What is the first step to solve the equation A. Square both sides of the equation. B. Add 5 to both sides of the equation. Square. 5, and -3. C. D. None, because there is no solution. 2x-5--3?​

Answer:

Distance = 15

Step-by-step explanation:

4 - (-11) = 4 + 11 = 15

The function that is graphed is y = |x -2| + 3. The correct option is D. y = |x -2| + 3

From the question, we are to determine the function for the given graph

From the graph,

When x = 2, y = 3

The equation that satisfy this condition is

y = |x -2| + 3

NOTE: This function satisfies all the points on the graph

Hence, the function that is graphed is y = |x -2| + 3

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The answers are :

a)

b)

Let's find point A by using g(x). A is clearly the y-intercept so take x = 0.

Points B and C can be found using f(x). As they are the x-intercepts, take y = 0.

As B lies to the left of the y-axis, its x-coordinate is negative.

As C lies to the right of the y-axis, its x-coordinate is positive.

Point D can be found using g(x). D is clearly the x-intercept so take y = 0.

Point E lies at the intersection of f(x) and g(x). So they have to be equated.

Answer:

see explanation

Step-by-step explanation:

(a)

A lies on the y- axis with x- coordinate of zero

substitute x = 0 into either of f(x) or g(x) for y- coordinate

g(0) = 2(0) + 1 = 0 + 1 = 1

then A (0, 1 )

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

B and C lie on the x- axis with y- coordinate of zero

let f(x) = 0 and solve for x , that is

1 - x² = 0 , then

x² = 1 ( take square root of both sides )

x = ± [tex]\sqrt{1}[/tex] = ± 1

then B (- 1, 0 ) and C (1, 0 )

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

D is the point on the x- axis where g(x) crosses

let g(x) = 0 and solve for x

2x + 1 = 0 ( subtract 1 from both sides )

2x = - 1 ( divide both sides by 2 )

x = - [tex]\frac{1}{2}[/tex]

then D (- [tex]\frac{1}{2}[/tex] , 0 )

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

(b)

E is the point of intersection of f(x) and g(x) so equate them, that is

2x + 1 = 1 - x² ( subtract 1 - x² from both sides )

x² + 2x = 0 ← factor out x from each term

x(x + 2) = 0

equate each factor to zero and solve for x

x = 0 ← x- coordinate of A

x + 2 = 0 ⇒ x = - 2 ← x- coordinate of E

substitute x = - 2 into g(x) for corresponding y- coordinate

g(- 2) = 2(- 2) + 1 = - 4 + 1 = - 3

then E (- 2, - 3 )

The 10the term of the sequence -1/1, -1/2, -1/9, -1/64....is -1/1,000,000,000

-1/1, -1/2, -1/9, -1/64

This can be written as;

-1/1° , -1/2¹, -1/3², -1/4³, -1/5⁴, -1/6^5, -1/7^6, - 1/8^7, -1/9^8, -1/10^9

So,

First term = -1/1,

Second term = -1/2,

Third term = -1/9,

Fourth term = -1/64,

Fifth term = -1/625,

Sixth term = -1/7,776,

Seventh term = -1/117,649,

Eighth term = -1/2,097,152,

Ninth term = -1 / 43,046,721,

Tenth term = -1/1,000,000,000

Therefore, the 10th term is -1/1,000,000,000

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Answer:

What is the expected value when rolling a fair 12-sided die?

132=6.5

Recall the definition of the expected value:

E[X]=∑ni=1xp(x)

Here, we have 12 possible values the die can take on, and the probability of each one is the same: 1/12. So we can just pull the term p(x), the probability of each outcome, out of the summation:

E[X]=112∑12i=1x

A useful trick here is that the sum of the numbers 1..N=N(N+1)2. So:

E[X]=11212(13)2

E[X]=12(13)12(2)

E[X]=132

Step-by-step explanation:

hope it helps you :)

Answer:

[tex]-8x^2 - 4x + 29 \\[/tex]

Step-by-step explanation:

Second expression evaluates to:

[tex](5 + x -2x)^2 = (5 -x)^2 = (-x+5)^2 = x^2 + 2(-x)(5) +5^2 = x^2 -10x + 25[/tex]  (1)

For (1) We are using the rule [tex](a+b)^2 = a^2 +2ab + b^2\\\\[/tex]

Here [tex]a = -x, b = 5\\\\[/tex]

First expression evaluates to

[tex](3x)^2 -6x - 4 = 9x^2 -6x -4[/tex]    (2)

Subtract (2) from (1)

[tex]x^2 - 10x +25 - (9x^2 -6x -4) = x^2-9x^2 -10x - (-6x) +25 -(-4)\\\\= -8x^2 - 4x + 29 \\[/tex]

Answer:

the height would be around 19.2 cm

Step-by-step explanation:

hyp length = 63

base = 60

length = sqrt(63^2 - 60^2) = sqrt(369)

The margin of error is 1.9%. and the interval that likely contains the true percent of all people who work out 3 or more days a week is: (71.1%, 74.9%)

Margin of error is the critical value (t score or z score) multiplied by the standard error (standard deviation of the sample). Thus;

ME = Critical value × S.E

Since n > 30, we can use the z-score as the critical value.

Assuming 95% confidence level, then z = 1.96

The standard error for a proportion is given by the formula:

s = √(p (1 − p) / n)

We are given;

p = 0.73

n = 2035:

Thus;

s = √(0.73 (1 − 0.73) / 2035)

s = 0.0098

Thus, the margin of error is:

ME = 1.96 × 0.0098

ME = 0.019

The margin of error is 1.9%.  

The interval that likely contains the true percent of all people who work out 3 or more days a week is:

73% ± 1.9% = (71.1%, 74.9%)

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The points would be matched with their polar coordinates as follows:

A polar coordinate can be defined as a two-dimensional coordinate system, wherein each point on a plane is typically determined by a distance (r) from the pole (origin) and an angle (θ) from a reference direction (polar axis).

In geometry, the relationship between a polar coordinate (r, θ) and a rectangular coordinate (x, y) based on the conversion rules is given by the following polar functions:

a = rcos(θ)    ....equation 1.

b = rsin(θ)     ....equation 2.

Where:

In Mathematics, a negative vector for a given vector has the same magnitude but acts in an opposite direction while an antiparallel vector for a given vector refers to any vector that acts in an opposite direction.

This ultimately implies that, a negative vector equals to an antiparallel vector, but an antiparallel vector isn't always a negative vector.

In this context, we can infer and logically deduce that the points would be matched with their polar coordinates as follows:

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The equation in term of p that models the above experience is:
2p + 10 = 0.8p + 20.

Any statement that models or captures the factors of a problem where in an equal sign is present to equate two of the factors or expressions therein is called an equation.

Total cost of baking p pizzas with brick oven = A =  p(cost of one pizza) + cost of baking = p(2) + 10 (in dollars).

Total cost of  baking p pizzas with electric oven = B =  p(cost of one pizza) + cost of baking = p(0.8) + 20 (in dollars).

B = A - 1 (as using electric oven saves $1 per day, as given)

Thus, we get:

2p + 10 = 0.8p + 20

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Answer:

The no. of student failed is 36.

Step-by-step explanation:

Given, the number of student enrolled= 216

Let us suppose number of student failed = x

Given,

no. of student passed is 5 times no. of student failed.

Then, no. of student passed = 5x

x +5x = 216

6x = 216

x = 216/6

x = 36

Thus, the no. of student failed is 36.

Answer:

(4x+5)

Step-by-step explanation:

4x(5x-3)+5(5x-3)

collecting like terms, first part is (5x-3) hence second part of the equation is (4x+5) from the equation above.

Answer:

Step-by-step explanation:

(20x2 – 12x) + (25x– 15)

4x(5x – 3) + 5(5x – 3)

(( (5x – 3)(4x +5) ))

Answer:

Step-by-step explanation:

....

By using the linear function which models the data in the given table, the cost of a textbook with 402 pages is equal to $47.4478.

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the linear function is given by:

y = 0.1057x + 4.9564

If x = 402, then y is given by:

y = 0.1057(402) + 4.9564

y = 42.4914 + 4.9564

y = $47.4478.

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The theoretical probability of randomly getting a black counter is P = 2/5.

In this case, we have 8 black counters and 12 white counters, so there is a total of 20 counters.

We assume that all the counters have the same probability of being randomly selected, then the probability of randomly selecting a black counter is just given by the quotient between the number of black counters and the total number of counters.

There are 8 black counters and 20 in total, then the probability is given by:

P = 8/20

Now we can simplify that fraction to get:

P = 2/5

The theoretical probability of randomly getting a black counter is P = 2/5.

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The first five terms of the sequence representing each bottle scheme for Mike is illustrated below.

From the information given, Mike and Tim are looking to earn a little extra money and the beach committee offers them the opportunity of picking up plastic bottles, paying them $0.20 per bottle.

For Mike, the price for the first bottle is $0.10.

The price for the second bottle will be:

= 0.10 × 1.02 = 0.102

The price for the third bottle will be:

= 0.10 × 1.02² = 0.10404

The price for the forth bottle will be:

= 0.10 × 1.02³ = 0.10612

The price for the fifth bottle will be:

= 0.10 × 1.02⁴ = 0.10824

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Complete question:

Mike and Tim are looking to earn a little extra money. The beach committee offers them the opportunity of picking up plastic bottles, paying them $0.20 per bottle. Mike realizes as they pick up it will get harder and harder to find more bottles. So as an incentive to keep looking he suggests a different form of payment. He suggests $0.10 for the first bottle and increase the pay by 2% for each bottle after that. Tim thinks Mike is crazy to propose an increase of just 2% per piece. He plans to ask for a one cent increase for every piece, starting at 15 cents for the first bottle. Write the first five terms of the. sequence representing each bottle scheme for Mike.

The direct variation function is y = 0.3x

The direct variation from y to x is represented as:

y = kx

When y = 1.5 and x = 5, we have

1.5 = 5k

Divide by 5

k = 0.3

Substitute k = 0.3 in y = kx

y = 0.3x

Hence, the direct variation function is y = 0.3x

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Answer:

Step-by-step explanation:

The perimeter formula and the given relation between length and width can be used to write and solve an equation for the field dimensions.

Let w represent the width of the field. Then (3w-120) is the length of the field, and its perimeter is ...

  P = 2(L +W)

  1040 = 2((3w-120) +w)

Dividing by 2 and simplifying, we have ...

  520 = 4w -120

  130 = w -30 . . . . . . divide by 4

  160 = w . . . . . . . . . add 30

  3w-120 = 3(160) -120 = 360 . . . the field's length

The dimensions of the field are 160 feet long by 360 feet wide.

The equation of the parabola with the given vertex and directrix in vertex form is y = (1/16)( x + 5 )² - 9.

Hence, option C is the correct answer.

Given the data in the question;

To find the equation, we use the equation of the parabola that opens up or down since the directrix ( y = -13 ) is vertical.

The equation is expressed as;

( x - h )² = 4p( y - k )

First, we find the distance from the focus to the vertex.

|p| is the distance rom the focus to the vertex and from the vertex to the directrix.

p = -9 + 13

p = 4

We substitute the values into the equation;

( x - h )² = 4p( y - k )

( x - (-5) )² = 4(4)( y - (-9) )

( x + 5 )² = 16( y + 9 )

Multiply both side by 1/16

(1/16)( x + 5 )² =  y + 9

Make y the subject of the formula

(1/16)( x + 5 )² - 9 =  y

y = (1/16)( x + 5 )² - 9

The equation of the parabola with the given vertex and directrix in vertex form is y = (1/16)( x + 5 )² - 9.

Hence, option C is the correct answer.

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1. Observe that

[tex]\nabla \dfrac{x^2y^2w^2}2 = \langle xy^2w^2, x^2yw^2, x^2y^2w\rangle[/tex]

is a gradient field, so the gradient theorem holds and the integral in question is indeed path-independent. Its value is

[tex]\dfrac{x^2y^2w^2}2\bigg|_{x=1,y=3,w=2}^{x=2,y=4,w=1} = 32 - 18 = \boxed{14}[/tex]

2. [tex]dz[/tex] is an exact differential if we can find a scalar function [tex]z=f(x,y)[/tex] such that

[tex]\dfrac{\partial f}{\partial x} = 3x^2 (x^2+y^2) = 3x^4 + 3x^2y^2[/tex]

[tex]\dfrac{\partial f}{\partial y} = 2y(x^3+y) = 2x^3y + 2y^2[/tex]

Integrating both sides of the first equation with respect to [tex]x[/tex] yields

[tex]f(x,y) = \dfrac35 x^5 + x^3 y^2 + g(y)[/tex]

Differentiating with respect to [tex]y[/tex] gives

[tex]\dfrac{\partial f}{\partial y} = 2x^3y + \dfrac{dg}{dy} = 2x^3y + 2y^2 \\\\ \implies \dfrac{dg}{dy} = 2y^2 \implies g(y) = \dfrac23y^3 + C[/tex]

and we ultimately find

[tex]f(x,y) = \boxed{z = \dfrac35 x^5 + x^3y^2 + \dfrac23 y^3 + C}[/tex]

(We can also use the same method here to determine the scalar function in part (1).)

Then the integral is path-independent, and its value is

[tex]f(2,1) - f(1,2) = \dfrac{418}{15} - \dfrac{149}{15} = \boxed{\dfrac{269}{15}}[/tex]

The equivalent expression of -14 - 6 is -14 - (+6)

Equivalent expressions are expressions that have the same value when evaluated

The expression is given as:

-14 - 6

Put the terms of the expression in brackets

-14 - (6)

Rewrite 6 as +6

-14 - (+6)

Hence, the equivalent expression of -14 - 6 is -14 - (+6)

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Step-by-step explanation:

6 and 7 was already answered so I'll do 5 and 8.

5. The point the curve crosses the x axis is the x intercept, to find the x intercept of a rational function, we set y=0, and solve for x.

[tex]0 = \frac{x - 4}{x} [/tex]

Set the numerator equal to 0.

[tex]x - 4 = 0[/tex]

[tex]x = 4[/tex]

So the x intercept is (4,0).

Next, to find gradient, we take the derivative of the function.

[tex] \frac{x - 4}{x} [/tex]

We could use product rule, but for simplicity, serperate the function

[tex] \frac{x}{x} - \frac{4}{x} [/tex]

[tex]1 - \frac{4}{x} [/tex]

Next using exponents rules,

[tex]1 - 4 {x}^{ - 1} [/tex]

Now we take the derivative,

Derivative of a constant is zero.

Derivative of a power function,

[tex]n \times x {}^{n - 1} [/tex]

We move the exponent to the front, then we subtract the exponent by 1.

So, we get

[tex]4 {x}^{ - 2} [/tex]

Now, we plug in. 4,

[tex]4(4) {}^{ - 2} [/tex]

[tex]4 \times \frac{1}{16} = \frac{1}{4} [/tex]

The slope or gradient at the x intercept is 1/4

8. The derivative of ax^2+bx, with respect to x is

[tex]2ax + b[/tex]

When x=2, we have a gradient of 8.

[tex]2a(2) + b = 8[/tex]

[tex]4a + b = 8[/tex]

When x=-1, we have a gradient of -10.

[tex]2a( - 1) + b = - 10[/tex]

[tex] - 2a + b = - 10[/tex]

We have two system of equations,

[tex]4a + b = 8[/tex]

[tex] - 2a + b = - 10[/tex]

Let subtract the system to eliminate b.

[tex]6a = 18[/tex]

[tex]a = 3[/tex]

Plug 3 for a, back in to solve for b.

[tex]4(3) + b = 8[/tex]

[tex]12 + b = 8[/tex]

[tex]b = - 4[/tex]

So a is 3

b is -4

The interquartile range of 48, 26, 31, 50, 38, 40, 42, 34, 44, 36, is: D. 10.

The interquartile range of a data distribution is determined as: upper quartile (Q3) - lower quartile (Q1).

The upper quartile of a data distribution is the center of the second half of a data distribution while the lower quartile is the center of the first half of a data distribution.

Given the data, 48, 26, 31, 50, 38, 40, 42, 34, 44, 36:

Order the data set as, 26, 31, 34, 36, 38, 40, 42, 44, 48, 50

The first half of the data is: 26, 31, 34, 36, 38.

The center is 34.

Lower quartile (Q1) = 34.

The second half of the data is: 40, 42, 44, 48, 50. The center is 44.

Upper quartile (Q3) = 44.

Interquartile range = 44 - 34

Interquartile range = 10

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Answer:

LHS=2(sin

6

θ+cos

6

θ)−3(sin

4

θ+cos

4

θ)+1

=2{(sin

2

θ+cos

2

θ)

3

−3sin

2

θcos

2

θ(sin

2

θ+cos

2

θ)}−3(sin

2

θ+cos

2

θ)

2

−2(sin

2

θcos

2

θ)}+1

We know, [sin²x+cos²x=1]

=2{1−3sin

2

θcos

2

θ}−3{1−2sin

2

θcos

2

θ}+1

=2−6sin

2

θcos

2

θ−3+6sin

2

θcos

2

θ+1

=0

=RHS

Step-by-step explanation:

Answer: B

Step-by-step explanation:

The horizontal change is 6.

The vertical change is 5.

So, the distance is [tex]\sqrt{6^2 + 5^2}=\sqrt{61}[/tex]

The future value interest earned semiannually at a  compound rate of 4% is $7598.89.

To calculate the future value in interest earned, we use the of compound interest

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

Formula:

Where:

From the question,

Given:

Substitute the values above into equation 1

Hence, the future value interest earned is $7598.89.

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Answer:

c

Step-by-step explanation:

Foreshortening is a technique used in perspective to create the illusion of an object receding strongly into the distance or background.

Foreshortening is a technique used to create the illusion of depth and three-dimensionality in a two-dimensional image.

Option B is the correct answer.

Foreshortening is a technique used in art to create the illusion of depth and three-dimensionality in a two-dimensional image.

It involves distorting the shapes of objects or figures to make them appear closer or farther away from the viewer, often by shortening the lengths of their features or changing the angle from which they are viewed.

Foreshortening is often used in drawing, painting, and other visual arts to create a sense of perspective and realism.

We have,

Foreshortening is a technique used to create the illusion of depth and three-dimensionality in a two-dimensional image.

It involves distorting the shapes of objects and figures to make them appear closer or farther away from the viewer, often by shortening the lengths of their features or changing the angle from which they are viewed.

Foreshortening can be used in drawing, painting, and other visual arts to create a sense of perspective and realism.

Thus,

Foreshortening is a technique used to create the illusion of depth and three-dimensionality in a two-dimensional image.

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The Two sets, A and B, are said to be disjoint sets if A n B=ϕ

The Two sets, A and B, are said to be disjoint sets if A n B=ϕ

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