Elliot is 2 times as old as Tanya. 10 years ago, Elliot was 4 times as old as Tanya​. How old is Elliot now?

DC=CF

We 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

Answer:

Step-by-step explanation:

12

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

Answer:

Step-by-step explanation:

m=7

c=5

balance=26.802

Answer:

Step-by-step explanation:

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

Step-by-step explanation:

(f*g) (x)=f(x) * g(x)

=(x+3)(2x^2-4)

=2x^3-4x+6x^2-12

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

Answer:

100,000 m²

Step-by-step explanation:

the area = l x w = 1000 x 100 = 100,000 m²

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

[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

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.

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

Answer: 20.58

Step-by-step explanation:

Answer:

441

Step-by-step explanation:

sqrt81=9

9 x 49=441

Answer:

441

Step-by-step explanation:

√ 9 ^2  ⋅  49

9  ⋅  49 = 441

Answer:

y=-4+2x

x=(4+y)/2

2x-y=4

Answer:

50

Step-by-step explanation:

Given,

96 + 2² / 2

96 + 4 / 2

100 / 2

50

Answer:

13.2%

or 115.2%

Step-by-step explanation:

hope it's correct. lemme know which one is correct

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

Answer:

84.78

Step-by-step explanation:

Used calculator and formula

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

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

you can go for option g cause ans is 14:5

Answer:

f(x +1 ) =14

Step-by-step explanation:

12= f(x +1) -2

f(x +1) = 12 +2

f (x+1 ) = 12

Answer:

-5x - 7y

Step-by-step explanation:

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°

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]  

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.

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