Rotate the point (7,8) around the origin 90 degrees counterclockwise.

Solve the linear equation: <img src="https://tex.z-dn.net/?f=4%5E%7B2x%2B7%7D%20%3D%208%5E%7B2x-3%7D" id="TexFormula1"

g100num [7]

Answer:

x = 11.5

Step-by-step explanation:

Taking the logarithm base 2 will transform this to a linear equation.

2(2x+7) = 3(2x -3)

0 = 3(2x -3) -2(2x +7) . . . . subtract the left side

0 = 2x -23 . . . . . . . . . . . . . simplify

0 = x - 23/2 . . . . . . . . . . . . divide by 2

11.5 = x . . . . . . . . . . . . . . . . add 11.5

The solution is x = 23/2 = 11.5.

_____

Check

This value of x makes the equation become ...

4^(2·23/2 +7) = 8^(2·23/2 -3)

4^30 = 8^20 . . . . . true

8 0

3 years ago

What is the area of a circle that has a radius of 3 miles?

mojhsa [17]

A=28.27 miles Sq
A= pie r2 = pie r.3 to 2nd power = 28.27 square miles

5 0

4 years ago

Please solve this question!!

GaryK [48]

Answer: (i) 1/221 (ii) 11/221 (iii) 95/663 (iv) 1/663

Step-by-step explanation:

(i) A deck of cards contains 4 Kings out of 52 total cards

1st draw: 4 Kings out of 52 total cards → 4/52 = 1/13

2nd draw: 3 remaining Kings out of 51 total remaining cards → 3/51 = 1/17

1st Draw 2nd Draw Outcome Probability

King: P(K) = 1/13 King: P(K₂/K₁) = 1/17 King, King (1/13) x (1/17) = 1/221

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(ii) A deck of cards contains 4 Jacks, 4 Queens, & 4 Kings out of 52 total cards

1st draw: 12 Face cards out of 52 total cards → 12/52 = 3/13

2nd draw: 11 remaining Face cards out of 51 total remaining cards → 11/51

1st Draw 2nd Draw Outcome Probability

Face: P(F) = 3/13 Face: P(F₂/F₁) = 11/51 Face,Face (3/13) x (11/51) = 11/221

*************************************************************************************************

(iiI) A deck of cards contains 26 black cards out of 52 total cards but there are 2 black Jacks, 2 black Queens, and 2 black Kings.

1st draw: 20 Black (not Face) cards out of 52 total cards → 20/52 = 5/13

2nd draw: 19 remaining Black (not Face) cards out of 51 total remaining cards → 19/51

1st Draw 2nd Draw Outcome Probability

Black: P(B~) = 5/13 Black: P(B~₂/B~₁) = 19/51 B~,B~ (5/13) x (19/51) = 95/663

*************************************************************************************************

(ii) A deck of cards contains 4 Aces out of 52 total cards

1st draw: 4 Aces out of 52 total cards → 4/52 = 1/13

2nd draw: 1 Queen of Hearts out of 51 total remaining cards → 1/51

1st Draw 2nd Draw Outcome Probability

Ace: P(A) = 1/13 Qh: P(Qh₂/A₁) = 1/51 Ace,Queen(h) (1/13) x (1/51) = 1/663

7 0

4 years ago

Find the value of a in this isosceles trapezoid. D. 11 A. 7 B. 15 C. 4

UNO [17]

Answer:

B

Step-by-step explanation:

Because 15-4=11

and both angles are equal

4 0

3 years ago

What is the volume of the ones that have it and how do I find the expression

kherson [118]

Answer:

For the shape you must do 3*3*3 + 2*2*2 + 1 unit cubed, or 36 units^3

For Jessy's jewelry box, you must multiply the side lengths, 3*10*3, or 90 inches^3

7 0

3 years ago