✨6 Grade Math✨ Pls help

For the polynomial functions f(x) = 3x - 2 and g(x) = x² + 1, then function (f + g)(x) is calculated to be

A polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable in an equation, such as the quadratic equation or the cubic equation.

The equation in the problem has integers as below

f(x) = 3x - 2: integer value here is 1

g(x) = x² + 1 integer value here is 2

In both conditions, the integer values are positive hence both are polynomial functions

(f + g)(x) is addition of the two polynomials

f(x) = 3x - 2 + g(x) = x² + 1

= 3x - 2 + x² + 1

= x² + 3x - 1

hence (f + g)(x) = x² + 3x - 1

Learn more about polynomial functions at;

https://brainly.com/question/2833285

#SPJ1

The equation for a tangent to the graph of y = arcsin(x/2) at the origin is y = x.

To find the equation for a tangent to a graph at a certain point, we need to find the slope of the tangent at that point. To do this, we can use the derivative of the function. In this case, the function is y = arcsin(x/2). Using the chain rule, we can find the derivative of this function:

y' = d/dx(arcsin(x/2))

= d/dx(sin^-1(x/2))

= 1/√(1 - (x/2)^2)

Now, to find the slope of the tangent at the origin (0,0), we can plug x = 0 into this derivative:

y'(0) = 1/√(1 - (0/2)^2) = 1

So the slope of the tangent at the origin is 1. To find the equation of the tangent, we can use the point-slope form of a line:

y - y1 = m(x - x1) where,

Plugging in the values for the origin and the slope we found above:

y - 0 = 1(x - 0)

or, y = x

So the equation for the tangent is y = x. But the options are incorrect.

Learn more about the Straight line here:

https://brainly.com/question/25969846

#SPJ4

The lines that are true in the following statements are, Parallel lines have the same slope. Parallel lines have equal slopes. Parallel lines have different y-intercepts. Parallel lines have different x-intercepts.

Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both horizontal and vertical shapes are possible.

The following key traits and qualities make it simple to recognize parallel lines:

They are usually parallel straight lines that are spaced equally apart.

These lines are coplanar.

No matter how far you extend them in any direction, they never come together.

All the statements mentioned are true.

Learn more about parallel lines here:

https://brainly.com/question/16701300

#SPJ1

61.67 oz of the 55% acid solution and 33.33 oz of the 30% acid solution must be mixed to produce 100 ounces of a 43% acid solution.

This is a mixture problem that can be solved using algebra. We can set up a system of equations to represent the amount of each solution being used and the final acid concentration.

Let x be the amount of 55% acid solution and y be the amount of 30% acid solution used.

We can set up the following system of equations:

(55/100)x + (30/100)y = (43/100)(x + y) (Equation 1) represents the final acid concentration.

x + y = 100 (Equation 2) represents the total amount of solution mixed

We can solve for one variable in equation (1) by isolating it and substituting it into equation (2).

Solving for x in equation (1) we get: x = (100*43/100 - y30/100)/55/100

Substituting this value into equation (2) we get: (10043/100 - y30/100)/55/100 + y = 100

Solving for y we get: y = (100*100 - 100*43)/30 = 33.33 oz

And then substituting this value back into the equation x = (100*43/100 - y30/100)/55/100 we get x = 61.67 oz

So, 61.67 oz of the 55% acid solution and 33.33 oz of the 30% acid solution must be mixed to produce 100 ounces of a 43% acid solution.

To learn more about Mixture, Visit

https://brainly.com/question/24647756

#SPJ1

The length of A'B' after undergoing the dilation is; A'B' = 2√2

The scale factor in the dilation of an object tells us how much larger or smaller the image will be when compared to the original object. Thus, the coordinates will be multiplied by the scale of dilation to get the new coordinates.

We are given the coordinates of Polygon ABCD as A(0, 4), B(-4, 8), C(3, 3), and D(4, -2). With a scale of dilation of ½, we will have the new coordinates as;

A'(0, 2), B'(-2, 4), C'(1.5, 1.5), and D'(2, -1)

The formula to find the distance between two coordinates is;

Distance = √[(y₂ - y₁)² + (x₂- x₁)²]

Thus;

A'B' = √[(4 - 2)² + (-2 - 0)²]

A'B' = √8

A'B' = 2√2

Read more about scale of dilation at; https://brainly.com/question/3457976

#SPJ1

Answer:

5 pens

Step-by-step explanation:

$10 - 6$ = $4

$4/$0.80

she can afford 5 pens

The equivalent expression to 4y²(6x³ + 4xy + 3y) is 24x³y² + 16xy³ + 12y³  

A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is called an algebraic expression.

In general, something is considered equal if two of them are the same. Similar to this, similar expressions in mathematics are those that hold true even when they appear to be different.

However, both forms provide the same outcome when the values are entered into the equation.

Here we have  

4y²(6x³ + 4xy + 3y)  

Simplify the given expression as follows

=> 24x³y² + 16xy³ + 12y³  

Therefore,

The equivalent expression to  4y²(6x³ + 4xy + 3y) is 24x³y² + 16xy³ + 12y³  

Learn more about Equivalent expressions at

https://brainly.com/question/28170201?referrer=searchResults

#SPJ1

The solution to the quadratic equation are x = 1 and -5/2

We have the quadratic function;

2x² + 7x + 5

Using the factorization method of solving quadratic equation. We need to multiply the coefficient of x² and the constant 5.

Then find the pair factors and substitute the values into the function.

Substitute the values, we have;

2x² + 2x + 5x + 5

Factor the expression in pairs

(2x² + 2x) + (5x + 5)

Factor the common terms, we get;

2x(x + 1) + 5( x+ 1)

We have the equations;

2x + 5 = 0

x = -5/2

And

x + 1 = 0

x = -1

Thus, the values are x = -5/2 and -1

Learn more about factorization here:

https://brainly.com/question/25829061

#SPJ1

The product of the expression is 8x²-10x

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

Given that, an expression 8x(x-5/4x) we are asked to find its product,

8x(x-5/4x)

= 8x²-10x

Hence, the product of the expression is 8x²-10x

Learn more about expressions, click;

https://brainly.com/question/14083225

#SPJ1

On solving the provided question of arithmetic , we can say that after five years, Offer A will offer a higher total income.

Every subsequent pair of terms in an arithmetic sequence has a constant difference. This resembles linear functions with the formula y=mx+b. There is a fixed ratio between every pair of subsequent terms in a geometric sequence. This would produce a constant multiplier effect.

Given that a candidate receives job offers from two different companies, with Offer A offering a starting salary of $ 55,000 and a 5% increase for 5 years and Offer B offering a starting salary of $ 56,000 and an increase of $ 2,000 per year, it is necessary to perform the following calculation to determine which offer will result in a higher total income after 5 years:

Offer A = Arithmetic

55000.r1.055 X

70, 195.48 — x

Offer B = Geometric

56000+ (5a•2000) X

56000+ 10000 = x

66,000 = x

To know more about arithmetic visit:-

brainly.com/question/11559160

#SPJ1

Therefore , the solution of the given problem of surface area comes out to be  0.2083 yard square.

A surface is a measurement of how much overall space an object's surface takes up. Surface area of a three-dimensional shape is determined by the total area of its surroundings. Surface area is the term used to describe a triangular shape's entire surface area. The particular area of each face on a cube with six square faces can be added up to determine the cube's surface area. Alternately, you can get the box's dimensions by using the following formula: Surface (SA) equals twice twice twice twice. A three-dimensional shape's surface area is calculated as the sum of all the space it occupies.

Here,

Given : width : 5/6 yard

and length = 1/4 yard

To find the area = length * width

=> area = 5/6 * 1/4

=> area = 5/24

=> 0.2083 yard square.

Therefore , the solution of the given problem of surface area comes out to be  0.2083 yard square.

To know more about surface area visit:

https://brainly.com/question/2835293

#SPJ1

The value of x = -3 in the given quadratic equation.

In mathematics, a quadratic equation is defined as an equation of degree 2, which means that the highest exponent of this function is 2. A quadratic has the standard form y = ax2 + bx + c, where a, b, and c are numbers and a cannot be 0.

Quadratic equations are unique in that they can have up to two real solutions. Solutions are found where the quadratic equals 0. Real solutions are those that are not fictitious and have real numbers.

8 to the power of X over 2 divided by 4 to the power of X over 3 = 2 to the power of -5 over 2.

In equation it will be written as

[tex]$ 8^{x/2} \div 4^{x/3} = 2^{-5/2}[/tex]

[tex]$ (2^3)^{x/2} \div (2^2)^{x/3} = 2^{-5/2}[/tex]

[tex]$ (2)^{3x/2} \div (2)^{2x/3} = 2^{-5/2}[/tex]

[tex]$ (2)^{\frac{ 3x}{2} -\frac{ 2x}{3} } = 2^{-5/2}[/tex]

[tex]$ (2)^{\frac{ 5x}{6} } = 2^{-5/2}[/tex]

By solving this

x = -3

Thus, the value of x = -3 in the given quadratic equation.

https://brainly.com/question/30098550

#SPJ1

Answer:

Step-by-step explanation:

1 Wanderer

2 moves on its own orbits the sun

3 Saturn

4 saturn

Answer: yes, you did

Step-by-step explanation:

21 divided by 25 is 0.84

the you times 0.84 with 100 and you would get 84%

I agree that Freddy ate 1 / 8 of the brownies in the pan because two brownies represents 1 / 8 of the brownies in the pan.

The large pan is said to have been used to make 16 brownies which means that if Freddy ate 2 brownies out of this, the proportion that he would have eaten of the cookies in the pan is:

= Number of brownies Freddy ate / Number of total brownies in the large pan

= 2 / 16

= 1 / 8

This therefore shows that Freddy's friend was right in saying that Freddy ate 1 / 8 of the brownies in the pan.

Find out more on brownies at https://brainly.com/question/12638126

#SPJ1

Full question is:

A large pan is used to make 16 brownies. Freddy had two of the brownies from a large pan. His friend said he ate 1/8 of the brownies in the pan. Tell why you agree or disagree.

When he replaces a coin that was taken out randomly, there is a 50% chance that he chose a dime and a nickel.

A branch of mathematics called probability theory determines the likelihood that an event will occur or that a statement is true. A chance is a number between 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or probability that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as a percentage form 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain occurrence relative to all possible outcomes.

given

There are six possible methods to select two coins (sequence is irrelevant): 1, 5, 1, 10, 1, 25, 5, 10, and 1, 25. (10,25).

Three of these add up to at least 25, thus 3/6 or 1/2 of them.

Alternatively, there are 4 ways to choose 2 coins from 4, or 4 C 2 = 6.

You then select one of the three remaining coins and the quarter (required to reach at least 25) as follows: 3 C 1= 3 ways.

When he replaces a coin that was taken out randomly, there is a 50% chance that he chose a dime and a nickel.

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ1

The discount as a percentage is 13.8%

The price of a picnic basket is marked as $31

The original price is $36

The discount percentage can be calculated as follows

36-31/36 × 100

= 5/36 × 100

= 0.138× 100

= 13.8%

Hence the percentage discount is 13.8%

Read more on discount here

https://brainly.com/question/22167292

#SPJ1

Answer:

D) 50%

Step-by-step explanation:

There are 5 weekdays, Monday through Friday.

In each of the 5 weekdays she runs 2.6 miles.

In a week, she runs 5 × 2.6 miles = 13 miles by running only on weekdays.

Now we need to find out what percent of 26 miles is 13 miles.

percent = part/whole × 100%

percent = 13/26 × 100%

percent = 0.5 × 100%

percent = 50%

Answer: D) 50%

Answer:

1:10

Step-by-step explanation:

30 boxes = 180 eggs

3 boxes = 18 eggs

18:180 = 1:10

By substitution; x = 4 and y = -31

An equation is a mathematical statement that shows that two mathematical expressions are equal. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. Equations can be solved to find the value of an unknown variable representing an unknown quantity.

y=-6x-7 --- 1

7x+y=-3 --- 2

Substituting y as 6x - 7 in equation 2

7x + (-6x - 7) = -3

7x - 6x - 7 = -3

x - 7 = -3

x = -3 + 7

x = 4

Substitute x as 4 in equation 1

y = -6x - 7

y = -6(4) - 7

y = -24 - 7

y = -31

Learn more about equations here: https://brainly.com/question/22688504

#SPJ1

The number of rocks in Willy’s collection is 30

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split

In this case, the number of rocks in Willy’s collection can be represented by x and the number of rocks in Billy’s collection is 2 2/3 times the number in Willy’s collection.

The appropriate equation to illustrate this will be:

x + 2 2/3x = 110

3 2/3x = 110

x = 110 ÷ 11/3

x = 110 × 3/11

x = 30

There'll be 30 rocks

Learn more about fractions on:

brainly.com/question/78672

#SPJ1

The features of the cosine function are given as follows:

The equation of the cosine function is given as follows:

y = 1/3cos(2(x - π/3)).

The cosine function is defined as follows:

g(x) = acos(b((x+c))+d.

The coefficients have these following roles:

The function oscillates between -1/3 and 1/3, hence the amplitude is of:

a = 1/3.

The period is of 2π/3 - (-π/3) = π, hence:

2π/B = π.

B = 2.

The horizontal shift is of -π/3, hence the equation is given as follows:

y = 1/3cos(2(x - π/3)).

More can be learned about cosine functions at brainly.com/question/21558626

#SPJ1

Answer:

ρ= 5 g/cm³

Step-by-step explanation:

density= mass/volume

ρ= m/v

As all  side of the cube is equal so the formula for volume is a³ 3³

which gives us volume 27.

ρ= 135g/27cm³

ρ= 5 g/cm³

Answer:

y = 3x

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

The slope = rise/run

Let's pick 2 points (0,0) (2,6), we see that the y increase by 6 and the x increase by 2, so our slope is

m = 6/2 = 3

Y-intercept is when the x = 0, we see that the y-intercept is located at (0,0)

So, our equation is

y = 3x

The length of the label is 121 over 28. (option C)

The length of the label is equivalent to the circumference of the cylinder. The circumference of an object is the distance round the object.

The formula for circumference of a cylinder = 2πr

Where:

π = 22/7

r = 2 3/4 = 11/4

2 x 22/7 x (11/4) = 121/28 cm

To learn more about the circumference of a cylinder, please check:https://brainly.com/question/29379980

#SPJ1

Answer: 121/7

Step-by-step explanation: I got it correct :)

Answer:

Y = 4

Step-by-step explanation:

5x-y=54

50-y=54

circle y and subtract 50 from itself then subtract 50 from 54.

after subtracting you should have y=4

26,706.08 nearest to  26,706.14

Purchasing is the set of functions associated with acquiring the goods and services that an organization requires. Purchasing is a small subset of the broader procurement function.

The 6 key steps of the purchasing process are:

Fair secured apr: 5.60% = 0.4666% for 1 month

28,125 x 1.075 = 30,234.38 - 3125 = 27,109.38

27,109.38 x 1.004666 = 27,235.87 - 529.79 = 26,706.08

Learn more about  purchased here: brainly.com/question/1489991

#SPJ1

The inequality that represents this sentence is 6 + 2 < 9 + 3

From the question, we have the following parameters that can be used in our computation:

Six plus two is less than nine plus three

Express as numbers

So, we have

6 plus 2 is less than 9 plus 3

Introduce the operators

6 + 2 < 9 + 3

Hence, the inequality is 6 + 2 < 9 + 3

Read more about inequality at

https://brainly.com/question/25275758

#SPJ1

Hi Bixby can you help me with this Mr. CV is making an area to display 9 pictures for for each pair of different functions there are 2 Irish he can we how many different areas can Mr. Semi make is in the number of a rice old number odd or even

The solution of the equation - (3/2) ÷ (7/4) = x - (2/3) ÷ (4/7) will be 13 / 42.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation is given as,

- (3/2) ÷ (7/4) = x - (2/3) ÷ (4/7)

Simplify the equation, then we have

- (3/2) x (4/7) = x - (2/3) x (7/4)

- 6/7 = x - 7 / 6

x = 7/6 - 6/7

x = (49 - 36)/42

x = 13 / 42

The solution of the equation - (3/2) ÷ (7/4) = x - (2/3) ÷ (4/7) will be 13 / 42.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ1