Hi! Please help me find the slope of the line.

Answer:

see explanation

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] a³ - [tex]\frac{3}{4}[/tex] a² - [tex]\frac{5}{2}[/tex] - ( [tex]\frac{5}{2}[/tex] a² + [tex]\frac{3}{2}[/tex] a³ + [tex]\frac{a}{3}[/tex] - [tex]\frac{6}{5}[/tex] ) ← distribute parenthesis by - 1

= [tex]\frac{1}{3}[/tex] a³ - [tex]\frac{3}{4}[/tex] a² - [tex]\frac{5}{2}[/tex] - [tex]\frac{5}{2}[/tex] a² - [tex]\frac{3}{2}[/tex] a³ - [tex]\frac{a}{3}[/tex] + [tex]\frac{6}{5}[/tex] ← collect like terms

= ([tex]\frac{1}{3}[/tex] a³ - [tex]\frac{3}{2}[/tex] a³ ) + (-[tex]\frac{3}{4}[/tex] a² - [tex]\frac{5}{2}[/tex] a² ) - [tex]\frac{a}{3}[/tex] + (- [tex]\frac{5}{2}[/tex] + [tex]\frac{6}{5}[/tex] ) ← change to common denominators

=   ([tex]\frac{2}{6}[/tex] a³ - [tex]\frac{9}{6}[/tex] a³ ) + (- [tex]\frac{3}{4}[/tex] a² - [tex]\frac{10}{4}[/tex] a² ) - [tex]\frac{a}{3}[/tex] + (- [tex]\frac{25}{10}[/tex] + [tex]\frac{12}{10}[/tex] ) ← simplify

= - [tex]\frac{7}{6}[/tex] a³ - [tex]\frac{13}{4}[/tex] a² - [tex]\frac{1}{3}[/tex] a - [tex]\frac{13}{10}[/tex]

Answer:

Step-by-step explanation:

[tex]\sf \dfrac{1}{3}a^3-\dfrac{3}{4}a^2-\dfrac{5}{2}-\left[\dfrac{5}{2}a^2+\dfrac{3}{2}a^3+\dfrac{a}{3}-\dfrac{6}{5}\right]=[/tex]

               [tex]\sf = \dfrac{1}{3}a^3-\dfrac{3}{4}a^2-\dfrac{5}{2}-\dfrac{5}{2}a^2-\dfrac{3}{2}a^3-\dfrac{a}{3}+\dfrac{6}{5}\\\\\\( Combine \ like \ terms)\\\\= \dfrac{1}{3}a^3 -\dfrac{3}{2}a^3 -\dfrac{3}{4}a^2-\dfrac{5}{2}a^2-\dfrac{a}{3}-\dfrac{5}{2}+\dfrac{6}{5}\\\\=\left[\dfrac{1*2}{3*2}-\dfrac{3*3}{2*3}\right]a^3 + \left[-\dfrac{3}{4}-\dfrac{5*2}{2*2}\right]a^2-\dfrac{a}{3}+\left[-\dfrac{5*5}{2*5}+\dfrac{6*2}{5*2}\right]\\\\\\[/tex]

               [tex]\sf ==\left[\dfrac{2}{6}-\dfrac{9}{6}\right]a^3+\left[-\dfrac{3}{4}-\dfrac{10}{4}\right]a^2-\dfrac{a}{3}+\left[-\dfrac{25}{10}+\dfrac{12}{10}\right]\\\\=\dfrac{2-9}{6}a^3+\dfrac{(-3-10)}{4}a^2-\dfrac{a}{3}+\dfrac{(-25+12)}{15}\\\\[/tex]

               [tex]\sf = \dfrac{-7}{6}a^3+ \dfrac{(-13)}{4}a^2-\dfrac{a}{3}+\dfrac{(-13)}{15}\\\\=-\dfrac{7}{6}a^3-\dfrac{13}{4}a^2-\dfrac{a}{3}-\dfrac{13}{15}[/tex]

Answer:

The graph of [tex]d(x)[/tex] is [tex]f(x)[/tex] shifted right by [tex]27[/tex] units.

Answer:

x = [tex]\frac{2}{7}[/tex]

Step-by-step explanation:

[tex]\frac{1}{2}[/tex](7x+2) = 2

   7x+2 = 2÷[tex]\frac{1}{2}[/tex]

            = 2×2

            = 4

       7x = 4-2

            = 2

       ∴x = 2÷7

            = [tex]\frac{2}{7}[/tex]

Answer:

[tex]\displaystyle \frac{2}{7} = x[/tex]

Step-by-step explanation:

[tex]\displaystyle 2 = \frac{1}{2}(7x + 2) \Rightarrow 2 = 3\frac{1}{2}x + 1 \hookrightarrow \frac{1}{3\frac{1}{2}} = \frac{3\frac{1}{2}x}{3\frac{1}{2}} \\ \\ \boxed{\frac{2}{7} = x}[/tex]

I am joyous to assist you at any time.

The new coordinates will be ( 7,5) and (11,9) , Option A is the correct answer.

The reciprocal function is the inverse of the function, such that 1/ f(x) is the reciprocal of f(x).

The given linear function has pairs of points

(5,7) and (9,11)

The reciprocal of this will be

interchanging of the coordinates

Therefore the new coordinates will be

( 7,5) and (11,9)

Option A is the correct answer.

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Answer:

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

The volume of the regular pyramid is 128 unit³.

Option D) 128 unit³ is the correct answer.

This question is incomplete, the missing image is uploaded along this answer below.

The volume of pyramid is expressed as;

V = ( 1/3 ) × l × w × h

Given that;

We substitute our given values into the equation above.

V = ( 1/3 ) × 8 × 8 × 6

V = 128 unit³

The volume of the regular pyramid is 128 unit³.

Option D) 128 unit³ is the correct answer.

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See below for the proof of the trigonometry identity

The identity is given as:

(sin(x) + cos(x))² / sin(2x)= csc (2x) + 1

Start by expanding the numerator

(sin²(x) + cos²(x) + sin(2x)) / sin(2x)= csc (2x) + 1

Express sin²(x) + cos²(x) as 1

(1 + sin(2x)) / sin(2x)= csc (2x) + 1

Expand the fraction

1/sin(2x) + sin(2x)/sin(2x) = csc(2x) + 1

Evaluate the quotient

csc(2x) + 1 = csc(2x) + 1

Hence, the trigonometry identity has been proved

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Answer:

NO

Step-by-step explanation:

Answer:

A, C, and D

Step-by-step explanation:

A) (4x + 3) (2x + 6) is equal to 8x² + 30x + 18 because when you multiply two binomials, you use the distributive property. The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac. So, (4x + 3) (2x + 6) can be rewritten as (4x)(2x) + (4x)(6) + (3)(2x) + (3)(6). This can further be simplified to 8x² + 24x + 18.

C) 2(4x² + 15x + 9) is equal to 8x² + 30x + 18 because when you multiply a number by a binomial, you use the distributive property. The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac. So, 2(4x² + 15x + 9) can be rewritten as 2(4x²) + 2(15x) + 2(9). This can further be simplified to 8x² + 30x + 18.

D) 4(2x² + 7x + 4) is equal to 8x² + 30x + 18 because when you multiply a number by a binomial, you use the distributive property. The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac. So, 4(2x² + 7x + 4) can be rewritten as 4(2x²) + 4(7x) + 4(4). This can further be simplified to 8x² + 28x + 16.

Answer:

Hence if the square of binomials needs to be find then we use square of binomial pattern and if the product of conjugate pair needs to determine then we use product of conjugate pattern.

Step-by-step explanation:

Explanation

Answer:

A

Step-by-step explanation:

because for black diamond its 10x+25

and for bunny hill its 5x+50

Option b. The oversight was discovered during the preparation of gators' 2021 financial statements. depreciation expense on this machine for 2021 should be $372,000.

The yearly straight-line devaluation cost for the machine would be $186,000 ($930,000/5). In any case, since no deterioration was perceived in 2020, the collected devaluation toward the start of 2021 would be $0 rather than $186,000. In this manner, the complete devaluation cost for 2021 would be the yearly deterioration of $186,000 in addition to the get up to speed devaluation for 2020 of $186,000, for a sum of $372,000. This make up for lost time devaluation is important to address the blunder made in the earlier year and guarantee that the resource is appropriately recorded on the asset report. Accordingly, the right response is $372,000.

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The complete question is:

On January 1, 2020, Oriole Corp. acquired a machine at a cost of $930000. It is to be depreciated on the straight-line method over a 5-year period with no residual value. Because of a bookkeeping error, no depreciation was recognized in Oriole's 2020 financial statements. The oversight was discovered during the preparation of Oriole's 2021 financial statements. Depreciation expense on this machine for 2021 should be

$232500.

$372000.

$186000.

$0.

6. The system of equations has no solution.

7. B. Tables - 15 lbs, chairs - 3.5 lbs.

The values of x and y that makes two equations equal is the solution of a system of equations.

6. 3x + 4y = 12 --> eqn. 1

y = 3 - 3/4x --> eqn. 2

Substitute y = (3 - 3/4x) into eqn. 1 to find x:

3x + 4(3 - 3/4x) = 12

3x + 12 - 3x = 12

12 = 12 [unable to solve further for x]

This means that the system of equations has no solution.

7. t = tables

c = chairs

3t + 5c = 62.5 --> eqn. 1

3t + 2c = 52 --> eqn. 2

Subtract

3c = 10.5

c = 3.5 [chairs]

Substitute c = 3.5 into eqn. 2

3t + 2(3.5) = 52

3t + 7 = 52

3t = 52 - 7

3t = 45

t = 15 [table]

Therefore, the answer is: B. Tables - 15 lbs, chairs - 3.5 lbs.

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The height of the tree which is the opposite side of the right triangle is 145 meters.

The angle of elevation is 36 degrees.

The situation forms a right angle triangle.

Therefore,

base of the triangle = 200 m

Hence, using trigonometric ratios,

tan 36 = opposite / adjacent

tan 36 = x / 200

x = 200 tan 36

x = 200 × 0.726542528

x = 145.308505601

x = 145.31 m

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Answer:

Correct answer not shown on the options.

y = -(1/2)+1

Step-by-step explanation:

Let's find an equation in the format of y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).

The slope can be calculated as the Rise/Run of the line between the two given points (-6,4) and (-2,2):

Rise = (2 - 4) = -2

Run = (-2 - (-6)) = 4

Slope = Rise/Run = -2/4 or -(1/2)

In fact, the actual full equation is y= -(1/2)x+1  (See attached graph).

None of the options have a slope of -(1/2).  Either the information on the two points or the options are incorrect.

Answer:

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

Step-by-step explanation:

y = mx plus c,where m is the gradient.

∴m =[tex]\frac{y2-y1}{x2-x1}[/tex]=[tex]\frac{2-4}{-2-(-6)}[/tex]=[tex]\frac{-2}{4}[/tex]=[tex]-\frac{1}{2}[/tex]

Equation of a line equals

y-y1=m(x-x1) (Using point (-6, 4) for x1 and y1 values)

y-4=[tex]-\frac{1}{2}[/tex](x-(-6))

y-4=[tex]-\frac{1}{2}[/tex](x+6)

y-4=[tex]-\frac{1}{2}[/tex]x-3

2(y-4)=-x-3(2)(multiply through by 2)

2y-8=-x-6

2y=-x+2(divide through by 2)

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

∴the equation of the line is y=[tex]-\frac{1}{2}x[/tex]+1

The average number of points will be 15 points.

It should be noted that average or mean simply means the total added values fall the data in a set which is then divided by the number of data.

Let the assumed points be 10, 12, 24, 15, 23, and 6.

In this case, the average number of points will be:

= (10 + 12 + 24 + 15 + 23 + 6)/6

= 90/6

= 15 points

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A. 12.08

9 + 2 = 11

(So, 11 across on our x - axis from - 9 to 2)

Then, up 5 from 2 on our x-axis

Join the 2 dots of coordinates, & creating a triangle. Base 11, height 5

Use Pythagoras Theorem, to find that distance between the coordinates (the hypotenuse)

Root 11^2 + 5^2 = 12.083056...

(root means square root)

Hope this helps!

Answer:

Hello! The answer to this question is A. 12.08.

Step-by-step explanation:

The distance formula is:

[tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2 }[/tex]

With the distance formula, we can now substitute the values from the points provided:

[tex]\sqrt{(2 - (-9))^2 + (5 - 0)^2} \\= \sqrt{11^2 + 5^2\\\\\\\\= \sqrt{121 + 25} \\=\sqrt{146} \\= 12.08[/tex]

The distance between the points is 12.08.

The inequality is explained below.

Inequality is a statement of an order relationship between two numbers or algebraic expressions

In this vase, with a number line with two points opposite from each other on a number line, the middle of it is always going to be 0.  

Therefore, both points are the same distance away from 0 just in opposite directions.

That means point Q is always going to equal the negative of point P. An example of this is if point p equals 5, point p equals -5.

This method only works when it is specifically stated that the two points are opposite from each other.

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Answer:

[tex] < 25 = 56. < { \times 4 \div hwh3 \times }^{?} [/tex]

Answer:

Attached

Step-by-step explanation:

See attached image

They should quote 150 hours so that they can get 98% of the batteries to meet the guarantee.

Given mean of 140 hours and standard deviation of 4 hours with confidence level=98%.

We have to find the lifespan which they should quote to get 98% confident that their batteries meet the guarantee.

We have to use z test for this .

μ=140 hours and σ=4 hours

Z=X-μ/σ

When p value is 0.98 then from z table z value will be 2.58.

Z=X-140/4

2.58=X-140/4

2.58*4=X-140

10.32=X-140

X=150.32

after rounding off we will get 150 hours.

Hence they should quote 150 hours of lifetime on batteries.

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Answer:

132

Step-by-step explanation:

Answer:

x=10, MB=19 CM=16 CB=35

Step-by-step explanation:

Since M is the midpoint of line CB

CM=MB

x+6=2x-4

6+4=2x-x

10=x

The rest is pretty simple, plug 10 in for x

Answer:

Below.

Step-by-step explanation:

Standard error  =

standard deviation / √n

=  7.89 / √300

= 0.456 approx.

The area of the rectangle is 240 square inches

The dimensions are given as:

Length = 15 inches

Width = 4/3 feet

Start by converting feet to inches

Width = 4/3 * 12 inches

Width = 16 inches

The area is then calculated as:

Area = Length * Width

This gives

Area = 15 * 16

Evaluate

Area = 240

Hence, the area of the rectangle is 240 square inches

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The proper sequence of steps in implementing the model in Excel presented in the textbook is option b which is organize the data, represent the decision variables, represent the objective function, represent the constraints and represent the bounds on the decision variables.

Given process of implementing the model in Excel and we have to choose the correct process.

The process of implementing the model in Excel is as under:

1) Organize the data: In excel, to organize the data we have to put similar items in the same column. We have to design the data so that all rows have similar items in the same column. We have to keep a range of data separate and leave at least one blank column and one blank row between a related data range.

2) Represent the decision variables: Now we have to represent the decision variables according to which logical function performs tasks.

3)Represent the objective function: It is important because on the basis of this all the logical function perform tasks.

4) Represent the constraints: In excel when we are using solver we have to now represent the constraints of the objective function.

5) Represents the bounds on the decision variables.

Hence the proper sequence of steps in implementing the model in excel is Organize the data, represent the decision variables, represent the objective function, represent the constraints, and represent the bounds on the decision variables.

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Since opposite angles and sides are equal, then the quadrilateral ABCD is a parallelogram.

Given that, ABCD is a quadrilateral, segment AB is congruent to segment CD, ∠1 is congruent to ∠2.

We need to prove that ABCD is a parallelogram.

If one pair of opposite sides of a quadrilateral are both parallel and congruent, then it’s a parallelogram.

From the given quadrilateral ABCD:

AB=CD (Given)

∠1=∠2 (Given)

AC=AC (Diagonal)

From ASA congruency ΔABC and ΔADC are congruent.

By CPCT, AD=BC and ∠ABC=∠ADC.

Since opposite angles and sides are equal, then the quadrilateral ABCD is a parallelogram.

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The equation of the given  line is y=2/3x-6

We have given the graph of the line and also the equation of the line

[tex]y=-6x+\frac{2}{3}[/tex]

[tex]y=\frac{2}{3}x-6[/tex]

[tex]y=-6x+\frac{3}{2}[/tex]

[tex]y=\frac{3}{2}x-6[/tex]

We have to determine which equations graph is given here

We have to draw a graph of the given equation of the line

To find the coordinate of the given line

The equation of the line second is

x=0 then y=-6

and when y=0 then x=9

We get the points (0,-6) and (9,0)

plot this point and we get the given graph of the line.

Therefore the second option is correct.

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El celular de contado costará 7500 pesos, mientras que el celular a crédito tendrá un costo de 9000 pesos.

7500 / 100 = 75 (valor del 1%)

75 x 20 = 1500 pesos

Celular a contado: El precio no aumenta por lo que el valor sería de 7500 pesos.

Celular a crédito: 7500 + 1500 = 9000 pesos

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Answer: (1,2)

Step-by-step explanation:

Reflecting across the y-axis means [tex](x,y) \longrightarrow (-x,y)[/tex]

So, [tex](-1,2) \longrightarrow \boxed{(1,2)}[/tex]