Find the coordinates of the midpoint M
(-3, 2) and K(9, 2)

We may get the same conclusion using either approach, which is that x—5 is a factor of the polynomial.

This will be discussed in further detail below.

Explain, taking into account the fact that, using either method, whether or not we can think of x-5 as a factor in the polynomial based on the given information.

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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The given function g(x) is positive for all real values of x, and increasing for the interval (-3,∞) , decreasing for the interval (-∞,-3) and

the end behavior is that g(x) → ∞ as x → -∞  an g(x) → ∞ as x → ∞ .

In the question ,

the graph of the function g(x) is shown  ,

we see that ,No part of the graph of function g(x) is below the x axis ,

So, the negative of the function g(x) does not exist .

Also from the graph we can see that the graph is above the x axis for all values of x,

So , the function g(x) is positive for all real values of x .

the graph shows that the function is decreasing for x<-3 means

function g(x) is decreasing in the interval (-∞,-3) .

the graph shows that the function is increasing for x>-3 means

function g(x) is increasing in the interval (-3,∞) .

From the graph ,

the end behavior of the function g(x) is that g(x) → ∞ as x → -∞   and g(x) → ∞ as x → ∞

Therefore , the given function g(x) is positive for all real values , and increasing for the interval (-3,∞) , decreasing for the interval (-∞,-3) and

the end behavior is that g(x) → ∞ as x → -∞   and g(x) → ∞ as x → ∞ .

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For every 500 g of reactants, 3.1 g of catalyst were required. The catalyst that was required for 900 g of reactant was 5.58g

The process of catalysis involves introducing a catalyst to chemical reaction to speed up the process. Catalysts are not destroyed during reaction and are unaffected by it. Very little amounts of catalyst are frequently sufficient when the reaction is swift and the catalyst recycles quickly; the velocity of the reaction is greatly influenced by mixing, surface area, and temperature. In most cases, catalysts interact with one or more reactants to produce intermediates that ultimately lead to the final reaction product, regenerating the catalyst in the process.

Homogeneous catalysis, in which all of the components are dispersed in the same phase as the reactant (often a gas or liquid), and heterogeneous catalysis, in which the components are not. It's common to think of enzymes and other biocatalysts as a a third category.

In all branches of the chemical business, catalysis is commonplace. 90% of all chemical compounds manufactured for commercial purposes are thought to use catalysts at some point during the manufacturing process.

500g of reactants = 3.1g of catalyst

1g of reactants = 3.1g of catalyst / 500g of reactants

900g of reactants = [tex]\frac{3.1}{500} * 900[/tex] = 5.58g

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The unknown angles are as follows:

The measures of angle 1 and 2 can be found as follows:

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.

Therefore,

∠1 + ∠2 = 180(sum of angle on a straight line)

∠1 = 118(alternate angles)

118 + ∠2  = 180

∠2 = 180 - 118

∠2 = 62 degrees

Therefore,

∠1 = 118 degrees

∠2 = 62 degrees.

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The special angle pair relationship between ∠2 and ∠3 is same-side interior angles.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.

Therefore, the angle pair relationship between angle 2 and 3 are same side interior angles.

The same-side interior angle theorem states that when two lines that are parallel are intersected by a transversal line, the same-side interior angles that are formed are supplementary.

Supplementary angles are those angles that sum up to 180 degrees. In other words, If the measures of two angles sum up to 180°, they are called supplementary angles.

Therefore, same side interior angles are supplementary angles.

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It will take 11 days to place all of the 100 tiles needed to finish the floor.

The slope of a line and any points it contains determine the point-slope form of the line. When a point on the line and the slope are provided, the form's objective is to represent the equation of the complete line.

Given Data

She had a tough time at first and placed only 5 tiles the first day. She started to go faster, and by the end of day 4, she had placed 35 tiles.

Points are:

(1,5) (4,35)

Slope = [tex]\frac{30}{3}[/tex]

Slope = 10

y - y₁ = m(x -x₁)

y - 5 = m(x- 1)

For 100, it will need,

100 - 35 = 10(x-4)

65 = 10x - 40

105 = 10x

x = 10.5

It will take 11 days to place all of the 100 tiles needed to finish the floor.

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Answer: I think the answer is -11/15

Step-by-step explanation:[tex]\frac{1}{6}[/tex]-0.5   0.5=[tex]\frac{1}{2}[/tex]

                                           [tex]-\frac{1}{3}[/tex] divided by [tex]\frac{5}{11}[/tex] = [tex]\frac{11}{15}[/tex]

method 1.

[tex] {x}^{2} - 7x - 18 = 0[/tex]

simplify:

[tex](x - 9)(x + 2) = 0[/tex]

so the answer is (D) x =9 or x = -2

method 2.

if

[tex] {a}^{2}x+ bx + c = 0[/tex]

[tex]x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} \: or \: \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

so

[tex]x = \frac{ - ( - 7) + \sqrt{ { - 7}^{2} - 4(1)(18)} }{2(1)} or\frac{ - ( - 7) - \sqrt{ { - 7}^{2} - 4(1)(18)} }{2(1)}[/tex]

[tex]x = \frac{ 7 + \sqrt{ 121 } }{2}or\frac{ 7 - \sqrt{ 121 } }{2}[/tex]

[tex]x = 9 \: \: \: \: or - 2[/tex]

Using algebraic expression and equation, he invested $2000 in fund b.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

Let x = amount he invested in fund b

If both funds together returned a 4% profit, then the sum of the profit in each investment is equal to 4% of the total investment.

$3000(0.02) + x(0.07) = (3000 + x)(0.04)

Solving for x,

$3000(0.02) + x(0.07) = (3000 + x)(0.04)

$60 + 0.07x = $120 + 0.04x

0.07x - 0.04x = $120 - $60

0.03x = $60

x = $2000

amount he invested in fund b = $2000

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Value of x [tex]\frac{36}{5}[/tex]

value of m∠3 = [tex]\frac{462}{5}[/tex]

When two rays meet at a point, they make an angle. An "angle" is the term used to describe the "opening" between these two rays, and it is symbolized by the symbol. Angles are typically expressed as 60°, 90°, etc. and are measured in degrees. A figure made up of two rays meeting at the vertex of the angle can be referred to as an angle.

Given Data

m∠3 = 17x - 30

m∠6 = 12x +6

Angle pair - exterior alternate angle

For the value of x,

17x - 30 = 12x + 6

17x - 12x = 6 + 30

5x = 36

x = [tex]\frac{36}{5}[/tex]

For m∠3,

17x - 30

Equating value of x,

17([tex]\frac{36}{5}[/tex]) - 30

[tex]\frac{612-150}{5}[/tex]

[tex]\frac{462}{5}[/tex]

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Answer:

30310$

Step-by-step explanation:

A nearby hamburger joint sold 416 hamburgers and cheeseburgers in total on Monday. 104 hamburgers were sold.

Given that,

A nearby hamburger joint sold 416 hamburgers and cheeseburgers in total on Monday. Three times as many cheeseburgers were sold as regular hamburgers.

We have to find on Monday, how many hamburgers were sold.

Let us take hamburgers were sold as h and cheeseburgers were sold as c.

Quantity equation is h+c=416

c=3h

Substitute c =3h in h+c=416

h+3h=416

4h=416

h=104

Now,

Substitute h=104 in c=3h

c=3×104

c=312

Therefore, 104 hamburgers were sold.

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Answer:-1/3

Step-by-step explanation:

3y+1=6x

Minus 1 on both side so,

3y=6x-1

Then divide 3 on both side so,

y=2x-1/3

The number behind x is y intercept which -1/3 and the - sign have to be inside.

Answer: 1/6

Step-by-step explanation:

Answer:

600000000000000000000000000[tex]x^{2}[/tex]

Answer: Its t=

32

−

23673−64h

​

+139

​

Step-by-step explanation:

If this year, Reba hands out the same number of buckets to each of the 12 teams in the contest. Each team gets 6 buckets. the total number of buckets Reba delivers is 72 buckets.

Let x represent the total number of buckets Reba delivers.

The equation to find the total number is:

x / 6  = 12

Let solve for x, to get the total number of buckets Reba delivers.

x = 12 × 6

x = 72 buckets

Therefore the  total number of buckets is 72.

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The no. of regular tube costing $15 were 12 and the cooler tube costing $7.5 each were 24

The entire family can participate in tubing. Change into swimwear, rent a tube and a life jacket, and float down the river—that it's easy. Numerous outfitters provide transportation to the best waterways and rent tubes from Blue Ridge to Columbus, via Helen and Columbus.

The total cost of rent on tube = $360

Price of regular tube = $15

Price of cooler tubes = $7.5

Let the no. of regular tubes be and cooler tubes be y

The equation forms

15x + 7.5y = 360           ...1

As we can notice regular tube is twice the price of cooler tubes, sthe the equation forms

2(7.5) = 15

This means when y = 2, x = 1

cross multiply them and we find

2/y = 1/x

x/y = 1/2

x = y/2               ...2

Putting the value of x in eq 1, we get

15(y)/2 + 7.5y = 360

7.5y + 7.5y = 370

15y = 360

y = 360/15

y = 24

Putting the value of y in eq 1, we get

15x + 7.5(24) = 360

15x + 180 = 360

15x = 360 - 180

15x = 180

x = 180/15

x = 12

Thus, The no. of regular tube costing $15 were 12 and the cooler tube costing $7.5 each were 24.

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Answer:

13. x = 3∛2

14 x = ± 4√6 = ± 4√2 √3

15. x =  2∛11

16 x =  -4∛2

17 x = ± 10√3

18. x =   ± 4 √3 √5

Step-by-step explanation:

13. x³ = 54

x = ∛4

Factor 54: 2 x 27

∛54 = ∛2 x ∛27

∛27 = 3

answer: 3∛2

14. x² = 96

x = ±√96

96 = 6 x 16
√16 = 4

√6

√96 = ± 4√6 = ± 4√2√3

15. x³ = 88

x = ∛88
88 = 8 x 11
∛88 = ∛8 x ∛11 = 2∛11

16. x³ = -128 means x has to be negative

x = -∛128

128 = 64 x 2

∛128 = ∛64 x ∛2 = 4∛2

So x = -4∛2

17. x² = 300

=> x = ± √300
300 = 100 x 3
√300 = √100 x √3 = 10√3

x = ± 10√3

18. x² = 240

x = ±√240
240 = 16 x 15

√240 = ± (√16 x √15)

= ± 4 √3 √5

Answer:

 (7 x 10) + (1 x 1) + (0/10) + (4/100)

70 + 1 + 0.04

70 + 1 + 4/100

Step-by-step explanation:

Here are all the expanded forms I can think of off the top of my head, sorry if this didn’t help much!

The new workshop can produce as many as 180 toys each year compared to the old workshop

The approximation of numbers is the estimates of the said number.

This means that the approximation of a number is close to the said number, but it has a slight different value

The given parameters are:

Old capacity = 22,912,546,992 toys per year

New capacity = 4,134,232,638,937 toys per year

The approximate number of times is calculated as

Number of times = New capacity/Old capacity

Substitute the known values in the above equation

So, we have

Number of times = 4,134,232,638,937 toys per year/22,912,546,992 toys per year

Remove the units

So, we have

Number of times = 4,134,232,638,937/22,912,546,992

Evaluate the quotient

So, we have

Number of times = 180.435315217

Approximate

Number of times = 180

Hence. the approximate number of times is 180

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The value of  m²+n²+p² is 46.

In mathematics, an identical element, also known as a neutral element, is an element of a set that, when subjected to a binary operation, leaves each element of the set intact. In algebraic structures like groups and rings, this idea is applied. Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Algebraic identities are employed in this manner for the computation of algebraic expressions and the solution of various polynomials.

Given Data

m + n+ p= 10

mn + np + mp = 27

For m² + n²+ p²

Using algebraic identities,

(m+ n +p)² = m² + n² + p² +2(mn + np + pm)

(10)² = m² +n² + p² + 2(27)

100 = m² + n² + p² + 54

100 - 54 = m² + n² + p²

46 = m²+n²+p²

The value of  m²+n²+p² is 46.

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Answer:

z=70    y=98

Step-by-step explanation:

180-110=70=z

70+87+105=262

360-262=98=y

Answer:

[tex]x=-1[/tex]

Step-by-step explanation:

[tex]\textsf{Given equation}:[/tex]

[tex]5x-6=3x-8[/tex]

[tex]\textsf{Subtract $3x$ from both sides}:[/tex]

[tex]\implies 5x-6-3x=3x-8-3x[/tex]

[tex]\implies 2x-6=-8[/tex]

[tex]\textsf{Add $6$ to both sides}:[/tex]

[tex]\implies 2x-6+6=-8+6[/tex]

[tex]\implies 2x=-2[/tex]

[tex]\textsf{Divide both sides by $2$}:[/tex]

[tex]\implies \dfrac{2x}{2}=\dfrac{-2}{2}[/tex]

[tex]\implies x=-1[/tex]

The probability is given by:

Therefore:

- The probability of spinning blue is:

Favorable outcomes = 1 (blue color)

Total outcomes = 3 (red, blue, and yellow)

- The probability of flipping heads is:

Favorable outcomes = 1 (head)

Total outcomes = 2 (head and tail)

- The probability of spinning a one is:

Favorable outcomes = 1 (number 1)

Total outcomes = 3 (numbers 1, 2 and 3)

Next, the probability of the compound event:

Answer: the probability of the compound event is 1/18

Answer:

Ok so first change the fractions to decimals and the top one is five

Answer:

0.003, 0.03, 0.303, 0.383, 3.03, 33.03

Step-by-step explanation: