negative speed, so this has no real meaning, and we can discard this solution.
The other solution is:
S' = (-628mi + 721mi)/44h = 2.1 mi/h
We can conclude that her walking speed is 2.1 miles per hour.
For the quadratic function below, what is the rate of change over the interval.
5 ≤ x ≤ 6
--
2
1
-2
-1
Answer:
Step-by-step explanation:
Intervals are always x values. When x = 5, y = 4 (look at the graph to se this); when x = 6, y = 2. The rate of change is the same thing as the slope. We can't get an exact slope here because this isn't a straight line, but we can find the average rate of change. We use the slope formula to do this: with the coordinates (5, 4) and (6, 2):
[tex]m=\frac{2-4}{6-5}=\frac{-2}{1}=-2[/tex]. Third choice down is the one you want.
the value of 456×6+35×2 is
Answer:
2806
Step-by-step explanation:
→ First complete the multiplication
456 × 6 = 2736 and 35 × 2 = 70
→ Add the totals
2736 + 70 = 2806
Answer:2806
Step-by-step explanation:
^﹏^
If mx*m7=m28 and (M5)y=m15 , what is the value of X+y
If U = { 1 , 2 , 3 , 4 , 5 ,6 , 7 , 8 , 9 }. A={1 , 2 , 3 , 4 } , B= {2 , 4 , 6 , 8 } .Find
(i) ( − )′ (ii) ∩
Answer:
(A - B)' = {2, 4, 5, 6, 7, 8, 9}
(A n B) = {2, 4}
Step-by-step explanation:
Given the set :
U = { 1 , 2 , 3 , 4 , 5 ,6 , 7 , 8 , 9 }
A={1 , 2 , 3 , 4 } , B= {2 , 4 , 6 , 8 }
(A - B) = elements of A which are not in B
(A - B) = {1, 3}
(A - B)' = the complement of A - B ; element in the universal set which are not in A - B
(A - B)' = {2, 4, 5, 6, 7, 8, 9}
(A n B) = elements in both set A and set B
(A n B) = {2, 4}
The area of a rectangular wall of a barn is 175 square ft.it’s length is 6feet longer than twice its width.find the length and width of the wall barn.
Answer:
[tex]L =21.945[/tex] --- Length
[tex]W = 7.9725[/tex] --- Width
Step-by-step explanation:
Given
Let
[tex]L \to Length[/tex]
[tex]W \to Width[/tex]
So:
[tex]Area = 175[/tex]
[tex]L = 6 + 2W[/tex]
Required
The dimension of the rectangle
The area is calculated as:
[tex]Area =L*W[/tex]
This gives:
[tex]175 =L*W[/tex]
Substitute: [tex]L = 6 + 2W[/tex]
[tex]175 =(6 + 2W)*W[/tex]
Open bracket
[tex]175 =6W + 2W^2[/tex]
Rewrite as:
[tex]2W^2+ 6W -175 = 0[/tex]
Using quadratic formula:
[tex]W = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
This gives:
[tex]W = \frac{-6 \± \sqrt{6^2 - 4*2*-175}}{2*2}[/tex]
[tex]W = \frac{-6 \± \sqrt{1436}}{2*2}[/tex]
[tex]W = \frac{-6 \± 37.89}{4}[/tex]
Split
[tex]W = \frac{-6+ 37.89}{4}, W = \frac{-6- 37.89}{4}[/tex]
[tex]W = \frac{31.89}{4}, W = \frac{-43.89}{4}[/tex]
The width cannot be negative;
So:
[tex]W = \frac{31.89}{4}[/tex]
[tex]W = 7.9725[/tex]
Recall that:
[tex]L = 6 + 2W[/tex]
[tex]L =6 + 2 * 7.9725[/tex]
[tex]L =21.945[/tex]
(08.07 MC)
A polynomial function is shown below:
f(x) = x3 − 3x2 − 4x + 12
Which graph best represents the function? (5 points)
Answer:
Graph A (first graph from top to bottom)
Step-by-step explanation:
Given [tex]f(x)=x^3-3x^2-4x+12[/tex], since the degree of the polynomial is 3, the function must be odd and will resemble the shown shape in the graphs. The degree of 3 indicates that there are 3 zeroes, whether distinct or non-distinct. Therefore, the graph must intersect the x-axis at these three points.
Factoring the polynomial:
[tex]f(x)=x^3-3x^2-4x+12,\\f(x)=(x+2)(x-2)(x-3),\\\begin{cases}x+2=0, x=-2\\x-2=0, x=2\\x-3=, x=3\end{cases}[/tex]
Thus, the three zeroes of this function are [tex]x=-2, x=2, x=3[/tex] and the graph must intersection the x-axis at these points. The y-intercept of any graph occurs when [tex]x=0[/tex]. Thus, the y-coordinate of the y-intercept is equal to [tex]y=0^3-3(0^2)-4(0)+12,\\y=12[/tex] and the y-intercept is (0, 12).
The graph that corresponds with this is graph A.
Consider the random experiment of tossing 3 fair coins and observing how many of them come to rest with the heads side of the coin facing upwards. (Assume that each of the coins comes to rest with either its heads side or its tails side facing upwards (i.e., none of the coins comes to rest balanced on its edge).) Letting A denote the event that at least 1 of the coins comes to rest with its heads side upwards, B denote the event that none of the coins comes to rest with its heads side upwards, and S denote the sample space, which of the following statements does not include an abuse of notation?
a. S = 16
b. S = AUB
c. S - 4
d. S = 3
e. P(B) = φ
Answer:
b. S = AUB
Step-by-step explanation:
Since the coins are tossed 3 times and each coin has head, H and tail, T(2 sides), the sample space is S = 2 × 2 × 2 = 2³ = 8
All the possible outcomes are HTT, HHT, HHH, THH, TTH, HTH,THT and TTT
Since S denote the sample space
S = {HTT, HHT, HHH, THH, TTH, HTH,THT, TTT}
Since A denote the event that at least 1 of the coins comes to rest with its heads side upwards, the possible outcomes are HTT, HHT, HHH, THH, TTH, HTH and THT
So, A = {HTT, HHT, HHH, THH, TTH, HTH,THT}
Also B denote the event that none of the coins comes to rest with its heads side upwards, that is no heads. The possible outcome is TTT
So, B = {TTT}
Since S denote the sample space
S = {HTT, HHT, HHH, THH, TTH, HTH,THT, TTT}
So, A ∪ B = {HTT, HHT, HHH, THH, TTH, HTH,THT} ∪ {TTT} = {HTT, HHT, HHH, THH, TTH, HTH,THT, TTT} = S
So, S = A ∪ B
So, S = A ∪ B does not denote an abuse of notation.
The answer is b.
Given: x - 8 > -3.
Choose the solution set.
Answer:
X=-2,-1,0,1,2,3,4,5,6,
Step-by-step explanation:
IF 8 IS LARGER THAN -3 YOU COULD GET THE FOLLOWING ANSWER
Answer:
x>5
Step-by-step explanation:
move -8 to the right side, change the sign and solve:
x > - 3 + 8
x > 5
what are functions in math
can anyone please solve this question using linear function?
Answer:
Step-by-step explanation:
Let Terri spent the 'x' hours in the river,
Per hour rental charged by Timmy's Tubes = [tex]\frac{\text{Rental charged}}{\text{Hours spent}}[/tex]
= [tex]\frac{18.75}{2.5}[/tex]
= $7.5
Charges for 'x' hours = $7.5x
Therefore, function that defines the rental of Timmy's tube will be,
f(x) = 7.5x
Another company Fred's float charges a base fee $2 plus $6.25 per hours.
For 'x' hours Fred's float will charge = 6.25x + 2
And the function that defines the charges will be,
g(x) = 6.25x + 2
1). If x = 1.5 hours,
Rental charged by Timmy's tube,
f(1.5) = 7.5(1.5)
= $11.25
Rental charged by Fred's float,
g(1.5) = 6.25(1.5) + 2
= $11.375
2). If Terri has $12 to spend,
For f(x) = 12,
12 = 7.5x
x = 1.6 hours
For g(x) = 12
12 = 6.25x + 2
10 = 6.25x
x = 1.6 hours
Therefore, both the companies charge the same for 1.6 hors.
Terri can opt any company to spend $12.
. Hannah is selling slices of pie at the bake sale. The pie has 8 slices. She has sold 1/4 of the slices. What fraction with a denominator of 8 is equal to 1/4?
Answer:
2/8 because each 1/4 0f the 8 slices is equal to 2/8 by multipliction or you can say 1/4 of 8
Answer:
2/8
Step-by-step explanation:
1/4
times everything by 2 as 8 / 4 = 2
2/8
Given the functions:
g(n) = 3n - 5
f(n) = n2 + 50
Find:
(g+f)(8)
Answer:
[tex](g + f)(8) =133[/tex]
Step-by-step explanation:
Given
[tex]g(n) = 3n - 5[/tex]
[tex]f(n) = n^2 + 50[/tex]
Required
[tex](g + f)(8)[/tex]
This is calculated as:
[tex](g + f)(n) =g(n) + f(n)[/tex]
So, we have:
[tex](g + f)(n) =3n - 5 + n^2 +50[/tex]
[tex]Substitute[/tex] 8 for n
[tex](g + f)(8) =3*8 - 5 + 8^2 +50[/tex]
[tex](g + f)(8) =24 - 5 + 64 +50[/tex]
[tex](g + f)(8) =133[/tex]
Which points in the graph are in Quadrant II?
Answer:
A, L, F
Step-by-step explanation:
Quadrant ll (2) is the top left one so points A, L, F are in it. Hope this is correct!
Answer: AL
Step-by-step explanation: THE OTHER ARE ON THE AXIS AND NOT NEITHER QUADRANTS
What is a formula for the nth term of the given sequence?
36, 24, 16...
Answer:
The formula to find the nth term of the given sequence is 54 · [tex]\frac{2}{3} ^{n}[/tex]
Step-by-step explanation:
The formula for nth term of an geometric progression is :
[tex]a_{n} = \frac{a_{1}(r^{n})}{r}[/tex]
In this example, we have [tex]a_{1}[/tex] = 36 (the first term in the sequence) and
r = [tex]\frac{2}{3}[/tex] (the rate in which the sequence is changing).
Knowing what the values for r and [tex]a_{1}[/tex] are, now we can solve.
[tex]a_{n} = \frac{a_{1}(r^{n})}{r}[/tex] = [tex]\frac{36 (\frac{2}{3} ^{n}) }{\frac{2}{3} }[/tex] = 54 · [tex]\frac{2}{3} ^{n}[/tex]
Therefore, the formula to find the nth term of the given sequence is
54 · [tex]\frac{2}{3} ^{n}[/tex]
Ethan and his friends went to a movie on Thursday afternoon. They left at 1:00 P.M. It took 1 hour and 5 minutes to drive to the theater. They arrived at the theater 1 hour and 10 minutes before the movie started. Once it started, the movie lasted for 1 hour and minutes. What time was it when the movie ended?
Spanish: Ethan y sus amigos fueron al cine el jueves por la tarde. Salieron a la 1:00 p.m. Tardaron 1 hora y 5 minutos en llegar al teatro. Llegaron al cine 1 hora y 10 minutos antes de que comenzara la película. Una vez que comenzó, la película duró 1 hora y minutos. ¿A qué hora terminó la película?
Answer:
4:15 p.m.
Step-by-step explanation:
There's something missing in this:
Once it started, the movie lasted for 1 hour and minutes. What time was it when the movie ended?
What is the minutes because thats missing.
Also can I get Brainliest please
there is 300ml of oil in the small bottle there is six times as much in the big bottle how much oil is in the big bottle?
Answer:
1800 ml of oil
Step-by-step explanation:
300*6
Help plsss !!!!!!Trying to get my grade up
Work Shown:
area of the triangle on the left = base*height/2 = 0.75*2/2 = 0.75
area of the triangle on the right = base*height/2 = 0.5*4/2 = 1
total area = 0.75+1 = 1.75 square feet
Find the volume of the cylinder pictured below. What is the exact volume in terms of pi?
The set of ordered pairs (–1, 8), (0, 3), (1, –2), and (2, –7) represent a function. What is the range of the function?
Answer:
8 3 -2 -7
Step-by-step explanation:
becoz the y values are the ranges of the function
Answer:
{y: y = –7, –2, 3, 8}
The measure of the vertex angle of an isosceles triangle is (a + 30)°. The base angles each measure (2a - 15)º. What is the measure in degrees of one of the base angles?
Consider the frequency distribution below, which has single values as classes: Value Frequency 10 11 12 13 14 15 16 17 18 19 20 21 1 3 7 18 10 4 2 7 16 10 6 2 Construct a new frequency distribution for this data with 4 classes.
The original table (attached to this response) shows single values as classes.
To construct a new frequency distribution for this data with 4 classes, follow these steps:
i. Starting from the least value (which is 10) create groups each of 4 values. For example, the first group will contain 10, 11, 12 and 13. Therefore, we have a class of 10 - 13.
The second group will contain 14, 15, 16 and 17. Therefore, we have a class of 14 - 17
The third group will contain 18, 19, 20 and 21. Therefore, we have a class of 18 - 21
ii. Get the frequency of these classes, we add the frequencies of the members of the class.
For example,
Class 10 - 13 will have a frequency of (1 + 3 + 7 + 18) = 29
Class 14 - 17 will have a frequency of (10 + 4 + 2 + 7) = 23
Class 18 - 21 will have a frequency of (16 + 10 + 6 + 2) = 34
The new table has been attached to this response.
9.5 sq. miles = _____ acres
2 acres = _______ square yards
Answer:
frist answer is
6080
second answer is 72 square yard
You are building a door frame. Both sides are 80.5 in long, and the top and bottom are both 36.5 in wide. Which additional statement does not give enough information to conclude that the door frame forms a rectangle
a) the door frame has a right angle
b) the diagonals of the door frame are congruent
c) The door frame has a pair of congruent, opposite angles
d) the door frame has a pair of congruent adjacent angles
I think the answer is number three but Im not sure why pls help ASAP.
Answer:
The answer is A.
Step-by-step explanation:
Rectangles is a quadrilateral shape that has four sides, two pairs of parallel lines, and all the corners MUST be right angles for it to be a rectangle. :)
I hope this helps :DD