Suppose you draw a line from the center of a clock face to the number 12. When the minute hand gets to 3 on the clock face, the line and minute hand form a 90 degree angle. What angle does the line and the minute hand make when the minute hand is on 2?

Answers

Answer 1

Answer:

The line and the minute hand make when the minute hand is on 2 make angle 60 degrees.

What is an angle?

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Given:

line is drawn from the center of the clock and face to number 12 on the clock.

When the minute hand gets to 3 on the clock face, the line and minute hand form 90 degree.

So, 1 on the clock face represent

=90/3

= 30 degrees.

If minute hand is on 2 then the angle between the line and the minute hand be

= 30*2

= 60 degrees.

Hence, the line and the minute hand make when the minute hand is on 2 make angle 60 degrees.

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Answer 2

Answer: Just divide 90 by three so whe it hits 3 its 90 then 2 is 60 degrees and the one is 30 degrees

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tickets to the fair cost $8 for children and $15 for adults on Thursday 177 people enter the fair and they collected $2053. what number of the children and what number of adults attended?

Answers

So,

Let

number of children tickets bought = c
number of adult tickets bought = a

We can now say that
c + a = 177
8c + 15a = 2053
because if you multiply c by the cost per child and a by the cost per adult, you will get the total revenue generated by all the tickets.

We now have a system of equations which can be solved by elimination (substitution).

Subtract a from both sides of the first equation.
c = 177 - a

Substitute 177 - a for c in the second equation.
8(177 - a) + 15a = 2053

Distribute.
1416 - 8a + 15a = 2053

Collect Like Terms.
1416 + 7a = 2053

Subtract 1416 from both sides.
7a = 637

Divide both sides by 7.
a = 91

Substitute 91 for a in the first modified equation.
c = 177 - 91
c = 86

Check.

The total number of people was 86 + 91 = 177 people.

The total revenue generated was 8(86) + 15(91) = 688 + 1365 = $2053.

There were 86 children and 91 adults.

Only problem 6a. Can someone demonstrate how to do this so I can do the rest solo?

Answers

as far as I can tell, is simply asking to write two more expressions, that are equivalent to the provided one, namely, grab the provided one and expand it, if you simplify the expanded version, you'd end up with the provided, for example

$\bf \boxed{6a.1}~\hfill \stackrel{changing}{\cfrac{29\cdot 3}{30\cdot 3}}\implies \stackrel{one}{\cfrac{87}{90}}~\hfill \stackrel{changing}{\cfrac{29\cdot 7}{30\cdot 7}}\implies \stackrel{t wo}{\cfrac{203}{210}}\n\n\n\boxed{6a.3}~\hfill \stackrel{ch anging}{\cfrac{15/ 3}{30/ 3}}\implies \stackrel{one}{\cfrac{5}{10}}~\hfill \stackrel{changing}{\cfrac{15/ 5}{30/ 5}}\implies \stackrel{two}{\cfrac{3}{6}}$

so let's do 6a1, 6a3 and 6a5.

$\bf \boxed{6a.1}~\hfill \stackrel{changing}{\cfrac{29\cdot 3}{30\cdot 3}}\implies \stackrel{one}{\cfrac{87}{90}}~\hfill \stackrel{changing}{\cfrac{29\cdot 7}{30\cdot 7}}\implies \stackrel{t wo}{\cfrac{203}{210}} \n\n\n \boxed{6a.3}~\hfill \stackrel{changing}{\cfrac{15/ 3}{30/ 3}}\implies \stackrel{one}{\cfrac{5}{10}}~\hfill \stackrel{changing}{\cfrac{15/ 5}{30/ 5}}\implies \stackrel{two}{\cfrac{3}{6}}$

$\bf \boxed{6a.5}~\hfill \stackrel{changing}{(9\cdot 10)/ (2\cdot 10)}\implies \stackrel{one}{90/ 20}~\hfill \stackrel{changing}{(9\cdot 70)/(2\cdot 70)}\implies \stackrel{two}{630/ 140}$

3x + 7y =47
-4x +7y =19

Answers

3x+7y=47
-1(-4x+7y=19)

Distribute the -1 and add the equations together...you'll get:

7x=28
x=4

Plug X=4 back in...
12+7y=47
7y=35
y=5

Verify the identity tan x + cot x / tan x - cot x = 1/ sin^2x - cos^2x

Answers

$(\tan x+\cot x)/(\tan x-\cot x)=(1)/(\sin^2x-\cos^2x)\n\n\text{use}\ \tan x=(\sin x)/(\cos x),\ \cot x=(\cos x)/(\sin x)\n\n\tan x+\cot x=(\sin x)/(\cos x)+(\cos x)/(\sin x)=(\sin x\cdot\sin x)/(\sin x\cos x)+(\cos x\cdot\cos x)/(\sin x\cos x)\n\n=(\sin^2x+\cos^2x)/(\sin x\cos x)\n\n\text{use}\ \sin^2x+\cos^2x=1\n\n=(1)/(\sin x\cos x)\n\n\tan x-\cot x=(\sin x)/(\cos x)-(\cos x)/(\sin x)=(\sin^2x-\cos^2x)/(\sin x\cos x)$

$L_s=(\tan x+\cot x)/(\tan x-\cot x)=((1)/(\sin x\cos x))/((\sin^2x-\cos^2x)/(\sin x\cos x))=(1)/(\sin x\cos x)\cdot(\sin x\cos x)/(\sin^2x-\cos^2x)\n\n=(1)/(\sin^2x-\cos^2x)=R_s\n\nL_s=R_s\Rightarrow The\ identity.$

A ball is thrown upward off of a 100 meter cliff with an initial velocity of 6 m/s. The function f(x)=-5x2+6x+100 (graphed below) represents this situation where x is time and y is the distance off of the ground.e. What would the new function be? What kind of transformation is this?
f. Would you still use the same domain and range? Why or why not?

Answers

Answer:

a) The domain of the function is . , , b)The range of the function is . , , c) The ball is 73 meters off of the ground at x = 3 seconds.Step-by-step explanation:The complete statement is: A ball is thrown upward off of a 100 meter cliff with an initial velocity of 6 m/s. The function represents this situation where x is time and y is the distance off of the ground. a) What domain does the function make sense? b) What range does the function make sense ? c) How far off the ground is the ball at time x = 3 seconds?a) Let and be the time, measured in seconds, and the distance of the ground, measured in meters, respectively. Time is a positive variable, so domain corresponds to the interval when and . That is: Therefore, the domain of the function is . , b) The distance off of the ground is also a positive variable, where ball is thrown upward at a height of 100 meters and hits the ground at a height of 0 meters. Hence, the range of the function is . , c) The distance of the ball off of the ground at x = 3 seconds is found by evaluating the function:The ball is 73 meters off of the ground at x = 3 seconds.

Step-by-step explanation:

Jodie bought some shirts for $6 each. Marge bought some shirts for $8 each. The girls spent the same amount of money on shirts. What is the least amount they could have spent?

Answers

$24.00 i hope this helped you

Answer:

Step-by-step explanation:

find the LCM

6,12,18,24

8,16,24

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