Mathematics High School

The function f(x) is defined as follows:
f(x)= 3x+1 if x is less than or equal to 0
2x^2 if 0 4 if c is greater than or equal to 2
determine the following values of the function
f(-3)= __
f(2)= ___

Answers

Answer 1
We have a function [tex]f(x)[/tex] defined by two rules: if [tex]x \leq 0[/tex], [tex]f(x)=3x+1[/tex], and if [tex]x \geq 2[/tex], [tex]f(x)=2 x^{2} [/tex]. Notice that when you are evaluating a function at a number, you are basically saying that [tex]x[/tex] is equal to that number. So, when you say [tex]f(-3)[/tex], you are saying that  [tex]x-3[/tex]. Since [tex]-3 \leq 0[/tex], we are going to use our first rule to evaluate our function at -3:
[tex]f(x)=3x+1[/tex]
[tex]f(-3)=3(-3)+1[/tex]
[tex]f(-3)=-9+1[/tex]
[tex]f(-3)=-8[/tex]

Similarly, when you are evaluating the function at 2, you are saying that [tex]x=2[/tex]. Since [tex]2 \geq 2[/tex], we are going to use our second rule to evaluate our function:
[tex]f(x)=2 x^{2} [/tex]
[tex]f(2)=2(2^{2} )[/tex]
[tex]f(2)=2(4)[/tex]
[tex]f(2)=8[/tex]

We can conclude that [tex]f(-3)=-8[/tex] and [tex]f(2)=8[/tex].
Answer 2
Final answer:

To determine the values of the function f(x) at specific points, we need to look at the different cases given in the definition of f(x).

Explanation:

To determine the values of the function f(x) at specific points, we need to look at the different cases given in the definition of f(x).

If x is less than or equal to 0, then f(x) = 3x + 1. So, f(-3) = 3(-3) + 1 = -8.If x is greater than 0 and less than 2, then f(x) = 2x^2. So, f(2) = 2(2^2) = 8.If x is greater than or equal to 2, then f(x) = 4. So, f(2) = 4.

Therefore, f(-3) = -8 and f(2) = 4.

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Related Questions

I will give brainliest.
What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2, 5)? y + 5 = x + 2 y − 2 = x − 5 y − 5 = −(x − 2) y + 2 = −(x + 5)

Answers

Answer:

You are requested to kindly provide the equation of line to which our to be found line is perpendicular.

Step-by-step explanation:

Simplify algebraic fraction

Answers

You can get common denominator in the denominator of the original fraction so it would look like:
[tex] \frac{4}{ \frac{1}{4}- \frac{10}{4} } = - \frac{1}{ \frac{9}{4} } [/tex]

You can reciprocalize and then multiply:
[tex]4* -\frac{4}{9} = -\frac{16}{9} [/tex]

So, your answer is C.

#16 ) BRAINLIEST + POINTS !!!!!

Answers

B is the answer hope this helps and please give me brainliest

Answer:

b is correct

Step-by-step explanation:

A new website was reviewed by 58 people. The creator of the website surveyed 8 of the reviewers at random. He asked them to rate the website on a scale from 1 to 10. Their ratings are below.

4, 7, 9, 5, 4, 9, 9, 5

Assuming that the sample was representative of all reviewers, what was the mean rating of the website for all reviewers?
A. 6.5
B. 6.25
C. 4.5
D. 6

Answers

Add up the data values: 4+7+9+5+4+9+9+5 = 52

Divide that sum by 8 (which is the sample size) to get 52/8 = 6.5

Answer: Choice A) 6.5

Which tasks are performed by individuals in the Science and Math pathway? Select all that apply.


research human behavior

design and test machinery

develop scientific theories

interpret designs and documents

perform calculations and make predictions

maintain lab equipment to perform experiments

Answers

design and test machinery
develop scientific theories
perform calculations and make predictions
maintain lab equipment to perform experiments

Tasks that are performed by individuals in the Science and Math pathway are design and test machinery, develop scientific theories, perform calculations and make predictions, and maintain lab equipment to perform experiments. They involve Science and Math tasks, and while they may not all apply to a single course, they are related in the same department.

Answer:

design and test machinery develop scientific theories perform calculations and make predictions maintain lab equipment to perform experiments

Step-by-step explanation:

Although science is quite broad, it may involve all or almost all of the alternatives, I suppose you are referring to the exact sciences, as you also want to know which of these options are studied by mathematicians.

Science is a term popularly used to refer to the natural and formal sciences, which use rigorous scientific research methods and benchmarking. In science there are quantitative, mathematical or logical-formal proofs. The sciences are those that encompass a range of various areas of knowledge, some of which are mathematics, computation, statistics, physics, chemistry, engineering, aeronautics, as well as parts of biology, psychology and economics. Generally, these sciences are closely linked to calculations and numbers, which are present in almost all of these fields.

Based on this conceptualization, we can say that the tasks that are performed by individuals in the path of science and mathematics are: design and test machinery, develop scientific theories, perform calculations and make predictions and maintain lab equipment to perform experiments.

Roman stands across from a flag pole.

What is the distance from Roman's feet to the base of the flag pole?

Round only your final answer to the nearest tenth.

https://learning.k12.com/d2l/common/viewFile.d2lfile/Database/MTM5NDQzMDQ/test%20-%20quest%205.JPG?ou=373236

Answers

The answer is 13.2 m.
Because we are only given the hypotenuse, adjacent, and theta measurements.
the opposite side is always opposite theta. In this case, theta is 39 degrees. The hypotenuse is always the slant of the triangle, so it is 17 m. And adjacent is obviously the only one left, in this case, it is x.

You have to use sin, cos, or tan for this problem. You would use cos because cos = adjacent /hypotenuse (x/17)

so you would do cos(39) times 17
x = cos(39) * 17
x = .777 * 17
x = 13.21 

And it says round to the nearest tenth, so it is 13.2 m.
Hope this helps.

The distance from Roman's feet to the base of the flag pole 13.2 m.

What is Trigonometry?

It is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given:

Angle of elevation= 39.

Hypotenuse = 17 m

Using Trigonometry

cos 39 = adjacent side /hypotenuse

cos 39= base/17

0.777= base/17

base= 0.777*17

base= 13.21m

base= 13.2 m.(rounding off)

Hence, the distance from Roman's feet to the base of the flag pole 13.2 m.

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Express the ratio of a's to n's in the word banana, in simplest form.

Answers

2:3 3:2 1:2 2:1 theres your answer.

The ratio of A's to N's in the word BANANA is 2:1. This means that there are twice as many A's as there are N's in the word. Therefore, the correct answer is D: 2:1.

To find the ratio of A's to N's in the word BANANA, we need to count the number of A's and N's in the word.

1. Count the occurrences of A and N:

  In the word BANANA, there are 3 A's and 1 N.

2. Express the ratio:

  The ratio of A's to N's is 3:1.

3. Simplify the ratio:

To simplify the ratio, we can divide both parts by their greatest common divisor (GCD), which is 1 in this case, because 3 and 1 have no common divisor other than 1.

[tex]\[ \text{Ratio} = \frac{3}{1} = 3:1 \][/tex]

4. Check the given options:

Now, let's compare the simplified ratio 3:1 with the given options.

  A. 2:3 - This doesn't match the simplified ratio.

  B. 3:2 - This doesn't match the simplified ratio.

  C. 1:2 - This doesn't match the simplified ratio.

  D. 2:1 - This matches the simplified ratio.

Therefore, the correct answer is D: 2:1.

The ratio of A's to N's in the word BANANA is 2:1. This means that there are twice as many A's as there are N's in the word.

The complete question is:

Express the ratio of A's to N's in the word BANANA, in simplest form.

A:  2:3

B:  3:2

C:  1:2

D:  2:1

Please help, Picture included.
Jason jumps from a plane at an altitude of 1000m. his parachute opens after 10 seconds. The graph shows the relationship between his altitude and time. How far does he fall in the first 40 seconds?

A) 400m

B) 500m

C) 600m

D) 700m

Answers

Final answer:

Jason falls 800m in the first 40 seconds.


Explanation:

To find how far Jason falls in the first 40 seconds, we need to look at the graph provided. The graph shows that for the first 10 seconds, his altitude decreases from 1000m to 200m. So, in the first 10 seconds, he falls 1000m - 200m = 800m. Then, from 10 seconds to 40 seconds, his altitude stays constant at 200m, so he does not fall any further. Therefore, Jason falls a total of 800m in the first 40 seconds.


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Andy is trying to determine the correlation between the number of math homework assignments he completes and his test score. Which is the BEST estimate for the correlation coefficient of the data? A) r = 1.5 B) r = 0.5 C) r = 0.96 D) r = −0.90

Answers

Answer option C:
The model is close to being linear. Therefore, there is a strong positive correlation.

Answer:

Option C

Step-by-step explanation:

It is really obvious that whenever the number of homework assignments he completes increases, his knowledge in the subject increases.  This will increase automatically his test score in Maths.

Thus we can expect a perfect linear association between number of assignments done and his test score.

The correlation coefficient which is a measure of linear association between two variables always lies between -1 and +1.

Hence Option a cannot be correct since the value is greater than 1.

b) r=0.5 gives a positive but not very strong association.  This is wrong as there is a strong association between the two variables

c) r=0.96 seems to be a correct answer as the positive and near to 1 r value confirms the linear strong positive association between the two variables.

D) r =-0.90 is wrong since there cannot be a negative association.

So only option right is option C

8.9 – 1.4x + (–6.5x) + 3.4

Answers

8.9 + 3.4 -1.4x - 6.5x = 12.3 - 7.9x

Answer:

12.3 – 7.9x

Step-by-step explanation:

the product of + and - is -

Therefore,

8.9 – 1.4x + (–6.5x) + 3.4

= 8.9 – 1.4x –6.5x + 3.4

collect like terms

= – 1.4x – 6.5x + 3.4 + 8.9

= –7.9x + 12.3

= 12.3 – 7.9x

How do you find a scale factor?

Answers

Look in the legend area or title block on the map or mechanical drawing.

Determine the ratio of corresponding linear dimensions of geometrically similar figures.

Read the problem statement.

___
The method is determined by the nature of the information you are given to work from.

Using satellite technology, the distance between two planes can be measured by keeping track of the angle between them and the distance of each plane to the tracking station. Assume plane 1 is 176.27 miles away d plane 2 is 222.34 miles away and the angle formed with the tracking station is 38.59. How far apart are the planes?

Answers

The best approach to this is to use the law of cosine which is stated as  
c2 = a2 + b2 â’ 2ab cos(C)
 distance a=176.27; distance b=222.34; angle C=38.59; distance c is the missing value. 
 Hence c²=176.27²+222.34² -2*176.27*222.34cos38.59°= 138.71 miles

We are learning polynomials in algebra one. Can anyone help explain trinomials like- n^3 - 5n^2 - 50n

Answers

Prefixes you will see in math (and other places) include mono-, bi-, tri-, quadri-, hexa-, poly- and others. Respectively, they mean 1, 2, 3, 4, 6, many. So, a "trinomial" is a 3-term expression. Yours has terms (n^3), (-5n^2), (-50n).

If you examine these terms, you can see that n is a factor of all of them.

There are a few things we like to do with polynomials (or trinomials, in this case). We like to perform arithmetic operations on them (addition, subtraction, multiplication, division). There is generally nothing tricky about this. The usual rules apply, and polynomial math is easier than multi-digit arithmetic in many ways.

We also like to factor polynomials. Binomials and trinomials are generally the easiest, so these are the ones you see most often. It can help to be familiar with the way binomials multiply.
.. (x +a)*(x +b)
.. = x*(x +b) +a*(x +b) . . . . . use the distributive property
.. = x^2 +bx +ax +ab . . . . . use the distributive property twice more
.. = x^2 +(a +b)x +ab . . . . . collect terms

Here, when we say "collect terms", we mean we want to combine the coefficients of "like" terms, that is, terms that have the same constellation of variables. Here, the only "like" terms are terms that have a constant multiplying the variable x. We add the terms bx and ax to get (a+b)x. (Again, the distributive property is involved. Know it backward and forward.)

When we factor out n from your trinomial, we have
.. = n(n^2 -5n -50) . . . . . . using the distributive property

Comparing this to the product of binomials above, we could factor this to binomial terms if we could find "a" and "b" such that ab = -50 and (a+b) = -5. Sometimes it helps simply to list factor pairs of a number to check for possiblities.
.. -50 = -50*1 = -25*2 = -10*5
The sums of these factor pairs are -49, -23, and -5. This last one matches what we are looking for as a coefficient of the linear term, so we could choose a=-10, b=5 and write your trinomial in factored form as
.. = n(n -10)(n +5)

Factoring is a little trickier if the coefficient of the squared term is not 1, but it generally follows the same pattern.

_____
In summary:
  a trinomial is a 3-term polynomial
  the unusal rules for multiplying and dividing arithmetic expressions apply
  the process of factoring a trinomial can be helped by remembering the pattern for the product of binomials

Please help ASAP!! 14 points

Answers

This graph has a positive slope, so we can immediately eliminate C and D (which have negative slopes).  Next, look at B:  Solving for 7y, we get 7x-49, which has a slope of +1 and a y-intercept of -7 (which matches the y intercept -7 on the graph).  Do the same thing for A.  Which is the correct answer, A or B?

PLEASE HELP ASAP! TONS OF POINTS

Answers

its B and report that other dude

Answer:

I would say it's B!

To be honest I got confused at a point but I think B is the correct answer.

Hope this helped

A survey with a two-point scale was conducted in an organization. It concluded that 85% of the respondents were unsatisfied with the career guidance they were provided. If 2,000 people participated in the survey, people were satisfied with the career guidance.

Answers

2000*(1-.85) = 300
300 individuals were satisfied with their careers

Answer:

See image

Step-by-step explanation:

Plato

What percent of 170 is 68?
393 is 60% of what number?

Answers

68 ÷ 170 = 0.4
0.4 * 100 = 40

68 of 170 = 40%

393 ÷ 60% = ?
60% ÷ 100 = 0.6
393 ÷ 0.6 = 655

393 is 60% of 655

HOLA FELLOW AMERICANS I AWAIT YOUR ASSISTANCE

Answers

the answer is d x=3 and y=2 

Answer:

2

Step-by-step explanation:

the sum of two fractions is three times their difference.six times the smaller fraction exceeds the larger fraction by 3/2.find the fractions

Answers

Let a and b represent the fractions.
.. a +b = 3(b -a)
.. 6a -b = 3/2
Rewriting the first equation, we have
.. 4a -2b = 0
or
.. 2a -b = 0
Subtracting this from the second equation gives
.. 4a = 3/2
.. a = 3/8
.. b = 2a = 3/4

The two fractions are 3/8 and 3/4.

Can Someone Please Help Me Factor (x^(2)+6x+58)

Answers

The last term is 58. List out the ways to multiply two whole numbers to get to 58

1*58 = 58
2*29 = 58
(-1)*(-58) = 58
(-2)*(-29) =58

Then go through those factors and see which two values add to 6 (which is the middle number in the given expression)

1+58 = 59
2+29 = 31
-1+(-58) = -59
-2+(-29) = -31

None of those sums are 6, so the original expression cannot be factored. It is said to be prime. 

The number 1,054 is?
< 1,045
= 1,045
> 1,045
Or none of these is correct

Answers

>1045 because 1054 is greater than 1045
The number 1054 > 1045

What is mSU?
A. 49
B. 77
C. 98
D. 161

Answers

The measure of an angle formed by a tangent and a secant intersecting outside the circle is equal to one-half the difference of its intercepted arcs. 

T = 1/2 (RU - SU)
21 = 1/2(119 - SU)
42 = 119 - SU
77 = SU

The answer is B. 77

Hope this helps =)

Answer:

77 degrees (option B)

Step-by-step explanation:

Use the formula A=bh , where A is the area, b is the base length, and h is the height of the parallelogram, to solve this problem. Jack makes a mosaic out of glass tiles. The mosaic covers a parallelogram-shaped piece of wood. The area of the wood piece is 456 in² and its base is 24 inches. What is the height of the wood piece?


Help I need this ASAP 99 points!!!

Answers

Th anwser is19 

hope this helps


Suppose a population of 40 crickets doubles in size every month. the function gives the population after x months. how many crickets will there be after 3 years?

Answers

The function is given by:
f(x)=40(2)^x
where x is in months
he population after 3 years will be found as follows:
x=3 years=3×12=36 months
thus the population after 3 years will be:
f(36)=40(2)^36
f(36)=2.748779069×10^12

Answer:

2,880

Step-by-step explanation:

just trust me, it's that one

There are 514 children in all at both Peter’s and Nada’s schools. Nada’s school has 185 children. About how many children go to Peter’s school?

Answers

When there are 514 children in total and 185 go to Nada's school, there are
514 - 185 = 329 children left.
Therefore, 329 (about 330) children go to Peter's school.

You are asked to draw a triangle with side lengths of 6 inches and 8 inches. What is the longest whole number length that your third side can be?
@iGreen,

Answers

Th triangle inequality rule states that the length of a side of a triangle must be less than the sum of the lengths of the other two sides. Therefore, with sides
A, B, and C:
Where A = 6 in
Where B = 8 in
C = ?

C < A + B
C < 6 + 8
C < 14

The answer must be expressed as a whole number, and 13 is the largest whole number less than 14. Therefore, the maximum length of the third side is 13 inches.

Find x so that the slope of the roof is one third 1/3.

Answers

dkcjcndkskfkvjcnzkalsufcjcn

A cone is inscribed in a regular square pyramid. If the pyramid has a base edge of 6" and a slant height of 9", find the volume of the cone. 12√2 18√2 27

Answers

check the picture below.

so, a cone inscribed in a square pyramid, like the blue one there, will have the a diameter that is the length of the base of the pyramid, as you can see there, is 6, now, since the radius is half of the diameter, that means r = 3.

we know the slant height is 9, since the slant height and the height segment make a right-triangle with the base's segment, then we use the pythagorean theorem to get the height "h".

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\quad \begin{cases} r=radius\\ h=height\\ -----\\ r=3\\ h=6\sqrt{2} \end{cases} \implies V=\cfrac{\pi (3)^2(6\sqrt{2})}{3}[/tex]
Final answer:

The volume of the cone inscribed in the pyramid, calculated using the formula for the volume of a cone and the Pythagorean theorem, is 18√2π cubic inches.

Explanation:

In this question, we're asked to find the volume of the cone inscribed in a regular square pyramid. The volume V of a cone can be calculated using the formula V = 1/3 * pi * r^2 * h, where r is the radius of the base and h is the height of the cone. Since the cone is inscribed in the pyramid, its height and base radius would be the same as those of the pyramid.

However, the pyramid is a square pyramid with a base edge of 6 inches and a slant height of 9 inches. The height of the pyramid (and thus the cone) can be calculated using the Pythagorean theorem as √(9^2 - (6/2)^2), which is √(81 - 9) = √72 = 6√2.

The radius of the base of the cone is half of the base edge length of the pyramid, or 3 inches. So the volume of the cone is V = 1/3 * pi * 3^2 * 6√2 = 18√2π cubic inches.

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The standard form of an exponential growth or decay equation is

f(x) = a(b)^x

What do each of the variables in this equation (a,b,x) represent?

Answers

a: represents the initial amount (before the growth or decay starts).

b: represents the factor of growth or decay (e.g. 0.75 or 1.32).

x: represents the variable. This can be an amount of time (which is mostly true), or (sometimes) the other meaning of the variable is given.

The exponential function, which means as you increase  in x ,  y increases exponentially.

It is required to represent the variable.

What is Exponential functions?

Exponential functions are patterns that get continuously multiplied by some number. It's exponential growth when the base of our exponential is bigger than 1, which means those numbers get bigger. It's exponential decay when the base of our exponential is in between 1 and 0 and those numbers get smaller.

Given that:

The standard form of an exponential growth or decay equation is

f(x) = a(b)^x

This is an exponential function, which means as you increase  x ,  y  increases exponentially. The initial amount is given by the value  a , which is easy to see (just let  x=0  and you have  y=a  left). The growth factor is the value  b .

If you restrict b such that  0<b<1 , the function will decay (represented below) and if  b>1 , the function will grow.

Therefore, the exponential function, which means as you increase  in x ,  y increases exponentially.

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Please help aassssaaaapppp

Answers

go to symbolab.com its really helpful
B
p/s : follow me and I will help you more about maths
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