Two functions f and g are defined on set R of real numbers by:

f: x
→
x2 – 2x – 1

g: x
→
x – 1

find the value of x for which f(x) = g(x) – 2

Answer:

x = 4/3

Step-by-step explanation:

move (combine) your X's on one side

combine like terms

divide and multiply

Answer:

Option B is the correct option.

Step-by-step explanation:

[tex] - x + \frac{3}{7} = 2x - \frac{25}{7} [/tex]

Move variable to L.H.S and change its sign

Similarly, Move constant to R.H.S and change its sign

[tex] - x - 2x = - \frac{25}{7} - \frac{3}{7} [/tex]

Collect like terms

[tex] - 3x = - \frac{25}{7} - \frac{3}{7} [/tex]

Calculate the difference

[tex] - 3x = - 4[/tex]

Divide both sides of the equation by -3

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

Calculate

[tex]x = \frac{4}{3} [/tex]

Hope this helps..

Best regards!

Answer:

x ≥ 64

Step-by-step explanation:

We want to find the average

Let x be the 5th grade

We want it to be no less than 80

Add up the scores and divide by 5

( 80+ 72+ 96+ 88+x)/5 ≥ 80

Combine like terms

( 336+x) /5 ≥ 80

Multiply each side by 5

336+x ≥ 400

Subtract 336 from each side

x ≥ 400-336

x ≥ 64

Answer:

Its D on edg :P

Answer:

679=49

Step-by-step explanation:

3838 is the one for 928 cause 666

Answer:

B∠119°

Step-by-step explanation:

Well first we need c.

And c + 112 = 180

So -112 is c = 68

68 + 51 + a = 180

68+51 = 119 + a = 180

a = 61

b + 61 = 180

b = 119

Answer:

$14,362

Step-by-step explanation:

The computation of the minimum unit cost is shown below:

Given that

0.6x^2 - 108x + 19,222

And as we know that the quadratic equation form is

ax^2 + bx + c

where

a = 0.6

b = -108

c = 19,222

Now for determining the minimal cost we applied the following formula which is

[tex]= \frac{-b}{2a} \\\\ = \frac{-(-108)}{2\times 0.6} \\\\ = \frac{108}{1.2}[/tex]

= 90

Now put these values to the above equation

[tex]= 0.6\times 90^{2} - 108 \times 90 + 19,222[/tex]

= 14,362

Answer: B. $16.13

Step-by-step explanation:

Formula : Sum of n observations = Mean x n

Given, 82 seniors earned an average $26.75 per student, 74 juniors earned an average $12.25 per student, 96 sophomores earned an average $15.50 per student, and 99 freshmen earned an average $10.85 per student.

Total students = 82+74+96+99 =351

Sum of earnings of 82 seniors  = $26.75  x 82= $2193.5

Sum of earnings of 74 juniors  = $12.25 x 74 = $906.5

Sum of earnings of 96 sophomores  = $15.50  x 96 = $1488

Sum of earnings of 99 freshmen  =  $10.85 x 99 = $1074.15

Total earnings =  $2193.5  + $906.5+  $1488 +$1074.15

= $5662.15

Average collection = (Total earnings) ÷ (Total students )

= $5662.15÷ 351

≈ $16.13

Hence, the  average collection for a student in this school = 16.31

So, the correct option is B.

Answer:

The hikers each receive 2 1/3 cups of trail mix.

1. Multiply 8 by 3 1/4 to get how much cups of trail mix they have in total which  will come out as 28.

2. Then divide the 28 cups by the 12 hikers, and you will get 2 1/3 as your answer.

Given Information:

Monthly payment = MP = $1500/4 = $375

Monthly interest rate = r = 25/12 = 2.083%

Required Information:

Present Value = ?

Answer:

[tex]PV = \$10,110[/tex]

Explanation:

n = 10*4

n = 40 monthly payments

The present value is found by

[tex]$ PV = MP \times \frac{ (1 - \frac{1}{(1+r)^n} )}{r} $[/tex]

Where r is monthly interest rate.

MP is the monthly payment.

[tex]$ PV = 375 \times \frac{ (1 - \frac{1}{(1+0.02083)^{40}} )}{0.02083} $[/tex]

[tex]PV = 375 \times (26.96)[/tex]

[tex]PV = \$10,110[/tex]

Therefore, $10,110 is the present value of 10 quarterly payments of $1500 each at 25% interest rate compounded each month.

Answer:

The answer is:

[tex]\bold{c\approx 20.2\ units}[/tex]

Step-by-step explanation:

Given:

In △ABC:

m∠A=15°

a=10 and

b=11

To find:

c = ?

Solution:

We can use cosine rule here to find the value of third side c.

Formula for cosine rule:

[tex]cos A = \dfrac{b^{2}+c^{2}-a^{2}}{2bc}[/tex]

Where  

a is the side opposite to [tex]\angle A[/tex]

b is the side opposite to [tex]\angle B[/tex]

c is the side opposite to [tex]\angle C[/tex]

Putting all the values.

[tex]cos 15^\circ = \dfrac{11^{2}+c^{2}-10^{2}}{2\times 11 \times c}\\\Rightarrow 0.96 = \dfrac{121+c^{2}-100}{22c}\\\Rightarrow 0.96 \times 22c= 121+c^{2}-100\\\Rightarrow 21.25 c= 21+c^{2}\\\Rightarrow c^{2}-21.25c+21=0\\\\\text{solving the quadratic equation:}\\\\c = \dfrac{21.25+\sqrt{21.25^2-4 \times 1 \times 21}}{2}\\c = \dfrac{21.25+\sqrt{367.56}}{2}\\c = \dfrac{21.25+19.17}{2}\\c \approx 20.2\ units[/tex]

The answer is:

[tex]\bold{c\approx 20.2\ units}[/tex]

Answer:

 is the correct answer.

Step-by-step explanation:

As per the question statement:  

Cost of Chocolate milk which is ordered already = $3.25.

Benjamin want his bill to be at most =  $30

Each stack of pancakes contains 4 pancakes.

Each stack of pancake costs= $5.50

Given that S represents the number of stacks of pancakes bought.

We have, Cost of 1 pancake = $5.50

Now, let us calculate the cost of the number of stacks of pancakes bought.

[tex]\text{Cost of one stack of pancakes}\times \text{Number of stacks of pancakes bought}[/tex]

i.e.  

[tex]5.50S[/tex]

So, total bill = Cost of chocolate milk shake + Money spent on stacks of pancakes = [tex]\$3.25+5.50S[/tex]

Now, this money should be lesser than or equal to $30 because maximum bill that Benjamin wants is $30.

So, the inequality can be written as:

[tex]\bold{3.25+5.50S \le 30}[/tex]

Please refer to https://brainly.com/question/17138529 as well.

3.25+5.50S < (with line under it) 30

To add on to what isyllus said...

3.25+5.50S < (with line under it) 30 is the equation

16 pancakes is the amount.

:) hope this helps!

Answer:

4x+15=7x+2

15_2=7x_4x

13=3x

13/3=x

4.33=x

Answer:

[tex]\boxed{x=\frac{13}{3} }[/tex]

Step-by-step explanation:

Subtract both sides by 15 and 7x.

Then, divide both sides by -3.

[tex]4x+15=7x+2\\4x-7x=2-15\\-3x=-13\\\displaystyle x=\frac{13}{3}[/tex]

Answer:

Step-by-step explanation:

Triangle is an example of a polygon with three sides. The types of triangle we have are the equilateral, isosceles, scalene and right angled triangle.

An equilateral triangle is a triangle that has all its 3 sides and angles equal.

An isosceles triangle is a triangle that has two of its sides and angles equal.

A scalene triangle is a triangle that has none of its sides and angles to be equal.

According to the question, we are given a triangle of lengths 9, 10 and 130. It is seen that all the length of each sides of the triangle is different, this makes it a scalene triangle.

Answer:  13.5

Step-by-step explanation:

Find the total volume of the melted cubes:

V₁ = 6³                V₂ = 8³                 V₃ = 12³

    = 216                   = 512                    = 1728

So the new cube will have a volume of 216 + 512 + 1728 = 2456

Volume of the cube = side³

 2456 = s³

[tex]\sqrt[3]{2456} = s[/tex]

    13.5 = s

Answer:

Step-by-step explanation:

Given

u = 14 , a = 8 , t = 4

Now, let's find the value of s

[tex]s = ut + \frac{1}{2} a {t}^{2} [/tex]

plug the values

[tex] = 14 \times 4 + \frac{1}{2} \times 8 \times {4}^{2} [/tex]

Reduce the numbers with G.C.F 2

[tex] = 14 \times 4 + 4 \times {4}^{2} [/tex]

Multiply the numbers

[tex] = 56 + 4 \times {4}^{2} [/tex]

Calculate the product

[tex] = 56 + {4}^{3} [/tex]

Evaluate the power

[tex] = 56 + 64[/tex]

Add the numbers

[tex] = 120[/tex]

Hope this helps..

best regards!!

a. True.

b. False.

c. True.

d. True.

e. True.

a. This statement is true because angles 6 and 8 are vertical angles. That means they are congruent.

b. This statement is false because Elm Street is a straight line, which means that angles 1 and 2 are supplementary angles and their measures will add up to be 180 degrees. 65 + 125 = 190, which is not equal to 180.

c. This statement is true because angles 5 and 1 correspond to each other.

d. This statement is true because angles 7 and 8 form a straight line.

e. This statement is true because they are interior angles that are alternate.

Answer: B

Step-by-step explanation:

When B is simplified, it becomes x^2-3x-10.  This is a polynomial because it has more than two terms(3).

Hope it helps <3

The solution is: the following is a polynomial, A. 4x^2+9x+12 & C. 15x^4

Option A and C are correct.

Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.

Here, we have,

we know that,

A polynomial is defined as an algebraic expression that consists of variables and constants involving operations of addition, subtraction, multiplication and non-negative exponents.

A. 4x^2+9x+12 is a polynomial

B. 3-√2x is not a polynomial

C. 15x^4 is a polynomial

D. 6x^2+2/x is not a polynomial

So, Option A and C are correct.

Hence, The solution is: the following is a polynomial, A. 4x^2+9x+12 &

C. 15x^4 , Option A and C are correct.

Know more about Polynomials here:

brainly.com/question/2833285

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Answer:

[tex]\huge\boxed{\cot\dfrac{3\pi}{2}=0}[/tex]

Step-by-step explanation:

[tex]\text{We know}\ \cot x=\cot(x\pm\pi)\ \text{and}\ \cot(-x)=-\cot x.\\\\\text{We have}\ \cot\dfrac{3\pi}{2}=\cot\dfrac{\pi+2\pi}{2}=\cot\bigg(\dfrac{\pi}{2}+\dfrac{2\pi}{2}\bigg)=\cot\bigg(\dfrac{\pi}{2}+\pi\bigg)=\cot\dfrac{\pi}{2}\\\\\cot\bigg(\dfrac{\pi}{2}\bigg)=0\\\\\text{Therefore}\ \cot\dfrac{3\pi}{2}=0.[/tex]

a. true

b. false ( angles should equal 180 125+65=190)

c. true

d. true

e. true

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

a. True (vertically opposite angles are equal)

b. False (angles on a straight line add up to 180 degrees)

c. True (corresponding angles are equal)

d. True (supplementary angles are angles that add up to 180 degrees)

e. True (alternating interior angles are equal)

Answer:

Step-by-step explanation:

1. 6x + 12 = 3x - 27

   3x + 12 = -27

   3x = -39

    x = -13

2. 2p - 3 = 3p + 2

    -p - 3 = 2

     -p = 5

      p = -5

3. 6x - 2 - 35x -28 = 18x - 27

   -29x - 30 = 18x - 27

   -47x - 30 = -27

    -47x = 3

    x = -3/47

Answer:

Step-by-step explanation:

Hello,

the line passes through (-8,11) means than y = 11 for x  = -8

I believe that you wanted to write the first one as below

[tex]y=-\dfrac{5}{8}x+6[/tex]

in that case for x = -8

y = - 5 * - 1 + 6 = 5 + 6 = 11

hope this helps

The solution is, : y = -5/8x +6, the equation represents the line that passes through (-8,11) and (4,7/2).

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

First we need to find the slope

m = (y2-y1)/ (x2-x1)

   = (7/2 -11)/(4--8)

   = (7/2 - 22/2)/(4+8)

   = (-15/2)/(12)

  = -15/24

Divide top and bottom by 3

  -5/8

Then we can use point slope form to write the equation

y-y1 = m (x-x1)

y- 11 =-5/8(x--8)

y- 11 =-5/8(x+8)

Distribute

y-11 =-5/8 x -5

Add 11 to each side

y-11 = -5/8x -5+11

y = -5/8x +6

Hence, The solution is, : y = -5/8x +6, the equation represents the line that passes through (-8,11) and (4,7/2).

To learn more on Equation 0f Straight-Line click:

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Answer: 22

Step-by-step explanation:

She sold two tubs of Oatmeal Raisins and it's 6 dollars a tub so we can do 6*2 or 6+6 (doesn't matter). We get $12. Then, she also sells 2 tubs of Peanut Butter, and since it's $5 a tub, then we do 5*2 or 5+5 to get 10. We add 12 and 10 (12+10) and get 22.

I'm not sure if this is right because you added $22, $24, $20, and $11 and I'm not sure what the purposes of those are.

Answer:

44 units²

Step-by-step explanation:

For triangles: (bases and heights of both triangles are equal)

Base = 4 units, height = 3 units

For trapezoid:

Base 1 = 5 units, base 2 = 3 units, height = 8 units

Area of figure = Area of two triangles + Area of trapezoid

= 2 *1/2 * base * height + 1/2(base 1+ base 2) *height

=4*3 + 1/2(5+3)*8

= 12 + 8*4

= 12 + 32

= 44 units²

The required area of the figure shown in the graph is given as 44 square units.

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

here,
The area of the given figure  is given as,
Area = Area of 1 + Area of 2 + Area  3 + Area 4
Area = length × width + [1/2× base × height] + [1/2× base × height] + [1/2× base × height]

Area = 8 × 3 + 1/2 × 4 × 3 + 1/2 × 4 × 3 + 1/2 × 8 × 2
Area = 44 square units.

Thus, the required area of the figure shown in the graph is given as 44 square units.

Learn more about the surface area here: https://brainly.com/question/2835293

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Answer: Degree of polynomial (highest degree) =4

Maximum possible terms =9

Number of terms in the product = 5

Step-by-step explanation:

A trinomial is a polynomial with 3 terms.

The given product of trinomial: [tex](x^2 + x + 2)(x^2 - 2x + 3)[/tex]

By using distributive property: a(b+c+d)= ab+ac+ad

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

Maximum possible terms =9

Combine like terms

[tex]x^4+x^3-2x^3+3x^2-4x+3x+6\\\\=x^4-x^3+3x^2-x+6[/tex]

Hence, [tex]\left(x^2\:+\:x\:+\:2\right)\left(x^2\:-\:2x\:+\:3\right)=x^4-x^3+3x^2-x+6[/tex]

Degree of polynomial (highest degree) =4

Number of terms = 5

Answer:

Sample Response: To determine the degree of the product of the given trinomials, you would multiply the term with the highest degree of each trinomial together. Both trinomials are degree 2, and when you multiply x2 by x2, you add the exponents to get x4. Thus, the degree of the product is 4. If the product is degree 4, and there is only one variable, the maximum number of terms is 5. There can be an x4 term, an x3 term, an  x2 term, an x term, and a constant term.

The degree of the product of the trinomials is 4 because the degree of each trinomial is 2.

The maximum number of terms in the product of the trinomials is 5.

There can be an x4 term, an x3 term, an x2 term, an x term, and a constant term.

Explanation:

This is the response on Edge 2020-21. Hope this helps, have a great day!

Answer:

Step-by-step explanation:

Total cookies = 12

Ate = 3 cookies

Now,

Percentage of the cookies that James are:

[tex] \frac{3}{12} \times 100 \: percent[/tex]

Calculate:

[tex] = 25 \: percent[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

answer is 25

Step-by-step explanation:

Complete Question

The complete question is shown on the first uploaded image  

Answer:

Yes the students are reasonably good at estimating one​ minute

a

  Option A is  correct

b

  The test statistics is  [tex]t = 0.354[/tex]

Step-by-step explanation:

From the question we are told that

    The  set of data is  

               68, 82 ,  38 ,  62 , 41, 25 , 57 ,  64, 67, 47, 61, 71, 91, 87, 64

     The  population mean is  [tex]\mu = 60[/tex]

The  level of significance is given as[tex]\alpha = 0.01[/tex]

    The  critical value for this level of significance obtained from the normal distribution table is  

         [tex]Z_{\alpha } = 2.33[/tex]

   The  null hypothesis is  

           [tex]H_o : \mu = 60 \ seconds[/tex]

   The alternative hypothesis is  

          [tex]Ha : \mu \ne 60 \ seconds[/tex]      

Generally the sample mean is mathematically represented as

       [tex]\= x = \frac{\sum x_i }{n }[/tex]

where  n = 15

 So  

      [tex]\= x = \frac{ 68+ 82 + 38 + 62 + 41+ 25 + 57 + 64+67+ 47+ 61+ 71+ 91+ 87+ 64}{15}[/tex]

      [tex]\= x = 61.67[/tex]

The standard deviation is mathematically represented as

     [tex]\sigma =\sqrt{ \frac{ \sum (x_i - \= x )^2}{n} }[/tex]

substituting values

      [tex]\sigma =\sqrt{ \frac{ \sum (68-61.67)^2 + ( 82-61.67 )^2 + (38 -61.67)^2 + 62-61.67)^2 + (41-61.67)^2 +(25-61.67)^2 +( 57+61.67)^2 }{15} }[/tex]           [tex]\sqrt{ \frac{ ( \cdot \cdot + ( 64-61.67)^2 + (67-61.67)^2 +(47-61.67)^2 + (61-61.67)^2+ (71-61.67)^2 + (91 -61.67)^2+( 87-61.67)^2 + (64-61.67)^2}{15} }[/tex]=>   [tex]\sigma = 18.23[/tex]

The  test statistics is evaluated as  

      [tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

       [tex]t = \frac{61.67 -60 }{ \frac{18.23 }{\sqrt{ 15} } }[/tex]

      [tex]t = 0.354[/tex]

Now comparing the statistics and the critical value of the level of significance we see that the the test statistics is less than the critical value

Hence the we fail to reject the null hypothesis which mean that these times are from a population with a mean equal to 60 seconds

So we can state that yes the students are reasonably good at estimating one minute given that the sample mean is not far from the population mean

Answer:

22.9 or round it up to 23

Step-by-step explanation:

SOHCAHTOA

C=A/H

acos (35/38)

=22.9

Answer: [tex]\dfrac{1}{6840}[/tex]

Step-by-step explanation:

According to the permutations:

The arrangement of n things in an order = n!

If we fix that the first, second, and third person for skating, then we to arrange only 17 of the skaters.

Number of ways to arrange rest of 17 skaters = 17!

Number of ways that Christie, Taylor, and Jona will  skate first, second, and third, respectively = 1 x 17!=17!

Number of ways to arrange all 20 skaters = 20!

Now, the required probability = [tex]\dfrac{\text{favourable outcomes}}{\text{total ways}}[/tex]

[tex]=\dfrac{17!}{20!}\\\\=\dfrac{1}{20\times19\times18}\\\\=\dfrac{1}{6840}[/tex]

Hence, the required probability = [tex]\dfrac{1}{6840}[/tex]

r = radius

h = r+12 = height, 12 more than the radius

[tex]V = \text{Volume of cone (oblique or not)}\\\\V = \frac{1}{3}\pi*r^2*h\\\\V = \frac{1}{3}\pi*r^2*(r+12)\\\\V = \frac{1}{3}\pi*r^2*r+\frac{1}{3}\pi*r^2*12\\\\V = \frac{1}{3}\pi*r^3+\frac{1}{3}*12\pi*r^2\\\\V = \frac{1}{3}\pi r^3+4\pi r^2\\\\[/tex]

ANSWER: SECOND OPTION

Answer:

-2 and -73

Step-by-step explanation:

simply divide 146 by any negative integer that can divide it fully

HINT:IT ENDS IN 6 SO TRY MULTIPLES AND FACTORS OF 6

and lastly don't forget that negative times negative equals positive

Answer:

Step-by-step explanation:

Hello,

[tex]2(x+3)^2-10\\=2[(x+3)^2-5]\\=2[(x+3)^2-(\sqrt{5})^2]\\\\=2[(x+3+\sqrt{5})(x+3-\sqrt{5})][/tex]

Hope this helps

Answer:

i like cheese and feet its  B A C D

Step-by-step explanation: