The value of g(-3) is 15 of the function: g(x) = 3(2-x)
Define function.A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
Given Data
Function
g(x) = 3(2-x)
g(-3)
Equating x = -3
g(-3) = 3(2-(-3))
g(-3) = 3(2+3)
g(-3) = 3(5)
g(-3) = 15
The value of g(-3) is 15.
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work out the circumference of the circle below, Give your answer to 1 d.p 7.6m
The circumference of given circle with the radius of 7.6m is 119.43
What is circumference?A circle's circumference is its perimeter. It is the total length of the circle's circumference. The circumference of a circle is equal to the product of the constant and the circle's diameter. This metric of the circumference of a circle is required for a person walking across a circular park or a circular table to be bordered.
Circumference is a linear value with the same units as length. A circle is a closed round figure whose boundary points are all equidistant from a fixed point known as the center. The area and circumference of a circle are the two most important metrics of a circle.
The formula for the circumference of a circle is
C = 2πr
We have given that radius = 7.6m
So, the circumference is
C = 2π(7.6)
= 38π
= 119. 43
Thus, circumference is 119.43
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At Marilyn's candy shop, she mixes gummy bears worth 50¢ a pound with chocolate kisses worth 30¢ a pound to create a 97 pound mixture worth 35€. To the nearest pound, how much of each type of candy is in the mixture?
Data:
Gummy bears: G
Chocolate kisses: C
G=50 ¢ a pound
C=30 ¢ a pound
97 pound mixture:
[tex]G+C=97[/tex]mixture worth € 35 (3500 ¢ ):
[tex]50G+30C=3500[/tex]To find how much of each type of candy is in the mixture you use the next system of equations:
[tex]\begin{gathered} G+C=97 \\ 50G+30C=3500 \end{gathered}[/tex]1. Solve one of the variables in one of the equations:
Solve G in the first equation:
[tex]G=97-C[/tex]2. Use the value you find in the fisr part in the other equation:
[tex]50(97-C)+30C=3500[/tex]3. Solve the variable:
- Distributive property to remove the parenthesis:
[tex]4850-50C+30C=3500[/tex]-Combine like terms:
[tex]4850-20C=3500[/tex]-Substract 4850 in both sides of the equation:
[tex]\begin{gathered} 4850-4850-20C=3500-4850 \\ \\ -20C=-1350 \end{gathered}[/tex]-Divide into -20 both sides of the equation:
[tex]\begin{gathered} \frac{-20}{-20}C=\frac{-1350}{-20} \\ \\ C=67.5 \end{gathered}[/tex]4. Use the value in part 3 to find the value of the other variable:
[tex]\begin{gathered} G=97-C \\ G=97-67.5 \\ \\ G=29.5 \end{gathered}[/tex]Then, the mixture has 29.5 pounds of gummy bears and 67.5 pounds of chocolate kissesHere are the amounts of money (cents) in coins carried by 10 students in a statistics class: 50, 35, 0, 46, 86, 0, 5, 47, 23, 65. to make a stemplot of these data, you would use stems.
a. 0, 2, 3, 4, 6, 8
b. 0, 1, 2, 3, 4, 5, 6, 7, 8
c. 0, 3, 5, 6, 7
d. 00, 10, 20, 30, 40, 50, 60, 70, 80, 90
e. None of these
The stems are 0, 2, 3, 4, 5, 6, 8. Therefore option e, is the correct answer
Stem and leaf plot are used in statistics to organize data that are collected. Any number in a data is broken down into a stem and a leaf.
Stem displays data on the left while leaf displays data to the right
The data for the amounts of money (cents) in coins carried by 10 students in a statistics class: 50, 35, 0, 46, 86, 0, 5, 47, 23, 65 can be represented in the stem and leaf plot below:
2 I 3 ⇒ 2 on the stem and 3 on the leaf read as 23
3 I 5 ⇒ 3 on the stem and 5 on the leaf read as 35
4 I 6 ⇒ 4 on the stem and 6 on the leaf read as 46
4 I 7 ⇒ 4 on the stem and 7 on the leaf read as 47
5 I ⇒ 5 on the stem as 5
5 I 0 ⇒ 5 on the stem and 0 on the leaf read as 50
6 I 5 ⇒ 6 on the stem and 5 on the leaf read as 65
8 I 6 ⇒ 8 on the stem and 6 on the leaf read as 86
Hence, stems are 0, 2, 3, 4, 5, 6, 8
Therefore, option e, is the correct answer
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What describes the graph of y = - |x + 1| - 5?
The graph of y = - |x + 1| - 5 will be like an inverted "V" letter, such that the vertex is on the point (-1, -5).
What describes the graph of the given function?
The general absolute value function can be written as:
y = |x - a| + b
This function looks like a "V", such that the vertex of the graph is located at the point (a, b).
Particularly, if we have a negative sign before the absolute value part, like in:
y = -|x - a| + b
The "V" will open downwards.
In this case, the function is:
y = - |x + 1| - 5
In this case, the vertex will be at (-1, 5).
And we can see a negative sign before the absolute value part, so the graph opens downwards.
That is the description of the graph.
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Classify each linear equation.
No Solution
:: 3x = 3(x + 3)
:: -2(x + 3) = -2x - 6
Infinitely Many Solutions
:: 2x + 2 = 2(x + 1)
::5(X + 1) = 5x +1
A linear equation is a mathematical expression that may be written as x 1+ldots +a n+x n+b=0, where x 1, ldots, and x n are the variables and display style b, a 1, ldots, and a n are the coefficients, which are frequently real integers.
What in mathematics is a linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and which includes only a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is referred to as a "linear equation of two variables" on occasion.A linear equation is a mathematical expression that can be written as x 1+ldots +a n+x n+b=0, where x 1, ldots, and x n are variables and b, a 1, ldots, and a n are coefficients, which are frequently real integers.To learn more about Linear equation refer to:
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PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
7x
Step-by-step explanation:
x is something you find in 2 parts of the equation. Simply do 10-3 and add an x to the end
the life of an electric component has an exponential distribution with a mean of 10 years. what is the probability that a randomly selected one such component has a life more than 7 years?
The probability is 0.4647.
What is probability?Probability is the branch of mathematics that deals with numerical descriptions of the likelihood of an event occurring or the likelihood of a statement being true.The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty. The higher the probability of an event, the more likely the event will occur. A simple example is tossing a fair coin. Both outcomes are equally likely because the coin is fair. The probability of heads or tails is 1/2. These concepts are an axiomatic mathematical formalization of probability theory that is widely used in research fields such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy. Infer the expected frequency from the event. Probability theory is also used to explain the underlying dynamics and laws of complex systems.To learn more about probability from the given link :
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Alang runs a farm stand that sells blueberries and grapes. Each pound of blueberries sells for $1 and each pound of grapes sells for $3.50. Alang sold 20 more pounds of grapes than pounds of blueberries and made $182.50 altogether. Write a system of equations that could be used to determine the number of pounds of blueberries sold and the number of pounds of grapes sold. Define the variables that you use to write the system.
By solving a system of equations we can see that Alang sold 25 pounds of blueberries and 45 pounds of grapes.
How to write and solve the system of equations?
Here we need to define the variables:
g = pounds of grapes bought.
b = pounds of blueberries bought.
We know that:
"Alang sold 20 more pounds of grapes than pounds of blueberries and made $182.50 altogether."
then we can write the system of equations:
g = b + 20
g*3.5 + b*1 = 182.50
To solve this, we can replace the first equation into the second one, so we get:
(b + 20)*3.5 + b*1 = 182.50
b*4.5 + 70 = 182.50
b*4.5 = 182.50 - 70
b*4.5 = 112.50
b = 112.50/4.5 = 25
And we know that:
g = b + 20 = 25 + 20 = 45
So he sold 25 pounds of blueberries and 45 pounds of grapes.
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Challenge An arts academy requires there to be 5 teachers for every 120 students and 3 tutors for every 36 students.
How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has
120 students?
The academy has students per teacher.
Answers:
24 students per teacher12 students per tutorThere needs to be 10 tutors if there are 120 students======================================================
Explanation:
Part 1
There are 5 teachers for every 120 students.
Think of it like this ratio
5 teachers: 120 students
Then divide both sides by 5 to turn the "5 teachers" into "1 teacher".
5 teachers: 120 students
5/5 teachers: 120/5 students
1 teacher: 24 students
There are 24 students per teacher
-------------------------
Part 2
There are 3 tutors for every 36 students
3 tutors: 36 students
3/3 tutors: 36/3 students
1 tutor: 12 students
There are 12 students per tutor
---------------------------
Part 3
The jump from 12 to 120 is "times 10"
We'll multiply 10 on both sides of the ratio we found in the previous part.
1 tutor: 12 students
10*(1 tutor) : 10*(12 students)
10 tutors : 120 students
What’s the answer plsss
The angle of inclination of the line to the nearest tenth of a degree is 25.4°.
So, the correct option is Option(c).
What is the Angle of Inclination?A line's angle inclination is the angle created by the line's intersection with the x-axis. Using a horizontal "run" of 1 and m for slope, the angle of inclination, theta = tan⁻¹(m), or m = tan⁻¹(m), may be calculated.
Given:
The length of the sides of the given triangle are,
Base = 9.7
Perpendicular = 4.6
So, Angle of Inclination = tan θ = Perpendicular/Base
θ = tan⁻¹(4.6/9.7)
θ ≅ 25.4°
Therefore, the angle of inclination of the line to the nearest tenth of a degree is 25.4°.
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If three consecutive term of an AP are x+4,2x+8 and 12. Find the value of x
Since the series is an Arithmetic progression, the difference between the consecutive terms is constant,
Therefore,
(2x+8) - (x+4) = 12 - (2x+8)
⇒ 2x + 8 - x - 4 = 12 - 2x - 8
⇒x + 4 = 4 - 2x
⇒ 3x = 0
⇒ x = 0
The value of x is 0,
So, the Arithmetic Progression is 4, 8, 12.......
What is an Arithmetic Progression?A numerical series in which the difference between the succeeding terms is constant is known as an arithmetic progression (AP). The number sequence 5, 7, 9, 11, 13, 15... is an example of an arithmetic progression with a common difference of 2.The term "finite arithmetic progression" or "arithmetic progression" refers to a finite segment of an arithmetic progression. An arithmetic series is the total of a finite arithmetic progression.There is a chance to come up with a formula for the nth term in an arithmetic progression. As an illustration, the number sequence 2, 6, 10, 14... is an example of an arithmetic progression (AP) since it follows a pattern in which each number is created by adding 4 to its preceding term. The nth word in this progression equals 4n-2.To learn more about Arithmetic Progression, refer to:
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lemons are sold in bags of 6 lemons for $4. if you bought 24 lemons, how much would you spend? write a ratio of 6 lemons to the cost of 6 lemons in $ and what is the unknown value you're looking for. (ik this is simple math its bc my head hurts and im doing it for my lil brother )
If you bought 24 lemons, you would have spent $16.
A ratio of 6 lemons to the cost of 6 lemons in $ is 3:2.
What is Ratio in Math?The relationship or comparison between two quantities of the same unit to determine how much larger one number is than the other is known as a ratio. The expression is expressed as a/b or a:b when b is not equal to 0.
Given:
Cost of 6 lemons in bag = $4
Cost of 24 lemons = (24 × 4)/6 = $16
The ratio of 6 lemons to the cost of 6 lemons in $ is 6:4 which can be reduced to 3:2.
Hence, the required ratio is 3:2.
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Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold 24 cards, which was 4% of the cards sold for Mother's Day. How many cards were sold for Mother's Day?
The most appropriate choice for percentage will be given by
Number of cards sold on mother's day = 600
What is percentage?
Percentage is any number which is expressed as a fraction of 100
In percentage,the denominator is 100
For example, 2% means [tex]\frac{2}{100}[/tex]
Here,
Let the number of cards sold for mother's day be x
A salesman sold 4% of the card sold for mother's day
Number of cards sold by the salesman = [tex]\frac{4}{100} \times x[/tex]
= [tex]\frac{x}{25}[/tex]
By the problem,
[tex]\frac{x}{25} = 24[/tex]
[tex]x = 24 \times 25\\[/tex]
[tex]x = 600[/tex]
Number of cards sold on mother's day = 600
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A submarine at -20 feet
descends 30 feet. What is the
submarine's current location
after the descent?
Answer:
The submarine will be at -50 feet after the descent.
Step-by-step explanation:
A submarine at -20 feet descends 30 feet. What is the submarine's current location after the descent?
If the starting point is -20 feet and it says that the submarine goes down another 30 feet we can write an equation and solve it.
Descending indicates going down or subtraction.
Let x=the current location after the descent.
-20+(-30)=x
-20-30=x
-50=x
The submarine will be at -50 feet after the descent.
Hope this helps :)
How do you determine how many significant digits should be in an answer?
Answer:
Look Down.
Step-by-step explanation:
The LEAST number of significant figures in any number of the problem determines the number of significant figures in the answer.
The width of a rectangle is 4 units less than the length. The area of the rectangle is 12 units. What is the width, in units, of the rectangle?
The width of a rectangle is 4 units less than the length. The width, in units, of the rectangle is 2 units.
Represent the length and width by L and W.
Then W = L - 4.
The area of the rectangle is 12 units
= Length x width
= L x W
= L(L - 4)
=L^2 - 4L = 12
L^2 -4L - 12 = 0
Now on solving this quadratic equation we get
L^2 -4L - 12 = 0
L^2 - 6L + 2L -12 = 0
L(L - 6 ) -2(L - 6) = 0
(L-6)(L-2) = 0
This factors easily into
(L - 2)(L - 6) = 0
so L must be 2,6.
When L = 2
The width of the rectangle is W = L - 4 = 2 - 4 = -2 units.
We ignore the negative values.
when L= 6
The width of the rectangle is W = L - 4 = 6 - 4 = 2 units.
The width of a rectangle is 4 units less than the length. The width, in units, of the rectangle is 2 units.
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The sum of two numbers is 5. Three times the first is thirteen more than ten times the second. Find the numbers
The two numbers with the sum of 5 are 0 and 5
How to determine the two numbers?The sum of the numbers is given as
Sum = 5
The relationship between the numbers is given as
Three times the first is thirteen more than ten times the second.
This can be rewritten as
3x = 15 + 10y
Where x and y represent the numbers
This means that
x + y = 5
Make x the subject
x = 5 - y
Substitute x = 5 - y in 3x = 15 + 10y
3(5 - y) = 15 + 10y
Expand
15 - 3y = 15 + 10y
Evaluate the like terms
13y = 0
This gives
y = 0
Substitute y = 0 in x =5 - y
x = 5 - 0
Evaluate
x = 5
Hence, the numbers are 0 and 5
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Write a justification for each step.
16. 5x3 = 4(x + 2)
Answer:
1.75 = x
Step-by-step explanation: I'm not sure if you meant 5x3 or 5 times 3 so I did the one that made sense
5 x 3 = 4(x+2)
First step: distribute so 5 x 3 = 4x + 8
Second step: 5 x 3 = 15 15 = 4x+8
Third step: Subtract 8 from both sides 15 - 8 = 7 7 = 4x
Fourth step: Divide by 4 on both sides 7/4 = 1.75 1.75 = x
Andrew and Dustin picked $3$ and $2$ pounds of strawberries, respectively. Their neighbor, Jessica, saw them and asked if she could share the strawberries with them. Andrew and Dustin agreed and the three of them shared the strawberries evenly. After the meal, Jessica gave Andrew and Dustin $\$5$ to thank them. If Andrew and Dustin distribute the $\$5$ fairly, how much does Andrew get?
Answer:
4
Step-by-step explanation:
Of the total 5 pounds of strawberries, each person ate 5/3 pounds. Thus, 3-5/3=4/3 pounds of Andrew's strawberries were given to Jessica and 2-5/3=1/3 pounds of Dustin's strawberries were shared. The ratio of pounds shared by Andrew to those shared by Dustin is 4/3:1/3 , or 4:1, so to be fair, the money should be split in the same ratio. Therefore, Andrew should get $4 and Dustin should get $1 .
Thanks to my dad for the help
Answer:
4
Step-by-step explanation:
right on aops
Write down all whole numbers that are between 25 and 50 and have a difference of 4 their digits
whole numbers that are between 25 and 50 and have a difference of 4 are 26, 30, 34, 38, 42, 46.
What is rational number?
Rational numbers are those numbers which include natural numbers, whole numbers as well as integers. And it is written in the form of a/b where a and b are integers. Sometimes, the values of the denominator is one then the given number is not fraction.
Here,
The whole numbers that are between 25 and 50 and have a difference of 4 their digits will start from 26 and next number will be at the gap of 4 that is 30 and so no :
all whole numbers = 26, 30, 34, 38, 42, 46.
Therefore, whole numbers that are between 25 and 50 and have a difference of 4 are 26, 30, 34, 38, 42, 46.
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Find the error(s) and solve the problem correctly.
Draw a diagram to show the given information.
Given:
AE is the perpendicular bisector of DF.
X is the midpoint of AE.
X is the midpoint of BC
Answer:
It is to be noted that the two inaccuracies were that angle 90 was not shown to be produced at the intersection points of the bisector and that congruent segments were incorrectly indicated. See the corrected diagrams below.
What is the explanation of the above assertion?Take notice of the following to better comprehend the flaws in the diagram: A perpendicular bisector cuts a line segment in half and produces a right angle at the point of intersection.
Congruent segments have an equal number of strokes. Specifically, little straight lines to demonstrate congruency.
Whenever it becomes pertinent to show that two bisected lines are equal, marks resembling an equal sign (=) must be used to cross the line on both sides of the bisector. The equals sign is vertical if the line is horizontal, and vice versa. See a sample of the same with the bisection of DF in the original image.
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Find the slope of the line graphed below.
Slope = 1
Slope of the line shown in the graph is 1.
What is slope?The slope of a line indicates its steepness.
The slope is defined as the ratio of the vertical change between two points, known as the rise, to the horizontal change between those same two points, known as the run.To find the slope of a line given the coordinates of two points on the line, use the slope formula. The slope formula is m=(y2-y1)/(x2-x1), or the difference between the y and x values.From the graph we can plot two points (2 , 2) and (4 , 4).
Equation to find slope ,
m = y2 - y1 / x2 - x1
By substituting values,
m = 4 - 2 / 4 - 2
= 2 / 2
= 1
∴ Slope ( 2 , 2) and ( 4 , 4 ) = 1.
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The table below gives values of an invertible function f(x):
Part A
f(0)
that means the value of f(x) for x=0
looking at the table
For x=0 ----> f(x)=4
therefore
f(0)=4
Part B
f(x)=0
looking at the table
f(x)=0 when the value of x=1
therefore
f(1)=0
Part C
f^-1(0)
For f(x)=0 -----> the value of x=1
therefore
f^-1(0)=1
Part D
f^-1(x)=0
looking at the table
For x=0 -----> f(x)=4
therefore
f^-1(4)=0
F is a point on segment EG. If EF = 19, FG = x + 13, and EG = 6x + 14, what is EG?Simplify your answer and write it as a proper fraction, mixed number, or integer.
You have the segment EG and point F in it.
Point F separates the segment in two smaller ones EF and FG.
You can say that
EG= EF + FG
You have to replace the name of the segments with their values to get the equation:
[tex]6x+14=19+(x+13)[/tex]Now that you have a one unknown equation you can clear X
[tex]\begin{gathered} 6x=19+x+13-14 \\ 6x-x=\text{ 18} \\ 5x=18 \\ x=\frac{18}{5}=\text{ 3.6} \end{gathered}[/tex]The value of x is 3.6
Is my friend correct or incorrect
Answer:
incorrect
Step-by-step explanation:
Answer: No, he's incorrect
Step-by-step explanation:
Generally you only move the symbol to face the other side when in the case of multiplying both sides by (-1). The correct solution hence would be, x > -27
If someone could please help me on the first three that would be great!
( please only answer if you know the answer! )
Substitution Property of Equality - (2) You replace one expression with another equivalent expression.
Segment Addition Postulate - (10) Parts of line segment combine to form longer segments.
Triangle Sum Theorem - (4)The measure of three interior angles in a triangle have a sum of 180 degrees.
Reflexive Property - (8) An expression is equal to itself
Angle Addition Postulate - (6)The measure of an angle formed by two adjacent angles is the sum of the measures of the two angles.
Symmetric Property - (9) You switch expressions from one side of the equals symbol to the other.
Angle Congruence Postulate - (1) If two angles are congruent their measures are equal.
Segment Congruence Postulate - (7)Two segments are congruent so they have the same length.
Definition of Right Angle - (5) An angle is a right angle so its measure is 90 degrees.
Transitive Property - (3) a = c because a = b and b = c.
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Find the first 5 multiples and all factors of 32
For the given question,
The provided number is 32.
The first 5 multiple of 32 = 2, 4, 8, 16 and 32.
Now, all factors of 32 = 2, 4, 8, 16 and 32.
Thus, the 5 multiples and the all factors of 32 are determined.
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your friends are planning a party for their parents anniversary. The caterer charges a delivery fee of $100 plus an additional $35.75 per person. if they can spend no more than $530, how many people can they invite? remember you cannot serve a partial person.
Answer:
3815699985588888548555006
Coordinate distance Decimal (6,-5) and (9,-1)
After applying distance formula, we have come to find that, distance from coordinate (6,-5) to coordinate (9,-1) is 5 unit.
What is a coordinate plane?A coordinate plane is a surface with two dimensions made up of two number lines. It is created when the origin, the point at which the X-axis and Y-axis intersect, is reached. To locate points, one uses the numbers on a coordinate grid.
A coordinate plane is useful for graphing points, lines, and many other things. It serves as a map and provides clear instructions for getting from one place to another.
The formula for distance of two given points is
Distance =√((x₂ – x₁)² + (y₂ – y₁)²)
Here, (x₁, y₁) is (6,-5) and
(x₂, y₂) is (9,-1)
Substituting the given values we get
Distance = √((9 – 6)² + ((-1) – (-5))²)
= √((3)² + (4)²)
= √(9 + 16)
= √(25)
= 5
Thus, Distance from point (6,-5) to point (9,-1) is 5 unit.
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Can someone help me with this
rude!we dont us such words here change it please
