What is the length of line
segment AB?

Answer:

f(x)= 1/4

(4)

x

for x=1→f(1)=

4

1

⋅4

1

=1→(1; 1)

for x=2→f(2)=

4

1

⋅4

2

=

4

1

⋅16=4→(2; 4)

Answer: The graph nr 4.

Other method:

f(x)=\dfrac{1}{4}\cdot4^x=4^{-1}\cdot4^x=4^{x-1}f(x)=

4

1

⋅4

x

=4

−1

⋅4

x

=4

x−1

Used:

\begin{gathered}a^{-1}=\dfrac{1}{a}\\\\a^n\cdot a^m=a^{n\cdot m}\end{gathered}

a

−1

=

a

1

a

n

⋅a

m

=a

n⋅m

Draw the graph of y = 4^x and next shift it 1 unit right.

Answer:

For the first circle: x=40°

For the second circle: x=94°

Step-by-step explanation:

First circle:

Second circle:

Answer:

1. The center is (-5, 6)

The radius is 11

2. The center is (3, -9)

The radius is 6

3. The center of the circle is (-4, -2)

The radius is 3

4. The coordinate of the center of the circle is (2, 2)

The radius of the circle is 4

5. The equation of the circle is (x - 4)² + (y + 3)² = 2²

6. The equation of the circle is (x + 1)² + (x - 10)² = 7²

7. The given point (6, 8) does not lie on the circumference of the circle

8. Yes, the point (√17, 4) lies on the circumference of the circle

9. Please find the attached graph created with the aid of MS Excel

10 Please find the attached graph created with the aid of MS Excel

11. The equation of the circle is (x - a)² + (y - b)² = c²

12. The equation of the circle is x² + y² = 1

Step-by-step explanation:

1. The equation of the circle is (x + 5)² + (y - 6)² = 121

The standard form of the equation of a circle is (x - h)² + (y - k)² = r²

Where;

The center of the circle = (h, k)

The radius of the circle = r

By comparison we have;

h = -5, k = 6, and r = √121 = 11

The center of the circle, (h, k) = (-5, 6)

The radius of the circle, r = 11

2. (x - 3)² + (x + 9)² = 36

Similar to question 1, above, we have by comparison;

h = 3, k = -9, r = √36 = 6

The center of the circle, (h, k) = (3, -9)

The radius of the circle, r = 6

3. From the graph of the circle on the coordinate plane, we have;

The center of the circle = (-4, -2)

The radius of the circle =  -1 - (-4) = 3

4. From the graph of the locus of the circle, we have;

The coordinate of the center of the circle, r = (2, 2)

The length of the radius of the circle = The distance from the center  to the point (-2, 2)

Therefore, the radius of the circle, r = 2 - (-2) = 4

5. The given radius of the circle, r = 2

The center of the circle, (h, k) = (4, -3)

The equation of a circle in standard form is  (x - h)² + (y - k)² = r²

By comparison, we have the equation of the circle given as follows;

(x - 4)² + (y - (-3))² =  (x - 4)² + (y + 3)² = 2²

The equation of the circle is (x - 4)² + (y + 3)² = 2²

6. The given radius of the circle, r = 7

The center of the circle, (h, k) = (-1, 10)

The equation of a circle in standard form is  (x - h)² + (y - k)² = r²

By comparison, we have the equation of the circle given as follows;

(x - (-1))² + (y - 10)² = (x + 1)² + (y - 10)² = 7²

The equation of the circle is (x + 1)² + (x - 10)² = 7²

7. The given point = (6, 8)

The radius, r = 4

The center of the circle = (3, 5)

The point lies on the circle if the distance. 'd', from the point to the center of the circle = The radius of the circle

∴ d = √((6 - 3)² + (8 - 5)²) = √((3² + 3²) = √(18) = 3·√2

Given that the distance from the point to the center of the circle, d = 3·√2 ≠ 4 = r, the point (6, 8), does not lie on the circumference of the circle

8. The point = (√17, 4)

Radius, r: 9

The center: (0, -4)

The distance from the point to the center of the circle, d = √((√17 - 0)² + (4 - (-4))²) = 9 = r, the radius of the circle

Therefore, given that the distance of the point from the center of the circle = The radius of the circle, the point, (√17, 4), lies on the circumference of the circle

9. The given equation of the circle is (x - 5)² + (y - 1)² = 49

Comparing with the equation of a circle in standard form, we have;

The center of the circle, (h, k) = (5, 1)

The radius of the circle, r = √49 = 7

Please find the attached graph created with the aid of MS Excel

10. The given equation of the circle is x² + (y - 3)² = 25

The center of the circle, (h, k) = (0, 3)

The radius of the circle, r = √25 = 5

Please find the attached graph created with the aid of MS Excel

11. Given that the center of the circle is (a, b) and the radius of the circle is c, the equation of a circle in standard form, (x - h)² + (y - k)² = r², becomes;

(h, k) = (a, b)

r = c

∴ (x - a)² + (y - b)² = c²

12. The diameter of the circle, d = 2 in.

The center of the circle = The origin with coordinates, (0, 0)

Therefore;

The radius of the circle. r = d/2 = 2 in./2 = 1 in.

The center of the circle, (h, k) = (0, 0)

The equation of the circle is therefore;

(x - 0)² + (y - 0)² = 1²

Which gives the equation of the circle as x² + y² = 1.

Answer:

97.12°

Step-by-step explanation:

the value of the highlight angle =

tan~¹ 1/3 + tan~¹ 5/1 =

18.43° + 78.69° = 97.12°

Answer:

B, E, F

Step-by-step explanation:

Answer:

B, F

Step-by-step explanation:

A is false; the slope of function Z is 1/4 and the slope of function W is 1/2. 1/2 is greater than 1/4.

B is true. The slope of function Z is less then the slope of function W.

C is false, the y-intercept of function Z is -2 and the y-intercept of function W is -1. They are not the same number.

D is false, the y-intercept of function W is greater than Function Z.

E is false, -3 and -3 are equal

Function W:

y = 1/2x - 1

y = 1/2(-4) - 1

y = -4/2 = -2

y = -2 - 1

y = -3

Function Z:

y = 1/4x - 2

y = 1/4(-4) - 2

y = -1 - 2

y = -3

F is true, if y = -4 for functions W and, they would both be equal.

Answer:

You can't find the probibilty of the event because it doesn't exist

Step-by-step explanation:

Answer:

A) (3, 6)

B) (2, 3)

C) (4, 2)

D) (6, 0)

Answer:

AD & BE

Step-by-step explanation:

1) AB+BD = AD

2)BC+CE = BE

Answer:

$986.84

Step-by-step explanation:

exchange rate is the rate at which one currency is exchanged for another currency

Amount of dollars bought = amount of RS / selling rate

75,000 / 76 = $986.84

Answer:

length = 15 feet.

Step-by-step explanation:

This paper is 15 feet across on any side. Who will deliver this monster?

Area = s^2 where s is the length of 1 side.

Area = 225 feet^2  (You sure this isn't inches).

s^2 = area

s^2 = 225        Take the square root of both sides of the equation.

sqrt(s^2) = sqrt(225)

s = 15

Answer:

c=3

Step-by-step explanation:

8=-5(-1)^2-10(-1)+c

8=5+c

c=3

Answer:

-1

Step-by-step explanation:

in negative numbers, it goes the opposite of positive numbers

Answer:

ab^2-(a-c)b-c

ab^2-ab+bc-c

ab(b-1)+c(b-1)

(b-1)(ab+c)

Answer:

Step-by-step explanation:

The ratio of boys is 4/11

You need a number that is divisible by 11.

11 represents the number of students in the class. That was obtained by adding 4 and 7 together. So there are 4/11 boys and 7/11 girls.

You could try 33 which is between 24 and 40

4/11 * 33 = 12

There are twelve boys in the class.

7/11 * 33 = 21

There are 21 girls in the class.

21 + 12 = 33 which is exactly what you need.

15

Answer:

Solution given;

m = -7/2 , T(13, 2), W(_x, -5)

m=(y2-y1)/(x2-x1)

-7/2=(-5-2)/(x-13)

-7/2=-7/(x-13)

doing crisscrossed multiplication

x-13=2

x=2+13

x=15

Answer:

the answer is 15

Step-by-step explanation:

correct me if I'm wrong thanks

Answer:

C is correct

Step-by-step explanation:

Just add the exponents leaving you with 2 squared which is 4

Answer:

[tex]a^b*a^c=a^{b+c}[/tex]

-----------------------

hope it helps...

have a great day!!

Answer:

D. -3,-2

Step-by-step explanation:

Let [tex]x^{2} +5x+6=0=(x+2)(x+3)\\[/tex], then  [tex]x+2=0[/tex] or [tex]x+3=0[/tex], thus [tex]x=-2[/tex] or [tex]x=-3[/tex]

Answer:

12.05

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√(2 - 1)² + [4 - (-8)]²

√(1)² + (12)²

√(1) + (144)

√145

12.05

Answer:

Step-by-step explanation:

Answer:

29.6925

Step-by-step explanation:

Answer:

1 dozen=12. 84/12=7. You answer SHOULD be 7:1 but I haven't done ratios in a while so don't quote me on it.

Step-by-step explanation:

Answer:

v = 12cm³

Step-by-step explanation:

v = lwh

v= 6 * 2 * 1

v = 12cm³

Answer:

its 9?

Step-by-step explanation:

Answer:

[tex]A=60m^2[/tex]

Step-by-step explanation:

formula for area of a parallelogram is [tex]A=bh[/tex] where [tex]b[/tex] stands for base and [tex]h[/tex] stands for height.

[tex]A=12(5)[/tex]

[tex]A=60[/tex]

Answer:

[tex]Max\ Area = \frac{x^2}{16}[/tex]

Step-by-step explanation:

Given

[tex]P = x[/tex] ---- the perimeter of fencing

Required

The maximum area

Let

[tex]L \to Length[/tex]

[tex]W \to Width[/tex]

So, we have:

[tex]P = 2(L + W)[/tex]

This gives:

[tex]2(L + W) = x[/tex]

Divide by 2

[tex]L + W = \frac{x}{2}[/tex]

Make L the subject

[tex]L = \frac{x}{2} - W[/tex]

The area (A) of the fence is:

[tex]A = L * W[/tex]

Substitute [tex]L = \frac{x}{2} - W[/tex]

[tex]A = (\frac{x}{2} - W) * W[/tex]

Open bracket

[tex]A = \frac{x}{2}W - W^2[/tex]

Differentiate with respect to W

[tex]A' = \frac{x}{2} - 2W[/tex]

Set to 0

[tex]\frac{x}{2} - 2W = 0[/tex]

Solve for 2W

[tex]2W = \frac{x}{2}[/tex]

Solve for W

[tex]W = \frac{x}{4}[/tex]

Recall that:

[tex]L = \frac{x}{2} - W[/tex]

[tex]L = \frac{x}{2} - \frac{x}{4}[/tex]

[tex]L = \frac{2x- x}{4}[/tex]

[tex]L = \frac{x}{4}[/tex]

So, the maximum area is:

[tex]A = L * W[/tex]

[tex]A = \frac{x}{4}*\frac{x}{4}[/tex]

[tex]Max\ Area = \frac{x^2}{16}[/tex]