The graph of f ′ (x), the derivative of f of x, is continuous for all x and consists of five line segments as shown below. Given f (0) = 7, find the absolute minimum value of f (x) over the interval [–3, 0].
A. 0
B. 2.5
C. 4.5
D. 11.5

Answer:

The rate of change in Erinn's hourly wage per year is [tex]1.25\$\ hour/year[/tex]

Step-by-step explanation:

we have that

x ----> the time in years that she worked at a company

y ----> represent the hourly wage

[tex]-5x+4y=32[/tex] ----> linear equation that represent the situation

Solve for y

[tex]4y=5x+32[/tex]

[tex]y=(5/4)x+32/4[/tex]

[tex]y=1.25x+8[/tex]

The slope m of the linear equation is

[tex]m=1.25\$\ hour/year[/tex]

The rate of change in Erinn's hourly wage per year is equal to the slope of the linear equation

so

The rate of change in Erinn's hourly wage per year is [tex]1.25\$\ hour/year[/tex]

Answer:

Add 6 to both sides.

Step-by-step explanation:

You are trying to solve for x in this type of question. In this case, note that there is a equal sign, and that what you do to one side you do to the other. Also note that to isolate the x (your goal), you must do the opposite of PEMDAS. (Note that PEMDAS = Parenthesis, Exponent (& Roots), Multiplication, Division, Addition, Subtraction).

So your first step is to add 6 to both sides.

2/5x - 6 (+6) = -16 (+6)

Simplify. Solve:

2/5x + (-6 + 6) = -16 + 6

2/5x = -10

_________________________________________________________

Finish finding for x.

Multiply the recipricol of the fraction to both sides to isolate the x. Multiply 5/2 to both sides:

(5/2)(2/5)x = (-10)(5/2)

x = (-10)(5/2)

x = (-50)/2

x = -25

x = -25 is your answer.

~

Answer:

1/3

Step-by-step explanation:

Slope intercept form: y=mx+b

m=rise/run (slope)

b= y-intercept

b=1/3

Answer: y=-2x+2/4

Step-by-step explanation:

Answer:

y + 4 =1/2 (x + 4)

Step-by-step explanation:

Your welcome uwu

Answer:

D

Step-by-step explanation:

g(x)=f(5x)

this means plugging in 5x for x in f(x):

g(x)=f(5x)=(5x)^2

which can be further simplified:

5^2x^2=25x^2

Since the coefficient of x being larger means a vertical stretch, the answer is D

example:

g(2)=f(5*2)=f(10)=f(10^2)=100

so for g(x), it has the coordinates (2,100), which is most definitely not C

The graph of g(x) = f(5x) is a parabola that is narrower than the graph of f(x) by a factor of 1/5, with the vertex remaining the same.

The graph of g(x) = f(5x) can be obtained by substituting 5x for x in the function f(x) = x^2. So, g(x) = f(5x) = (5x)^2 = 25x^2. This means that the graph of g(x) is a parabola that is narrower than the graph of f(x) by a factor of 1/5. The vertex of the parabola remains the same, but the x-values and the y-values are scaled.

Answer:

Second option: y = 8x-3

Step-by-step explanation:

The equation tha satisfies the given values will be the required linear equation

So,

y = 8x + 45

For x=3 and y=21

21 = 8(3) +45

21 = 24+45

21≠69

As this equation is not satisfied by the values, it is not the correct option..

For y = 8x-3

x=3,y=21

21 = 8(3)-3

21 = 24-3

21=21

x=5, y=37

37 = 8(5)-3

37=40-3

37=37

x=7, y=53

53 = 8(7)-3

53 = 56-3

53 = 53

As the equation is true for all values of x and y. This is this correct option..

Shown below

To solve this problem, we need to analyze the leading coefficient and the roots of the polynomial function:

[tex]f(x)=x^3-6x^2+11x-6[/tex]

Recall that a polynomial function can be represented by:

[tex]f(x)=a_{n}(x)+ \ldots +a_{1}x+a_{0}[/tex]

So the leading coefficient is [tex]a_{n}[/tex]. In our problem, this coefficient is [tex]a_{n}=1[/tex]

Since [tex]n[/tex] is odd and the leading coefficient [tex]a_{n}>0[/tex], then the graph must falls to the left and rise to the right. Also, the roots are [tex]x_{1}=1 \ x_{2}=2 \ and \ x_{3}=3[/tex]. So the only graph that matches this is the fourth one as indicated below.

Answer:

w

Step-by-step explanation:

for Plato

Answer:

y=3x+8, :m=3, b=8

Hope this helps!

The line y - 5 = 3(x + 1) in the form of slope intercept is y = 3x + 8 and slope of the line is 3, y-intercept is 8.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have a line:

y - 5 = 3(x + 1)

In slope intercept form:

y = 3x + 3 + 5

y = 3x + 8

Thus, the line y - 5 = 3(x + 1) in the form of slope intercept is y = 3x + 8 and slope of the line is 3, y-intercept is 8.

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Answer:

y = -5x + 39

Step-by-step explanation:

Plug either ordered pair into the Point-Slope Formula FIRST, y - y₁ = m(x - x₁), then convert to Slope-Intercept Form by moving whichever term is nearest to y, over to the right side of the equivalence symbol to get the above answer.

Answer:

what are the graphs?

Step-by-step explanation:

Answer:

(0,6)

Step-by-step explanation:

Answer:

Choice B

Step-by-step explanation:

Formula for slope:

[tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]y_2 = 1\\y_1 = -10\frac{2}{3} \\\\x_2 = -3\\x_1 = 4[/tex]

[tex]1 - (-10\frac{2}{3}) = 11\frac{2}{3} \\-3 - 4 = -7[/tex]

[tex]\frac{-11\frac{2}{3} }{-7} = \frac{5}{3} = 1\frac{2}{3}[/tex]

Answer:

х – 9 = +9

Step-by-step explanation:

The equation results from taking the square root of both sides of

(x- 9)² = 81 is x -9 = ±9.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have Equation,

(x- 9)² = 81

Now, simplifying for x we get

Take square root on both side

x-9 = √81

x -9 = ±9.

Then, the equation results from taking the square root of both sides is

x -9 = ±9.

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Answer:

30 minutes

Step-by-step explanation:

3 pipes takes 60 minutes, so one pipe must take 3*60 minutes as it would be 3 times slower. This equates to 180 minutes.

1 pipe takes 180 minutes so 6 pipes would take 1/6 of the time or 6 times faster.

The equation becomes 180/6

= 30 minutes.

Equation is; 3*60/6 = 30 minutes

This is inverse proportion.

The answer is 30 minutes

If it takes 3 pipes 60 minutes to water the field

The amount of time it will take one pipe can be calculated as follows

t= constant(k) × number of pipes

60= k/3

cross multiply

k = 60×3

= 180

Since it takes one pipe 180 minutes to water the field, then the amount of time it will take 6 pipes can be calculated as follows

= 180/6

=  30

Hence it will take 6 pipes 30 minutes to water the field

It is an inverse proportion because an increase in one quantity leads to a decrease in the other.

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Answer:

D. 9/4 ÷ 3/4

Step-by-step explanation:

In the question, the number line represents 9/4 divided into 3 equal units.

The size of each unit is 3/4 as shown.

Showing that 3/4 divides 9/4 into 3 divisions:

9/4 ÷ 3/4

= 9/4 x 4/3

= 9/3 x 4/4

= 9/3 x 1

= 3 x 1

= 3

Hence, the number line represents three divisions given by 9/4 ÷ 3/4.

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (t^9)^{-8}\implies t^{-8\cdot 9}\implies t^{-72}\implies \cfrac{1}{t^{72}}[/tex]

Answer:

P = 2x + 2y + 14

Step-by-step explanation:

Length (L) = x + 8 units

Width (W) = y - 1 units

Perimeter (P) = 2L + 2W

P = 2(x + 8) + 2(y - 1)

P = 2x + 16 + 2y - 2

P = 2x + 2y + 16 - 2

P = 2x +2y + 14

Answer:

P = 2x + 2y + 14

Step-by-step explanation:

Answer:

[tex]\sqrt{98}[/tex]

Step-by-step explanation:

Using the distance formula

with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (3, - 5)

d = [tex]\sqrt{(3+4)^2+(-5-2)^2}[/tex]

  = [tex]\sqrt{7^2+(-7)^2}[/tex]

  = [tex]\sqrt{49+49}[/tex]

  = [tex]\sqrt{98}[/tex]

C= [tex]\sqrt{98}[/tex]

We could say that the square root or the square cancel each other out. They are a inverse of each other. If we have the number written with the index two ( squared) then taking the square root simply means that we leave out the two ( this only applies on the positive numbers ).

Using the distance formula

with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (3, - 5)

[tex]d= \sqrt{(3+4)^{2} +(-5-2)^{2}} \\\\= \sqrt{7^{2} + (-7)^{2}} \\\\= \sqrt{49+49} \\\\=\sqrt{98}[/tex]

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Answer:

22

Step-by-step explanation:

Solve the inequality  (20 + 0.5x) + 0.15(20 + 0.5x)   ≤ $62.10 for x:

20 + .5x + 3 + 0.75x ≤ 62.10

Combining the x terms, we get:

20 + 3 + 1.25x ≤ 62.10.

Combining the constants on the left:

23 + 1.75x ≤ 62.10

Combining the constants:

1.75x = 39.10

Solving for x:  39.10/1.75 = 22.34

Thus, the max number of whole pages she can have in her book is 22.

Answer:

22

Step-by-step explanation:

Quantities that are proportional to 26/13 are any other fractions that can reduce to positive 2.

26/13 = 26 ÷ 13 = 2

10/5 = 10 ÷ 5 = 2

200/100 = 200 ÷ 100 = 2

Answer:

So any fraction equal to 2 will work.

Step-by-step explanation:

Don't know which but I could tell you some that are equivalent to or proportional to 26/13.

26/13 reduces to 2 so 2 is a quantity that is proportional to 26/13

So any fraction equal to 2 will work.

Answer:

x + 3x + 5 = 101

Step-by-step explanation:

Consider your problem and think of an equation of each person. We know that Aylen has a certain amount of money, which will be x. Rich though has 5 more than 3 times Aylen.

Aylen: x amount of money

Rich: 5 more than 3 times the amount of money of Aylen.

5 more indicates addition, 3 times indicates multiplication

So then:

Rich: 5 + 3x     (where x is the amount of money of Aylen)

Now both of them have $101 together, in other words, if you add up their money they would have $101. So we add their equations:

x + 5 + 3x = 101

Because the operation is addition, we can switch their places and the result will not change so the answer would be:

x + 3x + 5 = 101

Answer:

The missing information is attached in the picture below.

The company made $292.5 dollars in profit.

Step-by-step explanation:

Using the information provided by the table, we can calculate how much money was spent

1. gravel

12 and a half cubic yards * $15  = $187.5

2. tar/sealant

$0.15 per square foot * (75*20 ft^2) = $225

3. labor

$10 per hour * 25 hours = $250

4. insurance

fixed $45

We add all the expenses together

$(187.5 + 225 + 250 + 45)  = $707.5

The profit will be equal to

$1000 - $707.5 = $292.5

Step-by-step explanation:

Answer:

Point-slope equations:

y - 5 = 4/3 (x - 6)

or

y - 1 = 4/3 (x - 3)

Step-by-step explanation:

Given two coordinate points (6, 5) and (3, 1)

Slope = (5 - 1)/(6 - 3) = 4/3

Point-slope equations:

y - 5 = 4/3 (x - 6)

or

y - 1 = 4/3 (x - 3)

Two point-slope equations for the line passing through the points

(6, 5) and (3, 1) are,

Here, the line passes through the points (6,5) and (3,1).

Let,

[tex]$$(6,5)=\left(x_{1}, y_{1}\right)$$[/tex]

[tex]$(3,1)=\left(x_{2}, y_{2}\right)$[/tex]

Substitute

Slope(m) = [tex]\frac{1-5}{3-6}=\frac{-4}{-3}[/tex]

Slope(m) =[tex]\frac{4}{3}[/tex]

Point-slope equations of the line passing through [tex]$(6,5 \6})$[/tex] and [tex](3}, 1)$[/tex]

Substitute[tex]$m=4 / 3$[/tex], and [tex]$(a, b)=(6,5)$[/tex]into [tex]$y-b=m(x-a)$[/tex]

[tex]y-5=\frac{4}{3}(x-6)[/tex] (point-slope equation)

Substitute[tex]$m=4 / 3$[/tex], and [tex]$(a, b)=(3,1)$[/tex] into [tex]$y-b=m(x-a)$[/tex]

[tex]$y-1=\frac{4}{3}(x-3)$[/tex] (point-slope equation)

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The parenthesis tell you which equation to do first.

P arenthesis

E xponents

M ultiplication

D ivision

A ddition

S ubtraction

Answer:

the answer is C. Hope this helps

Answer:

Step-by-step explanation:

Answer:

It was A.

Step-by-step explanation:

the rate of change of item I is greater than the rate of change of item II.

I just had it and answer B. was wrong

The rate of change of item I is greater than the rate of change of item II. (Option A)

Suppose that the considered linear equation is of the form [tex]y = mx + c[/tex]

Then, when we change x by 1 unit, then:

[tex]y + \delta y = m(x + 1) + c\\mx + c + \delta y = mx + c + m\\\delta y = m[/tex]

where [tex]\delta y[/tex] shows the change in y as x changes by 1 unit.

We found that this change is the value of 'm'.

It is called slope of the line this equation represents (each linear equation represents a line).

Finding rate of each item:

The rate is 3 units increment in y per unit increment in x. In short, the rate is 3 unit / unit increment in x

Since graph of a straight line is given, we can find its slope which would represent its rate.

Consider x = 0, for which y = 0 is given in graph.

Now change x by 1 unit, so x becomes x = 1

At x =1 , y = 2

So we see that as x changes by 1 unit, y goes from 0 to 2 (change of 2 units).

Hence, the rate is 2 units increment in y per unit increment in x. In short, the rate is 2 unit / unit increment in x

Thus, the rate of change of item I is greater than the rate of change of item II. (Option A)

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For this case we have by definition, that the equation of a line in the point-slope form is given by:

[tex](y-y_ {0}) = m (x-x_ {0})[/tex]

Where:

m: It's the slope

[tex](x_ {0}, y_ {0}):[/tex] It is a point through which the line passes.

[tex]m = \frac {y2-y1} {x2-x1}[/tex]

We have as data two points, replacing:

[tex]m = \frac {1-6} {0 - (- 5)}\\m = \frac {1-6} {0 + 5}\\m = \frac {-5} {5}\\m = -1[/tex]

We substitute a point, then the equation is:

[tex](y-1) = - 1 (x-0)\\(y-1) = - x[/tex]

Answer:

[tex](y-1) = - x[/tex]

Answer: [tex]y-6=-(x+5)[/tex]

Step-by-step explanation:

The Point-slope form of the equation of the line is:

[tex]y-y_1=m(x-x_1)[/tex]

Where "m" is the slope of the line and [tex](x_1,y_1)[/tex] is a point on the line.

We know that this line passing through the points (-5,6) and (0,1), then we can find the slope with this formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substituting, we get:

 [tex]m=\frac{1-6}{0-(-5)}=-1[/tex]

Finally, we can substitute the point (-5,6) and the slope into  [tex]y-y_1=m(x-x_1)[/tex], then:

[tex]y-6=-(x-(-5))[/tex]

[tex]y-6=-(x+5)[/tex]

For this case we must simplify the following expression:

[tex]\sqrt [5] {\frac {10x} {3x ^ 3}}[/tex]

We rewrite the expression as:

[tex]\sqrt [5] {\frac {10x} {x * 3x ^ 2}} =[/tex]

We eliminate common factors:

[tex]\sqrt [5] {\frac {10} {3x ^ 2}} =\\\frac {\sqrt [5] {10}} {\sqrt [5] {3x ^ 2}}[/tex]

We multiply the numerator and denominator:

[tex](\sqrt [5] {3x ^ 2}) ^ 4:\\\frac {\sqrt [5] {10}} {\sqrt [5] {3x ^ 2}} * \frac {(\sqrt [5] {3x ^ 2}) ^ 4} {(\sqrt [5] {3x ^ 2}) ^ 4} =[/tex]

\frac {\ sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {\sqrt [5] {3x ^ 2} * (\sqrt [5] {3x ^ 2} ) ^ 4} =

[tex]\frac {\sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {(\sqrt [5] {3x ^ 2}) ^ 5} =\\\frac {\sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {3x ^ 2} =[/tex]

[tex]\frac {\sqrt [5] {10} * \sqrt [5] {(3x ^ 2) ^ 4}} {3x ^ 2} =\\\frac {\sqrt [5] {10} * \sqrt [5] {81x ^ 8}} {3x ^ 2} =\\\frac {\sqrt [5] {10} * \sqrt [5] {81x ^ 5 * x ^ 3}} {3x ^ 2} =[/tex]

[tex]\frac {\sqrt [5] {10} * x \sqrt [5] {81x ^ 3}} {3x ^ 2} =\\\frac {x \sqrt [5] {810x ^ 3}} {3x ^ 2}[/tex]

Answer:

[tex]\frac {x \sqrt [5] {810x ^ 3}} {3x ^ 2}[/tex]

[tex]\frac {\sqrt [5] {810x ^ 3}} {3x}[/tex]

Answer:

The simplified form is [tex]\frac{\sqrt[5]{810 x^{3}}}{3x}[/tex]

Step-by-step explanation:

we need to simplify the value of x in given expression:

[tex]\sqrt[5]{\frac{10x}{3x^{3}}}[/tex]

Re- write the above as,

[tex]\sqrt[5]{\frac{10}{3x^{2}}}[/tex]

[tex]\frac{\sqrt[5]{{10}}}{\sqrt[5]{3x^{2}}}[/tex]

Multiply numerator and denominator by [tex](\sqrt[5]{3x^{2}})^{4}[/tex]

[tex]\frac{\sqrt[5]{{10}}}{\sqrt[5]{3x^{2}}} \times \frac{(\sqrt[5]{3x^{2}})^{4}}{(\sqrt[5]{3x^{2}})^{4}}[/tex]

[tex]\frac{\sqrt[5]{{10}}{\sqrt[5]{(3x^{2}}})^4}{{3x^{2}}}[/tex]

[tex]\frac{\sqrt[5]{{10}}{\sqrt[5]{81x^{8}}}}{{3x^{2}}}[/tex]

[tex]\frac{x \sqrt[5]{810 x^{3}}}{3x^{2}}[/tex]

[tex]\frac{\sqrt[5]{810 x^{3}}}{3x}[/tex]

Hence, the simplified form is

[tex]\frac{\sqrt[5]{810 x^{3}}}{3x}[/tex]

Answer:

Q1: 2nd row 2nd tile

Q2: 1st row 1st tile

Q3: 1st row 3rd tile

Q4: 2nd row 3rd tile

Step-by-step explanation:

When

[tex]y = a {(x + p)}^{2} + q[/tex]

Vertex is (-p, q)

Answer:

[tex](-1,-\frac{3}{7} )-->f(x)=\frac{1}{2}|x+1|-\frac{3}{7}\\(5,\frac{2}{3} )-->f(x)=\frac{3}{5}|x-5|+\frac{2}{3}\\(0,-\frac{4}{5} )-->f(x)=\frac{1}{2}|x|-\frac{4}{5}\\(\frac{2}{5},\frac{5}{3} )-->f(x)=\frac{3}{2}|x-\frac{2}{y5}|+\frac{5}{3}[/tex]

Step-by-step explanation:

We can solve all of them by writing the equations in a general form

[tex]f(x)=a|x+b|+c[/tex]

This is a function transformation of

[tex]f(x)=|x|[/tex]

where:

a=Factor of vertical stretch

b=Horizontal shift (- shifts right, + shifts left)

c=Vertical shift (+ shifts right, - shifts left)

The original function has its vertex in [tex](0,0)[/tex] so the horizontal shift will be the new x coordinate in the new vertex and the vertical shift will be the new y in the new vertex like this:

[tex]f(x)=\frac{1}{2}|x+1|-\frac{3}{7}\\b=1=HorizontalShiftof-1\\c=-\frac{3}{7}=VerticalShiftof-\frac{3}{7}\\(-1,-\frac{3}{7})\\f(x)=-\frac{3}{5}|x-5|+\frac{2}{3}\\b=-5=HorizontalShiftof5\\c=\frac{2}{3}=VerticalShiftof\frac{2}{3}\\(5,\frac{2}{3})\\f(x)=\frac{1}{2}|x|-\frac{4}{5}\\b=0=HorizontalShiftof0\\c=-\frac{4}{5}=VerticalShiftof\frac{4}{5}\\(0,-\frac{4}{5})\\f(x)=-\frac{3}{2}|x-\frac{2}{5}|+\frac{5}{3}\\b=-\frac{2}{5}=HorizontalShiftof\frac{2}{5}\\c=\frac{5}{3}=VerticalShiftof\frac{5}{3}\\(\frac{2}{5},\frac{5}{3})[/tex]

Answer:

r = 7

Step-by-step explanation:

The common ratio r of a geometric sequence is

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex], that is

r = [tex]\frac{21}{3}[/tex] = [tex]\frac{147}{21}[/tex] = 7

The common ratio of the sequence 3, 21, 147 is 7.

Start with the first and second terms:
21 ÷ 3

= 7

Confirm with the second and third terms:
147 ÷ 21

= 7

Thus, the common ratio (r) is 7.

Answer:

(P + 2)(p+ 16)

Step-by-step explanation:

Factor p 2 + 18p + 32.

Consider the form  x² +bx +c. Find a pair of integers whose product is  c  and whose sum is b .

In this case, whose product is  32  and whose sum is  18 .

2,16 .

Write the factored form using these integers.

(P + 2)(p+ 16)

                                        CHECK

(P + 2)(p+ 16)

distribute

p(p+16) + 2(p+16)

simplify

p² + 16p + 2p + 32

combine 16p + 2p = 18p

p² + 18p + 32

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Answer:

(p + 2)(p + 16)

That's your answer!!