Answers
Answer:
Step-by-step explanation:
∠OAB is 90 degrees, tangent and a radius met at 90 degree angle
∠OCB=90 degrees, tan and radius meet at 90 degrees angle
OB=12
find angle BOC:
triangle BOA is right angle triangle:
cos(AOB)=adj/hyp=7/12=54.33
angle B= 180-(90+54.33)=35.67
angle COB=54.33 equal to angle AOB
angle AOC=54.33+54.33=108.66
the sum of angles of circle =360
360-108.66= 251.34( exterior angle at the center AOC)
length of the arc= angle (251.34 degrees*7)
convert degrees to radians=4.386 (251.34/π)
length=r*angle in radian=4.386*7=30.71
( i hope this is the answer)
Related Questions
Find the center and radius of the circle defined by the equation x^2+y^2-7x+3y-4=0
Answers
Answer:
C. center: (7/2, -3/2); radius: sqrt(74)/2
Step-by-step explanation:
x^2 + y^2 - 7x + 3y - 4 = 0
We can put the equation in standard form by completing the square in x and in y.
x^2 - 7x + ___ + y^2 + 3y + ___ = 4 + ___ + ___
x^2 - 7x + (7/2)^2 + y^2 + 3y + (3/2)^2 = 4 + (7/2)^2 + (3/2)^2
(x - 7/2)^2 + (y + 3/2)^2 = 16/4 + 49/4 + 9/4
(x - 7/2)^2 + (y + 3/2)^2 = 74/4
(x - 7/2)^2 + (y + 3/2)^2 = (sqrt(74)/2)^2
Answer: center: (7/2, -3/2); radius: sqrt(74)/2
HELP QUICKKK PLSSS The cross section of a right rectangular pyramid is a trapezoid if the pyramid is sliced BLANK . If the pyramid is sliced through the top vertex and perpendicular to the base, the cross section is a BLANK .
Answers
Answer:
Step-by-step explanation:
The cross section of a right rectangular pyramid is a trapezoid if the pyramid is sliced perpendicularly to the base and NOT passes trough the vertex.
If the pyramid is sliced through the top vertex and perpendicular to the base, the cross section is a triangle that does not have the same dimension as the pyramid
What is the perimeter of the rectangle?
Answers
Answer:
32
Step-by-step explanation:
P=2(l+w)
so 2(11+5)=P
2(11+5)=32
The world's tallest building is the Burj Khalifa in Dubai at 828 m tall. The CN Tower in Toronto is 553 m tall. Ryan wants to compare the Burj Khalifa and the CN Tower by creating rectangular prism models on a 10 cm by 10 cm square base. He has decided to represent the Burj Khalifa with a rectangular prism that has a height of 40 cm. What is the volume of each rectangular prism? Round your answer to the nearest cubic centimetre. Show your work for full marks.
Answers
Answer:
Volume of Burj Khalifa Prism = 4000 [tex]cm^2[/tex]
Volume of CN Tower Prism = 2671 [tex]cm^2[/tex]
Step-by-step explanation:
Given
Height of Burj Khalifa = 828 m
Height of CN Tower in Toronto = 553 m
Base of rectangular prism is a square with sides 10 cm [tex]\times[/tex] 10 cm.
Height of Burj Khalifa prism = 40 cm
828 m is represented as 40 cm
[tex]\Rightarrow 553 m[/tex] is represented as [tex]\frac{40}{828 } \times 553 = 26.71\ cm[/tex]
So, height of rectangular prism of CN Tower = 26.71 cm
Volume of a Prism is given by the Formula:
[tex]V=Area\ of\ Base \times Height[/tex]
Base is a square, so Area of base = [tex]Side^2[/tex]
Volume of Burj Khalifa Prism:
[tex]V_B=10^2 \times 40 = 4000\ cm^2[/tex]
Volume of CN Tower Prism:
[tex]V_C=10^2 \times 26.71 = 2671\ cm^2[/tex]
So, the answer is:
Volume of Burj Khalifa Prism = 4000 [tex]cm^2[/tex]
Volume of CN Tower Prism = 2671 [tex]cm^2[/tex]
Where will her cut be located? Round to the nearest tenth. x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 A number line goes from 0 to 60. A line is drawn from 2 to 60. Genevieve is cutting a 60-inch piece of ribbon into a ratio of 2:3. Since 2 inches are frayed at one end of the ribbon, she will need to start 2 inches in. This is indicated as 2 on the number line
25.2 in.
29.4 in.
35.1 in.
40.7 in.
Answers
Answer:
The correct answer is 25.2 in.
Step-by-step explanation:
It is given that number line goes from 0 to 60 which can be used to represent a ribbon of length = 60 inches.
2 inches of the ribbon are frayed so actual length = 58 inches
Please refer to the attached image for the ribbon.
A is at 0
C is at 60
B is at 2
P is the point to divide the remaining ribbon in the ratio 2:3.
Part AB of the ribbon is frayed.
BP: PC = 2:3
Let BP = 2[tex]x[/tex] and PC = 3[tex]x[/tex]
Now, BP + PC = BC = 58 = 2[tex]x[/tex] + 3[tex]x[/tex] = 5[tex]x[/tex]
So,
[tex]5x =58\\\Rightarrow x =11.6[/tex]
BP = [tex]2\times x = 2 \times 11.6 = 23.2\ inches[/tex]
Location of the Cut = 2 + 23.2 = 25.2 inches
Alternatively, we can use the formula directly:
[tex]x = \dfrac{m} {m + n } (x_2 - x_1) + x_1[/tex]
[tex]x_1 = 2\\x_2 = 60[/tex]
m: n is the ratio 2:3
[tex]x = \dfrac{2} {2 +3 } (60- 2) + 2\\\Rightarrow 0.4 (58 )+2\\\Rightarrow 23.2+2 \\\Rightarrow \bold{25.2\ inches}[/tex]
Answer:
Yes i confirm the answer above is correct. A.) 25.2
Step-by-step explanation:
I took the test duhh
PLEASE HELP ME TO COMPLETE THIS QUESTION
Answers
Answer:
Step-by-step explanation:
a) Increase in population =510,000 - 430,000 = 80,000
Percentage increase = [tex]\frac{80,000}{430,000}*100[/tex]
= [tex]\frac{800}{43}[/tex]
= 18.6 %
b) Percentage increase = 17.3%
Increase in population = 17.3% * 510,000
= 0.173 * 510,000
= 88,230
Predicted population in 2021 = 510,000 + 88,230
= 598,230
A printer ink cartridge that can print 550 pages has already printed 127 pages. Which solution represents the correct equation and answer to the question, "How many more pages, P, can still be printed?"
Answers
P + 127 = 550 P = 423
Answer:
P = 423
P + 127 = 550
Step-by-step explanation:
what is the value of y in the figure below? (Picture provided)
Answers
30 degrees= x
60 degrees= x root 3
90 degrees= 2x
In this case since you know 90 degrees is 14 then you would have to find c which is 7 when you divide it by 2
What transformation maps rectangle QRST to rectangle Q’R’S’T’?
reflection
rotation
stretch
translation
Answers
Answer:
Reflection
Step-by-step explanation:
Just took the test got a 100%
edg 2021
Answer:
A: Reflection
Step-by-step explanation:
Let's be honest, no one hardly ever pays attiontion to the explanation.
<3
Any help on this???????????
Answers
Answer:
x = 121°
Step-by-step explanation:
The angle supplementary to 115° is 180 - 115 = 65° and the angle that forms a full circle with 304° is 360 - 304 = 56°. Since the measure of an exterior angle is equal to the sum of its remote interior angles, we know that x = 65 + 56 = 121°.
f(x) = (x + 1)2
What is the domain of f?
Choose 1 answer:
All real values of x such that x = -1
All real values of such that > -1
All real values of x such that I + 0
All real values of x such that 2 > 0
غم عصتلحينلحصعالم
Answers
Answer:
all real numbers
Step-by-step explanation:
f(x) = (x + 1)^2
There is no restriction on x, so the domain is:
all real numbers
Determine whether the triangles are congruent. Explain you reasoning.
Answers
Triangles are congruent
Step-by-step explanation:
Law of Side, Side, Angle
Thier base are same (PR).
Thier 1 side is equal to 2 inch (PS = RQ).
Thier 1 angle is equal (/_ PRQ = /_ RPS)
So, Its prove that both triangles are congruent.
This table gives a few (x,y) pairs of a line in the coordinate plane.
Answers
Answer:
x-intercept → (-5, 0)
Step-by-step explanation:
Let the equation of the line having pairs given in the table is,
y - y' = m(x - x')
m = slope of the line
(x', y') is a point lying on the line.
From the given table,
Two points (33, -22) and (52, -33) lie on the line.
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{-33+22}{52-33}[/tex]
m = [tex]-\frac{11}{19}[/tex]
Equation of the line passing through (33, -22) and slope = [tex]-\frac{11}{19}[/tex] will be,
y + 22 = [tex]-\frac{11}{19}(x - 33)[/tex]
For x-intercept y = 0,
0 + 22 = [tex]-\frac{11}{19}(x-33)[/tex]
-38 = x - 33
x = -38 + 33
x = -5
Therefore, x-intercept of the line is (-5, 0).
Answer:
-5,0
Step-by-step explanation:
khan academy
o persoana depune la banca o suma de bani. banca ofera o dobanda anuala de 2%. dupa un an in cont se afla 8160 lei. Care a fost suma depuse la banca?
Answers
Answer:
8000 lei
Step-by-step explanation:
Ni se spune la întrebarea de mai sus să găsim suma depusă în bancă.
Ni se oferă următoarele valori
R = rata = 2% = 0.02
T = Timp = 1 an
Suma totală = A = 8160 lei
Trebuie să găsim principalul (suma depusă la bancă).
Formula de utilizat este dată ca:
P (Principal) = A / (1 + rt)
P = 8160 lei / 1 + 0.02 × 1
P = 8160 lei / 1.02
P = 8000 lei
Prin urmare, suma depusă în bancă este de 8000 de lei.
Answer:
the two percent of 8160 its 163.2 so its 7996.8
Step-by-step explanation:
Pleaseeee helpppppp plz❤️❤️❤️
Answers
Answer:
1: d. 3054^3
2: d. 20x
Step-by-step explanation:
1)
Well to find the volume of a sphere we use the following formula,
[tex]\frac{4}{3}\pi r^3[/tex]
So the radius is 9.
9*9*9 = 729
729*pi = 2290.22104447
So it is 2290 rounded to the nearest whole number.
2290 * 4/3 = 3053.3333333
Thus,
the answer is d. [tex]3054^3[/tex]
____________________________________________________________
So we have to factor 25x^2 - 9,
which is [tex]\left(5x+3\right)\left(5x-3\right)[/tex].
So if the l and w are 5x + 3 and 5x - 3,
= 10x
10x + 10x = 20x,
Thus,
the answer is d. 20x
Hope this helps :)
Efren is constructing a line parallel to EF¯¯¯¯¯ through point G. What step should be his next step? With the compass point on D, construct an arc that intersects EF¯¯¯¯¯ and GD←→ . With the compass point on G, construct an arc that intersects GD←→ . With the compass point on D, construct an arc that intersects EF¯¯¯¯¯ twice. With the compass point on G, construct an arc that intersects EF¯¯¯¯¯ .
Answers
Answer:
The correct option is;
With the compass point on G, construct an arc that intersect GD←→
Step-by-step explanation:
The steps for constructing a parallel line to a given point is as follows;
1) With the straightedge, a transversal is drawn intersecting the giving line and passing through point G
2) Copy the angle formed between the transversal and the given line and the to the point G starting by constructing an arc with the compass on point G to intersect GD←→ then with the compass opening still the same, place the compass on the point of intersection of the arc constructed from point G on GD and construct another arc to intersect the arc previous arc from G to GD
3) The line drawn from the intersection through is a parallel line to EF
Therefore, the correct option is that with the compass point on G, construct an arc that intersect GD←→.
Answer:
A. With the compass on point D , construct an arc that intersects EF¯¯¯¯¯ and GD←→.
Step-by-step explanation:
I just took the test!
Manuel y Rosa, desean hacer un regalo a sus tíos por Fiestas patrias, para lo cual visitaron distintos centros comerciales donde venden artículos o herramientas de carpintería. En uno de ellos, observaron que una caja de herramientas les costaba 180 soles. Al no contar con ese monto, decidieron volver la primera semana de Julio, después de juntar sus ahorros. Pero se dieron cuenta que el precio se había incrementado en un 10% . Al faltarles dinero, decidieron volver la siguiente semana, en la que observan que el precio de la caja de herramientas se había incrementado en un 20% del precio que observaron en la primera semana de Julio. Ellos cuentan con 250 soles. Manuel dice: "el precio se ha incrementado en 35% del precio del precio inicial pero nos alcanza y nos sobra 7 soles" A lo que Rosa dice: " no se ha incrementado en un 35% pero sí nos sobrarían 5 soles?
Answers
Answer:
El incremento total con respecto al precio inicial es de 32% y Rosa tiene razón con respecto al porcentaje (no se incrementó 35%).
En cuanto al dinero que les sobra, ninguno de ellos está en lo correcto pues les sobran 12 soles.
Step-by-step explanation:
En un principio, la caja de herramientas costaba 180 soles.
Después de una semana el precio se incrementó 10%, el 10% de 180 soles es 18 por lo que la caja costaba 180 + 18 = 198 soles.
Ellos volvieron la siguiente semana y vieron que el precio se había incrementado un 20% con respecto a la semana anterior, el 20% de 198 es igual a 198 x 0.20 = 39.6 por lo que el precio ahora era de 198 + 39.6 = 237.6 soles.
Para saber el incremento total con respecto al precio inicial podemos hacer una proporción:
180 soles : 100
237.6 soles : x
Despejando x tenemos que:
[tex]x= \frac{237.6(100)}{180}=\frac{23760}{180}=132[/tex]
Por lo tanto, el incremento total con respecto al precio inicial es de 32% y Rosa tiene razón con respecto al porcentaje (no se incrementó 35%)
Sin embargo, ellos cuentan con 250 soles y la caja cuesta 237.6 ≈238 soles, por lo tanto, les alcanza y les sobran 250 - 238 = 12 soles.
Maya decides to use the method of proportions and similar triangles to find the height of a tower. She measures the length of the tower's shadow and finds it is 20 feet long. Then she holds a 12-inch ruler perpendicular to the ground and finds that it casts a 4-inch shadow. How tall is the tower? a. 2.4 ft c. 60 ft b. 5 ft d. 240 ft
Answers
Answer: C: 60 ft
Step-by-step explanation:
Her pencil is 12 inches and its shadow is 4 inches. Her pencil is 3 times longer than its shadow, so using that logic we can conclude that the tower is 3 times longer than its shadow as well.
[tex]20*3=60[/tex]
The tower is 60 feet tall.
what happens to the resistance as the conductor is made thicker
Answers
Answer:
The resistance decreases.
Step-by-step explanation:
The resistance decreases as the conductor is made thicker.
First of all, resistance is like some sort of an obstacle right?
So if the conductor is made thicker it will be easy for the electrons to pass through.
And if the conductor is made thinner it won't be easy for the electrons to pass through. Which makes the resistance increase as there will be collision between the electrons.
Hope this helped ;) ❤❤❤
Wesley makes spherical fish tanks with a diameter of 30. A customer requests a smaller tank with half the volume of the tank that Wesley usually makes.
What is the approximate diameter of the smaller tank?
Round to the nearest tenth.
Answers
Answer:
23.8
Step-by-step explanation:
V = 4/3 π r³
V = 4/3 π (15)³
V = 4500 π
V = 4/3 π r³
4500 π / 2 = 4/3 π r³
1687.5 = r³
r ≈ 11.9
d ≈ 23.8
Answer:
23.8 is the diameter.
Step-by-step explanation:
a. 5y2 - 60 = 0
by Square root property
Answers
Answer:
y = ± 2sqrt(3)
Step-by-step explanation:
5y^2 - 60 = 0
Add 60 to each side
5y^2 = 60
Divide by 5
y^2 = 60/5
y^2 = 12
Take the square root of each side
sqrt( y^2) = ± sqrt(12)
y = ± sqrt(4*3)
y = ±sqrt(4) sqrt(3)
y = ± 2sqrt(3)
Paige launched a ball using a catapult she built. The height of the ball (in meters above the ground) ttt seconds after launch is modeled by h(t)=-5t^2+40th(t)=−5t 2 +40th, left parenthesis, t, right parenthesis, equals, minus, 5, t, squared, plus, 40, t Paige wants to know when the ball will hit the ground. 1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation. h(t)=h(t)=h, left parenthesis, t, right parenthesis, equals 2) How many seconds after launch does the ball hit the ground? seconds
Answers
Answer:
1) Factor form : [tex]h(t)=-5t(t-8)[/tex]
2) 8 second after launch.
Step-by-step explanation:
The height of the ball (in meters above the ground) t seconds after launch is modeled by
[tex]h(t)=-5t^2+40t[/tex]
To find the time when ball hit the ground, we need to find the factor form of the given function.
[tex]h(t)=-5t(t-8)[/tex]
When ball hi the ground, then height of the ball from the ground is 0.
[tex]h(t)=0[/tex]
[tex]-5t(t-8)=0[/tex]
Using zero product property, we get
[tex]-5t=0\Rightarrow t=0[/tex]
[tex]t-8=0\Rightarrow t=8[/tex]
Ball hit the ground at t=0 and t=8. It means ball hit the ground in starting and 8 second after launch.
Answer:
-5t(t - 8) and it hit 8 seconds after launch.
Students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey. Preference Male Female TOTAL Prefers dogs 36 20 56 Prefers cats 10 26 36 No preference 2 6 8 TOTAL 48 52 100 Of students in the sample, what fraction were male?
Answers
Answer:
12/25
Step-by-step explanation:
There were a total of 48 males, so 48/100 = 12/25.
+---------------+------+--------+-------+
| | Male | Female | Total |
+---------------+------+--------+-------+
| Prefers Dogs | 36 | 20 | 56 |
+---------------+------+--------+-------+
| Prefers Cats | 10 | 26 | 36 |
+---------------+------+--------+-------+
| No Preference | 2 | 6 | 8 |
+---------------+------+--------+-------+
| Total | 48 | 52 | 100 |
+---------------+------+--------+-------+
Randomization in an experiment means that the experimental units or
subjects are selected as a simple random sample from the whole population
under study.
Answers
Answer:
Randomization allows a sample or small groups with similar characteristics to determine a probability or to hypothesize an event, that is why this type of samples is important in an experiment, that is, to carry it out in a random way.
Step-by-step explanation:
For example;
If a crop at a certain time of year, for example in summer, is affected by a certain fungus, to know if it is really the time of year that affects this problem, random samples of the same crop with the same characteristics and put it to the test at another time of the year to see if the weather is really a risk factor in the spread of this fungus.
Parallel lines p and q are cut by transversal r. On line p where it intersects with line r, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are: 1, 2, 4, 3. On line q where it intersects with line r, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are: 5, 6, 8, 7. m∠3 is (3x + 4)° and m∠5 is (2x + 11)°. Angles 3 and 5 are . The equation can be used to solve for x. m∠5 = °
Answers
Answer:
77 degrees
Step-by-step explanation:
The diagram is drawn and attached below.
m∠3= (3x + 4)°
m∠5 = (2x + 11)°
Angles 3 and 5 are co-interior angles and are therefore supplementary (add up to 180 degrees).
(3x + 4)°+(2x + 11)°=180°
5x+15=180
5x=180-15
5x=165
x=33
Therefore, the measure of angle 5
m∠5 = (2x + 11)°
= (2(33) + 11)°
=66+11
=77°
The measure of angle 5 is 77 degrees.
Find the mean of the following data set. 42, 45, 58, 63 1. 42 2. 47 3. 52
Answers
Answer:
52
Step-by-step explanation:
42, 45, 58, 63
The mean is the sum divided by the number of terms
(42+ 45+ 58+ 63)/4
208/4
52
Answer:
Step-by-step explanation:
42 + 45 + 58 +631 + 422 + 473 + 52 = 1723
then divide by 7 to get 246.142857
hope this helps :)
Find x ÷ y, if x = 3 5/6 and y = 3 3/4 .Express your answer in simplest form.
Answers
Answer:
23/30
Step-by-step explanation:
x/y
(3 5/6)/(3 3/4)
((3*6)+5/6)/((3*4)+ 3/4)
(18+5/6)/(12+3/4)
(23/6)/(15/4)
(23/6)*(4/15)
(23*3)/(6*15)
(69/90)
23/30
Answer:
1 1/45
Step-by-step explanation:
What is the equation of a line, in general form, that passes through points (-1, 2) and (5, 2)? A. y - 2 = 0 B. y - x - 2 = 0 C. x - 2 = 0
Answers
Answer:
y=2 or y-2=0
Step-by-step explanation:
to find the equation first find the slope m points (-1,2) and (5,2)
m=y2-y1/x2-x1 =2-2/5-(-1)=0/6=0
y=mx+b the slope is zero then y=b=2
Find the values ofx and y for the triange.
x
60°
30°
у
Answers
Answer:
X=36.4 or 36.37306696.... and Y=42
Step-by-step explanation:
So you have a 30-60-90 triangle!
Do Not Worry this is a hard subject to understand, but I will try to do my best with helping you. Right now you need to find x and y. All you have is 21. Under your 60 angle, which is pointing downward, is the 21. And 21 is initially in the spot of x or 1. so 21 is the x(But not the x on the side of 90). I am sorry if this is a bit confusing.
You are then going to take your side which is x, the side that is directly in the path of 90, and it is going to be 21[tex]\sqrt{3[/tex]. Then on the side of your y, which is in the path of your 60, it will be 2 times your x.
The general layout of this is:
x is underneath the side of 90 degrees.
then on the side where 60 degrees and 30 degrees is, is going to be x[tex]\sqrt{3[/tex].
Then the last side, where 30 degrees and 90 degrees lay, will be 2(x).
So all you have to do is plug everything in.
x=36.4 in decimal
y=42(because all you had to do was plug 21 where the x is, because that is where x is in the general layout.)
The value of x = 42 units
The value of y = 21√3 units
What is Trigonometry?The study of the correlation between a right-angled triangle's sides and angles is the focus of one of the most significant branches of mathematics in history: trigonometry. Hipparchus, a Greek mathematician, introduced this idea.
As per the given diagram:
The triangle is a right angle triangle.
Using trigonometric ratios to find x and y:
tan30° = (P/B)
tan30° = (21/y)
(1/√3) = (21/y)
y = 21√3 units
sin30° = (P/H)
(1/2) = (21/x)
x = 2 × 21
x = 42 units
The value of x and y is 42 units and 21√3 units, respectively.
To learn more on Trigonometry, click:
brainly.com/question/17199821
#SPJ7
Find the common ratio of the geometric sequence: 2/3,−2,6,…
Answers
Answer:
-3
Step-by-step explanation:
Well to find the common ratio we need to figure out,
what * 2/3 = -2.
To find that we do -2 ÷ 2/3
= -3
To check -2 * -3 should be 6 which it is.
Thus,
the common ratio is -3.
Hope this helps :)
Answer:
-3
Step-by-step explanation:
Common ratio = 2nd term ÷ 1 st term
= -2 ÷ 2/3
= [tex]-2 * \frac{3}{2}\\\\[/tex]
= -3