What is the slope of the graph?
Oslope = -1/3
O slope = -3
O slope = 3
O slope = 1/3

Answer:

Yes, the relation is proportional because the ratios are equivalent between each pair of values

Step-by-step explanation:

 Proportional relationships are relationships with equal ratios.

Entries in the respective columns are:

        column 1 (Minutes)              column 2 (Blocks)                 Ratios

                   6                                           3                                    1/2                

                   14                                          7                                    1/2

                   20                                         10                                  1/2

  As the ratio of Blocks and Minutes is same for every row,

   the given table represent a proportional relationship.

  hence, option c is correct.

   Yes, because the ratios are equivalent between each pair of values.

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Answer: Yes, the relation is proportional because the ratios are equivalent between each pair of values :)

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:

B is the correct answer

Step-by-Step:

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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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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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: 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

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.

Answer:

A, B and E

Step-by-step explanation:

Answer: A,B and E i did the test

Step-by-step explanation:

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

The domain and the range of an exponential parent function, that is, y = eˣ are equal to all real numbers and non-negative numbers, respectively. (Correct choice: C)

In this problem we should determine what an exponential parent function is. The most common exponential functions have the following form:

[tex]y = A\cdot e^{B\cdot x} + C[/tex]     (1)

(1) is an exponential parent function for A = 1, B = 1 and C = 0.

All functions are relations with a domain and range, the domain is an input set related to the range, that is, an output set. In the case of an exponential parent function, the domain and the range of the expression are [tex]\mathbb{R}[/tex] and y ≥ 0, respectively. (Correct choice: C)

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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]

Answer:

5,6,8,8,9,18

Step-by-step explanation:

...................

Answer:

3

Step-by-step explanation:

because I sense three and You need

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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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.

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

Answer: C

Step-by-step explanation:

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

Answer:

R

H

S

=  cos

2

x

Step-by-step explanation:

Hope this helped!

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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[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]

Answer:

11.65

Step-by-step explanation:

45 cos 75 (in degrees not radians) =

11.6468570296

jiskha

raka

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.

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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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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[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's evaluate ~

[tex]\qquad \sf  \dashrightarrow \: 2 {x}^{2} - 1[/tex]

plug in the value of x :

[tex]\qquad \sf  \dashrightarrow \: 2(3) {}^{2} - 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2(9) - 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: 18 - 1[/tex]

[tex]\qquad \sf  \dashrightarrow \: 17[/tex]

The required value is 17

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

Answer:  [tex]\textsf{Option B, 17}[/tex]

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

Given:  [tex]\textsf{2x}^2\textsf{ - 1}[/tex]

Find: [tex]\textsf{When x = 3}[/tex]

Solution: In order to find the value when x is equal to 3 we just need to equate any x to the value of 3 and simplify.

Plug in the values

Simplify the expression

Therefore, the answer that would make most sense would be option B, 17.

By the Pythagorean theorem,

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