Answer:
Step-by-step explanation:
A quadratic function has an "a" value of (2) and a vertex at (5,-18) How many solution does the function have, and what are they?
The function bas solution (s), which is x=__ and x=___ (Write NA tar the second box at there is only one solution)
The function has 2 solutions which is x = 2 and x = 8.
What is a quadratic function?
A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two.
Solution:
Given :
a = 2 , vertex = (5, -18)
f(x) = a(x-h)² + K
f(x) = 2(x - 5)² - 18
f(x) = 2(x² -10x + 25) -18
f(x) = 2x² - 20x +50 - 18
f(x) = x² - 10x +16
∴ x² -10x + 16 = 0
x² - 8x - 2x + 16 = 0
x(x-8) -2(x-8) = 0
(x-2) = 0 and (x-8) = 0
∴ x = 2 and x = 8
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The quadratic function has 2 solutions which is x = 2 and x = 8.
What is a quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. A polynomial of degree two in one or more variables in mathematics is known as a quadratic polynomial. Any polynomial function that is defined by a quadratic polynomial is said to be quadratic.
The terms "quadratic polynomial" and "quadratic function" were almost interchangeable before the 20th century because it was difficult to tell a polynomial from its corresponding polynomial function. This is still true in many elementary courses where "quadratic" is frequently used to refer to both terms.
Solution:
Given :
a = 2 , vertex = (5, -18)
f(x) = a(x-h)² + K
f(x) = 2(x - 5)² - 18
f(x) = 2(x² -10x + 25) -18
f(x) = 2x² - 20x +50 - 18
f(x) = x² - 10x +16
∴ x² -10x + 16 = 0
x² - 8x - 2x + 16 = 0
x(x-8) -2(x-8) = 0
(x-2) = 0 and (x-8) = 0
∴ x = 2 and x = 8
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There are 32 teams in the first round of a basketball tournament. One half of the teams that play in each round of the tournament move on to play in the next round.
a. Explain why the expression 32 x 1/2^3 represents the number of teams that play in the fourth round?
b. How many teams play in the fourth round? Show your work.
Answer:
So there are 32/4= 8 such groups. In each group, every team plays once against every other team
Step-by-step explanation:
1. Calculate the expected value of the number of cups of coffee Alex drinks each day. 00.200 cups 00.163 cups 00.976 cups 01.881 cups
The expected value of the number of cups of coffee Alex drinks each day is 00.805 cups.
the mean/ average is gotten by dividing the sum of the values in the set by their number.
The concept of mean/average is used in this ques to calculate the expected value of the number of cups of coffee Alex drinks each day.
Mean/ Average= sum of values
number of values
Substituting the values into the equation we have:Mean/ Average= 00.200 cups +00.163 cups+ 00.976 cups+ 01.881 cups
4
Mean/ Average= 00.805 cups
Hence, The expected value of the number of cups of coffee Alex drinks each day is 00.805 cups.
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a 5.2 kg cat and a 2.3 kg bowl of tuna fish are at opposite ends of the 4.0-mm-long seesaw. (figure 1) you may want to review (page) .
Moment about the pivot must be equal for the seesaw to balance. Initially, the first cat and the bowl are at 2 m from the pivot.
The moment due to cat = 5.3*2 = 10.6 kg.m
The moment due to bowl = 2.5*2 = 5 kg.m
The unbalanced moment = 10.6 - 5 = 5.6 kg.m
Therefore, the 3.7 kg cat should stand at a distance x from the pivot in left to balance the 5.6 kg.m.
That is,
3.7*x = 5.6 => x = 5.6/3.7 = 1.5134 m to the left (on the side of the bowl)
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what's the answer? The double number line shows that Henrik has a mass of 60kg
The required solutions of percentages are below as :
100% of 60 kg = 60 kg, 20% of 60 kg = 12 kg, and 40% of 60 kg = 24 kg.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The double number line shows that Henrik has a mass of 60kg.
According to the given question, the required solution would be as:
100% of 60 kg
⇒ (100/100) x 60
⇒ 1 x 60
⇒ 60
So, 100% of 60 kg = 60 kg
20% of 60 kg
20% is expressed as 20/100 in fractional form
⇒ (20/100) x 60
20/100 is expressed as 0.20 in decimal form
⇒ 0.20 x 60
Apply the multiplication operation, and we get
⇒ 12
So, 20% of 60 kg = 12 kg
40% of 60 kg
⇒ (40/100) x 60
⇒ 0.40 x 60
⇒ 24
So, 40% of 60 kg = 24 kg.
Thus, the required solutions are 100% of 60 kg = 60 kg, 20% of 60 kg = 12 kg, and 40% of 60 kg = 24 kg.
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3 Find the x-intercept of the equation x + 5y = 20. A 1 B 4 C 5 D 20
Answer:
line | Cartesian equation x + 5 y = 20 | x-intercept = 20 thus: D
Step-by-step explanation:
Find f(-2) for f(x) = 2 • 3^x
Function f(x) is 2/9.
Which is a function example?F(x) = sin x, F(x) = x2 + 3, F(x) = 1/x, F(x) = 2x + 3, etc. are a few further instances of functions. Mathematical functions come in many different varieties. Among the crucial kinds are: injection technique or One-to-one relationship: when there is a mapping between two sets for a range for each domain.If a function depends on another variable, you write it as f(x), g(x), or even h(t), depending on the dependant variable. You read f(x) and h(t) as "f of x" and "h of t," respectively. Not all functions must be linear. The nonlinear function g(x) = -x2 -3x + 5 is defined as follows.f(-2) for f(x) = 2 • 3^x is 2/9.
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A rectangular piece of metal is 5 in longer than it is wide. Squares with sides 1 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 456 in³, what were the original dimensions of the piece of metal?
The width of the piece of metal will be 21 inches while the length will be 26 inches.
What is a rectangle?
A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Main body:
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Let's say the width of metal w then the length will be w + 5
Now if we cut 1 inch square from the corner of the metal and then fold then the resultant cuboid will have;
Length = w+5 - 2 -= w + 3
Width = w - 2
Height = 1
So,
Volume = (w+3)(w-2)1
456 = w² - 2w + 3w - 6
w² + w - 462 = 0
By solving this
w = 21 so width will be 21 and length will be 21 + 5 = 26.
Hence "The width of the piece of metal will be 21 inches while the length will be 26 inches".
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A rectangular carton is 80*60*40 i) how many packet of soaps can each of 10*5*4 cm can be kept insidethe carton? ii) by how many centimeters should the height of the carton be increased to keep 1200 packets of soaps
Answer:
i) 960 , ii) 10 cm
Step-by-step explanation:
V of rectangular carton = 80 · 60 · 40 = 192 000
V of a packet of soap = 10 · 5 · 4 = 200
192 000 / 200
1920/2
960
ii)
960 : 1200 = 192 000 : x
x = 192 000 · 1200 / 960
x = 192 000 · 120 / 96
x = 240 000
80 · 60 · x = 240 000
4800 · x = 240 000
x = 240 000/4800
x = 2400/48
x = 200/4
x = 50
50 - 40 = 10
Answer:
i) 960 packets of soap
ii) 10 cm
Step-by-step explanation:
volume of cuboid = l*w*h
volume of carton = 80*60*40 = 192000 cm³
i)
volume of a packet of soap = 10*5*4 = 200 cm³
192000/200 = 960 packets of soaps
ii)
I am assuming the height is 40 cm
volume of carton/volume of a packet of soap = number of soap
x = volume of carton
x/200 = 1200
x = 1200*200 = 240000 cm³
80*60*h = 240000
4800h = 240000
h = 240000/4800 = 50 cm
50cm (desired height) - 40cm (current height) = 10cm
The population of Orange County is represented by the function f(x)=87,000(0.9), where x is the number of years since 2010 The population of Greene County was 78,000 in 2010, and has decreased exponentially at a rate of 8% each year
How do the populations of these counties compare in 2015?
Drag a value or word to the boxes to correctly complete the statements
Question 1
In 2015, [tex]x=5[/tex]. [tex]P(5)=87000(0.9)^5 \approx \boxed{51373}[/tex]
Question 2
[tex]78000(1-0.08)^5 \approx \boxed{51408}[/tex]
Question 3
[tex]51408 > 51373[/tex], so Greene county was more populous.
Which of the following algebraic steps will solve the equation -6t = 2/3
Answer:
t= 0.1 or t= 1/9Step-by-step explanation:
divide each term in 6t = 2/3 by 6,6t/6 = 2/3/6
simplify the left sidecancel out the common factor of 6.6t/6 = t while were left with 2/3 /6
divide t by 1.t = 2/3 / 6.
simplify the left sidemultiply the numerator by the reciprocal of the denominator.t = 2/3 x 1/6
cancel the common factor of 2.Factor 2 out of 6.t = 2/3 x 1/2(3)
Cancel the common factor which is 2,and then rewrite the expression.t = 1/3 x 1/3
Multiply the expression like this:t = 1 / 3 x 3
multiply 3 by 3 to get...t=1/9
decimal form: 0.1
a balance of $11,670. The bank statement indicated a balance of $13,640 on April 30. Comparing the bank statement and the accompanying canceled checks and memos with the records revealed the following reconciling items:
Checks outstanding totaled $4,910.
A deposit of $5,120, representing receipts of April 30, had been made too late to appear on the bank statement.
The bank collected $2,660 on a $2,520 note, including interest of $140.
A check for $770 returned with the statement had been incorrectly recorded by Lakeshore Gelato as $700. The check was for the payment of an obligation to Sprinkles Supply Co. for the purchase on account.
A check drawn for $40 had been erroneously charged by the bank as $400.
Bank service charges for April amounted to $50.
The balance of the bank reconciliation statement is $3,640
How to prepare a bank reconciliation statement?A bank reconciliation is is defined as the process by which the bank account balance in an entity’s books of account is reconciled to the balance reported by the financial institution in the most recent bank statement
The bank Reconciliation statement appears thus
Bank reconciliation statement
$ $
Cash book balance 11,670
Add unpresented cheque 5,120
Over cast (400-40) 360
17,150
Cheque not credited 5120
Less Uncredited cheque 4910
Notes collected 2660
Dishonored cheque 770
Bank charges 50
bank interest 140
13500
Balance as per bank statement 3640
In conclusion the balance of the Statement is $3640
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What is 10% of 20? Hint: We can think of 10% as a common fraction. HELP ME PLS
Answer:
Step-by-step explanation:
10% of 20 is equal to 2. To calculate 10% of a number, we can multiply the number by 10% expressed as a decimal, which is 0.1. For example, 10% of 20 is equal to 20 * 0.1 = 2.
Alternatively, we can calculate 10% of a number by dividing the number by 100 and then multiplying the result by 10. For example, 10% of 20 is equal to (20 / 100) * 10 = 2.
Describe and correct error
A
07
06
O15
09
B
15 m
2x+3
Given that
ABCD is a parallelogram, find the x.
Given that ABCD is a paralle log ram, find the value of x.
D
C
Answer:
x = 6
Step-by-step explanation:
the opposite sides of a parallelogram are congruent , then
2x + 3 = 15 ( subtract 3 from both sides )
2x = 12 ( divide both sides by 2 )
x = 6
Suppose that you wish to obtain a confidence interval for a population mean. Under the
conditions described below, should you use the z-interval procedure, the t-interval
procedure, or neither?
- The population standard deviation is unknown.
The data contain outliers.
- The sample size is small.
To obtain a confidence interval for a population mean under the t-interval procedure.
What is meant by population mean?The major trend discovered from the sample data is the sample mean. The population is used to create the sample data. In statistics, the sample mean is denoted by the letter "x." The population mean, on the other hand, is the average value of all observations within a certain population or group.The population mean can be determined by dividing the total number of values in the given data/population by the sum of all values in the data/population. The whole sum of the numbers is referred to as summation. The sign stands for the population mean.The population is the total number of people residing in a certain area. Estimating the population enables us to determine how many beings there are and how best to respond.To learn more about population mean refer to:
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I don’t know how to do it, please teach me !!!
As described in z-distribution the answers are given below:
a) The 95% confidence interval estimate for the population mean spending by a customer on visiting salon per month is given as follows: (747, 853).
b) The sampling error at 95% confidence level is of: $35.78.
What is a z-distribution ?
The normal distribution with a mean of 0 and a standard deviation of 1 is referred to as the standard normal distribution (also known as the Z distribution) (the green curves in the plots to the right). It is frequently referred to as the bell curve since the probability density graph resembles a bell.
solution:
The bounds of the confidence interval are given as follows:
In which:
is the sample mean.
z is the critical value.
n is the sample size. is the standard deviation for the population.
The parameters for this problem are given as follows:
Hence the lower bound of the interval is of:
800 - 200 x 1.96/square root of 55 = 747.
The upper bound of the interval is of:
800 + 200 x 1.96/square root of 55 = 853.
The sampling error for a sample size of 120 is calculated as follows:
200 x 1.96/square root of 120 = $35.78.
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i need help especially for #4
The values of x in the first, second, third and fourth triangles are 4 units, 70°, 76° and 80° respectively
How to determine the values of x in the triangle?
To solve this problem, we need some angle geometry knowledge:
For the first triangle:
x = 4 (All sides in a rhombus are identical)
For the second triangle:
The missing side is also equal to x (base of isosceles triangles)
x + x + 40 = 180 (sum of angles in triangle)
2x+40 = 180
2x = 180-40
2x = 140
x = 70°
For the third triangle:
x = 76° (base of isosceles triangles are equal)
For the fourth triangle:
Check the image attached for labeling
m = 180-110 = 70° (angle on a straight line)
y = 70° (base of isosceles triangles are equal)
z = 180-70-70 = 40°
t = 90-40 = 50°
L = 50° (base of isosceles triangles are equal)
Thus, x = 180-50-50 = 80°
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What is the distance between the points (6.2, -4) and
(4.5, -4)
Answer:1.7
Step-by-step explanation:
HELP ASAP!
Find the volume of a cone with a radius of 6.5 inches and a height of 12 inches.
A) 670.2 in ³
B) 530.9 in³
C) 414.7 in ³
D) 513.1 in³
PLEASE HELP ME!!! I WILL GIVE BRAINLIST!!! PLEASE
Answer:
A: AB corresponds to FG
Step-by-step explanation:
The question is asking for which statement if not true/false.
Answer choice A is false because when you turn the rectangle, AB does not end up where FG is. Instead, AB ends up where EF is. Also, the length of AB is 6 units, while the length of FG is 4 units. So, they cannot correspond to each other.
Identify each as a function or not a function.
What is the greatest common factor between 24, 56, and 72? 01 2 5 08
Answer: The common factor is 8
Step-by-step explanation:
Each is a variant of the number 8 and 2 but it called for the greater common factor so 8
Kyle buys last years best selling hardcover for $19.50 . This is with a 25% discount from the original price. What was the original price of the novel ,
Use variable x to set up an equation to solve the given problem. DONT TAKE STEPS TO SOLVE
Answer:
original price is 26 dollars
Step-by-step explanation:
19.50/0.75=26
what is the area of the convince store
Answer:
please add screenshots of the question and/or illustrations
If the value of a commodity decreases at a monthly rate of 0.8%, by what percentage does it decrease in a year?
If the value of a commodity decreases at a monthly rate of 0.8%, by 9.6 percentage it decreases in a year.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that, the value of a commodity decreases at a monthly rate of 0.8%,
We have to find by what percentage the rate decreases in a year.
If there are 12 months in a year, the rate decrease in a year obtained as,
=0.8 × 12
=9.6 %
Thus, if the value of a commodity decreases at a monthly rate of 0.8%, by 9.6 percentage it decreases in a year.
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In a year, the value of commodity decreases by 9.6%, at the monthly rate of 8%.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Monthly decrease rate of change in commodity = 0.8 %,
To find the percentage decrease in year,
Use ratio property,
In 1 month, commodity decreases 0.8%
In 12 months commodity decreases = 12 x 0.8 = 9.6 %
The value of commodity will decrease by 9.6% in a year.
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A time series-based forecast is a form of ____ or, assuming that patterns observed in historical data will prevail in the future.
Time series forecasts are developed based on time series analysis, which comprises methods for analyzing time series data to extract meaningful statistics and other characteristics of the data.
One of the most often used data science techniques in business, finance, supply chain management, production, and inventory planning is time series forecasting.
A time component is often present in prediction difficulties, necessitating the extrapolation of time series data or time series forecasting. Another crucial field of machine learning (ML) is time series forecasting, which may be viewed as a supervised learning issue.
It can be subjected to ML techniques including regression, neural networks, support vector machines, random forests, and XGBoost. Using models created from historical data to anticipate future observations is known as forecasting.
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Fully simplify.
16x^5y^4(14x^2y^2)
16x
5
y
4
(14x
2
y
2
)
The fully simplified form of the given expression 16x⁵y⁴ / ( 14x²y² ) following from the laws of indices is; 8x³ y² / 7.
What is the fully simplified form of the given expression 16x⁵y⁴ / ( 14x²y² )?It follows from the task content that the fully simplified form of the given expression 16x⁵y⁴ / ( 14x²y² ) is to be determined.
Since the given expression is; 16x⁵y⁴ / ( 14x²y² ).
As evident in the task content; same base terms are present in the numerator and denominator; we therefore have that;
The expression can be simplified as follows using the laws of indices as follows;
[tex] \frac{16 {x}^{5} {y}^{4} }{14 {x}^{2} {y}^{2} } [/tex]
It follows from the quotient of exponents law of indices; we have that;
[tex] \frac{8}{7} {x}^{5 - 2} {y}^{4 - 2} [/tex]
= 8x³ y² / 7
Therefore, the fully simplified form of the given expression using the laws of indices is; 8x³ y² / 7.
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please help me on math very easy graphing! thank you!! due soon
The graph that shows the proportional relationship between the number of liters of water (y) supplied after some time (x), is shown below.
What is a Proportional Relationship?A proportional relationship can be defined as a relationship between two variables, say x and y, in such a way that the equation, y = kx, models their relationship, where k is the constant of proportionality.
Given that the faucet supplies 12 liters of water after 3 minutes, where:
y = liters of water
x = number of minutes
Constant of proportionality, k = y/x = 12/3 = 4
The equation that describes the relationship would therefore be written by substituting the value of k = 4 into y = kx:
y = 4x
Thus, the graph that shows this proportional relationship is attached below.
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Travelling at 24 km/h on a snowmobile makes an air temperature of 4°C feel like -6°C because of the wind chill. What is the difference in these temperatures?
The difference in temperature is currently six degrees Celsius. Therefore, the appropriate reaction is six degrees Celsius.
What is the difference in temperatures?When two independent temperature readings are subtracted, or when calculating the amount of temperature rise or fall, the result is a temperature difference, also referred to as a delta temperature (T).
Simply subtract the smaller amount from the larger one to determine the difference in temperature, in this case 19 degrees Celsius from 25 degrees Celsius. We now have a six-degree Celsius temperature difference as a result. Therefore, six degrees Celsius, is the appropriate response.
Due to the varied amounts of radiation the Earth receives from the Sun at various periods of the year, there are variations in climate all over the world. The equator receives more heat from the Sun than the north and south poles, where the angle of the Sun's beams is lower.
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