please show all work

Using either method, we can conclude that x - 5 is a factor of the polynomial

This is further explained below.

Explain, based on the fact that, using either approach, whether or not we can consider x-5 to be a factor in the polynomial.

Generally, the equation for the problem is mathematically given as

f(x)=x^3-x^2-17 x-15

Therefore,  If (x-5) is factor of f(x) then at x=5 ,f(x)=0 then apply this

[tex]\begin{aligned}f(x) &=5^3-5^2-17 \times 5-15 \\&=125-25-85-15 \\&=0\end{aligned}[/tex]

In conclusion,Since f(x) is equal to 0 when x = 5, the factor of f is (x-5) (x).

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Answer:

61

Step-by-step explanation:

The answer to the expression [2-|-2/3-2(-1/5)|] divided by 13 is 2/15 .

In the question ,

the expression is given as

=[2-|-2/3-2(-1/5)|] divided by 13

which means

= [2-|-2/3-2(-1/5)|] ÷ 13

Solving the terms inside [ ] first , we have

-2*(-1/5) = 2/5

Substituting the value of -2*(-1/5) in the expression , we get

= [2-|-2/3+2/5|] ÷ 13

Solving the norm(modulus) first

|-2/3+2/5| = |-10/15+6/15|  = |-4/15| = 4/15

Substituting the value of |-2/3+2/5| in the expression , we get

= [2-4/15] ÷ 13

Simplifying further we get ,

= [30/15-4/15] ÷ 13

= [26/15] ÷ 13

= [tex]\frac{\frac{26}{15} }{13}[/tex]

= [tex]\frac{26}{15} \times \frac{1}{13}[/tex]

= 2/15

Therefore , the answer to the expression [2-|-2/3-2(-1/5)|] divided by 13 is  2/15 .

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Considering the definition of an equation and the way to solve it, the girls will both pay the same if they buy six pairs of pants and one sweater.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear.

The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.

To solve an equation, keep in mind:

Being "x" the number of pairs of pants, you know that:

The equation in this case is:

17.95x + 24 = 18.95x + 18

Solving:

24 -18= 18.95x - 17-95x

6= x

Finally, this means that Kelsey and Jeana pay the same if they buy six pairs of pants and one sweater.

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Given the triangle LMN and the line (n)

We will find the image of the triangle LMN after the reflection over the line (n)

So, from each point, construct a line segment perpendicular to the line (n)

Then make sure the distance between the point and the line is the same as the line and the image point.

the reflection of the triangle will be as shown in the following figure:

The x-intercept of the function is found to be x = (y + 80)/5 and the values of x calculated are 17,18,19 and so on.

Given, the x-axis and y-axis are intersected by two intercepts, P(2,0) and Q(0,3). => 3x + 2y – 6 = 0, Consequently, the line's equation is 3x + 2y - 6 = 0. Figure.

A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.

The given function is:

f(x) = 5x¹ - 80

Let,

y = f(x)

∴ y = 5x – 80

  y + 80 = 5x

  (y + 80)/5 = x

∴ x = (y + 80)/5

If y = 5,

x = (5 + 80)/5 = 17

If y = 10,

x = (10 + 80)/5 = 18

If y = 15,

x = (15 + 80)/5 = 19

Thus, by substituting y values in multiples of 5, we can get x values as 17, 18, 19 and so on.

Thus, the x-intercept of the function is found to be x = (y + 80)/5 and the x values calculated are 17,18,19 and so on.

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Answer:

Proofs provided below

Step-by-step explanation:

[tex]\bold {\text{Prove } (a + b)^2 = a^2 + 2ab + b^2}}[/tex]

[tex]\\\\\implies (a + b)^2 = (a+b) \times (a+b)\\\\\implies (a + b)^2 = a \times (a+b) +b \times (a+b)\\\\\implies (a + b)^2 = a \times a + a \times b + b \times a + b \times b\\\\\implies (a + b)^2 = a^2+ab+ba+b^2\\\\\implies (a + b)^2 = a^2+ab+ab+b^2 \;\;\;\;\text{ since ab = ba}\\\\\implies (a+b)^2 = a^2+2ab+b^2\\\\[/tex]

[tex]\bold{\text{Prove } a^2-b^2 \,=\, (a+b)(a-b)\\\\}[/tex]

1. Add and subtract ab to LHS
[tex]\implies a^2-b^2 = a^2-b^2-ab+ab\\\\\implies a^2-b^2 = a^2-ab+ab-b^2\\\\[/tex]

2. Factorize the above expression
[tex]\implies a^2-b^2 = a(a-b)+b(a-b)\\\\\implies a^2-b^2 = (a-b)(a+b) \;\;\;\; \text{since (a-b) is a common factor in RHS }[/tex]

∴  (a² - b²) = (a - b) (a + b)

[tex]\bold{\text{Prove $\dfrac{\sqrt{3}+1}{\sqrt{3}-1}$= $2+\sqrt{\ensuremath{3}}$}}\\[/tex]

[tex]\text{1. Multiply LHS by $\dfrac{\sqrt{\text{}3}-1}{\sqrt{3}-1}$}\\\\\implies $\dfrac{\sqrt{\text{}3}+1}{\sqrt{3}-1}$ \times $\dfrac{\sqrt{\text{}3}-1}{\sqrt{3}-1}$ \\\\[/tex]

[tex]\implies \dfrac{ (\sqrt{3} + 1)(\sqrt{3}-1) }{(\sqrt{3} - 1)(\sqrt{3}-1) }\\\\[/tex]

Numerator is
[tex](\sqrt{3} + 1)(\sqrt{3}-1) = (\sqrt{3})^2 - 1^2 = 3 - 1 = 2\\\\[/tex]

Denominator is
[tex](\sqrt{3}-1)^2 = (\sqrt{3})^2 - 2\cdot \sqrt{3} \;\cdot 1 + (-1)^2\\\\= 3 - 2 \sqrt{3} + 1\\\\= 4 - 2 \sqrt{3}\\\\[/tex]

So LHS becomes
[tex]\dfrac{2}{4 - 2\sqrt{3}} \\\\[/tex]

Dividing numerator and denominator by 2 yields

[tex]\dfrac{2}{4 - 2\sqrt{3}} = \dfrac {1}{2 - \sqrt{3}}[/tex]

Multiply numerator and denominator by [tex]{2-\sqrt {3}}[/tex]

[tex]$\dfrac{1\cdot(2+\sqrt{3})}{(2-\sqrt{3})(2+\sqrt{3)}}$[/tex]

[tex]=$\dfrac{\ensuremath{2}+\sqrt{3}}{2^{2}-(\sqrt{3)^{2}}}=$$\dfrac{\ensuremath{\ensuremath{2}+\sqrt{3}}}{4-3}=\ensuremath{2}+\sqrt{3}$[/tex]

Hence Proved

Answer:

see explanation

Step-by-step explanation:

assuming the dilatation is centred at the origin

then multiply each of the original coordinates by the scale factor 2

A (1, 1 ) → A' (2(1), 2(1) ) → A' (2, 2 )

B (5, 2 ) → B' (2(5), 2(2) ) → B' (10, 4 )

C (3, 5 ) → C' (2(3), 2(5) ) → C' (6, 10 )

The inequality that represents the possible number of hours the chemistry club could rent the meeting room is 13 + 4t ≤ 33 or t ≤ 5.

The possible numbers of hours the chemistry club could rent the meeting room are  1, 2, 3, 4 and 5 hours.

Given that:-

Reservation fee charged to rent the meeting room by college = $ 13

Additional fee per hour charged by the college = $ 4

The maximum amount the chemistry club want to spend on meeting room = $ 33

Let t be the number of hours.

Hence,

13 + 4t ≤ 33

4t  ≤ 33 - 13

4t  ≤ 20

t  ≤ 5 hours.

Hence, the possible number of hours the meeting room can be booked by chemistry club are 1, 2, 3, 4 and 5 hours.

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If 1/4 of the box is green apples, then 3/4 of the box is red apples. Thus, 3 times the number of green apples is equal to the number of red apples, which would give 3 * 5 = 15 red apples.

The probability of winning the minimum award of $100 in the lottery is [tex]\frac{113}{140448}[/tex]

The probability of picking first winning number (out of 57 white balls) is [tex]\frac{1}{57}[/tex]

Now, out of the remaining 56 white balls, the probability of picking second winning number is [tex]\frac{1}{56}[/tex]

So total probability of the correctly matching two numbers drawn from the white balls is  [tex]\frac{1}{57} + \frac{1}{56}[/tex]

Next, to match the winning number on the gold ball, probability of this event is [tex]\frac{1}{44}[/tex]

Thus overall probability of winning the minimum award is calculated by multiplying the individual probabilities of aforesaid two independent events as follows:

[tex](\frac{1}{44}) (\frac{1}{57}+\frac{1}{56})[/tex]

= [tex]\frac{113}{140448}[/tex]

Above value is the probability of winning the minimum award of $100.

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Answer:

wouldn't y=8?

Step-by-step explanation:

if x is 3

-5(3)+2y=1

-15+2y=1

2y=16

y=8

oluition

or this case we have the folllowing:

Part a

e select (0,0) and (3,24)

the slope would be:

then the equation for this case would be:

y= 8x +b

Using (0,0) we can find b:

0 ) 8*0 +b

b= 0

Then the equation is:

y= 8x

Part b

or this case we can conclude that for each n8 passengers is required a new car for the rooller coaster

Answer:

B, D, E

Step-by-step explanation:

We can find the area of B since the height and lengths is known, so the area is just 2*4 = 8 cm^2
D also has the height and length given, it is 4*3 = 12 cm^2
E gives 3 values, but only focus on the height and length, which are 2 and 5 respectively. 3 is also a side length, but there is no height to match that length. The area of E is 2*5 = 10 cm^2

The reasons A, C, and F don't work:
A seems like it would work, until you realize that 5 is a height, not a length, and so is 2. They are both heights, and multiplying heights together won't usually get you an accurate area unless the shape is a rectangle.
C has a length, but no height. the 3 cm is pretty much an arbitrary measurement.
F has two lengths, which would only give the area if the shape was a rectangle, which it is not.

The given coordinate's line of reflection is the x-axis, Option D.

After intersecting the co-ordinates A(-3,5), B(2,8) and C(-4,-5) of line 1 and co-ordinates A'(-3,-5), B'(2,-8) and C'(-4,5) of line 2. It is deduced that both lines are similar.

The point of intersection of lines 1 and 2 is on the X-axis as the reflection of the coordinate,

A(-3,5) on the negative x-axis and positive y-axis is A'(-3,-5) on the negative y-axis and the negative x-axis.

B(2,8) on the positive x-axis and positive y-axis is B'(2,-8) on the negative y-axis and the positive x-axis.

C(-4,-5) on the negative x-axis and negative y-axis is C'(-4,5) on the positive y-axis and the negative x-axis.

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The division of  8 1/2 by the positive difference between 4 4/5 and 7 7/10 is 85/29.

We can find the difference between 4 4/5 and 7 7/10, but we will need to convert the mixed number into the improper fraction as

Then we have 24/5 and 77/10, then the difference between the values are:(77/10 - 24/5) = 29/10

Then we can proceed to find the division of this number that we got from the difference as ( 29/10)/  8 1/2

But we can make the  8 1/2 as improper fraction from the mixed fraction it was 17/2

Then the division of the values will be   ( 17/2)/ ( 29/10)  = 85/29

Therefore the division is 85/29.

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There are 14 students in set R.

There are 10 students in set R but not in set S.

There are 11 students in set S.

There are 21 total students in sets R and S.

There are 4 students common to sets R and S.

The music teacher will get $280 for the piano students.

The music teacher will get $140 for the saxophone students.

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[tex]x^{2} +5x-3=-4x-3\\x^{2} +5x+4x-3+3=0\\x^{2} +9x=0\\\\x(x+9)=0\\x=0 or x+9=0\\x= -9[/tex]

I hope this helps.

Answer:

x = 0

or

x = (-9)

Step-by-step explanation:

[tex] {x}^{2} + 5x - 3 = - 4x - 3[/tex]

transfer like terms to the same side of the equation

[tex] {x}^{2} + 5x + 4x = - 3 + 3[/tex]

Add/subtract like terms

[tex] {x}^{2} + 9x = 0[/tex]

Now we can factor terms

[tex] {x}^{2} = x \times x \: and \: 9x = 9 \times x[/tex]

we can write them with their common divisor

x*(9+x) = 0 for this equation to be correct either x = 0 or (9+x) = 0

if x = 0 well then that's the first value of x

if (9+x) = 0 then x = -9 and this is the second value of x

Answer:

The correct answer is 1/6 for the question, "In 3 billion repetitions of an experiment, a random event occurred in 500 million cases..."

The correct answer is 1/10 for the question, "A shelf has 20 bags of potatoes. Two of the bags have potatoes starting to go bad."

Hope this helps you! May I please get brainliest if I'm correct?

The number of quarters and dimes with Maria are 17 and 8 respectively.

Linear equations in mathematics are ones where the greatest power of the variable is one. A linear equation can only have one possible solution: a straight line. Thus, a simultaneous linear equation is a system of two linear equations in two or three variables that are solved concurrently to get a shared answer. Three methods are frequently used to solve simultaneous linear equations: substitution method, elimination method, and graphic method.

Let q be the number of quarters.

Let d be the number of dimes.

Given that the total amount is 5.05 in quarters and dimes

Therefore, 0.25 q + 0.10d = 5.05;

I once more, q = 2d + 1. — (ii) (ii)

Inferring from I and (ii), d = 4.80/0.60 = 8 and 0.25(2d + 1) + 0.10d = 5.05 and 0.60d = 4.80 respectively.

This is put into (ii), and the result is q = 2d + 1 = 2*8 + 1 = 17.

As a result, q = 17 and d = 8

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A linear equation has no solutions if both sides of the equation have distinct constant values but the same variable term.

An equation will have no solutions if the variables are the same on either side.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. An equation is a formula that uses the equals sign to connect two expressions to show that they are equal.

For example, an equation can be illustrated as:

x + 5 = x - 5

Collect like terms

x - x = 5 - 5

0

This illustrates that the equation gas no solution.

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The area of the figure is 144 square centimeters

The area of a shape is the amount of space on the shape

For most regular quadrilaterals, you multiply the side lengths to determine the area

The given parameters are

Shape = parallelogram

Base = 9 cm

Height = 16 cm

The area of a parallelogram shape is

Area = Base * Height

So, we have

Area = 9 * 16

Evaluate the expression

Area = 144

Hence, the area  is 144 square centimeters

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Answer:

x = (1/2)

x = -3

Step-by-step explanation:

Quadratic:

2x² + 5x = 3

           -3     -3

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

2x² + 5x - 3 = 0

-b ± √b² - 4(a)(c)

      -------------------

             2(a)

-5 ± √5² - 4(2)(-3)

---------------------------      

             2(2)

-5 ± √25 + 24

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

             4

-5 ± √49

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

      4

-5 ± 7

----------

    4

-5 + 7         2         1

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

   4             4         2

-5 - 7        -12

---------- = --------- = -3

   4              4

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

Factored (for fun):

(2x² + 6x) (-1x - 3) = 0

2x(x + 3) -1 (x + 3)

(2x - 1)(x + 3) = 0

2x - 1 = 0,    x + 3 = 0

     +1   +1         -3    -3

---------------    ------------------

  2x = 1             x = -3

 ÷2   ÷2

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

x = (1/2)

I hope this helps!

When a figure is dilated by a factor of 3, the statement about the image of the figure that is true is C Both the area and the perimeter decrease.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original.

The x and y coordinates of the original figure are multiplied by the scale factor to discover spots on the dilated image when a dilation in the coordinate plane has the origin as the center of dilation. The algebraic representation of the dilation is (x, y) for scale factor k. (kx, ky).

In this situation, since the figure is dilated by a factor of 3, there will be a reduction. In conclusion, the correct option is C.

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A figure is dilated by a factor of 3. Which of the following statements about the image of the figure is true?

A The perimeter decreases.

B The area decreases.

C Both the area and the perimeter

decrease.

D Both the area and the perimeter

increase.

The least water depth and greatest depth will be 0.97d and 1.03d.

An expression is used to show the relationship between the variables.

In this case, the depth of water d in a swimming pool increases and decreases by 3% over a one-month period.

The least water depth will be:

= d - (3% × d)

= d - 0.03d

= 0.97d

The greatest water depth will be:

= d + (3% × d)

= d + 0.03d

= 1.03d

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Answer: That is the answer

Step-by-step explanation:

The verdict on whether the frequency distribution given appears to be normal is; No, there is not a concentration of frequencies in the middle.

On this note, since a major distinctive feature of a normal distribution is that; there is a concentration of frequency in the middle and additionally, a normal distribution infers symmetry in the frequency distribution.

Therefore, since the middle data value in this scenario is; (80 - 84) which has a frequency of; 4 which is not the highest.

On this note, the frequency distribution is not a normal distribution and this is because there is not a concentration of frequencies in the middle.

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Answer:

Step-by-step explanation:

Drawing two marbles at once is the same as drawing one and then drawing the second  without replacing the first.

Starting with 8 red balls and 14 blue balls, the probability of drawing a red ball  is 8/22 = 4/11.

Assuming red was drawn in the first draw, the probability of getting a red ball in the second  draw means that you are  drawing from a collection containing 7 red balls and 14 blue balls, so the probability is: 7/21 = 1/3.

So when calculating the odds of the second draw, we took into account the change in the number of hits and the number of chances, so these two events are  independent and the total probability is the product of the two individual probabilities.

P(2 reds) = (4/11) (1/3) = 4/33

The probability that both marbles are red is 4/33.

It should be noted that from the information given, the jar contains 8 red marbles and 14 blue marbles.

The total marbles will be:

= 8 + 14 = 22

The probability of selecting the first red marble will be:

= 8/22 = 4/11

The probability of selecting the second red marble will be:

= 7/21 = 1/3

Therefore, the probability that both marbles are red will be:

= 4/11 × 1/3

= 4/33

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Answer:

2/9

Step-by-step explanation:

The possibilities that satisfy the condition are 4 and 8.

This is 2 numbers out of the possible 9, so the probability is 2/9.