According to the triangle inequality, the length of a triangle's third side must be greater than the sum of any two other triangle lengths, so the length of the steel piece will likely be 4 or 5 inches.
What is triangle inequality?Triangle inequality is a theorem in Euclidean geometry that states any two triangle sides added together must be greater than or equal to the third side; it is represented by the symbols a + b≥ c. The basic tenet of the theorem is that a straight line connects any two points.
Here,
If they are an integer number of inches long and less than six, the following lengths are possible: 4 ,5
According to the triangle inequality, any two other triangle lengths must be greater than the third side of a triangle's length:4+4 = 8 > 6
4+6 = 10 > 4
5+5 = 10 > 6
6+5 = 11 > 5
According to "The Triangle Inequality," which states that the length of a triangle's third side must be greater than the sum of any two other triangle lengths, the piece of steel's potential length will be 4 or 5 inches.
To know more about triangle inequality,
https://brainly.com/question/28823603?referrer=searchResults
#SPJ13
rite the equation for the logarithmic function that has the following
ansformations from the parent logarithmic function. The function will
ave a base of 10. You will not have to write the 10. It is assumed.
- Shifted 3 units left
Vertical compression by a factor of 2
Reflected across the y-axis
Shifted down 5 units
The given function shifted 3 units left is log(x+3), vertical compression by factor 2 is 2log(x+3), Reflection across the y-axis is 2log (-x+3) and shifted down by 5 units is 2log(-x+3)-5.
Given the parent function with base 10.
We want to find the given transformations.
The given parent function is y=log(x)
Firstly, we want to shift the given parent function 3 units left means we will add 3 in the parent function, we get
y=log(x+3)
Now, we want to do vertical compression by a factor of 2 means we will multiply the above function with 2, we get
y=2log(x+3)
Further, we want to reflected the above function across the y-axis means we will multiply the x with minus, we get
y=2log(-x+3)
Furthermore, we want to shift the above function down with 5 units means we will subtract 5 from the above function, we get
y=2log(-x+3)-5
Hence, the given parent function y=log(x) when shifted 3 units left is log(x+3), vertical compression by factor 2 is 2log(x+3), Reflection across the y-axis is 2log (-x+3) and shifted down by 5 units is 2log(-x+3)-5.
Learn more about the logarithmic function transformation from here brainly.com/question/20330517
#SPJ9
Dina pours 16-ounce containers of juice into a dispenser with a capacity of 960 ounces. The function y = 16x models this situation. What is the range of the function?
The range of the function is [0, 960]
How to determine the range of the function?From the question, we have the equation of the function to be
f(x) = 16x
Where
The size of the container is 16 ouncesThe capacity of the dispenser is 960 ouncesWhen the dispenser is empty, it means that f(x) = 0
When the dispenser is full, it means that f(x) = 960
When these values are combined, they represent the range
In other words, the range is 0 to 960
This can be rewritten as [0, 960]
Read more about range at
https://brainly.com/question/2264373
#SPJ1
Answer:
big black men
Step-by-step explanation:
(i have your search history)
the age of children in kindergarten on the first day of school is uniformly distributed between 4.74 and 5.85 years old. a first time kindergarten child is selected at random. round answers to 4 decimal places if possible. the mean of this distribution is the standard deviation is the probability that the the child will be older than 5 years old? the probability that the child will be between 4.84 and 5.34 years old is if such a child is at the 9th percentile, how old is that child? years old.
a) The mean distribution is 5.295.
b) The standard deviation is 0.1026
c) The probability that the child will be older than 5 years old is 0.7657
d) The probability that the child's age is between 4.84 and 5.34 is 0.4504
e) At the 9th percentile, the age of the child is 5.739 years old.
Given interval distribution is
4.74 - 5.85.
a) Firstly, we will find the mean distribution,
Mean distribution = Sum of intervals / Number of intervals
= 4.74+5.85 / 2
= 5.295.
Hence, the mean distribution is 5.295.
b) Now, we will find the standard deviation,
We use the formula:
SD = [tex]\sqrt{\frac{(b-a)^{2} }{12} }[/tex]
b = 5.85
a = 4.74
SD = [tex]\sqrt{\frac{(5.85-4.74)^{2} }{12} }[/tex]
SD = [tex]\sqrt{\frac{(1.11)^{2} }{12} }[/tex]
SD = 0.1026
Hence, the standard deviation is 0.1026
c) The probability that the child will be older than 5 years will be
p(older than 5) = 5.85 - 5 / 5.85 - 4.74
= 0.85 / 1.11
= 0.7657
Hence, the probability that the child will be older than 5 years old is 0.7657
d) The probability that the child will be between 4.84 and 5.34 years old will be
p(between 4.84 and 5.34) = 5.34 - 4.84 / 5.85 - 4.74
= 0.5 / 1.11
= 0.4504
Hence, the probability that the child's age is between 4.84 and 5.34 is 0.4504
e) If the child is at the 9th percentile, the age will be
At the 9th percentile = 4.74 + 9/100 ×(5.85 - 4.74)
= 4.74 +(0.9)(1.11)
= 4.74 + 0.999
= 5.739
Hence, at the 9th percentile, the age of the child is 5.739 years old.
To Learn more about Similar Probability Questions:
https://brainly.com/question/15582698
#SPJ4
the graph of y=f(x) is shown below. find the value of f(5)
Answer:
f(5) = -5
Step-by-step explanation:
To find the value of f(5), find the value of y when x = 5.
To find the value of y from a given value of x, find the position of x on the x-axis, then trace vertically until you meet the line.
Once you meet the line, trace horizontally to the y-axis to find the corresponding value of y.
Therefore, the value of f(5) is -5.
See attachment.
Answer:
f(5) = - 5
Step-by-step explanation:
Given the graph of the function f(x).
In order to find the value of f for any value of x on the graph, find the point x on the x-axis, then add a vertical line from this point to the graph. The y-coordinate of the intersection is the value of the function at given x-coordinate.
We are asked to find the value of f(5).
This is f(5) = - 5 as per above explanation.
See the attached for better understanding.
If 1400 dollars is invested in an account for 10 years. find the value of the investment at the end of 10 years if the interest is: (a) 4.6% compounded annually: $ 2195.05 correct (b) 4.6% compounded semiannually: $ (a) 4.6% compounded quarterly: $ 2211.88 correct (b) 4.6% compounded monthly: $ 2215.75 correct (a) 4.6% compounded daily (ignore leap years): $ 2217.63 correct
The compound interest calculated for 10 years annually, semi-annually, quarterly, monthly, and daily are (a) $2195.05, (b) $2206.18 (c) $2211.88 (d) $2215.75, and, (e) $2217.63
The formula for Compound Interest is
Amount = Principal X (1 + r/n100)ⁿˣ
where,
Principal = original mount
n = no. of times the interest is applied
t = time period
Here,
Principal = $1400
x = 10
r = 4.6
a)
Since it is compounded annually, the interest will be given 10 times in 10 years. therefore, once a year
Hence,
n = 1
Amount = 1400 X (1 + 4.6/100)¹⁰
= 1400 X (104.6/100)¹⁰
= 1400 X (1.046)¹⁰
= $2195.05
b)
Since the interest is compounded semi-annually here, it will be calculated twice a year.
Hence, n = 2
Therefore we get
Amount = 1400 X (1 + 4.6/200)²⁰
= 1400 X (204.6/200)²⁰
= 1400 X (1.023)²⁰
= $2206.18
c)
Since it is compounded 4 times a year now,
n = 4
Hence we get
Amount = 1400 X (1 + 4.6/400)⁴⁰
= 1400 X (1.0115)⁴⁰
= $2211.88
d)
Here, the interest is calculated 12 times a year
Hence we get
Amount = 1400 X (1 + 4.6/1200)¹²⁰
= 1400 X (10038)¹²⁰
= $2215.75
e)
Here we are told to ignore leap years, hence we are only going to consider a year to have 365 days.
Hence,
n = 365
Therefore, we get
Amount = 1400 X (1 + 4.6/36500)³⁶⁵⁰
= 1400 X (1 + 4.6/36500)³⁶⁵⁰
= 1400 X (1.00012)³⁶⁵⁰
= $2217.63
Correct Question
If 1400 dollars is invested in an account for 10 years. find the value of the investment at the end of 10 years if the interest is:
(a) 4.6% compounded annually
(b) 4.6% compounded semiannually
(c) 4.6% compounded quarterly
(d) 4.6% compounded monthly
(e) 4.6% compounded daily (ignore leap years)
To know more about Compound Interest visit
https://brainly.com/question/29311315
#SPJ4
Suppose that A and B are points on the number line.
If AB=5 and B lies at 12, where could A be located?
If there is more than one location, separate them with commas.
:0
Location(s) of A :
0.0....
X
Answer:
locations of A are 7, 17
Step-by-step explanation:
since B is positioned at 12 and AB = 5 , then
A = 12 - 5 or 12 + 5 = 7 , 17
The image of ΔABC after a reflection across Line E G is ΔA'B'C'.
2 triangles are shown. Line E G is the line of reflection. Line segment D D prime has a midpoint at point F. Line segment C C prime has a midpoint at point G. Points B and B prime share a point. Angle C G F is a right angle.
Which triangle must be a right triangle and why?
ΔBGC is right because Line EG is perpendicular-to CC'.
What is Reflection?A reflection image or reflection point is the mirror image of a figure in the axis or plane of reflection.
Each point of the original figure (the pre-image) has an image that is the same distance from the reflection line as the original point, but is on the other side of the line. This transformation is known as a reflection over line. The size and form of the image in a reflection are identical to those of the pre-image.
Given:
On the line of reflection will be the midpoints of the segments connecting a triangle vertex with its reflected image. The segment will be parallel to the reflection's line.
A triangle will be considered correct in this situation if it has a leg that is a part of the segment connecting the reflected points and a leg that is on the line of reflection. Such a triangle is the BGC.
Hence, BGC is right triangle.
Learn more about reflection here:
https://brainly.com/question/15487308
#SPJ1
Answer: D
Step-by-step explanation: Trust
flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet. what is the probability that a carpet that is 7 feet by 12 feet contains no flaws?
The probability that a carpet that is 7 ft × 12 ft contains no flaws is 0.732
What is the Poisson Distribution Formula?The Normal, Binomial, and Poisson Distributions are the three types of continuous and discrete data-based distributions used in probability and statistics. The distribution of unusual occurrences is another name for the Poisson distribution. This is mostly used to forecast the likelihood of future events based on how frequently the past events occurred. It offers the chance that a specific number of events might happen during a particular time frame.
The formula for Poisson distribution is given below:
P(x) = (e^-x * m^x) / x!
Here we have,
flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet
Given the dimensions of carpet = 7 feet × 12 feet
=> area of the carpet = 84 feet²
=> the expected mean of defects m = [1/270]*84 = 0.311
Now use the Poisson formula
P[x] = e^-m × m^x / x!
=> P(x = 0) = e^-(0.31) × 0.31^(0) / 0!
= (0.732 × 1)/1 = 0.732
Therefore,
The probability that a carpet that is 7 ft × 12 ft contains no flaws is 0.732
Learn more about Poisson Distribution at
https://brainly.com/question/28437560
#SPJ4
one year, the scores on the test were approximately normally distributed with a mean of 420 and a standard deviation of 70. the 81st percentile for this test was . . .
81 percentile of the given test is 482
The square root of the means of the squared deviations from the arithmetic mean is known as the standard deviation. Standard deviation is used in finance to quantify the risks associated with an investment instrument.
Given that the Marble Academy of Whoville conducts an annual test for all high school juniors one year, the scores on the test were approximately normally distributed with a mean of 420 and a standard deviation of 70
Here mean μ = 420 and Standard deviation σ = 70
We have find 81 percentile of this test = ?
The z score corresponding to the area 0.81 is
Z = 0.88 By standard normal table
X = μ + z σ
X = 420 + 0.88 x 70
= 420 + 62
= 482
Therefore 81 percentile of this test is 482
To learn more about standard deviation visit
https://brainly.com/question/16555520
#SPJ4
How many complete centerpieces can she make? Find the exact answer.
The number of centerpieces that she can make, using proportions, is of:
25.
What is a proportion?A proportion is a fraction of an amount, and this fraction is combined with the unit rates in the context of a problem, and basic arithmetic operations, especially multiplication or division, to find the desired amounts in the same context of this problem.
In the context of this problem, the number of centerpieces is given by the division of the the total number of flowers by the number of flowers in each centerpiece.
The amounts are given as follows:
Flowers: 430.Flowers per centerpiece: 17.Hence the division giving the number of flowers per centerpiece is:
n = 430/17 = 25.2.
The amount is rounded down to 25, as for 26 centerpieces, more flowers would be needed.
Missing InformationHailey is making floral centerpieces for a wedding. Each centerpiece has 17 flowers. She has 430 flowers for the project.
How many complete centerpieces can she make? Find the exact answer.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
the idea that a large number of sample means or proportions will approximate a normal distribution, regardless of the distribution of the population from which they were drawn, is known as: random error simple random sample sample variance population variance central limit theorem
The Central Limit Theorem gives the idea that a large number of sample means or proportions will approximate a normal distribution, regardless of the distribution of the population from which they were drawn .
Central Limit Theorem : In probability theory , the Central Limit Theorem establishes that , in many situations , when independent random variables are summed up , their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed .
The Central Limit Theorem gives the idea that a large number of sample means or proportions will approximate a normal distribution, regardless of the distribution of the population from which they were drawn .
To learn more on central limit theorem follow link:
https://brainly.com/question/14781796
#SPJ4
A bag of chocolate mix that weighed 1/4 of a kilogram could make enough brownies to feed 1/7 of the students at school. How many bags would be needed to feed all of the students?
Answer:
1/28 kilo
Step-by-step explanation:
sb help me on my recent please
"I have drawn a polygon who's sum of interior angles is 800"
explain why this is impossie
We know that the sum of all the interior angles of the polygon with sides n is (n - 2)*180.
It is given in the question that,
Sum of all the interior angles of the polygon is 800.
Hence, according to the data given in the question, we can write,
(n - 2)*180 = 800
n - 2 = 800/180
n - 2 = 40/9
n = 40/9 + 2
n = 58/9 = 6.44
As number of sides should always be in integer form, it is not possible to have the sum of all the interior angles of the polygon to be 800 degrees.
To learn more about polygon, here:-
https://brainly.com/question/24464711
#SPJ1
a person has a 5% chance of winning a free ticket in a state lottery. she plays the game 12 times. what is the probability she will win two or more tickets? round your answers to three decimal places.
The probability to win two or more tickets in the lottery is 0.118
It is given that there is a 5% chance to win a lottery ticket.
Therefore, the probability to win a lottery ticket is
0.05
The girl here plays the game 12 times. The above distribution is clearly a Binomial Distribution
ⁿCₓ X pˣ X (1 - p)ⁿ⁻ˣ
We need to calculate the probability to win 2 or more tickets
= 1 - the probability to win at least one ticket
= 1 - P(X = 0) + P(X = 1)
here,
p = 0.05
1 - p = 0.95
n = 12
P(X = 0)
= ¹²C₀ X 0.05⁰ X 0.95¹²
= 0.54036
P(X = 1)
= ¹²C₁ X 0.05¹ X 0.95¹¹
= 0.34128
Hence we get
P(X ≥ 2) = 1 - 0.54036 - 0.34128
= 0.118
Therefore, we get the probability that the person will win 2 or more tickets to be 0.118
To learn more about Probability visit
https://brainly.com/question/14210034
#SPJ4
work out the circumferecnce of this cricle take π to be 3.142 and write down all the digits given by your calculator 16.8cm
The circumference of the circle with a radius of 16.8 cm is 105.504 cm
How to calculate the circumference?The given parameters are
Radius = 16.8 cm
As a general rule, radius are represented by the variable r
So, we have the following representation equation
r = 16.8 cm
The circumference of the circle is then calculated as
C = 2πr
Next, we substitute the value of the variable r in the above equation
i.e. r = 16.8 cm
So, we have the following equation
C = 2π * 16.8 cm
From the question, we have
π = 3.14
So, we have the following equation
C = 2 * 3.14 *16.8 cm
Evaluate the products
So, we have the following equation
C = 6.28 *16.8 cm
Evaluate the products
C = 105.504 cm
Hence, the circumference is 105.504 cm
Read more about circumference at
brainly.com/question/12823137
#SPJ1
Lucia makes braided key chains out of cotton cord. For every 8 feet of cotton cord she has, she can make 3 braided key chains. Use a model to represent the relationship between the feet of cotton cord and the number of key chains.
(NEED HELP ASAP PLEASE)
A model for representing the relationship between the number of key chains and the number of feet of cotton cord is: 8x - 3y = 0.
Define the term linear equation?Linear equations are first-order equations. Lines with in coordinate system are determined by linear equations. When the equation contains a degree 1 homogeneous variableSince Lucia creates braided key chains from out cotton cord and can create 3 braided key chains per each 8 feet of cotton cord she does have, the following equations must be performed via cross multiplication to symbolize the relationship between both the feet of cotton cord as well as the number of key chains but also obtain the number of cotton cord Lucia requires to achieve 5 key chains:
8 cotton cords = 3 key chains
Let the total length in feet of cotton cords be x.
And the total number of key chain made be y.
Then, the linear equation formed as;
8x = 3 y
8x - 3y = 0
Thus, a model for representing the relationship between the number of key chains and the number of feet of cotton cord is: 8x - 3y = 0.
To know more about the linear equation, here
https://brainly.com/question/2030026
#SPJ4
monique and tara each make an ice-cream sundae. monique gets 3 scoops of cherry ice-cream and 1 scoop of mint chocolate chunk ice-cream for a total of 84g of fat. tara has 1 scoop of cherry and 3 scoops of mint chocolate chunk for a total of 60g of fat. how many grams of fat does 1 scoop of each type of ice cream have?
The amount of fat in Cherry ice-cream is 24 grams.
The amount of fat in the Mint Chocolate Chunk ice-cream is 12 grams.
Writing data into equations using Algebra,3C + M = 84...(1)C + 3M = 60...(2)
Multiplying equation (2) by 3 and then subtracting equation (1) from
the result gives, 3 * (C +3M) = 3 × 603C + 9M = 180...(3)(3C + 9M = 180) - (3C + M = 84) = 8M =96M= 12
The amount of fat in the Mint Chocolate Chunk ice-cream, M = 12
grams C + 12*3 = 60C = 60-36 = 24
The amount of fat in Cherry ice-cream C = 24 grams As a result, Cherry ice cream contains 24 grams of fat and Mint Chocolate Chunk ice cream contains 12 grams of fat.
Learn more about Algebra:
brainly.com/question/24875240
#SPJ4
if 1,000 points are selected randomly inside the square with all points equally likely to be selected, how many of those points are expected to lie inside the circle?
The number of points that are expected to lie inside the circle is 785.
A circle is a closed two-dimensional figure. In a circle, all points are equidistant from the centre.
As per the given question, the circle is inscribed in a square,
The radius of the circle ( r ) = 1 The side length of the square ( s ) = 2⇒ The area of the circle = π × r × r
= π × 1 × 1
∴ The area of the circle = π
⇒ The area of the square = s × s
= 2 × 2
∴The area of the square = 4
The probability that a randomly selected point inside the square will lie inside the circle,
p = π / 4
The probability that a randomly selected point inside the square will lie outside the circle,
q = 1 - p
q = 1 - ( π / 4 )
⇒ Binomial trial with n = 1000 and p = π / 4,
Number of points expected to lie inside the circle(N) = n × p
= 1000 × ( π / 4 )
= 1000 × ( 3.14 / 4 )
= 1000 × ( 0.785 )
N = 785
Therefore, 785 expected points lie inside the circle.
To know more about circles refer to:
https://brainly.com/question/24810873
#SPJ4
The complete question is
Answer: 56 square
Step-by-step explanation:
Amy’s restaurant has budgeted at most $60 to spend this month on gourmet coffee. All international blends cost
$8.50 per package and all house blends cost $6.00 per package. She would like to purchase some international
blends and at least 3 packages of the house blends. Write a system of linear inequalities that describes this
situation. Graph the system. Give a possible solution and describe what it means
Answer:
8.50x + 6.00y < 60 and y > 3.
Please consider the complete question.
Amy's restaurant has a budget of at most $60 to spend this month on gourmet coffee. All international blends cost $8.50 per package and all house blends cost $6.00 per package. She would like to purchase some global combinations and at least 3 boxes of the house blends. Write a system of linear inequalities that describes this situation.
Let x represent the number of international blends and y represent the number of house blends.
The cost of x international blends would be and the cost of y house blends would be.
Since Amy's restaurant has a budget of at most $60 to spend this month on gourmet coffee, so the cost of x international blends and y house blends should be less than or equal to 60.
We can represent this information in an inequality as:
Since Amelia wants to purchase at least 3 packages of the house blends, so y should be greater than or equal to 3. We can represent this information in an inequality as:
Therefore, our required system of inequalities would be 8.50x + 6.00y < 60 and y > 3.
Step-by-step explanation:
Find the value of x.
Answer: 25 degrees
Step-by-step explanation:
Assuming that both triangles are to be connected and that they form a rectangle,
angle x can be found by subtracting 65 degrees from 90 degrees.
(all corners of rectangle=90 degrees)
90-65=25
Four congruent parallelograms are joined to make the shape below.
24 cm
The total shaded area is 192 cm²
Work out the value of x.
x cm
5 cm
For the given four congruent parallelograms and the shaded area of 192cm² then value of x is equal to 8cm.
As given in the question,
Given four congruent parallelograms
Shaded area of the parallelogram is 192cm²
As four parallelograms are congruent
Let the area of each parallelogram is A
4A = 192
⇒A = 48cm²
For two parallelogram base length = 24cm
Base length of each parallelogram = 12cm
Area of parallelogram = base × height
48 = 12 × height
⇒ height = 4cm
Value of x = 2 times of height
= 2 (4)
= 8cm
Therefore, for the given four congruent parallelograms and the shaded area of 192cm² then value of x is equal to 8cm.
Learn more about area here
brainly.com/question/27683633
#SPJ1
how many ways are there to paint each of the integers 2, 3,..., 9 either red, green, or blue so that each number has a dierent color from each of its proper divisors?
432 ways are there to paint each of the integers 2, 3,..., 9 either red, green, or blue so that each number has a different color from each of its proper divisors.
What is counting principle?A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It claims that if there are n ways to do something and m ways to do something else after that, then there are n m n*m methods to do both of these acts.
Here,
(1) All prime number can take any of three colors, except one of 2 or 3 as both are connected via 6..
so 2, 5, 7 can have 3 ways each - 3*3*3 = 27 ways
(2) Let us take the multiples of 2..
4 can take any of the remaining 2 colors, while 8 would take the remaining colour. As like 4, 6 can also take any of 2 colors other than the colour of integer 2.
Thus 2*2*1=4
3 is restricted because of 6, so it cannot have the same color as 6 and therefore 3 can have any of the remaining 2 colors.
We could also have taken 3 colors for 6, and then 2 and 3 would have 2 colors each and overall 2*2*3.. We are still getting the same
Only integer left is 9, so it will take any of the 2 colors other than that of 3, so 2 ways..
Total 2*2=4
Combined way of integers = 27∗4∗4=432 ways
There are 432 different methods to paint the numerals 2, 3,..., 9 red, green, or blue so that each number has a different hue from each of its suitable divisors.
To know more about counting principle,
https://brainly.com/question/28384306
#SPJ4
divide 50x4-50x3+12x2+10x-2 by 5x-3
Dividing 50x⁴ - 50x³ + 12x² + 10x - 2 by 5x - 3 with the long division method will result to a quotient of 10x³ - 4x² + 2 and a remainder of 1.
Long division methodThe method of long division involves the following steps:
Divide.Multiply.Subtract.Bring down the next number and Repeat the process to end at zero or arrive at a remainder.We sall divide the 50x⁴ - 50x³ + 12x² + 10x - 2 by 5x - 3 by applying the long division method as follows;
50x⁴ divided by 5x equals 10x³
5x - 3 multiplied by 10x³ equals 50x⁴ - 30x³
subtract 50x⁴ - 30x³ from 50x⁴ - 50x³ + 12x² + 10x - 2 will result to -20x³ + 12x² + 10x - 2.
This process is repeated until we have a remainder of 1.
Therefore, by the long division method, we have quotient of 10x³ - 4x² + 2 and a remainder of 1.
Learn more about long division method here: https://brainly.com/question/25289437
#SPJ1
Vertex of f(x) = |2x + 3
The vertex of the equation given as .f(x) = |2x + 3| is (-3, 0)
What is the vertex?The vertex of a function or an equation is the minimum or the maximum point on the function
How to determine the vertex of the graph?From the question, we have the equation of the function to be
f(x) = |2x + 3|
The above function is an absolute value function
An absolute value function is represented as
f(x) = a|x - h| + k
Where the vertex is represented as
Vertex = (h, k)
By definition, a graph that has a vertex would have an obvious maximum or minimum point on it
By comparing the equations f(x) = a|x - h| + k and f(x) = |2x + 3| to determine the vertex, we have
(h, k) = (-3, 0)
This means that
Vertex = (-3, 0)
Hence, the vertex of the equation is (-3, 0)
Read more about vertex at
https://brainly.com/question/15709421
#SPJ1
At a carnival game, it cost Noah $12 to toss 30 rings. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
The equivalent ratios table is:
Toss Dollars
5 2
30 12
45 18
See the diagram in the attachment that shows the plotted points.
What are Equivalent Ratios?Equivalent ratios are ratios that have the same value when they are compared together.
For example, 4/6 = 2/3, therefore, the equivalent ratios are 2:3 and 4:6.
Create an equation that models equivalent ratios that can be used to complete the table if:
x = toss
y = dollars
Therefore, given that 30 toss equals $12,
Constant of proportionality, k = y/x = 12/30
k = 2/5.
Plug in the value of k into y = kx:
y = 2/5x.
Therefore:
2 dollars (y = 2), will give:
2 = 2/5(x)
x = 10/2
x = 5 toss
45 tosses (x = 45) will need:
y = 2/5(45)
y = 18 dollars
The equivalent ratios table would be:
Toss | Dollars
5 2
30 12
45 18
The graph below shows the points, (5, 2), (30, 12), and (45, 18), where y = dollars, and x = toss.
Learn more about equivalent ratios on:
https://brainly.com/question/2914376
#SPJ1
What two numbers = -48 (multiply) and does the two numbers = -13
Answer:
The two numbers are [tex]3[/tex] and [tex]-16[/tex].
Step-by-step explanation:
Two numbers that, when multiplied, result in a product of [tex]-48[/tex]:
[tex]x \cdot y = -48[/tex]
Same two numbers when added get a sum of [tex]-13[/tex]:
[tex]x + y = -13[/tex]
Solve for x in the summation identity:
[tex]y = -13 - x[/tex]
Plug the value back into the product identity and solve for [tex]x[/tex]:
[tex]x \cdot (-13-x) = -48\\-13x - x^2 = - 48\\x^2 + 13x = 48\\x^2 + 13x - 48 = 0\\(x-3)(x+16) = 0[/tex]
The roots we found for [tex]x[/tex] were:
[tex]x = 3\\x = -16[/tex]
Our two numbers are [tex]3[/tex] and [tex]-16[/tex]. We can test this:
[tex]3 + (-16) = -13\\3 * -16 = -48[/tex]
each day for four days, linda traveled for one hour at a speed that resulted in her traveling one mile in an integer number of minutes. each day after the first, her speed decreased so that the number of minutes to travel one mile increased by 5 minutes over the preceding day. each of the four days, her distance traveled was also an integer number of miles. what was the total number of miles for the four trips
The total number of miles for the four trips is 25 miles.
Given that;
Linda traveled for one hour each day for four days at a speed that made her cover one mile in an even number of minutes. After the first day, she started to lose speed, and it took her 5 minutes longer to complete a mile than the day before. Her journey distance was also an integer amount of miles throughout the four days.
We know that,
Distance is a product of speed and time. We need to find the distance here with the use of the given conditions, time is 1 hour.
Speed = Distance / Time
Hence, speed is 1 mile per x minutes because we want to distance by multiplying the time and speed together yielding 60 min * 1 mile / x mins.
Minutes cancel out, so now we have 60/x as our distance for the first day.
The distance for the given case;
⇒ [tex]\frac{60}{x},\frac{60}{x+5},\frac{60}{x+10},\frac{60}{x+15}[/tex]
It is given that x = 5;
⇒ [tex]\frac{60}{5},\frac{60}{10},\frac{60}{15},\frac{60}{20}[/tex]
= 12 + 6 + 4 + 3
= 25
The total number of miles for the four trips is 25 miles.
To learn more about Distance click here:
brainly.com/question/15256256
#SPJ4
Solve the equation by completing the square. x2 + 6x = 9
carter has 24 posters in his room. if he arranges them into 6 equal rows, how many posters will be in each row?
If he arranges them into 6 equal rows, 4 posters will be in each row.
Define division.One of the fundamental arithmetic operations in mathematics is the division, which is the process of dividing a group of items into equal pieces. Every day, we might employ the division approach in various situations. Fraction division differs significantly from natural number division. We must change the division operator into a multiplication operator when dividing fractions. Therefore, the dividend should be multiplied by the inverted divisor.
Given,
Total posters = 24
Arranging them into 6 equal rows,
Dividing:
24÷ 6
Reciprocating,
24 × 1/6
4
If he arranges them into 6 equal rows, 4 posters will be in each row.
To learn more about division, visit:
https://brainly.com/question/21416852
#SPJ4
Please help me with this question
Answer: The ladder reaches 4.8 ft up the wall
Step-by-step explanation:
Sin 53°=0.80
Cos 53°=0.60
Tan 53°=1.33
Cos 58°/1 = X/8
0.60/1 = X/8
X=4.8