A math class is having a discussion on how to determine if the expressions 4 x minus x + 5 and 8 minus 3 x minus 3 are equivalent. The class has suggested four different methods.

PLEASE HURRY:Which describes the correct method?
Both expressions should be evaluated by substituting one value for x. If the final values of the expressions are both positive after the substitution, then the two expressions must be equivalent.
Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent.
Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are positive, then the two expressions must be equivalent.
Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.

Step-by-step explanation:

in a number like 125,734,016

the right most position has the weight 10⁰ = 1

so, 6×1 = 6.

the second right most position has the weight 10¹ = 10.

so, 1×10 = 10

the third right most position has the weight 10² = 100.

so, 0×100 = 0

the 4th right most position has the weight 10³ = 1000.

so, 4×1000 = 4,000

the 5th right most position has the weight 10⁴ = 10000.

so, 3×10000 = 30,000

the 6th right most position has the weight 10⁵ = 100000.

so, 7×100000 = 700,000

the 7th right most position has the weight 10⁶ = 1000000.

so, 5×1000000 = 5,000,000

the 8th right most position has the weight 10⁷ = 10000000

so, 2×10000000 = 20,000,000

and so on.

as we can see, the 2 (the 8th most position from the right or the second position from the left) has the value of 20,000,000.

See below for the solution to each question

Yes, the graph is a function.

This is because all x values have different y values

This is the set of input values of the graph.

From the graph, we have

x = 0 to x = 17

Hence, the domain is [0, 17]

This is the set of output values of the graph.

From the graph, we have

y = 0 to y = 10

Hence, the range is [0, 10]

This is the maximum point on the graph.

From the graph, we have

Maximum = (12, 10)

This is the minimum point on the graph.

From the graph, we have

Minimum = (0, 0)

These are the intervals where the y values increase as x increase.

From the graph, we have

Increasing intervals = (0, 5) ∪ (10, 12) ∪ (14, 15)

These are the intervals where the y values decrease as x increase.

From the graph, we have

Decreasing intervals = (7, 10) ∪ (12, 14) ∪ (15, 17)

These are the intervals where the y values remain unchanged as x changes.

From the graph, we have

Constant intervals = (5, 7)

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The purchase price of the new car if the sales tax is $3500 is $50000

Let the amount of sales tax be A and the purchase price be p

If the amount of sales tax is directly proportional to the purchase price, this is expressed as:

S = kp

If S = $1750 and p = $25000, the;

k = S/p

k = 1750/25000

k = 175/2500

If the sales tax is $3500, the purchase price will be given as:

S = kp
3500 = 175/2500 p

175p = 3500*2500
175p = 8750000

p = 8750000/175

p = 50000

Hence the purchase price of the new car if the sales tax is $3500 is $50000

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The value of f from the given expression is 3

Given the expression below

cos(22f-1) = sin(7f+4),

This can also be expressed

cos(22f-1) = cos(90-7f-4)

cos(22f-1) = cos(86-7f)

22f - 1 = 86 - 7f

Collect the like terms

22f+7f = 86 + 1

29f = 87

f = 3

Hence the value of f from the given expression is 3

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Answer: 73

Step-by-step explanation:

I think she's 73? You have to take multiples of nine and see if they work! I did 72 since I knew that 72 goes into 9 equally and if she is 73 there would be a remainder of 1. After that, I stuck with 73 and since I knew that 18 times 4 is also 72, I knew that 73 divided by 4 would give me 18 with a remainder of 1.

The solution is 37 years, that is, Mrs. Laura's age is 37 years old.

Given information in the problem:

1. Mrs. Laura's, L age is between 50 and 80.

2. When you divide age by 9, the remainder is 1.

3. When you divide age by 4, the remainder is also 1.

To find L exact age, start by checking multiples of 9 that leave a remainder of 1 when divided by 4:

9 × 1 + 1 = 10 (remainder of 1 when divided by 4)

9 × 2 + 1 = 19 (remainder of 1 when divided by 4)

9 × 3 + 1 = 28 (remainder of 1 when divided by 4)

9 × 4 + 1 = 37 (remainder of 1 when divided by 4)

9 × 5 + 1 = 46 (remainder of 2 when divided by 4)

9 × 6 + 1 = 55 (remainder of 3 when divided by 4)

9 × 7 + 1 = 64 (remainder of 0 when divided by 4)

Check multiples of 4 that leave a remainder of 1 when divided by 9:

4 × 1 + 1 = 5 (remainder of 1 when divided by 9)

4 × 2 + 1 = 9 (remainder of 1 when divided by 9)

4 × 3 + 1 = 13 (remainder of 4 when divided by 9)

4 × 4 + 1 = 17 (remainder of 8 when divided by 9)

From the above calculations, see that the only common number between the two sets of multiples is 37.

So, L's age is 37 years old.

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The purchase value at the 20th percentile is $17.85 for the distribution with a mean of $30.44 and a standard deviation of $14.99.

The formula for the X is

X = μ + Z × σ

where,

Z- score, μ is the mean, and σ is the standard deviation

It is given that,

μ = $30.44

σ = $14.99

x% is given as the 20th percentile

So, α = 0.20

then, the Z score from the normal distribution table is -0.84

On substituting,

X = μ + Z × σ

  = 30.44 + (-0.84 × 14.99)

  = 30.44 - 12.59

  = 17.85

Therefore, the purchase value at the 20th  percentile is $17.88.

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For the given data,

Mean = 2.12

Median = 2

Mode = 2

Range = 3

From the question we are to determine the mean

From the given table

Scoops of Ice cream     Male      Female     Other         Total frequencies

1                                        7              3               3                       13

2                                       8              11              2                        21

3                                       10             1               0                        11

4                                        2              1              1                          4

∴ [tex]Mean = \frac{(1 \times 13) + (2 \times 21) +(3 \times 11) + (4 \times 4)}{13 +21+11+4}[/tex]

[tex]Mean = \frac{(13) + (42) +(33) + (16)}{49}[/tex]

[tex]Mean = \frac{104}{49}[/tex]

Mean = 2.12

Median = 2

Mode = 2

Range = 4 - 1 = 3

Hence, for the given data

Mean = 2.12

Median = 2

Mode = 2

Range = 3

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Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

Using compound interest, it is found that they must deposit $9,143.47 in order to have the desired amount.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

For this problem, the parameters are:

A(15) = 30000, r = 0.08, n = 4

Then we solve for P to find the initial deposit:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]30000 = P\left(1 + \frac{0.08}{4}\right)^{4 \times 15}[/tex]

[tex]P = \frac{30000}{(1.02)^{60}}[/tex]

P = $9,143.47.

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Answer:

B.) The graph of g(x) is shifted 4 units up

Step-by-step explanation:

In a linear function in slope-intercept form, b, or 4 in this case, represents the y-intercept which technically acts as a vertical shift

It's kind of self-evident. Any power of 21 will have a 1 in the units place, and adding 9 to it makes it 0 and hence the number is divisible by 5.

To prove the claim by induction, first establish the base case. I assume [tex]n\in\Bbb N[/tex], so for [tex]n=1[/tex] we have

[tex]21^1 + 9 = 21 + 9 = 30[/tex]

and of course 30 = 5×6 is divisible by 5.

Assume the claim is true for [tex]n=k[/tex], that [tex]5 \mid 21^k + 9[/tex]. This means that for some integer [tex]\ell[/tex], we can write

[tex]21^k + 9 = 5\ell[/tex]

Now the induction step: when [tex]n=k+1[/tex], we have

[tex]21^{k+1} + 9 = \bigg(21\times(21^k + 9) - 9\times21\bigg) + 9 \\\\ ~~~~~~~~~~~~~~ = 21\times5\ell - 9\times20 \\\\ ~~~~~~~~~~~~~~= 5\times(21\ell - 9\times4)[/tex]

which is divisible by 5. QED

The conversion factor of the chicken recipe used at the banquet is 4.5.

An equation is an expression that shows the relationship between two or more variables and numbers.

Conversion factor = (new amount * portion size) / (old amount * portion size)

Hence:

Conversion factor = (60 * 3) / (10 * 4) = 4.5

The conversion factor of the chicken recipe used at the banquet is 4.5.

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The best description of the geometric construction of the quotient z/w on the complex plane is; Option A; z is scaled by a factor of One-fifth and rotated 90 degrees clockwise

We are given;

z = 3(cos(15°) + i sin(15°))

w = 5(cos(90°) + i sin(90°))

Now, if we want to find the quotient z/w, it is clear that in geometric construction, the procedure will be to scale z by a factor of 1/5 and thereafter we will rotate by 90° clockwise.

Thus, option A is the correct answer.

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The best explanation for why the rotation is isometric is "The rectangle did not change shape or size". Hence the second option is the right choice.

There are four main categories of transformations:

A stiff transformation known as an isometry maintains perimeter and area while also preserving length and angle measurements. In other words, there is congruence between the preimage and the image. Translations, reflections, and rotations are therefore isometric, but dilations are not since the image and preimage are comparable, rather than congruent figures.

The transformation in the question will be isometric when the preimage of the rectangle before 360° rotation, will be congruent to the image after the rotation.

The congruency is best described by the option "The rectangle did not change shape or size", as that is the basis of congruency.

Thus, the best explanation for why the rotation is isometric is "The rectangle did not change shape or size". Hence the second option is the right choice.

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The provided question is incomplete. For the complete question, refer to the attachment.

Answer:

There were 12 cranes in class yesterday. For all the cranes, there were a total of 290 centimeters.

Step-by-step explanation:

41-29=12.

29*10=290

The additive inverse is:

(a) 4   (b) 18   (c) -620  (d) -60  (e) 244  (f) 8921

The additive inverse of a number x is the number that, when added to x  yields zero.

It is shown as [tex]x+(-x)=0[/tex]

To find the additive inverse of a number we just change the sign of the given number which means positive changes to negative and vice versa.

The additive inverse of the given numbers are:

(a) 4

(b) 18

(c) -620

(d)-60

(e) 244

(f) 8921

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The surface area of a rectangular prism with a height of 16 feet, a width of 10 feet, and a length of 13 feet is 996 ft².

A = Surface area

l = Length

w = Width

h = Height

A = 2 ( w l + h l + h w )

= 2 · ( 10 · 13 + 16 · 13 + 16 · 10 )

= 996 ft²

The gap occupied by using a dimensional flat surface is referred to as the region. it's far measured in rectangular gadgets. The location occupied by using a 3-dimensional object by means of its outer floor is referred to as the surface location.

The surface vicinity of a strong object is a degree of the total vicinity that the surface of the item occupies.

The floor location is the overall location included via all of the faces of a 3-d item. As an example, if we need to discover the amount of paint required to paint a cube, then the surface on which the paint will be implemented is its floor place. it is continually measured in square gadgets.

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The single transformation which takes shape A to shape B as in the task content is a 90° clockwise rotation and a 6 units shift rightward.

By observation, it follows that the orientation of the shape A differs from that of B as it lags by 90° in the clockwise direction.

Additionally, the resulting image from a 90° clockwise rotation about the left vertice of A still reguires that A be shifted 6 units rightwards to yield shape B.

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Answer:

Area of parallelogram = 9600 m²

Step-by-step explanation:

• We can find the measure of angle x using the cos rule:

[tex]160^2 = 100^2 +100^2 -2(100)(100) \cdot cos (x)[/tex]

Make x the subject of the equation:

⇒  [tex]20000 \cdot cos(x) = 100^2 +100^2 - 160^2[/tex]

⇒  [tex]cos(x) = -0.28[/tex]

⇒  [tex]x = cos^{-1} (-0.28)[/tex]

⇒  [tex]x = 106.26 \textdegree[/tex]

• Now we can find the area of one the triangles formed using the formula:

[tex]Area =\frac{1}{2} ab \cdot sin \theta[/tex]

where a and b are two sides of a triangle, and θ is the angle between them (angle x).

Substituting the values:

Area of one triangle = [tex]\frac{1}{2}[/tex]  × (100)(100) × sin(106.26°)

                             = 4800 m²

• Since the parallelogram is formed by two such triangles, we have to double the area of the triangle to find the parallelogram's area:

Area of parallelogram = 2 × 4800

                                     = 9600 m²

The resulted integral is [tex]I=\frac{8}{3} \times \frac{5 \pi}{16}=\frac{5 \pi}{6}[/tex].

In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or just an added to the initial, the derivative of which is initial function (indefinite integral).

Computation of the integrals:

Step 1: We employ the equations in cylindrical coordinates.

[tex]x=r \cos \theta, y=r \sin \theta, z=z[/tex]

Thus, in cylindrical coordinate system,

E lies above the paraboloid [tex]z=r^{2}[/tex] and below the plane [tex]z=2 r \sin \theta[/tex] .

Therefore, the top part E is  [tex]z=2 r \sin \theta[/tex] is the cross-section between paraboloid and the plane.

Now, at the cross-section use, [tex]r^{2}=2 r \sin \theta[/tex] and  [tex]z=2 r \sin \theta[/tex] .

Thus, the limits are given as ;

[tex]r^{2} \leq z \leq 2 r \sin \theta \quad 0 \leq r \leq 2 \sin \theta[/tex]

Apply the limits as compute the integration;

[tex]\begin{aligned}I=\iiint_{E} z d V &=\int_{0}^{\pi} \int_{0}^{2 \sin \theta} \int_{\tau^{2}}^{2 r \sin \theta} z r d r d z d \theta \\&=\int_{0}^{\pi} \int_{0}^{2 \sin \theta}\left[\frac{z^{2}}{2}\right]_{r^{2}}^{2 r \sin \theta} r d r d \theta \\&=\frac{1}{2} \int_{0}^{\pi} \int_{0}^{2 \sin \theta}\left[4 r^{2} \sin ^{2} \theta-r^{4}\right] r d r d \theta\end{aligned}[/tex]

                       [tex]\begin{aligned}&=\frac{1}{2} \int_{0}^{\pi} \int_{0}^{2 \sin \theta}\left[4 r^{3} \sin ^{2} \theta-r^{5}\right] d r d \theta \\&=\frac{1}{2} \int_{0}^{\pi}\left[r^{4} \sin ^{2} \theta-\frac{r^{6}}{6}\right]_{0}^{2 \sin \theta} d \theta \\&=\frac{8}{3} \int_{0}^{\pi} \sin ^{6} \theta d \theta\end{aligned}[/tex]

Step 2: Now, calculate for the [tex]I_{1}=\int_{0}^{\pi} \sin ^{6} \theta d \theta[/tex].

 [tex]\begin{aligned}\sin ^{6} \theta &=\left(\sin ^{2} \theta\right)^{2} \times \sin ^{2} \theta \\&=\left[\frac{1-\cos 2 \theta}{2}\right]^{2} \times\left[\frac{1-\cos 2 \theta}{2}\right] \\&=\frac{1}{8}\left(1-2 \cos 2 \theta+\cos ^{2} 2 \theta\right)(1-2 \cos 2 \theta) \\&=\frac{1}{8}\left(1-2 \cos 2 \theta+\frac{1+\cos 4 \theta}{2}\right)(1-2 \cos 2 \theta)\end{aligned}[/tex]

         [tex]\begin{aligned}&=\frac{1}{16}(3-4 \cos 2 \theta+\cos 4 \theta)(1-2 \cos 2 \theta) \\&=\frac{1}{32}(10-15 \cos 2 \theta+6 \cos 4 \theta-\cos 6 \theta)\end{aligned}[/tex]

Further compute the value of

   [tex]\begin{aligned}I_{1} &=\int_{0}^{\pi} \sin ^{6} \theta d \theta \\&=\frac{1}{32} \int_{0}^{\pi}(10-15 \cos 2 \theta+6 \cos 4 \theta-\cos 6 \theta) d \theta \\&=\frac{1}{32}\left[10 \theta-\frac{15 \sin 2 \theta}{2}+\frac{3 \sin 4 \theta}{2}-\frac{\sin 6 \theta}{6}\right]_{0}^{\pi} \\&=\frac{5 \pi}{16}\end{aligned}[/tex]

Therefore, the obtained integral is  [tex]I=\frac{8}{3} \times \frac{5 \pi}{16}=\frac{5 \pi}{6}[/tex].

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The complete question is -

Use cylindrical or spherical coordinates, whichever seems more appropriate. Evaluate ∫∫∫E z dV, where E lies above the paraboloid

z = x² + y²

and below the plane z = 2y. Use either the Table of Integrals or a computer algebra system to evaluate the integral.

F is located on the number 4.5 on the number line.

We know that point D is at -6

Point E is at 8.

Point F is between D and E, such that the ratio:

DF:FE is 3:1

So if we divide the distance between D and E in 4 parts, 3 of these parts are DF, and one of these parts is FE.

First, the distance between E and D is:

distance = 8 - (-6) = 14 units.

Now, if we divide that by 4, we get:

14/4 = 3.5

Then we have:

DF = 3*(3.5) = 10.5

This means that F is at 10.5 units to the right of D, then:

F = D + 10.5 = -6 + 10.5 = 4.5

F is located on the number 4.5 on the number line.

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Answer:

4.5 is the answer :D

Step-by-step explanation:

Answer:

The system of equation y=120+20x and y=30x

Step-by-step explanation:

Let the number of days be x and y be the total number minutes

Jamie has walked 120 mins. She will walk at a rate of 20 mins per day.

y=120+20x

Owen walks 30 mins a day. So

y = 30x

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Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the y-intercept of the equations, not the vertex.  This can be obtained using finding y intercept of both parabolas and vertex of parabola A.

Parabola A, (x + 3)² = y = x² + 6x + 9

Parabola B, y = mx + 9

x=0, y = 9

y coordinate of parabola A is (0,9)

⇒The vertex coordinate,

(-b/2a , -(b²-4ac)/4a) = (-3,0)          

x=0, y = 9  

y coordinate of parabola B is (0,9)    

Isabel claims one solution to the system of two equations must always be the vertex of parabola A which is wrong.  

Hence Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the y-intercept of the equations, not the vertex.

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: Parabola A can be represented using the equation (x + 3)2 = y, while line B can be represented using the equation y = mx + 9. Isabel claims one solution to the system of two equations must always be the vertex of parabola A. Which best describes the reasonableness of her claim?

Answer:

it is False

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

using the recursive rule [tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] - 1 and a₁ = 2 , then

a₂ = 3a₁ - 1 = (3 × 2) - 1 = 6 - 1 = 5

a₃ = 3a₂ - 1 = (3 × 5) - 1 = 15 - 1 = 14

a₄ = 3a₃ - 1 = (3 × 14) - 1 = 42 - 1 = 41

a₅ = 3a₄ - 1 = (3 × 41) - 1 = 123 - 1 = 122

Answer:

Step-by-step explanation:

true

Answer:

True

Step-by-step explanation:

It is determined while using the binomial distribution that there is still a 1.145=114.5% chance that she produces no more than 11 of them.

There are just two possible results for each throw. Either she succeeds or she fails. The binomial probability distribution is employed to answer this issue since the probability of completing a shot is regardless of all other throws.

Binomial probability distribution-

[tex]P(X=x) = C_{n,x} .p^{x}(1-p)^{n-x}[/tex]

[tex]C_{n,x} = n!/x! (n-x)![/tex]

where,

the no. of success= x

the no. of trials = n

the probability of a success on one trial = p

The probability of throwing not more than 11 will be:

P(X<11) = P(X=0) + P(X=1) +P(X=2) + P(X=3) +P(X=4) +P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)

Where,

[tex]P(X=x) = C_{n,x} .p^{x}(1-p)^{n-x}[/tex]

[tex]P(X=0) = C_{18,0} .(0.689)^{0}(0.311)^{18}[/tex]≈0

[tex]P(X=1) = C_{18,1} .(0.689)^{1}(0.311)^{17}[/tex]≈0

[tex]P(X=2) = C_{18,2} .(0.689)^{2}(0.311)^{16}[/tex]≈0

[tex]P(X=3) = C_{18,3} .(0.689)^{3}(0.311)^{15}[/tex]≈0

[tex]P(X=4) = C_{18,4} .(0.689)^{4}(0.311)^{14}[/tex]≈0

[tex]P(X=5) = C_{18,5} .(0.689)^{5}(0.311)^{13}[/tex]= 0.0003

[tex]P(X=6) = C_{18,4} .(0.689)^{6}(0.311)^{12}[/tex]=0.0016

[tex]P(X=7) = C_{18,7} .(0.689)^{7}(0.311)^{11}[/tex]=0.0062

[tex]P(X=8) = C_{18,8} .(0.689)^{8}(0.311)^{10}[/tex]=0.0188

[tex]P(X=9) = C_{18,9} .(0.689)^{9}(0.311)^{9}[/tex]=0.0463

[tex]P(X=10) = C_{18,10} .(0.689)^{10}(0.311)^{8}[/tex]=0.9232

[tex]P(X=11) = C_{18,11} .(0.689)^{11}(0.311)^{7}[/tex]=0.1488

So,

P(X<11) = P(X=0) + P(X=1) +P(X=2) + P(X=3) +P(X=4) +P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)

=0+0+0+0+0+0.0003+0.0016+0.0062+0.0188+0.0463+0.9232+0.1488 =1.145

Therefore, she makes 1.145=114.5% probability, no more than 11 of them.

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Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "equations, expressions". The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.