#1Change from standard form to vertex formy= x²-8x+15
Answers
Therefore, the vector form of the equation y = x² - 8x + 15 is y = (x - 4)² + 14. The vertex of the parabola is at the point (4, 14).
To convert the quadratic equation y = x² - 8x + 15 from standard form to vertex form, we need to complete the square by adding and subtracting a constant term. Here's the step-by-step explanation:
Factor the coefficient of x²: The coefficient of x² is 1, so we don't need to factor it.
Group the x terms: Rewrite the quadratic equation as y = (x² - 8x) + 15.
Complete the square: To complete the square, we need to add and subtract a constant term that will make the expression inside the parentheses a perfect square trinomial. The constant we need to add is half of the coefficient of x, squared: (8/2)² = 16.
y = (x² - 8x + 16 - 16) + 15 // add and subtract 16
y = (x - 4)² - 1 + 15 // factor and simplify
Simplify: Now we can simplify the expression by combining the constants -1 and 15 to get 14.
y = (x - 4)² + 14
To know more about vector,
https://brainly.com/question/30907119
#SPJ11
Related Questions
a negative number divided by a positive number have to equal 7
Answers
Answer:
That would not work
Step-by-step explanation:
because negative divided by positive is always negative only if it was negative divided by negative
Martin recorded the low temperatures at his house for one week. the temperatures are shown below -
-7, -3, 4, 1, -2, -8. 7
Approximately what was the average low temperature of the week?
Answers
Answer:
The average temp was 4
Step-by-step explanation:
prove that √-2 is irrational using strong induction
Answers
Using strong induction, we can prove that the square root of -2 is irrational by showing that it cannot be expressed as a fraction of coprime odd integers.
To prove that √-2 is irrational using strong induction, we need to show that for any natural number n, if the square root of -2 can be expressed as a fraction a/b, where a and b are coprime integers, then a and b must be odd.
We can start by using the base case, n = 1. Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers. Then, we have
√-2 = a/b
Squaring both sides gives
-2 = a^2/b^2
Multiplying both sides by b^2 gives
-2b^2 = a^2
This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means
-2b^2 = (2k)^2
Simplifying, we get
-2b^2 = 4k^2
Dividing both sides by -2 gives
b^2 = -2k^2
This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers.
Now, let's assume that for all n ≤ k, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. We want to prove that this also holds for n = k+1.
Assume that √-2 can be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Then, we have
√-2 = a/b
Squaring both sides gives
-2 = a^2/b^2
Multiplying both sides by b^2 gives
-2b^2 = a^2
This implies that a^2 is even, and therefore a is also even. We can express a as 2k for some integer k, which means
-2b^2 = (2k)^2
Simplifying, we get
-2b^2 = 4k^2
Dividing both sides by -2 gives
b^2 = -2k^2
This implies that b^2 is even, which means that b is also even. However, this contradicts our assumption that a and b are coprime integers with a and b odd. Therefore, √-2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd.
By strong induction, we have proven that for any natural number n, the square root of -2 cannot be expressed as a fraction a/b where a and b are coprime integers with a and b odd. Therefore, √-2 is irrational.
To know more about induction:
https://brainly.com/question/31099433
#SPJ4
When Mike graduated college, his dad bought him a new truck worth $22,000. One year later, the truck had dropped 15% in value. If the truck's value continued to drop by 15% each year, what is the trucks value after 3 years? Round your answer to the nearest dollar.
When Mike graduated college, his dad bought him a new truck worth $22,000. One year later, the truck had dropped 15% in value. If the truck's value continued to drop by 15% each year, what is the trucks value after 3 years? Round your answer to the nearest dollar.
need this asap
Answers
Answer:
If the truck's value dropped 15% each year, after one year the value of the truck is 22000*(1-0.15) = $18700
After the second year, the value of the truck would be 18700*(1-0.15) = $15995
After the third year, the value of the truck would be 15995*(1-0.15) = $13596.75
Rounding the answer to the nearest dollar, the value of the truck after 3 years is $13597
(05.02)The area of the parallelogram below is ___ square meters
Numerical Answers Expected!
Answer for Blank
Answers
Step-by-step explanation:
the area of a parallelogram is
baseline × height
which is in our case
9 × 7 = 63 m²
Answer:
ayo give the other guy brainilest
Step-by-step explanation:
(5) Set up a system of equations and solve:
38 people are playing pickle-ball in a park. 13 matches are in progress. How many double and
how many single matches are being played?
Answers
Step-by-step explanation:
Assume the number of double matches is x (matches)
the number of single matches is y (matches)
(Condition: x > 0 and y > 0)
Because there are 13 matches in progress, so:
x + y = 13 (1)
Because there are 38 people playing (4 people on each double match and 2 people on each single match), so:
4x + 2y = 38 (2)
A system of equation is made by combining (1) and (2):
x + y = 13 (1)
4x + 2y = 38 (2)
Take (2) - 2×(1):
=> 2x = 12
=> x = 6
Substitute the result on (1)
=> y = 7
So there are 6 double matches and 7 single matches being played
A particle moves along a horizontal line. Its position function is s(t) for t is greater than or equal to 0. For each problem, find the velocity function v(t) and the acceleration function a(t).
1. s(t) = -t^4 + 12t^3
2. s(t) = -t^4 + 8t^3
Answers
Answer:
1) Velocity
\(v(t) = -4\cdot t^{3}+36\cdot t^{2}\)
Acceleration
\(a(t) = -12\cdot t^{2}+72\cdot t\)
2) Velocity
\(v(t) = -4\cdot t^{3}+24\cdot t^{2}\)
Acceleration
\(a(t) = -12\cdot t^{2}+48\cdot t\)
Step-by-step explanation:
From Physics we remember that velocity (\(v(t)\)) and acceleration (\(a(t)\)) are the first and second derivatives of the function position in time. That is:
1) Let \(s(t) = -t^{4}+12\cdot t^{3}\), where \(t \ge 0\). The functions velocity and aceleration are, respectively:
Velocity
\(v(t) = -4\cdot t^{3}+36\cdot t^{2}\)
Acceleration
\(a(t) = -12\cdot t^{2}+72\cdot t\)
2) Let \(s(t) = -t^{4}+8\cdot t^{3}\), where \(t\ge 0\). The functions velocity and acceleration are, respectively:
Velocity
\(v(t) = -4\cdot t^{3}+24\cdot t^{2}\)
Acceleration
\(a(t) = -12\cdot t^{2}+48\cdot t\)
i need help with biconditnoal statement for the conditional statement
if a figure extends in only one direction, then it is a ray
Answers
Find the Surface area of the trapezoid
please help
show work
Answers
Answer:
259.5
Step-by-step explanation:
8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5
How do you solve this
Answers
Answer:
x = 8
Step-by-step explanation:
Use the Intersecting Chords Theorem...
why is the graph dashed line Rather than solid line?
Answers
Answer: Inqualities that use < and> with a line under them means solid line
Step-by-step explanation: whereas < and> by themselves is dashed
What is the percentage strength of neomycin in the final compounded product? (Answer must be numeric; no units or commas; include a leading zero when the answer is less than 1; round the final answer to the nearest ONE DECIMAL PLACE.)Rx:Neomycin (5%) cream 30gPolymyxin B 20gHydrocortisone 10gMix the ingredients to make a smooth creamSig: apply to affected area BID
Answers
The percentage strength of neomycin in the final compounded product is approximately 2.5%.
To determine the percentage strength of neomycin in the final compounded product, we need to calculate the weight of neomycin in the cream and divide it by the total weight of the cream.
Neomycin (5%) cream: 30g
The neomycin content is 5% of the total cream weight. To find the weight of neomycin in the cream, we multiply the cream weight by the neomycin percentage:
Weight of neomycin = 30g × 0.05 = 1.5g
Now, to calculate the percentage strength of neomycin in the final compounded product, we divide the weight of neomycin by the total weight of the cream and multiply by 100:
Percentage strength of neomycin = (Weight of neomycin / Total weight of cream) × 100
Percentage strength of neomycin = (1.5g / 60g) × 100 ≈ 2.5
Therefore, the percentage strength of neomycin in the final compounded product is approximately 2.5%.
For more such questions on percentage , Visit:
https://brainly.com/question/30744872
#SPJ11
When can a correlation coefficient based on an observational study be used to support a claim of cause and effect? Never When the correlation coefficient is close to -1 or +1. When the correlation coefficient is equal to -1 or +1. When the scatterplot of the data has little vertical variation.
Answers
Never. Correlation does not imply causation. A correlation coefficient based on an observational study can only be used to suggest a relationship between two variables, but it cannot be used to support a claim of cause and effect.
Correlation is a measure of the relationship between two variables. It is used to measure how two variables move together. A correlation coefficient based on an observational study can only be used to suggest a relationship between two variables, but it cannot be used to support a claim of cause and effect. This is because correlation does not imply causation. A correlation coefficient close to -1 or +1 is an indication of a strong linear relationship between the two variables, but this does not necessarily imply a cause-and-effect relationship. Additionally, even if the scatterplot of the data has little vertical variation, this does not guarantee a cause-and-effect relationship. In summary, correlation coefficients based on observational studies can never be used to support a claim of cause and effect.
Learn more about correlation here
https://brainly.com/question/28898177
#SPJ4
in triangle ABC, < A is the right angle, and m< B =45. find BC. if your answer is not the whole number, leave it in the simplest radical form
Answers
HELP URGENT!!! RESPOND QUICKLY!!!
Answers
Answer:
i think x = 7 y = 11
Step-by-step explanation:
have a nice dae
HELP I NEED HELP PLS FOR GODS SAKE
806 divided by 4
Answers
Answer:
201.5
Step-by-step explanation:
806/4=201.5
this is the answer
Answer:
201.5
Step-by-step explanation:
A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, C, after h hours of service. What will be the total cost for 8 hours of work? 10 hours of work? On a graph
Answers
The equation in slope intercept form is C(h) = 50h+25 ,the total cost for 8 hours of work is $425 , and for 10 hours of work is $525.
In the question;
it is given that
the fixed charge of plumber = $25
charge for per hour of service = $50
the hours of service be "h"
and the total cost be "C"
according to the question
C(h) = 50h+25
the equation in the slope intercept form is C(h) = 50h+25
to find the total cost for 8 hours of work , put h=8
C(8) = 50(8) + 25
= 400+25
= 425
to find the total cost for 10 hours of work , put h=10
C(10) = 50(10) + 25
= 500+25
= 525
Therefore , total cost for 8 hours of work is $425 , and for 10 hours of work is $525 .
The given question is incomplete , the complete question is
A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, C, after h hours of service. What will be the total cost for 8 hours of work? 10 hours of work?
Learn more about Equation here
https://brainly.com/question/11432755
#SPJ1
simplify 3a - 2(8 +4a)
Answers
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
Answer:
Let's simplify step-by-step.
3a − 2 ( 8 + 4a )
Distribute:
= 3a + ( −2 ) ( 8 ) + ( −2 ) ( 4a )
= 3a + −16 + −8a
Combine Like Terms:
= 3a + −16 + −8a
= ( 3a + −8a ) + ( −16 )
Answer:
= −5a − 16
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
Solve the following quadratic equation for all values of x in simplest form.
5x(x^2-4)+10=10
first person to answer right get branliest
people in com.ments who right get a tha.nks and fo.llow
Answers
Answer:
\(x=0,\:x=-2,\:x=2\)
Step-by-step explanation:
Do you want me to explain it?
The table shows a probability of drawing numbered tickets from a jar if 8 tickets are randomly drawn how many tickets would be expected to have a number that ends with a 6
Answers
Answer:
4
Step-by-step explanation:
If you do .50 x 8 from each ticket being drawn and the probability you get 4
I need the fraction but it can't be reduced
Answers
Answer:
3/4 or 75/100
Step-by-step explanation:
75/100 simplified is 3/4
Answer:
\(\frac{75}{100}\)
If each shelf can hold at most 20 books, what is the least number of shelves needed to store the 175 books?
Answers
Answer- 9 shelves
In order to find out how many shelves are need we must divided 175 into 20. 175 divided by 20 is 8.75. But, because you cannot have have .75 of a shelf, you have to round this to a whole. This means that 9 shelves will be the least needed number of shelves need to store 175 books. To check this answer 20 books X 8 shelves is 160 books, which means eight shelves can only store 160 books, we will need and additional shelf to store the last 15 books.
HOPE THIS HELPS & GOOD LUCK!
An investigator indicates that the power of his test (at a significance of 1%) of a sample mean resulting from his research is 0.87. If n increases, then the power of the test... doubles. increases. decreases. stays the same.
Answers
As the sample size (n) increases, the power of the statistical test also increases.
The power of a statistical test measures the ability of the test to detect a true effect or reject a false null hypothesis. In this case, the investigator states that the power of his test at a significance level of 1% is 0.87. If the sample size (n) increases, the power of the test increases.
Increasing the sample size generally leads to an increase in the power of a statistical test. This is because a larger sample size provides more information and reduces the variability in the data. With a larger sample size, the test has a greater chance of detecting a true effect and rejecting the null hypothesis when it is false. Consequently, the power of the test increases.
In summary, as the sample size (n) increases, the power of the statistical test also increases. This is because a larger sample size enhances the test's ability to detect true effects and reject false null hypotheses, resulting in higher statistical power. Therefore, in this scenario, increasing the sample size would lead to an increase in the power of the test.
Learn more about statistical test here:
https://brainly.com/question/31746962
#SPJ11
A strand of bacteria has a doubling time of 20 minutes. If the original population started with 10 organisms, how long will it take for the population to reach one million ( 1000000 )?
Answers
It will take 352 minutes for the population to reach one million (1000000) organisms.
How long will it take for the population of bacteria to reach one million (1000000)?To find the time it takes for the population to reach one million, we can use the formula for exponential growth: \(N = N_0 * 2^{t/d}\)
\(1000000 = 10 * 2^{t/20}\\100000 = 2^{t/20}\)
Taking the logarithm:
\(log_2(100000) = t/20\\17.6096 = t/20\\t = 352.192\\t = 352 minutes.\)
Read more about exponential
brainly.com/question/2456547
#SPJ4
It will take approximately 332.19 minutes for the population to reach one million organisms.
The doubling time of 20 minutes means that every 20 minutes, the population doubles in size.
To calculate the time it takes for the population to reach one million organisms, we can use the formula:
N = N0 * (2^(t/d))
Where:
N = Final population size (1,000,000)
N0 = Initial population size (10)
t = Time in minutes (unknown)
d = Doubling time (20 minutes)
Plugging in the values, we have:
1,000,000 = 10 * (2^(t/20))
Dividing both sides by 10, we get:
100,000 = 2^(t/20)
Taking the logarithm base 2 of both sides, we have:
log2(100,000) = t/20
Simplifying, we find:
t = 20 * log2(100,000)
Using a calculator, we can determine that log2(100,000) is approximately 16.60964.
Therefore, t ≈ 20 * 16.60964 ≈ 332.19 minutes.
So, it will take approximately 332.19 minutes for the population to reach one million organisms.
Learn more about logarithm here:
https://brainly.com/question/30340014
#SPJ11
A sampling technique used when groupsare defined by their geographical locationis:A.clustersampling.B.convenience sampling.C.judgment sampling.
Answers
A sampling technique used when groups are defined by their geographical location is cluster sampling. Hence, option A is correct.
Sampling technique refers to the method of selecting or choosing members from the given set of population.
Under cluster sampling method, population is divided or splitted into groups. The key objective is to minimize the cost and time taken.
For example: If a NGO wants to study the rural communities, the state is divided into small groups also known as clusters. Instead of visiting and studying all the locations a random cluster will be choosen and studied. Minimizing time and cost involved. However, it contains more sampling error as it might not represent the entire population accurately.
Therefore, Option A is the correct answer.
To learn more about Cluster sampling:
https://brainly.com/question/30180321
The formula C = f1 relates the speed (C), frequency (f), and the wave (d) of light.
Choose from the drop down lists to complete the sentence:
Answers
Answer:
Step-by-step explanation:
The volume of a box, V(x), is represented by the function V(x) = x(40-2x)(24-2x), where x represents the width of the box.
What is the domain of V(x)?
A. all real numbers greater than 0
B. all real numbers greater than 0 and less than 12
C. all real numbers greater than 0 and less than 20
D. all real numbers greater than 0 and less than 24
E. all real numbers greater than 0 and less than 40
I gotta do this ASAP. Ty, for helping me if u do!
Answers
Answer:
the answer is
Step-by-step explanation:
the temperature of fridge compartment of a refrigerator is set at 8 °C . the fridge compartment is set at -10°C . what is difference between these temprature sittings
Answers
Answer:
I don't understand the question, but I think its 18°
Step-by-step explanation:
Write equations for the horizontal and vertical lines passing through the point (5,2).
Answers
The required equation of the vertical line is x=5 and the horizontal line is y=2 when passing through the point (5,2).
What is equation?A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. This value c is known as the y-axis intercept. A linear equation has the algebraic form y=mx+b, where m and b are constants, x is the independent variable, and y is the dependent variable. A linear equation is stated in statistical terms as y=a+bx, where a and b are constants. The equation of a two-dimensional line is ax+by=c; it is fair to predict that the equation of a three-dimensional line is ax+by+cz=d; reasonable, but incorrect—it turns out that this is the equation of a plane.
Here,
As the coordinate is (5,2),
The vertical line is x=5
The horizontal line is y=2
When passing through the point (5,2), the vertical line's required equation is x=5, and the horizontal line's required equation is y=2.
To know more about equation,
https://brainly.com/question/10413253
#SPJ4
f(x) = x2. What is g(x)?
Answers
Answer:
Step-by-step explanation:
C