A student claims that tan^2 0+1 = sec^2 0 can be converted to sin^2 0 + cos^2 0 = 1. which sequence of steps supports this claim?

Answer:

9/8 cans of paint

Step-by-step explanation:

if the furniture maker used the same amount of paint for each chair ,

we have to divide 9/4 by two to get the answer

(9/4)/(2/1) = (9*1)/(4*2) = 9/8

=> 9/8

hope this helps :)

Answer:

9/8 is the answer.

Answer:

[tex]r = \dfrac{p}{2 + \pi}[/tex]

Step-by-step explanation:

[tex]~~~~~p = 2r +\pi r\\\\\implies p = r(2 + \pi)\\\\\implies r = \dfrac{p}{2 + \pi}[/tex]

Answer:

Step-by-step explanation:

2(6²)-3(6)+2=y

(2x36)-18+2=y

72-18+2=y

y=52 BODMAS

It may also be 56 tho im not sure if thats right

Put x in Equation

The range of salary is (a) the range of salaries is from $38,500 to $39,800.

The given parameters are:

Average salary = 39,800

Vary = Less than $1300

Let the salary be x.

So, we have:

x = 39,800

When the salary varies, the equation becomes

x = 39800 - 1300

Evaluate

x = 38500

This means that the salary is from 38500 to 39800

Hence, the range of salary is (a) the range of salaries is from $38,500 to $39,800.

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Answer:

1. Triangle 2. Pentagon 3. Hexagon 4. Parallelogram

Step-by-step explanation:

Step-by-step explanation:

A = (1, 3)

B = (3, 6)

C = (9, 2)

D = (7, -1)

the distance between 2 points is given by the Pythagoras equation based on the coordinate differences as legs of virtual right-angled triangles.

AD for example we get from

AD² = (7-1)² + (-1 - 3)² = 6² + (-4)² = 36 + 16 = 52

AD = sqrt(52) = sqrt(4×13) = 2×sqrt(13)

and AB we get from

AB² = (3-1)² + (6-3)² = 2² + 3² = 4 + 9 = 13

AB = sqrt(13)

the perimeter of the given rectangle is

2×sqrt(52) + 2×sqrt(13) = 2×2×sqrt(13) + 2×sqrt(13) =

= 6×sqrt(13) = 21.63330765...

and the area of the rectangle is

2×sqrt(13)×sqrt(13) = 2×13 = 26

Answer: 25

Step-by-step explanation:

[tex]\frac{23+27}{2}=\boxed{25}[/tex]

Answer:

6/11*5/10 = 3/11

Step-by-step explanation:

first we can get 6/11 which is the probability.

then we minus both sides by 1 to get 5/10

then we times them

Using it's concept, it is found that the probability that the first student chosen is a senior and the second student chosen is a sophomore is given by:

[tex]p = \frac{11}{320}[/tex]

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching this problem on the internet, we have that there are:

31 juniors, 10 sophomores, 17 juniors, 22 seniors.

Then:

The events are independent, hence the probability of both is given by:

[tex]p = p_1p_2 = \frac{11}{40} \times \frac{1}{8} = \frac{11}{320}[/tex]

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Answer:.2

Step-by-step explanation:.4/(.4+.3+.6+.7)

To calculate the cost of the fence, we have to find the length of the semi-circle. The cost of fencing the garden would be $328.52 approximately

To find the length of the fence, we have to calculate the circumference of the semi-circle and divide it by 2

[tex]C = 2\pi r\\l = \frac{c}{2} \\l = \pi r[/tex]

Data;

Let's substitute the values and calculate the length of the fence.

[tex]l = \pi r\\l = 3.14 * 13.5\\l = 42.39ft[/tex]

The length of the fence is equal to 42.39ft

The cost of fencing would be

[tex]42.39 * 7.75 = $328.5225[/tex]

The cost of fencing the garden would be $328.52 approximately

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= 17.50 or 25%

Answer:

43.43 degrees

Step-by-step explanation:

This is a right triangle with the opposite LEG = 11 km and the hypotenuse = 16 km

sin (angle) = opposite/hypotenuse

                 = 11/16

arc sin (11/16) = angle = 43.43 degrees

Answer:

it is an identity that was solved

Step-by-step explanation:

cosin - the a

Answer:

The "what" is 100

Step-by-step explanation:

Rewrite this as 37.6y = 3760 and set out to determine y:

y = 3760/37.6  = 100

The "what" is 100

Answer:

1/2

Step-by-step explanation:

13 total fish

remove one fish

12 total fish

6 total clown fish

6/12 simplified is 1/2

Using translation concepts, it is found that graph 3 represents the function [tex]f(x) = \sqrt{x} + 1[/tex].

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the function is:

[tex]f(x) = \sqrt{x} + 1[/tex]

Which is a shift up of one unit of [tex]\sqrt{x}[/tex]. The square root function has y-intercept at (0,0), hence the translated function will have y-intercept at (0,1). Additionally, [tex]\sqrt{4} = 2[/tex], since f(4) = 3, which means that graph 3 is represents the function.

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Answer:

1

Step-by-step explanation:

let x be the number to be added to 5 and 3

expressing the ratios in fractional form

[tex]\frac{5+x}{3+x}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )

3(3 + x) = 2(5 + x) ← distribute parenthesis on both sides

9 + 3x = 10 + 2x ( subtract 2x from both sides )

9 + x = 10 ( subtract 9 from both sides )

x = 1

then the number to be added to both is 1

Answer:

Does not lie

Step-by-step explanation:

The equation of the circle is

[tex] {(x + 7)}^{2} + {(y - 4)}^{2} = 25[/tex]

If we substitute x=-11, and y=2, we get that:

[tex] {( - 11 + 7)}^{2} + {(2 - 4)}^{2} = 25 \\ {4}^{2} + {2}^{2} = 25 \\ 20 = 25[/tex]

Which is false, meaning it does not lie on the circle

The probability that a player will be asked a math question and then a music question is 0.03125

The size of the sections are given as:

Music = 0.5

Sport = 0.5

Others = 1

So, the total size is:

Total = 0.5 + 0.5 + 1 + 1 + 1

Evaluate

Total = 4

The probability of asking a math question is:

P(Math) = 1/4 = 0.25

The probability of asking a music question is:

P(Music) = 0.5/4 = 0.125

The required probability is:

P(Math and Music) = P(Math) * P(Music)

This gives

P(Math and Music) = 0.25 * 0.125

Evaluate

P(Math and Music) = 0.03125

Hence, the probability that a player will be asked a math question and then a music question is 0.03125

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Answer:

x=0 y=0

x=1 y=5

x=2 y=8

x=3 y=9

x=4 y=8

x=5 y=5

x=6 y=0

Step-by-step explanation:

71% subtracted from 100% is 29%

Add or subtract the given percent from 100%.

71%

The percentage (p) is given as:

p = 71%

When subtracted from 100%, we have:

100% - p

Substitute p = 71%

100% - 71%

71 subtracted from 100 is 29.

So, we have:

100% - 71% = 29%

Hence, 71% subtracted from 100% is 29%

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Answer:

-13/20

Step-by-step explanation:

-0.65=-65/100

=13/20

Answer:

Quadrant 4

Answer is D........

Answer:

[tex]y=-5x-8[/tex]

Step-by-step explanation:

Given the following question:

To calculate the slope intercept of a line/point we need to use the formula for slope intercept, substitute, and solve for b.

Formula for slope intercept:
[tex]y=mx+b[/tex]
[tex]m=-5[/tex]
[tex]y=2[/tex]
[tex]x=-2[/tex]
[tex]2=-5(-2)+b[/tex]

Solve for b:
[tex]2=-5(-2)+b[/tex]
[tex]-5(-2)=10[/tex]
[tex]2=10+b[/tex]
[tex]10-10=0[/tex]
[tex]2-10=-8[/tex]
[tex]-8=b[/tex]
[tex]b=-8[/tex]

Substitute for the following:
[tex]y=mx+b[/tex]
[tex]b=-8[/tex]
[tex]m=-5[/tex]
[tex]y=-5x-8[/tex]

Your answer is "y = -5x - 8."

Hope this helps.

Answer:

area of a triangle =1/2 x b x h

which is half base x hieght

Answer:

y<_0

Step-by-step explanation:

The last answer.
Hope this helps! Have a great day :)

Let A(t) denote the amount of salt (in ounces, oz) in the tank at time t (in minutes, min).

Salt flows in at a rate of

[tex]\dfrac{dA}{dt}_{\rm in} = \left(17 (1 + 15 \sin(t)) \dfrac{\rm oz}{\rm gal}\right) \left(8\dfrac{\rm gal}{\rm min}\right) = 136 (1 + 15 \sin(t)) \dfrac{\rm oz}{\min}[/tex]

and flows out at a rate of

[tex]\dfrac{dA}{dt}_{\rm out} = \left(\dfrac{A(t) \, \mathrm{oz}}{180 \,\mathrm{gal} + \left(8\frac{\rm gal}{\rm min} - 8\frac{\rm gal}{\rm min}\right) (t \, \mathrm{min})}\right) \left(8 \dfrac{\rm gal}{\rm min}\right) = \dfrac{A(t)}{180} \dfrac{\rm oz}{\rm min}[/tex]

so that the net rate of change in the amount of salt in the tank is given by the linear differential equation

[tex]\dfrac{dA}{dt} = \dfrac{dA}{dt}_{\rm in} - \dfrac{dA}{dt}_{\rm out} \iff \dfrac{dA}{dt} + \dfrac{A(t)}{180} = 136 (1 + 15 \sin(t))[/tex]

Multiply both sides by the integrating factor, [tex]e^{t/180}[/tex], and rewrite the left side as the derivative of a product.

[tex]e^{t/180} \dfrac{dA}{dt} + e^{t/180} \dfrac{A(t)}{180} = 136 e^{t/180} (1 + 15 \sin(t))[/tex]

[tex]\dfrac d{dt}\left[e^{t/180} A(t)\right] = 136 e^{t/180} (1 + 15 \sin(t))[/tex]

Integrate both sides with respect to t (integrate the right side by parts):

[tex]\displaystyle \int \frac d{dt}\left[e^{t/180} A(t)\right] \, dt = 136 \int e^{t/180} (1 + 15 \sin(t)) \, dt[/tex]

[tex]\displaystyle e^{t/180} A(t) = \left(24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t)\right) e^{t/180} + C[/tex]

Solve for A(t) :

[tex]\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) + C e^{-t/180}[/tex]

The tank starts with A(0) = 15 oz of salt; use this to solve for the constant C.

[tex]\displaystyle 15 = 24,480 - \frac{66,096,000}{32,401} + C \implies C = -\dfrac{726,594,465}{32,401}[/tex]

So,

[tex]\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) - \frac{726,594,465}{32,401} e^{-t/180}[/tex]

Recall the angle-sum identity for cosine:

[tex]R \cos(x-\theta) = R \cos(\theta) \cos(x) + R \sin(\theta) \sin(x)[/tex]

so that we can condense the trigonometric terms in A(t). Solve for R and θ :

[tex]R \cos(\theta) = -\dfrac{66,096,000}{32,401}[/tex]

[tex]R \sin(\theta) = \dfrac{367,200}{32,401}[/tex]

Recall the Pythagorean identity and definition of tangent,

[tex]\cos^2(x) + \sin^2(x) = 1[/tex]

[tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]

Then

[tex]R^2 \cos^2(\theta) + R^2 \sin^2(\theta) = R^2 = \dfrac{134,835,840,000}{32,401} \implies R = \dfrac{367,200}{\sqrt{32,401}}[/tex]

and

[tex]\dfrac{R \sin(\theta)}{R \cos(\theta)} = \tan(\theta) = -\dfrac{367,200}{66,096,000} = -\dfrac1{180} \\\\ \implies \theta = -\tan^{-1}\left(\dfrac1{180}\right) = -\cot^{-1}(180)[/tex]

so we can rewrite A(t) as

[tex]\displaystyle A(t) = 24,480 + \frac{367,200}{\sqrt{32,401}} \cos\left(t + \cot^{-1}(180)\right) - \frac{726,594,465}{32,401} e^{-t/180}[/tex]

As t goes to infinity, the exponential term will converge to zero. Meanwhile the cosine term will oscillate between -1 and 1, so that A(t) will oscillate about the constant level of 24,480 oz between the extreme values of

[tex]24,480 - \dfrac{267,200}{\sqrt{32,401}} \approx 22,995.6 \,\mathrm{oz}[/tex]

and

[tex]24,480 + \dfrac{267,200}{\sqrt{32,401}} \approx 25,964.4 \,\mathrm{oz}[/tex]

which is to say, with amplitude

[tex]2 \times \dfrac{267,200}{\sqrt{32,401}} \approx \mathbf{2,968.84 \,oz}[/tex]