In the adjoining fig. In a circle with centre C and chord DE ,ahe CF perpendicular to chord DE.If diameter of a circle is 20cm and DE=16cm,then CF=?GIVE REASON
DC=CF
Diameter=20cmRadius=20/2=10cmWe know
[tex]\boxed{\sf L=\dfrac{\theta}{180}\times πr}[/tex]
[tex]\\ \large\sf\longmapsto L=\dfrac{90}{180}\times \dfrac{22}{7}\times 10[/tex]
[tex]\\ \large\sf\longmapsto L=\dfrac{1}{2}\times \dfrac{220}{7}[/tex]
[tex]\\ \large\sf\longmapsto L=\dfrac{110}{7}[/tex]
[tex]\\ \large\sf\longmapsto L=15.5[/tex]
Now
[tex]\\ \large\sf\longmapsto CF=L+r-DE[/tex]
[tex]\\ \large\sf\longmapsto CF=15.7+10-16[/tex]
[tex]\\ \large\sf\longmapsto CF=25.7-16[/tex]
[tex]\\ \large\sf\longmapsto CF=9.7cm[/tex]
[tex]\large\sf\red{⟼L=18090×722×10}[/tex]
[tex]\begin{gathered}\\ \large\sf\red{ ⟼ L=\dfrac{1}{2}\times \dfrac{220}{7}}\end{gathered}[/tex]
[tex]\begin{gathered}{ \large\sf\red{⟼ L=\dfrac{110}{7}}\end{gathered}[/tex]
⟼ L=15.5
Now
⟼ CF=L+r−DE
⟼ CF=15.7+10−16
⟼ CF=25.7−16
⟼CF=9.7cmjames cuts his neighbor's lawn the first is 1000 m long and 100 m wide what is the area
Answer:
100,000 m²
Step-by-step explanation:
the area = l x w = 1000 x 100 = 100,000 m²
f(x) = x+3
g(x) = 2x^2-4
find (f times g) (x)
Step-by-step explanation:
(f*g) (x)=f(x) * g(x)
=(x+3)(2x^2-4)
=2x^3-4x+6x^2-12
please help asap!!! i dont understand it
Answer:
a
Step-by-step explanation:
A perpendicular bisector, intersects a line at its mid point and is perpendicular to it.
Calculate slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13)
m = [tex]\frac{13-1}{9-(-7)}[/tex] = [tex]\frac{12}{9+7}[/tex] = [tex]\frac{12}{16}[/tex] = [tex]\frac{3}{4}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{4} }[/tex] = - [tex]\frac{4}{3}[/tex] ← slope of perpendicular bisector
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
([tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
using (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13) , then
midpoint = ( [tex]\frac{-7+9}{2}[/tex], [tex]\frac{1+13}{2}[/tex] ) = ( [tex]\frac{2}{2}[/tex], [tex]\frac{14}{2}[/tex] ) = (1, 7 )
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{4}{3}[/tex] , then
y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation
To find c substitute the midpoint (1, 7) into the partial equation
7 = - [tex]\frac{4}{3}[/tex] + c ⇒ c = [tex]\frac{21}{3}[/tex] + [tex]\frac{4}{3}[/tex] = [tex]\frac{25}{3}[/tex]
y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{25}{3}[/tex] ← equation of perpendicular bisector
is 23/17 a rational number?
Answer:
rational number
Step-by-step explanation:
a rational number can be written as a/b where a and b are integers
23/17 = a/b where a = 23 and b = 17
This is a rational number
porfavor ayudenme con esta radicacion no la entiendo√81 ∙ 49
Answer:
441
Step-by-step explanation:
sqrt81=9
9 x 49=441
Answer:
441
Step-by-step explanation:
√ 9 ^2 ⋅ 49
9 ⋅ 49 = 441
Find the interior angle sum for the following polygon
If you have the time mind helping me on this
you can go for option g cause ans is 14:5
Find the shortest side of a triangle whose perimeter is 64 if the ratio of two of its sides is 4:3 and the third side is 20 less than the sum if the other two
Answer:
The shortest side of the triangle is 18
Step-by-step explanation:
Let the sides the triangle be x, y and z.
From the question, the perimeter of the rectangle is 64, that is
x + y + z = 64 ...... (1)
Also, the ratio of two of its sides is 4:3, that is x:y = 4:3, then we can write that x/y = 4/3 ⇒ 3x = 4y ...... (2)
The third side, z, is 20 less than the sum of the other two, that is
z + 20 = x + y ...... (3)
Substitute equation (3) into (1)
Then,
z + 20 + z = 64
2z +20 = 64
2z = 64 - 20
2z = 44
z = 44/2 k
z = 22
From equation (3)
z + 20 = x + y
Then, k
22 + 20 = x +y
42 = x + y
x = 42 - y ...... (4)
Substitute this into equation 2
3x = 4y
3(42-y) = 4y
126 - 3y = 4y
4y + 3y = 126
7y = 126
y = 126/7
y = 18
Substitute this into equation (4)
x = 42 - y
x = 42 - 18
x = 24
∴ x = 24, y = 18 and z = 22
Hence, the shortest side of the triangle is 18.
Find the missing segment in the image below
Answer:
Step-by-step explanation:
An airplane travels 4020 kilometers against the wind in 6 hours and 4800 kilometers with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind?
Answer:
Rate of plane 735 km/hr
Rate of wind 65 km/hr
Step-by-step explanation:
Calculation to determine the rate of the plane in still air
Let Va represent the velocity of the airplane
Let Vw represent the velocity of the wind
When flying with the wind:
(Va+Vw)*(6 hours) = 4800
6Va + 6Vw = 4800
6Vw = 4800 - 6Va
Vw=4800/6-Va
Vw = 800 - Va
When flying against the wind:
(Va-Vw)*(6 hours) = 4020 km
6Va - 6Vw = 4020
Substitute 800-Va for Vw and solve for Va:
6Va - 6(800-Va) = 4020
6Va -4800 + 6Va = 4020
12Va = 8820
Va=8820/12
Va = 735 km/hr
Therefore the rate of the plane in still air is 735 km/hr
Calculation to determine the rate of the wind
Rate of wind:
Vw = 800 - Va
Vw= 800 -735
Vw= 65 km/hr
Therefore the rate of the wind is 65 km/hr
cho tam giác ABC vuông tại A < góc B=a chứng minh: a) 1+[tex]tan^{2}[/tex]a=[tex]\frac{1}{sin^{2}a }[/tex]
làm giúp mình với
[tex]\\ \sf\longmapsto 1+tan^2A[/tex]
[tex]\boxed{\sf tanA=\dfrac{sinA}{cosA}}[/tex]
[tex]\\ \sf\longmapsto 1+\dfrac{sin^2A}{cos^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{cos^2A+sin^2A}{cos^2A}[/tex]
[tex]\boxed{\sf cos^2A+sin^2A=1}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{cos^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{1-sin^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{1}-\dfrac{1}{sin^2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{sin^2A}[/tex]
Hence verified
find k so that x^2+2x+k is a factor of 2x^4+x^3-14x^2+5x+6. also find all the zeroes of the two polynomial
Compute the quotient and remainder,
[tex]\dfrac{2x^4+x^3-14x^2+5x+6}{x^2+2x+k} \\\\ = 2x^2 - 3x - (8+2k) + \dfrac{(21+7k)x+(6+8k+2k^2)}{x^2+2x+k}[/tex]
The remainder upon dividing [tex]2x^4+x^3-14x^2+5x+6[/tex] by [tex]x^2+2x+k[/tex] should leave no remainder, which means
[tex]21+7k = 0 \implies 21 = -7k \implies k=-3[/tex]
and
[tex]6+8k+2k^2 = 0 \implies 2(k+3)(k+1)=0 \implies k=-3\text{ or }k=-1[/tex]
Only k = -3 makes both remainder terms vanish.
Then the previous result reduces to
[tex]\dfrac{2x^4+x^3-14x^2+5x+6}{x^2+2x-3} = 2x^2 - 3x - 2[/tex]
so that
[tex]2x^4+x^3-14x^2+5x+6 = (x^2+2x-3) (2x^2 - 3x - 2) \\\\ 2x^4+x^3-14x^2+5x+6 = (x+3)(x-1)(2x + 1)(x-2)[/tex]
and so the zeroes of the quartic polynomial are x = -3, x = 1, x = -1/2, and x = 2.
¿Cual es el resultado de dividir 164.64 entre 8
Answer: 20.58
Step-by-step explanation:
Tamanika got a raise in her hourly pay, from $15.50 to $17.85. Find the percent increase. Round to the nearest tenth of a percent.
Answer:
13.2%
or 115.2%
Step-by-step explanation:
hope it's correct. lemme know which one is correct
I need help solving this
Answer:
E. 248
Step-by-step explanation:
1 to 500 in set A, 250 to 750 in set B
500 - 250 = 250
100 and 200 are divisible by 100.
250 - 2 = 248
hlpppppp plesaseeeeeeeeeeeeeeeee
Answer:
50
Step-by-step explanation:
Given,
96 + 2² / 2
96 + 4 / 2
100 / 2
50
Please answer I'll mark u the brialintest
1) 3 × --- = (-12)
8) 2/5 × 4 is equal to ------
Answer:
1. -4
2. 8/ 5 - 1. 6
Step-by-step explanation:
1 . 3 × -4
= (-12)
2. 2/5 × 4
= 8 / 5
= 1.6
Hope this answer helps you :)
Have a great day
Mark brainliest
You draw a red marble out of a bag and give it your friend. You draw another marble out of the bag. Are the events independent? Explain.
No; the red marble was not replaced, so it has an effect on drawing a second marble.
Yes; you may not get a red marble again.
No; you do not know which marble you will draw next.
Yes; the red marble was kept out, so you can not draw it again.
Answer:
the red marble was kept out so you can not draw it again
Answer:
Yes; you may not get a red marble again.
Step-by-step explanation:
there is a chance to get a red marble but it is not high
Monica plans to buy markers and colored pencils at an office supply store A box of markers cost $3.85 and a a box of colored pencils cost $1.85. She has $40 to spend Which inequality best represents how many boxes of markers m and colored pencils c she can buy
Answer:
Step-by-step explanation:
m=7
c=5
balance=26.802
Today only, a sofa is being sold at a 72% discount. The sale price is 218.40.
What was the price yesterday?
Answer:
780
Step-by-step explanation:
Let x be the original price
x - x*72% is the new price
x - .72x = 218.40
.28x = 218.40
Divide each side by .28
.28x/.28 = 218.40/.28
x =780
Using two independent samples, two population means are compared to determine if a difference exists. The population standard deviations are equal. The number in the first sample is fifteen and the number in the second sample is 12. How many degrees of freedom are associated with the critical value
Answer:
Hence the degrees of freedom are associated with the critical value is 25.
Step-by-step explanation:
Using two independent samples, two population means are
compared to determine if a difference exists, the population standard deviation is equal.
sample size 1 = [tex]n_{1}[/tex]= 15 and sample size 2 = [tex]n_{2}[/tex] = 12
since, population standard deviations are equal, required degrees of freedom
[tex]= n_{1} + n_{2} - 2 \\= 15 + 12 - 2\\ = 25[/tex]
Rewrite in simplest terms (-9x-2y)+(4x-5y)
Answer:
-5x - 7y
Step-by-step explanation:
what is the mass of raisins in a package
Answer:
Step-by-step explanation:
12
pls pls pls pls help me answer quickly
Break it into two shapes, a rectangle that is 7 x 10 x 6
And a triangle with a base of 12-10 = 2 and a height of 7
Volume of rectangle : 7 x 10 x 6 = 420
Volume of triangle: 1/2 x 2 x 7 = 7 x 6 = 42
Total volume = 420 + 42 = 462 cubic centimeters.
Answer: 462
Step-by-step explanation: 7 x 12 x 6 = 504 7 x 10 x 6 = 420
504 - 420 =84 84/2=42
420 + 42=462
1. Write three different solutions of 4x - 2y = 8. plzz answer fast
Answer:
y=-4+2x
x=(4+y)/2
2x-y=4
Let g(x) = f (x+1) - 2, find when g(x) = 12
I don't know how to evaluate this since I have both g(x) and an f(x).
Answer:
f(x +1 ) =14
Step-by-step explanation:
12= f(x +1) -2
f(x +1) = 12 +2
f (x+1 ) = 12
determine the dimension of cube when the volume is 1.468mcube
Answer:
1.137 m
Step-by-step explanation:
The volume of a cube is given as the cube of the side. A cube is a 3 dimensional shape with equal sides and 6 faces. If the volume is V and the side is s then
V = s * s * s
Given that the volume is 1.468mcube then
s^3 = 1.468
s = cube root of 1.468
= 1.137 m
Find the area of the shaded regions:
Answer:
84.78
Step-by-step explanation:
Used calculator and formula
HELP OVER HERE LOL !!
Find the measure of the intercepted arc
Answer:
arc GH = 74°
Step-by-step explanation:
The inscribed angle GFH is half the measure of the intercepted arc aGH, then
arc GH = 2 × 37° = 74°
