Answer:
f(4)=9
Step-by-step explanation:
The given function is
F(x)=3x-3
so,
f(4)=3*4-3
f(4)=12-3
f(4)=9
putting 4 in place of x we get answer of the question.
7 Write a problem you can solve using the fractions and 12. Explain how you can
solve by simplifying a complex fraction. Show your work.
Complex fraction 4²/₃ + 1/3 – 4¹/₃ = 2/3
A fraction defined as the part of the whole thing. For example, a pizza is divided into four equal pieces, then each piece is represented by ¼. Fractions help to distribute and judge the numbers easily and make the calculation faster.
Some steps to solve a fraction -
Step 1: Write the factors of numerator and denominator.
Step 2: Determine the highest common factor of numerator and denominator.
Step 3: Divide the numerator and denominator by their highest common factor (HCF). The fraction so obtained is in the simplest form.
For example -
4²/₃ + 1/3 – 4¹/₃
= (4 × 3 + 2)/3 + 1/3 – (4× 3 + 1)/3
= 14/3 + 1/3 – 13/3
= (14 + 1 - 13)/3
= (15 - 13)/3
= 2/3
Hence , in the mathematics problem can be solved by using the fractions.
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Simply and show how you got the answer
[tex] \frac{3}{ \sqrt{5} - 2 } [/tex]
Rationalize the denominator by multiplying the numerator and denominator by the denominator. (Important: if the denominator has a minus sign, change to plus and vice versa)
[tex]⟹\frac{3 \times \sqrt{5 + 2} }{ (\sqrt{5} - 2 ) \times ( \sqrt{5} + 2) } [/tex]
[tex] ⟹ \frac{3 \sqrt{5} + 6 }{ \sqrt{25} + 2 \sqrt{5} - 2 \sqrt{5} - 4 } ⟹\frac{3 \sqrt{5} + 6 }{5 - 4} [/tex]
[tex] ⟹\frac{3 \sqrt{5} + 6}{1} ⟹3 \sqrt{5} + 6[/tex]
Problem 2.[tex] \frac{6 - \sqrt{12} }{ \sqrt{3} + \sqrt{10} } [/tex]
Rationalize the denominator.
[tex] ⟹\frac{(6 - \sqrt{12} ) \times ( \sqrt{3} - \sqrt{10} )}{ (\sqrt{3} + \sqrt{10} ) \times ( \sqrt{3} - \sqrt{10} } [/tex]
[tex]⟹\frac{6 \sqrt{3} - 6 \sqrt{10} - \sqrt{36} + \sqrt{120} }{ \sqrt{9} - \sqrt{30} + \sqrt{30} - \sqrt{100} } [/tex]
[tex]⟹ \frac{6 \sqrt{3} - 6 \sqrt{10} - \sqrt{36} + \sqrt{120} }{3 - 10} ⟹ \frac{6 \sqrt{3} - 6 \sqrt{10} - \sqrt{36} + \sqrt{120} }{ - 7} [/tex]
[tex] ⟹\frac{6 \sqrt{3} - 6 \sqrt{10} - 6 + \sqrt{12 \times 10} }{ - 7}⟹\frac{6 \sqrt{3} - 6 \sqrt{10} - 6 + 4 \sqrt{3 \times 10} }{ - 7} [/tex]
[tex] ⟹ - \frac{6 \sqrt{3} - 6 \sqrt{10} - 6 + 2 \sqrt{30} }{7} [/tex]
Therefore:
1. [tex]3 \sqrt{5} + 6[/tex]
2. [tex] - \frac{6 \sqrt{3} - 6 \sqrt{10} - 6 + 2 \sqrt{30} }{7} [/tex]
I hope these helpThe picture is uploaded above. I will give brainliest
The question is question 2
4,12
represents that jorge takes 4 steps to walk 12 feet
or represents number of steps that it takes to walk 12 feet either is right
Jill and erika made 8 gallons of lemonade for their lemonade stand.How many quarts did they make?if they charge $1.00 per quart, how much money will they make if they sell it all?
Answer:
9
Step-by-step explanation:
because 8 gallons of lemonade will stand on charge $1.00 will add and answer will be 9
which of the following below is a solution to y=x2-1
(4,5)
(2,5)
(1,4)
(2,3)
Answer:
(2,3)
Step-by-step explanation:
[tex]y=(2)^{2}-1=4-1=3[/tex]
when x = 2, y = 3
Hope this helps
What is the slope of the line?
-7-6-5-4-3-2-
6
5
4
324
0 123 4 56
234567
+6
x
Answer:
6
Step-by-step explanation:
ya it of course sachi ta
P(x)= 2x^4 - 7x^3 + x^2 - 18x + 3
a) Use Descarters' Rule of Signs, we know that there are ____ or ____ or ____ positive real zeros P can have.
b) b) Use Descarters' Rule of Signs, we know that there are ____ negative real zeros P can have.
Using Descartes's Rule of Signs:
There are four positive real zeros P can have.
There are zero negative real zeros P can have.
What is Descartes's rule of sign?Descartes' rule of sign is used to determine the number of positive and negative real zeros of a polynomial function.
We have,
P(x) = 2[tex]x^{4}[/tex] - 7x³ + x² - 18x + 3
We have to look at the sign of the coefficient
Here,
2[tex]x^{4}[/tex] - 7x³ + x² - 18x + 3
(+)---(-)(-)---(+)(+)--(-)(-)---(+)
There are 4 variations so there are 4 positive real zeroes.
For finding negative real zeroes we Put x = -x.
P(-x) = 2[tex]x^{4}[/tex] + 7x³ + x² + 18x + 3
2[tex]x^{4}[/tex] + 7x³ + x² + 18x + 3
(+)---(+)(+)----(+)(+)--(+)(+)-- --(+)
There are no variations so there are zero negative real zeroes.
Thus,
a) Using Descartes's Rule of Signs, we know that there are four positive real zeros P can have.
b) Using Descartes's Rule of Signs, we know that there are zero negative real zeros P can have.
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the picture asks the question
What is the average rate of change of h over the interval −6 ≤ x ≤3
Answer:
-1/9
Step-by-step explanation:
Graphs are provided showing how two factors changed over time in a certain region: the number of animals that preyed on mice and the amount of plants the mice ate. Using the information from these graphs, predict which of the following years will see the highest increase in mouse population. 30 Predators 20 per km2 10 1996 1998 2000 2002 Density of Predators 1996 1998 2000 2002 30 Bushels 20 per km2 10 Availability of Food Plants 1996 1998 2000 2002
https://sis-union.tnk12.gov/scripts/wsisa.dll/WService=wsUNIStu/seplog01.w
Step-by-step explanation:
Based on the records for the past several seasons, a sports fan believes the probability the red team wins is 0.35. The fan also believes the probability the blue team wins is 0.40. In a season with 160 games, how many fewer games should the fan expect the red team to win?
If a sports fan believes that, the probability of the red team winning is 0.35 and that of the blue team winning is 0.40, then the fan expects the red team to win 9 matches less than the blue team in a season of 180 games.
As per the question statement, based on the records for the past several seasons, a sports fan believes that, the probability of the red team winning is 0.35 and that of the blue team winning is 0.40.
We are required to calculate the number of games, the fan expects the red team to win, lesser than the blue team in a season of 180 games.
As per the probability record, maximum number of games, the fan believes that the blue team can win all over the season of 180 games = [tex](0.40*180)=(\frac{40}{100}*180)=(4*18)=72.\\[/tex]
Similarly, maximum number of games, the fan believes that the red team can win all over the season of 180 games = [tex](0.35*180)=(\frac{35}{100}*180)=(7*9)=63.\\[/tex]
Hence, the fan expects the red team to win [tex][(72-63)=9][/tex] matches less than the blue team in a season of 180 games.
Probability: It is a branch of mathematics that deals with the possibility of occurrence of a random event.To learn more about Probability, click on the link below.
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Someone help meee!
Solve 4(x-3)-2(x-1)>0
Answer:
{x|x>5}
Explanation:
4(x-3)-2(x-1)>0
4x-12-2x+2>0
2x-10>0
2x>10
x>5
Question 9 of 25
Give the slope of y-3= 4(x+8) and a point on the line.
OA. The slope is 3 and (-8, 4) is on the line.
B. The slope is 8 and (3, 4) is on the line.
OC. The slope is 4 and (-8, 3) is on the line.
OD. The slope is 4 and (8, -3) is on the line.
SUI
The slope of the line y-3= 4(x+8) is 4 and (-8, 30 is a point on line y - 3 = 4(x + 8).
According to the given question.
We have a equation of a line y-3= 4(x+8).
Here, we have to find the slope of a line y-3= 4(x+8) and a point on the line.
Since we know that, the equation of a lines through a point (x1, y1) is given by y - y1 = m(x - x1), where m is the slope of the line.
And the equation of slope intercept form for a line is y = mx + c.
So, compare the given equation of line y-3= 4(x+8) with the standard equation of line y - y1 = m(x - x1) which passes through the point (x1, y1), we get
point ( -8, 3) on line y-3= 4(x+8).
Now, the slope intercept form of the line y-3= 4(x+8) is
y - 3 = 4x + 32
⇒ y = 4x + 32 + 3
⇒ y = 4x + 35
Thereofore, the slope of the line y-3= 4(x+8) is 4.
Hence, the slope of the line y-3= 4(x+8) is 4 and (-8, 30 is a point on line y - 3 = 4(x + 8).
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A group of friends wants to go to the amusement park. They have no more than $605 to spend on parking and admission. Parking is $17.25, and tickets cost $37.25 per person, including tax. Which inequality can be used to determine pp, the maximum number of people who can go to the amusement park?
Considering the definition of an inequality, the inequality that can be used to determine p, the maximum number of people who can go to the amusement park, is:
17.25 + 37.25×p ≤ 605
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Inequality in this caseIn this case, you know that:
A group of friends have no more than $605 to spend on parking and admission. Parking is $17.25, and tickets cost $37.25 per person, including tax.Being "p" the number of people who can go to the amusement park, the inequality that expresses the previous relationship is
17.25 + 37.25×p ≤ 605
Finally, the inequality that can be used to determine p, the maximum number of people who can go to the amusement park, is:
17.25 + 37.25×p ≤ 605
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What is (-1, 2) reflected across the y-axis?
If the coordinate is reflected over the y-axis, the resulting coordinates will be (1, 2).
Reflection of coordinatesImages that are reflected are mirror images of each other. For instance, given the coordinate points (x, y), if it is reflected across the y-axis, then the result of the expression is (-x, y).
Given the coordinate point (-1, 2), if the coordinate is reflected over the y-axis, the resulting coordinates will be (1, 2).
Note that the x-coordinate point is negated if the coordinate is reflected over the y-axis.
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Reduce the fraction to its simplest form 35/54
Answer:
it cannot be simplified anymore
Answer:
0.648148
Step-by-step explanation:
it is already in its simplest form but in decimal it is 0.648148(rounded up to six decimal places.
6. Answer the following questions given the following infinite geometric series:
8 + 12 + 18 + 27 + ...
For the given geometric sequence, we have that:
The first term is: [tex]a_1 = 8[/tex]The common ratio is: [tex]r = \frac{3}{2}[/tex]Since it is an infinite sequence with r > 1, the sequence diverges.What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
For the series given by:
8, 12, 18, 27, ...
We have that:
The first term is: [tex]a_1 = 8[/tex]The common ratio is: [tex]r = \frac{12}{8} = \frac{3}{2}[/tex] (simplifying by 4).When a geometric series is infinite and has a common ratio greater than 1, it diverges.
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Given this equation for converting temperature from Fahrenheit (f) to Celsius (c) is C = [5(f – 32)]/9, what is the Celsius temp when Fahrenheit is 104 degrees?
Answer:
40 degrees
Step-by-step explanation:
Substitute f = 104:
[tex]C = \frac{5(f - 32)}9 \\\\\to C = \frac{5(104 - 32)}9 \\\\\to C = \frac{5 \times 72}9 \\\\\to C = 5 \times 8 = 40 \text{ degrees}[/tex]
assuming I = E(R + r), prove that I/I = R/E + r/E
If we assume that I = E(R + r), then I/I = R/E + r/E.
The inverse of a value of a number is known as the reciprocal of the number. The reciprocal can be found out by replacing the numerator with the denominator and vice versa. For example, reciprocal of a number x will be 1/x and vice versa.
Here, we are given that I = E/(R + r)
Taking reciprocals of both sides we get-
Reciprocal of I will be- 1/I
Reciprocal of E/(R + r) will be- (R + r)/ E
Thus,
1/I = (R + r)/ E
Simplifying the equation further, we get-
1/I = R/E + r/E
Hence, proved
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BRAINLIEST
What is the least natural number that has exactly 6 factors and is not divisible by 2? How about 6?
The least natural number that has exactly 6 factors and is not divisible by 2 is 75.
How to illustrate the information?It should be noted the factors of 75 include 1, 3, 5, 15, 25, and 75.
Therefore, it should be noted that 2 isn't among the factors based on the information given in the question.
Therefore, the least natural number that has exactly 6 factors and is not divisible by 2 is 75.
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The number 56 is an integer, but not a whole number.
Answer:
False.
Step-by-step explanation:
Whole numbers can be described as the integers greater than and including zero. 56 has no fractional or decimal part, and is positive, so it is a whole number and an integer!
Damon has 37 inches of space on his car bumper that he wants to use for bumper stickers. How many short bumper stickers can Damon fit side by side on his car bumper?
Answer: Does it specify how long his short bumper stickers are?
Step-by-step explanation:
I don’t understand this question
Answer:
This is a one to one function
Step-by-step explanation:
From the function, we know that f(x) = x - 7 is a linear graph.
Using horizontal line test
the graph is one to one if the horizontal line only cross the graph at one point
Simplify 2(-x + 3y - z) - 6y giving out good points.. solve asap
Convert the fraction below into a decimal
13/30
Answer:
0.43repeating
Step-by-step explanation:
You simply divide 30 by 13, and you get 0.43333333333333333
3 is repeating
What is the value for x in the ordered pair 10,5
Answer:
10
Step-by-step explanation:
Ordered pairs are listed in this format: (x,y).
In the pair (10,5):
10 = x
and 5 = y
Answer:
In an ordered pair you will find (#,#) number one equals x and number two is y. So the answer is 10.
Step-by-step explanation:
(x,y)
What is the image of the point
(
1
,
−
4
)
(1,−4) after a rotation of
18
0
∘
180
∘
counterclockwise about the origin?
The image of the point after a 180∘ counterclockwise rotation about the origin is (-1, 4)
How to determine the image of the point?The given parameters are
Point = (1, -4)
Transformation: 180∘ counterclockwise about the origin
The rule of 180∘ counterclockwise about the origin is
(x, y) = (-x, -y)
When this rule is applied to the given point, we have the image to be
Image = (-x, -y)
This gives
Image = (-1, 4)
Hence, the image of the point after a 180∘ counterclockwise rotation about the origin is (-1, 4)
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Compare the steepness of the following functions. How does F3 compare to F1
Answer:
Function 3 is less steep.
Step-by-step explanation:
The steepness of a linear function is determined by its coefficient of x.
Since the coefficient of x in [tex]f_3(x)[/tex], 0.5, is smaller than that of [tex]f_1(x)[/tex], 2, function 3 is less steep than function 1.
Significance of the coefficient of x
We can think of the function as an equation of a line in the slope-intercept form. That is, y= mx +c, where m is the slope and c is the y-intercept.
Steepness and value of x
The larger the numerical value of m, the steeper the line is.
Significance of the sign of x
The sign (positive or negative) of m tells us the direction in which the line is sloping towards. A positive m value gives us a line sloping upwards from left to right, while a negative m value gives us a line that is sloping downwards from left to right.
Additional:
For a similar question on the steepness of functions, do check out the following!
https://brainly.com/question/13359759Mr. McDowell bought a block of fudge that weighed 7/10 of a pound. He cut the fudge into 7 equal pieces. What was the weight of each piece of fudge?
Answer: 1/10 of a pound
Step-by-step explanation:
The total weight was 7/10 of a pound. Cutting the fudge into 7 pieces implies dividing the fudge by 7.
7 is the same as 7/1.
When dividing fractions, we can multiply by the reciprocal. Essentially, we just flip the second number.
[tex]\frac{7}{10}/7 =\frac{7}{10} / \frac{7}{1} =\frac{7}{10} *\frac{1}{7}[/tex]
We can multiply this out to 7/70 and then simplify to 1/10,
or we could first cross simplify by dividing the 7s out of the numerator and denominator before multiplying. Either way, your answer ends up being 1/10 of a pound.
Hope this helps!
20p-8p-6p=12 please make sure it's right
Answer: step by step
Step-by-step explanation:
not totally sure what you're asking but in this equation p=2