Let f ( x ) = 1 x and g ( x ) = x 2 + 5 x . a. Find (f · g)(x). b. Find the domain and range of (f · g)(x).

Answer:

6 pack of t shirts for 15 :3

Step-by-step explanation:

The value of term a9 is 9k+32.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same value.

The formula of Arithmetic progression is

a(n) = a1 + (n - 1)d

given that the term of arithmetic sequence and common difference,

a1 = 4 and d = K+4.

now find the value of term a9.

a(n) = a1 + (n - 1)d

now, substitute a(n) = a9, a1 = k, d = k+4.

a9 = k + (9 - 1)(k+4)

a9 = k + 8(k+4)

a9 = k + 8k + 32

a9 = 9k +32

Hence,The value of term a9 is 9k+32.

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The subtraction equations written as addition equations are

a + (-9) = 6

p + (-20) = -30

z + 12 = 15

x + 7 = -10

From the question, we are to write each of the given subtraction equation as an addition equation

This equation written as an addition equation is

a + (-9) = 6

This equation written as an addition equation is

p + (-20) = -30

This equation written as an addition equation is

z + 12 = 15

This equation written as an addition equation is

x + 7 = -10

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The variables that

x + y = 2100  

5 x + 7 y = 11700  

Let x = total dollar amount of sales of phone;

      y = total dollar amount of sales of computer

for total sales of phones anna earns 5% commission

So anna 's commission = 5% of x

                                       = 0.05x

for total sales of computer anna earns 7% commission

So anna 's commission = 7% of y

                                       = 0.07y

Given the total sales; x + y = 2100

And commission; 0.05x + 0.07y = 117; or 5x + 7y = 11700

Therefore the system of equations are

x + y = 2100   …….equation (1)

5 x + 7 y = 11700  ……equation (2)

In mathematics, a variable is a symbol and placeholder for any mathematical object. In particular, a variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set.

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Answer: 1

Step-by-step explanation:

s = 5, t = 2

10/5*2

= 10/10

=1

The amount raised in the west in scientific notation is 8.650  × 10³.

The four region raised 5.38 × 10⁴ dollars(53800)

According to the table,

Amount east raised = 1.46 × 10⁴ = 14600

Amount North raised = 2.38 × 10⁴ = 23800

Amount South raised =  6.75 × 10³ = 6750

Therefore, the amount raised in the west can be calculated as follows;

amount raised in the west = 53800 - 14600 - 23800 - 6750

amount raised in the west = 8650

amount raised in the west = 8.650  × 10³

Therefore, the amount raised in the west in scientific notation is 8.650  × 10³.

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The answer is 360 miles

so you do

15 times 8 and that equals 120

so then you also o 120 times 3 and the answer is 360 :>

you are so welcome

42%  is the probability that exactly one is paid by the hour.

In statistics, what does a probability mean?

P( exactly one paid by hour ) =

[tex]\frac{71}{100} . \frac{29}{100} + \frac{29}{100} . \frac{71}{100} = \frac{2059 + 2059}{10000}[/tex]

[tex]\frac{4118}{10000} = 42%[/tex]%

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The cost of the toothbrush will be equal to $14.40. The correct option is A.

The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that an electric toothbrush costs $72, including a 20% price markup.

The price of the toothbrush will be calculated as,

P = ( 72 x 20 ) / 100

P = 1440 / 100

P = $14.40

Therefore, the cost of the toothbrush will be equal to $14.40. The correct option is A.

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Answer: 60.00

i did the test.

The total surface area of the pyramid 806.12 [tex]m^{2}[/tex].

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

Side (s) = 12

Altitude (h) = 6

Area = 3√3/2*s² + 3*s*√(h²+3s²/4)

Area = 3√3/2*(12)² + 3*(12)*√[6²+3(12)²/4]

Area = 806.12 [tex]m^{2}[/tex]

A 3D object's surface area is the entire area that all of its faces cover. For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it.  

Area of a square is equal to the sum of the lengths of its sides, where an is a square side.

The surface area of a three-dimensional shape refers to the amount of open space that it occupies. A solid shape's volume is the amount of space it takes up.

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The expected value of chi-square statistics is not significantly different from the observed value.

What is chi-square statistics?

Chi-square statistics is defined as a measure that is used to denote the difference between the expected frequencies and the observed frequencies of an event. It is illustrated using the symbol, 'χ2'.

Deciding for the goodness of a fit

The assigned value of chi-square is 1.273 while the critical value is 13.388

The hypotheses for the goodness of fit test are given below:

Null Hypothesis: the expected value is not significantly different from the observed values

Alternate Hypothesis: the expected value is significantly different from the observed values

We know that the chi-square test is right-tailed.

Further, the value of test statistics is 1.273, which is less than the critical value, 13.388

Thus we fail to reject the null hypothesis and we accept it.

Hence, we can conclude that the expected value is not significantly different from the observed value.

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Answer:yes b

Step-by-step explanation:

because you subtract it

Answer:

95

Step-by-step explanation:

Because they are opposite angle. Since TRV and SRV is opposite that means they are equal each other

The center of a circle is the point at which the tip of our compass is placed when drawing a circle. It is the center of the circle's diameter.

A circle is a two-dimensional closed figure in which the set of all points in the plane is equidistant from a given point known as the "centre."

The center of a circle is the point at which the tip of our compass is placed when drawing a circle. It is the center of the circle's diameter. The radius of a circle is the distance from the center to any point on its circumference that is always the same.

The center of the circle that is internally tangent to all three triangle sides; the orthocenter, the intersection of the triangle's three altitudes; and the nine-point center, the center of the circle that passes through nine key triangle points.

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The distance of AB is 2√5.

Given that the point A is (2,-1) and point B is (4,3).

The distance formula gives us the shortest distance between the given two points in a plane of two dimensional.

The given points is point A(x₁,y₁)=(2,-1) and point B (x₂,y₂)=(4,3).

Now, we will use the distance formula to calculate the distance that is D=√(x₂-x₁)²+(y₂-y₁)².

Further, we will substitute the given values in the above formula, we get

D=√(4-2)²+(3-(-1))²

D=√2²+(3+1)²

D=√2²+4²

D=√4+16

D=√20

D=2√5

Hence, the distance of AB from the given points point A is (2,-1) and point B is (4,3) is 2√5.

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The equation in slope-intercept form for the line given (-3,12) and (15,0) is

[tex]y=-\frac{2}{3}x+ 10[/tex]

Given,

The points = (-3,12) and (15,0)

We know,

Slope of the equation m= [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Substitute the values and find the value of m

m= [tex]\frac{0-12}{15--3}[/tex]

m=[tex]-\frac{12}{18}=-\frac{2}{3}[/tex]

Slope intercept form of the equation is y= mx + b

where b is y intercept form.

Consider one point and substitute the values.

[tex]0=-\frac{2}{3}(15)+b \\0=-10+b\\b=10[/tex]

Then the slope intercept form is

[tex]y=-\frac{2}{3}x+ 10[/tex]

Hence, The equation in slope-intercept form for the line given (-3,12) and (15,0) is [tex]y=-\frac{2}{3}x+ 10[/tex]

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   The equation of the parabola that has vertex at (1,4) and focus (1,6) is

  A parabola is a quadratic function that can move on any axis, it is composed of:

   The equation that defines a parabola can be given by:

(x - h)² = 4p(y - k)

(y - k)² = 4p(x - h)

  This will depend on its aperture

  Since the vertex and the focal axis are on the same axis, we analyze that:

(x - 1)² = 4p(y - 4)

f = (1, 4 + p)

4 + p = 6

p = 6 - 4

p= 2

(x - 1)² = 4*2(y - 4)

(x - 1)² = 8(y - 4)

x² - 2x + 1 - 8y + 32 = 0

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For the area of triangle, the constant of variation is 1/2.

The link between the independent (x) and dependent (y) variables is shown by a constant of variation. A continuous relationship between the variables indicates to the user that there is one; it does not alter regardless of how the scenario changes.

It can be employed to ascertain how the dependent variable will alter in response to changes in the independent variable. For instance, if a person drives continuously at the same pace, they may calculate their distance by multiplying the number of hours they spent driving by the speed they were moving at. In this instance, the speed is the constant since it remained constant regardless of how long or how far they travelled during the journey.

A triangle's area is equal to (1/2) * (base) * (height).

It fluctuates in tandem with both the base length and the height.

The (1/2) represents the variational constant.

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Answer:

57

Step-by-step explanation:

2 out of 3 can be expressed as 2/3. Since we are looking at the 1 out of 3 people, we can use the expression 1/3 x 171 or 171/3, which equals 57

The average is calculated by adding up all the data sets, then dividing that total by the total number of data points. She used 6 gallons of gas on her trip.

In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

The two unit rates of (30 miles per gallon) and can be used to convert three hours to gallons of gas (60 miles per hour).

30 miles = 1 gallon of gas used

For (30 × 2) 60 miles = 2 gallons of gas used

2 gallons of gas she used per hour.

Susan goes 180 miles in 3 hours (60 miles per hour).

Therefore,

For 3 hrs = 3 × 2 = 6 gallons of gas used.

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According to the question, the given parameters with different numbers for the line LH is as follows:

LM =3, MH = k/9 and LH =5

To calculate the distance of the line LH, the expression can be written as:

LH = LM+MH

Substitute the given parameters in the above expression:

5 = 3 + (k/9)

Now, solving above expression, we get the calculated value for the variable 'k':

k = 18 units

Hence, the calculated value for the variable k = 18 units.

How to define distance for the line?

Distance defines the length segment of the line in the coordinate geometry. It is respective length between the two points. In this, the line segment is divided into two parts.

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Answer:

(Some textbooks describe a proportional relationship by saying that " y varies proportionally with x " or that " y is directly proportional to x .") This means that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.

10:4 = 5:2

6:2 = 3:1      

Not equal.

The expression to find the population of fruit flies Lavania observed after 6 days is 9 + 5 * 20 and the value is 109

The given parameters are

Day 1 = 20 fruit flies

Day 6 = 9 more than 5 times as many fruit flies on day 1

The above expression can be rewritten as

Day 6 = 9 + 5 * Day 1

This gives

Day 6 = 9 + 5 * 20

Evaluate the product

Day 6 = 9 + 100

Evaluate the sum

Day 6 = 109

Hence, the expression to find the population of fruit flies Lavania observed after 6 days is 9 + 5 * 20 and the value is 109

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Answer:

a: 57.3

b: 3.8

Step-by-step explanation:

a: The formula to solve a triangle is a=height*base/2

that makes a= 9.96*11.5/2

a=57.27~=57.3

b: because there is 15 balls take 57.27 and divide it by 15

57.27/15=3.8

Simplification of the given complex fraction [tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }[/tex]  is equal to 3/(x-6).

As given in the question,

Given complex fraction is [tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }[/tex]

Simplify the denominator by taking least common multiple,

[tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }\\\\\\= \frac{3}{\frac{x-4}{\frac{x-4-2}{x-4} } }\\\\\\= \frac{3(x-4)}{(x-6)(x-4)} \\\\\\=\frac{3}{x-6}[/tex]

Therefore, simplification of the given complex fraction [tex]\frac{3}{\frac{x-4}{1-\frac{2}{x-4} } }[/tex]  is equal to 3/(x-6).

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The equivalent expression of (5 ^3/4)^2/3 is √5

Expressions are mathematical statements that are represented by variables, coefficients and operators

Rational expressions are expressions that are represented by the quotient of two polynomials or radicals.

This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals

The expression is given as

(5 ^3/4)^2/3

Evaluate the product of the exponents

So, we have

(5 ^3/4)^2/3 = 5^(3/4 x 2/3)

Evaluate the product of the exponents

So, we have

(5 ^3/4)^2/3 = 5^(2/4)

Evaluate the quotient

So, we have

(5 ^3/4)^2/3 = 5^(1/2)

Express as square roots

So, we have

(5 ^3/4)^2/3 = √5

Hence, the equivalent expression of (5 ^3/4)^2/3 is √5

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The area of the floor on which Connie is laying the carpet is 9.88 m²

An equation is an expression that shows the relationship between two or more numbers and variables.

Area is the amount of space occupied by a two dimensional shape or object.

Connie is ordering new carpet for a room 2.6m*3.8m*8.3m. Hence:

Area of the floor = 2.6 m * 3.8 m = 9.88 m²

The area of the floor on which Connie is laying the carpet is 9.88 m²

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The solutions for each of the equations provided in the reference picture is as follows:

(1) [x = (-3)]

(2) [y = (-10)]

(3) (m=3/4)

(4) (b = 0)

(5) (r = 7)

(6) (v = -60)

As per question statement and reference picture, we are provided with 6 different equations which are

(1) [(4 x+1)=(2 x-5)]

(2)[(y-3)=(-3 y-43)]

(3) [(7-14 m)=(2 m-5)]

(4)[(-10 b+5)=(7 b+5)]

(5)[(r+15)=(4 r-6)]

(6)[(10-2 v)=(-5 v-50)]

We are required to find the solution of all the equations mentioned above.

Considering equation (1), we get,

{[(4 x+1)=(2 x-5)] }

or,(4 x-2 x)=[(-1)-5]

or, 2 x=-(1+5)

or, 2 x=-6

or, x={-6}/{2}=(-3)

Considering equation (2), we get,

{[(y-3)=(-3 y-43)] }

or, (y+3 y)=(3-43)

or, 4 y=(-40)

or, y=(-10)

Simplifying equation (3), we get,

{[(7-14 m)=(2 m-5)] }

or, (7+5)=(2 m+14 m)

or, 12=16 m

or, m={12}/{16}={3}/{4}

Simplifying equation (4), we get,

{[(-10 b+5)=(7 b+5)] }

or, (5-5)=(7 b+10 b)

or, 17 b=0

or, b=0

Simplifying equation (5), we get,

{[(r+15)=(4 r-6)] }

or, (15+6)=(4 r-r)

or, 3 r=21

or, r=7

Finally, Simplifying equation (6), we get,

{[(10-2 v)=(-5 v-50)] }

or, (5 v-2 v)=[(-10)-50]

or, 3 v=-(10+50)

or, 3 v=-60

or, v=(-20)

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