Sort the expressions into the correct categories based on their value. Note that some expressions may not belong to any of the categories.

(help with the circled ones)

Answer:

min: (-2;-6) & (1; 3/4); max: (0;2).

Step-by-step explanation:

1) f`(x)=3x³+3x²-6x;

2) f`(x)=0, ⇒ 3x³+3x²-6x=0;

3) 3x³+3x²-6x=0; ⇒ x(x²+x-2)=0; ⇒ x(x-1)(x+2)=0; ⇒ x₁=0; x₂=1; x₃=-2;

other steps are provided in the attachment.

Answer:

Father is 80 years old and the son is 30

Step-by-step explanation:

Let father be x and son be y:

x-5 = 3(y-5)

x = 3y-10 ------ eq1

x+y = 110

x = 110 -y -------- eq2

Now if we combine the 2 equations we get:

3y + y = 110+10

y=30 (sons age)

Substituting in equation 2 we get:

x = 110 - 30

x = 80

Therefore, the fathers age is 80 and the sons age is 30.

Answer: $15.90/hr

Step-by-step explanation:

We need to add 6% to her $15/hr current pay.  This can be calculated with:

$15/hr *(1+0.06) = $15.90/hr

The "(1+0.06)" represents a) 1  the current salary, and b) the 6% raise.

Answer:

12 12 18 1816 2888

Step-by-step explanation:

Just add on top and subtract on bottom

Answer:

3.5 hours

Step-by-step explanation:

8.75/2.5=3.5

Answer:

3.5 miles

Step-by-step explanation:

The numbers given can be placed in the bubbles in each row to sum up to 100 as shown in Figure 2 attached below. (See attachment).

The diagram (Figure 1) attached below shows the bubbles to be filled with the given numbers such that in each row, four of the numbers placed in the bubbles will add up to 100.

Hint:

Every row will have 4 numbers, 1 in each bubble which will give us 100.

The rest of the arrangement is shown in the figure 2 attached below. (See attachment).

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Step-by-step explanation:

it is a linear function, if the increases in y are constant from point (ordered pair of x and y) to point reissue to the increase in x.

the first table (top left) increases x constantly by 1.

but y increases first by 2 and then by 3 and then again by 3.

this is not constant, so it does not follow the pattern of x.

in technical terms : the slope of the function is not the same for every point of the function.

in other words : it is not a straight line all the way.

so, it is not a linear function.

the second table (top right) increases x constantly by 2.

and y increases constantly by 2.

this is constant also in relation to x.

in technical terms : the slope of the function is the same for every point of the function.

in other words : it is a straight line all the way.

so, it is a linear function.

the third table (bottom left) increases x constantly by 1.

but y increases first by 4 and then by 1 and then again by 1.

this is not constant, so it does not follow the pattern of x.

in technical terms : the slope of the function is not the same for every point of the function.

in other words : it is not a straight line all the way.

so, it is not a linear function.

the fourth table (bottom right) increases x constantly by 2.

but y increases first by 2 and then by 3 and then again by 3.

this is not constant, so it does not follow the pattern of x.

in technical terms : the slope of the function is not the same for every point of the function.

in other words : it is not a straight line all the way.

so, it is not a linear function.

Answer:

$7

Step-by-step explanation: Five step plan

1. How much is each hamburger?

Variables

Price paid : $50

Change: $22

No. of hamburgers: 4

2. Price for all hamburgers. 50-22 = 28

3. y(price of each hamburger) = 28/4

4. y = 7

5. The price of each hamburger is 7

Answer:

2.70$

Step-by-step explanation:

Answer:

(36/12)×(4y/8y)×(z2/z2)×6×(x/x)=

3× 1/2 ×6

3/2×6=9

The polynomial division problem can be concluded finished if; their is no remainder or the Divisor is larger than the remainder.

According to the question:

In polynomials, the division of a polynomial NY the Divisor gIves a quotient and a remainder.

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Based on the information given, the length will be 68 yards while the value of the width will be 52 yards.

The calculation will go thus:

Perimeter = 2l + 2w

240 = 2(w + 16) + 2w

240 = 2w + 32 + 2w

240 = 4w + 32

4w = 240 - 32

4w = 208

w = 208/4 = 52

Therefore, the length will be:

= w + 16 = 52 + 16 = 68

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Answer:

43/8 or 5 and 3/8

Step-by-step explanation:

This is because if you find the lcd, its 24. 36/6, or 6, in 24 is 144/24.

5/8 is 15/24.

144/24-15/24 is 129/144, which simplified is 43/8, or 5 and 3/8

Answer:

A. 2(a+5) = 16

2a + 10 = 16

2a = 16-10

2a = 6

2a÷2 = 6÷2

a = 3

B. 4p-2/3 = 7/3

4p = 7/3 + 2/3

4p = 3

4p÷4 = 3÷4

p = 3/4

C. 3y/2 + 8 = -4

3y/2 = -4 - 8

3y/2 = -12

[ 3y/2 = -12 ] 2

3y = -24

3y ÷ 3 = -24 ÷ 3

y = -8

[tex] \: \: \: \: \: [/tex]

A.) a = 3

B.) p = ¾

C.) y = -8

refer to the attachment

[tex] \: \: \: \: \: \: \: \: [/tex]

Answer:

1500-8000

Step-by-step explanation:

It depends what type of truck and what its carrying

Answer:

D, y+8=2(x_4)

Step-by-step explanation:

Answer:

= 78

Step-by-step explanation:

Step One:

1 + 4= 5

Step Two:

5+9= 14

Step Three:

14+64= 78

= 78

Hope it helps :)

Answer: 441

Step-by-step explanation:

The formula for an arithmetic sum is

[tex]$\frac{\text{number of terms}}2 \cdot (\text{first term + last term})$[/tex]

We know that the [tex]\text{first term + last term} = -1 + 64 = 63[/tex]. So now all we need is the [tex]\text{number of terms}[/tex]. Well, if you draw each number onto the number line, you get something like

---|------|------|------|------|------|-----|------|-----|------|-----|------|-------|----------

 -1      0      1      2      3     4     5     6     7     8     9     10     11  ...

You can see that your numbers are spaced 5 apart, and they go from -1 all the way up to 64. So what you're really asking is, "how many segments of five can I draw from -1 up to 64?" The length of the line from -1 to 64 is 65 (think about it), so the number of line segments is 65/5 = 13. However, we didn't count 64 itself, since there's no line segment past it! So really there are 14 terms in this sequence. Thus the total sum is

[tex]$\frac {14}2 \cdot (63) = \boxed{441}.$[/tex]

The inverse function will have x intercept additive inverse of this.

Now

equation of line in intercept form

[tex]\\ \sf\longmapsto \dfrac{x}{a}+\dfrac{y}{b}=1[/tex]

[tex]\\ \sf\longmapsto \dfrac{x}{5}+\dfrac{y}{1}=1[/tex]

[tex]\\ \sf\longmapsto \dfrac{x+5y}{5}=1[/tex]

[tex]\\ \sf\longmapsto x+5y=5[/tex]

Graph attached

The Graph of the inverse of the function is given below.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

From the given graph,

x intercept=-5

y intercept=1

The inverse function will have x intercept additive inverse of this.

The inverse of the line's intercepts

x-intercept = 1

y-intercept = -5

Now

equation of a line in intercept form

x/a + y/b = 1

x/1 +y/-5 = 1

5x - y = 5

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Answer:

The answer is 11,316,108

Step-by-step explanation:

[tex]58^{4} - 388[/tex]

(58)(58)(58)(58) - 388

11,316,496 - 388

= 11,316,108

Answer:

Each friend will pay 13.60 dollars.

Step-by-step explanation:

68/5 is 13.6

Answer:

x+y=-15

y=-x-15

Step-by-step explanation:

Answer:

24 miles

Step-by-step explanation:

50 minutes = 8 miles

100 miles = 16 miles

150 minutes = 24 miles

Answer:

Jason can travel 24 miles in 150 minutes.

Step-by-step explanation:

8= miles. 50&150= mins

8=50.

Your trying to find how many miles Jason can travel in 150 mins. So your going to divide the new amount of minutes to the old amount.

150÷50= 3.

So since 50 can go into 150 3 full times that means you will multiply the original amount of miles by 3 to get your new amount.

3×8= 24

So, if Jason can travel 8 miles in 50 mins (8=50) Then, he can travel 24 miles in 150 mins (24=150)

Hope this wasn't too confusing,

Hope this helps!

Answer:

1. Loss ₹50

2. - 60

3. 50 km towards North

4. 1000

5. - 30

6. - 15° C

Answer:

3

Step-by-step explanation:

so we know that this question is asking for the y value when x is equal to -1, so according to the graph its 3

Answer:

y = -(5/6)x + 0.917

Step-by-step explanation:

We can calculate a slope with the two given points:

(-2.5,3) and (3.5,-2)

Rise (change in y) = -2 - (3) = -5

Run (change in x) = 3.5 - (-2.5) = 6.0

Slope = Rise/Run = -5/6

The line has the following form:

y = -(5/6)x + b

We can find b, the y-intercept, by using one of the two points in the equation and then solve for b.  I'll choose (-2.5,3):

y = -(5/6)x + b

3 = -(5/6)*(-2.5) + b

3 = 2.083 + b

b = 0.917

y = -(5/6)x + 0.917

Step-by-step explanation:

a=b as it is alternative angles

so 6x+5=4x+45

6x-4x =45-5

2x=40

x=40 /2

x=20

Answer:

-100, -14.5, -2, -2/3, 0, 10, 15, 20 1/6

All the numbers

Step-by-step explanation:

A rational number is a number that can be expressed as in a fraction or decimal (m/n form)

All numbers above can be defined.

A rational number is a number that c\an be written in the form of p/q where q is not equal to zero.

The rational numbers are -100, -14.5, -2, -2/3, 0, 10, 15, 20 1/6.

A rational number is a number that can be written in the form of p/q where q is not equal to zero.

We have,

-100, -14.5, -2, -2/3, 0, 19, 15, 20, 1/6

-100 = -100/1

It is in the form of p/q.

It is a rational number.

-14.5 = -145/10

It is in the form of p/q.

It is a rational number.

-2 = -2/1

It is in the form of p/q.

It is a rational number.

-2/3 = -2/3

It is in the form of p/q.

It is a rational number.

0 = 0/1

It is in the form of p/q.

It is a rational number.

19 = 19/1

It is in the form of p/q.

It is a rational number.

15 = 15/1

It is in the form of p/q.

It is a rational number.

20 = 20/1

It is in the form of p/q.

It is a rational number.

1/6

It is in the form of p/q.

It is a rational number.

We see that all the numbers given are rational numbers.

Thus,

The rational numbers are -100, -14.5, -2, -2/3, 0, 10, 15, 20 1/6.

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