how to find the range of a function

The sum of the two polynomials 4x³+2x²-4x+3 and 7x³-4x² +7x+8 is 11x³-2x²+3x+11.

Algebraic expressions called polynomials include coefficients and variables. For polynomial expressions, we can perform mathematical operations like addition, subtraction, multiplication, and positive integer exponents. Polynomial addition is the process of adding like terms from two or more algebraic equations while maintaining the sign of each term.

Here, given two polynomials 4x³+2x²-4x+3 and 7x³-4x² +7x+8.

First, arrange the given polynomials. The polynomials were already arranged from the increasing to decreasing order of degree. Then,

(4x³+2x²-4x+3)+ (7x³-4x² +7x+8)

Second, group the like terms from both polynomials.

(4x³+7x³)+(2x²-4x²)+(-4x+7x)+(3+8)

Now, simplifying the combining terms, we get,

11x³-2x²+3x+11

The answer is 11x³-2x²+3x+11.

The complete question is -

Add the following polynomials, then place the answer in the proper location on the grid. write the answer in descending powers of x. Find the sum of 4x³+2x²-4x+3 and 7x³-4x² +7x+8.

To know more about polynomials:

https://brainly.com/question/17822016

#SPJ4

Answer:

The answer is 13.2

Step-by-step explanation:

d = 10

e = 3.2

d + e = 10 + 3.2 = 13.2

Thus, The answer is 13.2

Answer: [tex]y=-\frac{1}{2} x-3[/tex]

Step-by-step explanation:

[tex]3x+6y=-18[/tex]

[tex]-3x[/tex]             [tex]-3x[/tex]

[tex]6y=-3x-18[/tex]

[tex]\frac{6y}{6} =\frac{-3x}{6} -\frac{18}{6}[/tex]

[tex]y=-\frac{1}{2 } x-3[/tex]

The number of hours that plan A last is 1 hour and the number of hours that plan B last is 1 1/2 hours.

The first step is to form a system of equations using the information in the question:

3a + 8b = 15  equation 1

5a + 2b = 8 equation 2

Where:

The elimination method would be used to determine the required values

In order to determine the value of a, multiply equation 2 by 4

20a + 8b = 32 equation 3

Subtract equation 1 from equation 3 :

17a = 17

Divide both sides of the equation by 17

a = 17/17

a = 1 hour

Substitute for a in equation 1 :

3(1) + 8b = 15

3 + 8b = 15

8b = 15 - 3

8b = 12

b = 12 / 8

b = 1 4/8 = 1 1/2 hours

To learn more about system of equations, please check: https://brainly.com/question/25875552

#SPJ1

Answer:

3

Step-by-step explanation:

Figure A is a dilation of Figure B by a factor of 3

That means that Figure A is 3 times larger than Figure B.

From Figure B to Figure A, the scale factor is 3.

The sample type is option (D) Systematic random sample

Here they randomly select one of the first 25 users each day and show them a message asking for a donation

They also show the message to every 25th user from that point on

The random sample is the selecting one from a large population

The systematic random sample is defined as the probability sampling method from a large population, the random samples are selected periodically. The periodical selection of random variable means the random variables are selected in regular interval.

Here the random samples are selected as one of the first 25 users each day

Therefore, the random sample is systematic random sample

Learn more about Systematic random sample here

brainly.com/question/24317913

#SPJ4

The equation illustrates that the variable that represents the greatest number is E. This cannot be determined with the given information.

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 vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

From the information, the variable is given as 1/2m = 1/3n = 1/4p = 1/5q.

It should be noted that the greatest variable cannot be determined based on the information. In conclusion, the correct option is E.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

For the  given  quadratic function, the  highest  point  that the object  reaches is  (5, 768).

Since we are given with the quadratic function of h(t)=−16t2+160t+368, where  Let a = -16, b = 160, and c = 368, so the vertex for the equation will be  :t = -b/2a = -(160)/2(-16) = -160/(-32) = 5, so substituting this value  in the equation for the value of t is

h(5) = -16(5)2 + 160(5) + 368 = -400 + 800 + 368 = 768

Here the highest point that the object reaches is (5, 768), which means that  at a time of 5 seconds, the object reaches the building after being launched at the height of  768 feet  

To know more about quadratic equations refer to the link  brainly.com/question/19030778

#SPJ4

We are standing on the top of a 368 feet tall building and launching a small object upward. The object's vertical position, measured in feet, after t seconds is

We are standing on the top of a 1200 feet tall building and launch a small object upward. The object's vertical position, measured in feet, after t seconds is  What is the highest point that the object reaches?

Answer:

$1.25

Step-by-step explanation:

150 / 120

Answer:

$1.25

Step-by-step explanation:

You can find the average cost per coconut by dividing the total price by the number of coconuts. 150 divided by 120 is $1.25. Therefore, each coconut costs $1.25.

[tex]Answer:\ cos(\theta_1)=\boxed{-\frac{40}{41} }[/tex]

Step-by-step explanation:

[tex]\displaystyle\\sin(\theta_1)=\frac{9}{41}\ \ \ \ \ \ 90^0 < \theta_1 < 180^0\ \ \ \ \ \ \ cos(\theta_1)=?\\\\sin^2(\theta_1)+cos^2(\theta_1)=1\\\\cos^2(\theta_1)=1-sin^2(\theta_1)\\\\cos^2(\theta_1)=1-(\frac{9}{41})^2\\\\cos^2(\theta_1)=1-\frac{81}{1681} \\\\cos^2(\theta_1)=\frac{1(1681)-81}{1681} \\\\cos^2(\theta_1)=\frac{1600}{1681} \\\\[/tex]

Extract the square root of both parts of the equation:

[tex]\displaystyle\\\cos(\theta_1)=б\sqrt{\frac{1600}{1681} } \\\\\cos(\theta_1)=б\sqrt{\frac{40^2}{41^2} } \\\\\cos(\theta_1)=б\sqrt{(\frac{40}{41})^2 } \\\\\cos(\theta_1)=б\frac{40}{41}[/tex]

[tex]\displaystyle\\Since\ 90^0 < \theta_1 < 180^0, \\\\ therefore\ cos(\theta_1)=-\frac{40}{41}[/tex]

The line that would appear parallel to HG and would go through point D, is DC.

When describing parallel lines, we describe two lines in the same plane that are equally spaced apart and never cross each other. Both horizontal and vertical shapes are possible.

The only line that would go through point D and would be parallel to line HG, would therefore be Line DC. This is because this line is equally spaced from line HG and would never cross it.

In conclusion, line DC would be parallel to line HG.

Find out more on parallel lines at https://brainly.com/question/26961508

#SPJ1

Answer:

4x+y=-2

Step-by-step explanation:

y=-4x-2

Write this in standard form:

Ax+By=C  ==> C is a constant

First, put x and y on one side of the equation:

y+4x=-4x+4x-2 ==> isolate -2 by adding 4x on both sides

y+4x=-2

4x+y=-2  ==> switch x and y to make the equation in standard form

The terminal point is 0.36 radii to the right of the circle's center.

The terminal point is 0.93 radii above the circle's center.

Here, the 3 O'clock line is OA and the terminal point is on the line OP.

The angle θ = 1.2 radians

Let the radius = r

The distance of the terminal point to the right of the center = OQ

= r × cos θ

= r × cos 1.2  

= r × 0.36

So, it is equal to 0.36 radii

The distance of the terminal point above the center = PQ

= r × sin θ

= r × sin 1.2

= r × 0.93

So, it is equal to 0.93 radii.

To learn more about circumference and radius,

https://brainly.com/question/12512221

#SPJ4

A true average strain in a way that converys information about precision and reliability  (23.0616, 26.9384)

In this question we have been given:

sample size n = 15

the mean failure strain x(bar) = 25.0

the standard deviation s = 3.5

Assuming a normal distribution for failure strain, we need to estimate true average strain in a way that converys information about precision and reliability.

A 95% confidence interval is necessary; other confidence intervals can be calculated in a similar way.

c = 0.95 or 95%

In the table with the critical values for t distributions in the appendix, locate the row beginning with degrees of freedom.

Here, the degree of freedom :

df = n - 1

df = 15 - 1

df = 14

and the column with α =(1-c)/2

                                   =0.025

To find the t-value:

t_(α/2) = 2.145

Therefore, the error margin is:

E = t_(α/2) × s/√n​

E = 2.145× 3.5/√15​

E ≈1.9384

The confidence interval's outer limits are thus:

x{bar} - E = 25.0 - 1.9384

               = 23.0616

x{bar} + E = 25.0 + 1.9384

                = 26.9384

Therefore, the confidence interval is: (23.0616, 26.9384)

Learn more about the confidence interval here:

brainly.com/question/13067956

#SPJ4

Hence for miles greater than 45, the Company A will charge less than Company B.

Given:

Jina is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.

we are asked to find for what mileages will Company A charge less than Company B = ?

from the question we frame  the inequality as:

⇒ 91< 55+0.80m

⇒ 36<0.80m

⇒ 45<m

or

m>45

Check answer

55+45(0.8)=91 check

Hence for miles greater than 45, the Company A will charge less than Company B.

Learn more about Inequality here:

brainly.com/question/25275758

#SPJ4

If the supplied functions are f(x) = - 3x 2 + x - 9 and g(x) = x 3 + 6x and the value of x is -4, the value of (f + g)(- 4) is -137.

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable). Functions are typically categorized into four categories. Depending on the Element: One function to one function, many functions to one function, onto function, one function to one and onto function, into function A "vertical line test" can be used to identify whether a relation is a function when looking at a graph. If a vertical line can be drawn anywhere on the graph and cross the relation twice, the relationship is not a function.

Here,

(f+g)(x)=f(x)+g(x)

f(-4)=-3*(-4)²-4-9

f(-4)=-61

g(-4)=(-4)³-3*4

g(-4)=-76

(f+g)(-4)=f(-4)+g(-4)

=-61-76

(f+g)(-4)=-137

If the supplied functions are f(x) = - 3x 2 + x - 9 and g(x) = x 3 + 6x and x is -4, the value of (f + g)(- 4) is -137.

To know more about function,

https://brainly.com/question/28278690

#SPJ1

From the given question, relation set - {(9, 1), (6,2), (3, 3), (6,4), (9,5)} does not represent the function.

In mathematics, a connection between one variable (the independent variable, x) and another variable is defined as an expression (the dependent variable, y).For example - f(x) = 4x + 6

The collection of ordered pairs from the question is presented.

It is evident that the relation set exists.

{(9, 1), (6,2), (3, 3), (6,4), (9,5)}

It not accurately depict the function since for x = 6, [y] has two potential values, none of which is possible.

so that's why relation set - {(9, 1), (6,2), (3, 3), (6,4), (9,5)} can not represent a function.

To know more about functions visit:

https://brainly.com/question/28193995

#SPJ4

You will pay a price of $72.31 if you wait to purchase tickets at the door

Discount is defined as a deduction from the usual cost of something. You will save 22% off the door price by prepay $56.40 per ticket now.

Let P represent the original price. We can write that:

P - 22% of P = $56.40. It should be noted that this can be rewritten as:

P - (22% × P) = 56.40

P - 0.22P = 56.40

Subtract

0.78P = 56.40

Divide through by 0.78

P = 56.40/0.78

P = $72.31

Therefore the price is $72.31.

Learn more about discount on:

brainly.com/question/7459025

#SPJ1

3/11 is the probability of choosing an L or an S

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

The given word is SQUIRRELLED.

We need to choose single letter from the word.

We have to find the probability of choosing an L or an S

If we were to select a letter that was either an L or S from eleven letters. 1 of them being an S and 2 of them being an L.

We simply add:1+2/11

Three divided by eleven

3/11

Hence, 3/11 is the probability of choosing an L or an S

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ1

(Option D. Incentre) The incentre of a triangle is the point equidistant from all three of the triangle's vertices. This means that its distance from each vertex is the same.

The incentre of a triangle is an important point of reference for geometry. It is located at the center of the triangle's inscribed circle, which is the circle that touches each of the triangle's three vertices. This is why the incentre is also known as the triangle's inner center or center of the triangle's inscribed circle. As it is equidistant from all three of the triangle's vertices, the incentre is useful for finding the angles of the triangle and for finding the lengths of the triangle's sides. It can also be used to calculate the area of the triangle.

Learn more about the Triangles: https://brainly.com/question/17335144

#SPJ4

a) The wording for the random variable is given as follows:

n X = the number of 337 randomly selected people who get the vaccine and do not get the flu;

b) The symbol is: n = 337.

c) The symbol is: p = 0.8.

d) P(X = 265) = 0.0426.

e) P(X < 265) = 0.2451.

f) P(X > 265) = 0.7123.

g) P(X = 268) = 0.0545.

h) P(X < 268) = 0.3859.

i) P(X > 268) = 0.5596.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for the binomial distribution in this problem are given as follows:

n = 337, p = 0.8.

Hence the mean and the standard deviation for the approximation are given as follows:

Using continuity correction, the probability that exactly 265 people do not get the flu is the p-value of Z when X = 265.5 subtracted by the p-value of Z when X = 264.5.

X = 265.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (265.5 - 269.6)/7.34

Z = -0.56

Z = -0.56 has a p-value of 0.2877.

X = 264.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (264.5 - 269.6)/7.34

Z = -0.69

Z = -0.69 has a p-value of 0.2451.

Hence:

0.2877 - 0.2451 = 0.0426.

Then:

e) P(X < 265) = 0.2451 -> p-value of Z when X = 264.5.

f) P(X > 265) = 1 - 0.2877 = 0.7123 -> one subtracted by the p-value of Z when X = 265.5.

For exactly 268, we have the same logic as follows:

X = 265.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (268.5 - 269.6)/7.34

Z = -0.15

Z = -0.15 has a p-value of 0.4404.

X = 267.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (267.5 - 269.6)/7.34

Z = -0.29

Z = -0.29 has a p-value of 0.3859.

Hence:

0.4404 - 0.3859 = 0.0545.

Then:

h) P(X < 268) = 0.3859 -> p-value of Z when X = 267.5.

i) P(X > 268) = 1 - 0.4404 = 0.5596.

More can be learned about the normal distribution at https://brainly.com/question/25800303

#SPJ1

The correct answer is  People in Canada who are happier are less likely to suffer cardiac problems.

We have been given four options from which we have to select the correct one.

a. Happiness causes better heart health for all people.

b. Happiness causes better heart health for Canadians.

c. Happiness causes better heart health for the people in the study.

d. Happier people in Canada are less likely to have heart problems.

e. Happier people in the study were less likely to have heart problems.

The researchers followed up with each person 10 times later and discovered that those who had been deemed pleased at the start were no longer so. People in Canada who are happier are less likely to suffer cardiac problems.

Therefore, the conclusion is people in Canada who are happier are less likely to suffer cardiac problems.

To learn more about the sampling refer here

https://brainly.com/question/24466382

#SPJ4

If we suppose that x is equal to 0, then the value of y is 2(0)+3y = 3, and y is equal to 1. Therefore, (0,1) is one of the answers to this equation.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, etc.

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. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.

According to our question-

The formula is 2x + 3y = 3. There are an infinite number of solutions to this equation.

We must first enter any random value for any variable, followed by the matching value for the other variable, in order to find any solution to this equation.

Now, if we suppose that x is equal to 0, then the value of y is 2(0)+3y = 3, and y is equal to 1. Therefore, one of the solutions to this equation is (0,1).

Hence, If we suppose that x is equal to 0, then the value of y is 2(0)+3y = 3, and y is equal to 1. Therefore, (0,1) is one of the answers to this equation.

learn more about equations click here:

brainly.com/question/2972832

#SPJ4

Complete question-

Find the one of the solution of 2x + 3y = 3?

Answer:

1) 60

2)  15

3) 45

4) 105

5) 75

Step-by-step explanation:

7y + 5y = 180  A straight angle is 180  Combine like terms

12y = 180  Divide both sides by 12

y = 15

The sum of the interior angles is 180

y = 15

180 - (5y + 3y) = x

180 -(5(15) + 3(15)) = x

180 - (75 + 45) = x

180 - 120 = x

60 = x

Angle c

3y

3(15)

45

Angle DBC

7y

7(15)

105

Angle CBA

5y

5(15)

75

a) Amy's monthly budget for Rent based on the total budget for housing and food is $853.

b) Amy's monthly budget for Utilities based on the total budget for housing and food is $142.

c) Amy's monthly budget for Food based on the total budget for housing and food is $427.

The total budget for Housing, Utilities, and Food for nine months = $12,798

Rent = 60%

Utilities = 10%

Food = 30%

Budget period = 9 months

Budget for rent = $7,679 ($12,798 x 60%)

Monthly budget for Rent = $853 ($7,679/9)

Budget for utilities = $1,280 ($12,798 x 10%)

Monthly budget for Utilities =  $142 ($1,280/9)

Budget for food = $3,839 ($12,798 x 30%)

Monthly budget for Food =  $427 ($3,839/9)

Learn more about monthly budgets at https://brainly.com/question/19162407

#SPJ1

Therefore solution to this problem is  the  function is odd if  f(-x) = -f (x).

In mathematics, a function from a set X to a set Y assigns each element of X precisely one element of Y. The domain and codomain of the function, respectively, are the sets X and Y.

Here,

We can know the function is even or odd by substituting the values in the function f(x) as f(-x)

Thus

If f(-x) = f, then f(x) is an even function (x). If the function is odd, then f(-x) = -f (x). Reflection symmetry around the y-axis exists for an even function. The rotational symmetry of an odd function is at the origin.

Therefore the  function is odd if  f(-x) = -f (x).

To know more about function , visit

https://brainly.com/question/5975436

#SPJ4

Answer:

Only I

Step-by-step explanation:

I. √36 > 5

√36 = 6

6 > 5

Its true

II. 7 < √10

√10 = 3.16 approximately

Hence, 7 > √10

But 7 < √10 is wrong

III. √(17 - 8) > √(17 + 8)

√(17 - 8) = √9 = 3

√(17 + 8) = √25 = 5

√(17 - 8) < √(17 + 8)

But, √(17 - 8) > √(17 + 8) is wrong

Answer:

1.) √36 > 5

Step-by-step explanation:

1.) √36 > 5

= 6 > 5( it is true because 6 is greater than 5)

2.) 7 < √10

= 7 < 3.16 ( it is false because 7 is greater than 3.16)

3.)√17–√8 > √17 + √8

= 4.12 – 2.82 > 4.12 + 2.82

= 1.3 > 6.94( it is false because 6.94 is greater than 1.3)

pls rate as brainliest

Answer:

Step-by-step explanation:

When sides 'z' and 'y' and included angle X is known, the area of the triangle is:

Area (∆XYZ) = 1/2 × yz × sin(X)

1/2 x 7.9 x 6.1 x Sin(62) = 21.27

Answer:

I'm sure its x>10

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x+7>27

Subtract 7 from both sides

2x+7−7 27−7

2x>20

Divide both sides by 2

2x/2 > 20/2

= x>10

Answer:

Step-by-step explanation:

dudjdjd