If a polynomial f(x) has a remainder of -6 when divided by x-5, what is f(5)?

Answer:

Inverse property

Step-by-step explanation:

3/4 is the reciprocal of 4/3 which means they would cancel each other out. So you would only be left with x=x

Based on the given parameters, the explicit rule of the sequence is b(n)= 2^n

The given parameters are

b(1) = 2

b(n) = 2 * b(n - 1) for n >= 2

Calculate b(2) and b(3) using the above equation

When n = 2, we have

b(2) = 2 * b(2 - 1)

This gives

b(2) = 2 * b(1)

So, we have

b(2) = 2 * 2

Evaluate

b(2) = 4

When n = 3, we have

b(3) = 2 * b(3 - 1)

This gives

b(3) = 2 * b(2)

So, we have

b(3) = 2 * 4

Evaluate

b(3) = 8

So, the sequence is

2, 4, 8.....

The above sequence is a geometric progression

The common ratio (r) is calculated as

r = b(2)/b(1)

So, we have

r = 4/2

Evaluate

r = 2

The explicit rule of the sequence is calculated as

b(n)= b(1) * r^n-1

So, we have

b(n)= 2 * 2^n-1

Evaluate

b(n)= 2^n

Hence, the explicit rule of the sequence is b(n)= 2^n

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Possible question

Calculate the explicit rule of the sequence

b(1)=2, b(n)=2⋅b(n−1)−1 for n≥2.

Answer:

0.3456432 repeating

Step-by-step explanation:

divide both numbers and then multiply.

Answer: 5/14 is the answer

Step-by-step explanation:

4/7 * 5/8 = 5/14 first you multiply 4 and 5 which equals 20, then you multiply  7 and 8 which is 56 so now you have 20/56 after that you simplify and divide by 4 so 20/4 is 5 and 56/4 is 14 that makes it 5/14

Based on the number of cups of fresh cranberries needed for a recipe that serves 16 people, the number of cups of cranberries to make 28 servings of cranberry sauce is 7 cups

The number of cups of cranberries varies with the servings of cranberry sauce in a direct relationship.

If 4 cups of fresh cranberries can make 1 servings of cranberry sauce then 28 servings would need:

4       :        16

c       :         28

112 = 16c

c = 112 / 16

c = 7 cups

In conclusion, 7 cups of fresh cranberries are needed.

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Answer:

Step-by-step explanation:

if f(x)=2x-4

then f(n+5)= 2(n+5)-4

                 =2n+10-4
                 =2n+6

The equation will be 3 y = 2 x + 12 for the graph given.

We are given a graph of the equation.

We need to find the equation of the graph.

Now, first we will see the x and y intercept of the graph.

So, we get that:

x intercept:

( - 6 , 0)

y intercept:

(0 , 4)

Now, we know that equation of the line is given by:

y = a x + b    … (1)

Put the points in the equation:

for (-6 , 0)

0 = - 6 a + b

6 a = b     … (2)

for (0 , 4)

4 = b

Put in (2)

6 a = 4

a = 4 / 6

a = 2 / 3

Put in equation (1):

y = 2 / 3 x + 4

y = ( 2 x + 12 ) / 3

3 y = 2 x + 12

Therefore, we get that, the equation will be 3 y = 2 x + 12 for the graph given.

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The average number of miles he would have to ride each day to meet his goal is 8 miles

From the question, we are to write an equation that can be used to determine m, the average number of miles he would have to ride each day to meet his goal

From the given information,

Landon wants to ride his bicycle 36 miles this week and he has already ridden 4 miles.

The average number of miles, m, he would have to ride for 4 more days to meet his goal is

m = (36-  4)/4

This is the equation that can be used to determine m, the average number of miles he would have to ride each day to meet his goal

Now, determine m

m = (36 - 4)/4

m = 32/4

m = 8

Hence, the average number of miles he would have to ride each day to meet his goal is 8 miles

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The histogram based on the data distribution where sample mean is less than sample median, the histogram would be skewed to the left.

Histogram is a type of visual (graphical) representation a set of data arranged in a user specific range. It is used summarize data – both discrete and continuous, measured on a interval scale.

When a data whose mean value or average value is less than the median or middle term in an ordered set is represented by a histogram, the shape of the histogram would be skewed to the left. Most of the data in such a histogram will be on the right side of the graph.

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he spends 86 dollars, thus 100-86=14

your answer is 14

The concentration of hydrogen ions in seawater is 3.126 × 10⁻⁶ mol / dm³.

The pH level of seawater is 8.5.

If the pH is 8.5, and If the pH is 8.5, Assuming that this is measured under normal circumstances, we can apply the following relationship:

pH + pOH = pK_(w)

At 25 degrees Celcius, pK_(w) = 14

Where K_(w) is the dissociation constant for water = 1.0 × 10⁻¹⁴,

(At 25° C) but pK_(w) is the negative logarithm of K_(w).

pK_(w) = − log₁₀[ K_(w) ]

From this, we can convert pH, the measure of H₃O⁺ ions, into pOH, the measure of OH⁻ ions in the seawater:

pH + pOH = 14

8.5 + pOH = 14

pOH = 14 - 8.5

pOH = 5.5

Now,

pOH = − log₁₀[ OH⁻ ]

10^{−pOH} = [ OH⁻ ]

So,

10⁻⁵·⁵ = [ OH⁻ ] ≈ 3.126 × 10⁻⁶ mol / dm³

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Answer:

[tex]5 \dfrac{2}{3}\; \textsf {pounds}[/tex]

Step-by-step explanation:

Each dig gets 17/3 lbs of dog food

173 = 5 2/3

Answer: -0.7

Step-by-step explanation:

Answer:

-0.7

Step-by-step explanation:

x = 4 is not an extraneous solution.

Given equation [tex]2(2x)^{1/3}[/tex] + 1 = 5

Subtracting 1 on both the sides of the equation, we get

[tex]2(2x)^{1/3}[/tex] + 1 - 1 = 5 - 1

[tex]2(2x)^{1/3}[/tex] = 4

Dividing the equation by 2, we get

[tex]2(2x)^{1/3}[/tex] = 2

Taking cube of both the sides of the equation, we get

2x = 8

x = 4

Check for extraneous solution by keeping the value of x in original equation

[tex]2(2x)^{1/3}[/tex] + 1 = 5

[tex]2(2(4))^{1/3}[/tex] + 1 = 5

[tex]2(8)^{1/3}[/tex] + 1 = 5

2(2) + 1 = 5

5 = 5

LHS = RHS

Thus, x = 4 is not an extraneous solution.

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A polynomial function with rational coefficients and the given roots √3,-5 is :  x² + (5-√3)x -5√3

In mathematics, polynomial function can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as monomials, quadratic equation, cubic equation, linear equation of one degree, two degree and more  which has non  negative number as their powers all are part of polynomial equation and can be taken as types of the polynomial equations.

Some examples of polynomial equation are :

According to question,

roots are √3 , -5

Thus the factors are :

(x - √3 ) ( x - (-5) )

=> ( x - √3 )( x + 5 )

=> x²+ 5x - √3x - 5√3

=> x² + (5-√3)x -5√3      

Thus polynomial function for given roots is x² + (5-√3)x -5√3

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Answer:

[tex]\frac{8}{27}[/tex]

Step-by-step explanation:

[tex]\frac{9}{4} ^{-\frac{3}{2} }[/tex]

reciprocate to remove the minus sign

[tex]\frac{4}{9} ^{\frac{3}{2} }[/tex]

take square root to remove the 2

[tex]\sqrt({\frac{4}{9}) ^{3} }[/tex]

[tex](\frac{2}{3} )^{3}[/tex]

[tex]\frac{8}{27}[/tex]

hope this helped :)

The lowest common multiple of 4 and 6 is 12

The lowest common multiple of 3 and 7 is 21.

The lowest common multiple of 5 and 10 is 10.

The lowest common multiple of 6 and 9 is 18.

The lowest common multiple of 4 and 6:

Multiple of 4 = 4 , 8, 12, 16, 20.

Multiple of 6 = 6, 12, 18, 24, 30

The lowest common multiple of 3 and 7:

Multiple of 3 =3, 6, 9, 12, 15, 18, ,21

Multiple of 7 = 7, 14, 21

The lowest common multiple of 5 and 10:

Multiple of 5 = 5, 10,

Multiple of 10 = 10, 20

The lowest common multiple of 6 and 9:

Multiple of 6 = 6, 12, 18, 24.

Multiple of 9 = 9, 18, 27

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The percentage of the students who go to the movies twice a month or less and the percentage of the students that prefer comedies

40%

74%

This is further explained below.

Generally, the equation for is  mathematically given as

(a) Total number of students =200

Number of students who prefer action movies twice a month or less =60 Triceamonth or more =20

Therefore students prefer action makes =(60+20)/200

[tex]=\frac{\theta \phi}{200} 100\%[/tex]

=40%

(b) Number of students who go to movies twice a month er less,

For action =6o

For comely 88

Therefore % of students go to the movies twice a month or less -[tex]\left(\frac{60+80}{200}\right) \times 100 \%=(80+44)[/tex]$.

=74%

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When all the four operations namely addition, subtraction, multiplication and division are involved in a problem, we perform the operations in the following sequence from left to right i.e. division, multiplication, addition and subtraction, remember the order as DMAS.

Easy and simple way to remember PEMDAS rule!!

P → Parentheses first

E → Exponent (Powers, Square Roots, Cube Roots, etc.)

MD → Multiplication and Division (start from left to right)

AS → Addition and Subtraction (start from left to right)

Note:

(i) Start Multiply/Divide from left side to right side since they perform equally.

(ii) Start Add/Subtract from left side to right side since they perform equally.

For Example; (7 + 8) × 3

First solve inside ‘parentheses’ 7 + 8 = 15, then 15 × 3 = 45.

Next solve the mathematical 'Exponent'.

For Example; 32+ 5

First solve ‘exponent’ part 32= 3 × 3 = 9, then 9 + 5 = 14.

Next, the part of the equation is to calculate 'Multiplication' and 'Division'.

We know that, when division and multiplication follow one another, then their order in that part of the equation is solved from left side to right side.

For Example; 21 ÷ 7 × 12 ÷ 2

‘Multiplication’ and ‘Division’ perform equally, so calculate from left to right side. First solve 21 ÷ 7 = 3, then 3 × 12 = 36, then 36 ÷ 2 = 18.

In the last part of the equation is to calculate 'Addition' and 'Subtraction'. We know that, when addition and subtraction follow one another, then their order in that part of the equation is solved from left side to right side.

For Example; 9 + 11 - 13 + 15

‘Addition’ and ‘Subtraction’ perform equally, so calculate from left to right side. First solve 9 + 11 = 20, then 20 - 13 = 7 and then 7 + 15 = 22.

These are simple rules need to be followed for simplifying or calculating using PEMDAS rule.

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Answer:

(C) is correct.

Step-by-step explanation:

-12.8308

- as you can see this is a terminating decimal, with last digit = 8.

Time taken by the copier to copy 60 color pages and 35 black and white pages is 3.7 minutes ( Option I ).

Given,

Time taken to copy pages ⋉ The number of pages being copied

Number of colour pages that can be copied in 1 minute = 21

Number of black and white pages that can be copied in 1 minute = 35

To find : Time taken by the copier to copy 60 color pages and 35 black and white pages

Given options :

(F) 0.9 minute (H) 2.9 minutes(G) 2.5 minutes (I) 3.7 minutes

Time taken by the copier to copy 60 colour pages

= 60 * 1 / 21 = 60 / 21 = 2.857 minutes

Time taken by the copier to copy 35 black and white pages

= 35 * 1 / 40 = 35 / 40 = 0.875 minutes

Total time taken by the copier to copy 60 color pages and 35 black and white pages

= 2.857 + 0.875 = 3.732 minutes

Therefore, time taken by the copier to copy 60 color pages and 35 black and white pages as 3.7 minutes.

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Answer:

166 degrees

Step-by-step explanation:

So first we need to find the angles in the triangle. One of the angles is 83 degrees since it's 180-97. Since the triangle is isosceles, the angle 'on top' of it is also 83 degrees. To find the last angle, you do 180-83-83, which is 14 degrees. To find x, you need to subtract 14 from 180, which is 166 degrees

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}}{\stackrel{slope}{\cfrac{2}{3}}~\hfill \stackrel{reciprocal}{\cfrac{3}{2}}~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{2}}}[/tex]

so, we're really looking for the equation of a line whose slope is -3/2 and that it passes through (2 , -6)

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{- \cfrac{3}{2}}(x-\stackrel{x_1}{2}) \implies y +6= -\cfrac{3}{2} (x -2) \\\\\\ y+6=-\cfrac{3}{2}x+3\implies y=-\cfrac{3}{2}x-3[/tex]

Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width

now we also know that

length = 1/3 × width + 5

so, when we bring this into the main equation for the perimeter :

2× (1/3 × width + 5) + 2×width

2/3 × width + 10 + 2×width

2/3 × width + 10 + 6/3 × width

8/3 × width + 10

Expression as a single natural logarithm. 1/3(ln x+ln y)-4 ln z is

[tex]ln( xy^{1/3})[/tex] -[tex]ln (z^{4} )[/tex]

[tex]ln (xy^{1/3} /z^{4} )[/tex]

The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

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Answer:  [tex]y=-\frac{14}{5}[/tex]

Solving Linear Equations:

Solution with Steps:

[tex]14 =-5y[/tex]

[tex]\frac{14}{-5}=\frac{-5y}{-5}[/tex] - divide both sides by -5 to isolate for the variable

[tex]-\frac{14}{5}=y[/tex] - simplify to get your final answer

Answer: Not the solution

Step-by-step explanation:

Answer:

x=5+4

x=9

hope this helps

Answer:

28 = x

Step-by-step explanation:

We have two similar triangles.  The ratio of the sides must be in the same proportion

12           8

------- = -------

x-7         14

Using cross products

12 * 14 = 8(x-7)

168 = 8(x-7)

Divide each side by 8

168/8 = 8(x-7)/8

21 = x-7

Add 7 to each side

21+7 = x-7+7

28 = x

The algebra property used on -9.97 + (4.68 + 13.08)= (-9.97 + 4.68) + (13.08) is; Associative property of addition.

We are given the number expression;

-9.97 + (4.68 + 13.08) = (-9.97 + 4.68) + (13.08)

There are different algebraic properties such as Associative Property, Commutative Property, distributive property, e.t.c

Now, Associative property of addition states that changing the grouping of addends does not change the sum.

For example, (4 + 5) + 6 = 4 + (5 + 6)

Similarly; (7 + 8) + 9= 7 + (8 + 9)

Looking at our question, we see that the only thing that was changed is the grouping of addends and it did not change the sum. This, we conclude that algebra property used is Associative property of addition.

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