Mr. Gaffy asked his students to pick a number, add
3 to it, multiply by 5 and then reduce it by 12.
Jermaine calls out his answer of 15. What number
did Jermaine start with?

By applying the definitions of trigonometric functions, the exact values of the sine, secant and tangent of the point on the terminal side are [tex]\sin \theta = \frac{2}{\sqrt{53}}[/tex], [tex]\sec \theta = -\frac{\sqrt{53}}{7}[/tex] and [tex]\tan \theta = -\frac{2}{7}[/tex].

In this question we need to find the exact values of three trigonometric functions associated with the terminal side of an angle. The following definitions are used:

Sine

[tex]\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex]     (1)

Secant

[tex]\sec \theta = \frac{\sqrt{x^{2}+y^{2}}}{x}[/tex]     (2)

Tangent

[tex]\tan \theta = \frac{y}{x}[/tex]     (3)

If we know that x = - 7 and y = 2, then the exact values of the three trigonometric functions:

Sine

[tex]\sin \theta = \frac{2}{\sqrt{53}}[/tex]

Secant

[tex]\sec \theta = -\frac{\sqrt{53}}{7}[/tex]

Tangent

[tex]\tan \theta = -\frac{2}{7}[/tex]

By applying the definitions of trigonometric functions, the exact values of the sine, secant and tangent of the point on the terminal side are [tex]\sin \theta = \frac{2}{\sqrt{53}}[/tex], [tex]\sec \theta = -\frac{\sqrt{53}}{7}[/tex] and [tex]\tan \theta = -\frac{2}{7}[/tex].

The statement reports typing errors, correct form is shown below:

Let (x, y) = (- 7, 2) be a point on the terminal side of θ. Find the exact value of sin θ, sec θ and tan θ.

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Let [tex]A(x_A,\ y_A),\ B(x_B,\ y_B)[/tex]. Then a slope of the line AB represent the formula:

[tex]m=\dfrac{y_B-y_A}{x_B-x_A}[/tex]

Substitute the coordinate od the points to the formula of a slope.

[tex]A.\\(4,\ 6),\ (2,\ 2)\\\\m=\dfrac{2-6}{2-4}=\dfrac{-4}{-2}\\\\\huge\boxed{m=2}[/tex]

[tex]B.\\(8,\ 8),\ (2,\ 4)\\\\m=\dfrac{4-8}{2-8}=\dfrac{-4}{-6}\\\\\huge\boxed{m=\dfrac{2}{3}}[/tex]

[tex]C.\\(8,\ 2),\ (2,\ 4)\\\\m=\dfrac{4-2}{2-8}=\dfrac{2}{-6}\\\\\huge\boxed{m=-\dfrac{1}{3}}[/tex]

[tex]D.\\(6,\ 2),\ (2,\ 4)\\\\m=\dfrac{4-2}{2-6}=\dfrac{2}{-4}\\\\\huge\boxed{m=-\dfrac{1}{2}}[/tex]

The smallest digit of the smallest number is at the thousands place.

The system of representing numbers is called Number System.

The given numbers are 6895 , 4875 , 5689

The smallest number among these is 4875

The smallest digit in this number is 4

4 is at thousands place

Therefore , The smallest digit of the smallest number is at the thousands place.

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The mole ratio of hydrogen to ammonia will be 3:2.

A depiction of a chemical reaction using elements' indicators to determine how much of each source and result is present-typically in moles.

The chemical equation is given below.

N₂ + 3H₂ = 2NH₃

Then the mole ratio of hydrogen to ammonia will be 3:2.

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C. y= |x-5|

you have the right idea, it's being shifted horizontally so the shift would be shown inside of the brackets. However, it would be |x-5| not |x+5| because the graph is shifting to the right.

Answer: B. The reflection preserves the side lengths and angles of the triangle. The dilation preserves angles but not side lengths.

Step-by-step explanation:

Reflections are congruency transformations, but dilations are similarity transformations.

Using the permutation formula, it is found that the number of ways to distribute the books is given by:

c. 8,204,716,800

The order is important, as the books are different, hence the permutation formula is used to solve this question.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 8 books are distributed among 21 children, hence the number of ways is given by:

[tex]P_{21,8} = \frac{21!}{13!} = 8,204,716,800[/tex]

Which means that option c is correct.

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Answer:

B is the correct answer

Step-by-Step:

According to the computations, this rhombus's value of x is equal to 55°.

The total of all the angles in a rhombus should be 360 ° because the opposing angles in a rhombus are always identical.

We may infer the preceding information from the rhombus's picture:

Neighboring angles= 2x+ 20 & 50°

Opposite angles=2x+ 20 & 50°

Combining the angles results in:

2x+20+50+2x+20+50=360

⇒4x+140= 360

⇒4x=360-140

⇒4x=220

⇒x=220/4

⇒x=55°

Hence, it is concluded that the value of x is (b) 55°.

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Step-by-step explanation:

just breathe and read it carefully. no need for panic. all you need is common sense, nothing fancy.

the tools and definitions to use are given in the description. we only need to use them.

the height of the point of view is 44 + 6 = 50 ft (because the eyes are again 6 ft above the top of the hill, and we are dealing with what the eyes can see).

so, the seeable distance D in miles is then

D = sqrt(2×50) = sqrt(100) = 10 miles

she will be able to see approximately 10 miles to the horizon.

By the Pythagorean theorem,

[tex]a^{2}+12^{2}=13^{2}\\\\a^{2}+144=169\\\\a^{2}=25\\ \\ a=\boxed{5}[/tex]

Answer: 2m/s

Step-by-step explanation:

The boat goes twice as fast down the river, which means it goes twice as slow up the river.

Because the river flows at 2m/s, I think the answer is 2m/s

The graph of h(x) is the graph of g vertically shifted down 5 units. Then the correct option is C.

Functions are found all across mathematics and are required for the creation of complex relationships.

The function g(x) = x² is transformed to obtain function h:

h(x) = g(x) − 5

h(x) = x² − 5

The graph h(x) get shifted downward by 5 units.

Then the correct option is C.

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The equation of the sine function will be y = -3 sin [2(x + π)] + 2. Then the correct option is A.

It is a function that repeats itself in a particular time interval.

The equation is given as

y = A sin (ωx + Ф) + C

Where A is the amplitude, ω is the frequency, Ф is the phase difference, and C is the constant.

From the graph, we have

A = -3

ω = 2

Ф = 2π

C = 2

Then we have the equation will be

y = -3 sin [2(x + π)] + 2

Then the correct option is A.

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Answer: C

Step-by-step explanation:

[tex]\sqrt{48x^{5}}=\sqrt{16x^{4}}\sqrt{3x}=\boxed{4x^{2}\sqrt{3x}}[/tex]

Answer:

x≥20

Step-by-step explanation:

-3(6-2x)≥4x+12

or, -18+6x≥4x+12

or, -18-12≥4x-6x

or, -40≥-2x

or, -40/2≥-x

or, -20≥-x

or, 20≥x

= x≥20

[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=2x^2+3x\\g(x)=x-2\\\\(f+g)(2)=2\cdot2^2+3\cdot2+2-2=8+6=14[/tex]

When Ф lies in quadrant IV the value of cos Ф lies in [0, 1].

One fourth of the part of a circle is said to be the quadrant of the circle.

Given the angle Ф lies in quadrant IV.

As we know, cos Ф is positive only in first and fourth quadrant i.e when Ф lies in 0<Ф<90 and 270<Ф<360.

cosФ range from [-1,1]

So, cos Ф is positive when Ф lies in 1st and 4th quadrant.

&  cos Ф is negative when Ф lies in 2nd and 3rd quadrant.

If cos ∅ lies in the quadrant IV, anything between [0, 1] can be the value of cos ∅.

Hence, when Ф lies in quadrant IV the value of cos Ф lies in [0, 1].

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Answer:

see explanation

Step-by-step explanation:

the domain is the set of x- coordinates from the ordered pairs , that is

domain : { - 7, - 3, 0, 5 }

the range is the set of y- coordinates from the ordered pairs, that is

range : { - 2, 1, 2, 5 }

Welming's spending is $1164.8 and his savings is $291.2

The given parameters are:

Weekly pocket = $28

Save = 20%

There are 52 weeks in a year.

So, the yearly pocket is:

Yearly pocket = $28 * 52

Evaluate

Yearly pocket = $1456

He saves 20%.

So, we have:

Savings = 20% * $1456

Evaluate

Savings = $291.2

His spending is then calculated as:

Spending = $1456 - $291.2

Evaluate

Spending = $1164.8

Hence, Welming's spending is $1164.8 and his savings is $291.2

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Answer:

y = -2x + 16

the y intercept is the y value at x = 0. On the graph there is a dot at 16 on x= 0, so the y intercept would be 16.

the only answer choice adding 16 sis y = -2x + 16

Answer: [tex]59^{\circ}[/tex]

Step-by-step explanation:

In triangle ABC, we know that [tex]\angle ABC=130^{\circ}-\theta[/tex]. So, by the inscribed angle theorem, minor arc AC is equal to [tex]260^{\circ}-2\theta[/tex].

Thus, major arc AC is equal to [tex]100^{\circ}+2\theta[/tex].

Using the fact that the angle formed by the two tangents is 38 degrees,

[tex]\frac{(100^{\circ}+2\theta)-(260^{\circ}-2\theta)}{2}=38^{\circ}\\\\100^{\circ}+2\theta-260^{\circ}+2\theta=76^{\circ}\\\\4\theta-160^{\circ}=76^{\circ}\\\\4\theta=236^{\circ}\\\\\theta=\boxed{59^{\circ}}[/tex]

The magnitude of the electric field at the point (-2, 2, 0) is 46.52 V/m

Since in a certain region of space, the potential is given by v = 2x − 5x²y 3yz²,

The electric field, E = -grad(V) where grad(V) = (dV/dx)i + (dV/dy)j + (dV/dz)k

Since V = 2x − 5x²y + 3yz²

dV/dx = d(2x − 5x²y + 3yz²)/dx

= d2x/dx - d5x²y/dx + d3yz²/dx

= 2 - 10xy + 0

= 2 - 10xy

dV/dy = d(2x − 5x²y + 3yz²)/dy

= d2x/dy - d5x²y/dy + d3yz²/dy

= 0 - 5x² + 3z²

=  - 5x² + 3z²

dV/dz = d(2x − 5x²y + 3yz²)/dz

= d2x/dz - d5x²y/dz + d3yz²/dz

= 0 - 0 + 6z

=  6z

So, E = -grad(V)

= -[(dV/dx)i + (dV/dy)j + (dV/dz)k]

= -[(2 - 10xy)i + (- 5x² + 3z²)j + (6z)k]

So, the electric field at (-2, 2, 0) is

E = -[(2 - 10xy)i + (- 5x² + 3z²)j + (6z)k]

E = -[(2 - 10(-2)(2))i + (- 5(2)² + 3(0)²)j + (6(0))k]

E = -[(2 + 40)i + (- 5(4) + 0)j + (0)k]

E = -[42i + (-20 + 0)j + (0)k]

E = -[42i - 20j + 0k]

E = -42i + 20j - 0k

So, the magnitude of E at (-2, 2, 0) is

|E| = √[(-42)² + 20² + 0²]

=  √[1764 + 400 + 0]

= √2164

= 46.52 V/m

So, the magnitude of the electric field at the point (-2, 2, 0) is 46.52 V/m

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Answer:

y=5/3x+4

Step-by-step explanation:

Slope intercept formula: y=mx+b

m=slope

b=Y-Intercept

Answer:

[tex]\sf y=\dfrac{5}{3}x+4[/tex]

Step-by-step explanation:

Given:

[tex]\textsf{slope of $\dfrac{5}{3}$, and a y-intercept of $4$}[/tex]

⇒ Slope-Intercept Form: y = mx + b

where:

Substitute the given values:

[tex]\sf\\ \implies y=mx+b\\\\\implies y=\dfrac{5}{3}x+4[/tex]

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Answer:

3

Step-by-step explanation:

because I sense three and You need

It takes 16,064 years for the 500g of radium to decay to 5g.

Here we have the decay equation:

[tex]Q(t) = Q_0*e^{-k*t}[/tex]

Where Q₀ is the initial amount, and k is the decay constant.

We know that:

Q₀ = 500g

k = 0.00043

And we want to find the value of t such that Q(t) = 5g, so we need to solve:

[tex]5 = 500*e^{-0.00043*t}\\\\5/500 = e^{-0.00043*t}\\\\0.001 = e^{-0.00043*t}[/tex]

Now we can apply the natural logarithm in both sides:

[tex]ln(0.001) = ln(e^{-0.00043*t})\\\\ln(0.001) = -0.00043*t\\\\\frac{ln(0.001)}{-0.00043} = t = 16,064.5[/tex]

So it takes 16,064 years for the 500g of radium to decay to 5g.

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The correct expression is (82/n) - 26 ,The operations include division and subtraction , To evaluate, substitute 2 for the variable in the equation , the value of the expression is 15 , Option D, E and F is the answer.

An expression is the mathematical statement consisting of variables , constant and mathematical operators .

It is given that the expression has to be formed from the data

the quotient of 82 and a number, decreased by 26

Let the number from which it is divided is n then

quotient * divisor = 82

quotient = 82 /n

(82/n) - 26 is the expression formed from the data

When n =2

the expression value is

41 -26

15

The correct expression is StartFraction 82 Over n EndFraction minus 26.

The operations include division and subtraction.

To evaluate, substitute 2 for the variable in the equation , the value of the expression is 15.

Therefore Option D, E and F is the answer.

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Answer:D.E.F

Step-by-step explanation:

Step-by-step explanation:

the picture and its text explain it actually already.

each block (or square) on each side represents a fraction.

the whole block is 1. the colored parts are the fraction of that whole (1).

we see the example 2/3 × 3/4

the left block with 2 out of 3 strips marked in pink shows us 2/3 (2/3 of the block is pink).

the right block with 3 out of 4 strips marked in purple shows us 3/4 (3/4 of the block is purple).

it is essential for this method to orient the strips in one block to be at a right angle with the strips of the other block.

now, to do the multiplication you overlay the strips of both blocks.

you see this creates a chess board pattern. the total number of little squares or rectangles is the denominator (bottom part) of the result. in this case 12.

the number of little squares or rectangles that are in both original strips is the numerator (the top part) of the result. in this case 6.

so, yes, 2/3 × 3/4 = 6/12, which can then be refined to 1/2.

now, you have to do the same thing with the actual examples (I cannot draw here, sorry) :

1/4 × 3/5 = 3/20

the left block with 4 strips (one in pink, or whatever color you want), the right block with 5 strips (and 3 marked in e.g. purple).

and then the result block with 4 columns and 5 rows creating 20 little squares or rectangles, and 3 of them are in all original strips.

and the same

3/5 × 2/3 = 6/15 = 2/5

1/2 × 2/5 = 2/10 = 1/5

Answer:

5,6,8,8,9,18

Step-by-step explanation:

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