cho hàm số f(x) liên tục trên đoạn [a;b] và có nguyên hàm F(x) thỏa F(a)=10;F(b)=2022 Khi đó \int _a^b\: f(x) dx bằng

Multiplying the linear expressions, the correct sequence is given as follows:

They are multiplied applying the distributive property, in which all the terms are multiplied and the like terms are combined.

Hence:

5x(-3 -7x)

(5x)(-3) + (5x)(-7x)

-15x - 35x²

Hence the last option is correct.

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Answer:

No

Step-by-step explanation:

If these two individual statements are true, it means they share the same elements of set C. In addition to this, sets A and B could have additional elements, hence this cannot be true.

Answer:

8

Step-by-step explanation:

You should have this in mind , one raise to the power of any number is one and also any number with the power zero is 1.

{(1)¹⁰⁰ + (−1)¹⁰¹+(2500)⁰} x2³

= 1 - 1 + 1 × 8

= 1 - 1 + 8

= 1 +7

= 8

The equation that models the data on pandas is FV = 25(1.066)^t.

The formula for calculating future value of the pandas is:

FV = P (1 + r) ^n

FV = 25(1.066)^t

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Answer:

h^24

Step-by-step explanation:

hope that helpssndbfbsb

Answer: The function is odd and symmetric with respect to the origin.

Step-by-step explanation:

A function is even if f(x)=f(-x), and odd if f(x)=-f(-x). If a function satisfies neither of these, it is neither even nor odd.

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

Therefore, the function is odd, and thus the function is symmetric about the origin

Answer:

1. The data show that skipping breakfast is associated with earning lower exam grades.

2. There is an increase in B's for those who do eat breakfast before the exam.

Solving the given equations we get,

If the quadratic equation is [tex]ax^2+bx+c=0[/tex] then the solutions of this are given by,

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

Here in the problem given that,

The first quadratic equation is [tex]9x^2-25=-12-10x[/tex]

Converting it into standard form of quadratic equation we get,

[tex]9x^2-25=-12-10x\\9x^2-25+12+10x=0\\9x^2+10x-13=0[/tex]

So here a=9,b=10,c=-13

The solutions of the equation is given by,

[tex]x=\frac{-10\pm\sqrt{10^2-4\times9\times(-13)}}{2\times9}=\frac{-10\pm\sqrt{100+468}}{18}\approx\frac{-10\pm23.83}{18}[/tex]

So either,

[tex]x=\frac{-10+23.83}{18}=\frac{13.83}{18}\approx0.77[/tex]

Or,

[tex]x=\frac{-10-23.83}{18}\approx-1.88[/tex]

So the solutions are given by x=0.77 and -1.88

Second quadratic equation is [tex]4n^2-1=12n+3n^2+11[/tex]

Converting the equation in its standard form we get,

[tex]4n^2-1=12n+3n^2+11\\4n^2-1-12n-3n^2-11=0\\n^2-12n-12=0[/tex]

so here a=1,b=-12,c=-12

Solutions are given by,

[tex]n=\frac{-(-12)\pm\sqrt{(-12)^2-4\times1\times(-12)}}{2\times1}=\frac{12\pm\sqrt{144+48}}{2}\approx\frac{12\pm13.86}{2}[/tex]

So either

[tex]n=\frac{12+13.86}{2}=12.93[/tex]

Or,

[tex]n=\frac{12-13.86}{2}=-0.93[/tex]

Solutions are given by n = 12.93 and -0.93

Hence the solutions are x=0.77 and -1.88 for first equation and n=12.93 and -0.93 for second equation.

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Answer:

d because the point satisfied both

Answer:

D

Step-by-step explanation:

Answer:

D. 2

E. -2

Step-by-step explanation:

The surface area of the exterior of the building rounded to the nearest hundred square feet is 40700 feet².

Surface area is the amount of space covering the outside of a three-dimensional shape.

Given, base of prism = 60 feet, height of the prism h₁= 150 feet, and height of the pyramid h₂ = 1/6 (150)

                    = 25 feet.

The surface area of the exterior of the building = lateral surface area of prism + pyramid.

                SA = ( 4ah₁ ) +(a√(a² + 4h₂²) )

                SA = ( 4(60)150 ) + ( 60(√60² + 4(25)² )

                      = ( 240* 150 ) + 60(√3600 +2500 )

                      = 36000 + 60(√6100)

                      = 36000 + 60(78.1024)

                      = 36000 + 4686.15

                      = 40686.15

                      ≈ 40700 feet².

Therefore, the surface area of the exterior of the building rounded to the nearest hundred square feet is 40700 feet².

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Answer:

The surface area of the exterior of the building is approximately 40700 feet

Answer:

-3(-4-4) would work giving you 24

Step-by-step explanation:

im sorry that qustion doesnt make sense, if you mean higher then 21, less than 30 than -3(-4-4) would work giving you 24

Answer:

1-irrational 2-rational 3-rational 4-rational 5-irrational

Step-by-step explanation:

Answer:

The answer is OPTION (D)log(y)=0.326x+0.687

It is a linear model, e.g. a model that assumes a linear relationship between the input variables (x) and the single output variable (y)

The Linear regression equation for the transformed data:

We transform the predictor (x) values only. We transform the response (y) values only. We transform both the predictor (x) values and response (y) values.

(1, 13) 1.114

(2, 19) 1.279

(3, 37) 1.568

(4, 91) 1.959

(5, 253) 2.403

X            Y           Log(y)

1              13           1.114

2             19         1.740

3             37        2.543

4             91        3.381

5            253      4.226

Sum of X = 15

Sum of Y = 8.323

Mean X = 3

Mean Y = 1.6646

Sum of squares (SSX) = 10

Sum of products (SP) = 3.258

Regression Equation = ŷ = bX + a

b = SP/SSX = 3.26/10 = 0.3258

a = MY - bMX = 1.66 - (0.33*3) = 0.6872

ŷ = 0.3258X + 0.6872

The graph is plotted below:

The linear regression equation is  log(y)=0.326x+0.687

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Answer:

value of car depreciate each year = $2000

y + 2000x = 16,500

slope of line = -2000

No, not proportional

Step-by-step explanation:

Value of depreciation of an object is given by :-

Depreciation = [tex]\frac{ total Cost-scrap value}{estimated life}[/tex]

according to question ;

total cost = $16500

scrap value = $500

estimated life = 8 years

therefore,

depreciation = [tex]\frac{16500 - 500}{8}[/tex] = [tex]\frac{16000}{8}[/tex] = $2000

now,

let the value of car after 'x' years be 'y'

therefore linear equation showing the relation of x and y is

y + 2000x = 16500

The graph of a linear equation is a line.

If c = 0 in a linear equation (so y = mx), then the equation is a proportional linear relationship between y and x.

If c ≠ 0, then y = mx + c is a non-proportional linear relationship between y and x.

here equation is of type,

y = mx +c, thus it is not linear.

also in the equation y = mx +c,

'm' is the slope of line

therefore by comparing the equation,

y +2000x = 16500

y = -2000x + 16500

slope is - 2000

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Answer:

1st set of equations - parallel

2nd set - perpendicular

3rd set - neither

Step-by-step explanation:

First set:

simplify the equation for line 1  by dividing by -4: y = 0.5x + 1

simplify the equation for line 1  by dividing by -6: y = 0.5x - 1.5

Both have the same slope: 0.5 so the lines are parallel.

Second set:

simplify the equation for line 1  by dividing by 3: y = -2/3x + 4

simplify the equation for line 1  by dividing by -4: y = 3/2x - 7/4

-2/3 * 3/2 = -1, so the lines are perpendicular

Third set

simplify the equation for line 1  by dividing by 1/2: y = -2x+4

simplify the equation for line 1  by dividing by 2: y = -1/4x +2

-2x+4=-0.25x+2

-2x+0.25x=2-4

-1.75x=-2

x=1.14

y=-2(1.14)+4 = 1.7143. So there is an intersection point

The pair of lines 2x - 4y = -4 & 3x - 6y = 9, 2x + 3y = 12 & and 6x - 4y = 7, and x + (1/2)y = 2 & (1/2)x + 2y = 4 will be parallel lines, perpendicular lines, and neither parallel nor perpendicular, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The pair of lines is given as,

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

3x - 6y = 9      ⇒        y = (1/2)x - 3/2

The pair of lines are parallel to each other because the slope is equal.

2x + 3y = 12     ⇒        y = -(2/3)x + 4

6x - 4y = 7       ⇒        y = (3/2) x - 7/4

The pair of lines are parallel to each other because the product of slopes is -1.

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

(1/2)x + 2y = 4      ⇒        2x + 4y = 8

The pair of lines are neither parallel nor perpendicular to each other.

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Answer: The data cannot be modeled by an exponential function because the data is for a linear function (as there is a constant increase in f(x) each time x increases by 1)

Body design, muscular power and steadiness, flexibility and cardio-respiratory endurance are the components of fitness. Fitness is a major component of a healthy lifestyle.

While performing tasks during gymnastics she needs balance so that she can maintain and control a particular position.

Body design, muscular power and steadiness, flexibility and cardio-respiratory endurance are the components of fitness. Fitness is a major component of a healthy lifestyle.

Balances are of two types dynamic and static. Balance used while moving and performing the task is dynamic balance while performing in a standing position is static balance.

Gymnasts require balancing as the main component cause they use poles and beams to perform their tasks.

Therefore, balance is the skill mainly required in gymnastics.

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Answer:

X1 2/7

Step-by-step explanation:

Step-by-step explanation:

We can write it in radical form, and the denominator of the exponent became the power of the radical. That is

And

We can also write it as

And that's the simplified form of the given exponential form .

Using translation concepts, the equation for the transformed logarithm is given by:

[tex]f(x) = \log{(x + 3)} - 3.48[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The logarithm function is given by:

[tex]f(x) = \log{x}[/tex].

We have that:

Hence:

[tex]f(x) = \log{x + 3} + b[/tex]

To find the shift up/down, we consider that f(0) = -3, hence:

[tex]-3 = \log{0 + 3} + b[/tex]

[tex]b = -3 - \log{3}[/tex]

b = -3.48.

Hence the function is given by:

[tex]f(x) = \log{x + 3} - 3.48[/tex]

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Answer: 4/30

Step-by-step explanation:

it does

9.7 to one significant figure is 10

We have:

9.7

To approximate to one significant figure, we have to estimate the number such that it is represented by a non zero digit.

When 9.7 is approximated, we have:

10

Hence, 9.7 to one significant figure is 10

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The basic parabola is stretched in the y-direction by a factor of 2 (and hence made steeper) and translated.

To create a new parabola that resembles the fundamental parabola, we can translate the parabola vertically. The graph of the function y=x2+b simply resembles a regular parabola with the vertex moved b units down the y-axis. The vertex is so situated at (0,b). The parabola shifts upward if b is positive and downward if b is negative.

The parabola can also be translated horizontally. The graph of the function y=(x-a)^2 resembles a conventional parabola with the vertex moved one unit down the x-axis. then, the vertex is found at (a,0). Observe how we go to the right if an is positive and to the left if an is negative.

All parabolas can be obtained from the basic parabola by a combination of:

Thus, all parabolas are similar.

Hence the basic parabola is stretched in the y-direction by a factor of 2 (and hence made steeper) and translated.

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Answer: -24

Step-by-step explanation:

I am assuming you want the value of (f × g)(-2)

[tex]f(-2)=(-2)^2+4\\f(-2) = 4+4\\f(-2)=8[/tex]

[tex]g(-2)=2(-2)+1\\g(-2)=-4+1\\g(-2)=-3[/tex]

8 × -3 = -24

The members of a possible set C are {6, 9, 12}

The universal set is the set that contains all other sets. Given the following sets

ξ = {x:x is an integer, 2 ≤ x ≤ 14}

B = {x:x is a prime number}

A = {x:x is a multiple of 3}

The sets B and A are:

B = {2, 3, 5, 7, 11}

A = {3, 6, 9, 12}

If C is a subset of A with a cardinality of 3, hence the required set will be {6, 9, 12}. Note that 3 is excluded since B n C must be an empty set.

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a)  Z-score for Patrisse test grade is 0.7288

b) z-score for Makayla test grade is -0.7441

c) Patrisse did better.

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.

Z-score for Patrisse test grade.

X= 81.4, [tex]\mu[/tex] = 72.8, [tex]\sigma[/tex] = 11.8

Z= x-  [tex]\mu[/tex] /  [tex]\sigma[/tex]

Z= 81.4 - 72.8/ 11.8

Z= 0.7288

Now, z-score for Makayla test grade.

X= 60.6, [tex]\mu[/tex] = 67, [tex]\sigma[/tex] = 8.6

Z= x-  [tex]\mu[/tex] /  [tex]\sigma[/tex]

Z= 60.6 - 67/ 8.6

Z= -0.7441

Hence, Patrisse did better as she had better z- score.

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Answer:

Equation is 20 = 0.8 time x

x=25

Step-by-step explanation:

80% = 0.8

So to find x we 20/8

and we get 25 as the final answer