expand g(x)=8x−1 in powers of (x−1).

The distance between the points (23,-33) and (4,9) rounded to two decimal places is 46.10.

The distance between two points on a graph can be determined using the equation;

D = √[ ( x₂ - x₁ )² + ( y₂ - y₁ )² ]

Given that;

We substitute our values into the equation above.

D = √[ ( x₂ - x₁ )² + ( y₂ - y₁ )² ]

D = √[ ( 4 - 23 )² + ( 9 - (-33) )² ]

D = √[ ( -19 )² + ( 42 )² ]

D = √[ 361 + 1764 ]

D = √[ 2125 ]

D = 46.10

Therefore, the distance between the points (23,-33) and (4,9) rounded to two decimal places is 46.10.

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Answer:

30000J or 30 KJ

Step-by-step explanation:

Formula for finding Gravitiational Potential Energy or GPE = mgh (or Wh since W = mg)

Given

W = 100N

h = 300m,

GPE = Wh = 100 x 300 = 30000J or 30 KJ

Answer: All real numbers

Step-by-step explanation:

The domain is the set of inputs.

I think it is 6. It may be because we can see the intersect of line is in (1,6) and (-1,-6). So I think that it is 6.

(a) The median mark is 44

(b) The number of students who scored 54 marks or less is 120

(c) The number of students who scored 60 marks or more is 20

From the question, we are to determine the median mark

The median mark for a cumulative frequency curve corresponds to the second quartile (Q₂)

Q₂ = 1/2(n+1)th mark

Where n is the total frequency

In the graph,

n = 160

∴ Q₂ = 1/2(160+1)th mark

Q₂ = 80.5th mark

The 80.5th mark is 44

∴ The median mark is 44

(b)

The number of students who scored 54 marks or less = 120 - 0

The number of students who scored 54 marks or less = 120

(c)

The number of students who scored 60 marks or more = 160 - 140

The number of students who scored 60 marks or more = 20

Hence, (a) The median mark is 44

(b) The number of students who scored 54 marks or less is 120

(c) The number of students who scored 60 marks or more is 20

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By this equation y = 1,716 - 112x he find that how much money he still owes after each month of the plan.

According to the statement

Jonathan bought a new computer for $1,716

He will pay $143 a month for 12 months.

Total amount he will for 12 months is 143(`12)

Now,

y = the money he still owes

x = the number of months (from x = 0 to x = 12)

y = 1,716 - 112x

So, By this equation y = 1,716 - 112x he find that how much money he still owes after each month of the plan.

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The volume of wood in the tree's trunk as it grows is [tex]16\pi r^3[/tex]

The capacity of a cylinder, which determines how much material it can carry, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, may be immersed in it uniformly. A cylinder is a three-dimensional structure having two parallel, identical bases that are congruent.

Thus, the volume (V) of a right circular cylinder, using the above formula, is, [tex]V = \pi r^2h[/tex] , where

'r' is the radius of the base (circle) of the cylinder

'h' is the height of the cylinder

Given:

Height(h) = 8 x diameter = 16 x radius (r)      (diameter = 2 x radius )

∴ h = 16r.

V= [tex]\pi r^2h[/tex]

Substituting h = 16r in the volume formula we get

V = [tex]\pi r^2(16r)[/tex] =  [tex]16\pi r^3[/tex]

Thus the volume of wood in the tree's trunk as it grows is [tex]16\pi r^3[/tex].

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Answer:

1.x=0, –10

2.x=3, 4

Step-by-step explanation:

1.

x(x+10)=0===> x=0, –10

2.

x²–3x–4x+12===> x²–7x+12=0

(x–3)(x‐4)=0====> x=3, 4

Answer:

Step-by-step explanation:

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     3

                     B   =    -2

                     C   =  -10

 B2  -  4AC   =

       4 - (-120) =

             =  124

Applying the quadratic formula :

              2 ± √ 124

  x  =    —————

                   6

 √ 124 simplified

 The prime factorization of  124   is

  2•2•31

To be able to remove something from under the radical, there have to be  2  instances of it

√ 124   =  √ 2•2•31   =

               ±  2 • √ 31

 √ 31, rounded to 4 decimal digits, is   5.5678

So now we are looking at:

          x  =  ( 2 ± 2 •  5.568 ) / 6

Two real solutions:

x =(2+√124)/6=(1+√ 31 )/3= 2.189

or:

x =(2-√124)/6=(1-√ 31 )/3= -1.523

Answer:

Step-by-step explanation:

3x^2-2x-10=0

This is a quadratic equation that can be solved using the quadratic formula where

a = 3, b = -2, and c = -10

x=−b±(b^2−4ac)^(1/2)/2a

x=−(−2)±((−2)2−4(3)(−10)^(1/2)/2(3))

x=2±(124)^(1/2)/6

Simplify the Radical:

x=((2/6) ±2(31)^(1/2))/6

x=26±231−−√6

Simplify fractions and/or signs:

x=1/3±√31/3

which becomes

x=2.18925

See the attached image for a more clear display of solving using the quadratic equation.

x=−1.52259

Answer: 768

Step-by-step explanation:

3, 6 ,12 ,24, 48, 96, 192, 384, 768

12 x 2 = 48

48 x 2 = 96

96 x 2 = 192

192 x 2 = 384

384 x 2 = 768

The correct option is C. Isolating a variable in one of the equations.

The first step in solving a system of nonlinear equations by substitution is to isolate a variable in one of the equations.

A set of two or more equations in two or more variables that includes at least one nonlinear equation is referred to as a system of nonlinear equations.

The method to solve a system of nonlinear equations by substitution is-

The importance of systems of nonlinear equations are-

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The complete question is-

Which is most likely the first step in solving a system of nonlinear equations by substitution?

A. Substituting a number for one of the variables

B. Substituting one equation into the other equation

C. Isolating a variable in one of the equations

D. Taking the square root of both sides of one of the equations

Answer:

Isolating a variable in one of the equations.

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

35 - 2x = 23

35 - 23 - 2x = 0

35 - 23 = 2x

12 = 2x

x = 6

35- 2x = 23

Subtract 35 from both sides.

Subtract 35 from 23 to get −12.

Divide both sides by −2.

Divide −12 by −2 to get 6.

The odds in favor of winning $5 or more is 3 : 13

The odds of winning $5 or more can be determined by finding the ratio of the total value of tickets that have a value of $5 or greater to the total value of tickets.

Total number  of the tickets that have a value of $5 or more = 25 + 5 = 30

Total number of ticket  = 25 + 5 + 100 = 130

Ratio : 30 : 130

3 ; 13

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Answer:

[tex]-\frac{61}{14}[/tex]

Step-by-step explanation:

Question: 5 - 7(z+1) = 7(-9-3z)

We multiply the number in front of the bracket first, since that is multiplication.

--> 5 -7z -7 = -63 - 21z

--> -7z -2 = -63 - 21z

Now, we move all the z and all the numbers to each side.

--> -7z +21z = -63 +2

--> 14z = -61

--> z = -61/14

This cannot be simplified further, so z is -61/14.

Based on the calculations on this parallelogram, the correct equations are:

Based on the image of the parallelogram shown in the image attached below, we can logically deduce that the opposite sides of this parallelogram are all equal. Thus, we have:

Side DE = Side CF

6n - 1 = 5n + 9

6n - 5n = 9 + 1

n = 10.

From Side CF, we have:

CF = 5n + 9

CF = 5(10) + 9

CF = 59.

For the measure of side FE, we have

FE = 4n + 2

FE = 4(10) + 2

FE = 42.

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Complete Question:

Figure CDEF is a parallelogram.

Parallelogram C D E F is shown. The length of F C is 6 n minus 1, the length of C D is 4 n + 2, and the length of D E is 5 n + 9.

Which equations are correct? Select three options.

n = 10

n = 7

CF = 59

FE = 42

CD = 30

Answer:

A,C,D

Step-by-step explanation:

Using multiplication, the total score on the exam if you answered 13 questions correctly, leave 7 questions blank and answer 5 questions incorrectly is 39 point.

According to the question,

For each correct question, you get 2 points, and there are 22 correct questions, so multiply 22 by 2

22 * 2 = 44 points.

For each question left blank, you get 0 points, and there are 7 questions left blank, so multiply 7 by 0

7 * 0 = 0 points

For each incorrect question, you get -1 point, and there are 5 incorrect questions, so multiply 5 by -1

5 * (-1) = -5 points.

The total number of score = 22*2 + 7*0 + 5*(-1) = 44 + 0 - 5 = 39 points.

Hence, using multiplication, the total score on the exam if you answered 13 questions correctly, leave 7 questions blank and answer 5 questions incorrectly is 39 point.

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Answer:

A. f(-x) = f(x)

Step-by-step explanation:

When plugged into a graph, we can see that the y value of -x is equal to x.

This means, that if we compare the y value of x=3 and x=-3, they will be the same on the graph.

Answer:

a. 25 seniors are randomly selected; 14 plan to go to a 4 year college

b. 420 students

Step-by-step explanation:

a. the less they have in common, the better

b. 14/25 is only between 25 students. make the denominator the same (750) and multiply the same to the numerator

750/25 = 30

14/25 x 30 = 420/750

Answer:

see explanation

Step-by-step explanation:

(a)

play ends at 9 : 55 pm

15 minutes to get to bus stop , then time is

9 : 55 + 15 min = 10 : 10 pm = 22 : 10

the earliest bus she can catch is 22 : 25

(b)

time to wait 22 : 10 → 22 : 25 = 15 minutes

Answer:

  $70,300

Step-by-step explanation:

The amount Kaydence saved is the value of an arithmetic series with first term 100 and common difference 100. The number of terms in the sum is 37. The formula for the sum can be used.

The formula for the sum of n terms of an arithmetic series is ...

  Sn = (2a1 +d(n -1))(n/2) . . . . . . first term a1, common difference d

The number of terms being added is ...

  2050 -2014 +1 = 37 . . . . . . years Kaydence made deposits

The formula with a1=100, d=100, and n=37 is ...

  [tex]S_{37}=(2\cdot100+100(37-1))\dfrac{37}{2}=\dfrac{(200+3600)\cdot37}{2}\\\\S_{37}=70,\!300[/tex]

Kaydence would have saved $70,300 by the end of Jan 1, 2050.

Question 2

1) [tex]\overline{PR} \perp\overline{QS}, \overline{PQ} \cong \overline{PS}[/tex] (given)

2) [tex]\overline{PR} \cong \overline{PR}[/tex] (reflexive property)

3) [tex]\angle PRQ, \angle PRS[/tex] are right angles (perpendicular lines form right angles)

4) [tex]\triangle PRQ, \triangle PRS[/tex] are right triangles (a triangle with a right angle is a right triangle)

5) [tex]\triangle PRQ \cong \triangle PRS[/tex] (HL)

Question 3

1) [tex]\angle C[/tex] is a right angle, [tex]\overline{AC} \cong \overline{AE}, \overline{DE} \perp \overline{AB}[/tex] (given)

2) [tex]\angle DEA[/tex] is a right angle (perpendicular lines form right angles)

3) [tex]\triangle ACD, \triangle DAE[/tex] are right triangles (a triangle with a right triangle is a right angle)

4) [tex]\overline{AD} \cong \overline{AD}[/tex] (reflexive property)

5) [tex]\triangle ACD \cong \triangle AED[/tex] (HL)

6) [tex]\angle CAD \cong \angle DAE[/tex] (CPCTC)

7) [tex]\overline{AD}[/tex] bisects [tex]\angle BAC[/tex] (if a segment splits an angle into two congruent parts, it is an angle bisector)

Answer:

4 is the smallest possible number of integers in the list.

Answer:

16. C

17. C

Step-by-step explanation:

16.

this is just a multiplication of the 2 functions.

that means we multiply the functional expressions, and the result is the new functional expression of the multiplied functions.

2(3x - 5) × (-2x + 1) = (6x - 10) × (-2x + 1) =

= 6x×-2x + 6x×1 + -10×-2x + -10×1 =

= -12x² + 6x + 20x - 10 = -12x² + 26x - 10

17.

the domain of a function is the interval or set of all valid x values (or input values).

the range is the interval or set of all valid y or functional result values.

so, for the domain we need to see what values x may have for a 4th root.

for this we can imagine that a 4th root is the square root of the square root of x.

this is directly related to x⁴ being the square of the square of x.

the valid input values for a square root are all positive numbers (incl. 0). the result will be again a positive number (incl. 0), which is again a valid input number for the second square root.

therefore, the valid values of x for a 4th root are also the valid values for a square root. and vice versa.

and that is

0 <= x < infinity

FYI : we can never say x = infinity, because infinity is not a number, just a generation concept. so, infinity can never be included in any interval, it can only be listed as an excluded limit concept.

Using translation concepts, the graph that represents a reflection across the x-axis of [tex]g(x) = \frac{3}{4}(3)^x[/tex] is:

On a coordinate plane, an exponential function approaches y = 0 in quadrant 4. The function comes up from quadrant 3 and increases into quadrant 4. It goes through (negative 2, negative 5), (0, negative 3), and (4, negative 1).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

A reflection across the x-axis of g(x) means that:

f(x) = -g(x).

g(x) increases from the second quadrant into the first, hence for f(x) it will be from quadrant 3 into quadrant 4.

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Answer:

Option B

Step-by-step explanation:

Edge 2022

Using a system of equations, it is found that 10,000 children attended the park that day.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

The attendance at the amusement park is 30,000 attendees, hence:

c + a = 30,000, which is the first equation in matrix form.

Then:

a = 30,000 - c

The cost of attending an amusement park is $10 for children and $20 for adults. The total money earned by the park is $500,000, hence:

10c + 20a = 500,000, which is the second equation in matrix form.

Since a = 30,000 - c, we replace:

10c + 20a = 500,000

10c + 20(30000 - c) = 500,000

10c = 100,000

c = 10,000.

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The relationship is not an inverse variation because the product xy is not a constant.

Inverse variation is the relationship between two quantities whereby an increase in one quantity cause a decrease in the other quantity.

In this type of variation the product of the two quantities is constant.

Analysis:

if x is one quantity and y is the other,

Mathematically, x = [tex]\frac{k}{y}[/tex]

Where, k is a constant,

it means k = xy

from the table, when, x =2, y = 409, xy = 2 x 409 = 818

Also, x = 3, y = 240, xy = 3 x 240 = 720

Therefore, 720 not equal to 818.

In conclusion, The product xy is not a constant, so the relationship is not an inverse variation.

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Answer:

Step-by-step explanation:

You have 35 coins. they are all quarters and nickels. if you have $3.15, how many nickels and how many quarters do you have?

Based on the number of years till maturity and the required rate of return, the price of the zero-coupon bond is $852.22.

When a bond's par value is not given, assume it is $1,000.

the price of a zero coupon bond is:

= par value / (1 + rate) ^ number of years till maturity

solving gives:

= 1,000 / (1 + 3.25%)⁵

= 1,000 / 1.17341139582939453125

= $852.22

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Step-by-step explanation:

vat of a cap=13/100*452

=58.76

price after vat=58.76+452=510.76

price after vat of 5 cap = 510.76*5=2553.8