How many combinations with repetition are allowed if n = 7 and r = 2?
a. 21
b. 14
c. 49
d. 28​

Given:

The worlds largest flower, the Rafflesia, has a circumference of 286 centimeters.

To find:

The diameter of the flower.

Solution:

We know that, the circumference of a circle is:

[tex]C=2\pi r[/tex]

Where, r is the radius.

[tex]C=(2r)\pi [/tex]

[tex]C=d\pi [/tex]                            [tex][\because 2r=d][/tex]

Where, d is the diameter.

Putting [tex]C=286, \pi=3.14[/tex] in the above formula, we get

[tex]286=d(3.14)[/tex]

[tex]\dfrac{286}{3.14}=d[/tex]

[tex]91.0828=d[/tex]

[tex]d\approx 91.08[/tex]

Therefore, the diameter of the flower is about 91.08 centimeters.

Answer:

Step-by-step explanation:

7. <A + <B = 180° [Since Co-interior angles]

=> 51° + <B = 180°

=> <B = 180° - 51°

=> <B = 129° (Ans)

8. <M + <N = 180° [Since Co-interior angles]

=> 95° + <N = 180°

=> <N = 180° - 95°

=> <N = 85° (Ans)

here are 8 different possible outcomes in the sample space. There are 2 outcomes for the coins, heads and tails. And 4 colors for the spinner.

If you put them together, you have:

H - R

H - G

H - Y

H - O

T - T

T - G

T - Y

T - O

Answer:

1) C. 4 - 3·i

2) D. The second graph shares the same vertex, is inverted, and opens wider than the first graph

3) C. y = (x - 2)² + 3 would shift right two units

4) B. Figure B' is congruent but not similar to figure B

5) A. m∠k' = m∠k

Step-by-step explanation:

1) Given that the real part of the complex number = 4

The imaginary of the complex number = -3

The general form of representing complex numbers is z = a + b·i, we have;

The binomial equivalent to the complex number is z = 4 - 3·i

2) The first graph equation is y = 2·x²

When x = 1, y = 2 and when x = 2, y = 8

The vertex = (h, k)

Where;

h = -b/(2.a) and b = 0, a = 2

∴ h = 0/(2 × 2) = 0

h = 0

k = f(h) = f(0) = 2 × 0² = 0

k = 0

The vertex, (h, k) = (0, 0)

The coefficient, 'a' is positive, therefore, the graph opens down

The second function, y = -(1/2)·x² also has a vertex (h, k) = (0, 0)

The coefficient, 'a' is positive, therefore, the graph opens up

When x = 1, y = -1/2 and when x = 2, y = -2

Therefore, the second function is wider

Therefore;

The second graph shares the same vertex, is inverted, and opens wider than the first graph

3) The given functions are;

First function; y = x² + 3 and second function; y = (x - 2)² + 3

First function;

When x = 1, y = x² + 3 = 1 + 3 = 4

∴ When x = 1, y = 4

Second function;

When y = 4, y = 4 = (x - 2)² + 3

√(1) = x - 2

x = 3

∴ When x = 3, y = 4

First function;

When x = 2, y = x² + 3 = 4 + 3 = 7

∴ When x = 2, y = 7

Second function;

When y = 7, y = 7 = (x - 2)² + 3

√4 = 2 = (x - 2)

x = 2 + 2 = 4

x = 4

∴ When x = 4, y = 7

Therefore, the second function, y = (x - 2)² + 3, has the x-value shifted 2 units to the right for a given value of 'y'

4) The lengths of the sides of figure B are 3 by 4, the lengths of the sides of figure B' 4.5 by 6

The ratio of the corresponding length and width of figures B and B' are;

3/4.5 = 4/6

Therefore, figure B' is similar but not congruent to figure B

5) A rotation and a reflection are rigid transformations and therefore, the dimensions and measure of the original figure and the image are the same;

∴ m∠k' = m∠k.

Answer:

41

Step-by-step explanation:

A pair of consecutive numbers is written as: N and N + 1

(where the larger page number is N + 1)

And we know that the product of these numbers is 1640.

Then:

(N)*(N + 1) = 1640

Solving for N, we get:

N^2 + N = 1640

N^2 + N - 1640 = 0

This is a quadratic equation, remember that for a general quadratic equation:

a*x^2 + b*x + c = 0

The solutions are:

[tex]x = \frac{-b\pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]

In our case, the solutions are:

[tex]N = \frac{-1 \pm \sqrt{(1)^2 - 4*1*(-1640)} }{2} = \frac{1 \pm 81}{2}[/tex]

Then the two solutions are:

N = (-1 + 81)/2 = 40

N = (-1 - 81)/2 = -41

Because N represents the number on a page, it only can be a positive value, then we take the positive solution.

Then the two consecutive numbers, N and N + 1

are:

N = 40

N + 1 = 41

The value of the larger page number is 41.

42.57 x 46630= 75769 =3794874 =37489438790=3474936

Answer:

Answer:

I think after 1.6 s it Will catch the dog

Given:

[tex]\text{cosec}\theta -\cot \theta =\dfrac{1}{M}[/tex]

To find:

The value of [tex]\text{cosec}\theta +\cot \theta [/tex].

Solution:

We have,

[tex]\text{cosec}\theta -\cot \theta =\dfrac{1}{M}[/tex]

We know that,

[tex]\text{cosec}^2\theta -\cot^2 \theta=1[/tex]

It can be written as:

[tex](\text{cosec}\theta -\cot \theta)(\text{cosec}\theta +\cot \theta)=1[/tex]

[tex]\dfrac{1}{M}\times (\text{cosec}\theta +\cot \theta)=1[/tex]

[tex]\text{cosec}\theta +\cot \theta=1\times M[/tex]

[tex]\text{cosec}\theta +\cot \theta=M[/tex]

Therefore, the value of [tex]\text{cosec}\theta +\cot \theta [/tex] is [tex]M[/tex].

Answer:

tell whether the number 13 is prime or composite

You need 2 half-teaspoons, since

1/2 tsp + 1/2 tsp = (1 + 1)/2 tsp = 2/2 tsp = 1 tsp

Answer:

x = 5

Step-by-step explanation:

Simplify the like terms:

15x - 8x = 7x

so, 7x = 35

divide: 35/7 = 5

x=5

Answer:

19,683

Step-by-step explanation:

Answer:

4 multiplied by 1. 3/4

Step-by-step explanation:

4 x 7/4 _____answer 7

Answer:

J: (-3,1) K: (4,2) L: (3,-4)

Step-by-step explanation:

Answer:

y = - [tex]\frac{7}{4}[/tex] x + 5

Step-by-step explanation:

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{7}{4}[/tex] and c = 5 , then

y = - [tex]\frac{7}{4}[/tex] x + 5 ← equation of line

Answer:

13/3

Step-by-step explanation:

Try it

Answer:

52

Step-by-step explanation:

1) 7x + 6(3x-8)

2) 7(4) + 6(3(4)-8)

3) 28 + 6(12-8)

4) 28 + 6(4)

5) 28 + 24

6) 52

Answer:

148.49

Step-by-step explanation:

105 x √2 = 148.49

have a great day

Answer:

42.71

Step-by-step explanation:

268.26-12.00=256.26 total owed

256.26/6 payments =42.71

Answer:

x = 9

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 6) and (x₂, y₂ ) = (x, - 5 )

m = [tex]\frac{-5-6}{x-2}[/tex] = [tex]\frac{-11}{x-2}[/tex] , then

[tex]\frac{-11}{x-2}[/tex] = - [tex]\frac{11}{7}[/tex] ← numerators are equal, so equate the denominators

x - 2 = 7 ( add 2 to both sides )

x = 9

The distributive property indicates that multiplying a number by the sum of two addends is equal to multiplying each addend individually by the number and then adding the products together.

In general terms:

‎      ‏‏‎

In this exercise:

Let's apply the distributive property:

[tex]\mathsf{2(3w - 5y)}[/tex]

[tex]= \mathsf{2(3w) - 2(5y)}[/tex]

[tex]= \boxed{\mathsf{6w - 10y}}[/tex]

‎      ‏‏‎

‎      ‏‏‎

Answer:

x=7

Step-by-step explanation:

8x-5y=16

8x-40=16

8x=56

x=7

Answer:

Step-by-step explanation:

hello :

put x = -5 in this equation : a(4-x) =-3x + b

a(4+5) =15 + b

9a = 15 +b

b = 9a - 15

the values of a and b is all order  pair :   ( a  ; 9a-15)  a real number

Answer:

#7

Ratio of corresponding sides (determined by opposite angles)

The ratios are equal, the polygons are similar

# no number

Ratios:

Yes, similar

# 8

The triangles are isosceles.

The ratios of bases and sides:

B. ABC ~ MNO, SSS

Answer:

Below.

Step-by-step explanation:

You need to know the volume or total surface area of the prism and 2 of the dimensions.

The formula for the volume = wlh   where w = width , l = length and h = height.

So knowing say w = 4, l = 8 and V =  192 we have:

V = wlh

192 = 4 * 8 * h

h = 192/4*8

= 192/32

= 6.

Answer:

Michaela scored 140/5 = 28 points; Aleah scored 140/10 = 14 points.

Step-by-step explanation: