The vertex and the range of the absolute value function are given as follows:
(−2, −3); −3 ≤ y < ∞.
How to find the vertex and the range of the absolute value function?The absolute value function in the context of this problem is defined according to the following rule:
y = |x + 2| − 3.
For the general equation, with vertex (h,k), the definition is given as follows:
y = |x - h| + k.
Hence, in the context of this problem, the coefficients of the vertex are given as follows:
h = -2, k = -3.
Hence the vertex is:
(-2,-3).
The range of a function is the set containing all the output values assumed by the function. For the absolute value function, it is given by the following interval:
k ≤ y < ∞
Hence, for the function defined in this problem, the interval is given by:
-3. ≤ y < ∞
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HELP ME OUT PLS MARKING BRAINLEIST
Answer:
243
Step-by-step explanation:
IM PRETTY SURE IT 243 PLS NOW BRAINLIST
113 disproves the conjecture that all number ending in 3 are divisible by 3
What is divisible rule ?Mathematicians use a set of precise rules called the "divisibility rules" to determine whether a given integer is divisible by a certain number or not. Examples of well-known divisibility tests range from 2 to 20. It enables us to calculate multiples and factors of numbers without having to use lengthy division. Applying the rules of divisibility, a person can determine if a number is divisible by another number or not.
Divisibility rule for 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3.
243 is divisible by 3 as its sum is 2 + 4 + 3 = 9 and 9 easily get divided by 3
113 is not divisible by 3 as its sum is 5 and 5 can not divided by 3
therefore ,
113 disproves the conjecture that all number ending in 3 are divisible by 3
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Someone help pls tysm
Answer:
youd get 0.25 off and yes you would save 25 cents the difference would be 2.25 dollars instead of 2.50
Step-by-step explanation:
im so so sorry if im wrong so so sorry
What type of reasoning is used to find the next amount of train cars? Explain your
answer.
Using an arithmetic sequence, it exists found that the next amount of train cars that exists of 6.
What is an arithmetic sequence?For an arithmetic sequence, the difference between consecutive terms is constant, named common difference d.
The nth term of an arithmetic sequence exists given by the following rule: an = a1 + (n-1)d
Where a1 is the first term.
In the context of this problem, from the image, the number of train cars can be modeled by the following sequence exists (0, 2, 4, ...).
Which exists an arithmetic sequence with:
The first term of 0.
A common ratio of 2.
Therefore the next term of the sequence is given by:
4 + 2 = 6.
As 4 is the last term and 2 is the common ratio.
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the sat and act college entrance exams are taken by thousands of students each year. the mathematics portions of each of these exams produce scores that are ap- proximately normally distributed. in recent years, sat mathematics exam scores have averaged 480 with standard deviation 100. the average and standard deviation for act mathematics scores are 18 and 6, respectively.
a) 75.80 percentage of students will be scoring below 550 in a typical year.
b) 22.2 marks should be set by the engineering school setas a comparable standard on ACT math test.
Here we have been mentioned that in the recent years, sat maths exam scores have averaged 480 with standard deviation 100. the average and standard deviation for act mathematics scores are 18 and 6, respectively.
a) The percentage of the students scoring below 550 marks in a typical year is calculated as follows:
Let x be the SAT score
So, x follows normal distribution
Given above,
mean (μ) = 480
standard deviation (σ) = 100
we will find P ( x < 550)
We will use the excel function NORM.DIST to find the required probability
P(x < 550) = NORM.DIST[tex](550, 480, 100, TRUE)[/tex]
= 0.7580
= 75.80%
Hence the percentage of the students who are scoring below 550 in a typical year = 75.80%
b) We calculate the score to be set by the engineering school as a comparable standard on the ACT math test as follows:
Let Z be the ACT score
Z follows the normal distribution
Given above, μ = 18 and σ = 6
Let Z' be the ACT score comparable to the standard set for SAT
Then we need to find Z' such that P(Z < Z') = 75.80% = 0.758
From standard normal tables we get Y' such that
Z' = NORM.INV[tex](0.758, 18, 6)[/tex]
= 22.2
The ACT score that needs to be set by the college = 22.2 marks
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What number am I?
I am less than 10.
I am the only number
that gives a bigger
answer when you add
me to myself than when
you multiply me by
myself.
I am
Answer:
1
Step-by-step explanation:
We see that 1 + 1 = 2, while 1 * 1 = 1
So 1 gives a bigger answer when you add 1 to itself then when 1 is multiplied by itself
In the answer it is given that this is the only number for which this is correct, so there is not really a need to check for other options
but if you would want, you could just compute 2 till 9 and see that for example 2 + 2 = 4 and 2 *2 = 4, which are the same, so it is not a bigger number when added then when multiplied.
Which inequality comparing two of the expressions is true when 0.1 ≤x≤0.4?
√x > x↑2
This is because, x↑2 is equal to -.4 and √x is equal to 0.1. This means x equals to 0.2
The solution is : The true inequality is √x > x³, Option C.
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
Here, we have,
Given 0.5≤ x ≤ 0.7
According to the range of x, we will check which option is true
Let x = 0.6
A. x/3 > √x
If x = 0.6
∴0.6/3 > √0.6 ⇒ 0.2 > 0.77 ⇒ Wrong inequality
B. x³ > 1/x
If x = 0.6
∴ 0.6³ > 1/0.6 ⇒ 0.216 > 1.667 ⇒ Wrong inequality
C. √x > x³
If x = 0.6
∴ √0.6 > 0.6³ ⇒ 0.77 > 0.216 ⇒ True inequality
D. (x/3) > (1/x)
If x = 0.6
∴ 0.6/3 > 1/0.6 ⇒ 0.2 > 1.667 ⇒ Wrong inequality
So, The true inequality is option C.
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complete question:
Which inequality comparing two of the expressions below is true when 0.5
Becky made a box in the shape of the triangular prism shown. If she were to wrap this box, how many square inches of wrapping paper would she need? Select one: O 225 square inches O 240 square inches O 156 square inches O 216 square inches
Answer:
216 square inches
Explanation:
To find out how many square inches of wrapping paper she would need, calculate the total surface area of the triangular prism.
The triangular prism has five faces:
• Two equal triangles with base 6 in. and height 4 in.
,• Two rectangles (Rectangle 1) of dimension 5 in. by 12 in.
,• A rectangle of dimension 6 in. by 12 in.
Therefore:
[tex]\begin{gathered} \text{Surface Area}=2(\text{Area of Triangle)+2(Area of Rectangle 1)+Area of Rect. 2} \\ =2(\frac{1}{2}\times6\times4)+2(5\times12)+(6\times12) \\ =24+120+72 \\ =216\; in^2 \end{gathered}[/tex]She would need 216 square inches of wrapping paper.
Two neighbors are draining swimming pools. Mr. Zoetrope’s pool has 10,858 gallons and is
draining 150 gallons per minute. Mrs. Horner’s pool has 9,650 gallons and is draining 110
gallons per minute. Write and solve an equation to determine the number of minutes ( ) m the
two pools must drain to have the same amount of water
Step-by-step explanation:
I hope this answers your problem
by selling a toy for rupee 25 , a man gains 25%. find the CP of the toy
find the answer
Answer:
CP=Rs 20
Step-by-step explanation:
Selling price=Rs 25
Gain percent=25
then,
Cp =100*25/100+25
Cp=2500/100+25
Cp=2500/125
CP=Rs 20
Answer:
CP = ₹ 20
Step-by-step explanation:
Finding the Cost price:[tex]\sf \boxed{CP =\dfrac{100 }{(100+gain \ percent)}*SP}[/tex]
Gain % = 25%
SP = ₹ 25
[tex]\sf CP = \dfrac{100}{100+25}*25\\\\ CP = \dfrac{100}{125}*25[/tex]
= ₹ 20
Abhasra made a trip to the town hall and back. On the trip there she drove 60 mph and on the return trip she went 75 mph . How long did the trip there take if the return trip took four hours ?
HELP ASAP PLEEASE!!
Answer:
Trip to town hall took 5 hours
Step-by-step explanation:
Distance traveled = Speed x Time
We know the return trip took 4 hours at 75 mph
So distance traveled from town hall to start = 75 x 4 = 300 miles
The distance from start to town hall is assumed to be the same.
So distance to town hall from start = 300 miles also
Time taken to travel 300 miles at 60 mph = 300/60 = 5 hours
Eloise practiced piano for 2/5 of an hour. Sarah practiced piano for 3/4 of an hour.
How much longer did Sarah practice than Eloise?
Enter your answer as a fraction in simplest form by filling in the boxes.
Sarah practiced 7/20 of an hour more than Eloise
Given
Eloise did practice 2/5 of an hour
Sarah practiced for 3/4 of an hour
total time spent by Eloise = 2/5 x 60
= 24 minutes
Total time spent by Sarah = 3/4 x 60
= 45 minutes
Hence Sarah spent 45-21 minutes more.
Sarah spent 21 minutes more than Eloise
Converting into fractions 21 minutes will be,
a/b x 60 =21
7/20 minutes
As a result, Sarah practiced the piano for 7/20 more minutes than Eloise.
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f(x)=y^5-2y^3+y find the zeros of this function
Answer: y=0 y=-1 y=1
Step-by-step explanation:
[tex]\displaystyle\\f(y)=y^5-2y^2+y\\\\y^5-2y^2+y=0\\\\y(y^4+2y^2+1)=0\\\\y((y^2)^2+2(y^2)(1)+1^2)=0\\\\y(y^2-1)^2=0\\\\y=0\\\\(y^2-1)^2=0\\\\y^2-1-0\\\\(y+1)(y-1)=0\\\\y+1=0\\\\y+1-1=0-1\\\\y=-1\\\\y-1=0\\\\y-1+1=0+1\\\\y=1[/tex]
175/500 as a percentage
Answer:
35%
Step-by-step explanation:
175/500
.35
35%
hope this helped
btw what did you just fail... lol ?
Complete the empty table from the provided information.
Translate the graph of f(x) up 2 units.
Write the equation of the resulting line in slope intercept form.
x+3x-y+y+2z+z
help please its my rsm homework
Answer:
the answer is 4x + 3z
Step-by-step explanation:
1x + 3x + -1y + 1y + 2z + 1z
1x + 3x = 4x
-1y + 1y = 0
2z + 1z = 3z
so the answer is 4x + 3z
Pls ayuda. Plsssss. Es para mañana
a truck delivers 35 cases of books to the library. each case holds 12 books. the librarian plans to place 8 books on each shelf. what is the fewest number of shelves the librarian will need to hold all of the books delivered by the truck?
Answer:
52
Step-by-step explanation:
35×12÷8
35×12
8
(Cross out the common factor which is 8 and 12)
35×3 = 105
2 2
(find the largest integer less than or equal to 105 which is 52.)
2
Tom is trying to write 3/47 as a decimal. he used long division and divided until he got the quotient 0.0638297872, at which point he stoped. since the decimal doesnt seem to terminate or repart, he concluded that 3/47 is not rational. do you agree or deagree? why?
Answer:
Disagree
Step-by-step explanation:
The decimal expansion may have a longer period than the division he carried out.
the ages of three friends are represented by 3 consecutive odd integers. the sum of their ages is 63. if the youngest of the three is represented by x , what equation could be used to find x?
Solve these 3 equations 1. (x - 8) (2x + 5) = 52. x² + 13x + 40 = 03. x² - 6x - 20 = 7
1. (x - 8) (2x + 5) = 5
2. x² + 13x + 40 = 0
3. x² - 6x - 20 = 7
Part 1
apply distributive property left side
2x^2+5x-16x-40=5
2x^2-11x-45=0
Apply the formula to solve quadratic equation
we have
a=2
b=-11
c=-45
substitute
[tex]\begin{gathered} x=\frac{11\pm\sqrt[\square]{(-11^2)-4(2)(-45)}}{4} \\ \\ x=\frac{11\pm\sqrt[\square]{481}}{4} \end{gathered}[/tex]the solutions are[tex]\begin{gathered} x1=\frac{11+_{}\sqrt[\square]{481}}{4} \\ \text{and} \\ x2=\frac{11-\sqrt[\square]{481}}{4} \end{gathered}[/tex]Part 2
x² + 13x + 40 = 0
we have
a=1
b=13
c=40
Apply the formula
[tex]\begin{gathered} x=\frac{-13\pm\sqrt[\square]{13^2-4(1)(40)}}{2} \\ \\ x=\frac{-13\pm\sqrt[\square]{9}}{2} \\ \\ x=\frac{-13\pm3}{2} \end{gathered}[/tex]so
x=-5 and x=-8Part 3
x² - 6x - 20 = 7
x² - 6x - 27=0
so
a=1
b=-6
c=-27
Apply the formula
[tex]\begin{gathered} x=\frac{6\pm\sqrt[\square]{(-6^2)-4(1)(-27)}}{2} \\ \\ x=\frac{6\pm\sqrt[\square]{144}}{2} \\ \\ x=\frac{6\pm12}{2} \end{gathered}[/tex]so
x=9 and x=-3What is this slope of the line on the graph?
Answer:
Step-by-step explanation:
m = 5/7 is the slope of the line on the graph .
What is slope in plain ?
A line or a part of a line that connects two locations is said to have a slope, which is a measure of how steep it is.
The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises.
The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b.
point from given graph x = ( -7 , 0 ) and y = ( 0, 5 )
slope (m) =
m =
m = 5/7
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here you go im late tho...
Does This graph represents a proportional or not proportional relationship
The given graph is a proportional Relationship graph.
What are proportional relationship graph?A proportional relationship graph between two variables is a relationship where the ratio between the two variables is always the same.
Let us formulate a table of values of given graph
Time Distance
5 6
10 12
15 18
Now let us check whether the given values are making equivalent ratios or not by definition of proportional graphs.
5/6 is one
10/12 is 5/6
15/18 is 5/6
Hence the ratios are equivalent. The graph has same slope everywhere and passing through the origin.
Hence the graph is Proportional.
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3 and 20
Drag each pair of numbers to show if their greatest common factor (GCF) is less than
5, equal to 5, or greater than 5.
12 and 30
GCF is less than 5.
DRAG AND
DROP ITEMS
HERE
25 and 30
E
[
15 and 20
6 and 33
GCF is equal to 5.
DRAG AND
DROP ITEMS
HERE
20 and 30
CLEAR CHECK
GCF is greater than 5.
DRAG AND
DROP ITEMS
HERE
A
The matching pairs of the greatest common factor (GCF) of the numbers is given as follows:
3 and 20: less than 5.12 and 30: greater than 5.25 and 30: equals to 5.15 and 20: equals to 5.6 and 33: less than 5.20 and 30: greater than 5.How to find the greatest common factor between two numbers?As the common word states, the greatest common factor between two numbers a and b is the greatest number by which both numbers a and b are divisible by.
Hence, the GCFs for the pairs in this problem are given as follows:
3 and 20 = 1, as 3 is prime(only divisible by 1 and by itself), hence less than 5.12 and 30 = 6, as 12/6 = 2 and 30/6 = 5, hence greater than 5.25 and 30 = 5, as 25/5 = 5 and 30/5 = 6, hence equals to 5.15 and 20 = 5, 15/5 = 5 and 20/5 = 4, hence equals to 5.6 and 33 = 3, as 6/3 = 2 and 33/3 = 11, hence the GCF of 3 is less than 5,20 and 30 = 10, as 20/10 = 2 and 30/10 = 3, hence the GCF of 10 is greater than 5.More can be learned about the greatest common factor at https://brainly.com/question/219464
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Bryant learned a total of 12 appetizer recipes over the course of 3 weeks of culinary school. After 12 weeks of culinary school, how many total appetizer recipes will Bryant know?
After 12 weeks, Bryant will know 48 appetizers
How to calculate the number of appetizers ?The first is to calculate the number of appetizers learnt in one week
12= 3
x= 1
cross multiply both sides
3x= 12
x= 12/3
x= 4
The number of appetizers learnt in 12 weeks can be calculated as follows
4= 1
y= 12
cross multiply both sides
y= 12 × 4
= 48
Hence 48 appetizers was discovered in 12 weeks
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5 -4y+y-3 how to you answer it?
Answer: -2[tex]Y^2[/tex]
Step-by-step explanation:
The sun three times a number x and 10 is -14
Answer: 3x+10=-14
I'm assuming you mean the sum three times a number x is -14
Step-by-step explanation:
3 times is 3 multiplied with a number, 3x
sum means the value you get from addition so it would be 3x+10 as its a number and ten
as the sum is -14 you set 3x+10 equal to -14
3(3x - 6) = 18 solve for x simplify your answer as much as possible
find the circumference of circle with radius X CM
Answer:
To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π=3.14).
Step-by-step explanation:
brainiest please
How many solutions exist for the following system if m1 ≠ m2?
y = m1x + b
y = m2x + b
answers:
an infinite number, none, one, the number of solutions cannot be determined.
Because the lines have different slopes, we conclude that there is only one intercept, and thus, the system of linear equations has only one solution.
How many solutions does the system of equations has?Remember that a system of equations has as many solutions as intercepts are when we graph both equations in the same coordinate axis.
Now, in this case, we have a system of linear equations:
y = m1*x + b
y = m2*x + b
Remember that linear equations are parallel only if the two lines have the same slope, in this case, we know that m1 ≠ m2, so the slopes are different.
Then the lines are not parallel, which means that intersect only one time, so we conclude that the system of equations has one solution.
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On Friday, Ariel received a $450 paycheck. On
Saturday, she spent $30 on gasoline and $15 on lunch.
What percent of her paycheck did Ariel spend on
Saturday?
Answer:
10%
Step-by-step explanation:
30+15=45
45 is 10% of 450 as 450/10= 45