In the figure E is the midpoint of AB

If a sentence is defined recursively by f(0)=3 and f(n+1) = f(n) +5 for n ? 0, then f(2) is A) 2 B) 3 C) 5 D) 8

VladimirAG [237]

The recursive formula $f(n+1)=f(n)+5$ means that the next term in the sequence is 5 more than the previous one.

So, we know that we start from $f(0)=3$ , which means that the next term is

$f(1) = f(0)+5 = 3+5 = 8$

Similarly,

$f(2) = f(1)+5 = 8+5 = 13$

8 0

3 years ago

Ms Harris has a taco stand. She has found that her daily costs are approximated by the following equation:

mrs_skeptik [129]

a. find the number of units of tacos she must sell to minimise her cost.
to find a minimum we need to find the function derivative and make it equal to zero:
dc/dx = 2x - 40 = 0
2x = 40
x = 20
therefore to minimize the cost, she needs to sell 20 units of tacos

b. find the minimum cost.
that can be done by substituting the previous result, 20 tacos, in the original equation:
C(x) = x^2 - 40x + 610
C(20) = (20)^2 - 40(20) + 610
= 400 - 800 + 610
= 210
the minimum cost will be 210 dollars

3 0

3 years ago

you go shopping and your bill comes to $54. The sales tax added on equals 7%. What is the amount of sales tax added to you bill?

Andreyy89

7.78 is the sales tax’s

6 0

3 years ago

Find the equation of the sphere in standard form centered at (−6,10,5) with radius 5.

Dovator [93]

Answer:

The equation of the sphere in standard form is

$x^{2} +y^{2}+z^{2} +12 x-20 y-10 z+136=0$

Step-by-step explanation:

Step 1:-

The equation of the sphere having center and radius is

$(x-h)^{2} +(y-k)^{2} +(z-l)^{2} = r^{2}$

Given centered of the sphere is (-6,10,5) and radius r=5

$(x-(-6))^{2} +(y-10)^{2} +(z-5)^{2} = 5^{2}$

on simplification,we get

$using (a+b)^{2} =a^{2} +2 a b+b^{2}$

$using (a-b)^{2} =a^{2} -2 a b+b^{2}$

simplify , we get

$x^{2} +y^{2}+z^{2} +12 x-20 y-10 z+136=0$

8 0

3 years ago

Help me answer these PLEASE ASAP

Hoochie [10]

Answer:

Answered below

Step-by-step explanation:

Sheet 1: Question 3

Vertically opposite angles are equal so you will equate the angles given,

∠LPN = ∠OPM

7 + 13x = -20 + 16x

27 = 3x

x = 9

Sheet 1: Question 4

Vertically opposite angles are equal so you will equate the angles given,

∠ABD = ∠EBC

2x + 20 = 3x + 15

-x = -5

x = 5

Sheet 1: Question 5

Step 1: Find the value of x

Vertically opposite angles are equal so you will equate the angles given,

∠SOP = ∠ROQ

5x = 4x + 10

x = 10

Step 2: Find angles

Angle SOP = 5x = 5(10) = 50°

Angle ROQ = 50° (because it is vertically opposite to angle SOP)

Angle SOR = 180 - 50 (because all angles on a straight line are equal to 180°)

Angle SOR = 130°

Angle POQ = 130° (because it is vertically opposite to angle SOR)

Sheet 1: Question 6

Angle 1 = 72° (because vertically opposite angles)

∠4 + ∠1 + 41 = 180° (because all angles on a straight line are equal to 180°)

∠4 + 72 + 41 = 180

∠4 = 67°

∠3 = 41° (because vertically opposite angles)

∠2 = 67° (because vertically opposite angles)

Sheet 2: Question 3

Step 1: Find the value of x

Sum of complementary angles is equal to 90°

Angle A + Angle B = 90°

7x + 4 + 4x + 9 = 90°

11x = 90 - 13

11x = 77

x = 7

Step 2: Find angle A and angle B using x

Angle A: 7x + 4

7(7) + 4

Angle A = 53°

Angle B: 4x + 9

4(7) + 9

Angle B = 37°

Sheet 3: Question 3

Step 1: Find the value of x

Sum of supplementary angles is equal to 180°.

Angle A + Angle B = 180°

3x - 7 + 2x + 2 = 180°

5x = 185

x = 37

Step 2: Find angle A and angle B using x

Angle A: 3x - 7

3(37)-7

Angle A = 104°

Angle B: 2x + 2

2(37) + 2

Angle B = 76°

Sheet 3: Question 4

Sum of supplementary angles is equal to 180°.

Step 1: Find x

1/4(36x-8) + 1/2(6x-20) = 180°

Take LCM

[36x - 8 + 2(6x - 20)]/4 = 180°

36x - 8 +12x - 40 = 180 x 4

48x - 48 = 720

48x = 768

x = 16

Step 2: Find both angles with the help of x

Angle 1: 1/4(36x-8)

1/4[36(16)-8] = 568/4

Angle 1 = 142°

Angle 2: 1/2(6x-20)

1/2[6(16)-20] = 76/2

Angle 2 = 38°

Sheet 4: Question 1

All angles on a straight line are equal to 180°

Angle z + 138° = 180°

Angle z = 180 - 138

Angle z = 42°

Sheet 4: Question 2

Linear pair 1: 5 and 7 (because both angles are on a straight line and are equal to 180°)

Linear pair 2: 6 and 8 (because both angles are on a straight line and are equal to 180°)

Sheet 4: Question 3

Step 1: Find the value of x

All angles on a straight line are equal to 180° or linear pairs are equal to 180°

Angle LMO + Angle OMN = 180°

7x + 20 + 10 + 5x = 180°

12x = 180 - 30

x = 150/12

x = 12.5

Step 2: Find angles using the value of x

Angle LMO: 7x + 20

7(12.5) + 20

Angle LMO = 107.5°

Angle OMN: 10 + 5x

10 + 5(12.5)

Angle OMN = 72.5°

Sheet 4: Question 4

Linear pairs are equal to 180°.

Angle 1 + Angle 2 = 180°

1/3(27x-6) + 1/2(6x-20) = 180°

Take LCM = 6

[2(27x-6) + 3(6x-20)]/6 = 180

54x - 12 + 18x - 60 = 1080

72x - 72 = 1080

72x = 1152

x = 16

!!

7 0

3 years ago