Jeff and Jemaine go to an indoor ice skating ring. Jeff has to rent skates at $3.50 a pair while Jermaine has brought her own skates. Every hour of skating costs two dollars per person. Jeff can spend at most $10 while Jermaine can spend most $9. If they combine their money, how many hours could they skate together? Show work

In triangle ABC, when ∠A = 20°, then ∠B = 70°, ∠C = 90°. In triangle CAD, when ∠CAD = 20° and ∠CDA = 90°, ∠ACD = 70°. In triangle CBD, with ∠CBD = 90° and ∠BCD = 70°, ∠CDB = 20°.

In triangle ΔABC, ∠C is a right angle and CD is the height to AB. Considering ∠A = 20°, by the angles sum property of a triangle, ∠B = 180° - ∠A - ∠C = 180° - 20° - 90° = 70°.

Moving on to triangle ΔCAD, this is a right triangle with ∠CDA=90°. ∠CAD is given as 20° (the same as ∠A of triangle ΔABC). Therefore, ∠ACD = 180° - ∠CAD - ∠CDA= 180° - 20° - 90° = 70°.

For triangle ΔCBD, ∠CBD is 90°, and ∠BCD corresponds to ∠B of triangle ΔABC, which we've determined as 70°. Hence, ∠CDB = 180° - ∠CBD - ∠BCD = 180° - 90° - 70° = 20°.

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In triangle ΔCBD, the angles are: m∠CDB = m∠CBD = 90° and m∠BCD = 90°. In triangle ΔCAD, the angles are: m∠CDA = 70° and m∠CAD = 70°. Finally, m∠ACD = 40°.

In triangle ΔCBD, since ∠C is a right angle, ∠CBD = 90° and ∠BCD = 90°.

In triangle ΔCAD, using the fact that the sum of angles in a triangle is 180°, we can find that ∠CDA = 90° - ∠CBD = 90° - 20° = 70°.

Similarly, ∠CAD = 90° - ∠BCD = 90° - 20° = 70°.

Finally, since ∠CDA = ∠CAD, ∠ACD = 180° - ∠CDA - ∠CAD

= 180° - 70° - 70°

= 40°.

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The volume drop is 432-297= 135

135 books is a fraction 135/432 of the original volume 432. That is (x100): 31.25%

So the sales went down by 31.25%

31.25 percent of sales go down in second week as compared to first week.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, the sales volume for an online bookstore was 432 books in the first week.

Then due to the new policy of tax for on-line shopping, the sales volume dropped to 297 books at the second week.

Percentage dropped= 297/432 ×100

= 0.6875×100

= 68.75%

Now, 100-68.75=31.25%

Therefore, 31.25 percent of sales go down in second week as compared to first week.

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The graph of the tangent function approaches vertical asymptotes at x=±π/2. The inverse function will have horizontal asymptotes of y=±π/2. The only viable choice among your graphs is ...

... Graph C

_____

The graph of the inverse of a function is the function's graph with the x- and y-coordinates swapped. Essentially, the graph is reflected across the line y=x. The graph of the tangent function has a vertical aspect. Its inverse has a horizontal aspect.

30 percent

22% of 200 is 44, 44 students play football

12 of 200 is 24, 24 students play baseball

44+24=68

The teams have a total of 68 players

because 8 play both sports you subract 8

68-8=60

The answer is a tolal of 60 students play sports

I think the answer is 60

Answer:

x     6  0    3    -3  

y     0  -2   -1   -3

Step-by-step explanation:

We substitute x value in the equation and find y.

When x =0, -6y = 12 or y =-2

Likewise all pairs are found out.

Similarly put y =0:  x = 6

When x =3, 2(3)-6y =12 :y =-1

When x=-3, 2(-3)-6y=12 or y = -3

Plot these on a graph and join the line.

Graph is attached below:

a. 2x-6y=12: y = (12-2x)/6.

b. Graph the line using (0,2) and (3,0).

(a) To create a table of values for at least 4 points, we can solve the equation for y in terms of x:

y = (12 - 2x) / 6

We can then choose different values for x and plug them into the equation to find the corresponding y values.

Here is a table of values for at least 4 points:

x y

0 2

3 0

-3 4

6 -2

(b) To graph the line, we can use the two points from the table of values that are closest to each other.

In this case, we will use the points (0, 2) and (3, 0).

First, plot the two points on the coordinate plane.  

Then, use a straightedge or ruler to draw a line that passes through both points.

Here is the graph of the line 2x − 6y = 12:

For similar question on Graph the line.

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I think you need to think about the problem carefully. My guess is 1,that's my guess. sorry i couldn't give an accurate answer or you divide 300 by 5

Answer:

60

Step-by-step explanation:

the standard form of a quadratic is :  y = ax² + bx + c : (a ≠ 0 )

note that (x - 0 )² = x²

distributing by - 0.3 gives

y= - 0.3x² + 3 ← in standard form

with a = - 0.3, b = 0 and c = 3

Rewriting this symbolically, (-3/8)n = -0.1.  Let's solve for n.  To do this, multiply both sides of the equation by (-8/3).  This results in n = 8/30, or n= 4/15.

We assume the slope is a constant, so the rise is proportional to the run.

... y/(4 ft) = (31 ft)/(3 ft)

... y = (4/3)·(31 ft)

... y = 41 1/3 ft = 41 ft 4 in

Answer: [tex]\text{P(A or B)}=0.90[/tex]

[tex]\text{P(A and B)}=0.18[/tex]

Step-by-step explanation:

Given : P(A)=0.60 and P(B)=0.30

We will say A and B are independent events if :

[tex]\text{P(A or B)=P(A)+P(B)}\\\\=0.60+0.30=0.90[/tex]

[tex]\text{P(A and B)=P(A) x P(B)}\\\\=0.60\times0.30=0.18[/tex]

Thus , A and B are independent events if :

[tex]\text{P(A or B)}=0.90[/tex]

[tex]\text{P(A and B)}=0.18[/tex]

Answer: P( A and B)= 0.18

The initial pay rate is $16.00. It is also mentioned that the price is marked up by 78.7%. It means that the prices are increased by 78.7%. Also, there is a profit of 10% too. So, the pay rates after mark up will be

$16.00 + (78.7% of 16.00)

= $16.00 + $12.592

=$28.592

And the pay rates after estimated profit is

$28.592 + (10% of $28.592)

= $28.592 + $2.8592

= $31.4512

Hence, the revised bill rate, rounded to the nearest cent is $31.45.

ANSWER

[tex]y=12[/tex]

EXPLANATION

One way is to make x the subject in one equation and substitute into the other.

[tex]2x+2=y[/tex]

[tex]\Rightarrow 2x=y-2[/tex]

[tex]\Rightarrow x=\frac{y}{2}-1--(1)[/tex]

The second equation is

[tex]2y=5x-1--(2)[/tex]

Let us put equation 1 in 2

[tex]\Rightarrow 2y=5(\frac{y}{2}-1)-1[/tex]

[tex]\Rightarrow 2y=\frac{5y}{2}-5-1[/tex]

[tex]\Rightarrow 2y=\frac{5y}{2}-6[/tex]

Multiplying through by 2 gives;

[tex]\Rightarrow 4y=5y-12[/tex]

[tex]\Rightarrow 4y-5y=-12[/tex]

[tex]\Rightarrow -y=-12[/tex]

[tex]\Rightarrow y=12[/tex]

D

given the 2 equations

2x + 2 = y → (1)

2y = 5x - 1 → (2)

Substitute y = 2x + 2 into (2)

2(2x + 2) = 5x - 1

4x + 4 = 5x - 1 ( subtract 5x from both sides )

- x + 4 = = - 1 ( subtract 4 from both sides )

- x = - 5 ( multiply through by - 1 )

x = 5

substitute x = 5 into (1)

y = (2 × 5 ) + 2 = 10 + 2 = 12 → D

Answer:

y=-1

Step-by-step explanation:

The first step to solving this problem is to write it out like this-->

4x+2y=6

x-3y=5    

Next you want to eliminate the X's or the Y's, I chose to elininate the X's-->

4x+2y=6

-4(x-3y=5) [You MUST distribute the -4 to each of the numbers in the equation]

Then you get--->

4x+2y=6

-4x+12y=-20 Then you add them top to bottom--->

0x+14y=-14 [At this point you dont have to write the X]Next you solve for y-->

14y=-14 Divide both sides by 14, in order to get the y by itself-->

y=-1 And theres your answer hope it helps :D

we have the 2 equations

4x + 2y = 6 → (1)

x - 3y = 5 → (2)

multiply (2) by 4

4x - 12y = 20 → (3)

(3) - (1) to eliminate the terms in x

- 14y = 14 ( divide both sides by - 14 )

y = - 1

substitute y = - 1 into (1) and solve for x

4x - 2 = 6 ) add 2 to both sides )

4x = 8 ( divide both sides by 4 )

x = 2

solution is x = 2, y = - 1

We have to break each degree in terms of 90

A) [tex]sin180^\circ=sin(90\times2+0)[/tex]

Which is in third quadrant, therefore sine is negative hence

[tex]sin(90\times2+0)= -sin0 ^\circ = 0[/tex]

B) [tex]cos180^\circ =cos(90\times2+0)[/tex]

Which is in third quadrant, therefore cosine is negative hence

[tex]cos(90\times2+0)= -cos0^\circ = -1 [/tex]

C) [tex] tan180^\circ=tan(90\times2+0)[/tex]

Which is in third quadrant, therefore tangent is positive hence

[tex]tan(90\times2+0)= tan0^\circ = 0[/tex]

D) [tex]csc180^\circ=csc(90\times2+0)[/tex]

Which is in third quadrant, therefore cosec is negative hence

[tex]cosec(90\times2+0)= -csc0^\circ =[/tex]not defined

E)[tex]sec180^\circ=sec(90\times2+0)[/tex]

Which is in third quadrant, therefore secant is negative hence

[tex]sec(90\times2+0)= -sec0^\circ = -1 [/tex]

F) [tex] cot180^\circ=cot(90\times2+0)[/tex]

Which is in third quadrant, therefore tangent is positive hence

[tex]cot(90\times2+0)= cot0^\circ = [/tex] not defined

Hence only [tex] cos 180^\circ [/tex] and

[tex] sec180^\circ [/tex] have value -1

Hope this will help

Answer:

Cos and Sec

Step-by-step explanation:

thats the short of the guy above

I hope this might be able to help you.

Since the value of the car slowly decreases each year and each year is represented by y, the function is 24,000-1750y=f(x).

<SRQ Because if you go any other way other than its opppsite you would get a different angle.

Another way to name ∠QRS is ∠SRQ as R is the vertex of the angle.

A vertex is a common endpoint between two rays that forms an angle.

We know when an angle is represented by three letters the vertex of the angle is the middle letter.

∴ Another name ∠for QRS is ∠SRQ because here R is the vertex of the angle and we can not place R in the first or the third place as it would completely change the vertex of the angle which are not the same angles, of Ofcourse their measure can be same but they are different.

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Answer:

[tex]\boxed{F=\dfrac{9}{5}c+32}[/tex]

Step-by-step explanation:

[tex]\dfrac{5(F-32)}{9}=c\qquad\text{multiply both sides by 9}\\\\5(F-32)=9c\qquad\text{divide both sides by 5}\\\\F-32=\dfrac{9}{5}c\qquad\text{add 32 to both sides}\\\\\boxed{F=\dfrac{9}{5}c+32}[/tex]

The total amount of the purchase was ...

... $2.50 + 3c = $5.05

This equation can be solved by subtracting 2.50 and dividing by 3. Both these operations are done to both sides of the equation in accordance with the rules of equality.

... 3c = $2.55

... c = $0.85

The cost of a bag of chips was $0.85.

The cost of a bag of chips can be found by subtracting the juice price from the total cost and then dividing by the number of chip bags. This gives us an answer of $0.85 per bag.

To solve this problem, we need to subtract the cost of the juice from the total cost, then divide that answer by the total number of chip bags bought to find the cost of one bag. First, we subtract the juice price ($2.50) from the total spent ($5.05), which gives us $2.55. This is the total cost of the chips. Then, we divide that $2.55 by the number of chip bags bought (which is three) to find the cost of one bag. This can be represented by the equation: c = (total cost - juice price) / number of chip bags, or c = ($5.05 - $2.50) / 3. Calculating this, we find that c equals $0.85, so a bag of chips costs $0.85.

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12 gallons of white paint

divide 20 gallons by 5 to obtain 1 part of the ratio

[tex]\frac{20}{5}[/tex] = 4 gallons ← 1 part

white paint = 3 × 4 = 12 gallons ← 3 parts

Answer:

The edge length of the storage cube is 30 centimeters.

Step-by-step explanation:

All sides/edges of a cube has equal length.

Let's take the length of a edge as [tex]a[/tex] centimeters.

The volume a the cube = Height * Width * Length

All height, width and length are equal([tex]a[/tex] centimeters).

Now we can write the equation again as,

The volume a the cube = [tex]a*a*a[/tex]

Volume of the cube is given as 27,000 cubic centimeters.

Therefore,

[tex]a*a*a=27,000[/tex]

[tex]a=\sqrt[3]{27,000}[/tex]

[tex]a=30[/tex]

Therefore, the edge length of the storage cube is 30 centimeters.

40% of $350, 000

40% = [tex]\frac{40}{100}[/tex] = 0.4, hence

expected amount = 0.4 × $350, 000 = $140, 000

The first step in any problem is to look at what you are given. When solving systems of linear equations, it is often helpful to eliminate one or more of the variables by adding or subtracting a multiple of one equation with a multiple of another. It is convenient when at least one of the multipliers is 1.

Here, we can cancel the y-terms in the 2nd and 3rd equations simply by adding them together. This gives

... (5x +y -4z) +(-3x -y +5z) = (41) +(-45)

... 2x +z = -4 . . . . simplified

Likewise, we can add 3 times the second equation to the first to cancel y in that sum.

... 3(5x +y -4z) +(2x -3y +z) = 3(41) + (-1)

...15x +3y -12z +2x -3y +z = 123 -1

...17x -11z = 122 . . . . simplified

Now that we have 2 equations in x and z, we can go through the same process. We observe that the coefficient of z is +1 in the first equation and -11 in the second. The means we can cancel the z terms by adding 11 times the first equation to the second:

... 11(2x +z) +(17x -11z) = 11(-4) +122

...22x +17x = 78 . . . . . . simplify a little bit

... x = 78/39 = 2 . . . . . . divide by 39

From above, we find

... z = -4 -2x = -4 -2·2 = -8

... y = 41 -5x +4z = 41-5(2) +4(-8) = 41 -42 = -1

The solution is (x, y, z) = (2, -1, -8).

_____

The method of elimination used here will vary with the system of equations. If you want to employ a consistent method, you can use Cramer's Rule, Gaussian elimination, or matrix methods. Since you apparently don't mind help from technology, learning to do this on your graphing calculator can also be a good idea.

Running 2 miles at 8:15 per mile takes 16:30 minutes.

Running 3 miles at 7:12 per mile takes 21:36 minutes.

The total running time is 16:30 + 21:36 = 38:06 minutes. That length of time after 6:52 am is 7:30:06 am.

You get home for breakfast at 6 seconds past 7:30 am.

By adding the times spent on each individual run to your start time, you should arrive home at approximately 7:30 am.

To begin with, this is a question about time calculation, where you need to know exactly how to calculate time durations. First, you start running at 6:52 am. Your easy pace is 8 minutes 15 seconds, or 8.25 minutes, per mile and you do this once before and once after your tempo run. So, for 2 miles, it's 2*8.25 = 16.5 minutes.

Then you have a tempo pace at 7 minutes 12 seconds, or 7.2 minutes, per mile. You run 3 miles at tempo pace, so that's 3*7.2 = 21.6 minutes.

Adding these two results together, you have a total running time of 38.1 minutes (16.5 minutes easy pace + 21.6 minutes tempo pace). Adding this to your start time of 6:52 am gives you a rough end time of 7:30 am. Please note that this estimation rounds your running time to the nearest minute.

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Try this solution; note, this way is not the shortest one.

The solutions for the modular equation are:

[tex]x = \frac{c - b}{a}[/tex] or [tex]x = -\frac{c + b}{a}[/tex]

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

A modular equation |f(x)| = a means that:

[tex]f(x) = a[/tex] or [tex]f(x) = -a[/tex]

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

The equation given is:

[tex]|ax + b| = c[/tex]

Which means that:

[tex]ax + b = c[/tex]

[tex]ax = c - b[/tex]

[tex]x = \frac{c - b}{a}[/tex]

Or

[tex]ax + b = -c[/tex]

[tex]ax = -c - b[/tex]

[tex]ax = -(c+b)[/tex]

[tex]x = -\frac{c + b}{a}[/tex]

The solutions are [tex]x = \frac{c - b}{a}[/tex] or [tex]x = -\frac{c + b}{a}[/tex]

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The commutative property of addition lets you rearrange this to

(3/4 +5/3) - 2/3

The associative property of addition lets you regroup this to

3/4 + (5/3 -2/3)

= 3/4 + 3/3

= 1 3/4 . . . . take your pick of the final form

= 7/4

= 1.75

Answer:

70.2

Step-by-step explanation:

Multiply the weight in pounds by the conversion factor.

[tex]156\,lb\times\dfrac{0.45\,kg}{1\, lb}=70.2\,kg[/tex]

Answer:

70.2 kilograms

Step-by-step explanation:

In order to calculate this you just have to do a rule of three, where you use the equivalence of the pounds by the kilograms, in the table you see that 1 pound equals .45 kilograms, so you use that for your equivalence:

[tex]\frac{1pound}{.45kilograms}= \frac{156 pounds}{x}[/tex]

[tex]x=\frac{165*.45}{1 pound}[/tex]

[tex]x=70.2 kilos[/tex]

So we know that the patient weights 70,2 kilograms.

Answer:

f(2) = 0

Step-by-step explanation:

Plug x = 2 into the formula for f(x):-

f(2) = 2(2) - 4

= 4 - 4

= 0

f(2) = 0

substitute x = 2 into f(x)

f(2) = (2 × 2 ) - 4 = 4 - 4 = 0

x + x - 3 + 2x - 3 = 78  

4x = 84  

x = 21  

Answer: 21 Schnauzers.