Let f be the continuous function defined on [-4,3] whose graph, consisting of three line segments and a semicircle centered at the origin, is given above. Let g be the function given by g(x) = integral^x_1, (t) dt. Find the values of g(2) and g(-2). For each of g'(-3) and g"(-3), find the value or state that it docs not exist. Find the x-coordinate of each point at which the graph of g has a horizontal tangent line. For each of these points, determine whether g has a relative minimum, relative maximum, or neither a minimum nor a maximum at the point. Justify your answers. For -4 < x < 3, find all values of v for which the graph of g has a point of inflection. Explain your reasoning.

Answer:x=11/14

Step-by-step explanation:

3(2x+7)=8(4-x)

Multiply the first part of the equation

6x+21=
multiply the 2nd half of the equation

32-8x

6x+21=32-8x

Move the -8x to the left side of the equation making it a positive 8x

8x+6x+21=32

Move the 21 to the right side of the equation

8x+6x=32-21

Add the x’s on the left and subtract the 21 from 32 on the right

14x=11

Divide the 14 into the 11

x=11/14

let's convert the mixed fractions to improper fractions and then let's proceed.

[tex]\stackrel{mixed}{12\frac{3}{35}}\implies \cfrac{12\cdot 35+3}{35}\implies \stackrel{improper}{\cfrac{423}{35}} ~\hfill \stackrel{mixed}{5\frac{31}{35}}\implies \cfrac{5\cdot 35+31}{35}\implies \stackrel{improper}{\cfrac{206}{35}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]12\frac{3}{35}~~ + ~~x~~ = ~~5\frac{31}{35}\implies \cfrac{423}{35}+x=\cfrac{206}{35}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{35}}{35\left( \cfrac{423}{35}+x \right)=35\left( \cfrac{206}{35} \right)} \\\\\\ 423+35x=206\implies 35x=-217 \\\\\\ x=\cfrac{-217}{35}\implies x=\cfrac{-31}{5}\implies {\Large \begin{array}{llll} x=- 6\frac{1}{5} \end{array}}[/tex]

to convert an improper fraction like -31/5 to a mixed fraction, well, first off, we nevermind the sign, so we only use 31/5 and then we divide 31 ÷ 5.

hmm 31 ÷ 5 gives us a quotient of 6, and a remainder of 1, we put the quotient upfront and the remainder as the numerator, with the old denominator and sign back in.

Answer:

12 km

Step-by-step explanation:

4.4 * 2.727 km = 11.9988   ( using a calculator)

              since the smallest factor (4.4)  has only 2 significant digits , your answer should be rounded to only 2 S.D.      so   = 12 km

We know that,

By definition, no function is symmetrical about the x-axis (or any other horizontal line). Because the one flipped with respect to the horizontal violates the vertical line test.

On the other hand, functions can be symmetric about a vertical line or a point. In particular, functions symmetric about the y-axis are also "even" functions, and functions symmetric about the origin are also "odd" functions. Because of this correspondence between graph symmetry and function equality or oddness, "symmetry" in algebra is usually applied to the y-axis and the origin.

To know more about y-axis visit

https://brainly.com/question/29003298

#SPJ1

Answer:

  yes: f(x) = 0

Step-by-step explanation:

You want to know if a function exists that is symmetrical about the y-axis and the origin.

A graph is symmetrical about the y-axis if and only if ...

  f(-x) = f(x)

A graph is symmetrical about the origin if and only if ...

  f(-x) = -f(x)

For both conditions to be met, we must have ...

  f(x) = -f(x)

  2f(x) = 0 . . . . . add f(x)

  f(x) = 0 . . . . . . . divide by 2

The graph of f(x) = 0 will be symmetrical about the y-axis and the origin. (It is the x-axis.)

The area of the rectangular yellow region is of:

30 cm².

The area of a rectangle of base b and height h is obtained as the multiplication of these dimensions, as follows:

Area = base x height.

From the image given at the end of the answer, these dimensions are given as follows:

Then the area of the yellow region is calculated as follows:

Area = 10 x 3 = 30 cm².

The problem asks to obtain the area of the rectangular region, considering that:

The region is given by the image shown at the end of the answer.

More can be learned about the area of a rectangle at https://brainly.com/question/25292087

#SPJ1

The reported confidence interval will contain the population proportion of consumers 95% of the time.

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.

To know more about confidence intervals visit: brainly.com/question/24131141

#SPJ4

Answer:

  A – see below

Step-by-step explanation:

You want to identify the graph of f(x) = (x -1)/(x² -x -6).

The function can be factored as ...

  [tex]f(x) = \dfrac{x-1}{(x-3)(x+2)}[/tex]

The numerator is zero when x=1, so that is where the x-intercept lies.

The denominator is zero for x=-2 and x=3, so those are the locations of the vertical asymptotes.

The graph that has vertical asymptotes at x=-2 and x=3, and an x-intercept of x=1 is Graph A.

<95141404393>

Answer:

x= -4 y= -1

6x - y = - 23

-y=-23-6x

y=6x+23, use this to plug in for y in the second equation.

2x + 5y = -13

2x + 5(6x+23) = -13

2x+30x+115=-13

x= -4, use this to plug in for x in the first equation.

6x - y = - 23

6(-4)-y=-23

-24-y=-23

-y=-23+24

-y=1

y= -1

Step-by-step explanation: not doing this to steal points

Answer:

here is your solution.

Step-by-step explanation:

x=4 & y=1

Answer: 15 days

Step-by-step explanation:

Pasta salad; 5  10  15  

Pretzel salad; 3  6  9  12  15

The gallons you can afford if you have $40 is 13 gallons.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is a relationship between two expressions that is expressed as an equality on either side of the equal to sign. An equation would be 3x = 18, for instance.

From the information, the local gas station is offering a deal to their customers. If they purchase $8.00 car wash, the cost per gallon of gas is $2.60.

Here, we want to solve a linear equation to find the gallons you can afford if you have $40.

The linear equation to find how many gallons you can afford if you have $40 will be illustrated as x

This would be:

2.60 × (40 / 8) = x

x = 2.60 × 5

x = 13 gallons

The gallons will be 13.

Learn more about equations on:

brainly.com/question/297232

#SPJ1

Answer:

k is greater or equal to -5

Step-by-step explanation:

[tex] - 5 \leqslant k[/tex]

here, -5 is on the left side of the inequality sign which means it is less than or equal to k.

Using simplification by factorisation and division

(x² + 6x + 9)/(x² - 9) = (x + 3)/(x - 3) and (3x² - 9)/(x² - x - 6) = 3x/(x + 2)

To simplify the equations, we shall factorize both the numerator and the denominator, and divide through by a common factor.

for the equation (x² + 6x + 9)/(x² - 9);

the numerator:

x² + 6x + 9 = x² + 3x + 3x + 9

x² + 6x + 9 = x(x + 3) +3(x + 3)

x² + 6x + 9 = (x + 3)(x + 3)

the denominator:

x² - 9 = x² - 3²

x² - 9 = (x + 3)(x - 3) {difference of two squares}

(x² + 6x + 9)/(x² - 9) = (x + 3)(x + 3)/(x + 3)(x - 3)

divide through by the common factor (x + 3)

(x² + 6x + 9)/(x² - 9) = (x + 3)/(x - 3)

For the equation; (3x² - 9)/(x² - x - 6)

the numerator:

3x² - 9 = 3x(x -3)

the denominator:

x² - x - 6 = x² -3x + 2x - 6

x² - x - 6 = x(x - 3) + 2(x - 3)

x² - x - 6 = (x + 2)(x - 3)

divide through by the common factor (x - 3)

(3x² - 9)/(x² - x - 6) = 3x/(x + 2)

Thus, (x + 3)/(x - 3) and 3x/(x + 2) are the results for simplifying (x² + 6x + 9)/(x² - 9) and (3x² - 9)/(x² - x - 6) respectively using factorization.

Learn more about factorization here:https://brainly.com/question/25829061

#SPJ1

- The null hypothesis Is: [tex]$H_0: \mu=4.5$[/tex]

- The alternative hypothesis Is: [tex]$H_1: \mu \neq 4.50$[/tex]

- The test statistic is: t=-0.43

- The p-value of the test is of 0.6684.

What is p-value?

The p-value Is of 0.6684>0.05, which means that we can conclude that the population of student course evaluations has a mean equal to [tex]\mathbf{4 . 5 0}$.[/tex]

We are going to test If the mean Is equals to 4.50, thus, the null hypothesis Is:

[tex]H_0: \mu=4.5[/tex]

At the alternative hypothesis, we test If the mean Is different to 4.50, that is:

[tex]H_1: \mu \neq 4.50[/tex]

Since we have the standard devlation for the sample, the t-distribution is used. The value of the test statistic Is:

[tex]t=\frac{\pi-\mu}{\frac{\sqrt{n}}{\sqrt{n}}}$$[/tex]

For this problem:

[tex]$$\begin{aligned}& t=\frac{4.30-1.5}{\frac{2.21}{\sqrt[3]{80}}} \\& t=-0.43\end{aligned}$$[/tex]

We are testing If the mean is dlfferent from a value, thus, the p-value of test is found using a two-talled test, wlth t=-0.43 and [tex]$80-1=79 \mathrm{df}$[/tex].

Using a t-distribution calculator, the [tex]$\mathrm{p}$[/tex]-value is of [tex]$\mathbf{0 . 6 6 8 4}$[/tex].

The p-value is of 0.6684 > 0.05, which means that we can conclude that the population of student course evaluations has a mean equal to 4.50.

To learn more about hypothesis  visit:https://brainly.com/question/29519577

#SPJ4

Based on the SAS, SSS, and the transitive property of congruence, the reason why ΔABC ≅ ΔGHJ is because of option B.

The SAS is a triangle theorem that states that two triangles are congruent if they both have two pairs of congruent sides and a pair of included congruent angles.

On the other hand, the SSS states that two triangles that have three pairs of congruent sides are equal.

The transitive property of congruence states that if two triangles are congruent to a third triangle, then all three triangles are congruent to each other.

Based on the SSS, triangle ABC is congruent to triangle DEF.

Based on the SAS, triangle DEF is congruent to GHJ.

Therefore, based on the transitive property of congruence, triangle ABC is congruent to triangle GHJ.

Therefore, the reason why ΔABC ≅ ΔGHJ is because of the reason given in option B.

Learn more about the SAS and SSS on:

https://brainly.com/question/3999145

#SPJ1

By ratios ,orange = 15 , apple = 10 , coconut = 20 are needed to make 45 liters of this cocktail.

What does the math ratio mean?

When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. A proportion is an equation that sets two ratios at the same value.

                   As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls)

orange = 3

apple = 2

coconut = 4

total = 9

orange =  3/9  * 45  = 15

 apple = 2/9  *  45  = 10

coconut = 4/9  * 45  = 20

Learn more about Ratio

brainly.com/question/13419413

#SPJ1

The complete question is -

In a fruit cocktail, the ratio of orange juice to apple juice to coconut milk is 3:2:4, respectively. How much of each type is needed to make 45 liters of this cocktail?

The equations for the horizontal line and the vertical line are y = - 3 and x = 4, respectively.

Herein we find the case of a point (x, y) = (a, b), from which we must derive the equations for the horizontal line and the vertical line, whose forms are described below:

Horizontal line

y = b

Vertical line

x = a

If we know that (x, y) = (4, - 3), then the equations for the horizontal and vertical lines are, respectivelly:

Horizontal line

y = - 3

Vertical line

x = 4

To learn more on equations of the line: https://brainly.com/question/2564656

#SPJ1

Answer: x : x e R and R >

Step-by-step explanation:

We can find the test statistic and the critical value by the  distributed the test statistic under the assumption that the null hypothesis hold.

It is the study of external and the internal force.

When the first data will be  pretext and the 2nd  the joe will be the first test, the d will be mu joule  -1. The alternative hypothesis to em d is the  smaller than the 0. The first time we need to find the rest  that sticks by the tree is when we were given the question n equal to the 15 and the d p equal to -15.1. The formula with the  werther to the end has a big  square root of 15 points.

times square 15 equal to the 1.399 point, and the next  time we need to find a p value for this, we will use by  left hand test.To  The 14 degree freedom will be smaller than the minus 1.399 point if the value of the d n -1 degree, freedom and equal to the 15 minus 1 is equal. Energy use the t distribution when it is = 14 degree- freedom is smaller = 1.399 point. I going to compare to 918 point.

We're gong to regent the noon because the alpha is smaller than the 11.

Thus,

We can defined The mean difference is  less than 0 points.

To know more about statistic click-

https://brainly.com/question/15525560

#SPJ1

Equations representing the total costs for plan A and B are A = 19 + 0.50x and B = 13 + 1.5x, respectively, where x is the number of movies watches.

Cost of both the plans will be equal for 6 movies.

What is a linear equation?

Given that, Wyatt is deciding between two different film streaming sites to subscribe to, plan A costs $19 per month plus $0.50 per film watched, plan B costs $13 per month plus $1.50 per film watched.

According to question,

A = 19 + 0.50x and

B = 13 + 1.5x

For costs being equal, we have,

A = B

19 + 0.50x = 13 + 1.5x

x = 6

Hence, for 6 films the costs of both the plans will be equal and equation for both the plans are A = 19 + 0.50x and B = 13 + 1.5x

To know more about linear equation check the below link:

https://brainly.com/question/11897796

#SPJ4

The equation of each quadratic in the picture of formula and graphs attached is y=-1(x+8)^2 +9 and y=1/4*(x-6)^2 +3

What is Graph Transformation?

When a graph is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects." For instance, by simply pushing the graph of the function g(x) = x2 up by 3 units, the graph of the function f(x) = x2 + 3 is generated. graph transformations are highly useful for graphing functions without having to start from scratch since they allow you to move, extend, compress, or reflect the curve. The graph of the parent function is either "moved," "resized," or "reflected" by a graph transformation. The three primary categories of graph transformations are as follows:

A)

first of all we need to find which type of parabolic graph is it

from the picture give we can clearly see it is a x^2=-4ay type of graph

and using graph transformation formula

i.e. y= a(x-h)^2 + k

where h = -8

k=9

we get y=a(x+8)^2+9

as we know (-5,0) lie on this graph

so,

0=a(-5+8)^2+9

a=-1

so the equation is y=-1(x+8)^2 +9

B)

first of all we need to find which type of parabolic graph is it

from the picture give we can clearly see it is a x^2=-4ay type of graph

and using graph transformation formula

i.e. y= a(x-h)^2 + k

where h = 6

k=3

we get y=a(x-6)^2+3

as we know (0,12) lie on this graph

so,

12=a(0-6)^2+3

a=1/4

so the equation is y=1/4*(x-6)^2 +3

Learn more about Graph transformation from the link below

https://brainly.com/question/10059147

#SPJ1

Answer:

A.x=-7/6

B.x=-19/9

C.x=-23/14

D.x=-5/3

E.x=-7/5

Step-by-step explanation:

A. 30x+35, 30x=-35 x = -7/6

B. 45x+90, 45x=-90, x=-19/9

C. 28x+46, 28x=-46, x=-23/14

D. 72x+120, 72x=-120, x=-5/3

E.77+55x, 55x=-77, x=-7/5

The serving size of a certain brand of yoghurt has 4.6 grams of protein. The yoghurt is consumed in three portions. They eat 13.8 grams of protein daily.

A field of mathematics known as arithmetic operations deals with the study of numbers and the operations on those numbers that are relevant to all other branches of mathematics. The basic operations included in it are addition, subtraction, multiplication, and division.

Calculations involving numbers are done using arithmetic operators. The numerical results that are produced by arithmetic operators are associated from left to right.

The following are the three properties you should consider: Commutative addition applies to full numbers. Associative math is the addition of whole integers. When adding whole numbers, the number 0 serves as an identity.

In several contexts, including multiplication (repeated addition), division, and other operations, the fundamental operations of addition and subtraction are applied (repeated subtraction). These operations are used to transform the word problems into mathematical expressions.

= 4.6 x 1 = 4.6

= 4.6 x 3 =13.8

Hence the total grams of protein consumed is 13.8

To learn more about mathematical operations refer to:

https://brainly.com/question/20628271

#SPJ1

Answer: 13.8 grams of protein

Step-by-step explanation:

     If there are 4.6 grams of protein in 1 serving, then to find the number of grams in 3 servings we can use multiplication to solve this question.

4.6 grams of protein * 3 servings = 13.8 grams of protein

Answer:25

Step-by-step explanation:

We have the rate: 35 deliveries in 3.5 hours. or 35/3.5

Find the unit rate -> 35/3.5/

                                /3.5/3.5

10/1

10

10 deliveries per hour

in 2.5 hours

10*2.5

25

*Assuming the rate of deliveries is constant*

Answer:

1.) Feeds on dead organisms – Decomposer

2.)obtain energy nutrients from producers – Consumer

3.)Network of interconnected food chains – Food web

4.)Manufactures food using energy from the sun – Producer

5.)Simple model used for showing how energy passes through an ecosystem – Food chain

6.) Relationship between organisms where both members benefit – Mutualism

Step-by-step explanation:

pls if this answer helped you kindly rate it as brainliest

Answer: 180

Step-by-step explanation:

all 3 angles equal 180 degrees if you divide by 3 each angle will be 60 degrees

well, we know it was 480, then we reduce it by 50.

if we take 480 to be the 100%, what's 50 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 480 & 100\\ 50& x \end{array} \implies \cfrac{480}{50}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 48 }{ 5 } ~~=~~ \cfrac{ 100 }{ x }\implies 48x=500\implies x=\cfrac{500}{48}\implies x=\cfrac{125}{12}\implies \boxed{x\approx 10.4}[/tex]

now, the TV is only 480 - 50 = 430, then it gets reduced another 50.

if we take 430 to be the 100%, what's 50 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 430 & 100\\ 50& y \end{array} \implies \cfrac{430}{50}~~=~~\cfrac{100}{y} \\\\\\ \cfrac{ 43 }{ 5 } ~~=~~ \cfrac{ 100 }{ y }\implies 43y=500\implies y=\cfrac{500}{43}\implies \boxed{y\approx 11.6}[/tex]

hmmm the absolute change of the reductions?   that sounds like 480 - 50 - 50 = 380.

well, the overall percentage hmmm well, that's the $100 reduction total.

if we take $480 as the 100%, what's $100 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 480 & 100\\ 100& z \end{array} \implies \cfrac{480}{100}~~=~~\cfrac{100}{z} \\\\\\ \cfrac{ 24 }{ 5 } ~~=~~ \cfrac{ 100 }{ z }\implies 24z=500\implies z=\cfrac{500}{24}\implies z=\cfrac{125}{6}\implies \boxed{z\approx 20.8}[/tex]

JK is a midsegment of triangle FGH. Hence, the values of x and y are 18 and 14 respectively.

A triangle's midsegment is a line segment that connects the midpoints or centers of two of its opposite or adjacent sides.

Given that, JK is a midsegment of triangle FGH.

Also the values of:

FG = 28

FJ = x

JH = 10

JK = y

As, JK is midsegment of FG, we have:

JK = FG / 2

y = 28 / 2

y = 14

So, the value of y could be 14.

Also, FG = 28

FJ + JH = FG

10+x = 28

x = 28 - 10

x = 18

So, the value of x could be 18.

Hence, the values of x and y are 18 and 14 respectively.

Learn more about triangles here:

https://brainly.com/question/2773823

#SPJ1

Answer:

x=10

Y=14

Step-by-step explanation:

big ideas

A line's steepness can be determined by looking at its slope. Slope is determined mathematically as increase over run.

According to the slope equation, the slope of a line may be calculated by dividing the rise of the line between any two places by the run of the same line between the same two sites.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

Slope of y =f(x)

Slope (m) = ΔY / ΔX = 14 / 1 = 14

y = 14x + 22

When x=0, y = 22

When y=0, x = -1.5714285714286

Slope of y = g(x)

Slope (m) =ΔY / ΔX = 14 / 1 = 14

y = 14x + 24

When x=0, y = 24

When y=0, x = -1.7142857142857

To learn more about slope refer :

https://brainly.com/question/16949303

#SPJ1

The required simplified solution of the given expression is given as √3(√7 - 2).

Given that,
To determine the simplified solution of the √(√21-2√3)²

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
= √(√21-2√3)²
=√21-2√3       (√a² = a)
= √3(√7 - 2)

Thus, the required simplified solution of the given expression is given as √3(√7 - 2).

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ1